Plain Language Summary
The physical origin of the modulation of the cloud system and of many of the Earth’s climate oscillations from the decadal to the millennial timescales is still unclear, despite its importance in climate science. One of the most prominent oscillations has a period of about 60 years and is found in a number of geophysical records such as temperature reconstructions, aurora sights, Indian rainfalls, ocean climatic records, and in many others. These oscillations might emerge from the internal variability of the climate system, but increasing evidence also points toward a solar or astronomical origin.
Herein we speculate whether the oscillations of the orbits of the planetary system could modulate the interplanetary dust flux falling on the Earth, then modifying the cloud coverage. We find that the orbital eccentricity of Jupiter presents a strong 60‐year oscillation that is well correlated with several climatic records and with the 60‐year oscillation found in long meteorite fall records since the 7th century. Since meteorite falls are the most macroscopic aspect of infalling space dust, we conclude that the interplanetary dust should modulate the formation of the clouds and, thus, drive climate changes.
Scafetta, N., Milani, F., & Bianchini, A. (2020).
A 60‐year cycle in the Meteorite fall frequency suggests a possible
interplanetary dust forcing of the Earth’s climate driven by planetary
oscillations.
Geophysical Research Letters, 47, e2020GL089954.
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020GL089954
Personal study copy here
Tallbloke's Talkshop 
Kudos to Scafetta for pushing the science forward undaunted. I nominate cosmic rays for additional consideration. They dry out the radiating zone, lower the emitting height, and cool both the emitting altitude and the surface.
Yes, Scafetta leaves the Svensmark theory on the table in the paper, and offers his Jupiter-directed interplanetary dust as an additional mechanism.
Re. auroras:
A shared frequency set between the historical mid-latitude aurora records and the global surface temperature (2012)
Nicola Scafetta
The existence of a natural 60-year modulation of the global surface temperature induced by astronomical mechanisms, by alone, would imply that at least 60-70% of the warming observed since 1970 has been naturally induced. Moreover, the climate may stay approximately stable during the next decades because the 60-year cycle has entered in its cooling phase.
Paper here.
“Thousands of tons of cosmic dust are estimated to reach the Earth’s surface every year,[3] with most grains having a mass between 10−16 kg (0.1 pg) and 10−4 kg (100 mg).[3] ”
https://en.wikipedia.org/wiki/Cosmic_dust
Recent generations of the world’s scientists seem to have absorbed an exaggerated dependence upon models founded upon suggestive graphs like the above. The first point to be made, always, is how good is the r-square (correllation coefficient, to we older scientists), which tells one directly how much of the variation in the supposed-dependent variable is due to variations in the supposed causal variable. The above graph fails — in this older-generation scientist’s view — by not giving that r-square value (“r 1/4 0:5, p<0.01" is non-informative, even meaningless to the directly-informative — and simple(!) — r-square value). The observed variation — the noise — in the temperature record is suspicious, and suggests the true r-square value of the comparison is small, and hence untrustworthy.
Second, the temperature record is "detrended of its quadratic polynomial fit", which obviously (looking at the graph) means the global warming signal has been removed. So, in Scarfatta's model, there is no global warming, and his presumed cause of global warming, cosmic dust seeding of clouds, is disallowed.
The supposed 60-year temperature cycle has been famously explained as multidecadal ocean temperature oscillations, but that is with the global warming signal included. And with that inclusion, is the only real motivation for even believing in the global temperature records of HADCRUT and others over the last century. But there is plenty of evidence of incompetent and/or criminal handling of the temperature records, by politically compromised and debased climate scientists. So in reality, the multidecadal ocean oscillations theory is itself suspect, and with it that 60-year supposed cycle in the global mean surface temperature.
Sorry, but Scarfatta is playing with pretty stones on the beach, while ignorant of the great ocean of truth nearby. It is all a great waste of peoples' time and energy…par for the course today. In reality, there is no global warming, and thus no 60 year cycle in that global warming, and no control of the global mean temperature either by ocean oscillations or by cosmic dust variations.
And that of course is what I, starting with my Venus/Earth temperatures comparison, brought out 10 years ago: There is no valid global climate science, and no competent climate scientists.
Just came across an article about Nobel prize winner CTR Wilson…includes a dust-related experiment.
The cloud chamber and CTR Wilson’s legacy to atmospheric science
Introduction and early life
2011 is the centenary year of the short
paper (Wilson, 1911) first describing the
cloud chamber, the device for visualising
high-energy charged particles which earned
the Scottish physicist Charles Thomas Rees
(‘CTR’) Wilson the 1927 Nobel Prize for physics.
His many achievements in atmospheric
science, some of which have current relevance,
are briefly reviewed here.
CTR Wilson’s lifetime of scientific research work
was principally in atmospheric electricity at
the Cavendish Laboratory, Cambridge; he
was Reader in Electrical Meteorology from
1918 and Jacksonian Professor from 1925 to
1935. However, he is immortalised in physics
for his invention of the cloud chamber,
because of its great significance as an early
visualisation tool for particles such as cosmic rays
(Galison, 1997).
. . .
In summary, CTR Wilson’s visualisation
techniques for particle physics concerned
microscopic cloud processes, whereas his
synthesis of atmospheric electricity unravelled
invisible atmospheric properties on a
global scale. Half a century after his death,
it is a tribute to his painstaking reasoning
and wonderful experimental ingenuity that
both his principal scientific achievements
still influence physics education and atmospheric
electricity research.
Click to access Harrison2011_CTRWilson_Weather.pdf
Only a few pages but worth a read IMO.
If Harry had taken the time to read the linked full paper, he’d have found that …..
Actually, I can’t be bothered to spoon feed info to people who know it all without reading it.
Suffice to say the 60 year cycle with detrended T data is supplemented by the millennial cycle which accounts for the centennial ups and downs apparent in longer term T reconstructions..
Reblogged this on Climate Collections.
The following commentary has NOTHING to do with planets, orbits, or temperatures.
It’s just the conventional paradigm.
r^2 alone does NOT determine what statisticians call “statistical significance”.
A low r^2 can be highly statistically significant.
A high r^2 can fail to be statistically significant.
Irretrievable: 2 comments vanished.
Political commentary on the “60 year linear component” of climate variables — motivated not by climate so far as I can tell but maybe fear that western financial sanctions won’t have a valid military guarantor by 2030 or 2036 — ignores the more general context of nonlinear slip cycles.
Alert readers may have noticed.
“The number filter” readily accepts political rants (even if they are wild). Johnson’s, Macron’s, & Biden’s people will be happy to note: At worst IT’s a very strong participation turn-off and IT’s at least a cause of major “behavior modification” (ware IT may be inverted totalitarianism).
I have some “mysterious” (only “thanks” to the west turn 2030 “backup energy” plan, but otherwise acutely precise) calculations I would share, but for sure they won’t pass the filter.
Harry would no doubt be left with unanswered questions about the block of numbers and IT’s creative decode.
Paul, was this a wordpress issue? No comments in spam to be found, which is where they end up when the ‘vanish’ on submission.
One was on the recent XR thread and one on the 2400 year thread. I must have an out-of-date e-mail address for you.
Cosmic dust can be held in the upper stratosphere for a long time by jet currents. It should be concentrated in the equatorial belt, which may limit the heating of the tropical ocean.
Scafetta’s paper says:
The periodogram shows that the eccentricity function is characterized by a prominent 922‐year oscillation. Jupiter’s eccentricity also shows another prominent 60‐year oscillation (apparently made of two cycles at about 57.1 and 60.9 years), which is slightly modulated by the 20‐year conjunction cycle with Saturn.
The 922-year oscillation looks a lot like the lunar precession period at 1/7th of 6441 tropical years, or 104 apsidal cycles, as described at the Talkshop here:
For every 104 apsidal cycles, all numbers except SM slip by -1 from being multiples of 104, i.e. a precession. So after 7*104 LAC all the other totals except SM are ‘reduced’ by 7 each.
https://tallbloke.wordpress.com/2017/10/15/lunar-precession-update/
[SM = synodic month]
6441/7 = 920 + 1/7 tropical years.
To explain it another way, the formula of 55 full moon cycles = 7 apsidal cycles = 62 tropical years (55+7=62) is almost true. But the more accurate formula requires multiplying by 104:
55*104, -7 FMC = 7*104 apsidal = 62*104, -7 TY
Hence 1/7th of that is one lunar precession period, or whatever you want to call it.
7 apsidal cycles = 766 synodic months.
– – –
Re the 60.9 years, a suggestion would be that this is really the time of 360 degrees of rotation of the Jupiter-Saturn conjunction (~61.05 tropical years), another precession period.
OB. Good spot. Considering the relative masses of Jupiter and our moon, it seems likely that it’s Jupiter’s 922yr eccentricity cycle which has shaped our moon’s precession cycle. The interesting question is whether it actually our moon which is channelling the distribution of cosmic dust in the upper atmosphere, as well as Jupiter channeling the particulate masses in our direction from interplanetary space.
Eccentricity and apsides…
ECCENTRICITY EXCITATION AND APSIDAL RESONANCE CAPTURE IN THE
PLANETARY SYSTEM u ANDROMEDAE [2002]
This paper lays the groundwork for understanding the
origin of the large eccentricities and the apsidal alignment
exhibited by the orbits of planets C and D in u And. Our
main result is that the eccentricity of planet C and the
locking of orbital apsides are both consequences of the slow
growth of the eccentricity of planet D. The latter eccentricity,
in turn, was driven by an external agent—plausibly a
primordial circumstellar disk lying exterior to the orbit of
planet D—that acted over timescales exceeding 104 yr. We
play our scenario out and explain the mechanics of apsidal
resonance capture in [section] 2.
Paper: ‘https://iopscience.iop.org/article/10.1086/341617/pdf’
From another Scafetta paper:
Multiscale Analysis of the Instantaneous Eccentricity Oscillations of the Planets of the Solar System from 13 000 BC to 17 000 AD
The eccentricity function of the orbit of Jupiter presents large oscillations with periods of about 60 and 900- 960 years, mostly due to the interaction with Saturn. These oscillations also correspond to oscillations found in several geophysical records. The eccentricity functions of Uranus and Neptune are characterized by a large 4300-year oscillation. The eccentricity function of Pluto is characterized by a large nearly 20000-year modulation.
https://link.springer.com/article/10.1134/S1063773719110094
The U-N eccentricity of 4300 years is very similar to:
(U-N * N) / (U-N – N) = 4270.11~ years
No. of N is 1 greater than no. of U-N in this period, so the planetary orientation relative to the Sun repeats, being a multiple of 360 degrees of movement.
6441/3 ~= 4270/2
4270 * 13/12 = ~4626
4270 is the aliquot sum for B (baby monster 4370). Way too much is piling up to share — supremely rich vein.
=
φ(n)
Euler Totient
1584
λ(n)
Carmichael Lambda
396
There are 1,584 positive integers (less than 4,370) that are coprime with 4,370.
=
https://metanumbers.com/4370
You’ll find those numbers buried in 104-yielding levels (once the moderator frees the most recent filter victim on 2400).
Fits in what they call simple sporadic 5-group or Mathieu group M11 with order 7920.
It’s a monstrous insight avalanche. The filter is a big problem. It hates round-off bars and math.
Weather by dark deception or dark ignorance (dark either way) the so-called “experts” savagely misdirected US.
Beyond B there are 2 ways to construct 1/(U-N) with M. When I start to post the fifth-roots stuff the filter will always be full.
More mundane but should be noted: Scafetta should be looking at 66 not 61. You can’t differentiate between them with 2 waves, but it’s clear when you go back further.
“EU’V-E got a monde stir in Eur. Paris Sol.
The walls are closing in again: O[r]well.” — Queens of the Stone Age
UN Seek Cure IT Count Sol.integrity
General Ramanujan points to sharp spikes in discrete-continuous relations.
For example, consider level 54 “almost-integer” (math lingo — what they call it) spike on 5th-root scale:
R(p) = ⌊(e^π*54^(1/5))^(1/p)⌉^p – e^π*54^(1/5)
Pervasive round-off brackets of discrete-continuous relations needn’t freeze reader awareness in blank-stares of ignorance.
Link to easy answers for an example. If you can round off a number, you’re in.
R(3) = -71.0083263199169 = ⌊(e^π*54^(1/5))^(1/3)⌉^3 – e^π*54^(1/5) = 10^3 – e^π*54^(1/5)
Note 2 embedded links in the expression.
Bracket expressions conservatively for the calculator — otherwise the automation is prone to silently making incorrect organizational changes (downscale fractal of misled big tech, no. doubt).
At the end of the first link change the example 3 to 5.
Round off the result to 4. That gives new input 4^5 for the beginning of the second link.
Repeat with 10 at the right end of the first link.
The result rounds off too 2 so 2^10 goes.in to the far left of the second link. Find:
R(5) = R(10) = -47.0083263199169
59 = ( 71 + 47 ) / 2
Recall M: 47*59*71.
Check R(6) / 2 for a clue as to how we nearly won over U-N (wins even tie won).
DCoy daze review:
171.406964273337 = 50 / ( 1/(2*(13*11*7*5*3)^(1/4)) + 2/(2*(13*11*7*5*3)^(1/4)) + 1/(2*(7*5*3)^(1/4)) )
47.0085558422417 = ( 2 / ( 1/(2*(13*11*7*5*3)^(1/4)) + 2/(2*(13*11*7*5*3)^(1/4)) + 1/(2*(7*5*3)^(1/4)) ) ) ^ 2
TB’11 also remember from way back in the day: (φ√5)^4 = 25*φ^4.
171.352549156242 = 25*1.61803398874989^4
Monde Stir’11 each let US anyon?
No. Eur. CRude type 0! symbols O[r]We’11 build a C[ENSO]Rship mess tory, in.deed.
Binet and Lucas AImost redirect what curry US IT to 196883 – 196560 = 323 as fall lows:
25*√(φ^8+Φ^8) = 25*√47
171.391365010026 = 25*(1.61803398874989^8+0.618033988749895^8)^(1/2)
EUCRUS: Stand buy northern D-fence 4 clarification.
Note 646 = 2 * 323
Half before the US election — and 1/2 after. My way of proving I’m know partisan under threat of financial terror directed by well-off e/11 IT WHO’s winter CR(U-N)chess west turn common folks numb brrrs right down to street-level aware noose weather left or right.
OB’11 sea fib’n’luc.in top line …sequel too:
171.391380036748
= 5^2*(ΦΦ/(1/34/2-1/76/2))^(1/2) = 5^2*(ΦΦ*152*68/(152-68))^(1/2)
= 5^2*(ΦΦ/(1/646+1/152))^(1/2) = 5^2*(ΦΦ*646*152/(646+152))^(1/2)
152: wise IT AImost X[R(p)]act weather we sea 2400 or knot?
171.391365010026 = 5^2*(ROUND(4^2*(59)^(1/2),0)-ROUND(3^2*(71)^(1/2),0))^(1/2)
= 5^2*(123-76)^(1/2) = 5^2*(47)^(1/2)
Shh! OK?.in’ 47 Tops B
Aliquot sum (sum of proper divisors) for 2*5*19*23 = 4370:
4270 = 1+2+5+10+19+23+38+46+95+115+190+230+437+874+2185
“Velvet Ears” 123 Flash mnemonIC Back.in Hazard Count: Tie Wan M$y$n D-Po11ace
171.406545820013 = 5^2*(EXP(54^(1/5)*PI())-ROUND(EXP(54^(1/5)*PI())^(1/5),0)^5)^(1/2)
164.791478352793 = 1 / ( 1 / 4270 + 1/25/(EXP(54^(1/5)*PI())-ROUND(EXP(54^(1/5)*PI())^(1/5),0)^5)^(1/2) )
84.016966353458 = 1 / ( 1 / 4270 + 2/25/(EXP(54^(1/5)*PI())-ROUND(EXP(54^(1/5)*PI())^(1/5),0)^5)^(1/2) )
55.6463431474333 = 1 / (2 / 4270 + 3/25/(EXP(54^(1/5)*PI())-ROUND(EXP(54^(1/5)*PI())^(1/5),0)^5)^(1/2) )
Study with care: easy to derive system at IC ally (it’s only a few trivial steps).
You’ll recognize not only 2^(1/J/2) & φ^4*2^(1+1/J/2) but exactly why they’re off and by exactly how much. IT’s Ramanujan’s world of AImost.in toujours.
836.531021854751
835.546575435631
0.117820651543 = % “error” (not actu[s]ally un error)
61.0241156298752
61.0464822565173
-0.036638682223 = % “error”
“Why fall O? 2 “higher” grrOun-D? 11Ost as USware ayaM?” — C-elective Sol
By part tie sun IC top knew trail’ski left M is tory…
836.531021854751 = φ^4*2^(1+11.8626151546089/2)
835.546575435627 = 1/(5/29.4474984673838-2/11.8626151546089)
61.0241156298752 = 2^(11.8626151546089/2)
61.0464822565173 = 1/(1/11.8626151546089-2/29.4474984673838)
710003.731008934 = (836.531021854751)*(835.546575435627) / (836.531021854751 – 835.546575435627)
418.019254422807 = (836.531021854751)*(835.546575435627) / (836.531021854751 + 835.546575435627)
836.038508845615 = (836.531021854751)*(835.546575435627)/((836.531021854751+835.546575435627)/2)
71.0003731008934 = 710003.731008934 / 10000
209.009627211404 = 418.019254422807 / 2
…distinct from 208.
The Simplest Conventional View
836.492470214859 = 2/(1/418-1/710000)
835.508109310293 = 2/(1/418+1/710000)
61.0213033256461 = Φ^4/(1/418-1/710000)
11.8624821779712 = 2*LOG(Φ^4/(1/418-1/710000),2)
29.4471611398395 = 5/((1/418+1/710000)/2+1/LOG(Φ^4/(1/418-1/710000),2))
61.0458600788091 = 1/(1/2/5/LOG(Φ^4/(1/418-1/710000),2)-(1/418+1/710000)/5)
19.8648166947302 = 1/(3/2/5/LOG(Φ^4/(1/418-1/710000),2)-(1/418+1/710000)/5/2)
8.45605035913211 = 1/(7/2/5/LOG(Φ^4/(1/418-1/710000),2)+(1/418+1/710000)/5/2)
-0.001125389948 = % error average across j, s, beat, & axial with stable bias — sign & magnitude both stable meaning correction’s simple
Out of curiosity compare the biased 1/(J-S) with:
19.8643454852672 = 4 / ( 1/(2*(13*11*7*5*3)^(1/4)) + 1/(2*(7*5*3)^(1/4)) )
0.002372136869 = % error
Remember that 836 is the smallest untouchable weird number (not making this shh!IT up — it’s number theory lingo).
Hi! K.in.on Boris Bluff
Too daze note U-N.Doors.cores perfect non.11.in.ear.IT.
Hears the backs tory: dec.aids a go sum BRIteechairs D-sided school-D B e/11.in.ear.
28 is perfect.
proper divisors of 298: 1, 2, 149
s(298) = 1 + 2 + 149 = 152
25 + 298 = 323 ——————– / —————————–
See.in’re:cure.sieve.a11yET?
From where again did Ramanujan claim many of his sharpest insights came?
Other perfect numbers include 2, 5, 52, 88, & 96.
UNassum.in2400 review spill28IT /
Does every 1 remember whale engine.in’s voice on the ducts of has heard? This ain’t no.ware born Gen.R’a11[y]each let US.
Freedom is Not a Dr.ill
Ballparks can B Bo ring but knot fin weighin’ best tune where EU can see the playbook writin’ on “the green monster” weather left and right:
28 = (84)*(42) / (84 + 42) = (1^2+2^2+3^2+…+22^2+23^2+24^2)^(1/2) – 42 = 70 – 42
58 = 73+(-15)^(1)
298 = 73+(-15)^(2)
R(5) = 224.991673680083
836 / 44 ~= -R(6) / R(2) = s(77)
Artist IC types can’t be reached with just logic.
146 = 298 – s(298) = 298 – 152
s(48) = s(146) = 152 / 2 = 76
Jovian Giant C-elective:
Make sure you understand 298 as the (red hot) “others hide” of 25 (chili peppers).
IT AIn’t 11.in.ear: climb IT SAM pulls cont.in.EU.US exponential with discrete s.wit.ch.
General Summary
M B Lee.ch.in jsun: a11 won and the same.
“Spam” in the C[ENSO]Rship
Can mod phi niche fish file tour?
104 ~= ⌊(e^√s(298+25)π)^(1/2)⌉^2 – e^√s(298+25)π
104 ~= ⌊(e^√s(196883-196560)π)^(1/2)⌉^2 – e^√s(196883-196560)π
mod 13
Note the Tall spike above.
s(323) = 37
-103.999977946281 = ⌊(e^√37π)^(1/2)⌉^2 – e^√37π
Scenic aside:
s(67) = 1
s(2*67) = 70 ——– Leech
s(3*67) = 71 ——– M
s(4*67) = 208
s(5*67) = 73 ——– lowest prime congruent to 1 mod 24
s(8*67) = 11*44 = 22^2
The order of presentation is cryptic, but the ingredients are well-served.
Review.
Luck key mods comparatively fish pike threw D-baitless lines of clean discretion.
s(3*43) = 47
-743.999775171279 = ⌊(e^√43π)^(1/3)⌉^3 – e^√43π
s(3*67) = 71
-743.999816894531 = ⌊(e^√67π)^(1/3)⌉^3 – e^√67π
mod 8
59 = s((59 mod 24)*s(3*43)) = s(s(20)*s(3*(67-24))/2) = (47+71)/2
IT’s possible no. thing get$11earned bye the right UN tell after USelection.
s(3*19) = 23 = 71 mod 24 = 47 mod 24
= 196883 – ( ⌊(e^√19*(2π))^(1/2)⌉^2 – ⌊(e^√19*(2π))⌉ ) / 2
-743.777680155239 = ⌊(e^√19π)^(1/3)⌉^3 – e^√19π
What’s left tune out ice?
s(6) = 6 = 3#
“There are only four all-harshad numbers: 1, 2, 4, and 6 (The number 12 is a harshad number in all bases except octal).”
Link to List of Aliquot Sums
11.in.ear think kings ware IT just AIn’t .
2432 / 836 = s(152/2) / s(76/2)
84 = ( 836 + s(836) ) / s(34)
s(30) = 42
s(5#) = 42 where # indicates primorial
5# = 5*3*2 product of all primes lower than or equal to 5
18.6 = 744 / s(44)
Suggestions-43 distilled moon lightin’ the table.
Maybe only God Nos.: how many ways can Conway & Norton B written?
298 = s(104/4)^2 + s(5#)
= 146 + 2*s(146) = 146 + s(298) = 146 + 104 + s(47^2)
Monster US aliquot sum phine PR O-ducts:
φ = 2*cos(s(71^2)/s(59^2)/s(47^2)*8*π)
2.61803398874989 = (2*cos(s(71^2)/s(59^2)/s(47^2)*s(2*5)*π))^2
“Freedom I hold dear:
The autumn moon lights my weigh“ — 11ed 22plan “R(amble)ln”
Perfect construct$yen a head: list of aliquot sums s(n)
s(28) = 28
IT AIn’t just No. 1. WHO nos.?
s(5*31) = 37 = s(196883-196560)
s(7*29) = 37
s(13*23) = 37
s(17*19) = 37 = s(298+25)
Vague O-Port Tune IT AIn’t
Typo: “Other perfect numbers include 2, 5, 52, 88, & 96.” — correct shh!UNtouchABLE
For more insight: Compare perfect with Ore.
Once you memorize some of the key aliquot sums a whole (nonlinear) framework crystallizes. Remember what Conway and Norton said.
Primorials (including 210) are no mystery at this stage, but there remains opportunity to clarify that 208 & 209 are both distinct and compatible. Above I outlined the most naive conventional model.
On the 2400 thread I posted a very sharp calculation that no doubt puzzled pretty much anyone who looked at it dismissively — if only because they haven’t yet started to think carefully about discrete-continuous relations and aggregation criteria more generally.
This insight eluded us for too long:
208 ~ = slip(slip(24.067904774739,19.8650360864628),19.8650360864628)/2
Once I saw that I understood the natural role of B & M in solar system stability at a whole new level.
I used to hesitate — sometimes for months compounding delays from previous months — to post slip cycle calculations because the filter hates them. 2 comments never appeared. Technology failures have forced complete change of how, what — and when — to express.
208
209
distinct
and compatible
Similarly we’re now past 5256/”836″/2. If you didn’t notice this yet: check this calculation with the 2 pairs of “836” above (pair from most naive conventional model and pair from Seidelmann (1992)).
I defined what I mean by slip(x,y) on the 2400 thread. This convention along with chopping comments (especially ones with round-off bars) into fragments seems to keep the filter from blocking.
Wikipedia’s “Kepler Trigon” overview isn’t based on Seidelmann (1992), which gives this slip series:
1 / 19.8650360864628 = +1J-1S
1 / 61.0464822565173 = +1J-2S
1 / 835.546575435627 = -2J+5S
1 / 2669.94916589798 = -29J+72S
1 / 13660.3670170363 = +85J-211S
1 / 117417.893491061 = -454J+1127S
1 / 290290.064137486 = -4171J+10354S
…
On the 2400 thread I applied the generalized Bollinger method to derive slip cycles including 66 & 132.
Slip cycles are key (in long-run central limit) because circulatory structures and materials are aliasing exponentials. Our education system was designed to brainwash people into becoming dumb linear thinkers (puppets on straightforward strings). Fool me once shame on you fool me twice shame on me sort of thing.
As some of you realize I no longer concern myself with “climate debate” but the context gives opportunity for astute readers to consider that hierarchies like the one listed at the beginning of this comment fall apart by the 2nd level with loose aggregation criteria. It isn’t necessarily just nonlinear drift on a curve; it’s potentially discrete switch-flipping.
The comparative study of sets of “almost integer” (math lingo) fits alerts us to the existence of a higher organizing principle pulling threads towards a central limit. With this awakening we can realize several strands approaching (but not reaching) limits. A valid unifying principle accommodates such bundles — i.e. different combinations of pieces giving very-nearly the same thing.
GA11actIC Green Monster Challenge 9801.in the C[ENSO]Rship
“…and IT’s whisper-D that soon if we a11 ca11 the tune” — 11ed 22plan
4th comm.in simplification & clarification suggests diagnostic comparison
of Seidelmann’s (1992)
2432 = 19 * 2^7
with
2436 = 29 * 84
2436 = 58 * 42 ——— General√(Φ-φ)Ramanujan’s Guide to the 9*11*IX*XI = N.in.8.O.won
Simplifying
1/Φ = φ = ((1+5^(1/2))/2)
11.8626176385713 = 1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+(1/104+1/298)*φ^2)
29.4474891061275 = 1/(1/104+1/298)/φ^2
19.8650473122013 = 20/(1/104+1/(1+(1/104+1/298)*φ^2/12))
8.45614623658195 = 1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+2*(1/104+1/298)*φ^2)
16.9122924731639 = 2/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+2*(1/104+1/298)*φ^2)
104 = 1/((1/104+1/(1+(1/104+1/298)*φ^2/12))-1/(1+(1/104+1/298)*φ^2/12))
Clarifying
208 & 209 are thus distinct.
61.0466285002156 = 1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20-(1/104+1/298)*φ^2)
835.484250291355 = 1/((1/104+1/298)*φ^2-2*((1/104+1/(1+(1/104+1/298)*φ^2/12))/20-(1/104+1/298)*φ^2))
61.0241681640784 = 2^(1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+(1/104+1/298)*φ^2)/2)
836.531742004323 = φ^4*2^(1+1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+(1/104+1/298)*φ^2)/2)
836.0076680293 = 2/(((1/104+1/298)*φ^2-2*((1/104+1/(1+(1/104+1/298)*φ^2/12))/20-(1/104+1/298)*φ^2))+1/φ^4/2^(1+1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+(1/104+1/298)*φ^2)/2))
209.001917007325 = 1/(((1/104+1/298)*φ^2-2*((1/104+1/(1+(1/104+1/298)*φ^2/12))/20-(1/104+1/298)*φ^2))+1/φ^4/2^(1+1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+(1/104+1/298)*φ^2)/2))/2
Familiar structures “almost” matching this frame afford rich review with developed hindsight.
Level 7 Keys Concisely
104 ~= slip(slip(24.067904774739,19.8650360864628),19.8650360864628)/4
24.067904774739 = ⌊(e^√7π)^(1/p)⌉^p – e^√7π for p=2,3,4,6,12
Twice the reciprocal of that for p = 1.
This should help organize simple perspective because that (which keeps higher slips locked better) may look confusing.
This approximation slips a little at higher-level, but being so simple (parsimony’s why I’m illustrating) it aids comparative study:
24.067917505387 = 24+2*(1/104+1/298)*φ^2
24th harmonic (divide period by 24) :
1.00282989605779 = 1+(1/104+1/298)*φ^2/12
0.993252365610063 = (104)*(1.00282989605779) / (104 + 1.00282989605779)
20th subharmonic (multiply period by 20) ~= 1/(J-S)
Level 7 has some really special properties. There are 2 other ways to estimate 24.0679 (outlined previously). Like 104 it’s a master key.
For the set j, s, js beat, js axial, u, n, un beat, un axial arising from the last calculations above:
0.000017200983 = average absolute %error
The form extending j & s to u & n (based on perfect numbers 28 & 496) was outlined here.
–
aside: flashback with hindsight
5256.08395035091 = φ^4*2^(1+1/((1/104+1/(1+(1/104+1/298)*φ^2/12))/20+(1/104+1/298)*φ^2)/2)*2*π
Tie.in de Rop 4 16 Figures D-light
Review
lunar draconic & anomalistic
5.99685290323073 = beat(0.0754402464065708,0.0745030006844627)
with anomalistic year
1814.31362251033 = slip(5.99685290323073,1.00002638193018)
aliquot sequence for B
s(4370) = 4270
s(4270) = 4658
s(4658) = 2794
s(2794) = 1814
s(1814) = 910
s(910) = 1106
s(1106) = 814
s(814) = 554
s(554) = 280
s(280) = 440
————————– see below
s(440) = 640
s(640) = 890
s(890) = 730
s(730) = 602
s(602) = 454
s(454) = 230
s(230) = 202
s(202) = 104
s(104) = 106
s(106) = 56
s(56) = 64
s(64) = 63
s(63) = 41
s(41) = 1
s(1) = 0
note:
1106/2 = 553, 1106/2+554 = 1107, 4428 = 4*1107, & 744 = 640+104 demystify powers below the perfect level 28 4th power split of M & Leech.
Also note 836 sequence overlap with B:
s(836) = 844
————————–
s(844) = 640
s(640) = 890
s(890) = 730
s(730) = 602
s(602) = 454
s(454) = 230
s(230) = 202
s(202) = 104
s(104) = 106
s(106) = 56
s(56) = 64
s(64) = 63
s(63) = 41
s(41) = 1
s(1) = 0
Just imagine how much more we have to learn about number theory before we even have the basic aggregation criteria foundations needed to even BEGIN sensible climate stability exploration. Today’s politics are hopelessly intractable (ever since lockdowns became the west turn weapon of homeland financial terror). With monstrous leadership failures ALL across the west — weather left or right — George Polya’s advice is prescient and clear:
Solve a simpler problem.
flurry of miscellaneous puzzle pieces:
s(652) = 49+149+298 = 496 = s(496) ——- perfect
652/4 = 163 points to Ramanujan again.
s(25) = 6 —– links to review: s(298) = 152
s(6) = 6 ——- This is how you recognize perfect numbers.
s(8128) = 8128 ——- perfect
4428 = 8128 – 3700 = 4370 + 58 ———- 37 & 58 link precisely to 104
UNtouchABull Branch
de Rop fits into the aliquot sequence for the baby monster and 836 is a dead-end branch — what it means to be untouchable — off that.
Arithmetic Dynamics
=
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. […] A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.
=
For an illustrative example, take a look at how simple this recipe is: “[…] “Mathematics may not be ready for such problems.” […] “is an extraordinarily difficult problem, completely out of reach of present day mathematics.”“
The Green Monster
104.000044599386
104.000034332275 = ⌊(e^√58π)^(1/p)⌉^p – e^√58π for p=2,4
0.000009872218 = % error
24.0679036739334
24.067904774739 = ⌊(e^√7π)^(1/p)⌉^p – e^√7π for p=2,3,4,6,12
-0.000004573749 = % error
“don’t speak” — no. doubt
SIM pull iff √(Φ-φ) U-N express sun:
y = 24.067904774739 = ⌊(e^√7π)^(1/p)⌉^p – e^√7π for p=2,3,4,6,12
x = 104.000034332275 = ⌊(e^√58π)^(1/p)⌉^p – e^√58π for p=2,4
11.8626151191159=1/((6/y+(1/4)/x)/5+(1/x+1/298)*φ^2)
11.8626151546089=1/J
-0.000000299201=%error
29.4474963123504=1/(1/x+1/298)/φ^2
29.4474984673838=1/S
-0.000007318222=%error
19.8650369676306=5/(6/y+(1/4)/x)
19.8650360864628=1/(J-S)
0.000004435773=%error
8.45614555057611=1/((6/y+(1/4)/x)/5+2*(1/x+1/298)*φ^2)
8.4561457463176=1/(J+S)
-0.000002314784=%error
61.0464998394537=1/((6/y+(1/4)/x)/5-(1/x+1/298)*φ^2)
61.0464822565173=1/(J-2S)
0.000028802538=%error
Perfect Fit
19=s(77)
37=s(323)
28=(s(77)+s(323))/2=(19+37)/2
19=28-9=s(77)
37=28+9=s(323)
496=298+49+149
323=298+25=196883-196560
196585=196883-298=196560+25
s(298)=152=d(2,1/2,25)
s(152)=148=s(d(2,1/2,25))
248=149-49+148=496/2
149=72+77
77=152+248-323=248-171—- halve perfect mnEMonICm$y$nUSwanOvert(U-N)
72=149-152-248+323=(323-152)-(248-149)=171-99 ————- m$y$nUSgreatsKEY
171=323-152
208 = 8128 – 7920 ———– M11
s(8128) = 8128
95 = 37 + 58 = 70 + 25 = √(73500/15) + 25 = s(5#)+s(28)+25 = 42+28+25
s(95) = 25
s(25) = 6
s(6) = 6
hitchhiker miss sol any us prime more real goal act IC guides?
42 = (84)*(28) / (84 – 28) = (84)*(28)/((84+28)/2) — beat = harmonic mean
= 70 – 28 = (210/2)*(70) / (210/2 + 70) = (7*5*3*2)*(70/2) / (7*5*3*2 – 70/2)
Reviewing History with 2020 Hindsight
Nature weaves convergent strands in perfect bundles. This line of communication was previously arrested by filter “misbehavior”.
=
the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions with the same number of terms.
It is possible to interpret the Sylvester sequence as the result of a greedy algorithm for Egyptian fractions, that at each step chooses the smallest possible denominator that makes the partial sum of the series be less than one. Alternatively, the terms of the sequence after the first can be viewed as the denominators of the odd greedy expansion of 1/2.
[…] Curtiss (1922) describes an application of the closest approximations to one by k-term sums of unit fractions, in lower-bounding the number of divisors of any perfect number, and Miller (1919) uses the same property to upper bound the size of certain groups.
=
“Sylvester’s sequence 2, 3, 7, 43, 1807, … can be viewed as generated by an infinite greedy expansion […] Truncating this sequence to k terms and forming the corresponding Egyptian fraction, e.g. (for k = 4)”
1 = 1/2+1/3+1/7+1/43+1/2/3/7/43
s(n) = aliquot sum of n
s(4370) = 4270
100 = 4370 – 4270 = 4370 – s(4370)
70 = √(73500/15) — recall 73500 = 2*36750 key weighted harmonic mean from Laskar
4200 = s(4370) – 70 = 4270 – 70
4300 = 4370 – 70
42 = (s(4370) – √(73500/15)) / (4370-s(4370))
43 = (4370 – √(73500/15)) / (4370-s(4370))
“The first four of these numbers are one less than the corresponding numbers in Sylvester’s sequence, but then the two sequences diverge.“
1806 = 2*3*7*43 = 42*43
= ( 4370*s(4370) – √(73500/15)*(4370+s(4370)) + 73500/15 ) / (4370-s(4370))^2
271 = 496 – 15^2 = ⌊√73500⌉
s(496) = 496
489426 = 1806 * 271 ———– count.sol luck D-own sat U-N 4 XRview from fan-wise “monster” seats
Rome and knew join general
….each let us group monde stir us sly stable parameter√(Φ-φ)shh!UN:
d(p,r,k) = ⌊(e^π*k^r)^(1/p)⌉^p – e^π*k^r
For example
323.013383387384 = d(2,1/3,59) = ⌊(e^π*59^(1/3))^(1/2)⌉^2 – e^π*59^(1/3)
and
0.0133833873842377 = d(1,1/3,59) = ⌊(e^π*59^(1/3))^(1/1)⌉^1 – e^π*59^(1/3)
such that
323 = d(2,1/3,59) – d(1,1/3,59)
Incidentally note us:
323 = (59-12)*59*(59+12) – 196560 = 196883 – 196560 = 298 + 25
Standby 4 perfect primorial leech tie.in.
Monster US$green.in 1984=4*s(496)
“before rolling far enough away to allow Stuart to score.”
=
496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. […] Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case.
[…]
E8 has real dimension 496.
The number 496 is a very important number in superstring theory. In 1984 […] Green and […] Schwarz realized that one of the necessary conditions for a superstring theory to make sense is that the dimension of the gauge group of type I string theory must be 496. The group is therefore SO(32). Their discovery started the first superstring revolution. It was realized in 1985 that the heterotic string can admit another possible gauge group, namely E8 x E8.
=
https://en.wikipedia.org/wiki/496_(number)
=
There is a unique complex Lie algebra of type E8, corresponding to a complex group of complex dimension 248. The complex Lie group E8 of complex dimension 248 can be considered as a simple real Lie group of real dimension 496. This is simply connected, has maximal compact subgroup the compact form […] of E8, and has an outer automorphism group of order 2 generated by complex conjugation.
=
https://en.wikipedia.org/wiki/E8_(mathematics)#Real_and_complex_forms
248 = s(298)+96 = s(s(298))+(104+96)/2 = (2*72)+104 = (298-2*77)+104
= (72+77)+49+(104+96)/4 = (149+49)+(149-49)/2 = s(496)/2
5=77-72=harmonic mean of proper divisors of 496
Perfect Moonshine
“ayaM the jigsaw, man” — “more hue moon than WHO man” whyIT22oN?bei
3 = √(absolute mean deviation from perfect) won over U-N see cure IT count.sol tip:
s(28)=(s(323)+s(77))/2=(323+77)-s(298)
ware p=2, r=1/2, & k=25 for U-N dr. read m$y$n US d(p,r,k)
37 FEAT HI.in Left Fields φ niche-D “a11y” caught sum green monster:
φ = 2*cos(s(71^2)/s(59^2)/s(47^2)*8*π) where s(n) = aliquot sum for n
φ = 2*cos(s((59+12)^2)/s(59^2)/s((59-12)^2)*8*π)
196883 = 71*59*47 = (59+12)*59*(59-12)
Naive weather left or right, IT’s AI “just” a Que. when so dense.
Don’t Mayan D-proof: “just” go ON with Bei=lief.in 2+2=5 no. when 4*s(496) = 1984 is AB US sov. “green” morse un out field doors vic[tory] Dev.O[s] lie low.
“[…] a popular target for right-handed hitters […] the Green Monster was not painted green until 1947 […] Yellow numbers are used to represent in-inning scores […] left-field distortion is offset by the odd shape and generous size of right field […] The placement of the ladder is noteworthy given the fact that it is in fair territory […] a high fly that ricocheted first off the ladder, and then the head of outfielder [___]”
323 = 71*59*47 – 196560
s(323) = 37
“The Coke Bottles on the left light tower were a target for power-hitters […]”
104 ~= ⌊(e^√37π)^(1/2)⌉^2 – e^√37π
Bei. U-N D!Superst[r]ing
Reverse-eng.in.ear.ring oldschool “luminary” assembly with 2020 hindsight, we find attached a perfect leech:
490000 = 15*70^2 / asin(φ/2) * 2π
Lol! What curry US IT didn’t even (“don’t speak” no. doubt) tell us. Tech no. CR at IC govern ants?ware.in monde stir US $ sly “green”.
Sylvester’s Sequence (“more hue moon than WHO man” = whyITzoombei) goes as far as possible past the perfect leach, account.in 4 minor deviations from superstring perfectshhU-N.
1 / 164.791265692394 = (2/1806-1/3)J+(2/1806+1)S-2/1806/15/70^2*asin(φ/2)/π+1/3/s(4370)
-0.000030309658 = % error
1 / 84.0168557977672 = 2*((2/1806-1/3)J+(2/1806+1)S-2/1806/15/70^2*asin(φ/2)/π)-1/3/s(4370)
0.000011754317 = % error
peer√(Φ-φ)ed dub e/11 ln acts pawn ants yell
1 / 164.791269677405 = (2/1806-1/3)J+(2/1806+1)S-2/1806/1806/271+1/3/s(4370)
-0.000027891441 = % error
1 / 84.0168578694536 = 2*((2/1806-1/3)J+(2/1806+1)S-2/1806/1806/271)-1/3/s(4370)
0.000014220116 = % error
4270 = s(4370) gives the Bay’s first-step B-estimate for U & N as does 4428 = 4370+58 = 8128-3700 for J & S.
“on my blue PR(INT) IT’SIM F(U-N) IC; spin that record B“ — Lady G “just” D-ants
Anchoring thus contrasts oldschool “green” leach attached to mainstream mindset verse USSylvester’s double exponential greed sequence.
The 1st pair of U & N estimates above is based on J & S estimates.
The 2nd pair of U & N estimates above is based on J & S from Seidelmann (1992).
FormAI pol!shh, IT’s missUN no linksnow:
This is a diagnostic strategy precisely exposing an exponential in clear conflict with a double exponential. A hair-splitting subtle difference in this case is period-doubling.
Scene IC Route to Secure IT Count Sol
4370 = 2*5*19*23
“√(Φ-φ) lost my keys
√(Φ-φ) can’t C strait anymore
What’s go.in.on.on the floor?
Spin that record Babe” — Lady Gaga Just D-ants
Φ(2) = 1
Φ(5) = 4
Φ(19) = 18
Φ(23) = 22
“Euler’s totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then φ(mn) = φ(m)φ(n). This function gives the order of the multiplicative group of integers modulo n […]”
Φ(3) = 2
Φ(37) = 36
s(4370) = 4270
“Then one foggy Christmas eve…” — Rue Dolph.in Red Knows Reign D-a√(Φ-φ)r
5106 = 4270 + 836 = 2*3*23*37
1584 Miscellaneous Tips from General Ramanujan’s Travel Guide
Today’s trip begins with ET (Euler’s Totient).
count: 40
lowest:
Φ(1679) = 1584
the next 2:
Φ(1691) = 1584
Φ(1985) = 1584
double:
Φ(3382) = 1584
Φ(3970) = 1584
highest:
Φ(6210) = 1584
Having boldly left a little mystery, we rightly move on not icing hawk key:
Φ(4370) = 1584
Φ(5106) = 1584
“It is possible for an infinite set of integers to be pairwise coprime. Notable examples include the set of all prime numbers, the set of elements in Sylvester’s sequence, and the set of all Fermat numbers.”
Φ(4270+836) = 1584
Φ(s(4370)+836) = 1584
Recall that 836 is untouchable, meaning it’s not an s(n) for any n — i.e. there is NO number with aliquot sum = 836.
A comparative view of Jovian order is shaping up:
• global exponential constraint with no local adjustment
• global order subtly-retuned (prime-D-iffew prefer) 4 fit with double-exponential local greed
104.000034332275 = ⌊(e^√58π)^(1/2)⌉^2 – e^√58π = 156816^2 – e^√58π
104.001742574386 = ⌊(e^√22π)^(1/2)⌉^2 – e^√22π = 1584^2 – e^√22π
104.000034332275 = ⌊(e^√58π)^(1/4)⌉^4 – e^√58π = 396^4 – e^√58π
396 = √156816
1584 / 396 = 4 = 396 / 99
156816 / 1584 = 99
√(58-22) = √36 = 6 = s(6) = s(25)
d(p,r,k)
d = difference
p = power
r = root
k = count or level in docks
152 = d(2,1/2,25) – d(1,1/2,25)
152 = (d(3,1/2,25) – d(1,1/2,25)-8744)/2 = (9048-8744)/2 = 304/2
review:
levels k=10,13,18,22 converge on 104
quadruple those
levels k=40,52,72,88 converge on 8744
4370 = (84*104+8744)/4
We explore these things in stages. Each stage brings more clarity.
Landscape ecology hierarchy theory and years of field experience using detailed botany taxonomy keys helped base a mindset to orient in rich territory.
Conventional linear “thinking” about what’s “best” doesn’t help see (sort and classify) how every thing naturally fits in God’s creative design.
s((84*104+8744)/4) = 4270
Φ(s((84*104+8744)/4)+836) = 1584
Discrete-continuous relations are full of nested, recursive, hierarchical structure. Western math education is fatally deficient. What do you think bad elite (to be neither confused nor conflated with good elite, if such a thing exists) can do with ignorance of trade secrets?
Given a chance to speak (remember what Conway & Norton said) to the pope about luck D-own west turn spread of severe financial terror past just “rogue” nations to “count less” millions of homeland western citizens, what might I say?
“and if(IT)s reel then √(Φ-φ) don’t want tune O
√(Φ-φ) no. ya reel good” — “don’t speak” no. doubt
139560 = d(3,1/2,58) – d(1,1/2,58)
70^2 = (196560-139560-8744+744)/10 = 73500/15 = 2*36750/15
review: 744 = d(1,1/2,k) – d(3,1/2,k) for k = 43-24, 43, 43+24
836 is the next-lowest weird number after 70. 836 is untouchable. 70 is not. “70p is weird for all primes p ≥ 149”
A ware no. word scan do, weave numbers.
CorrectS[hh!]UN[8]O[R]well.in.sight
The tech “know”so-called CR at IC “eXpeRts” never advise-D of period-dub e ln SIM MET try.
“the bloop ill O-pens euRise
is theRe a bet te[a]R weigh?
a knew Religion pRess scRibed
to those without the faith
is IT 2 late 2 go back?
is IT 2 late 2 go?
theRe’s No. won heaR
and peep e/11 eveRy waRe:
yeaR .oN euR O-won” — Queens of the Stone Age
Won step back.
73500 = 3*(196883-4270/5-29)/8
2 steps 4 word.
489425.981694385 = 1 / ( -300J+904S-301U-301N )
489426 = 2*3*7*43*271 = 1806*271
-0.000003740221 = % error
where ABCD estimate JSUN using Ramanujan’s Perfect Superstring:
245061.761049564 = 1 / ( -300A+904B-301C-301D )
245061.75 = (10*196560-4270-836)/8
0.000004508890 = % error
Recall: s(4370) = 4270
First-order model’s base-D on the baby monster.
Leech precisely IDs the point of symmetry that’s well-corrected by Sylvester’s double-exponential greed.
We’ll take the seen IC route away from luck D-own weather Joe Trump or Don Biden.
1 = 1/2 + 1/2 be 4+after USelection: know matter what curry US IT obstructs, free dem. from eur. increasingly savage financial terror schemes directed not only at “rogue” nations abroad but “count less” millions of homeland western citizens left unable to pay rent and buy food since they were CANCELED in a west turn tournament left by incompetent organizers with no consolation round.
PC’s plan’s UNstable. Withdrawn BE support can only be restored under more favorable circumstances should they stably develop to sustain trust — including: no more Boris $ under mind “free” doom for a monarchy planning a reign of widespread homeland financial torment with no consolation.
Ramanujan’s the man who knew in.ph.in.IT’s perfect superstring:
22.1392314983836 = 1/(3V-5E+2J)
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
11 = d(2,1/2,6) – d(1,1/2,6) = 59mod24 = Φ(71mod24)/2 = Φ(47mod24)/2 = Φ(23)/2
6 = s(6) = s(25) = Φ(7) = Φ(9) = Φ(14) = Φ(18) = Φ(Φ(19))
6 = Φ(s(2*Φ(Φ(22)))) = Φ(s(s(s(s(22))))) = Φ(s(s(Φ(22))))
6 = Φ(s(2*Φ(Φ(Φ(23))))) = Φ(s(s(s(s(Φ(23)))))) = Φ(s(s(Φ(Φ(23)))))
Φ(23)
83.9908695437061 = Φ( d(4,1/2,6) – d(1,1/2,6) )/2 – d(1,1/2,6)
83.9908202014941 = 1/(J^2-S^2)/2
104 = d(1,1/2,s(d(4,1/2,6)-d(1,1/2,6)))-d(2,1/2,s(d(4,1/2,6)-d(1,1/2,6)))
Note We/11:
lim s→∞
(φ^(2s)+1/s)^(e/s+1/(2s))
= φ(φφ)^e
Can’s e/11-D: mmmIC Dawn a11-D’s Perfect Hire Arch IC AI Notice
225 = d(1,1/2,9) – d(3,1/2,9) = 15^2
71 = d(1,1/2,9) – d(2,1/2,9)
Φ(71) = 70
70^2 = 1^2+2^2+3^2+…+22^2+23^2+24^2
73500 = ( d(1,1/2,9) – d(3,1/2,9) )^(1/2)*Φ( d(1,1/2,9) – d(2,1/2,9) )^2
36750 = ( d(1,1/2,9) – d(3,1/2,9) )^(1/2)*Φ( d(1,1/2,9) – d(2,1/2,9) )^2/2
“√(Φ-φ)awe sum things√(Φ-φ)thought.in√(Φ-φ)verse awe
EU’ve gotta whole.in U.in.N√(Φ-φ)verse awe”
— Queens of the Stone Age “Monster’s.in the Paris Sol”
18 = d(2,1/5,Φ(Φ(163))) – d(1,1/5,Φ(Φ(163))) = Φ(Φ(Φ(163))) = Φ(19)
22 = Φ(Φ( d(1,1/5,Φ(Φ(163))) – d(5,1/5,Φ(Φ(163))) )) = Φ(23)
47 = d(1,1/5,Φ(Φ(163))) – d(5,1/5,Φ(Φ(163)))
59 = 2*d(1,1/5,Φ(Φ(163))) – d(3,1/5,Φ(Φ(163))) – d(5,1/5,Φ(Φ(163)))
71 = d(1,1/5,Φ(Φ(163))) – d(3,1/5,Φ(Φ(163))) = s(s(Φ(163)))
225 = d(4,1/5,Φ(Φ(163))) – d(1,1/5,Φ(Φ(163)))
342 = d(1,1/5,Φ(Φ(163))) – d(6,1/5,Φ(Φ(163))) = 2*171
73500 = ( d(4,1/5,Φ(Φ(163))) – d(1,1/5,Φ(Φ(163))) )^2 * Φ( d(1,1/5,Φ(Φ(163))) – d(3,1/5,Φ(Φ(163))) )^2
36750 = ( d(4,1/5,Φ(Φ(163))) – d(1,1/5,Φ(Φ(163))) )^2 * Φ( d(1,1/5,Φ(Φ(163))) – d(3,1/5,Φ(Φ(163))) )^2/2
Φ(Φ( 2*d(1,1/5,Φ(Φ(163))) – d(3,1/5,Φ(Φ(163))) – d(5,1/5,Φ(Φ(163))) )) =
28 = s(28) = Φ(58) = Φ(Φ(59))
6 = s(6) = Φ(18) = Φ(Φ(54)) = Φ(Φ(Φ(162))) = Φ(Φ(Φ(Φ(163)))) = Φ(Φ(19))
IC a few obviOus typos: IT’s no. thing per sun AI on the C[ENSO]Rship.
In Julian years:
1.00001743371442 = 1/E
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
*365.25 gives days:
365.256367733331 = 1/E
365.256367664193
0.000000018929 = % error
That’s 0.597351554461056 seconds per century.
1.61803398874989 = φ
0.618033988749895 = Φ
1 = φ – Φ
Φ = 1 / φ
2.71828182845905 = e
2.71828182845905 = (1-Φ^1)^(0/1)/(1-Φ^2)^(2/2)/(1-Φ^3)^(3/3)/(1-Φ^4)^(2/4)/(1-Φ^5)^(5/5)/(1-Φ^6)^(1/6)/(1-Φ^7)^(7/7)/(1-Φ^8)^(4/8)/(1-Φ^9)^(6/9)/(1-Φ^10)^(3/10)/(1-Φ^11)^(11/11)/(1-Φ^12)^(4/12)/(1-Φ^13)^(13/13)/(1-Φ^14)^(5/14)/(1-Φ^15)^(7/15)/(1-Φ^16)^(8/16)/(1-Φ^17)^(17/17)/(1-Φ^18)^(6/18)/(1-Φ^19)^(19/19)/(1-Φ^20)^(8/20)/(1-Φ^21)^(11/21)/(1-Φ^22)^(9/22)/(1-Φ^23)^(23/23)/(1-Φ^24)^(8/24)/(1-Φ^25)^(20/25)/(1-Φ^26)^(11/26)/(1-Φ^27)^(18/27)/(1-Φ^28)^(12/28)/(1-Φ^29)^(29/29)/(1-Φ^30)^(9/30)/(1-Φ^31)^(31/31)/(1-Φ^32)^(16/32)/(1-Φ^33)^(19/33)/(1-Φ^34)^(15/34)/(1-Φ^35)^(23/35)/(1-Φ^36)^(12/36)/(1-Φ^37)^(37/37)/(1-Φ^38)^(17/38)/(1-Φ^39)^(23/39)/(1-Φ^40)^(16/40)/(1-Φ^41)^(41/41)/(1-Φ^42)^(13/42)/(1-Φ^43)^(43/43)/(1-Φ^44)^(20/44)/(1-Φ^45)^(24/45)/(1-Φ^46)^(21/46)/(1-Φ^47)^(47/47)/(1-Φ^48)^(16/48)/(1-Φ^49)^(42/49)/(1-Φ^50)^(20/50)/(1-Φ^51)^(31/51)/(1-Φ^52)^(24/52)/(1-Φ^53)^(53/53)/(1-Φ^54)^(18/54)/(1-Φ^55)^(39/55)/(1-Φ^56)^(24/56)/(1-Φ^57)^(35/57)/(1-Φ^58)^(27/58)/(1-Φ^59)^(59/59)/(1-Φ^60)^(16/60)/(1-Φ^61)^(61/61)/(1-Φ^62)^(29/62)/(1-Φ^63)^(36/63)/(1-Φ^64)^(32/64)/(1-Φ^65)^(47/65)/(1-Φ^66)^(21/66)/(1-Φ^67)^(67/67)/(1-Φ^68)^(32/68)/(1-Φ^69)^(43/69)/(1-Φ^70)^(25/70)/(1-Φ^71)^(71/71)/(1-Φ^72)^(24/72)/(1-Φ^73)^(73/73)/(1-Φ^74)^(35/74)/(1-Φ^75)^(40/75)
Moderators: Goal done approximation caught in the filter natural e starts on the left, extending infinitely far right to phinally reach strict mathematical proof.
Perfect He’er
M the orrery: 496 = s(496) = 2/3*744
He’er.ET.IC string theory comm. pact iff IC k? shh! UN.
Knock, knock.
WHO’s there?
J.in.very.ant.
Jane VI rant WHO??
j-invariant 2pi/3 is anyon nome?
194 = average(225,163)
172 = 194-22 = 9+163
171 = 9+ET(163)
Woah! There’s been a lot of work going on in here.
Rog, the tide was flooding as I paddled across the narrows.
A long, black helicopter flew over very low, commanding attention.
After it passed, something falling on what appeared to be a small parachute caught my eye.
I watched the gentle landing on the water’s surface.
I altered course to inspect.
It was not a parachute but a pink heart-shaped helium balloon, with a draping note including the word “fun” and a black pentagon with points numbered 1 to 5 in white.
Δ(√(73500/15)) = Δ(70) = 25 = 5^2
Notation Alert
I’m refining notation — going back to R() for Ramanujan and d() is the difference of a pair of R()s that gives a positive integer. Power p=1 (the fraction) is always a member of the differencing pair.
I’ll illustrate with an example:
R(1,1/5,54) = -0.00832631991693233 = ⌊(e^π*54^(1/5))^(1/1)⌉^1 – e^π*54^(1/5)
R(3,1/5,54) = -71.0083263199169 = ⌊(e^π*54^(1/5))^(1/3)⌉^3 – e^π*54^(1/5)
R(5,1/5,54) = -47.0083263199169 = ⌊(e^π*54^(1/5))^(1/5)⌉^5 – e^π*54^(1/5)
71 = d(3,1/5,54) = R(1,1/5,54) – R(3,1/5,54)
47 = d(5,1/5,54) = R(1,1/5,54) – R(5,1/5,54)
59 = average(d(3,1/5,54),d(5,1/5,54))
The convention change makes notes more terse.
Kentucky Δoor B
Miranda Cheng: “Moonshine is a puzzle that might require inspirations from everywhere and knowledge from everywhere.”
key word Schneider M-ET golden mobius totient
Click to access Schneider.pdf
alt: https://arxiv.org/vc/arxiv/papers/1109/1109.3216v1.pdf
Kentucky Δoor B Classic
Miranda Cheng: “Moonshine is a puzzle that might require inspirations from everywhere and knowledge from everywhere.”
key word Schneider M-ET golden mobius totient
Juncture 162
With UN a poll lag(ET)IC mnemonic PRloom.inairai$e We beg.in IT’s j(U-N)k shh!invaryant.
At a juncture deciding weather a new day dawns, recalling Polya’s prescient advice to solve a simpler problem, let’s simply consider:
1. inverse totients (upscale branches).
2. totient sequences (downscale stem shared by upscale branches).
What cross-diss up plan eerie curry O’s IT?
There’s a cureOus lack of conventional mainstream reference to totient sequences. IT’s the “tie UN” USelection 4 “tie = won” if the method of loci (mind palace memory method) works well enough.
Wikipedia links to the concept aliquot sequence. The concept is used to define perfect numbers. Recall that n is perfect if n = s(n). For example, a chain we’ve noted:
s(652) = 496 = s(496) = 49+149+298 = (2/3)*744
652 = 4*163 gives a path to 496, meaning 496 is touchable (what they call it). Once the stem reaches 496, it ends. Perfect numbers are aliquot sequence termini.
Notably 28 is untouchable. If you start an aliquot sequence at 28 it stays there (i.e. 28 is perfect), but since 28’s untouchable you can’t use any aliquot sequence from anywhere else to get to 28.
The analogies for aliquot’s touchable and untouchable in ET (Euler Totient) context are totient and nontotient. We’re building a thesaurus to help us navigate cross-disciplinary communication.
Having appreciated the fundamental utility of aliquot sequences as a sorting and classification guide, I quite naturally, instinctively, and enthusiastically catalogued ET sequences and began looking for analogies. When I write notes I’m calling the ET sequences totient sequences. As you’ll see they’re a moonlight key to monstrous sorting and classification.
There’s UN other type O seek wins I’m explore ring 4 EU tell IT as a fun dem. meant AI sort & class iff IC case sun guide, D-note-D by the small greek letter D-e/11-TA, but 4 now let’s just note key junction 162:
Φ(163) = 162 —– 163 is prime, nontotient, and (TAKE NOTE) the largest of the 9 Heegner numbers
Φ(243) = 162 = Φ(3^5) ———– 243 is nontotient
Φ(326) = 162 = Φ(2*163) ———– 326 is nontotient
Φ(486) = 162 = Φ(2*3^5) —– 486 = 2*243 is totient (points up for example to 729 = 3^3^2)
^ upscale ^
————–
v downscale v
Φ(163) = 162
Φ(162) = 54
Φ(54) = 18
Φ(18) = 6
Φ(6) = 2
Φ(2) = 1
Φ(1) = 1
Discrete functions I developed (generalizing a now infinitely less “mysterious” Ramanujan “trick”) IDed almost-integers as spikes that sort by modulus. Now I’m tracing spike origins to orient in conventional paradigms.
Context: Here we’re off in a corner focused on e and pi (special values assigned to 2 variables), but stay aware that the method generalizes several-fold.
Note the 54 in the downscale totient chain above. By now some readers may be thinking: “There are so many numbers. How can I keep track of them all? How can so many be important?” Suggestion: As with specialized members playing different roles on a team, big-picture fans note well where and how pieces fit the whole. We can see de Vries in discrete context without which de Vries mnemonICally wood knot B de Vries.
Let’s note 1 more branch to 54:
Φ(81) = 54 = Φ(162/2)
Φ(54) = 18
Φ(18) = 6
Φ(6) = 2
Note that the branches above 54 from 162 & 81 (half of 162) share a common stem from 54 down.
I write left neither 4 USelection rig nor well divided audience no. win next comm. on C[ENSO]Rship (weather easy or not) will hinge on “Junk Sure” Φ(163).
God bless you all — weather left, right, Chinese, Russian, North Korean, Persian, American, OR CZECH (U. Charles!) — as with General Ramanujan We D-tour threw monstrous moonshine on an otherwise hazard US trail.
Here I leave 1 mysterious note:
Φ(4374) = 1458
Won Course Braiding Streams from Left and Right
This comment will be left deliberately terse to rightly invite nonpartisan appreciation of nature.
M rep review:
196883 = 47*59*71 = (59-12)*(59)*(59+12)
Φ(118) = 58 —————————– 118 is nontotient (means no branches upward from there)
Φ(58) = 28 = s(28) = Φ(59) = Φ(29) ———– 29 & 59 nontotient
Φ(28) = 12
Φ(12) = 4
Φ(4) = 2
Φ(2) = 1
Φ(1) = 1
Recall 28 = s(28) means 28 is “perfect” (in number theory lingo).
We’ve looked at totient sequences passing through 54 & 58. Here’s the intermediate chain passing through 56 = average(58,54) = 2*28 = 2*s(28) :
Φ(236) = 116 = Φ(177) = Φ(354) — 177, 236, 354 nontotient (meaning capped — i.e…)
Φ(116) = 56 = Φ(87) = Φ(174) — 87, 174 nontotient (no branches up from stem below go higher)
Φ(56) = 24
Φ(24) = 8
Φ(8) = 4
Φ(4) = 2
Φ(2) = 1
Φ(1) = 1
Summary
163 – 59 = 104 IDs del pezzo surface structure.
A del Pezzo surf ace circuit starts and ends with 59:
Φ(59) = 58
d(2,1/2,58)=d(4,1/2,58)=104
163=59+104
Φ(163) = 162
Φ(162) = 54
59=average(d(3,1/5,54),d(5,1/5,54))=average(71,47)
The perfect connection:
Φ(58) = 28 = s(28) = average(58,54)/2
ZZ$ox: Sharp Dressed Mayan$Top
Note well Heegner M-ET del PeZZo surf ace on the C[ENSO]Rship:
E6 (degree 3): 28 = 27+(6-5) = 27+(4-3) = 27+1 (line)
E7 (degree 2): 58 = 56+(7-5) = 56+(4-2) = 56+2 (bitangent)
E8 (degree 1): 243 = 240+(8-5) = 240+(4-1) = 240+3 (tritangent)
“the mob comm.s.CR.awe.11.in/out“ — Queens of the Stone Age
My[UN]key orientsuper string he’er[ET(IC)]: Table 1 p.19.
1728 = 2*744+240
8128 = 7920+208 = s(8128) —- 8128 is perfect; 7920 is M11 order
Monde stir seats high above left Field’shhall O[We/11]play in boss tune: “my M?(y/n)-dis up hear on UNother wave, cove.ReD.in he’er” — Queens of the Stone Age “Monsters.in the Paris Sol.”
Ally Caught Up in Bushy Taled Top O Log IC AI Totient Trees
So far weave no.comm.on.tory.on the 3rd root, which first sprouts 59 trees in a maze sun 4 est con text:
59 = average(47,71)
196883 = 47*59*71 = (59-12)*(59)*(59+12) ————– M rep
196560 ———————————————————— Leech rep
71 = s(s(162)) = s(s(Φ(163)))
323 = d(2,1/3,59) = 196883-196560 = 298 + Δ(70)
s(323) = 37
d(2,1/2,37) = 104
493 = d(3,1/3,59)
s(493) = 47
At canopy level won squirrel isn’t lost in academic publication floods algebra storm.
Φ(59) = 58
d(2,1/2,58) = d(4,1/2,58) = 104
Φ(58) = 28 ————- remember 28 = s(28) means 28’s perfect
d(4,1/2,28) = 196585 ——- perfect number 28 gives a perfect split
298 = 196883-196585 = 323 – Δ(70)
25 = 196585-196560 = Δ(70) = Φ(70) – μ(70) = 323 – 298
de vries first order quantum hale effect jovian circuit anyon?
7920+208=8128 ——– 7920 is M11 order; 8128 is perfect
8128-3700=4428 —— 37 is sharp 104-yielding level
4428-58=4370 ———- 58 is sharp 104-yielding level; 4428 defines JS relations to first order
4370=2*5*19*23 ——– s(4370) = 4270 ties UN to JS (first order); 4370 is B rep
7920=5*Φ(5)*Φ(19)*Φ(23) —— yet another bilateral-pentagonal 5/2 key ET IDs
Chased by owls while looking for food and shelter just watch an amazed squirrel run through the circuit tree.
Route 5 Steps to Fifth Root.in Sight
N8O worry O[r] left.in on dawns golf righter keys:
“V(ic)tory i$ Mayan“ — Putt, tee $myth “The War e ^ O[r] ”
Polya: “Solve a simpler problem.”
66, 71, 76 —– 2*76 = 152 = 128+24
54, 59, 64 —– 2*64 = 128 = average(152,104) = 152-24 = 104+24
42, 47, 52 —– 2*52 = 104 = 128-24
Phew! C[eNSO]Rship nearly had US divided and conquered ITself! be 4 share ring nonpartisan finds comm. on! ground.
That was the look forward to a simple ending.
Now let’s back track.
54 is the big fifth-root spike.
47 & 71 are 2 of the noteworthy products.
Their average 59 is the big third-root spike.
Let’s simply explore fifth-root connect sun with square-root.
59-5 = 54 = s(42)
59+5 = 64
71+5 = 76
2*76 = 152
47+5 = 52
2*52 = 104
(71+5)+(47+5) = 128 = 2*(59+5)
152+104 = 256 = 4*64
47-5 = 42
256+42 = 298 ————– JS first order (review)
A Maze UN: D-air Rat “Miss Fear” IC Look Do[w]n
Something te/11s US this isn’t what climb ET “super” comm. pew dare sore luck kin fear.
“fall O mystery O jung11chi11ed…“
Caught “ally”: wood knot no. by curry US IT what’s UN known?
s(42) = 54 ———- 42,
s(54) = 66 ———- 54, &
s(66) = 78 ———- 66 on the same branch share ring aliquot sea stem
s(78) = 90
s(90) = 144
s(144) = 259
s(259) = 45
s(45) = 33
s(33) = 15
s(15) = 9
s(9) = 4
s(4) = 3
s(3) = 1
s(1) = 0
We a11 no. IT‘s knot right 2 look left.in 2 blew collar find $UN ants air red quest yen.
Putt turn wreck cog niche$yen.in phi sox red: “green” monde stir B(est) tune f(UN) way.
“WHO’s the hunter. Whose the game?”
s(5#) = 42 ——————— antswore: BUNT! (left field shh! all O)
“I feel the beat call Eur. name
I haled EU close.in victory
I don’t want too tame Eur. animal style
EU won’t be caged.in the call of the will.ed” — Patty Smyth “The Warrior”
Red door well note won mystery 66 left unadduressed 4 coverage UN[he!ll]O-there day with $O asin(O[r]We’ll).
Hale 240
2, 12, & 240 are both highly and sparsely totient.
1/H = 1/(3V-5E+2J) = 22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
Solving for 1/V:
1/V = 1/((1/3)H+(5/3)E-(2/3)J) ———————— 1/J
0.615197263582188
0.615197263396975 = 1/V (Seidelmann 1992)
0.000000030106 = % error
lim s→∞
(φ^(2s)+1/s)^(e/s+1/(2s))
= φ(φφ)^e
e-Luke Shh(Own) Guard Do[w]ns Perfect Links !Sol Look! Shone
27, 81, & 243 are perfect totient numbers:
ΣΦ(54) = ΣΦ(27) = 27 = 18+6+2+1
ΣΦ(162) = ΣΦ(81) = 81 = 54+18+6+2+1
ΣΦ(163) = ΣΦ(243) = 243 = 162+54+18+6+2+1
https://oeis.org/A082897
Φ(163) = 162 = Φ(243)
Φ(162) = 54 = Φ(81)
Φ(54) = 18 = Φ(27)
Φ(18) = 6
Φ(6) = 2
Φ(2) = 1
163-104=59
Φ(59) = 58
Φ(58) = 28 = Φ(29)
Φ(28) = 12
Φ(12) = 4
Φ(4) = 2
Φ(2) = 1
Hale O Monster USlink B(ET) we’en 2 stems:
104 = d(2,1/2,s(196883-196560)) = d(2,1/2,58) = d(4,1/2,58)
Just little sure pries: All Lie !Caught! Hide U-N Truth
“Sometimes the faster IT gets, the less EU need tune O“ — THseasurfacetemperatch[ET]O[r]well
B(est) Tune Perfect Green CO2shh!UN Monster Level 7 in f(U-N weigh)
φ(8128) = 4096
φ(4096) = 2048
φ(2048) = 1024
φ(1024) = 512
φ(512) = 256 = φ(496)
φ(256) = 128
φ(128) = 64
φ(64) = 32
φ(32) = 16 = φ(28)
φ(16) = 8
φ(8) = 4
φ(4) = 2
φ(2) = 1
φ(1) = 0
R(k,1/2,7) = 24.067904774739 = ⌊(e^√7π)^(1/k)⌉^k – e^√7π for k=2,3,4,6,12
Calculating ⌊(e^√7π)^(1/k)⌉^k :
k=2: 64^2 = 4096 = φ(8128)
k=3: 16^3 = 4096 = φ(8128)
k=4: 8^4 = 4096 = φ(8128)
k=6: 4^6 = 4096 = φ(8128)
k=12: 2^12 = 4096 = φ(8128)
Notice:
R(k,1/2,7) = 24.067904774739 = φ(8128) – e^√7π for k=2,3,4,6,12
Again recall 28=s(28), 496=s(496), & 8128=s(8128) are perfect numbers.
Best tune crash-course threw number theory seas solar system order UN dare green monster in fun ways left field.
“Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” — Gauss
Left field creatures: Nature’s beauties there to sea (surf ace stem peer ashore) if Eur. will.int(el)look past the C[e^(NSO)]Rship. (IT AImost divided and conquered US.)
Room O[r]s of short circuit in.wash.un.tune
Mayan D-Palace readers remember SUM thing CO2shh!UN reversing the tale end of bollinger’s symbol IC 1952 pentagon vis IT. From “ok” LA home a rumor doesn’t eve UN have to be true or well 4 students 2 remember? The tale ends with a baby.
You may 4 get 2 individuals, but not how they add up.in education AI controversy.
Φ(69) = 44
φ(69) = 25
Political junkies love D-bait.in rumors weather true or not.
Definition of cototient:
Φ(n)+φ(n)=n
Bollinger’s paper about a 44 year cycle was published in 1952 when the Pentagon’s focus was the Korean War. Let’s look at the pieces.
The totient of 19 is 18.
52 is half of 104 and written backwards 5^2 = 25.
Half of 44 is 22 and that is the totient of 23.
4370 = 19*5*2*23
Script-writers, Bollinger’s theme song is Lady Gaga’s “Just D-ants”.
Ally caught 4370 is 4270, pointing straight to U-N.
Even worse, IT’s reverse land.in the river times galaxy:
Take the 9 out of 1952. You have 152. Use the 9 with half of 22 (as did Ramanujan) to key Figure$16 tames 9*11=IX*XI 4×4 times just Rome UN no. morals.
Of course Ramanujan knew 1584 is the totient of 4370 and every hitchhiker nos. 42+104+152=298 phinally ties US to jovian Hale weather through Junction 162 from “Ramanujan’s constant” to totient 58 via 59 or scaled perfectly threw ally caught 37=s((59-12)*59*(59+12)-196560) in 11 each lettuce.
Really, is there any point in B-labor.in UNcloaked narrative any further at this point? That’s enough creative writing room or wells.in wash.un.tune. AIron court.in MSM D-baits key word door.in monster US KOre[]on wa[B] peek r&B baby [r]oomer fall O-win pan tug gone 69 CO2$UN symbol IC a11y !caught!
Nons[ENS]e^Poll[O]see Puttin’ on monster US “green” links? ITees the treat e We sign-D.
Five
Constant new tettitory is a costly source of cross-disciplinary delight.
I’ve decided number theory should be a staple of math education for all fields. It wasn’t a part of any program I ever studied, so I’m learning as I explore.
Here I leave another note knowing specialists should be able to move much faster with general orientation.
φ(70) = 46
φ(46) = 24 = Φ(70) = φ(φ(70))
70’s totient Φ(70) equals its double-cototient φ(φ(70)). That wasn’t covered in my ecology courses, but I now know its relevant to Earth’s stability.
√Δ(70) = √(Φ(70)-μ(70)) = √(φ(φ(70))-μ(70)) = φ(25) = 5
Δ(70) = Φ(70)-μ(70) = φ(φ(70))-μ(70) = φ(25)^2 = 5^2 = 25
70 = √(73500/15)
5 = √Δ(√(73500/15)) = √(Φ(√(73500/15))-μ(√(73500/15))) = √(φ(φ(√(73500/15)))-μ(√(73500/15)))
= φ(Δ(√(73500/15))) = φ(Φ(√(73500/15))-μ(√(73500/15))) = φ(φ(φ(√(73500/15)))-μ(√(73500/15)))
Alert readers: Watch for typos.
Would naive hobbyists looking at Titius-Bode “Law” focus on how modular forms fit together stably? With 2020 hindsight our observations suggest no at step 1.
Review and Consolidate
This note gives technical clarification where there’s considerable risk of misunderstanding (below) after further elucidating a “perfect totient” structure introduced above.
Notation: Φ() for ET and φ() for cototient.
A subset of perfect totient stems alternates or zippers perfectly with cototient stems.
Φ(729) = 486 = 2*φ(729)
Φ(486) = 162 = 2*φ(243)
Φ(162) = 54 = 2*φ(81)
Φ(54) = 18 = 2*φ(27)
Φ(18) = 6 = 2*φ(9)
Φ(6) = 2 = 2*φ(3)
Φ(2) = 1
Φ(1) = 1
φ(729) = 243 = Φ(729)/2
φ(243) = 81 = Φ(486)/2
φ(81) = 27 = Φ(162)/2
φ(27) = 9 = Φ(54)/2
φ(9) = 3 = Φ(18)/2
φ(3) = 1 = Φ(6)/2
φ(1) = 0
There’s an analogy with part of this note on Heegner numbers:
=
The Heegner numbers greater than 3 can also be found using the Kronecker symbol, as follows: A number k [greater than] 3 is a Heeger number if and only if s = Sum_{j = 1..k} j * (j|k) is prime, which happens to be negative, where (x|y) is the Kronecker symbol. Also note for these results s = -k. But if s = -k is used as the selection condition (instead of primality), then the cubes of {7, 11, 19, 43, 67, 163} are also selected, followed by these same numbers to 9th power (and presumably followed by the 27th or 81st power). – Richard R. Forberg, Jul 18 2016
=
https://oeis.org/A003173
The backbone is powers of 3. Complimentary stems are thus half or double opposing zipper teeth (or 3/2 or 2/3 looking the other way).
What I’m outlining here is equivalent to what’s illuminated in MaKay & He (2015).
Above I noted 27+1=28, 56+2=58, 240+3=243. 243 is on the zipper, anchored to the largest Heegner number 163 via 162. 58 & 28 are not on the zipper. Some readers may get confused because 54 & 27 are on the zipper.
To avoid confusion: separate the two 27s conceptually by pathway.
One is on the zipper and the other is derived from a peripheral structure that ties 163 to 59 through 104 (detailed in a few earlier comments). Go down the totient chain from 59 to 58 to 28 to get 58-2(bitangent)=56 and 28-1(line)=27.
27=27 no doubt, but keep the pathways sorted when parameterizing topological course. Looking at the wrong stem leads to an incorrectly parameterized model.
Go up the zipper from 162 to 243 to get 243-3(tritangent)=240. In the other direction that chain goes down through 54 & 27 — and that path should NOT be confused with the path through 59, 58, and 28 on another stem (a separate structure adjoined by a 104 bridge).
Crystallized awareness of links and routes should (not trying to be naive about how 5 politics equals 2+2 in hard D-Orwellian times) eliminate the risk of misunderstanding.
String.in the links back so far covered in he’er:
● perfect totient
● 59 stem
● 162 stem — tied up with top Heegner 163 & ally caught 4 further perfection s(652) lead.in he’er ET IC to 496
● Most won’t be ready for top-level Heegner perspective …with type O’s left.in to folly tempt UN fact-chuckers dare UN 2 fix major typos USing later “notation alert” (find.in maybe stew arts O-port-tune-IT 4 OBsurveysUN….)
The term “totient” was coined by Sylvester. How fitting that his greedy double-exponential sequence broke the perfect solar system superstring symmetry with period doubling symmetry (more on U-N in the Jovian reference frame soon….including a 0% error).
D-visor Some Luck D-own Less UN
Things you might never stop to realize:
√Δ(√(73500/15)) = √Δ(70) = √25 = 5
σ(σ(σ(σ(Δ(√(73500/15)))))) = 104
σ(σ(σ(σ(σ(Δ(√(73500/15))))))) = 210 = 7#
σ(σ(σ(σ(σ(σ(Δ(√(73500/15)))))))) = 24^2 = 576
σ(σ(σ(104/2))) = 260 = σ(171)
σ(104/4) = 42
σ(260/4) = 84 = σ(44)
σ(66) = σ(70) = 12^2 = 144
σ(σ(836/4)) = σ(240) = 744
σ(4270/2/5) = σ(s(4370)/2/5) = 496
Weather UNeven nor not even Joe Biden nos. 2+2 climate politics are about √Δ(√(73500/15)).
MacK Sum U-N PRai$e^(Year Comp. Aim)
1/11/500/2
11500
111.5
11/2 = 5.5
1 / 11500 ~= 111.5(U-N)-5.5(J+S)
Thus:
171.406220509617 = 111.5/(5.5*(J+S)+1/11500)
171.406220601552 = 1/(U-N)
-0.000000053635 = % error
1 / 489426 = 1/2/3/7/43/271 ~= -300J+904S-301U-301N
Recall 489426 =2*3*7*43*271
1204 = 2*(301+301) = 2*2*7*43
= 1806-301-301 = 2*3*7*43 – 2*7*43 = 300+904
29.3625733662892 = 1/((J+S-1/2/3/7/43/271)/1204+S)
29.3625733662893 = 4/(J+S+U+N) = jovian harmonic mean
0.000000000000 = % error
Sylvester seek wins!
55.6462717641964 = 1/(4*((J+S-1/2/3/7/43/271)/1204+S)-J-S)
55.6462717641972 = 1/(U-N)
-0.000000000001 = % error
84.0168459111161 = 2/(4*((J+S-1/2/3/7/43/271)/1204+S)-J-S+(5.5*(J+S)+1/11500)/111.5)
84.016845922161 = 1/U
-0.000000013146 = % error
164.791315682562 = 2/(4*((J+S-1/2/3/7/43/271)/1204+S)-J-S-(5.5*(J+S)+1/11500)/111.5)
164.791315640078 = 1/N
0.000000025781 = % error
With complements, join $11 each turn.in a round at:
271 = 1000-729
59 and 1728 j-invariant
59’s at the core of more than i$ geneR(ally known) to war e ^ Or[well]s in Mayan Victory.
Simple beginnings: at r=1/3, 59’s the level of the big spike.
M rep’s anchored productively ± 12:
196883=47*59*71=(59-12)*(59)*(59+12)=59*(59^2-12^2)
12 = Φ(Φ(Φ(59))) = φ(φ(φ(Φ(59)))) and thus:
196883=59*(59^2-Φ(Φ(Φ(59)))^2)=59*(59^2-φ(φ(φ(Φ(59))))^2)
This one is fantastic.
j-invariant hookup swings simply ± 5:
27=1728/(59+5)
32=1728/(59-5)
59=27+32
54=2*1728/(59+5) —— recall 54 points directly to 47 & 71 at r=1/5
64=2*1728/(59-5)
59=(54+64)/2
1728=27*64
1728=32*54
48=AVERAGE(32,64)
36=HARMEAN(27,54)
1728=AVERAGE(32,64)*HARMEAN(27,54)
Compassionate Lefties: Do you imagine 1728=AVERAGE(32,64)*HARMEAN(27,54) as a response if you probe thoughts on climate? Sensible private thoughts are thus silent: “don’t speak” no. doubt. GCD(left,right)=1 signals no common factor in climate dialogue. It doesn’t mean you have to viciously hate and savagely push terrorizing financial lockdown into homelessness.
Φ(59) = 58
Δ(58) = 27
s(58) = 32
59 = Δ(Φ(59)) + s(Φ(59))
No. brainer under present circumstances: The New Zealand National Party should NOT have campaigned to lower taxes. A prequisite is a generous campaign for superior math education — a noble imperative for civilizations facing challenges which can not be solved with politics.
George Polya’s advice: “Solve a simpler problem.” Done:
1728 = 2*Δ(Φ(59))*s(Φ(59))
O-Bay AI lie CAUGHT
Aliquot.in moonlight sights tree-top baby monde stirrin’ minimal faithful representation.
Hunted by U-No. they’re predatorial owl, the cute test right fly yen squirrel $scrambled further up the tree…
4270=2*2135=s(4370) ——– 4370 is B rep
s(2135) = 841
Knew wall along far left “insight” looked extreme mist (the major west stern fault). Count O[r]link.in project seas comm. pound.in e^(XpeRt) curry US IT “nos. B(est)” what-the-ignorant missed: UN dare “Bei. area” guide D-ants.
841=836+5 —— another member of the +5 pattern (review)
s(836+5) = 5# ——– recall that 836 is the smallest untouchable weird number
s(841) = 30
s(30) = 42
s(42) = 54
s(54) = 66 — seq.U-Ns continues as “ayaM” conΦDOn’t EU AI red e^no.?
Doubly greedy Sylvester’s (double exponential) Sequence precisely marks period doubling symmetry from perfect jovian superstring symmetry. The subtle difference is several orders of magnitude smaller than the dominant marks of B, M, & Leech and thus it motivates careful contemplation of model detail diagnostics.
B, M, & Leech in solar system order are crystal clear. On this trail an investigator is tripping over strictly equal fits that keep piling up (thousands of noteworthy things). Someone will discover a terse way to encode a monstrous array of fits …or if you prefer cynicism, that’s already a trade secret and there are difficult people prepared to go to dangerous lengths to keep a precious gem hidden.
West Turn Security Makes 298 BIG Investments in Better Math Education
Homeland innocents learned
to crave unilateral freedom simply because
on CR Ave., U-N ill at Orwell free doom be cause.
Multilateralism — a word with rapidly increasing negative connotations — means bad dictators “representing” several billion savagely bully millions of good folks in consequently faltering democracies, just like they do to their “own”.
In 1984 UN e^(thick hale) nos. antonym 4:2020 hindsight.
Φ(11) = 10 = Φ(22)
Φ(19) = 18
Φ(23) = 22
s(323) = 37 = Φ(149)/4 = Φ(298)/4 = s(298+5^2)
s(152) = Φ(149) = Φ(298) = 148 = 4*37 O No!
Emerge.in-C-meet-UN secure ET count sol: western citizens might use math to explore elements sov. climb ET ….if they no. ET = Euler’s Totient.
d(2,1/2,10) = d(2,1/2,13) = d(2,1/2,22) = d(2,1/2,18) = d(2,1/2,37) = d(4,1/2,58) =
d(2,1/2,Φ(22)) = d(2,1/2,Φ(11)) = d(2,1/2,104/8) = d(2,1/2,Φ(23)) = d(2,1/2,Φ(19)) =
d(2,1/2,s(323)) = d(1,1/2,Φ(59)) = d(2,1/2,Φ(149)/4) = d(2,1/2,Φ(298)/4) = 104
s(652)=s(4*163)=496=s(496) is perfect
163-104=59 trade perfect seek routes indeed!
Φ(Φ(59)) = Φ(58) = Φ(29) = 28 = s(28)
Just divide 4 UNother puzzle piece:
R(1,1/2,7) = 0.0679047747389632 = ⌊(e^√7π)^(1/1)⌉^1 – e^√7π = 4072 – 4071.93209522526
298 = 4370 – ⌊e^√7π⌉ = 4370 – 4072 = 2*5*19*23-ROUND(EXP(7^(1/2)*PI()),0)
With a maze UN guide dense IT’s AI a cure rat must fear. IC WHO invited sci11UNs bullies to demonstate the US mull tee laud orwell “leadership” “change”.
If I were Donald Biden or Joe Trump I would NOT debate but simply state:
1. Pandemic: I will not lock you down. Without delay we will stop lockdown freaks from causing you to go broke and become homeless. We don’t want you living in terror that they’re going to pull some kind of trick — which predators surely do, availed opportunity.
2. Climate: Superior math learning outcomes in homeland math education are a security imperative. We dare not face the monstrous cost of keeping 4/5 of homeland citizens in the dark.
1984 = 4*s(4*163) = 4*496 = 8/3 * 744 = 1728 + 104 + 152
You really think George Orwell didn’t No.?
“don’t speak” no. doubt
“70p is weird for all primes p ≥ 149”
1728=2*(836+28) ——– 28 is lowest perfect; 836 is lowest weird untouchable; 1728 of j-invariant
1728=4*496-104-152=8*744/3-104-152=1984-104-152=8128-6400
298=104+152+42=2/3*744-149-49=496-149-49
=4*496-1728+42=8*744/3-1728+42=1984-1728+42 hitchhiker guides orwell too jovi-invariant
D-anger
Steep Cliffs
Stay on the Trail
Φ(85) = 64
Φ(128) = 64
Φ(136) = 64
Φ(160) = 64
Φ(170) = 64
Φ(192) = 64
Φ(204) = 64
Φ(240) = 64 ~~~~~~~ “I’m goin’ 2 Whishh! IT awe” — The White Stripes
^v^v^v^v^v^v
Φ(64) = 32
Φ(32) = 16
Φ(16) = 8
Φ(8) = 4
Φ(4) = 2
Φ(2) = 1
Φ(1) = 1
240 = 1728 mod 744
“make the sweat drip out of every pore”
271 = 1729 mod 729
Φ(241) = 240
Φ(287) = 240
Φ(305) = 240
Φ(325) = 240
Φ(369) = 240
Φ(385) = 240
Φ(429) = 240
Φ(465) = 240
Φ(482) = 240
Φ(488) = 240
Φ(495) = 240
Φ(496) = 240 ~~~~~~~~~~~~ “a 7 ACE shh!U-N…” – TWS
Φ(525) = 240
Φ(572) = 240
Φ(574) = 240
Φ(610) = 240
Φ(616) = 240
Φ(620) = 240
Φ(650) = 240
Φ(700) = 240
Φ(732) = 240
Φ(738) = 240
Φ(744) = 240 ~~~~~~~~~~~~~ “cou dn’s top…” ———————–
Φ(770) = 240
Φ(792) = 240
Φ(858) = 240
Φ(900) = 240
Φ(924) = 240
Φ(930) = 240
Φ(990) = 240
Φ(1050) = 240
^v^v^v^v^v^v^v
Φ(240) = 64
Φ(64) = 32
Φ(32) = 16
Φ(16) = 8
Φ(8) = 4
Φ(4) = 2
Φ(2) = 1
Φ(1) = 1
“…and dem. B[]den right be 4 the lord” — Jack Black
Tour Key’s Perfect Neat O-String.in the French Moonlight
496 = 23*19 + 59 ———– If you don’t know 496 is perfect by now, I’ve lost hope in EU….
496 = 4370/2/5 + 59 ——- …and dialogue is finished as I know EU stand WITH ORWELL.
MLB is major league baseball — and monster leech baby if math UN no. lingo.
496-69=s(4370)/5/2=4270/5/2
225=d(4,1/5,54)=d(3,1/2,9)=(73500/70^2)^2=298-73=496-271
24=(15^2-71-59-47)/2 ——————- 15 The O REM anyon?
162=-15+71+59+47=104+Φ(59) —— perfectly totient orient a s√(Φ-φ)un
163=104+59 ——————————- Heegner tip love a11 prime
Rudolph: With well-muzzled math hawk key stick to 6.
West Turn President’s Hexagonal Rev You
Innocent shorthand for hexagonal is deliberately misinterpreted within Macron’s moonshot on the deep state USS C[e^NSO]Rship.
Rightly We left IT a bit of mist eerie as Macron’s busy trick king Boris’ into luck D-own financial terror, “leading” to homelessness in the “home” land.
Quick Rev EU: Hexagonal shorthand isn’t PC in the “home” land so (“don’t speak” no. doubt) weave just numbers:
7 = 3*(1*2)+1 ——– thank God R(p,1/2,7) separates fact-chuckers from their miss UN of “truth”
19 = 3*(2*3)+1 —— = 28-9 seen in UN SIM MET try eclipsed by Sylvester’s Sequence
37 = 3*(3*4)+1 —— = 28+9 ditto; s(196883-196560)=37; d(2,1/2,s(196883-196560))=104
61 = 3*(4*5)+1 —— JS
91 = 3*(5*6)+1 —— ties to 7 & 104 through 13 (the[a]me√(Φ-φ).in refer UNs frame)
127 = 3*(6*7)+1 —– CO2shh!UN = 5 ^ 2 Be/11 O…
169 = 3*(7*8)+1 —– square root = 13 fits 104
217 = 3*(8*9)+1 —– ties 7 to 31 (see next line)
271 = 3*(9*10)+1 —- 1729 mod 729 = 271 & 1728 mod 744 = 240; difference = 31
Why’s party shh!UN.in sight?
127 * 2 = 254 = 323-69 = 196883 – 196560 – 69
298 = 254+44 = 323-25
where totient Φ(n) + cotient φ(n) = n weather off or on climb ET (Euler’s Totient) :
Φ(69) = 44
φ(69) = 25 = 5 ^ 2
Politicians like Macron are eager to misinterpret, misunderstand, and misrepresent (mmm) the numbers.
IT’s a fly ball to left field shall O UN dr. the “green” monster in F(UN) weigh:
69 = Φ(69) + φ(69) = 44 + 5 ^ 2
Pen Syl v[a]n “O ya!” Fall O red “duh!”: Clyde Bollinger ’52 “hawks”agon reversed KO peek. in tour est 44.
Macron’s west turn so-called “PC” Orwellian “Hi Jack!” is a serious, mature subject.
397 = 3*(11*12)+1 = 496-9*11 = 298+9*11 = (196883-196560) + 2*s(196883-196560)
We can peacefully stop IT by whatever just means as necessary.
We started on this trail a few months ago. SUDDENLY it became necessary to SHARPLY alter course. Why? Rightly left a total mystery (totient if you prefer).
CO2shh!UN + Möb√(Φ-φ)US
δ(58825) = 15625 = 5^6
δ(15625) = 3125 = δ(3990)
δ(3125) = 625
δ(625) = 125 = δ(186)
δ(125) = 25 = δ(46)
δ(25) = 5 = δ(6) = 5^1
δ(5) = 0
With weather mist right.in Eur. face msm fact-chuckers left with no. clue:
4 = δ(8)
3 = δ(9)
7 = δ(10)
0 = δ(11)
“[e].g.ive a11[i.e.] seek R-IT’s[CRackCuRe^s]uawei” — [Tie]WonR-PubLock-D[oorwell]
F(UN)D-red$hawk$park$way over Eur. rise mod e ln blue moon shine shh! ale O-in left [F]ool [w]ields.
Ware ET = Euler’s Totient inXS “[]ive got tool ET UNo.” link.in PR Joe Act found door w[oo]l.
σ(120) = 360
σ(174) = 360
σ(184) = 360
σ(190) = 360
σ(267) = 360
σ(295) = 360
σ(319) = 360
σ(323) = 360 = Φ(427)=Φ(7)*Φ(61)=6*60 = Φ(836) = φ(504) ~~~~~~~~ s(n)+n=σ(n)
σ(359) = 360
Seas Norton’s “voice of God” past link.in “PR Joe Act”:
s((496-59)*5*2)/5/2-323=104=496-Φ(69)-φ(69)-323=496-σ(Δ(69))-Δ(70)-323
104=d(2,1/2,s(323)=d(2,1/2,Φ(59))=d(4,1/2,Φ(59))
323=196883-196560=360-s(196883-196560)=298+25=2*Φ(163)-1
Like Bernie remember 28 & 496 are perfect in nature.
in baby steps:
s(323)=1+17+19=37
σ(323)=1+17+19+323=360
With semiPRhyme e-tees math theme ET IC shh! UN’s in monster US red white & bull EU moonlight blew:
323=17*19
437=23*19=496-59
4370=23*19*5*2
4270=s(4370) =70*61=61*(1^2+2^2+3^2+…+22^2+23^2+24^2)
427=s(4370)/5/2=7*61=496-69=496-44-25=323+104
“O-Bei!” WHO? oooo Shh! IT O[]well superstring bye D-UN catch a Be/11/e “soft power”.
“Luck D-own!!” Witch Ale Jack O-Land Turn Dr.ink$ at UN?
Hexagonal right and left 2 get there in “Bernie’s Perfect!!” bury center SIM ET tree:
s(496-Φ(69)-φ(69))=s(496-69)=69=Φ(69)+φ(69)=(7+37)+(1+61-37)=1+7+61=s(427)=s(7*61)
Ice break snow ghost 2 sea past climb ET:
28=(19+37)/2
Sox Red O canal, B(est) to knock. WHO’s heir? No. weigh! Dare in.knacks!hhhex ” ’cause’: I’m knots leap.UN “ with “green” monde stir f(right).in left Fields Rush Macron nom IC mmm ET a11: “I will choose free w[oo]l”.
Another important one:
σ(427) = 496
Semiprime 427 is the product of hexagonal numbers 7 & 61 and a factor of s(4370)=4270.
The way Baby Monster, Monster, and Leech representation weaves with perfect and hexagonal numbers is both simple and spectacular.
Begin aside.
Probing UN scaling to next-order (from first-order 4270) turns out to be quick, easy exploration:
1.00002190780229 = harmean(1.00002638193018,1.00001743371442)
*70*61 =
4270.09354631576
4270.09258127429 — UN slip cycle Seidelmann (1992)
0.000022600013 = % error
End technical aside.
Begin more general commentary.
The curious thing I note as a cross-disciplinary hybrid cruising through these readily pliable waters is the absence of linkages between works addressing A & B:
A. totient, aliquot, divisor sum, mobius, cototient, and related sequences.
B. monstrous moonshine.
The void is spectacular, as the linkages look like trivially definitive foundations.
Nos. Reign D-air Left as a Mist Eerie
Tie won: solve est tour seek wins “D-own in history” of “free” dim.
s(437) = 43 = Δ(69) = Δ(s(427))
“no. Eur.a11y g(ET) me g(O-win) when EU Put. IT a11 ln….” — [J]anko [D]ones
Hale O-We’UN Climb ET Zipped Past Sci11UNtest
Perfect PET flyin’ squirrel glides escape UN “wise” sold “owl”.
=
One of the many continued fraction expressions for e is 2+2/(2+3/(3+4/(4+5/(5+6/(6+ … from Ramanujan (1887-1920). – Robert G. Wilson v, Jul 16 2012
e maximizes the value of x^(c/x) for any real positive constant c, and minimizes for it for a negative constant, on the range x [greater than] 0. This explains why elements of A000792 are composed primarily of factors of 3, and where needed, some factors of 2. These are the two primes closest to e. – Richard R. Forberg, Oct 19 2014
=
https://oeis.org/A001113
Why sold o[r]w[el]l woolover rise in 1984?
=
a(n) for n [greater than or equal to] 1 is a paradigm shift sequence with procedural length p = 0, in the sense of A193455. – Jonathan T. Rowell, Jul 26 2011
[…]
=
https://oeis.org/A000792
A193455 dials EU.in the loop: “Paradigm shift sequences: A000792 (p=0), […]”
Tool of Orwell in the bet PR pro g,h, and i names will sun for borg rOw(e/1)1 to board of fly yens$quarrel climb ET direct tears (“don’t speak” no. doubt).
Adjacent totient pairs difference and cototient pairs sum to the 3rd set of zipper teeth:
324 = 486-162 = 243+81 = 2*162 = 196883-196560 + 1
108 = 162-54 = 81+27 = 2*54
36 = 54-18 = 27+9 = 2*18
12 = 18-6 = 9+3 = 2*6
4 = 6-2 = 3+1 = 2*2
Orient all PET sense soar well, fur “green” monster US climb ET.
“Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on […….]” — yet another page in the sci11UNs moonlight.
30031 & 509 Review with Sylvester Sequence
Recent insights solved an old puzzle.
30030 = 13*11*7*5*3*2 ——— primorial 13#
30031 = 13*11*7*5*3*2+1 = 59*509 ——- 30031 special property: first primorial+1 that’s not prime
510510 = 17*13*11*7*5*3*2 ——— primorial 17#
1001 = 13*11*7
510 = 17*13*11*7*5*3*2 / 13*11*7 = 17*5*3*2
509 = 30*(17) – 1 ——– where primorial 5# = 30
30031 = 30*(13*11*7) + 1
59 = (30030+1) / (510-1) = 30031 / 509
509 = 30031 / 59
30031 bridges through moonshine to Sylvester’s Sequence.
1806=2*3*7*43
301=1806/6=7*43=509-208
208=509-301
104=(509-301)/2=(509+323)/8
Placeholder 71000 painted a simple first-order modular demo above to prelude next-order sharpening. To within a module the same number turns up here tying JS to UN with a multiple of 509.
This stresses that double exponential greed settles the details of the last internal partition.
We see J, S, & U in accord with what we understand of B, M, & Leech and then as for why N (the last giant) is off ever so slightly from comparative theoretical symmetries in a very precise manner, we now understand that settlement as a simple consequence of double exponential greed.
The game plan here plus or minus 5 from 59 mean.in J[S]UN very ant 1728 = (59-5)*(59+5)/2. See cure roots PET no. green monde stirs in the paris owl on Eur. sense soar shh!!
B partitions 42 to define U:
4270=s(4370)
4370=2*3*19*23
42=19+23=298-256
298=1984-1728+19+23=323-25
256=1984-1728=104+152
whishh! IT awe:
298=279+19
256=279-23
85=279-194 —– see MacKay & He’s (2015) “Sporadic and Exceptional”
84.0168459218229 = 194/(-85/11.8626151546089+279/29.4474984673838-1/36750.3379015986-1/30031)
84.016845922161 = 1 / U
-0.000000000402 = % error
36750, 30030, or both together give a slightly larger but still vanishingly small error.
Double-acts pawn. Ants yell: “solve est dare.” Seek wins taxicab dis(put)in counterbalUNs.
1 / 489425.981694385 = -300J+904S-301U-301N
1 / 489426 ~= -300J+904S-301U-301N
489426 = 2*3*7*43 * 271
1 / 489426 +300J-904S+301U ~= -301N
1/N ~= -301/(1/2/3/7/43/271+300J-904S+301U)
164.791315640071 = -301/(1/2/3/7/43/271+300J-904S+301U)
164.791315640078 = 1/N
-0.000000000004 = % error
Laskar converges to 36750.3379015986 not 36750 = 73500/2.
30031 primorial+1 has special property as noted above.
Suddenly 4*496 superstrings 1728+298-42 no. mystery in 1984. Left IT shelved right up UNtil note far above point-D to 4270 & 1584 from 4370.
Last spring the missing link was math taxonomy keyed nowhere near biology cataloguing standards to “solve a simpler problem” left right hearin’ “home” land D-vision.
US: Retune IT Deep O-Locked to Jo.vi.UN.axis
Dozens of comments I had prepared months ago were deleted following an abrupt change of course (~2 months ago). An excerpt of 1 was delayed rather than deleted.
30.4320075307947 = (835.546575435631)*(29.3625733662892) / (835.546575435631 – 29.3625733662892)
65.0170708690834 = slip(30.4320075307947,19.8650360864628)
708.556226479596 = slip(65.0170708690834,19.8650360864628/4)
This relates back to OB’s comments on the 2400 thread.
708 = 4*(47+59+71) = 12*59
–
“[…] speak openly about catering to the support of those “fed up” by state restrictions […] encouraged chants […] calling for the imprisonment of local officials who have instituted them.”
Exceedingly few jurisdictions have sensible, well-balanced pandemic leadership.
For abusive jurisdictions where extreme measures are taken (things we expect only in places under the control of The Communist Party) I agree in resolute solidarity with calls to swiftly and decisively remove from public office those savagely pushing psychological and financial terrorism against their own people.
It should be ensured that they — and all others in our society — are able to remain financially stable and adequately housed. Euthanasia should be made readily available hassle-free to those without the will to deal with strictly unbearable tyrants who are — for whatever contrived reason — to remain in power.
Lockdowns never occur in free countries, so a mark of liberation leading nations can pursue is swift alteration of their constitution.
–
I’m repeating the following to underscore that simple groups are tied perfectly to hexagonal numbers:
28=(19+37)/2
s(496-Φ(69)-φ(69))=s(496-69)=69=Φ(69)+φ(69)=(7+37)+(1+61-37)=1+7+61
=s(427)=s(7*61)=496-7*61=σ(427)-427=496-323-104=496-(196883-196560)-104
=111-42 where 111 is Lyons rep (see first 2 embedded links in next comment)
So-called “experts” could have simply pointed this out a dozen years ago.
Weather ignorance or deception: dark either way — and undermined trust.
Jan. KO Lie UN’s Group Representation
104=2*(8*111-836)=d(2,1/2,37)=d(2,1/2,s(196883-196560))
744=d(3,1/2,19)=d(3,1/2,43)=d(3,1/2,67)
28056 = d(3,1/2,37)
28=MOD(d(3,1/2,37),1333-3*111)/2=28=ROUND(d(3,1/2,37)/(1333-3*111),0)=s(28)
“what I saw that night was real and not just fantasy” — ire UN made dem
7920=5256+(836+496)+(1333-1)
7920=5256+24*111
1333=43*(MOD(1729,729)-MOD(1728,744))=43*31
271=MOD(1729,729)=1333-3*111-3^3^2=s(4370)-3*1333=4270-3*1333
240=MOD(1728,744)
163=496-3*111
φ=-2*SIN(2π*(σ(427)+836)/(Φ(836)+Φ(427)))
“monster group”? “baby monster”? What names could more effectively discourage and undermine public discussion of “simple sporadic groups”? Perhaps only “number of the beast” (suspiciously located exactly at the cross-roads of perfect superstring, smallest weird untouchable, Janko & Lyons).
The nomenclature chosen by mathematicians sure doesn’t make for a very palatable mainstream message.
I’ve become quite cynically suspicious that these names were deliberately chosen to “help” make public mention appear toxicly extreme mist. “don’t speak” no. doubt kind of thing to encourage just knowing about it privately for share ring with an “insider” group.
Whatever stupid or just plain inconvenient names the mathematicians want to call these things, they all fit together perfectly in a puzzle that isn’t even difficult.
Of course the crazy names do very strongly aid memory, as does the song “monsters in the paris sol” by queens of the stone age ….especially since 4 times perfect superstring number 496 = 1984. As they say in the song: “O[]well”.
We might as well decide even if only just for f(UN) that weave proof of a biased ant math group dismissing simple logic on the basis of attached names. Imagine a “Donald Trump Theorem”: “O well” then no. answer needed by dem work-around.
The Cross Roads Sov. Representation Theory
111=3*37
111=3*s(196883-196560)
Luck D-own: WHO’s at UN?
(836+496)/2=(1333-1)/2=2*3*111
Someone had fun naming all these things — satisfied their supervisor IC.
5256 = Φ(111)*φ(1333)
37=111/3=δ(1333)/2=s(196883-196560)
104=d(2,1/2,37)=d(2,1/2,111/3)=d(2,1/2,δ(1333)/2)=d(2,1/2,s(196883-196560))
163=104+59=111+52=2*111-59=47+71+104-59
111=(47+71+104)/2=59+104/2
1333=43*(2*71-111)
Δ(111) = 71
“Start Again”
“There is no. thing fair in this world.”
836 = 1333-497
497 = 1333-836
“There is no. thing safe in this world.”
2432 = 2*1216 = 4*608
“….and there’s no. thing sure in this world.”
496 = s(496) = s(652) = s(s(608))
8128 = s(8128)
1000 = s(s(1216)) = 1333 – 3*111
640 = φ(1216) = δ(1216)
320 = φ(608) = δ(608)
“…and there’s no. thing pure in this world:”
640320 = s(s(1216))*φ(1216)+φ(608) = 1000*640+320
640320 = s(s(1216))*δ(1216)+δ(608)
640320 = 69*(1152+8128)
1152 = δ(1728) = φ(1728) = Φ(2432) = Δ(2432) = 2*σ((3*5*7*11*13)/(3+5+7+11+13))
576 = Φ(1728) = Δ(1728) = Δ(1216) = Φ(1216) = 24^2 = σ(210) = σ(497) = σ(1333-836)
576 = σ(385) = σ((3*5*7*11*13)/(3+5+7+11+13))
385 = (3*5*7*11*13) / (3+5+7+11+13)
“Look for sum thing left.in this world. ” — Billy IDo[rwel]l
Green Monster “Free” Will eXpeRt Orw[oo]lover Eur. Rise
“Hey little sister, WHO is IT Eur. with?” — Billy I[woo]l
δ(2*Δ(Φ(59))*s(Φ(59))) = φ(2*Δ(Φ(59))*s(Φ(59))) = 8*(59^2-196883/59)
Φ(2*Δ(Φ(59))*s(Φ(59))) = Δ(2*Δ(Φ(59))*s(Φ(59))) = 4*(59^2-196883/59)
2*Δ(Φ(59))*s(Φ(59)) = 1728
2*δ(Φ(59))*s(Φ(59)) = 1984
Link 1
σ() = divisor sum
https://oeis.org/A000203
https://oeis.org/A000203/b000203.txt
s() = aliquot sum
https://oeis.org/A001065
https://oeis.org/A001065/b001065.txt
Link 2
Φ() = euler’s totient
https://oeis.org/A000010
https://oeis.org/A000010/b000010.txt
φ() = cototient
http://oeis.org/A051953
http://oeis.org/A051953/b051953.txt
notation overlap distinction:
golden ratio if no (argument’s in brackets)
Link 3
Δ(n) = Φ(n) – μ(n) = totient – möbius
http://oeis.org/A053139
http://oeis.org/A053139/b053139.txt
δ(n) = φ(n) + μ(n) = cototient + möbius
http://oeis.org/A228620
http://oeis.org/A228620/b228620.txt
Remember: 652 = 4*163
This stuff is stunning. It’s such a pleasure to work on it and see all the connections.
TheO[rwell]Airs:IDweight
What curry US IT?
2*s(s(Φ(59)))*s(Φ(59)) = 1984 = 4*496 = 8/3*744
D:phi calltosea witchpressOdauntiewon ?
2*Δ(Φ(59))*s(Φ(59)) = 1728 = 1984-104-152 = 1984-298+42
e con nom IC pope EU lost: luck “D-own!!” with Joe win sob miss UN to comm.UN.us-part e:
2*δ(Φ(59))*s(Φ(59)) = 1984
“I can still recall the time: wait!..TRIED to breakONthrew to THEO[]airsID” — The DOORS
Press O “Don’t!”
Another “perfect” name they came up with was “pariah”.
496 = s ( 652 ) = s( s ( 608 ) ) = s(496)
496 = s(4*163) = s(s(2432/4)) = s(496)
I’m convinced “elite” “leaders” plan to give western “working class populists” the luck D-own D-ea[r]th bull O for not be[]ing quick fall O-in a “tie won” plan. Just.in took “aha!” stage hop.in IT’s just UNoff dawns a port forge[]O2 sea just in.history’s trait show door.
“Hey Joe, ware EU go!in with that … .. …. …. ?” — j.handrocks
The DOORSequence
“the gate is strait
deep and wide”
1, 2, 3, 7, 11, 19, 43, 67, 163
42 = 1*2*3*7 = 7# / 5
“found.D-UN.island.in.Eur.arms
count.try:in.Eur.rise
arms that ch[a]in US
e^yes that Lie” — the doors
489426/7/3/2/1=43*271
Φ(7#)/2=1+2+3+7+11=24
43-24=19
43+24=67
Sylvester coined the term “totient”.
163=271-108
162 = Φ(163) = Φ(162) + φ(162) = 54 + 108 = φ(7#) = 7#-Φ(7#)
(19+43+67+163)/2=146
146-42=104
163-104=59; 59-12=47; 59+12=71
average(71mod24,59mod24,47mod24)=average(23,11,23)=19=43-24=67-48=67-Φ(7#)
“EVorrery body loves my baby”
“the number 24 is the only integer bigger than 1 with this property”
67+43-19=91 shh!..
1806 is no longer a mystery. I introduced the theme on the last XR thread. One of the most important comments I’ve ever submitted never appeared. That led to a decision to sharply alter course, similar to when I began my strict boycott of WUWT & CE about 4 years ago.
As with the solar terrestrial weave (cyclic volatility of semi-annual mid-latitude westerly circulation at Schwabe-timescale), 1806 is conclusive. Monstrous moonshine ties Farey sequences and Ford circles through Egyptian fractions to Heegner numbers. Sylvester’s sequence bounds solar system order. (The final puzzle piece was the 2-page mathematical proof — somewhere down the link-trail I gave over here.)
=
Thus we are asking for integers which make the expression
1 − 1/p − 1/q − 1/r
strictly positive and as small as possible. This minimal value is 1/42, and
1 − 1/2 − 1/3 − 1/7 = 1/42
=
The first 4 Heegner numbers:
1, 2, 3, 7 — and their reciprocals:
1, 1/2, 1/3, 1/7
Explore some properties:
1/(1-1/2-1/3-1/7)
1*2*3*7
Note well:
1+2+3+7+11
average(19,43,67,163)
73 mod 24
So the Heegner numbers point directly to the lowest prime congruent to 1 mod 24.
CT(ET(163))=2*ET(ET(163))=2*(11+43)
271=163+CT(ET(163))
The first 4 primary pseudoprimes are constantly offset from Sylvester’s sequence.
(CT=cototient; ET=Euler’s totient)
Once you start looking at how all of the pieces fit together it becomes really simple.
There are plenty more examples beyond these:
52=323-271=323-163-108
496=271+2*177-129
496=323-52+2*177-129
496=196883-196560-52+2*(47+59+71)-(19+43+67)
496=271+129+96
177=(47+59+71)
129=(19+43+67)
271=323-52=163+108=298-27
323=271+52=196883-196560
196883=(59-1728^(1/3))*(59)*(59+1728^(1/3))=47*59*71=59*(59^2-1728^(2/3))
884736=2*(1984-1728)*1728 (That’s a sample from a stack that IDs everything from solar equatorial rotation through Chandler, QBO, perigy, evection, and whatever else you want to name.)
194=323-129
323=194+129
129=323-194
48=177-129
225=2*(47+59+71)-(19+43+67)=2*177-129=354-129
225=48+(47+59+71)
225=96+(19+43+67)
48=225-177=225-(47+59+71)
96=225-129=225-(19+43+67)
62=225-163
208=177+31
194=225-31
225=163+43+19
31=(225-163)/2=208-177=225-194 = average(19,43,67,163) mod 42 = 73 mod 42
42=1/(1-1/2-1/3-1/7)=1*2*3*7
298=(1984-1728)+42=(152+104)+42=225+73
s(298)=225-73=152
Whatever’s Mayan
“The last free daze:
The reign was UN. Stop a bull.” — Tom Petty
1 = 1 mod 24
2 = 2 mod 24
3 = 3 mod 24
7 = 7 mod 24
11 = 11 mod 24
The 5 lowest Heegner numbers sum to 24.
19 = 19 mod 24
19 = 43 mod 24
19 = 67 mod 24
19 = 163 mod 24
The 4 highest Heegner numbers average 73.
1 = 73 mod 24
73 is:
the first prime above top-level M prime 71.
the smallest prime congruent to 1 mod 24.
Remarkably none of the introductory materials I encountered on Heegner numbers pointed this out.
“Workin’ on a mystery — goin’ wherever it leads
I’m pickin’ up whatever’s Mayan” — Tom Petty
Review
Number of fractions in Farey series of order n
Compare with: Sum of totient function
“James J. Sylvester, On the number of fractions contained in any Farey series of which the limiting number is given […] (1883)”
|F_1|=2
|F_2|=3
|F_4|=7
|F_11|=43
|F_29|=271
1806=|F_1|*|F_2|*|F_4|*|F_11|=2*3*7*43
489426=|F_1|*|F_2|*|F_4|*|F_11|*|F_29|=2*3*7*43*271
Recall that we’ve discussed how this shows up precisely in Jovian order.
A little more tricky to fathom, but should be noted:
3=|F_2|
29=|F_9|=|F_3^2|=|F_|F_2|^2|
271=|F_29|=|F_|F_9||=|F_|F_3^2||=|F_|F_|F_2|^2||
Orientation
You can derive euler’s totient from farey.
You can derive mobius from farey.
Thus you can derive e from farey (recall Schneider’s classic).
There’s a cute, simple trick for generating farey sequences using floor functions. It’s among the most delightful little piece of magic I’ve ever encountered in mathematics. See equation 3:
=
If a/b and c/d are neighbors in a Farey sequence of order N, the next term in the same sequence is given by the following expression:
⌊(N+b)/d⌋*c – a [numerator]
⌊(N+b)/d⌋*d – b [denominator]
[equation] (3)
where ⌊x⌋ is the floor function. Therefore, the Farey sequence of order N can be generated very efficiently starting from the elements a/b = 0/1 and c/d = 1/N.
=
Typo: “primary pseudoprimes” should read “primary pseudoperfect numbers”
Gathering some links all in one place for convenience:
1, 2, 3, 7, 11, 19, 43, 67, 163 — Heegner
2, 3, 7, 43, 1807, … — Sylvester
2, 6, 42, 1806, … — primary pseudoperfect
1, 2, 6, 42, 1806 — intersection
1806 — pinpoint
Here’s a noteworthy sequence that’s not in the OEIS — sums are from 0 to N :
Σ|F_0|=1
Σ|F_1|=3
Σ|F_2|=6
Σ|F_3|=11
Σ|F_4|=18
Σ|F_5|=29
Σ|F_6|=42
Σ|F_7|=61
Σ|F_8|=84
A few other noteworthy values:
Σ|F_10|=146
Σ|F_14|=360
Σ|F_15|=433
Review
Why phi?
Ford Circles Sines Pythagorean Triangles + supplementary Ford Pythagorean
Ford Circles Fibonacci Lucas Phi Root 5
The math affords us many avenues for equivalent expresssion.
Oldbrew may view Sylvester’s 2, 3, 7, 43, 1807 Sequence in this light:
2*2-1 = 3
2*3-1 = 5
2*7-1 = 13
2*43-1 = 85
2*1807-1 = 3613
Pythagorean spiral: a(n-1), a(n)-1 and a(n) are sides of a right triangle. 3, 5, 13, 85, 3613, 6526885,
mods: right triangle spiral translation for OB is stuck in the filter
IT Ski Rev EU: “Win September” 1984
Joe thank cue: Constitution of 1806 left in file truth tour press “I don’t tell” [B]lock-D from 2020 piece search. West turn-(D Clock)-back 36 years.
Monster US Moon Ch!nes Won and UN[all]lie Pure[D]fect L!nkin “too Heegner” PR Joe Act
Let us order sum partition of supersingular PR rhymes:
24=2+5+17 = 71 – 47 = 67 – 43 = 43 – 19
47=3+13+31
59=7+11+41
71=19+23+29
177=47+59+71 = 3*59
378 = 24+47+59+71+177 = 78 + 111 + 189
78=2+3+7+19+47
111=5+13+11+23+59 = 189 – 78 = 3*37 = 3*s(196883-196560) ————– Lie UNs Group
189=17+31+41+29+71
Sporadic simple group primes include only 1 perfect 496=s(496) D-visor:
31 = 496/16 = ( 19 + 43 ) / 2
378=2+3+5+7+11+13+17+19+23+29 +31 +41+47+59+71=1+2+3+7+11+2*19+2*43+67+163
316=2+3+5+7+11+13+17+19+23+29 -31 +41+47+59+71=1+2+3+7+11+1*19+1*43+67+163
129=2+3+5+7+11+13+17+19+23+29 = 19 + 43 + 67 = 2*31 + 67 = 3*43
201=2+3+5+7+11+13+17+19+23+29+31+41 = 129 + 3*24 = 3*67
3^2 = 129 mod 24 = 201 mod 24 = 177 mod 24
3 = 129/43 = 201/67 = 177/59 = 111/s(196883-196560)
s(129) = 47
s(201) = 71
496=378+47+71=378+2*59
D-liberate Am. BIG glue IT: Donair weather profoundly simple or(well)s imply PR(O)f(O)UN-D()Near-tune herd “the voice of God”.
111=Φ(323)-(47+59+71)=Φ(196883-196560)-(47+59+71)
Ly : 163=2+3+5+7+11+31+37+67
“The 15 supersingular primes: primes dividing order of Monster simple group.”
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71
Put them in the 3 by 5 block (as I did just above). Add rows. Add columns. Clue in.
2 5 17
3 13 31
7 11 41
19 23 29
47 59 71
Count Sol Clear Ants Or Well
Luck D-own human writes “eXpeRt” WHO’s at UN nos. ware seek “cure IT” counts ill f(IT)sin.
177 = 47+59+71 = 3*59
y = (177-((19+43+67)-s(196883-196560))/2-59)^5 – (((19+43+67)-s(196883-196560))/2)^5
x = 19^5 + 43^5 + 67^5
37 = s(196883-196560)
Monster US Jan. KO Lie UNs group Bei. B:
47 = s(19+43+67) = (y-x)^(1/5) = s(3*s(4370/5/2))
71 = s(67+67+67) = s(s(Φ(163)))
“ON my blew PR INT (IT SIM f**** O!N) UK” — LG
“breakfast ware the news is red“ — the doors
177=288-111=47+59+71=288-(189-78)
Φ(323) = 288
496=378+177-59
496=378+288-111-59
496=378+Φ(323)-111-59
496=378+Φ(Φ(1333))-111-59
496=378+Φ(196883-196560)-111-59
Sea Lie Way?
BRI be. $0[]well!
Sporadic simple “pariah groups” J4 & Ly bridge perfectly (i.e. s(496)=496) in monster US moon shh! UN from “too super” sing allure “tee hee” he ignores in afar age review of factorized order call ’em.
6, 28, & 496 are Perfect
Note how they piece together with the top Heegner (163) prime (wit chisalls O some of Lie UN PR rhymes), the top 3 monster group (M) primes (47, 59, 71), and the “minimal faithful representation” of Ly & J4 (111 & 1333).
s(608) = 652 = s(4*152) = s(2432/4)
s(652) = 496 = s(4*163)
s(496) = 496
1260=608+652=Φ(1333)
1260=2432/4+4*163
1260=4*152+4*163
152=118+28+6=2*59+28+6=(47+71)+28+6=(177-59)+28+6=(288-111-59)+28+6
=(Φ(323)-111-59)+28+6=(Φ(1260)-111-59)+28+6=(Φ(Φ(1333))-111-59)+28+6
Alternate aspects partially overlap puzzle-explore “Or” awareness US eerie to bridge mainstream gaps.
Again: The role of perfect numbers in ordering sporadic groups simply appears, overlook-D$buy$Convention.
1333=1260+73
1333=652+608+73
1333=4*(163+(Φ(Φ(1333))-111-59)+28+6)+average(163,67,43,19)
Recall that
average(163,67,43,19) mod (1+2+3+7+11) = 73 mod 24
is the lowest prime congruent to 1 mod 24.
1333 = 1332+1 make chron nom IC mist eerie is no longer “what cure US$” buy bore US slink UN PR Joe Act:
2432=4*(1333-4*163-73)=4*608=4*(1333-4*163-average(163,67,43,19))
608=1333-4*163-73=1333-4*163-average(163,67,43,19)
Remember WHO’s at UN, as the throat of freedom is gnashed buy big te[a]ch media’s “demO CR at IC” transform m[a]ze UN:
average(836,496) = (1333-1)/2 = 6 lyons (“minimal faithful representation”)
Homeless “home” land leave $0[]well the freeze $in luck D-own.
By “just 1” constitution of 1806, US mull a tory corrects UN method.
“In God We Trust”
Obvious to alert readers from the last comment, but pointing it out explicitly:
φ(1333) = 73
Throwing this a111literation in here “just” for puzzler fun:
1333=1111+φ(1111)+φ(1111)=1111+111+111=φ(3333)
“Hey lit a111 sister what have EU D-UN? WHO’s the only 1…?” (B111y11do1)
Forest-level stuff OBviUS 2 alert readers “pickin’ up whatever’$Mayan” (Tom Petty) :
Lucas no. 76 = 19 mod 24 + 43 mod 24 + 67 mod 24 + 163 mod 24 = 19+19+19+19 = 152/2 = 608/8 = 2432/32
CRACK UN
“Hit crews control…” — Tom Petty
“n = 3: {3, 4, 5; 6}”
27 = 3^3
64 = 4^3
125 = 5^3
216 = 27+64+125 = ET(average(836,496))
216 = 6^3 = ET((1333-1)/2)
108=216/2=CT(162)=CT(ET(163))
54=108/2=ET(162)=ET(ET(163))
27=54/2
“work kin on a mystery …that neverwood comm. tommy” — To:MP(ET)(TY)
271=163+108=298-27
1 = 1^2
4 = 2^2
9 = 3^2
16 = 4^2
25 = 5^2
55 = 1+4+9+16+25
784 = 28^2
729 = 27^2
55=784-729
TP “go win wherever IT leads:”
271=216+55
Every Christmas the family “put together a puzzle”.
Remember the George Polya method:
Solve a simpler “problem”.
s(4*163) = 70^2 / Σ(Heegner numbers mod 24) + 149 + 298 = 496 = s(496) = 1 / 4 * 1984
70^2 = 1^2 + 2^2 + 3^2 + … + 22^2 + 23^2 + 24^2
100 = 1+2+3+7+11+19+19+19+19
D-no. Hints $O “well” We Can’t a Ford Circles. IT’s “Not. the Perfect” Christmas gift for red nos. JSUN.
“70p is weird for all primes p ≥ 149”
Jan. YOU wary “sol ID D-air IT” $savagely threatens DARK, COLD WINTER nightmares FAR, FAR BEYOND THE WORST of George Orwell’s WORST luck D-own fears. I don’t think people even realize what Can. happen if IT (inverted totalitarianism) keeps pushing $0 savagely, but I do hope they volunteer to take a very, very long walk alone and solve the traditional family Christmas puzzles online for one “sporadic and exceptional” Christmas, so we don’t find “Joe’s Globe HELL KNEW YEAR Sin 1984“.
In last comment this was opportunistic pivot (begging Alberta$0[]we’ll not give Joe ammunition) :
“s(4*163) = 70^2 / Σ(Heegner numbers mod 24) + 149 + 298 = 496 = s(496) = 1 / 4 * 1984”
Above that exactly matches earlier notes — generalized pythagorean means of equivalent expression, including “the zipper”. I explore wildly and sometimes later note sharp refinements. Junction 162 got precisely refined after a wild introduction. Probably few noticed after dismissing first impressions that floored expectations.
HarmonIC mean lie U+N $ 0 [ ] well:
111=Φ(323)-(47+59+71)=Φ(196883-196560)-(47+59+71)
PERFECT Jupiter-Saturn Framing — Part I
First, we frame Jupiter-Saturn for exploration using the generalized Bollinger (1952) method. This part’s review.
Beat Period
19.8650360864628 = (29.4474984673838)*(11.8626151546089) / (29.4474984673838 – 11.8626151546089)
9.93251804323141 = 19.8650360864628 / 2
4.9662590216157 = 19.8650360864628 / 4
Axial Period
8.4561457463176 = (29.4474984673838)*(11.8626151546089) / (29.4474984673838 + 11.8626151546089)
4.2280728731588 = 8.4561457463176 / 2
2.1140364365794 = 8.4561457463176 / 4
Harmonic Mean
16.9122914926352 = (29.4474984673838)*(11.8626151546089)/((29.4474984673838+11.8626151546089)/2)
Orientation
61.0464822565173 = slip(29.4474984673838,11.8626151546089)
835.546575435631 = slip(61.0464822565173,19.8650360864628)
Note: 836 is the smallest untouchable weird number.
Split Harmonic Mean Orientation
right side:
17.2616851219298 = (835.546575435631)*(16.9122914926352) / (835.546575435631 – 16.9122914926352)
8.63084256096492 = 17.2616851219298 / 2
4.31542128048246 = 17.2616851219298 / 4
left side:
16.5767613988929 = (835.546575435631)*(16.9122914926352) / (835.546575435631 + 16.9122914926352)
8.28838069944647 = 16.5767613988929 / 2
4.14419034972324 = 16.5767613988929 / 4
PERFECT Jupiter-Saturn Framing — Part II
Next, we derive base-level slip cycles:
right:
131.716392653884 = slip(19.8650360864628,17.2616851219298)
65.8581963269421 = slip(19.8650360864628,8.63084256096492)
50.0715412599931 = slip(19.8650360864628,4.31542128048246)
left:
100.143082519986 = slip(19.8650360864628,16.5767613988929)
50.0715412599931 = slip(19.8650360864628,8.28838069944647)
96.1829470900285 = slip(19.8650360864628,4.14419034972324)
From the base we review familiar combinations:
104.443321929454 = slip(50.0715412599931,19.8650360864628)
178.266850068779 = slip(65.8581963269421,9.93251804323141)
208.886643858908 = slip(65.8581963269421,19.8650360864628)
356.533700137559 = slip(131.716392653884,19.8650360864628)
504.413226524327 = slip(131.716392653884,9.93251804323141)
504.413226524329 = slip(131.716392653884,104.443321929454)
504.413226524326 = slip(178.266850068779,131.716392653884)
504.413226524325 = slip(208.886643858908,131.716392653884)
PERFECT Jupiter-Saturn Framing — Part III
Finally, we focus on the PERFECT connection to Heegner numbers:
304.031799474187 = slip(96.1829470900285,9.93251804323141)
608.063598948353 = slip(50.0715412599931,4.9662590216157)
608.063598948353 = slip(100.143082519986,4.9662590216157)
608.063598948375 = slip(96.1829470900285,19.8650360864628)
608.06359894839 = slip(178.266850068779,65.8581963269421)
608.063598948387 = slip(178.266850068779,104.443321929454)
1216.12719789671 = slip(50.0715412599931,9.93251804323141)
1216.12719789671 = slip(100.143082519986,9.93251804323141)
1216.12719789674 = slip(96.1829470900285,50.0715412599931)
1216.12719789676 = slip(104.443321929454,50.0715412599931)
1216.12719789675 = slip(104.443321929454,96.1829470900285)
1216.12719789679 = slip(178.266850068779,96.1829470900285)
1216.1271978968 = slip(208.886643858908,50.0715412599931)
1216.12719789679 = slip(208.886643858908,65.8581963269421)
1216.12719789678 = slip(208.886643858908,96.1829470900285)
1216.12719789678 = slip(208.886643858908,178.266850068779)
1216.12719789679 = slip(356.533700137559,96.1829470900285)
1216.12719789678 = slip(356.533700137559,131.716392653884)
1216.12719789678 = slip(356.533700137559,208.886643858908)
1216.12719789679 = slip(504.413226524325,208.886643858908)
1216.12719789679 = slip(504.413226524325,356.533700137559)
2432.25439579341 = slip(100.143082519986,19.8650360864628)
2432.25439579349 = slip(100.143082519986,96.1829470900285)
2432.25439579353 = slip(104.443321929454,100.143082519986)
2432.25439579362 = slip(208.886643858908,100.143082519986)
The aliquot sequence beginning at 608 ends at perfect number 496.
s(608) = 652
s(652) = 496
s(496) = 496 = s(652) = s(s(608))
s(608)=652=32+16+8+4+2+1+304+152+76+38+19
19 is the only odd prime divisor of 608.
19 = x mod 24 for x = 19, 43, 67, 163 ——- the top 4 Heegner numbers
s(652)=496=4+2+1+326+163
The only odd prime divisor of 652 is 163 —— the TOP Heegner number
F2 or B : 178=2+3+5+7+11+13+17+19+23+31+47
Comm. PR UN D-Comm. red?
No. Comm. Meant 163178
496=s(496)
496=248+124+62+31+(16+8+4+2+1)
496=(8+4+2+1+(1))*31 —— Remember this number: 31.
Sum of prime divisors:
652: 165 (22 Taxis Bunanajam)
608: 21=42/2=84/4
496: 33=66/2=132/4
496=(163+2)*3+1
652=(19+2)*31+1
496=(31+2)*15+1
PERFECT Jupiter-Saturn Framing — Encore
323=196883-196560
292=323-31=19+43+67+163
354=323+31=2*(47+59+71)
323 = 19+43+67+163 + 31
323 = 2 * (47+59+71) – 31
42 = 73 – 31
104 = 73 + 31
“Sporadic and Exceptional”
s(496) = 496 = 16+8+4+2+1 + 248+124+62+31
31 is the only odd prime divisor of perfect number 496.
average(19,43,67,163) mod (1+2+3+7+11) = 73 mod 24 = 1
194
Ly : 163 = 2+3+5+7+11+31+37+67
F1 or M : 378 = 2+3+5+7+11+13+17+19+23+29 +31 +41+47+59+71
F2 or B : 178 = 2+3+5+7+11+13+17+19+23+31+47 —- recall 4270=s(4370)
Only 1 of the odd supersingular primes (and more generally the odd sporadic simple group primes) is a divisor of perfect no. 496: 31.
316 = 2+3+5+7+11+13+17+19+23+29 -31 +41+47+59+71
Compare with M sum above to spot the bold ( + vs. – ) difference.
Compare with Heegner sum:
316 = 1+2+3+7+11+19+43+67+163
Note well the lowest prime congruent to 1 mod 24:
average(19,43,67,163) mod (1+2+3+7+11) = 73 mod 24 = 1
“Sporadic and Exceptional” … and perfectly D-visible:
194 = 163 + 31 ———————————- superstring answers to McKey miss s(496)tory
132 = 163 – 31 = Corbyn lookback period = 2 * 66
100 = sum of Heegner numbers mod 24 = (2+3+7+19+19)+(1+11+19+19) = 50+50
104 = 73 + 31 = 4 * 26
42 = 73 – 31
Scale to squarely devise some supersupersingular monster group differing perfectly from Mayan level 5 calendar:
26 = divisor^2 sum for 5
130 = 378 – 248 = divisor^2 sum for 10
260 = 2*378 – 496 = divisor^2 sum for 15
Perfect number 28 = s(28) frames 56 faces, 84 edges, and 24 vertices.
harmonic mean (28,84) = 42 = 66 – 24 = beat period of (28,84)
axial period of (56,42) = 24 = 66 – 42 — Table 2
100
1 = 1 mod 24
2 = 2 mod 24
3 = 3 mod 24
7 = 7 mod 24
11 = 11 mod 24
19 = 19 mod 24
19 = 43 mod 24
19 = 67 mod 24
19 = 163 mod 24
100 = (1+2+3+7+11)+(19+19+19+19) = average(96,104)
96 = 163-67 = 104+59-67 = 37+59 = s(323)+59 = s(196883-196560)+59
52 = 76-24 = (19+19+19+19)-(1+2+3+7+11) = 104 / 2
100-52 = 2*(1+2+3+7+11) = 48 = 2 * 24 = 96 / 2
100 = 4370-4270
271=196883-196560-52=323-52=496-194-31
1=ROUND(19/24,0)
2=ROUND(43/24,0)
3=ROUND(67/24,0)
7=ROUND(163/24,0)
42=ROUND(19/24,0)*ROUND(43/24,0)*ROUND(67/24,0)*ROUND(163/24,0)=1806/43
=489426/271/43
11 may look left out …but IT (as in inverted totalitarianism) has a place in this:
10=11-1
9=11-2
8=11-3
4=11-7
$0[]well D-UN McKay!
They sum to the only odd prime divisor of s(496)=496 : average(19,43) = 496/16 = 31
Noel that 11 makes a difference notable in Heegner numbers mod 24.
4*(19-11)=4*8=32
992=31*32=2*496 ——————————————– superstring 61 tip $5: “call ’em 11!”
31=(11-MOD(1,24))+(11-MOD(2,24))+(11-MOD(3,24))+(11-MOD(7,24))
32=(MOD(19,24)-11)+(MOD(43,24)-11)+(MOD(67,24)-11)+(MOD(163,24)-11)
31=44-MOD(1,24)-MOD(2,24)-MOD(3,24)-MOD(7,24)
32=MOD(19,24)+MOD(43,24)+MOD(67,24)+MOD(163,24)-44
156=992-836=652-496=132+24=132+(31-7)=132+(489-465) (see below)
=100+2*28=(589-489)+(63-7) ——- obvious with large & small divisor partitions below memorized
s(496)
=496=465+31
=248+124+62+31
+1+2+4+8+16
s(608)
=652=589+63
=304+152+76+38+19
+1+2+4+8+16+32
s(652)
=496=489+7
=326+163
+1+2+4
Lots of things simply fit a perfect frame.
Review notes on generalized pythagorean theorem above:
216 = 24*(FLOOR(19/24,1)+FLOOR(43/24,1)+FLOOR(67/24,1)+FLOOR(163/24,1))
We’ll come back to this after reviewing almost-integer generation (the method I formulated to mimic Ramanujan’s “tricks”).
Heegner McKey’s Free Will
God knows we can learn perfect fits weather left or right:
496=(196883-196560)+2*(47+59+71)-(19+43+67)-104/2
323=(196883-196560)
37=s(196883-196560)
323 = d(2,1/3,59) = R(2,1/3,59) – R(1,1/3,59)
104 = d(2,1/2,58) = R(2,1/2,58) – R(1,1/2,58)
104 = d(2,1/2,37) = R(1,1/2,37) – R(2,1/2,37)
47 = d(5,1/5,54) = R(1,1/5,54) – R(5,1/5,54)
71 = d(3,1/5,54) = R(1,1/5,54) – R(3,1/5,54) = d(2,1/2,9) = R(1,1/2,9) – R(2,1/2,9)
225 = d(4,1/5,54) = R(4,1/5,54) – R(1,1/5,54) = d(3,1/2,9) = R(1,1/2,9) – R(3,1/2,9)
54+108=φ(162)+Φ(162)=Φ(163)=162
225=2*(47+59+71)-(19+43+67)=Φ(Φ(323))+(19+43+67)=194+31=15^2=496-271
59=average(47,71)
Split the 9 Heegner numbers into 2 groups and simply OBserve.
73=average(19,43,67,163) = divisor^3 sum for 4 = 4^3+2^3+1^3 = 64+8+1
24=1+2+3+7+11
73 mod 24 = 1 ——- 73 is the lowest prime congruent to 1 mod 24
1 = average(163,67,43,19) mod (11+7+3+2+1)
Remember the paper “Sporadic and Exceptional” was written by McKay & He.
152=225-73
152 = d(2,1/2,25) = R(2,1/2,25) – R(1,1/2,25)
194=152+42
298=225+73=104+152+42=104+194
323=298+25=1984-1728+42
111=Φ(323)-(47+59+71)
1333 = 32*( x mod (11+7+3+2+1) ) + 4*163 + average(163,67,43,19) where x = 163,67,43,19
1333=AVERAGE(19,43)*AVERAGE(19,67)
1332=divisor^3 sum for 11=496+836=12*111
31=AVERAGE(19,43)=2^5-1
992 = σ(25)*σ(σ(25)) = 31*32 = 2*496 = 2*s(496) —————– see $5 tip in last comment
216 & 55
271=163+108=163+CT(162)=163+CT(ET(163))=489426/43/7/3/2=489426/1806
21 = sum of prime divisors of 608 = 19+2
292 = 271+21
292 = 163 + 67 + 43 + 19
76 =163 mod (11+7+3+2+1) + 67 mod (11+7+3+2+1) + 43 mod (11+7+3+2+1) + 19 mod (11+7+3+2+1)
76 = 55+21
55=378-323 = sum of supersingular primes minus s(196883-196560)
55=1^2+2^2+3^2+4^2+5^2
55=28^2-27^2
55=AVERAGE(43,67)
323=196883-196560=378-55
216=292-76
216=271-55
216=3^3+4^3+5^3
216=6^3
216=378-162=378-ET(163)
ET(163)=162=378-216=4*129-2*177=2*(2*(19+43+67)-(47+59+71))
216 = 316 – 100 = sum of heegner minus sum of each heegner number mod 24
216 = 24*(FLOOR(19/24,1)+FLOOR(43/24,1)+FLOOR(67/24,1)+FLOOR(163/24,1))
378=316+31+31=248+σ_2(10)=248+5*σ_2(5)=(496+σ_2(15))/2=(496+10*σ_2(5))/2
—————————————————————————————————- Mayan calender
144=163-19
144=12^2
144=59^2-196883/59
0=59^2-196883/59-163+19
177=59^2-196883/59+163-19-111
111=59^2-196883/59+163-19-(47+59+71)
111=59^2-196883/59+(163-19)-(47+59+71)
111=59^2-196883/59+(163-163mod24)-(47+59+71)
67=(47+59+71)-(19+43+67)+19
59=(47+59+71)-(19+43+67)+11
67=(47+59+71)-(19+43+67)+67mod24
59=(47+59+71)-(19+43+67)+59mod24
260 = σ_2(15) = 15^2 +5^2+ 3^2 +1^2 = 225 +25+ 9 +1 = 225+35
130 = σ_2(10) = 10^2 +5^2+ 2^2 +1^2 = 100 +25+ 4 +1 = 129+1
= 5^3 + 5 = 125 + 5 (225-100) + (9-4)
Something I suspect few would realize:
The perpendicular sum 125 turns up more times than any other (1728/2) while scrambling the 3 components of each of 24, 47, 59, 71, & 177 in 5*3 blocks of the 15 supersingular primes.
I suggest Mayan sages knew what Norton calls “the voice of God” and the connection to Heegner numbers. They wouldn’t need computers. As you can see the math is simple. There’s just a lot of it.
390=260+130
390-6^2=354=2*177
225=354-129
177=47+59+71
129=19+43+67
Re video of N Scafetta posted on other thread (link to video https://www.youtube.com/watch?v=bW5-h9wn3OQ )
Interesting: at 16:23, mention of the 60 yr and 20 yr cycles. Kepler trigon?; the latter possibly moon cycle.
But more interesting at 44:49 see displayed on board the words ‘983 yr cycle’. The appellation of millennial cycle is misleading; it is specifically the Eddy cycle. Over a period of 8000 yrs that cycle correlates nicely (more like ‘in an ugly way’) with great historical changes.
He Ignore Numbers Bro
The solar cycle length thread (a worthwhile diversion but with significant cost) stole time available for clarifying Heegner connections.
DC-ID-ed. to post CRude math by today with out organizing to ease digestion.
We’re left rightly imagine in clear simple connect shh! UN between Heegner numbers and simple sporadic groups as a secret of what curry US sly miss story US trades.
Better west turn math education up exponentia11y without delay to match the comprehensively superior Chinese math education system. D-C’s UNs ABout west turn luck D-own PUBLIC math education were left up to those hood (WHO’s at UN?) $0[]well sabotage.
In private we know “the cause” of west stern backlash ON populism is deeply rooted in poor math education that D-evil ops eXpeRt deepen D-ants-C.
The Owl on the Signpost
oldmanK wrote Dec. 21, 2020 “mention of the 60 yr and 20 yr cycles. Kepler trigon?”
My yen call UN door well! tee hee hee he ignore bro
Some say important communication has to be repeated:
Only 1 of the odd supersingular primes (and more generally the odd sporadic simple group primes) is a divisor of perfect no. 496: 31.
table 2 — p.9
“spin-offs” of 20 & 60
Seasons Best
“McKey’s Perfect” Sol’s Test
small list odd prime divsor well chain sov. s(496) = 496 = s(652) = s(s(608)) sci11UNs
50=31+19=194-144
144=163-19
194=163+31
recall D-for UN sov. squares
59*(59-12)*(59+12)
CR is mess $0 merry:
Found door well!
Perfect Mayan Supersingle Days =
260 = sum of supersingular primes each mod 59
= 248+12 = 496/2+(71-59) = (496+71-47)/2 = 2*(59+71) = 2*130
This keeps getting easier every step of the way.
The easily remembered symbols are a key — a key from which to build other things which are less easy to remember.
The thought processes about how to organize for reliable memory were presumably different without computers (duh!)
“Dough!” more my yen$SIM Sun
super sing yule lure sum 378 plus or minus (59+average(47,71))
sure lock average(260,496) (my UN,perfect) SIM MET try
oldmanK wrote “see displayed on board the words ‘983 yr cycle’. The appellation of millennial cycle is misleading”
980 & 1470 are a source of ill-founded mainstream hubris. Difficult communication is on the horizon. That is all I can say for now.
PV says “980 & 1470 are a source of ill-founded mainstream hubris.”
Pls allow me to point to something ‘definite’. Pls look here: https://melitamegalithic.wordpress.com/2020/05/31/searching-evidence-keplers-trigons-and-events-in-the-holocene-2/
( or at that site, the posts: Searching Evidence -2; Searching Evidence -3; Searching Evidence – 4: Prehistoric Mass Burials. )
Do note that the 980yr Eddy cycle, from 6150bce to ~1700ce appears to have produced some effect on the Earth, without missing a step. Specifically at the roots. The source of the Eddy curve was from https://judithcurry.com/2018/06/28/nature-unbound-ix-21st-century-climate-change/ fig 122 The dates were not fitted to the Eddy curve, they just fell in place; had already been established some years before.
The many number sequences above are to me somewhat alien, though I think I perceive, perhaps mistakingly, resonance points. What is the 980yr period? The response date is never so accurate. The strain release or fracture point of a non homogeneous body like earth (or a metal alloy) is never precise. The failure point can be early or late from a driving force that also peaks cyclically. Or a changing driving frequency on an object with a more stable resonant response? Or ???? (multiple forcing frequencies of varying power, acting on a body with multiple resonant points ??).
Whatever, the evidence for the response is there; clear; in several-to-many unrelated proxies. I do not think one should lose sight of that fact.
oldmanK,
I have isolated the unification bridge. Standby.
PV thank you. Take your time, and make the best of the coming days. Whatever, stay safe, and peace to you and all the rest here.
Seasons Best Tabulation
Seasons Best Merger: 1470 & 2400
4900 = 70^2 = 1^2 + 2^2 + 3^2 + … + 22^2 + 23^2 + 24^2
Recall:
1. the 2400 thread.
2. two 1470 threads.
3. U’s at 1/2 while others whole (as in whole number) with Laskar’s harmonic mean tuning.
2940 = (1470)*(980) / (1470 – 980)
993.243243243243 = (73500)*(980) / (73500 – 980)
1185.48387096774 = (1470)*(993.243243243243)/((1470+993.243243243243)/2)
1986.48648648649 = (2940)*(1185.48387096774) / (2940 – 1185.48387096774)
844.827586206896 = (2940)*(1185.48387096774) / (2940 + 1185.48387096774)
1689.65517241379 = (2940)*(1185.48387096774)/((2940+1185.48387096774)/2)
Divide those by 100 and study column 1 slip cycles comparatively.
Rudolph: “That’s the crude intro …”
1470 = (1470)*(735) / (1470 – 735)
490 = (1470)*(735) / (1470 + 735)
980 = (1470)*(735)/((1470+735)/2)
980 = (73500)*(993.243243243243) / (73500 + 993.243243243243)
“… to ‘Santa’s quick’ red nos. informal fog.”
Seasons Best Controversy
Have no. con tact.
Give no. Am. UN IT shh!own.
God nos. IT: on “day won We’11” sea dawns 19th “hindsight is 1984”.
0: Original (Seidelmann 1992)
2432.25439579341
1: UNstable CRude Est Worldview (73500)
1469.99999999966
2: crude find tuning 73500/4
2450.00000000031
11.8624919302776 = (18375)*(11.8548387096774) / (18375 – 11.8548387096774)
29.4471153846154 = (18375)*(29.4) / (18375 – 29.4)
3: UNsharp source SOV. CONTROVERSY !
2400.9799918338
11.8625505633652 = (2400000)*(11.8624919302776) / (2400000 – 11.8624919302776)
29.4474766943004 = (2400000)*(29.4471153846154) / (2400000 – 29.4471153846154)
4: SIMPLY sharpUN no. controversy!!
2433.85038856765
11.8626091970325 = (1200000)*(11.8624919302776) / (1200000 – 11.8624919302776)
29.4474766943004 = (2400000)*(29.4471153846154) / (2400000 – 29.4471153846154)
5: La2011 Table 6 Reign D-air !!!!!
2433.5510445144
11.8626108257537 = (1183561.64383561)*(11.8624919302776) / (1183561.64383561 – 11.8624919302776)
29.4474820471031 = (2364963.50364963)*(29.4471153846154) / (2364963.50364963 – 29.4471153846154)
1/(s4-s3) =
1183561.64383561 = (72993.5229512813)*(68753.3156498674) / (72993.5229512813 – 68753.3156498674)
1/(g4-g3) =
2364963.50364963 = (74619.9907876555)*(72337.575351641) / (74619.9907876555 – 72337.575351641)
6: Exploring symmetrically balanced residuals:
2432.23243052504
11.862621031421 = (1090000)*(11.8624919302776) / (1090000 – 11.8624919302776)
29.4475131572382 = (2180000)*(29.4471153846154) / (2180000 – 29.4471153846154)
in 2020 We
CO[V]well IT’s
CO[2]IDoorwell
WHO’s at UN.
Bye don19 NY 8:4 warn in buy D-UN mess age:
“Hear comms. year 19th nerve US brake D-own” — Roll UN Stones
CRews[.4]miss story red some ware Norton D-scribe monster US moonsh!nos. “the voice of God”.
“IN GOD WE TRUST“
Seidelmann (1992) Table 5.8.1 matches sidereal periods listed here.
ALERT: Table 15.6 says “sidereal” but is off from this while matching quantities listed as “tropical” on pages in this series. Table 15.6 has propagated into other books. The quantities for Earth are an immediate tell-tale sign.
F(IT) Faith in-Eur. Favor IT Orrery
Years ago while studying and teaching stats and living in university residence I had a memorable late-night laundry room conversation with a beautiful math grad student.
She expressed respect for dealing with messy real-world data and underscored that she chose math because it’s clean, pure, and stable.
3 or 4 years ago I began a boycott of solar and climate exploration (briefly interrupted recently), motivated by (a) incromprehensibly inappropriate and excessive harassment in solar and climate discourse (whether founded in ignorance or deception intolerably dark either way) and (b) intransigently pesky data manipulation.
Readers will note that I switched to expressing cynicism while exploring stable math (where the goalposts aren’t being moved politically). I had come to appreciate the perspective of the bright young lady I met in the laundry room years earlier.
Little did I realize the convergence of streams that would result. I suspect some readers will not fathom the questions raised by the “Seasons Best” trilogy.
Hindsight 2020 in Light of Seidelmann Typo — Part I
Me, V, E, Ma beats with Seidelmann (1992) tables 5.8.1 & 15.6:
25811.3691836373 = (0.240846697327135)*(0.24084445) / (0.240846697327135 – 0.24084445)
25757.05496809 = (0.615197263396975)*(0.61518257) / (0.615197263396975 – 0.61518257)
25763.987503107 = (1.00001743371442)*(0.99997862) / (1.00001743371442 – 0.99997862)
25902.4692610417 = (1.88084761346252)*(1.88071105) / (1.88084761346252 – 1.88071105)
Compare:
25808.590009763 = harmean(25811.3691836373, 25757.05496809, 25763.987503107, 25902.4692610417)
25808.3716263561 — tight match with previously noted Earth-Moon slip cycle (look near end of linked comment)
-0.000846165586 = % error
Hindsight 2020 in Light of Seidelmann Typo — Part II
J, S, U, & N:
23094.6280196893 = (11.8626151546089)*(11.85652502) / (11.8626151546089 – 11.85652502)
36133.4834429379 = (29.4474984673838)*(29.42351935) / (29.4474984673838 – 29.42351935)
26114.2236547808 = (84.016845922161)*(83.74740682) / (84.016845922161 – 83.74740682)
25259.6956047047 = (164.791315640078)*(163.7232045) / (164.791315640078 – 163.7232045)
Note carefully Saturn’s special weigh with numbers.
25759.505729618 = (1+MOD(29.42351935,1)+1+1) / (1/23094.6280196893 + MOD(29.42351935,1)/36133.4834429379 + 1/26114.2236547808 + 1/25259.6956047047)
25763.987503107 — compare
-0.017395496285 = % error
25811.0487949114 = (1+MOD(29.4474984673838,1)+1+1) / (1/23094.6280196893 + MOD(29.4474984673838,1)/36133.4834429379 + 1/26114.2236547808 + 1/25259.6956047047)
25808.590009763 — compare
0.009527003015 = % error
2020 Tropical Rabbit Sequence
1.59868953279706 = (0.99997862)*(0.61518257) / (0.99997862 – 0.61518257)
0.761743683794994 = (0.99997862)*(0.61518257)/((0.99997862+0.61518257)/2)
0.814043357147551 = (11.85652502)*(0.761743683794994) / (11.85652502 – 0.761743683794994)
22.1348191900864 = slip(1.59868953279706,0.407021678573776)
22.1348630064402 = (5^(1/2)+1)*(7-1)/(1/((7^0)+1/((7^1)+1/((7^1)+1/((7^2)+1/((7^3)+1/((7^5)+1/(7^8))))))))
-0.000197951773 = % error
Links for review now that we see the rabbit sequence appearing most clearly in Venus-Earth tropical context: _1_ & _2_
“Perhaps even more remarkably […] we can replace the base 2 by any real number bigger than 1 […]”
“This is a book I go back to so very often […] chapter 3 on Integer Functions has a marvellous section on Floors and Ceilings and spectra.”
“Concrete Mathematics (2nd edition, 1994) by Graham, Knuth and Patashnik, Addison-Wesley.“
k.[0,m).Σ ⌊(nk+x)/m⌋ = k.[0,n).Σ⌊(mk+x)/n⌋, integers m, n greater than 0
last equation p.94 (pdf p.107)
review:
let n = 146, m = 208, & x = 0
15008 = ⌊ 5482096 / 365.256367733331 ⌋ ——- where 5482096 is a famous Mayan number
JEV sidereal review to compare and contrast with tropical:
1.59868955949705 = (1.00001743371442)*(0.615197263396975) / (1.00001743371442 – 0.615197263396975)
0.761766209372164 = (1.00001743371442)*(0.615197263396975)/((1.00001743371442+0.615197263396975)/2)
0.814040387734912 = (11.8626151546089)*(0.761766209372164) / (11.8626151546089 – 0.761766209372164)
22.1392314983837 = slip(1.59868955949705,0.407020193867456)
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
-0.000000038239 = % error
lim s→∞
(φ^(2s)+1/s)^(e/s+1/(2s))
= φ(φφ)^e —- the link is to Schneider’s classic proof
Recall: 2, 12, & 240 are both highly and sparsely totient.
Just replace φ with 240 in the calculation to switch from e to 1/E where E is Earth’s sidereal orbital frequency. 240 doesn’t need as many terms to converge.
Forthcoming: simple exploration of 240 in the context of perfect numbers, Heegner numbers, supersingular primes, and generalized Pythagorean theorem.
Symbolic Western Outreach
The “Seasons Best” trilogy above demonstrates how ever-so-gentle, systematic orrery parameter tweaks switch between the “Charvatova 2400” and “1470” worldviews from a “Siedelmann’s Perfect” (as in perfect numbers) reference frame.
Remember that 19 = x mod 24 where x = 19, 43, 67, & 163.
We’re not done with Heegner numbers and monstrous moonshine.
I suspect some will be studying the structure of the equations used in Seidelmann & Laskar.
In God (but maybe knot SIM MET trick polynomials) We Trust
Season’s Best everyone. Let’s eliminate western financial terrorism on homeland citizens. The pandemic has left some more wealthy and free while crushing $0[]well others. IT isn’t right.
Substituting JSUN harmonic mean for JS harmonic mean:
30.4320075307947 = (835.546575435631)*(29.3625733662892) / (835.546575435631 – 29.3625733662892)
7.60800188269868 = 30.4320075307947 / 4
208.880684806261 = slip(65.0170708690834,8.4561457463176)
51.0763050439315 = slip(19.8650360864628,7.60800188269868)
982.019421406588 = slip(208.880684806261,65.0170708690834)
2331.75304290408 = slip(208.880684806261,51.0763050439315)
171.406220601552 = (164.791315640078)*(84.016845922161) / (164.791315640078 – 84.016845922161)
with JSUN harmonic mean
35.4322620251755 = (171.406220601552)*(29.3625733662892) / (171.406220601552 – 29.3625733662892)
8.85806550629388 = 35.4322620251755 / 4
25.0682769387836 = (171.406220601552)*(29.3625733662892) / (171.406220601552 + 29.3625733662892)
163.772511943922 = slip(35.4322620251755,19.8650360864628)
81.8862559719609 = slip(19.8650360864628,8.85806550629388)
95.7061647054583 = slip(25.0682769387836,19.8650360864628)
280.639256382227 = slip(95.7061647054583,16.9122914926352)
656.951889222652 = slip(280.639256382227,81.8862559719609) ————————————-
979.858094471807 = slip(280.639256382227,163.772511943922) —————————————–
14.7232679147118 = (11.8626151546089)*(6.56951889222652) / (11.8626151546089 – 6.56951889222652)
29.4465358294237 = 2*14.7232679147118
25808.9894765272 = (1+MOD(29.4465358294237,1)+1+1) / (1/23094.6280196893 + MOD(29.4465358294237,1)/36133.4834429379 + 1/26114.2236547808 + 1/25259.6956047047)
0.001547805456 = % error
5255.61511378122 = 8*656.951889222652
5256 = ⌊5255.61511378122⌉ = 7920 – 2400 – 240 – 24 ————————– 7920 = M11 order
3.14501624941799 = 5255.61511378122 / 835.546575435631 / 2
14.7237492336919 = 29.4474984673838 / 2
We’ve given this side plenty of attention…
61.0464822565173 = (14.7237492336919)*(11.8626151546089) / (14.7237492336919 – 11.8626151546089)
…but not the other:
6.56961471832961 = (14.7237492336919)*(11.8626151546089) / (14.7237492336919 + 11.8626151546089)
0.001458647196 = % error
656.961471832961
5255.69177466369
3.14506212410931
4270.09258127429 = slip(164.791315640078,84.016845922161)
48590.8284812209 = slip(4270.09258127429,171.406220601552)
29.3803273755345 = (48590.8284812209)*(29.3625733662892) / (48590.8284812209 – 29.3625733662892)
7.34508184388362 = 29.3803273755345 / 4
61.3371935567961 = slip(29.3803273755345,19.8650360864628)
67.2332876489389 = slip(19.8650360864628,7.34508184388362)
2734.13856809656 = slip(67.2332876489389,16.9122914926352)
6441.4623444278 = slip(2734.13856809656,61.3371935567961)
25765.8493777112 = 4*6441.4623444278
5221.17476429629 = slip(2432.25439579341,131.716392653884)
25765.8493777112 = 4 * 6441.4623444278
20884.6990571851 = 4 * 5221.17476429629
110242.867945166 = (25765.8493777112)*(20884.6990571851) / (25765.8493777112 – 20884.6990571851)
Hindsight 2020 in Light of Seidelmann Typo — Part III
Alternate weighting…
8.45107360405992 = (29.42351935)*(11.85652502) / (29.42351935 + 11.85652502)
0.418531083199004 = MOD(8.45107360405992*φ/4,1)
…gives:
25748.7187156079
Alternate weighting…
8.4561457463176 = (29.4474984673838)*(11.8626151546089) / (29.4474984673838 + 11.8626151546089)
0.420582807841181 = MOD(8.4561457463176*φ/4,1)
…gives:
25753.1582384253
25759.9581995811 = (1+5^2/59+1+1)/(1/23094.6280196893+5^2/59/36133.4834429379+1/26114.2236547808+1/25259.6956047047)
25810.4394697625 = (1+1/√5+1+1) / (1/23094.6280196893 + 1/√5/36133.4834429379 + 1/26114.2236547808 + 1/25259.6956047047)
Alternate Derivation of Sylvester’s Sequence
Terse formulation + easier to grasp geometrically.
harmonic means:
UN:
111.292543528394 = (164.791315640078)*(84.016845922161)/((164.791315640078+84.016845922161)/2)
JS:
16.9122914926352 = (29.4474984673838)*(11.8626151546089)/((29.4474984673838+11.8626151546089)/2)
their beat:
19.9428577113341 = (111.292543528394)*(16.9122914926352) / (111.292543528394 – 16.9122914926352)
slip on JS frame:
5090.68769455895 = slip(19.9428577113341,19.8650360864628)
489425.980666482 = slip(5090.68769455895,8.4561457463176)
489426 = 2*3*7*43*271
489426 = 1806*271
Absolutely fantastic and simple.
Classic Review
18.7636626447678 = (171.406220601552)*(16.9122914926352) / (171.406220601552 – 16.9122914926352)
4.69091566119194 = 18.7636626447678 / 4
338.432743555958 = slip(19.8650360864628,18.7636626447678)
2311.47726940065 = slip(338.432743555958,4.9662590216157)
I need to switch focus now. Someone else can be doing this type of work. It isn’t hard; there are just a lot of combinations to explore. Teamwork: It concerns me that others aren’t focused on monstrous moonshine and Heegner numbers. It makes me suspicious.
Something new (the idea resulting from the JS conjunction and the Croatia earthquake at the full moon).
Major earthquakes Croatia :
1667 Dubrovnik earthquake
1880 Zagreb earthquake
2020 Petrinja earthquake
the gaps are multiple of 70. coincidence?????
oldmanK says: Coincidence?
December 30, 2020 at 10:02 am
– – –
Perhaps, but 1880 and 2020 both in first year or so of low solar cycles (expected for current SC), and 1668 in the Maunder Minimum.
https://en.wikipedia.org/wiki/List_of_solar_cycles
alright 1 encore note gentlemen before resuming more fundamental attention:
113.780000311666 = (19.8650360864628)*(16.9122914926352) / (19.8650360864628 – 16.9122914926352)
208.09114070835 = (1216.12719789676)*(113.780000311666)/((1216.12719789676+113.780000311666)/2)
same calculation with the “1470 worldview” gives 196 & 210 (for 735 & 1470 respectively)
———————————
Strategic Parity
104 = d(4,1/2,58) = R(4,1/2,58) – R(1,1/2,58)
104.000034332275 = ⌊(e^√58π)^(1/4)⌉^4 – e^√58π
a = 0.000034332275390625 = ⌊(e^√58π)⌉ – e^√58π
395.999999581314 = (e^√58π)^(1/4)
396 = ⌊(e^√58π)^(1/4)⌉
b = 396 – 395.999999581314 = ⌊(e^√58π)^(1/4)⌉ – (e^√58π)^(1/4)
82 = a / b
186 = 104+82
744 = 4*186
496 = 2/3*744
1984 = 4*496
73=AVERAGE(42,104) ————- “Sporadic & Exceptional” indeed
73=AVERAGE(19,43,67,163)
104=73+31
42=73-31
194=163+31
132=163-31
The Mayan sages simply keyed the following with pythagorean theorem:
50=31+19=194-144
144=163-19
194=163+31
59*(59-12)*(59+12) = 196883
12^2 = 144 = 59^2-196883/59
323=196883-196650
323-31=292=19+43+67+163
354+31=354=2*(47+59+71)
378=sum of supersingular
316=sum of supersingular with sign of +31 flipped to -31
316=sum of heegner
271=292-31 —————————————————————— Sylvester Sequence
“ally” UN count “Or” flaw lane
162=ET(163)=66+96
s(496-108)=s(496-CT(163))=298
298=152+104+42
s(298) = 152
s(s(152)) = 118 = 2*59 = 47+71
s(118) = 62 = s(2*59) = 2*31
248 = 104 + 144 = 496/2
186 = 144 + 42 = 744/4
496 = s(s(298)) + sum of supersingular primes = 8 * s(s(s(298)))
31=AVERAGE(19,43)
589=1333-744
589=608-19
589=31*19
589=19*496/16
744=652+73+19=4*163+73+19=25*29+19
There’s a reason no one noticed: it isn’t obvious (duh!)
“But this has nothing to do with the sun…” — conservatives voices lost in 1984…
Ignorance (…or maybe deception) …due for bright light either way
“163 is the number of Z-independent McKay-Thompson series for the monster group. This fact about 163 might be a clue for understanding monstrous moonshine.[4] […] 4. He, Yang-Hui; McKay, John (2015). “Sporadic and exceptional”. pp. 1–49. arXiv:1505.06742 [math.AG]. (See p. 13)”
Orientation
Note links in the left call ’em here:
“A complete revision of the Classification has been underway for twenty years, and is still continuing. […] However there are coincidences as yet unexplained, one of which concerns the number 163.”
“the classification theorem has been called one of the great intellectual achievements of humanity […] Why is the proof so long?“
While retaining hope that the number theory community will quickly and formally clarify for the world the link between Heegner numbers and monstrous moonshine, I do realize some observers here are looking for something else.
Very well. This is crude but those in the know will easily recognize it nonetheless.
JEV tropical and sidereal:
111063.836252585 = (22.1392314983837)*(22.1348191900864) / (22.1392314983837 – 22.1348191900864)
22.1370251243719 = (22.1392314983837)*(22.1348191900864)/((22.1392314983837+22.1348191900864)/2)
490 = 22.1348191900864 * 22.1370251243719
…980, 1470, 36750, 73500
1.00002643794033 = (111063.836252585)*(1.00001743371442) / (111063.836252585 – 1.00001743371442)
1.00002638193018
0.000005600867 = % error
There’s a lot more that can be said around this. Clean, simple stuff — surely widely known already, yet we haven’t seen it addressed (curiously).
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
14.7237492336919 = 29.4474984673838 / 2
13.1392294366592 = (14.7237492336919)*(11.8626151546089)/((14.7237492336919+11.8626151546089)/2)
plus 9 equals:
22.1392294366592
-0.000009350777 = % error
22.1392285019811 = 2 * 5090 / 744 * φ
-0.000013572596 = % error
Just putting in new combinations familiar numbers.
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
22.1392314983837 = 1/(3/V-5/E+2/J)
0.000000038239 = % error
Replace φ with 240 in the expression for e here.
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
1.00001743371442 = 1/E
0.000000018929 = % error
0.61519726351855 = 3/(1/22.1392315068494+5/1.00001743390371-2/11.8626151546089)
0.615197263396975 = 1/V
0.000000030106 = % error
So what’s left tune notice?
992 = 1*2*16*31
496 = 16*31
Perfect sci11UNs comm. UN IC k? s(496)hh!…..
Tropical UN slip-cycles match with sidereal JS slip-cycles:
2432 &
20884 = 4*5221
171.444289533663 = (163.7232045)*(83.74740682) / (163.7232045 – 83.74740682)
110.812300014126 = (163.7232045)*(83.74740682)/((163.7232045+83.74740682)/2)
55.4061500070632 = (163.7232045)*(83.74740682) / (163.7232045 + 83.74740682)
27.7030750035316 = 55.4061500070632 / 2
3635.42278750964 = slip(163.7232045,83.74740682)
29.3305236493692 = harmean(JSUN tropical periods)
29.5690864909714 = (3635.42278750964)*(29.3305236493692) / (3635.42278750964 – 29.3305236493692)
7.39227162274285 = 29.5690864909714 / 4
891.227241339459 = slip(171.444289533663,7.39227162274285)
20884.3849304411 = slip(891.227241339459,110.812300014126)
849.121646024845 = slip(171.444289533663,29.5690864909714)
2431.67883089196 = slip(849.121646024845,27.7030750035316)
That clarifies the distinction from Laskar’s p = 25685 (follow the hyperlink in the last comment) :
0.999978499031851 = (20884.3849304411)*(1.00002638193018) / (20884.3849304411 + 1.00002638193018)
25683.9369504749 = (1.00001743371442)*(0.999978499031851) / (1.00001743371442 – 0.999978499031851)
Compare with:
25763.987503107 = (1.00001743371442)*(0.99997862) / (1.00001743371442 – 0.99997862)
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
22.1348478401313 = (245/(φ^22+1/11)^(e/11+1/22)+√((245/(φ^22+1/11)^(e/11+1/22))^2+980))/2
111789.639177999 = (22.1392315068494)*(22.1348478401313) / (22.1392315068494 – 22.1348478401313)
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
1.00002637966847 = (111789.639177999)*(1.00001743390371) / (111789.639177999 – 1.00001743390371)
1.00002638193018 = terrestrial anomalistic year period
-0.000000245095 = % error ——————— 7 seconds per century
111759.01908408 = (1.00002638193018)*(1.00001743371442) / (1.00002638193018 – 1.00001743371442)
-0.027390815593 = % error
The second line in the preceding comment is simply solving the quadratic equation that ties JEV tropical and sidereal to 4900 = 70^2 = 1^2 + 2^2 + 3^2 + … + 22^2 + 23^2 + 24^2 to check how tight the fit is (off by 7 seconds per century as noted).
260 & 64000
8.45305064436623 = (29.4474984673838)*(11.85652502) / (29.4474984673838 + 11.85652502)
8.45416725812087 = (29.42351935)*(11.8626151546089) / (29.42351935 + 11.8626151546089)
64000.2003304946 = (8.45416725812087)*(8.45305064436623) / (8.45416725812087 – 8.45305064436623)
19.8619536084148 = (19.8759632567693)*(19.8479636956574)/((19.8759632567693+19.8479636956574)/2)
11.8595693054519 = (11.8626151546089)*(11.85652502)/((11.8626151546089+11.85652502)/2)
29.4355040251508 = (29.4474984673838)*(29.42351935)/((29.4474984673838+29.42351935)/2)
19.8619536084148 = (29.4355040251508)*(11.8595693054519) / (29.4355040251508 – 11.8595693054519)
19.8759632567693 = (29.42351935)*(11.8626151546089) / (29.42351935 – 11.8626151546089)
19.8479636956574 = (29.4474984673838)*(11.85652502) / (29.4474984673838 – 11.85652502)
19.8619536084148 = (19.8650360864628)*(19.8588720868409)/((19.8650360864628+19.8588720868409)/2)
260 ~= 259.996348149018 = 5*φφ*19.8619536084148
73=AVERAGE(19,43,67,163)
73=365-19-43-67-163
120=163-43
240=163-19+163-67
360=163-19+163-67+163-43
129=19+43+67
194=323-129
194=163+31
323=194+19+43+67
163=194-31
271=489426/43/7/3/2
271=240+31
209=240-31
836=4*209
Perfect Mayan Symmetry
260=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71-(47+71)
496=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71+(47+71)
260=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71-(2*59)
496=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71+(2*59)
260=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71-(59+AVERAGE(47,71))
496=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71+(59+AVERAGE(47,71))
260=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71-2*196883/71/47
496=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71+2*196883/71/47
Earthly 240
378=2+3+5+7+11+13+17+19+23+29+31+41+47+59+71
316=2+3+5+7+11+13+17+19+23+29-31+41+47+59+71
316=1+2+3+7+11+19+43+67+163
240=1+2+3+7+11+19+43+67+163-MOD(19,24)-MOD(43,24)-MOD(67,24)-MOD(163,24)
240=1+2+3+7+11+19+43+67+163-19-19-19-19
240=1+2+3+7+11+19+43+67+163-76
240=2+3+5+7+11+13+17+19+23+29-31+41+47+59+71-MOD(19,24)-MOD(43,24)-MOD(67,24)-MOD(163,24)
240=2+3+5+7+11+13+17+19+23+29-31+41+47+59+71-19-19-19-19
240=2+3+5+7+11+13+17+19+23+29-31+41+47+59+71-76
76=MOD(19,24)+MOD(43,24)+MOD(67,24)+MOD(163,24)
76=19+19+19+19
[H]edge [O]ption (…and this saint nicholas stir red yen!)
360 = (196883-196560) + s(196883-196560)
360 = (323) + s(323) = 323 + 37
“Walk like an Egyptian” — The Bangels
104 = d(2,1/2,37) ~= 2*φφ*19.8619536084148
mic on a11 scene at or[well 1984]
speech so “free eu” can’t eve un safe flee warn all lies push un too herd
“a11 the COP$in the dough nut$shhop” — the ban gel$
“WA11 cli. con e.g. op$shh!un” — The B-angels
“wei hua wei hua wei hua wei hua: woke lie con edge ops yen”
163(Can’t Talk Key PR air)980
Roads
“Troubles will come and they will pass
and don’t forget son there is someone up above”
Fair
“Be a simple kind dove man…love and understand“
178.266850068779 = beat(131.716392653884,504.413226524325)
178.266850068779 = beat(96.1829470900285,208.886643858908)
178.266850068779 = beat(65.8581963269421,104.443321929454)
178.266850068779 = axial(208.886643858908,1216.12719789676)
178.266850068779 = harmean(104.443321929454,608.06359894839)
178.266850068779 = harmean(96.1829470900285,1216.12719789676)
Bridge
“and if you do this IT’11 help you some sunny day” — Lynyrd Skynyrd “Simple Man”
5256 = 73*72 = φ(1333)*Φ(111) = 7920-2400-240-24
s(608) = 652; s(652) = 496; s(496) = 496
36750.3379015986 = 8/(g_6+s_6+s_3+5*g_4+s_4+5*g_3+g_2+s_2) —– Laskar
323 = 196883 – 196560
37 = s(323)
Φ(1333) = 1260 = 608 + 652 = 608 + s(608) = d(2,1/2,33) = R(1,1/2,33) – R(2,1/2,33)
993.252375718881 = 36750.3379015986 / 37
496.626187859441 = 993.252375718881 / 2
497 = 993 – 496 = 993 – s(652) = 993 – s(s(608))
1333 = 497 + 836 = Φ(1333) + φ(1333) = 1260 + 73 = 608 + 652 + average(19,43,67,163)
1332 = 496 + 836 = 1260 + 72 = Φ(1333) + Φ(111)
1984 = 496 + (836 + 652) = 496 + (1488) = 496 + (3*496) = 4*496
1987 = 2*497 + 993
1986.50475143776 = 993.252375718881 * 2
check balance:
112 = 73 + 39 = φ(1333) + φ(111) —————– _L_ ; _J4_
1444 = 1332 + 112 = 1333 + 111
216 = Φ(Φ(1444)) = 3^3 + 4^3 + 5^3 = 6^3
= sum of Heegner numbers minus sum of (Heegner numbers mod(1+2+3+7+11))
= 19+43+67+163-19-19-19-19
= 4*Φ(Φ(163)) = 2*φ(Φ(163))
216 = 2432/2 – Φ(1111) = 2*608 – Φ(1111) = 1216 – 1000
1333 = 1111 + φ(1111) + φ(1111) = 1111 + 111 + 111 = φ(3333)
recall:
111 = Φ(196883-196560)-(47+59+71)
111 = Φ(323)-(47+59+71)
111 = Φ(1260)-(47+59+71) = Φ(608+652)-(47+59+71) = Φ(608+s(608))-(47+59+71)
111 = Φ(608)-(47+59+71)
111 = Φ(365)-(47+59+71)
all Heegner numbers appear in lines 2 & 3:
196883/59 = 47*71 = 59^2-Φ(196883-196560)/2
= s(19+43+67)*s(s(Φ(163)))
= 59^2-((1+2+3+7+11)/2)^2
47 = 59-12 = s(19+43+67)
71 = 59+12 = s(67+67+67) = s(s(Φ(163)))
24 = 71 – 47 = s(s(Φ(163))) – s(19+43+67) = 1+2+3+7+11
576 = (1+2+3+7+11)^2 = 24^2
288 = Φ(323) = Φ(1260) = Φ(608) = Φ(365)
144 = ((1+2+3+7+11)/2)^2 = 12^2
L: 163 = 652 / 4 = s(608) / 4 = 2+3+5+7+11+31+37+67
113.757966840464 = slip(24.067904774739,19.8650360864628)
113.760416666667 = (163)*(67) / (163 – 67)
113.780000311666 = (19.8650360864628)*(16.9122914926352) / (19.8650360864628 – 16.9122914926352)
1333 ~= (323)*(260) / (323 – 260)
323 ~= (1333)*(260) / (1333 – 260)
144 = 12^2 ~= (1333)*(130) / (1333 – 130)
260 ~= (323)*(144) / (323 – 144)
194 ~= (260)*(111) / (260 – 111)
111 ~= (260)*(194) / (260 + 194) ~= (43)*(31) / (43 – 31)
3337 = 47*71 = 196883/59
292 = 19+43+67+163
320.0013136289 = (3337)*(292) / (3337 – 292)
64000.26272578 = 200*320.0013136289
64000.2003306467
0.000097492091 = % error
The small distinction between 64000.26 & 64000.2 has diagnostic utility.
There will be a series of comments on sporadic simple groups, 70^2 = 1^2 + 2^2 + 3^2 + … + 22^2 + 23^2 + 24^2, 260, & 64000 making hairline distinctions.
Few will have the patience and interest to stay the course (e.g. $speed-chess$$ addicts$slaving destructively under the trolllionairfirehosepress$$sure of menacing political timetables$$).
14.7237492336919 = 29.4474984673838 / 2
13.1392294366592 = harmean(14.7237492336919,11.8626151546089)
22.1392294366592 = 9 + 13.1392294366592
22.134848529967 = = (245/22.1392294366592+√((245/22.1392294366592)^2+980))/2
22.1370387665684 = harmean(22.1392294366592,22.134848529967)
22.1370383309738 = (7920/√(2*64000.2003306175)
0.000001967719 = % error
490 = 22.1370387665684 * 22.134848529967
64000.1978119299 = (7920/22.1370387665684)^2/2
64000.2003306175
-0.000003935437 = % error
This alerts us to simple J & S tropical structure relative to J & S sidereal.
It also helps clarify the structure of what’s on vs. near (but systematically off) the 70^2 frame.
Years ago I knew I should investigate that suspicious list of numbers I shelved from Seidelmann (1992). There’s always an endless list of other things to explore — enough to consume many lifetimes.
A half-dozen times over the years I thought about the list but focused on competing things. Not sure why but last month I dusted off the old file — and verified the simple typo (one that propagated into other published books).
Since then insights are pouring like a string of domino’s. A good side-effect of the long delay: the temporary obstruction diverted me to first quantitatively master Bollinger’s (1952) symbolic method (eased intuitive link to Mayan & Egyptian methods and simple sporadic groups).
Why $0men?
Careful readers should already see the links between 22 & 70^2.
“some peep hill ‘calm me’ ‘the bad apple’ but I may be ‘the sweet test’ APoll on the tree” — David Wilcox
Note that there are 2 groupings of “22.137”, just as there are 2 groupings of “64000.2”.
We’re drawing a diagnostic hairline distinction between the 2 groups.
292 = 5256/18 = average(19,43,67,163)
3337 = 47*71 = 196883/59
320.0013136289 = beat(3337,292)
22.1370275400459 = 7920 / √128000.52545156
22.1370251243719 = harmean(22.1392314983837,22.1348191900864)
-0.000010912368 = % error
typo:
“292 = 5256/18 = average(19,43,67,163)”
correction:
292 = 19+43+67+163
73 = average(19,43,67,163)
supplementary:
“657 = 3^2 × 73, the largest known number not of the form a^2+s with s a semiprime”
Rusty NASA JPL press realease:
=
It’s very puzzling […] At first, I totally didn’t believe it. It shouldn’t exist based on the conditions present on the Moon […]
[…]
One major clue was the rust was more concentrated on the side of the moon that faces Earth — suggesting it was somehow linked to our planet.
[…]
During these six days, Earth’s magnetic tail covers the moon’s surface with electrons, and all sorts of strange things can happen.
=
This one’s important.
Earlier I introduced something left subtly imbalanced. Here I righten the balance:
208.886643858907 = 1/(-8J+20S)
208.886658253856 = beat(49000,207.999955892562)
0.000006891272 = % error
y = R(p,1/2,7) = 24.067904774739 = ⌊(e^√7π)^(1/p)⌉^p – e^√7π for p=2,3,4,6,12
x = R(p,1/2,58) = 104.000034332275 = ⌊(e^√58π)^(1/p)⌉^p – e^√58π for p=2,4
z = -R(2,1/2,37) = 103.999977946281 = e^√37π – ⌊(e^√37π)^(1/2)⌉^2
2z = 207.999955892562 = 2 * 103.999977946281
11.8626151191159 = 1/((6/y+(1/4)/x)/5+(1/x+1/298)*φ^2)
11.8626151546089 = 1/J
-0.000000299201 = % error
29.4474983942016 = 20/(1/(2z)+8*((6/y+(1/4)/x)/5+(1/x+1/298)*φ^2)-1/49000)
29.4474984673838 = 1/S
-0.000000248518 = % error
2432.25097753771
2432.25439579341
-0.000140538576 = % error
Using the sharpened J & S estimates (see last comment) :
19.8650360202345 = beat(29.4474983942016,11.8626151191159)
19.8650360864628 = beat(29.4474984673838,11.8626151546089)
-0.000000333392 = % error
8.45614572224745 = axial(29.4474983942016,11.8626151191159)
8.4561457463176 = axial(29.4474984673838,11.8626151546089)
-0.000000284647 = % error
16.9122914444949 = harmean(29.4474983942016,11.8626151191159)
16.9122914926352 = harmean(29.4474984673838,11.8626151546089)
-0.000000284647 = % error
Review
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
22.1392314983836 = 1/(3V-5E+2J) = 1/H —- Jupiter-Earth-Venus SIDEREAL
0.000000038239 = % error
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
1.00001743371442 = 1/E
0.000000018929 = % error
H = 3V-5E+2J (algebra in frequency = 1/period)
V = (1/3)H+(5/3)E-(2/3)J
0.615197263582188 = 1/V = 1/((1/3)/22.1392315068494+(5/3)/1.00001743390371-(2/3)/11.8626151191159)
0.615197263396975 = 1/V
0.000000030106 = % error
64000 & 260 Review
Mayan sages embedded these symbols symbolically (probably a mnemonic device — e.g. “mind palace” = method of loci).
16.9083345162417 = harmean(29.42351935,11.8626151546089) — S trop with J side
16.9061012887325 = harmean(29.4474984673838,11.85652502) — S side with J trop
128000.400661193 = beat(16.9083345162417,16.9061012887325)
8.45416725812087 = axial(29.42351935,11.8626151546089) — S trop with J side
8.45305064436623 = axial(29.4474984673838,11.85652502) — S side with J trop
64000.2003304946 = beat(8.45416725812087,8.45305064436623)
19.8650360864628 = beat(29.4474984673838,11.8626151546089) — S side with J side
19.8588720868409 = beat(29.42351935,11.85652502) — S trop with J trop
64000.2003306175 = beat(19.8650360864628,19.8588720868409)
19.8619536084148 = harmean(19.8650360864628,19.8588720868409)
52 ~= 51.9992696298035 = 1 * φφ * 19.8619536084148
104 ~= 103.998539259607 = 2 * φφ * 19.8619536084148
208 ~= 207.997078519214 = 4 * φφ * 19.8619536084148
260 ~= 259.996348149018 = 5 * φφ * 19.8619536084148
Now, pay careful attention as the hairline difference between the two “22.137” clusters emerges from 70^2 and propagates to the 2 corresponding “64000.2” clusters.
Note well the MUCH larger %errors in this calculation chain (compared with those in this comment). They signal a systematic divergence of J, S, & JEV sidereal and tropical structure which we’re diagnosing.
22.1348478401313 = (245/(φ^22+1/11)^(e/11+1/22)+((245/(φ^22+1/11)^(e/11+1/22))^2+980)^(1/2))/2
22.1348191900864 = = 1/(3V-5E+2J) —- Jupiter-Earth-Venus TROPICAL
0.000129434284 = % error
22.1370394564725 = 490/((245/(φ^22+1/11)^(e/11+1/22)+((245/(φ^22+1/11)^(e/11+1/22))^2+980)^(1/2))/2)
22.1370251243719 = harmean(JEV sidereal & tropical periods)
0.000064742667 = % error
490 = 22.1348478401313 * 22.1370394564725
489.999048534373 = JEV tropical period * harmean(JEV sidereal & tropical periods)
0.000194177036 = % error
64000.193822779 = ( 7920 / 22.1370394564725 )^2 / 2
64000.2766936711 = ( 7920 / 22.1370251243719 )^2 / 2
-0.000129485209 = % error
Monstrous moonshine and Heegner numbers together appear to define the offset.
64000.193822779 = (7920 / 22.1370394564725)^2 / 2
64000.2003306175 = long JS sidereal & tropical cycle (embedded in Mayan symbolism)
-0.000010168466 = % error
22.1370394564725 = 7920 / √(2*64000.193822779)
22.1370383309738 = 7920 / √(2*64000.2003306175) = 7920 / √(128000.400661193)
0.000005084233 = % error
3337 = 47*71 = 196883/59 —————- _M_
292 = 19+43+67+163 = 5256/18 ——— Heegner
320.0013136289 = beat(3337,292)
64000.26272578 = 200 * 320.0013136289
64000.2766936711
0.000021824740 = % error
22.1370251243719 = 7920 / √(2*64000.2766936711)
22.1370275400459 = 7920 / √(2*64000.26272578)
-0.000010912368 = % error
Almost-integers appear to minimize rotation (of frames relative to one another) where exact integer equality isn’t physically possible (because of competing minimizations).
Review
22.1392315068494 = (1.61803398874989^MOD(47+71,24)+1/MOD(59,24))^(2.71828182845905/MOD(59,24)+1/MOD(47+71,24))
phi as monstrous aliquot trig function:
φ = 2*cos(s(71^2)/s(59^2)/s(47^2)*8*π) where s(n) = aliquot sum for n
φ = 2*cos(s((59+12)^2)/s(59^2)/s((59-12)^2)*8*π)
Seriously: How many people know this familiar φ identity in monstrous aliquot form?
71^2 = 5041; s(5041) = 72
59^2 = 3481; s(3481) = 60
47^2 = 2209; s(2209) = 48
72/60/48 = (6/5/4)/12 = 1/40 = 0.025
0.2 = 1/5 = 6/5/4/3*2 = 8/40
φ = 2*cos(6/5/4/3*2π) = 2*cos(π/5)
Here’s another one to mull: 240
240 is both sparsely and highly totient.
Schneider’s classic — alternate link: golden mobius totient
I love this stuff.
It’s fantastic.
I remember years ago a video by a researcher named Cuk about “Jovian evection resonance” and now with dominoing insights after suddenly hurdling past the Seidelmann (1992) typo delay it looks like there’s fun work available for academics studying our solar system as a local example of number theory. By God’s gracioius guidance some bright mathematical spark(s) will (a) formally clarify Heegner number links to monstrous moonshine and (b) help peers see the classification theorem in beautifully succinct form.
“Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” — Gauss
=
Conway said of the monster group: “There’s never been any kind of explanation of why it’s there, and it’s obviously not there just by coincidence. It’s got too many intriguing properties for it all to be just an accident.” Simon P. Norton, an expert on the properties of the monster group, is quoted as saying, “I can explain what Monstrous Moonshine is in one sentence, it is the voice of God.”
=
Better West Turn Math Education
By God’s gracious guidance some bright mathematical spark(s) will (a) formally clarify Heegner number links to monstrous moonshine and (b) help peers see the classification theorem in beautifully succinct form.
“Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” — Gauss
Comparing JS sidereal with JEV estimate based on φ & e:
22.1370387665684
22.1370394564725
-0.000003116515 = % error
64000.1978119299 = (7920/22.1370387665684)^2/2
64000.193822779 = (7920/22.1370394564725)^2/2
0.000006233029 = % error
Comparing JS sidereal with Seidelmann (1992) JEV:
22.1370387665684
22.1370394536512
-0.000003103770 = % error
64000.1978119299 = (7920/22.1370387665684)^2/2
64000.193839092 = (7920/22.1370394536512)^2/2
0.000006207540 = % error
Comparing JEV estimate based on φ & e with Seidelmann (1992) JEV:
22.1392315068494
22.1392314983837
0.000000038239 = % error
22.1348478401313 = (245/22.1392315068494+√((245/22.1392315068494)^2+980))/2
22.1348478429522 = (245/22.1392314983837+√((245/22.1392314983837)^2+980))/2
-0.000000012745 = % error
22.1370394564725 = harmean(22.1392315068494,22.1348478401313)
22.1370394536512 = harmean(22.1392314983837,22.1348478429522)
0.000000012745 = % error
490 = 22.1348478401313 * 22.1370394564725
490 = 22.1348478429522 * 22.1370394536512
0.000000000000 = % error
64000.193822779 = (7920/22.1370394564725)^2/2
64000.193839092 = (7920/22.1370394536512)^2/2
-0.000000025489 = % error
Demonstrating how 27.03 days ties to lunar draconic across the range 22.13 to 22.14:
22.13 / 2 = 11.065
22.14 / 2 = 11.07
0.0745030006844627 = 27.212221 / 365.25
0.0740047112086532 = axial(11.065,0.0745030006844627)
0.0740049347670639 = axial(11.07,0.0745030006844627)
27.0302207689606 = 0.0740047112086532 * 365.25
27.0303024236701 = 0.0740049347670639 * 365.25
27.03 day ref:
Neugebauer, Ruzmaikin, Feynman, & Vaughan (2000). The solar magnetic field and the solar wind – existence of preferred longitudes. JGR.
Crude comparative hindsight ignoring bundle$struck$”sure!” D-tale$….
7920^2=62726400
62726400/64000=980.1
980.1/2=490.05
490.05 ~= 22.135 * 22.139
490.05*3=1470.15
1470.15*25=36753.75
36753.75*2=73507.5
73500/2=36750
36750/25=1470
1470/3=490
490 ~= 22.135 * 22.137
490*2=980
980*64000=62720000
√62720000=7919.59594928933
7920.40403, 62732800, 980.2, 490.1 ~= 22.137 * 22.139, 1470.3, 36757.5, 73515
…but the relationships are 11inear in frequency — not period — and:
0.000__%errors compared with
0.00000___%errors guided diagnostics past this crude memorrery aid for “980 & 1470 lovers” too strained buy D-tale$.
Crudely indulging D-taste for mmm = misunderstanding, misinterpretation, and misrepresentation.
Yes (sarc) ‘b!g oi11’ pays for luck D-own calculation $0[]well (/sarc). Fact: check$, U Never.ca.me.
Estimating JEV sidereal from J & S sidereal & tropical, 70^2, & M11:
22.1370383309738 = 7920/√(2*64000.2003306175)
22.1348489655186 = 490 / 22.1370383309738
22.1392281295736 = beat(22.1348489655186,11.0685191654869)
22.1392314983837 = Seidelmann (1992) sidereal JEV period
-0.000015216473 = % error
Comparing JEV sidereal estimate from J & S sidereal & tropical, 70^2, & M11 with JEV estimate from 9 & J & S sidereal (without tropical) :
22.1392294366592
22.1392281295736
0.000005903935 = % error
The Perfect Garden
The 3 lowest perfect numbers:
s(6)=6; s(28)=28; s(496)=496
The perfect key to the dimension of monster group minimal faithful representation:
59=s((496+28+6)/2)
59=s((s(496)+s(28)+s(6))/2)
59=s(836/2-67-43-19-11-7-3-2-1) —————— note well: all non-163 Heegner nos!uphere
The smallest weird untouchable number:
836=496+28+6+2*(1+2+3+7+11+19+43+67) ————— again hear:
836=s(496)+s(28)+s(6)+2*(1+2+3+7+11+19+43+67) —- ALL non-163 Heegner numbers appear
836=(196883-59^3)/59+980
[WHEEL CLOCKS] Don’s Guard [DAV]oscar[ID]UN D-[COV]air sov. Lo$Scar[e] (Bridge Fare[$]Road)
980=836+144
980=836+12^2
980=836+(59^3-196883)/59
980=2*(496-6)=2*(s(496)-s(6))
490=496-6=s(496)-s(6) —————————– peerfactlieUNdarestunDemoCrazy
=
B-lock WHO’11 sun?
B-lock Hale’s: UN!
Washuawei D-Reign…………. — Sound Guard don[e]
=
1470=3*(s(496)-s(6))
73500=75*(836+(59^3-196883)/59)
73500=75*(836+(s(836/2-67-43-19-11-7-3-2-1)^3-196883)/s(836/2-67-43-19-11-7-3-2-1))
260=(836-163-67-43-19-11-7-3-2-1)/2 —– my!my!my!yen!more!!beer!mmm…
196883 = 47 * 59 * 71
196883 = (59-12)*59*(59+12)
196883 = 59^3 – 59*12^2
196883 = 59^3 – 59*144
196883 = 59^3 – 59*(980-836)
“Times are gone for honest men” — Soundgarden
US Route 22: West Turn Math
Except shown ally sporadic McKey, He ignore side real true pick calls at turn Joe putter.
64000.26272578 = 2*100/(1/(19+43+67+163)-s(836/2-67-43-19-11-7-3-2-1)/196883)
where:
100 = sum of Heegner nos. each mod 24
24 = 1+2+3+7+11 = sum of LOW west [turn up at math] Heegner nos. [AD:UK$UN]
292 = 19+43+67+163 = some of HIGH est Heegner know$[up eerie ‘Or’ ski11$m[y]th]
836 = smallest weird UNtouchable number
196883 = D-mention of mmminimmmummm faith full-monde star-grip Rep. Pres. sent Ace Sun
59 = s(836/2-67-43-19-11-7-3-2-1) where s(RI[!]NO[!]) D-note$(“ally”[!]caught[!]sum) :
1+2+3+7+11; 19+43+67+163
AB out 111’s CRude$t “Irreducible” “Faithful” Point
111.293375394322 = axial(490,12^2)
111.292543528394 = harmean(164.791315640078,84.016845922161)
0.000747458815 = % error
φ(111) = 8^2 – 5^2 = 39
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8^2
Split this sum into 2 categories:
A. not prime:
1 + 9 + 15 = 25 = 5^2
B. prime:
3 + 5 + 7 + 11 + 13 = 39 = 64 – 25 = 8^2 – 5^2 = 39
13# = (8^2-5^2)*(7920/10-22) = φ(111)*(7920/10-22) = 39*(7920/10-22) = 13*11*7*5*3*2 = 30030
“[…] 11 points gives a complex irreducible representation in 10 dimensions. This is the smallest possible dimension of a faithful complex representation […]”
Piece Fully
This is the “m[y]th or math?” series and “no. free speech” luminaries miss the point of hope and peace 836/209=$128000/$32000 a11.
$sea weather UK can figure IT out “peace fully” with “0.000000000000 = % error” “green a11 lie$” (already shown).
PRO Moon No.[39]Morale
“With a word [11] Can. ‘get ‘ what sh[e!]k aim 836/209=$128000/$32000″ -Led 22plan
196883 = s(836/2-67-43-19-11-7-3-2-1)^3-s(836/2-67-43-19-11-7-3-2-1)*(980-836)
There’s no. room left in the dug-out grean (not a typo) music bees ID “sentimentale”. Eye sun how ear Norton honey moon here’s $64000 quest yen.
=
President Dwight […] did not want to be disturbed while the show was on […] Foghorn […] “Fox-Terror” […] spoof […] “reaching the first plateau” […] Scandal and cancellation […] fictitious $99,000 Answer […] Art Carney […] who identified three times in a man’s life when he wants to be alone, with the third being “when he’s in the isolation booth of The $64,000 Question” […] answering the 11th question […] contestant had been given answers in advance […] the so-called “Original 39”
=
Review, with 3 Suggestions
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
This differs from Seidelmann’s (1992) Jupiter-Earth-Venus cycle period by 3.01679387133036 seconds per century. Above I showed the limit. I urge readers to consider this: why does 11 give the sharpest insight here?
22.1348478401313 = (245/(φ^22+1/11)^(e/11+1/22)+√((245/(φ^22+1/11)^(e/11+1/22))^2+980))/2
111789.639177999 = beat(22.1392315068494,22.1348478401313)
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
This differs from Seidelmann’s value by 1.493352581686 seconds per century.
Suggestion: Study Schneider’s delightful proof and strive to understand why replacing φ (which gives e) with 240 which gives Earth’s sidereal orbital period so precisely.
1.00002637966847 = beat(111789.639177999,1.00001743390371)
This is off from the terrestrial anomalistic year period by 17.8431319091906 seconds per century.
Going through this the other way, starting with terrestrial anomalistic & sidereal years and Seidelmann’s JEV to arrive at 128000:
111759.01908408 = beat(1.00002638193018,1.00001743371442)
22.1348466308557 = axial(111759.01908408,22.1392314983837)
22.1370388474829 = harmean(22.1392314983837,22.1348466308557)
128000.394688135 = (7920 / 22.1370388474829)^2
128000.400661193
-0.000004666437 = % error
1.00002638193018 is a placeholder value not yet scrutinized.
Others might begin there exploring further refinement.
Nominal Simplicity
378 = monster factors sum
496 = s(496) = 378+2*59
490 = 496-6 = s(496)-s(6) — difference of perfect numbers
These notes are not exhaustive, but they should be enough to clue some folks in:
980 = 2*(496-6) = 2*(s(496)-s(6))
980 = 836 + 144 = 836 + 12^2 = 836 + (59^2-196883/59) = 836 + (163-19)
836 = smallest weird untouchable no.
504 = 2*836-4*(163+67+43+19)
418 = 836 / 2
356 = 2 * 178
209 = 836 / 4
178 = baby monster factors sum
100 = sum of Heegner nos. each mod 24
50 = sum of Heegner nos. each mod 19
14C & 10Be periods give us a lesson on modular features of nonlinear stability.
In the days before Seidelmann’s (1992) precision, “2400 year” probably took memorable root from nominal integer origins:
2400.12903225806 = beat(418,356)
1200.06451612903 = beat(209,178)
The nominal cases look quite simple with earned hindsight.
Diagnostics
More diagnostics on 70^2 and M11 appearance in solar system stability. This makes pretty clear the way Jupiter, Saturn and Venus (which is coupled with Earth) shape Earth’s anomalistic year.
From Laskar
183829.787234043 = 1 / s_2 ——- Venus node
173913 = 1 / g_2 ———————- Venus perihelion
68753.3156498674 = 1 / s_3 ——- Earth node
178733.967728589 = harmean(183829.787234043,173913.043478261)
111733.770152599 = beat(178733.967728589,68753.3156498674)
With Seidelmann (1992) sidereal Earth year:
1.00002638395227 = beat(111733.770152599,1.00001743371442)
1.00002638193018 = 365.259636 / 365.25 ——– Earth anomalistic year
0.000000202203 = % error (absolute: 15.9525968265692 seconds per century)
With Seidelmann (1992) sidereal Jupiter-Earth-Venus (JEV) :
22.1348456401858 = axial(111733.770152599,22.1392314983837)
22.1370383520498 = harmean(22.1392314983837,22.1348456401858)
489.999926853495 = 22.1348456401858 * 22.1370383520498
490
-0.000014927858 = % error
128000.400417504 = (7920 / 22.1370383520498)^2
128000.400661193 = 1 / ( –Jside/2 + Sside/2 + Jtrop/2 – Strop/2 )
-0.000000190381 = % error (absolute: -15.0199398937022 seconds per century)
It’s a beautiful sight.
Next, J & S sidereal & tropical with JEV, all from Seidelmann (1992) :
22.1370383309774 = 7920 / √128000.400661193
11.0685191654887 = 22.1370383309774 / 2
22.1348455980494 = beat(22.1392314983837,11.0685191654887)
489.999925454285 = 22.1348455980494 * 22.1370383309774
490
-0.000015213411 = % error
111732.696485953 = beat(22.1392314983837,22.1348455980494)
1.00002638403827 = beat(111732.696485953,1.00001743371442)
1.00002638193018 = 365.259636 / 365.25 ——– Earth anomalistic year
0.000000210803 = % error (absolute: 16.6311136296105 seconds per century)
111733.770152599
111732.696485953
0.000960924313 = % error
68752.9091228114 = axial(178733.967728589,111732.696485953)
68753.3156498674 = 1 / s_3 ———- Earth node
-0.000591283565 = % error
Anyone taking this further, I suggest starting by scrutinizing this value, because I haven’t yet done so:
1.00002638193018 = 365.259636 / 365.25 ——— terrestrial anomalistic year
Wish!own Tune Found Door Well
59 = average(+496, -2-3-5-7-11-13-17-19-23-29-31-41-47-59-71)
31 = average(+2+3+5+7+11+13+17+19+23+29+31+41+47+59+71, -1-2-3-7-11-19-43-67-163)
61.0461538461538 = harmean(1984, 31)
61.0464822565173 = slip(29.4474984673838,11.8626151546089)
-0.000537967711 = % error
Tee Ignore
Look past what tops 1984 “perfect” try gone:
71 = 42+21+8
71 = φφ/(J+S)+1/(J-S)+1/S-1/(J+S)+1/(J-S)-1/J ———————- frequencies
71 = φφ/(J+S)-1/(J+S)+1/(J-S)+1/(J-S)+1/S-1/J
71 = φ/(J+S)+2/(J-S)+1/S-1/J
71 = φ/(1/j+1/s)+2/(1/j-1/s)+s-j
71 = 1.61803398874989/(1/j+1/s)+2/(1/j-1/s)+s-j ———————- periods
s = 29.44889869193547 and j = 11.863057204318362
s = 29.44889869193547 and j = 11.863057204318362
The Miss Sun Link
216 = 378-Φ(163)
216 = (2+3+5+7+11+13+17+19+23+29+31+41+47+59+71)-Φ(163)
271 = 163+Φ(378)
271 = 163+Φ(2+3+5+7+11+13+17+19+23+29+31+41+47+59+71)
2,3,5,7,11,13,17,19,23,29,31,41,47,59,71
Leaving no ambiguity:
Standby for peaceful resolution.
Clarity
In memory of Srinivasa Ramanujan, whose precious life ended at a mysteriously young age:
58 = 19-MOD(19,24)+43-MOD(43,24)+67-MOD(67,24)+163-MOD(163,24)-10-13-18-22-37-58
keywords: 104, 744, Heegner numbers
supplementary to last comment
24 = 1+2+3+7+11
1,2,3,7,11,19,43,67,163
Quick Review of Ramanujan’s 104 with Plato
104.212132286568 = ⌊(e^√10π)^(1/2)⌉^2 – e^√10π
-103.947369666712 = ⌊(e^√13π)^(1/2)⌉^2 – e^√13π
104.007114381762 = ⌊(e^√18π)^(1/2)⌉^2 – e^√18π
104.001742574386 = ⌊(e^√22π)^(1/2)⌉^2 – e^√22π
-103.999977946281 = ⌊(e^√37π)^(1/2)⌉^2 – e^√37π
= round(exp(37^(1/2)*pi())^(1/2),0)^2-exp(37^(1/2)*pi())
104.000034332275 = ⌊(e^√58π)^(1/2)⌉^2 – e^√58π
Plato’s number = 216 balances:
58 = 216-10-13-18-22-37-58
Heegner 744 Review with Plato
316 = 1+2+3+7+11+19+43+67+163
100 = MOD(1,1+2+3+7+11)+MOD(2,1+2+3+7+11)+MOD(3,1+2+3+7+11)+MOD(7,1+2+3+7+11)+MOD(11,1+2+3+7+11)+MOD(19,1+2+3+7+11)+MOD(43,1+2+3+7+11)+MOD(67,1+2+3+7+11)+MOD(163,1+2+3+7+11)
216 = (1+2+3+7+11+19+43+67+163) – ( MOD(1,1+2+3+7+11)+MOD(2,1+2+3+7+11)+MOD(3,1+2+3+7+11)+MOD(7,1+2+3+7+11)+MOD(11,1+2+3+7+11)+MOD(19,1+2+3+7+11)+MOD(43,1+2+3+7+11)+MOD(67,1+2+3+7+11)+MOD(163,1+2+3+7+11) )
216 = (19+43+67+163) – ( MOD(19,1+2+3+7+11)+MOD(43,1+2+3+7+11)+MOD(67,1+2+3+7+11)+MOD(163,1+2+3+7+11) )
-743.777680155239 = round(exp(19^(1/2)*pi())^(1/3),0)^3-exp(19^(1/2)*pi())
-743.999775171279 = round(exp(43^(1/2)*pi())^(1/3),0)^3-exp(43^(1/2)*pi())
-743.999816894531 = round(exp(67^(1/2)*pi())^(1/3),0)^3-exp(67^(1/2)*pi())
744 ~= ⌊ ⌊(e^√163π)^(1/3)⌉^3 – e^√163π ⌉ —- not all calculators can handle this calculation
PV’s ‘number salad’ – Plato’s number – this time has cherries as a main ingredient. TY Paul.
I had no idea what lurked behind it so I looked it up. This here ref is important.
https://www.academia.edu/243917/Four_Mathematical_Texts_from_the_Temple_Library_of_Nippur
Apparently Plato seemed influenced by the sexagesimal counting of the Babylonians. Quote “–what proved to be a very successful numerological-mythological manipulation of a much older Babylonian story”.
And: “It goes without saying that the number 3600 rests upon the Babylonian sexagesimal system.”
Then “— in the life of the universe, in which the world waxes and wanes alternately.” This seems to hark back to the Eddy cycle. Plato was not referring to the last 2kyr but to much earlier times.
Further “expressed in years, 360 days counted per year,” Why? And when “Seven, eleven and thirteen are not divisors of 12,960,000, and to this day are still regarded as unlucky numbers.” Seven times thirteen equals ninty one (7*13=91) is the number of days per season to make a year of 364 days, with 7 days per week. There is other evidence that the Akkadian world had knowledge of -and links to- the megalithic calendar (where the best divisor scale for the quadrant was of 90 divisions).
Further down “We know from Berossus, writing in the third century BC, that a period of 36,000 years, is called the ‘Great Platonic Year’, in early astronomical treatises, and that this was the duration of a Babylonian cycle.” Both Plato and Berossus had tales about changes and disturbances of the heavens that were permanent.
Additional “On the contrary, in Plato’s words: ‘Whenever our guardians promote marriages inopportunely, the offsprings cannot be well provided.’. Since working on this subject I have had occasion to note from ancient graves, and mediaeval dress of both sailors and aristocracy, periodic change in human stature, in line with Eddy cycle.
However there is quite a long time between 4th millennium Akkadians and Plato. Did Plato get the story and the numbers right?
oldmanK, herd insight avalanches Norton called “the voice of God”.
typo above
744 ~= ⌊ ⌊(e^√163π)^(1/3)⌉^3 – e^√163π ⌉
should read
744 ~= | ⌊(e^√163π)^(1/3)⌉^3 – e^√163π |
May peace be with you.
Jupiter-Saturn Axially 323, not 322
One narrative contends solar system order’s based on Lucas numbers.
1.62053454741122 = √(100/(1/11.8626151546089+1/29.4474984673838)/322)
1.61803398874989 = φ
0.154543024356 = % error
The error grows absolutely with scale.
An accurate Lucas model relies on hierarchically nested Lucas & Fibonacci corrections.
Found: neat fractal correction = delight fully unnecessary.
Note nearby. Comparison sharpens further.
1.61650633853492 = √(1/(1/11.8626151546089+1/29.4474984673838)/(1+√5))
1.61803398874989 = φ
-0.094413975578 = % error
1.6180240353733 = √(100/(1/11.8626151546089+1/29.4474984673838)/323)
1.61803398874989 = φ
-0.000615152504 = % error
Key lessun: 323 = 196883-196560 fits ~250 times better than 322.
Ramanujan supposedly had nearly-incomprehensible intuition about numbers (consciously distinct from ‘most logic AI’).
‘Correct’ exploration scales (but not politically) this shape: 262537412640768744.
322.996026177168 = axial(26253741.2640769,323) = 1/(1/323+1/26253741.2640769)
1.61803398862436 = √(100*(1/323+1/26253741.2640769)/(1/11.8626151546089+1/29.4474984673838))
1.61803398874989 = φ
-0.000000007759 = % error
Sporadic simple group math historians may find AImost-lukeUS numbers act sea ally enlightening joviun-fractal hindsight.
8.43006944377466 = φφ*322/100 __________________________ -0.308371015889 = % error
8.47213595499958 = φφ*(1+√5) = 2*φ^3 _____________________ 0.189095708159 = % error
8.45624978366216 = φφ*323/100 ___________________________ 0.001230316360 = % error
8.45614574762977 = φφ/(1/323+1/26253741.2640769)/100 ______ 0.000000015517 = % error
8.4561457463176 = axial(Jupiter period, Saturn period)
“if ITkeepsunreignunloveease going to B___” — Led 22plan
May peace be with you.
Van Hale UN
“but then my homework was never quite like this”
5 is to 12 as
10 is to 24.
ZZ(12)ignore(34)republic(56)’cant’op“11nos.how22US$mmm” ($seenITorwell).
big dipper side wise quest yen-mark
5 = average(163,-67-43-19-11-7-3-2-1)
play dough nos. bog deeper
12 = √(3456+5*5-47*71)
3456 = (59-5)*(59+5)
morals 12-G no. rome mmmore SIM$UN
12 = 71-59 = 59-47
3^3 = 27
4^3 = 64
5^3 = 125; 125+64+27 = 216; 216000 = 125*64*27 —– “memoria” nirvana
6^3 = 216
perfect play “doh!”
12/2 = 6 = s(6)
34 = s(6)+s(28)
56/2 = 28 = s(28)
71-47 = 1+2+3+7+11
orion can reach auriga
(71+5)-(47-5) = 28+6 = 163-67-43-19
May peace be with you. Response[ability] “and also with you.”
“Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” — Gauss
Thanks for drawing our attention back to this post Paul. I don’t understand what your comment is driving at, but Oldbrew and I were just discussing longer term gas giant cycles that appear to be linked to Milankovitch and other important EOP periodicities. More soon.
Optimal Nonlinear Seas Time
TB surely seas each number has to be understood in the context of every other number…
…and maybe only God nos. the full depth available to sea.
Since ‘time limits’ supply ‘no. infinite tee’, Pareto Principled learning can balance insight…
…e.g. net zero:
“The existence of such an integral vector of Lorentzian norm zero relies on the fact that 1^2 + 2^2 + … + 24^2 is a perfect square (in fact 70^2); the number 24 is the only integer bigger than 1 with this property. This was conjectured by Édouard Lucas […]”
Tip for those awakening to the nonlinear nature of our number system:
73 is the lowest prime congruent to 1 mod 24; “24 is 5–hemiperfect“.
31 Lincoln
If f(UN) awoke can “Sporadic and Exceptional” mystery US sly points to 42, 104, & 163.
73 = average(42,104) = average(19,43,67,163)
177 = 104+73 = 323-104-42
177 = 288-111 = 47+59+71
Φ(196883-196560) = Φ(323) = 288
496 = 378+177-59
496 = 378+288-111-59
496 = 378+Φ(323)-111-59
496 = 378+Φ(Φ(1333))-111-59
496 = 378+Φ(196883-196560)-111-59
496 = 4^2 * ( 5^2 + s(5^2) ) = 16*(25+6) = 16*((31))
490 = 4^2 * ( 5^2 + s(5^2) ) – s(5^2) = 16*25 + (16-1)*6
490 = s(4^2*(5^2 + s(5^2))) – s(5^2) = s(496)-s(6) = 496-6
490 = 16*25 + 15*6
490 = 16*25 + 15*6 ————– ((31)) = 16+15
490 = 16*25 + 15*6 ————– ((31)) = 25+6
378 = 2+3+5+7+11+13+17+19+23+29+((31))+41+47+59+71 ——- sum of supersingular primes
316 = 2+3+5+7+11+13+17+19+23+29-((31))+41+47+59+71
A simple polarization isolated strict equality:
-316 = -1-2-3-7-11-19-43-67-163 —————————————————— Heegner nos.
((31)) = average(-316,378) = 16+15 = 25+6 = 496/16
Summary:
31 = 25 + s(25)
31 = ‘kingpin link UN’ 163 to supersingular primes (monster ‘group factors’) of 70^2 seen threw perfect no$. 496 & 6.
31 is the only sporadic simple group prime dividing perfect number 496.
31 = average(-42,104) ————————- completing “Sporadic and Exceptional” in-the-loop
Together let US find peace, prosperity, and tranquility shared equally by all.
Ramanujan’s Perfect Links to Heegner, Monster, & Baby
6=s(6); 28=s(28); 496=s(496) — the 3 lowest perfect numbers
323 = 196883-196560
323 = average(496,28+6+2*58)
323 = average(496,28+6+316-378+178)
19 = (496-28-316)/8 = 163 mod 24 = 67 mod 24 = 43 mod 24 = 19 mod 24
38 = (496-28-316)/4
76 = (496-28-316)/2 = 163 mod 24 + 67 mod 24 + 43 mod 24 + 19 mod 24
152 = 496-28-316
304 = 2*(496-28-316)
608 = 4*(496-28-316) —— s(608) = s(652) = s(4*163) = s(496) = 496
1216 = 8*(496-28-316)
2432 = 16*(496-28-316)
4900 = 70^2
490 = 496-6
49 = 73-24 = 73-11-7-3-2-1
73 = average(496-6,47*71-59*59-378+178)
73 = average(496-6,-28-316) = average(19,43,67,163)
146 = 496-6-28-316 = average(19+43,67+163)
292 = 2*(496-6-28-316) = 19+43+67+163 = 316-11-7-3-2-1
104 = d(4,1/2,58) = -d(2,1/2,37)
216 = average(316,2*58) = Plato’s Number
360 = 323 + s(323) = 323 + 37 = 1 full circle in degrees
‘Sort of’ Organizing 100, 70, & 260 from Heegner, Monster, & Baby
100 = sum of Heegner numbers each mod 24
100 = average(378,-178) = average(316,-2*58)
316 = Heegner number sum
216 = Plato’s Number = average(316,2*58)
116 = 2*58
378 = supersingular prime sum = unique monster factor sum
178 = unique baby monster factor sum
200 = 29+41+59+71 — sum of monster factors that are not baby monster factors
With balanced partitioning:
100 = 29+71
100 = 59+41
It’s not as effortlessly recognizable with Mayan symbolic partititioning:
70 = 29+41 = 378-178-71-59 = 316-2*58-71-59
130 = 59+71 = 378-178-41-29 = 316-2*58-41-29
260 = 59+71 + 378-178-41-29 = 316-2*58-41-29 + 59+71
Monster order:
196883 = 47*59*71 = (59-12)*59*(59+12)
dividve by 59:
3337 = 47*71 = (59-12)*(59+12) = 59*59-12*12
rearrange pieces:
144 = 12*12 = 59*59-47*71
Summary:
In sober second: thought.
Ancients knew “monstrous moonshine” but maybe they simply didn’t call it that.
Imagine there: why’s reaction? “A future tribe calls this mathematical structure ‘baby monster’.”
Insider trade secrets well-protected. Buy awakeUNspeakable name only.
Before creative labeling: ‘just math’. Knew regulation names “The Party” of [re]discovery.
I’ll share a few more examples. That may be enough.
WHO’s Home M[mmm]ore SIM$UN Play “Doh?”
Comm. mist tree lag rains point sh!ape.
216 = 489426/43/7/3/2-2-3-5-7-11-13-17-19-23-29-31-41-47-59-71+(196883-196560)
216 = (163+Φ(2+3+5+7+11+13+17+19+23+29+31+41+47+59+71))-2-3-5-7-11-13-17-19-23-29-31-41-47-59-71+(196883-196560)
“Apart from all other reasons, the parameters of the geoid depend on the distribution of water over the planetary surface.” – Nikolay Sidorenkov
52 = (196883-196560)-(163+Φ(2+3+5+7+11+13+17+19+23+29+31+41+47+59+71))
52 = 323-271 = (196883-196560) – 489426/43/7/3/2
37 = average(-55, 129) = average(-(28^2-27^2), 19+43+67) = average(-(5^2+4^2+3^2+2^2+1^2), 19+43+67)
37 = s(196883-196560)
52 = average(⌊(e^√37π)^(1/1)⌉^1-e^√37π, e^√37π-⌊(e^√37π)^(1/2)⌉^2)
58 = average(1+2+3+7+11+19+43+67,-s(196883-196560))
52 = average(e^√58π-⌊(e^√58π)^(1/1)⌉^1, ⌊(e^√58π)^(1/k)⌉^k-e^√58π) for k=2,4
“Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” — Gauss
180 = 496-1-2-3-7-11-19-43-67-163 = average((196883-196560),s(196883-196560))
360 = 496-1-2-3-7-11-19-43-67-163 + average( (196883-196560),s(196883-196560))
360 Degrees
153 = (52 + 52) + 70^2 / 2^2 / 5^2 = 104+(25^2-24^2)
153 = 37+2*58
153 = 111+42 = 104+49
153 = mod(496-163+average((196883-196560),s(196883-196560)),360)
153 = 496-163+average((196883-196560),37)-360
153 = 1+2+3+7+11+19+43+67
153 = 5^3 + 3^3 + 1^3 ——————————————————– sci11UNs
153 = 496-7^3 ———————————————————– comm. UN IC case sun
153 = mod(average(836,496)-153,360)
153 = average(836,496)-153-360
323 = mod(836-153,360)
323 = 836-153-360
496 = 7^3 + 5^3 + 3^3 + 1^3 —————————— perfect borg cube primes (method of loci)
496 = 7^3 + 1+2+3+7+11+19+43+67
496 = (5^3 + 3^3 + 1^3 + 163) + 180 = 316 + 180
496 = 7^3 + mod(496-163+average((196883-196560),s(196883-196560)),360)
“Win tour” warm up exercise:
271 = 216+(1^2+2^2+3^2+4^2+5^2)
378 = 323+(28^2-27^2) = 323+(27+28)
100 = average(-178,378)
Knew Don wins ‘heaven too’ weight?
…3456 J
in very hint half not iced?
“the sweet test: tap, pull on the tree” – David Wilcox
Everyone’s “obviously” aware?
59 = s((496+28+6)/2)=s((s(496)+s(28)+s(6))/2) —- 3 perfect numbers
59 = s(836/2-67-43-19-11-7-3-2-1)
59 = s(836/2-67-43-19-24)
59 = s(163+67+59-24)
59 = s(163+43+59+0)
59 = s(163+19+59+24)
59 = s(260-19+24)
59 = s(490-163-43-19)
59 = s(490-163-67-19+24)
59 = average(496/2,-260/2)
59 = average(71,47)
260 = average(496,71-47)
378 = average(496,260)
no. doubt…
Earth-Venus Modular Resonance
Sharp readers will notice a key detail left out (already covered above).
_
Note a divergence crystallizing at level 5.
sidereal slip hierarchy review
1.59868955949705 = beat(1.00001743371442,0.615197263396975)
2.67043906295843 = slip(1.00001743371442,0.615197263396975)
8.10187610587681 = slip(2.67043906295843,1.59868955949705)
238.911497097738 = slip(8.10187610587681,2.67043906295843)
489.155247011449 = slip(238.911497097738,8.10187610587681)
tropical slip hierarchy
1.59868953279706 = beat(0.99997862,0.61518257)
2.67016237493693 = slip(0.99997862,0.61518257)
8.09678584788177 = slip(2.67016237493693,1.59868953279706)
250.522048989645 = slip(8.09678584788177,2.67016237493693)
4240.7928948521 = slip(250.522048989645,8.09678584788177)
sidereal with tropical basic review
25757.05496809 = beat(0.615197263396975,0.61518257)
25760.5207691867 = harmean(25763.987503107,25757.05496809)
25763.987503107 = beat(1.00001743371442,0.99997862)
hierarchical extension to modular resonance drift
25770.9237709108 = slip(2.67043906295843,2.67016237493693)
25774.3933055453 = 2 * slip(8.10187610587681,8.09678584788177)
25775.0873245853 = 5 * slip(250.522048989645,238.911497097738)
Queens of the Stone Age — Live in London 2005 “16278263789…“
25672.6551628575 = 2 * slip(4240.7928948521,489.155247011449)
Note the reset after drifting up from ~25760. For comparison:
25259.6956047047 = beat(164.791315640078,163.7232045)
25679.8527338811 = harmean(26114.2236547808,25259.6956047047)
25685 = Laskar’s p
26114.2236547808 = beat(84.016845922161,83.74740682)
Interpretation: Jovian responsibility for EV tropical offset from sidereal.
Probing around the Seidelmann (1992) typo since December 2020 has brought many things swiftly and effortlessly into focus. My estimate based on new scope: it would take at least 70 years (and maybe several lifetimes) to thoroughly explore and report everything noteworthy — hence the sample reporting.
UN Faithful Lyons Rep Reviews Baby Monster Aliquot
‘Plato’s backcountry treasure map’ won bright young clueseaSAMsun.
Homer nos. Plato UN D-air$stand$’better’ then hymn…
216 = 2*φ(Φ(163)) = 378-Φ(163) = ⌊harmean(4270,111)⌉
437 = average(378,496)
4370 = 2*5*average(378,496)
4370 = dimension of minimum faithful representation of baby monster group
4270 = s(4370)
111 = dimension of minimum faithful representation of Lyons group.
Nominal Level 1 Review
4270 ~= beat(Uranus period, Neptune period / 2) = 1/(2N-U)
111 ~= harmean(Uranus period, Neptune period) = 1/(U/2+N/2) where U & N are frequencies
Neptune period ~= 3*axial(4270,111/2)
Uranus period ~= 3*beat(4270,111/4)
Nominal Level 2 Review
144 = 59*59-47*71
84.0174899796991 = 3/(4/144+4/490-1/4270)
164.792485578641 = 3/(2/144+2/490+1/4270)
171.407635533372 = 3/(2/144+2/490-2/4270)
55.6466876971609 = 1/(2/144+2/490+0/4270)
111.293375394322 = 1/(1/144+1/490+0/4270)
111.293375394322 = axial(490,144)
111.292543528394 = 2/(U+N) = harmonic mean = 2*axial period
0.000747458815 = % error
164.792485578641 = 3 * axial(4270,axial(490,144)/2)
164.791315640078 = 1/N
0.000709951588 = % error
84.0174899796991 = 3 * beat(4270,axial(4270,axial(490,144)/4))
84.016845922161 = 1/U
0.000766581429 = % error
171.407635533372 = 3 * beat(axial(4270,axial(490,144)/2),beat(4270,axial(4270,axial(490,144)/4)))
171.406220601552 = 1/(U-N)
0.000825484522 = % error
Level 3 went past nominal (already covered) – but not with Plato.
Thus left exercises 4D-elect ably rural state sov. US.
Urban ‘fact’-check industry’s enslaved buy-master$sov. D-bait. Summary of their 489426 page report: Dem claim 2+2=5. So-called ‘trump supporters’ countered with 2+2=3. Link UN PR Joe actors then left no. doubt with their assurance 2+2=1 but not when 2+2=7.
Link UN Creative Support PR Joe Act: Funding Feminine Rural Arts
Harmoniously a rose peaceful rural math (minus thorn) uplifted past mmmost-outgoing type sov. ‘D-bait chasing’ “political dude-look”.
IC Homer can’t tell a needle of truth from a haystack of lies and $0 needs a peaceful course well-away from master$ov. D-bait.
May peace be with ‘you win the backcountry luke sea!’ – both during and after long-overdue recalibration for true piece weather left, right, home or abroad.
The Free Won: Weather Left or Right ….and Especially Center
Just in time, “the dawn of elect trick banjo tunes” peace by piece write in the middle of some “won freedom”. Note carefully Heegner, Plato, and Sylvester on Pythagorean steps offset at the base by 16 = 31-15.
63 = 16+(24^2-23^2) = 16+(23+24) = 10+13+18+22 = 216-37-2*58
163 = 63+(26^2-24^2) = 63+((24+25)+(25+26)) = 63+100
“Open up Eur. rise….” — Queens of the Stone Age
216 = 163+(27^2-26^2) = 163+(26+27)
216 = 10+13+18+22+37+2*58 = sum of Heegner nos. minus sum of Heegner nos. each mod 24
216 = 6^3 = 3^3+4^3+5^3 = 378-Φ(163)
271 = 216+(28^2-27^2) = 216+(27+28) = 216+(1^2+2^2+3^2+4^2+5^2)
271 = 489426/(2*3*7*43) —— this link gives a fantastic constraint
271 = 163+Φ(378)
100 = average(-178,378) ————– sum of B & M factors
100 = 26^2-24^2 = sum of Heegner numbers each mod 24
This natural framework accounts for Neptune & Uranus relations with Saturn & Jupiter. Here’s the coarse outline:
4270 = s(4370) & 111 give first level nominal impression ——- B & Ly
323 = 196883-196560 ———— M & Leech
37 = s(196883-196560)
52 = average(⌊(e^√37π)^(1/1)⌉^1, -⌊(e^√37π)^(1/2)⌉^2)
271 = 323-52
104 = round(exp(37^(1/2)*pi())^(1/1),0)^1-round(exp(37^(1/2)*pi())^(1/2),0)^2
427 = 323+104 = 4270/5/2 = 316+111 ———– 316 is sum of Heegner nos.
4270 = s(4370)
Overview of more precise scaling initially quantized with Bollinger’s (1952) method:
19 = x mod 24 for x = 19,43,67,163
4370 = (23*5*2)*19
11500 = (23*5)*(5*2)^2
5.5 = 55 / (5*2)
55 = 271-216 = 27+28 = 28^2-27^2 = 1^2+2^2+3^2+4^2+5^2
55 = 163+Φ(378)-378+Φ(163) = 163+108-378+162
111.5 = ⌊4/(U+N)⌉
111.5/(5.5*(J+S)+1/11500) = 1/(U-N) = U & N beat period
(-0.000000053635 = % error with Seidelmann (1992) periods
1/(3*(J+S-1/2/3/7/43/271)/1806/2+S) = 4/(J+S+U+N) = jovian harmonic mean period
0.000000000000 = % error with Seidelmann (1992) periods
Using these J & S estimates to estimate U & N:
84.016845845182
84.016845922161
-0.000000091623 = % error
164.791315879816
164.791315640078
0.000000145480 = % error
171.40622002178
171.406220601552
-0.000000338244 = % error
55.6462717577651
55.6462717641972
-0.000000011559 = % error
“Won the weather ‘gets’ ‘ruff!’ ” — Dove ID Will C(-11)ox (in the ‘year of rome’, UN ‘no?morals’….)
111.29254351553
111.292543528394
-0.000000011559 = % error
Review: 1806 = 2*3*7*43 tied clearly to primary pseudoperfect numbers, Sylvester’s sequence, and greedy Egyptian fractions.
Hindsight: 489426 = 271*(2*3*7*43) = 271*1806
271’s origin is now peacefully clear.
Wishing well-balanced peace, security, and freedom for “won human being” on Earth.
May “the voice of God” sh!ape our intellectual capacity to negotiate a superior course for all.
“Unity Honeymoon” Nears: CR Am. D-UN, a11 ice
“Bizarre how they truncated the SAM cycle, acting as if it is trending and they are trying to control that“
72 = 1*((average(-71,163)^5+47^5)+(19^5+43^5+67^5))^(1/5)
144 = 2*((average(-71,163)^5+47^5)+(19^5+43^5+67^5))^(1/5)
216 = 3*((average(-71,163)^5+47^5)+(19^5+43^5+67^5))^(1/5)
288 = 4*((average(-71,163)^5+47^5)+(19^5+43^5+67^5))^(1/5)
360 = 5*((average(-71,163)^5+47^5)+(19^5+43^5+67^5))^(1/5)
There are 163 reasons to exercise “sober second” thought: n=5.
“[…] unless you have the “correct keys” to sequence the cells DNA – you will not be able to decode the information stored in it […]”
“We’re very excited about this potential…the idea of being able to conceal information in plain sight […]”
490 = Partition Function ( 19 )
“Each step in the story is a work of art,’ Dyson says, “and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.”
“The proof of Rademacher’s formula involves Ford circles, Farey sequences, modular symmetry and the Dedekind eta function.”
partition function divisor sum recursion:
a(n) = (1/n) * Sum_{k=0..n-1} sigma(n-k)*a(k), where sigma(k) is the sum of divisors of k (A000203).
Since 1800: Lunisolar Sci11UNs 66 96 208
Low NY, $0 lure Am. ‘big glue’ IT.
“Whatchya doin’ Homer?” ——– Link
” ‘niffin’ [C]lue ” —————- UN PR Joe Act
WHO lie weed’s lip sly CA11? “Comm. UN IC ace sun break D-own” — Led 22plan
Past climate discourse ineffectively (with words ) failed to relate quantities now tersely D-find.
Tropical
0.0748024157783867 = axial(0.999978614647502,0.0808503463381246)
18.6129709123853 = beat(0.0748024157783867,0.0745030006844627)
8.84735293159855 = beat(0.0754402464065708,0.0748024157783867)
179.333323110834 = slip(18.6129709123853,8.84735293159855)
1879.26478947996 = slip(179.333323110834,5.99685290323073)
491.132481334807 = slip(179.333323110834,16.8627856518082)
IT’s “$sure!” DCoy Homer. “No. win to hole dem – know when to fool dem …when too’UK’awei…&winterUN…” – KR
Anomalistic
0.0748026830551271 = axial(1.00002638193018,0.0808503463381246)
18.5964370693548 = beat(0.0748026830551271,0.0745030006844627)
8.85109350901809 = beat(0.0754402464065708,0.0748026830551271)
16.8899949413115 = beat(18.5964370693548,8.85109350901809)
184.063510192393 = slip(18.5964370693548,8.85109350901809)
600.241396282931 = slip(184.063510192393,5.99685290323073)
1800.72418884878 = slip(184.063510192393,16.8899949413115)
“We11comm.22theJung11″ _UNsunRose$goG-ale meekCRews$soft dr. ink a maze UN for “IT’s human” experimentAI subjects.
Sidereal
0.0748026329881375 = axial(1.00001743371442,0.0808503463381246)
18.5995319875902 = beat(0.0748026329881375,0.0745030006844627)
8.85039257541183 = beat(0.0754402464065708,0.0748026329881375)
16.8848913580487 = beat(18.5995319875902,8.85039257541183)
183.158541510238 = slip(18.5995319875902,8.85039257541183)
400.297181344069 = slip(183.158541510238,5.99685290323073)
1200.8915440322 = slip(183.158541510238,16.8848913580487)
Events can be exactly defined (strict mathematical equality) as deviations from modular central limits. A major multidisciplinary dove ID in superior climate communication thus “flies-free” (naively assume UN no. pole-IT talk Cal. interfere ruins).
Anomalistic-Sidereal
1201.70988258678 = beat(600.241396282931,400.297181344069)
240.145602009621 = axial(600.241396282931,400.297181344069)
5 ~= 5.00408865509281 = 1201.70988258678 / 240.145602009621
3605.12964776031 = beat(1800.72418884878,1200.8915440322)
720.436806028858 = axial(1800.72418884878,1200.8915440322)
5 ~= 5.00408865509282 = 3605.12964776031 / 720.436806028858
360 lovers no. 120’s 3-perfect: σ(120) = 360
Can instantly “The Party mmmyen!” $sagely ‘wise dem’:
0.0745030006844627 = 27.212221 / 365.25 ———- draconic
0.0754402464065708 = 27.55455 / 365.25 ———– anomalistic
0.0808503463381246 = 29.530589 / 365.25 ———- synodic
Peacefully sea weather pieces really fit to gather 22 states no. win sol ID err IT.
Parody in Atlantic ‘Cause zones’
3.90828049899173 = slip(1.00002638193018,0.0754402464065708) ——— sea-hawk key puck
Homer’s DCoy alias$sing “AMO!”
66.0278743780447 = slip(22.1392314983837,3.90828049899173) ———– fict.IT.US$sly!lieUN$
Less extreme missed link con project:
1728 = (3^3+4^3+5^3)*2^3 = 6^3*2^3 = 216*8 = (2*3)^3+(2*4)^3+(2*5)^3 = (2*6)^3
Just weight, eventually EU’11 sea peacefully-blue collar biweekly$secures$financial equal=IT of comm.pose!ITory: all numbers like $1728.
Be[11]owe$EU$IC(AI)
210.705073993676 = beat(96.1613372617316,66.0276945924851) …QBO’s[11]ips$like a11
Response 2 north poll quest yen ABout flywheel winds$: “$suddenly ice-sea!” KTUNsta11
Multidecadal NAO ≠ multidecadal “AMO” (really Hazzard US ‘comm. Bo-nation’ sov. 3-count tease). IT’s “snot on the net” rich herd land$ “UN mail!” IT tory (“doh!”) “river of climate” contro[11]vertsy’s profITable fact chuck king west turn book$$sail$$MET math with myth, weather won inside buy-right or left[node]outside Homer’s inner-circles.
Plato’s at Turn
I’m not giving this an exhaustive treatment — just a “suggest dove won“.
=
“Using an ancient Greek mathematical method described by the philosopher Parmenides, the UCL team not only explained how the cycles for Venus and Saturn were derived but also managed to recover the cycles of all the other planets, where the evidence was missing,”
[…]
[…] the mechanism’s front-dial ring is a 354-day lunar calendar, opposed to a 365-day calendar as previously suggested.
[…]
“Our finding that the Antikythera mechanism did not have a 365-day calendar as previously thought, presents an important and exciting challenge to the research community. We have presented clear data regarding a fundamental attribute of the machine that is verifiably different to what was long held to be true, and this of course leads to a cascade of interesting and exciting consequences […]
=
354 = 2*(47+59+71) ——— top monster factors
Recall that lunar cycles 18.6, 31, 62, 93 fit in 744 (Ramanujan, Heegner).
oldmanK linked from Suggestions-44 to an article on the Antikythera Mechanism (AM).
The authors didn’t note some obvious connections to their gearing summaries — a few examples:
Venus
1.59868955949705 = beat(1.00001743371442,0.615197263396975)
1.59861315657607 = 1/beat(744/20,0.615197263396975)
1.59861591695502 = 462 / 289
Elaboration on the last one:
462 = 496-28-6 = s(496)-s(28)-s(6) —– all perfect numbers
289 = 323-28-6 = (196883-196560)-s(28)-s(6) —- monster, Leech, & perfect nos.
1.59861591695502 = (496-28-6) / (323-28-6)
Jupiter
1.0920796543202 = beat(11.8626151546089,1.00001743371442)
1.0920245398773 = 178 / 163 —- sum of baby monster factors over top Heegner no.
1.09206349206349 = 344 / 315
344 = 378-28-6 = sum of monster factors minus the 2 smallest perfect nos.
315 = sum of Heegner numbers minus 1
Jovian & lunisolar periods can be neatly tied to this scale:
216 = 3^3+4^3+5^3 = 6^3
1728 = 6^3+8^3+10^3 = 12^3
884736 = 48^3+64^3+80^3 = 96^3 ——- JS phi nos. anomalistic-draconic bridge
Recall from hexagonal number (1, 19, 37, & 61) notes above:
427 = (196883-196560) + d(2,1/2,s(196883-196560)) = 323 + 104
360 = (196883-196560) + s(196883-196560)
σ(427) = 496
σ(323) = 360 = Φ(427)
28=(19+37)/2
Now, pay careful attention AM fans.
Plato’s at turn:
3456 = (496-442)*(442-378) ——- 496 is perfect; 378 is monster sum = supersingular prime sum
Trump apparently had lousy “climate advisors”. I suspect trolllionair mi$$guidance directing agents$ provacateurs$ to mmmisunderstand, mmmisrepresent, and mmmisrepresent with “commmandand con troll opportunismmm”. We learned as much about (bad) human nature as numbers last year.
Trump should dove tale peacefully to dominate the middle ground with an urban feminine touch — maybe 100% cure homelessness to demonstrate that strong will can shed “the bad trolllionair mi$$guidance” to do good.
Poor backs are breaking. The rich will have to carry “the climate burden” because they are the ones able to make the sacrifices needed in a fight they champion. Joe Trump and Don Biden work together on “70^2 dove tale”:
Did the AM authors underscore the Plato’s number links? (I only skimmed the paper in a few minutes. Someone else can check…)
Saturn
1.0351711566943 = beat(29.4474984673838,1.00001743371442)
1.03512880562061 = 442 / 427
IT’s a maze UN what “climate advisors” curryUSsly PRmoat for poll IT talk Cal. sci11UNs.
‘Hummmor’well?well?well$0$SIM$UN$says”DO!..ugh!!”
3600 = beat(1800,1200)
720 = axial(1800,1200)
1200 = beat(600,400)
240 = axial(600,400)
73500 = beat(1500,1470)
49000 = beat(1000,980)
1500 = beat(73500,1470)
1000 = beat(49000,980)
1200 = axial(6000,1500)
2400 = harmean(6000,1500)
1500 = beat(6000,1200)
1000 = axial(6000,1200)
6000 Herd Dull$
Let US pray: May peace naturally ‘B with’ EURepeatedly for ‘weather UNnatural’ has heard.
A crude check on implicit conventional assumptions verifies “adjustments” instinctively predicted from 04 pattern before even seeing 13 & 20 ‘up’dates:
Totally remarkable is the sci11UNs weave herd AB out this. Using generalized wavelets that can flex to mimic the methods of others (see note above) there was no problem figuring out what assumptions others (people we trusted…too naively) made implicitly.
Review with augmented hindsight:
Underscores modularity. Rich layers of geometry, circulatory topology, nonlinear aliasing. No point masses (plates, layers, shells, material boundaries, flow guides, differential pulses, etc.) Countless years of work to be done by a lot of careful, patient people (ethically well-paid and free from political harassment). Maybe classy folks all-ready have ‘the trade’ secrets….rightly left a mist eerie – vanishing from “the conscious thought with adjustment”.
PV: your last posted chart -the Bond event- looked familiar. I have superimposed that chart on other data with same chronological datum. See link below.
https://melitamegalithic.wordpress.com/2018/06/29/searching-evidence-3/
The chart -in blue matches/is same as curve ‘B’ in the D’Andrea paper. In latter paper curve ‘C’ shows spikes in between, linking to other events. The dates 5200bce and 3200bce stand out as major events of tectonic nature. It is not just a ‘climate’ affair. What is also clear is the predominance of the 980yr cycle.
Heegner Honeymoonsh…
…shy yen nome aura11a$karing:
18.6129709123853 = 1/LNC
8.84735293159855 = 1/LAC
6.40939079526111 = slip(0.999978614647502,0.0745030006844627/2)
1.18483367770519 = slip(0.499989307323751,0.0745030006844627/2)
2.36966735541038 = slip(0.999978614647502,0.0745030006844627)
D-UK ace sun luke? sea$imply phi e^duke-case UN?
19 MET tune IC = 163 mod 24 = 67 mod 24 = 43 mod 24 = 19 mod 24
76 Cal. lip IC = 163 mod 24 + 67 mod 24 + 43 mod 24 + 19 mod 24
Bold nos. pea & she11 game.
37 = s(196883-196560)
360 = (196883-196560) + s(196883-196560) = 323 + 37
58 = 216-58-37-22-18-13-10 ———– Plato nos. Heegner: 1+2+3+7+11 = 24
179 = 10+13+18+22+58+58 = 216-37 = 323-144 = 360-144-37 = 2*71+37 —- low NY $0 11’air
Note$0[]we11aware phi11oss$offer next ‘tip here’.
95 = 37 + 58
s(95) = 25; s(25) = 6; s(6) = 6 —————————————— perfect
The point’s perfectly balanced partition of ‘one 19’.
3337 = 41*71; s(3337) = 119; s(119) = 25; s(25) = 6 = s(6)
“no. just what you mean” — Queens of the Stone Age “mmm[e^11]CO[2]LA” hivein11unDunZooS
119 = 3456-41*71 = s(41*71) = 95+24
25 = 59*59-3456 = s(3456-41*71); 144 = 3456-41*71 + s(3456-41*71)
whooooosh!………
‘Cause 6000 deep states’ $sovexhaustUN, “free” list in-clued “won” DCoy:
119 = 178-59 = 12^2-5^2 = 19+100 = 43+76 = 67+104/2 = 163-59*59+47*71+100
ban[k]corruptshh!yen no. how the cue test list UN too average (43,67) :
119 = 64+55 = 8^2+1^2+2^2+3^2+4^2+5^2 = 8^2+28^2-27^2
63 = 22+18+13+10 = 163-100
MightBe.[$]sumfearsov.DO$who-thinkIT’sno[w]thing? If $0, let US pray, Be. ‘Cause’:
28 = average(-63,119) = s(28) —————————————————– is perfect
316 = sum of Heegner nos.; 100 = sum of Heegner nos. each mod 24
24 = √σ(σ(σ(σ(σ(σ(59*(163-104)-3456)))))) — “point & sh![IT]” — Queens of the Stone age “Mexicola”
11^2 = 63+58 = 216-95 = 179-58 = (119+178-47-71)-58
121 = average(37,323)-59 = average(-37,323)-59+37
“setting sun deals hands of gold….” — Queens of the Stone Age
σ(63) = 104; σ(58) = 90 = (323+37)/4
194 = σ(63)+σ(58) = 104+90 ———————— “Sporadic and Exceptional” 194
490 = σ(σ(194))-194 = 5/3*σ(194) = 496-6 = s(496)-s(6) —- ( $skips$write 2 the endUN )
73 = average(19,43,67,163) = 194-11^2 ——— the low west prime can grew when 2 “won” mod 24
Owls $sea even better in moonlight:
640 = 744 – 104 ———————- Ramanujan:
18.6 = 744/10/4 ———————- sol. air-seas$time
1860 = σ(σ(216)) = σ(25*24)
884736 = 216*64^2 = (163 – 67)^3
1728 = 27 * 64 ————– note: 27 = 2+3+4+6+12
24 = 64^2 – ⌊(e^√7π)⌉ = d(k,1/2,7) for k=2,3,4,6,12
7 = 323-316 = 196883-196560-163-67-43-19-11-7-3-2-1 = 216-209
“24 is the only integer bigger than 1 with this property“
31 = 1^2+2^2+3^2+4^2+5^2 – 24 = 28^2-27^2 – 24 = average(43,67) – 24
31 = 194-163 = σ(59*(163-104)-3456) = average(19,43) = 496/16 = 744/24
rightly left tale IT tall misstory freeUNwe11$UN
1.18518518518519 = beat(6.4, 1 )
0.0745052386495925 = harmean(1.18518518518519,4/104)
0.0748048814206895 = beat(18.6,0.0745052386495925)
0.0808530870067242 = beat(1,0.0748048814206895)
0.0754427537633223 = beat(8.84736,0.0748048814206895)
True: pack-Cal. tight UN with 0.999978614647502 = 365.242189 / 365.25.
1.18515514607101 = beat(6.4,0.999978614647502) ——– alt. route: 237 = 178+59
27.2124530689878 = 365.25 * 0.0745036360547235
27.3218928734485 = 365.25 * 0.0748032659095099
29.5309517513699 = 365.25 * 0.0808513394972482
27.5548656406489 = 365.25 * 0.0754411105835699
comm. par[]$0[]well:
0.0745030006844627 = 27.212221 / 365.25 ——————– draconic
0.0748024157783867 = 27.3215823630557 / 365.25 ——— tropical
0.0808503463381246 = 29.530589 / 365.25 ——————– synodic
0.0754402464065708 = 27.55455 / 365.25 ———————- anomalisitc
Joe Trump & Don Biden = 70^2 / 10 D-owning “if USA $0”, who knew clear est image UN IT?
490 = “The Party” IT shh!UN [not $0] f(UN) shh!UN $0 v.19
There ‘might B-19 west’ turn mess ages herd around town Be. ‘Cause sov.’ infearmazeUNwarmmmops$0[]well.
typo: “mmmisunderstand, mmmisrepresent, and mmmisrepresent” —- WHO’s DOwing IT?
mmm = mmmisunderstand, mmmisinterpret, and mmmisrepresent —– No. why D-y’a[11]
“B[11]yen US D-air www(eight^2) he$ave UN“ — 11ed22plan B-11ink UN PR Joe Act-Rome: UN no morals
7200 Year Lunisolar
“…and a11$he$aid was true:” — QOTSA “Mexicola”
7200 / preceding:
“…a ‘one door’ that those [funds] don’t point at [clue]” — Queens of thus-tune neige
oldmanK ( March 23, 2021 at 10:51 am ) emphasized 980.
There’s quite a lot more than just 980 to note.
Hear Comms. The…
OB V-yes can’tr[us]t see1eve1800.
6000 / 1stable AB[d]ove:
x y beat axial harmean
14.98886397 9.995978347 4.992885627 24.98484232 12.49242116
4.996287991 3.331992782 1.664295209 8.328280773 4.164140387
14.98886397 4.996287991 9.992575982 19.98515196 9.992575982
14.98886397 3.331992782 11.65687119 18.32085676 9.160428378
9.995978347 4.996287991 4.999690356 14.99226634 7.496133169
9.995978347 3.331992782 6.663985564 13.32797113 6.663985564
“DO’$what’ ever ‘US pie’ D-air can” — Spied Air Man[]
The OBvious Scale$ Odd $now:
x y beat axial harmean
400 600 1200 240 480
1200 1800 3600 720 1440
400 1200 600 300 600
400 1800 514.2857143 327.2727273 654.5454545
600 1200 1200 400 800
600 1800 900 450 900
1470 / preceding:
x y beat axial harmean
3.675 2.45 1.225 6.125 3.0625
1.225 0.816666667 0.408333333 2.041666667 1.020833333
3.675 1.225 2.45 4.9 2.45
3.675 0.816666667 2.858333333 4.491666667 2.245833333
2.45 1.225 1.225 3.675 1.8375
2.45 0.816666667 1.633333333 3.266666667 1.633333333
$aid better with numbers than words: won decade ago.
7200$he$in$rich
7200 / preceding:
Berg-Queens$Sov. West Turn UN IT
24 = √σ(σ(σ(σ(σ(σ(25)))))) — “setting$UNdeal$handsovgold…”
“in NA-world that’
SFu11 of sh!IT:
UN graphs a11ign” — Queens of D-US$Tuneag[//]e
Rome: UN no morals??? ( “IT’s a ‘won’ D-air that…..” )
24 = √σ(σ(σ(σ(σ(σ(5^2)))))) —— “and a11[11]$aidWA$true” — Queen$sov.J-US$Tone-neige “mmm[e/11]CO[2]LA”
Left[node]out
1470 = axial(73500,1500)
980 = axial(49000,1000)
x y beat axial harmean
400 600 1200 240 480
1200 1800 3600 720 1440
400 1200 600 300 600
400 1800 514.2857143 327.2727273 654.5454545
600 1200 1200 400 800
600 1800 900 450 900
6000 / preceding:
x y beat axial harmean
15 10 5 25 12.5
5 3.333333333 1.666666667 8.333333333 4.166666667
15 5 10 20 10
15 3.333333333 11.66666667 18.33333333 9.166666667
10 5 5 15 7.5
10 3.333333333 6.666666667 13.33333333 6.666666667
comparative interpretation:
6000 without 1800
7200 with 1800
Spook EU’11ace $UN:
1. NATO & Russia together$hood’VE D-taled mode11ove DO, Bond, & Heinrich EVents.
2. Neither seas solar cycle length aggregation CR IT eerie awe $0 Φicy UN t(ally) …well.
Lunisolar
16.8627856518082 = beat(18.6129709123853,8.84735293159855)
491.132481334807 = slip(179.333323110834,16.8627856518082)
JEV
491.049532939153 = slip(146.000401793899,44.2784629967674)
146.000401793899 = slip(44.2784629967674,1.59868955949705)
73.0002008969497 = slip(22.1392314983837,0.799344779748523)
5256 = 7920-2400-240-24 ——– M11, E8
5256.63939957554 = slip(44.2784629967674,0.0952207761715205)
Puttin’ dem on defense?…
360 = 37+323 ———————– Monster, Leech
360.180290240748 = slip(146.000401793899,22.1392314983837)
…$sieve tooo gather.
180 = AVERAGE(37,323)
180.090145120374 = slip(73.0002008969497,11.0696157491919)
Lo:LAs[n]iff there’s any miss story left ABout D-meaning of “monster US moon [sh!]ine”.
Can JSUN play a winning hand? No. doubt….(“DON’T$PEAK”….) $0 11ong JSUN! EU failed.
Bon Nos. $Sum Ware in the “Original 39”, USA?
Image: UN IT in spy Eur. ring “Ramanujan’s Encryption” of sol air-seas time order.
39 = MOD(323,71)
39 = 331-292 = 331-163-67-43-19
39 = 354-315 = 354-316+178-47-59-71 = 47+59+71-316+178
178 = baby monster sum
316 = Heegner nos. sum
177 = top monster (supersingular) sum = 47+59+71
292 = top Heegner sum = 19+43+67+163
322.996026127048 = 100*ΦΦ/(1/11.8626151546089+1/29.4474984673838)
26253410.1345891 = 1/(φφ*(1/11.8626151546089+1/29.4474984673838)/100-1/323)
10 = ⌊LOG_10 (262537412640768744 / 26253410.1345891)⌉
26253741 = ⌊262537412640768744 / 10^10⌉
331 = 26253741 – 26253410
331 = 163+67+43+19+MOD(196883-196560,71) —— this is “The Remain D-air”
⌊262537412640768744 / 10^10 – (163+67+43+19 + (196883-196560) mod 71) ⌉
322.996026127027 = axial(26253410,323)
8.45614574631707 = 322.996026127027*φφ/100
8.4561457463176 = axial(29.4474984673838,11.8626151546089)
-0.000000000006 = % error
39 = 64 – 25 = 8^2 – 5^2
39 = (331-323)^2 – (331-2*163)^2
331 = 8 + 323
331 = 5 + 2*163
φ(111) = 8^2 – 5^2 = 39
171.406220509606= 111.5/(5.5*(J+S)+1/11500)
171.406220601552 = beat(164.791315640078,84.016845922161)
-0.000000053642 = % error
The √2 Deep Hole
“dr. 11!” led US astray…
“[…] the covering radius of the Leech lattice is √2; in other words, if we put a closed ball of this radius around each lattice point, then these just cover Euclidean space. The points at distance at least √2 from all lattice points are called the deep holes of the Leech lattice. There are 23 orbits of them […]”
Review: Lunisolar deep hole was drilled with √2, φ & 96^3 on Suggestions-43. “First order” simplifications appear above. Weave time to explicitly cover ~0% of the SIM MET trees dial UN in the (no longer mysteriously-named) monstrous moonshine.
“Sea Buy”$peakTrumPReview: Vasiliev Dergachev 2002 14C Bispectrum
Recall amiss story US “curious” IT‘$noted earlier.
V&D suggested 2400 splits 710 into 570 & 940…
547.909967845659 = axial(2400,710)
1008.28402366864 = beat(2400,710)
…whereas 2900’s the number that does that.
570.360110803324 = axial(2900,710)
940.182648401826 = beat(2900,710)
We looked at (19 mod 24) JS slip cycle (can D)-dates (in pari$11ol). One‘$now restated 4 comm. Paris$UN with 11’UN-US$0lure $he$aveUN (note well what’$PRint’don back Sov. $19 bill) :
574.604095118134 = axial(2959.13381403679,713.067400275117)
ThePRsentacesun$notPRoofUS$UNa11″enough!”tooSIMbilllies “the baby monster” (wtf did you think was going on?…lol)
939.447668560927 = beat(2959.13381403679,713.067400275117) — compare what follow$
“Le Ruse Sea 940” B-est 2 [Mute]
Y(e/11) “UN$careSFull!”
too seas aqua [11]INO:
what $ain’t N(IC)
Auriga “$no. don!e”
Pole IT test isn’t $0 SIM pully “ad just in can’t afford DO tool $saveUNgrrace:
5.99685290323073 = beat(0.0754402464065708,0.0745030006844627)
diversity:
1986.46983643213 = slip(5.99685290323073,0.999978614647502)
1844.25352645575 = slip(5.99685290323073,1.00001743371442)
1814.31362251033 = slip(5.99685290323073,1.00002638193018)
unity:
1878.75398044817 = harmean; 939.376990224084 = harmean / 2
1878.75398044786 = slip(5.99685290323073,1.00000747633418)
Hole “D-UN there” cards ever $0 Close 2 Ratchet most in$π-red D-est$ware “frontline con” text.
2.99842645161536 = beat(0.0377201232032854,0.0372515003422313)
diversity:
993.234918216065 = slip(2.99842645161536,0.499989307323751)
922.126763227873 = slip(2.99842645161536,0.500008716857211)
907.156811255165 = slip(2.99842645161536,0.500013190965092)
unity:
939.376990224084 = harmean
939.376990223931 = slip(2.99842645161536,0.500003738167089) —– ($alt.turn net$CR(US|e) )
“What ever!est π-DO Or[We11]Can ” — spied air-mmman[EU ] will
1879.26478947996 = slip(179.333323110834,5.99685290323073)
1879.26478947996 / 2 = 939.63239473998
PRscript$UN “D-note’$in turn a11′ imageUNair rise“:
0.0374012078891933 = axial(0.499989307323751,0.0404251731690623)
9.30648545619264 = beat(0.0374012078891933,0.0372515003422313)
4.42367646579927 = beat(0.0377201232032854,0.0374012078891933)
2.99842645161536 = axial(9.30648545619264,4.42367646579927)
89.6666615554168 = slip(9.30648545619264,4.42367646579927)
939.63239473998 = slip(89.6666615554168,2.99842645161536) ——– (Homer no$. )
B[11]art 11’UN-US $0 lure “$19B[11]lies” con-f(US)yen mag (net IC) i.e.: luke sea
tames comm. red$ain’t no. baby monster play pen (Merge: 44sea28 Be. low ).
NearAD[11]ove tale$now EU-wood B-leave[?] IT’s D-liberate con f(use)UNframmeUN[mic:CRowe$]offline[sci11UNs].
WHO’s $19 UN bill “luck CA11 Cairo” PR actors f(air) 43(sea)70 what’s next “in ever give UN $sue west turn$ can AI”? D-ON lie pla[y]TO no. $can[D]a11ove green NAtoo:
Which Typo
“Suggestion: Study Schneider’s delightful proof and strive to understand why replacing φ (which gives e) with 240 [typo] gives Earth’s sidereal orbital period so precisely.”
73 = average(19,43,67,163) = average(104,42) = 194-11^2
11^2 = 63+58
194 = σ(63)+σ(58)
63 = 22+18+13+10 = 163-100; 100 = sum of Heegner nos. each mod 24 = 1+2+3+7+11+19+19+19+19
58 = 216-58-37-22-18-13-10
490 = σ(σ(194))-194 = 5/3*σ(194) = 496-6 = s(496)-s(6) = partition function of 19
4900 = 70^2 = 24^2+23^2+22^2+…+3^2+2^2+1^2
95 = 37+58
s(95) = 25; s(25) = 6
σ(95) = 120; σ(120) = 360 = (196883-196560) + s(196883-196560) = 323 + 37
265 = 360 – 95 = 323 – 58; s(265) = 59
s(120) = 240 = 216 + √σ(σ(σ(s(47+59+71)))) = 216 + √σ(σ(σ(63)))
s(240) = 504 = 744 – 240; σ(240) = 744 = 504 + 240
“That’s 0.597351554461056 seconds per century.”
σ(63) = 104; σ(104) = 210 = 7# = 7*5*3*2*1
σ(210) = 576 = 24^2 = 4*144 = 4*(59*59-47*71)
MonsterUSAuthorIT
Review
4428 = 4370 + 58 = 4370+216-58-37-22-18-13-10
37 = s(196883-196560)
323 = (196883-196560)
360 = (196883-196560)+s(196883-196560) = 323 + 37 = σ(196883–196560) = σ(323)
104 = d(2,1/2,37) = d(4,1/2,58) = d(2,1/2,58)
4428 = 8128 – 3700; 8128 = s(8128) —- perfect no.
104 = average(-7920,8128); 7920 = M11 order
Crude
29.4541077985279 = ΦΦbeat(104,44.28)
11.8626876026982 = ΦΦaxial(104,44.28)
323 ~= 100ΦΦΦΦ/(1/beat(104,44.28)+1/axial(104,44.28))
22.14 = 1/(1/beat(104,44.28)+1/axial(104,44.28)) = 44.28 / 2
52 = 1/(1/beat(104,44.28)-1/axial(104,44.28)) = 104 / 2
Refined
298 = σ(323)-104+42 = 360-104+42 = 19+43+67+163+216-58-37-22-18-13-10 – 52
240 = 496-256 = σ(323+104)-σ(323)+104 = 19+43+67+163 – 52
58 = 298-240 = 216-58-37-22-18-13-10
58 = 100 – 42 = sum of Heegner nos. each mod 24 – 42 = 19+19+19+19+11+7+3+2+1 – 42
58 = 104-((average(59*59,-47*71))^5-67^5-43^5-19^5-47^5)^(1/5)
58 = 104-average(-71,163)
Lunisolar “Spider Web$” N0! D-ou[B]t
490.178476738918 = √(400.297181344069*600.241396282931) —- geometric mean
22.1399746327524 = √490.178476738918
4427.99492655047 = 200 * 22.1399746327524
4428 = ⌊4427.99492655047⌉
1470.53543021674 = √(1200.8915440322*1800.72418884878) ——— geomean
490.178476738915 = 1470.53543021674 / 3
22.1399746327523 = √490.178476738915
4427.99492655046 = 200 * 22.1399746327523
4428 = ⌊4427.99492655046⌉
B: 4370 = 4428 – 58
Play DO$19 bill * 4 UN IT
164.791315640078 +
84.016845922161 +
29.4474984673838 +
11.8626151546089 +
1.88084761346252 =
291.999122797694 ——————– no.%-error
– 1.88084761346252 +
1.00001743371442 +
0.615197263396975 +
0.240846697327135 =
291.97433657867 ———————- $0 11air $seas$ time$ alter-net coarse
292 = 163 + 67 + 43 + 19
292 = 163mod24 + 67mod24 + 43mod24 + 19mod24 + 216 = 19+19+19+19+216 = 76+216
Jupiter-Saturn Offset$
600 = σ(216)
1800 = σ(1691) = σ(760)
400 = s(2401) = s(496+28) = s(836-42); σ(σ(400)) = 993 = 1986/2
1200 = σ(378+178-100) = 744+378+178-100
744 = s(378+178-100) = 1200-378-178+100
perfect recall: 28 = s(28); 836 = lowest weird untouchable no.
378 = sum of supersingular primes = monster factors sum
178 = baby monster (B) factors sum
100 = sum of each Heegner no. mod 24
Monster “US$ Heegner” — Some Loop Hale$
73 = s(378-43) = s(s(993)) = s(s(1986/2)) = average(19,43,67,163) = average(42,104)
49 = s(378-163) = s(378-19-59*59+47*71) = 7^2 = 73-11-7-3-2-1 = 73 – 24
95 = s(378+67) = 37+58 = 216-58-22-18-13-10
multiperfect recall s(95) = 25; s(25) = 6 = s(6); σ(95) = 120; σ(120) = 360
360 = σ(378-19) = σ(378-163+59*59-47*71)
7 = √s(378-163) = √s(378-19-59*59+47*71) = 323-316 = 196883-196560-(Heegner sum)
Wood $UN B-ring perfect lunisolar record$ :
400 = σ(496-s(378-163)-104)
600 = σ(496-s(378-163))
1200 = σ(2*(496-s(378-163)-104))
1800 = σ(2*(496-s(378-163)))
Aim$Bond DOn’t $peak: average sea cure IT count$sol node 13*7.2=93.6out “Sporadic & Exceptional” McKay & He in rich.
Semi-Perfect “Bei. B No$.” 940
σ(1879) = 1880
σ(1880) = 4320 —- Plato “$wing from the Chand11ier“ — C!A
216 = σ(average(-178,496))
4320 = average(4370,4270) = average(4370,s(4370))
2 is 3-hemiperfect; 24 is 5-hemiperfect
4320 = lowest 7-hemiperfect no.
7 = 323-316 = 196883-196560-163-67-43-19-11-7-3-2-1
“There’s more to the picture than meets the [sky]” — Neil Young
Ally Caught Some Chande/11ier$wingUN
DCice$sovCO[2]UN[T]sol 13 * 7200 with average in form ace yen wharf…..
4370 = 4370
s(4370) = 4270
s(4270) = 4658
s(4658) = 2794
s(2794) = 1814
s(1814) = 910
s(910) = 1106
s(1106) = 814
s(814) = 554
s(554) = 280
s(280) = 440
s(440) = 640
s(640) = 890
s(890) = 730
s(730) = 602
s(602) = 454
s(454) = 230
s(230) = 202
s(202) = 104
s(104) = 106
s(106) = 56
s(56) = 64
s(64) = 63
s(63) = 41
s(41) = 1
s(1) = 0
sum = 26193
433 = 26193 – 25760
432 = average(4370,s(4370)) / √(4370-s(4370))
25760 = ⌊25760.434943341⌉ = ⌊26 * beat(1.18483367770519,1.18341848397804)⌉
25760 = ⌊25760.4349434063⌉ = ⌊beat(1.00001743371442,0.999978614647502)⌉
Tropical (semi-annual & nodes (semi-draconic))
1.18483367770519 = slip(0.499989307323751,0.0372515003422313)
433 = ⌊432.76050078182⌉ = ⌊365.25 * 1.18483367770519⌉
Sidereal
1.18341848397804 = slip(0.500008716857211,0.0372515003422313)
432 = ⌊432.243601272978⌉ = ⌊365.25 * 1.18341848397804⌉
“[D-air] $’more [’22] the pick t[ru]e than meets the [sky]…” — Neil Young
QBO equivalent:
865.521001563641 = 365.25 * 2.36966735541038
866 = 2*(26193-25760)
864.487202545956 = 365.25 * 2.36683696795607
864 = (4370+s(4370)) / √(4370-s(4370))
….. “hey, hey, My My …” — NY …..
…..air is sol T.
“hey, hey, My My …”
There’s more to the picture,
Than meets the eye.
Not a fan of Neil Young’s politics myself, but I can actually play this song on my guitar!
Introduction: Tip of Lunisolar Confounding Iceberg
6.07098113178251 = beat(491.132481334807,5.99685290323073)
72.9984824166731 = slip(19.8650360864628,6.07098113178251)
208.899107282611 = slip(72.9984824166731,9.93251804323141)
208.886643858908 = JS slip cycle
Nominal comparisons:
6.07438016528926 = beat(490,6)
73.5 ~= 73.4929686622967 = slip(19.8650360864628,6.07438016528926)
210 = slip(73.5,10)
6.07420653406045 = beat(491.132481334807,6)
73 ~= 73.5 ~= 73.4675602385511 = slip(19.8650360864628,6.07420653406045)
6.07115457866136 = beat(490,5.99685290323073)
73 ~= 73.0235673639375 = slip(19.8650360864628,6.07115457866136)
209 ~= 208.812149943122 = slip(73,9.93251804323141)
Review comparatively:
6.01674004100847 = beat(1814.31362251033,5.99685290323073)
65.8594372352303 = slip(19.8650360864628,6.01674004100847)
50.0701067244605 = slip(19.8650360864628,3.00837002050424)
96.1935351354127 = slip(19.8650360864628,1.50418501025212)
208.849200346502 = slip(65.8594372352303,19.8650360864628)
178.330515859016 = slip(65.8594372352303,9.93251804323141)
503.940520714068 = beat(356.661031718033,208.849200346502)
0 slip at:
491.122639395668
1815.25586361718
744’s “Only Won” Seas$[360]UN
738 = -d(3,1/2,11) —– 39 no. mystery “well B low”
745 = d(3,1/2,16) —— too dem-miss[TX]tify
—————————————–
744 = d(3,1/2,28) —- perfect no. (s^1)(28) tie one-and-only-won anti-aliquot (s^(-1))(28)
—————————————–
744 = -d(3,1/2, 19)
744 = -d(3,1/2,43)
744 = -d(3,1/2,67)
744 = -d(3,1/2,163)
Φ-command air-laps past.
Biden, “Don seas trees”. “UN Trump”, Joe putters $at turn quest yen:
19.8650360864628 = beat(29.4474984673838,11.8626151546089) — sidereal
19.8588720868409 = beat(29.42351935,11.85652502) ————- tropical
64000.2003306175 = beat(19.8650360864628,19.8588720868409)
Overseas navy: We blue secure IT.
640=744-104
320 = average(744,-104)
320=19+43+67+163+28
360 = σ(19+43+67+163+28-378+178)
“can keep EU-WA11 2 mmm-ice[sh]elf; DO EU wanna B free? ‘$0 free’ Eur. S[H]elf” — Queen: $solve THUS tune-neige
Earth’s Most Prime AI-insight$240
1.00001743371442 = 1/E
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
1.00001745798498 = average(-178,378)*2.92005097731613/(19+43+67+163)
Seed the algorithm as follows to reach all primes up to exactly 19 and no further:
2.92005090699884 = (19+43+67+163)/average(-178,378)*(1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
2.92005090644612 = 1.00001743371442*(19+43+67+163)/average(-178,378)
Repeating as many times as necessary:
● “Suggestion: Study Schneider’s delightful proof and strive to understand why replacing φ (which gives e) with 240 [typo] gives Earth’s sidereal orbital period so precisely.”
● “That’s 0.597351554461056 seconds per century.”
Janko: “Monster tie” when Lyons “the original 39” Leech
70 = √(24^2+23^2+22^2+…+3^2+2^2+1^2)
71 = Δ(111)
72 = average(71,73) = average(59*59,-47*71) = Φ(111) = Φ(73)
73 = average(42,104) = average(19,43,67,163) = φ(1333)
5256 = 72*73 = 7920-2400-240-24
144 = 2*72 = 2*Φ(111) = 288/2 = Φ(1260)/2
144 = 12^2 = 59*59 – 47*71 = 71 + 73
144 = average(-(71^2),73^2) = average(-(Δ(111)^2),φ(1333)^2)
144*4 = 576 = 24^2 = 70^2 – (23^2+22^2+21^2-…+3^2+2^1+1^1)
288 = 73^2-71^2 = φ(1333)^2-Δ(111)^2 = Φ(323) = 2*Φ(111) = Φ(Φ(1333))
φ(1333) = 73
Φ(1333) = 1260
Φ(1260) = 288 = 4*72 = 4*Φ(111) = Φ(Φ(1333))
Φ(111) = 72
φ(111) = 39
111 “snow done” miss story lie UN$he ignore
-378 = -2-3-5-7-11-13-17-19-23-29-31-41-47-59-71
59 = average(-378,496)
111 = 378+Φ(196883-196560)-496-59
111 = Φ(323)-(47+59+71) = Φ(196883-196560)-(47+59+71)
163 = 2+3+5+7+11+31+37+67 = Ly factor sum of Lyons group
316 = Heegner number sum
111 = 163 – 104/2 = 316-67-43-19-11-7-3-2-1-104/2
111 = 153 – 42 = 316-163-42
Δ(111) = 71 = top monster factor[well]
Care Actor$[194]Table
“The character table of the monster, a 194-by-194 array […]”
Review: 360 = 323+37. Study the squares around the top of the monster.
323 = 196883-196560
37 = s(323) = average(-104,178); 104 = -d(2,1/2,37)
71^2 = 73^2 – Φ(323)
71^2 = 70^2 + 141 —————————– 141 ± 37
71^2 = 70^2 + 378-178-59
141 = average(104,178) = average(42,240) = 3*47 = 104+37 = 178-37
141 = average(19+43+67,1+2+3+7+11+19+43+67) = average(129,153)
141 = 378-178-59 = 200-59
292 = 104+178+163-153; average(104,178,163,-153) = 73
McKay & He left 104 & 42 a mystery. “can go with the flow: DO EU B-leave IT in Eur. head? IT’s$not safe 2 play along“ — QOTSA
May peace be with you.
6000 Sense 1800 Janko
X: 8, 12, 20, 44, 68, 164 = 4*B —————- caution: mixing symbols here — sea B low
Y: 8, 12, 20, 20, 20, 20 = X mod 24 —— “setting $UN deals[]and$sov. goaled” — qotsa
Z: 19, 19, 19, 19 = I mod 24
sums
X: x = 316
Y: y = 100 = average(378,-178)
Z: z = 76
Some “won” nos. EU[]R lucky 2 remember: 240 ± 76; σ(240) = 744
σ(745) = 900
R(3,1/2,16) = 744.68686334684 = ⌊(e^√16π)^(1/3)⌉^3 – e^√16π
745 = d(3,1/2,16) = R(3,1/2,16) – R(1,1/2,16)
Φ(1333) = 1260; φ(1333) = 73 = average(19,43,67,163)
1333 = Φ(1333) + φ(1333) = 1260 + 73
“no. just what EU mean” — qotsa
R(3,1/2,11) = -738.143065592427 = ⌊(e^√11π)^(1/3)⌉^3 – e^√11π
738 = -d(3,1/2,11) = R(1,1/2,11) – R(3,1/2,11)
4368 = 42*104 = σ(σ(738)) = σ(1638) = σ(1260) = σ(Φ(1333)) = σ(1500)
1638 = 42*39 = σ(738)
The Original 39 Peace
keeper $cantrust:
240 = 61^2 – 59^2 ————————— (key to differentiating “982” from 980)
240 = mod(1728,744) ———————- “and all [11]’$aid WA$[SH!]true” — qotsa
61 = 100 – 39
100 = average(378,-178)
378 = 2+3+5+7+11+13+17+19+23+29+31+41+47+59+71
178 = 2+3+5+7+11+13+17+19+23+31+47
200 = 378 – 178
Honeymoonshine: Baby knows some luck[]key.
194 = 378 – 178 – 6 = 200 – d
A: 1, 2, 3, 7, 11, 19, 43, 67, 163 = Heegner nos.
B: 2, 3, 5, 11, 17, 41 = Euler’s “lucky” nos.
C: 7, 11, 19, 43, 67, 163 = 4*B-1
D: 1, 2, 3 = A not in C
E: 1, 2, 3, 7, 11, 19, 19, 19, 19 = A mod 24
F: 2, 3, 5, 11, 17, 17 = B mod 24
G: 7, 11, 19, 19, 19, 19 = C mod 24
H: 1, 2, 3, 7, 11 = subset of A summing to 24
I: 19, 43, 67, 163 = subset of A not in H = subset of A with mod 24 = 19 (see E)
J: 163 = top Heegner no.
K: 1, 2, 3, 7, 11, 19, 43, 67 = Heegner nos. non[$]top
sums
A: a = 316
B: b = 79
C: c = 310
D: d = 6 = 1 + 2 + 3 = 3 + 2 + 1 ——— “Sporadic & Exceptional” — McKay & He (2015)
E: e = 100
F: f = 55
G: g = 94
H: h = 24
I: i = 292
J: j = 163
K: k = 153
C!A“$wing from the ChanDO[!]11ears”:
316 = a = j+k = 163+153 = 4*b = 4*79
158 = a/2 = 316/2 = average(j,k) = average(163,153) = 2*b = 2*79
158 = 58+37+22+18+13+10 = 104-yielding levels sum = 100+58 = 216-58
79 = a/4 = 316/4 = average(j,k)/2 = average(163,153)/2 = b = 79
42 = 100-58 = 200-158 — 744 D-tales+11+16 above 320 note added symmetry of 738 & 745.
365 = c+f = 310+55
194 = 100+94 = e+g = 100+70+24 = 200-6
216 = 310-94 = c-g = 316-100 = a-e = 158+58
271 = 216+55 = c-g+f = a-e+f = c-f+h = 310 – 39
recall:
55 = 1^2+2^2+3^2+4^2+5^2 = 28^2-27^2 fits inside of:
70 = √(24^2+23^2+22^2+…+5^2+4^2+3^2+2^2+1^2)
194 = 24 + 70 + 100
“24 is the only integer bigger than 1 with this property“
194 = 24+√(24^2+23^2+22^2+…+5^2+4^2+3^2+2^2+1^2)+4370-s(4370)
194 = 378-178-3-2-1 where 3, 2, 1 are from set D ….left over from EU1ure$1o[]ckey$heignore[$0 B IT!]union
39 = g-f = 94-55 = 24+70-55 —- well-balanced lunisolar SIM MET tree
39 = 24+√(24^2+23^2+22^2+…+5^2+4^2+3^2+2^2+1^2)-(1^2+2^2+3^2+4^2+5^2)
No matter your nation, race, and politics: may peace be with you.
Crude Lunisolar Summary
Recall:
73500 = beat(1500,1470)
Tie $USqotsawan: N/A
Norton called it “the voice of God” because once well-placed, buckets overflow with numeric torrent sov. insight. Revealing terse classification theorem proof can$save US from pick UN ~0% of the numeric ∞ lifetimes afford for $sharing.
“another heart has made the trade
DOn’t understand how a heart is a spade?
94 = 55+Δ(55) = (1^2+2^2+3^2+4^2+5^2)+Δ(1^2+2^2+3^2+4^2+5^2) = 55+39 = 24+70
“sum how: the vital connection is made” — Elastica
24 & 5 mark the partition boundaries:
39 = 24+√(24^2+23^2+22^2+…+5^2+4^2+3^2+2^2+1^2)-(1^2+2^2+3^2+4^2+5^2)
39 = 64 – 25 = Δ(240)-Δ(70) = δ(δ(194)) = 58-19 = ΣΦ(70) —– E8, Leech, monster character table
We no. WHO take$scare of public awareness$sov. IT:
58 = 39+19 = 216-58-37-22-18-13-10
Adds up to “better learn to know good” from “bad rich” symbols printed on ‘the back sov.’ $19 bills (D-liberate mmm = misunderstanding, misinterpretation, misrepresentation is how sum AI is programmed too give add vice to ‘IT’s lead D-airs$’).
58±5 = (53,63)
153 = 1+2+3+7+11+19+43+67
163 = 163
100 = 1+2+3+7+11+19+19+19+19
53 = 153-100
63 = 163-100
23 = Δ(39) = Δ(Δ(240)-Δ(70)) = Δ(δ(δ(194))) = Δ(ΣΦ(70))
top factor of dimension of minimum faithful representation of baby monster
$0 Homer knew world nos. order SIM bill US$ m[$]m in can’t talk key….
Cure US IT at what cost? $19 bill yen
elastica: “another heart has made the grade
understand how the last card is played”
146 = 70+19+19+19+19
152 = 70+19+19+19+19+3+2+1
298 = 70+19+19+19+19+70+19+19+19+19+3+2+1
194 = 24+70+19+19+19+19+24
104 = 70+19+19+19+19+3+2+1-24-24
24 = 1+2+3+7+11
Timely review of what’s now ancient history:
“DOn’t USteal my$UNshine“ — D-light
298±58:
298 = average(240,2*178)
298±53:
298 = average(378-178+1+2+3+7+11+19+43+67,ΣΦ(163))
Top Peacekeepers no. the importance of math.
24 = δ(δ(76)) = δ(δ(δ(δ(292))))
1+2+3+7+11 = δ(δ(19+19+19+19)) = δ(δ(δ(δ(19+43+67+163))))
Miss story left Schneider & He to right terse proof of classification theorem = great test achievement in human history.
IT‘s Read Word Air DO We
“The study of psychills reveal$too US R ‘rig no. rants’ and is the[T]air4 very D-US$tar ban for ‘peep hill WHO’sideasar CR US DO 11 i.e. $D.”
IT’$0 whirled wild deep state of ‘math We no.’ $0[]well now:
4428 = 4370 + 19 + 39 = 4370+216-58-37-22-18-13-10
for terrestrial tropical year length = 0.999978614647502 = 365.242189 / 365.25 and
11.8626151546089 = 1/J
29.4474984673838 = 1/S
1368.23312313647 = (4370-s(4370))φ/(J+S)
2999.612648502 = beat(1368.23312313647,939.63239473998)
2736.46624627294 = (378-178)φ/(J+S)
5999.22529700399 = beat(2736.46624627294,1879.26478947996)
comm. paris $UN for terrestrial tropical year length = 0.99997862 —— same comparison repeated
3008.30696170427 = beat(1368.23312313647,940.483841064968) —— in examples below
6016.61392340853 = beat(2736.46624627294,1880.96768212994)
no.mmmUNa11i.e.6000 “mmmUN$tar$inD[$]pairUS$sol” – qotsa
1368.24995673243 = (196883-196560)φφφ
2736.49991346486 = 2*323*φφφ
2999.5317445019 = beat(1368.24995673243,939.63239473998)
3008.22558803381 = beat(1368.24995673243,940.483841064968)
5999.0634890038 = beat(2736.49991346486,1879.26478947996)
6016.45117606762 = beat(2736.49991346486,1880.96768212994)
2736.65450218453 = 4428Φ
1368.32725109227 = 4428Φ/2
2999.16034139499 = (1368.32725109227)*(939.63239473998) / (1368.32725109227 – 939.63239473998)
3007.8520289912 = (1368.32725109227)*(940.483841064968) / (1368.32725109227 – 940.483841064968)
5998.32068278998 = (2736.65450218453)*(1879.26478947996) / (2736.65450218453 – 1879.26478947996)
6015.7040579824 = (2736.65450218453)*(1880.96768212994) / (2736.65450218453 – 1880.96768212994)
V&D “DO[!]n’t$peak” – no. doubt
1000 = 400+600 — ‘no. naive’ 11inear addIT sh!UNfalsely assume’n’point masses$swear
3000 = 1200+1800 — true material bound eerie conduce$yens$ are [not!] UNreal
using JS tropical-sidereal cycle previously derived (based on 128000 year cycle, M11, & Leech) :
2999.38954661383 = beat(1368.2795468771,939.63239473998)
3008.08256467804 = beat(1368.2795468771,940.483841064968)
5998.77909322766 = beat(2736.5590937542,1879.26478947996)
6016.16512935608 = beat(2736.5590937542,1880.96768212994)
from JEV (Jupiter-Earth-Venus) :
2999.38854614549 = beat(1368.27975508034,939.63239473998)
3008.08155840206 = beat(1368.27975508034,940.483841064968)
5998.77709229099 = beat(2736.55951016068,1879.26478947996)
6016.16311680413 = beat(2736.55951016068,1880.96768212994)
with 22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
2999.38854363134 = beat(1368.27975560355,939.63239473998)
3008.08155587331 = beat(1368.27975560355,940.483841064968)
5998.77708726268 = beat(2736.5595112071,1879.26478947996)
6016.16311174663 = beat(2736.5595112071,1880.96768212994)
Conclusion: At the peak of the Korean War Bollinger (1952) directed modular geometric attention to minimal destructive resonance, using public navy figures that were imprecise at the time compared with Mayan & Seidelmann’s (1992) figures.
‘Free’ Win DO[!]$95 for Home More SIM $UN in [$BRI] ngfield
“Can EU keep up? Bei. B-buoy…” — B-UN$Sea
Geopolitical Summary: Conventional mainstream overlooked symmetry in boundary conditions.
47 = Σφ(323)
Monster character table “start” B11inkUN immediate D-mention $sov. top monster factor[well] :
Δ(194) = 95
71 = ΣΔ(95) = Δ(95) = Δ(Δ(194)) = ΣΔ(Δ(194))
95 winDowe$0rt of remindUN US$sov.what$scenes$past:
378 = sum of monster factors = s(s(354)) = s(s(2*(47+59+71)))
354 = 360-6 = σ(σ(95))-s(s(95)) = 2*(47+59+71)
95 = 37+58
63 = 10+13+18+22 = s(47+59+71) = s(836-19) = 163-100
158 = 95+63 = average(1+2+3+7+11+19+43+67,163)
153 = 216-s(47+59+71) = 1+2+3+7+11+19+43+67
111 = ΣΦ(95) = dimension of minimum faithful representation of Lyons group
Φ(95) = average(59*59,-47*71) = 72
Σφ(95) = Φ(Φ(95)) = 24 = Φ(72) = 1+2+3+7+11
φ(95) = 23 = top factor of dimension of minimum faithful representation of baby monster
Carefully review ordered sums of primes up to 23, noting well-ordered ties with Heegner nos.:
42 = (23+19) = 378-178-average(1+2+3+7+11+19+43+67,163)
53 = (17+13+11+7+5) = 1+2+3+7+11+19+43+67-(1+2+3+7+11+19+19+19+19)
58 = (17+13+11+7+5+3+2) = average(1+2+3+7+11+19+43+67,163)-(1+2+3+7+11+19+19+19+19)
95 = (23+19)+(17+13+11+7+5) = 1+2+3+7+11+19+19+19+19-average(-1-2-3-7-11-19-43-67,163)
100 = (23+19)+(17+13+11+7+5+3+2) = 1+2+3+7+11+19+19+19+19
“Given 163, the Mertens function returns 0, it is the fourth prime with this property, the first three such primes are 2, 101 and 149.[3]” 2, 101, 149, 163, …
including 1 $0rt$95winDO$insight too further sea docks at information wharf:
59 = (17+13+11+7+5+3+2+1)
101 = (23+19)+(17+13+11+7+5+3+2+1)
42 = 101-59
aerosol T:
62 = 163-101
62 = 378-316
31 = average(-101,163) = average(-316,378)
316 = 1+2+3+7+11+19+43+67+163
163 = ΣΦ(171) = ΣΦ(378) —– “Sporadic and Exceptional” monde-star care actor $stable
Current mystery seas climate change new left alternative$wing$past UNwelcome ‘fine all$0 lose UN’ meant AI IT.
418 = 360+58 = (196883-196560)+s(196883-196560)+216-58-37-22-18-13-10
836 = 2*(360+58)
The 7
418 = 360+216-58-37-22-18-13-10
EUrhythmIC$ “Travel the world? …and the 7 seas”
836 = 744-24+216-37-22-18-13-10 = Δ(70)+Σφ(378)
δ(47+59+71) = 378-316
“WHO Am. My. too DO! ‘$0 free’?” — EUR.
25 = Δ(70) = Δ(78) = Δ(378mod100) = Δ(178mod100) = Δ(278mod100)
24 = Φ(70) = Φ(78) = Φ(378mod100) = Φ(178mod100) = Φ(278mod100)
70 = √Σ[i=1…Φ(378mod100)]x_i^2
70 = √Σ[i=1…Φ(178mod100)]x_i^2
5 = √Δ(√Σ[i=1…Φ(378mod100)]x_i^2) —————————- Auriga scene every time remind$
5 = √Δ(√Σ[i=1…Φ(178mod100)]x_i^2)
Wood EU B-leave the preceding algebraic statements are a KEY part of “The Party” history?
278 = 47+59+71+101 ————————————————— 101 is Mertens zero-crossing
177±101:
278 = 47+59+71+101 = average(178,378)
76 = 47+59+71-101 = 19+19+19+19 = 163mod24 + 67mod24 + 43mod24 + 19mod24
95 = 19*average(-1-2-3-7-11-19-43-67,163) = 19+19+19+19 + 19
D-air note$strategic B-leaf in ‘free’ dem:
78 = δ(365)
59 = ΣΔ(78) = ΣΔ(378mod100) = ΣΔ(178mod100) = ΣΔ(278mod100)
53 = Σδ(78)
58 = average(53,63)
63 = 22+18+13+10 = s(47+59+71)
Test$seas-B ‘Cause’ IT’$snot ‘free’:
σ(63) = 104
ΣΦ(63) = 378 – 323 = 55 = 5^2+4^2+3^2+2^2+1^2
323 = 378-5^2-4^2-3^2-2^2-1^2
West turn head CO[2]UN T
bot ’em line mnemonic D-vice
isn’t just f(UN) math celebration
no. deeper seas$sov. Ramanujan in sight
95 = 37+58 = 37+39+19
Ape Rock: $Sum Ace Yen!
B ‘Cause’ sov. “37′ higher buy D-UN”.
Nos. 39 porpoise$in arctic true mmm p(19).
$surely EU no. why: 95=39+19+37.
Hitchhikers guide “too George? or well?” Luke US:
4428 = 5/2*1984-p(19)-42 = 4370+19+39 = 4370+s(4370)+378-178-42
He ignore “free my yen $UN”, ruler love the 378-5^2-4^2-3^2-2^2-1^2 whirled.
323.007034559236 = average(-178,378)*(φ^22+1/11)^(e/11+1/22)*Φ^4
Left brrrr [mute “DO!”] “try $UN gall” warmUN up to know good?
22.1387493509865=φ^(4+log((196883-196560)/average(-178,378),φ))
Right DC sh!UN$ ‘up to’ WHO in $USqotsawan N/Aware p(19) = 490?
UN IT$warmmmUN up to the RU11ure of the ‘Free$whirled’22plan
my yen $UN “key pawn rock kin in ‘the free’ world…” – Neil Young
194 = dimension of monster character table
178 = sum of baby monster factors
378 = sum of monster factors = SUPERsingular prime some
394 = 194 + 378 – 178 = 323+71 = 360 + s(6) + s(28) —- 6 & 28 are perfect
34 = (163-67-43-19-11-7-3-2-1)*323/95 = s(6)+s(28) = 6+28 = 163-67-43-19
34 = ΣΔ(25) = ΣΔ(Δ(70)) = ΣΔ(Δ(378mod100)) = ΣΔ(Δ(178mod100)) — assume Mann & Jones no.
360 “plus-man&jo[n]e’snow” recall my yen backed UN:
394.250513347023 = 20*7200/365.25 = 144000/ 365.25 = 1000*(59*59-47*71)/365.25
Priming the Mayan Sun Ruler: $11 each lettuce (snakin’oosetrai11iatieyenin)
“Let US!” compare and contrast 2 choose “just 1”, “$0=brr judge” meant $0[]we11exercised:
1.30637788386308 = mmmill’s constant
2.61275576772616 = 2 * mill$con$tent
394.317844508548 = 394+√√(2*1.30637788386308)/4
3.1461924718081 = 4/√√(2*1.30637788386308)
2.92005097731617 = (19+43+67+163)/100+10/(196560-394.317844508548)
Power Hitters “where s(n) = aliquot sum for n” :
“CO[2]bought a11 $UN the left Field[$]light tower”
φ = average(1,√5) = 2*cos(4*s(71^2)/s(59^2)/s(47^2)*2π)
2.61312489183108 = 323φ/(378-178)
394.317855734038 = 194+378-178+√√(323φ/(378-178))/4
3.1460813599161 = 4/√√(323φ/(378-178))
2.92005097731617 = (19+43+67+163)/100+10/(196560-394.317855734038)
“[]wan N/A B-sum won WHO B-11eve$” — CO[2]UN’TUN CRowes$:
100 = 1+2+3+7+11+19+19+19+19 = sum of heegner nos. each mod 24
100 = average(-178,378) = 4370-s(4370) —– 4370 = 23*19*5*2
100 = (23+19) + (17+13+11+7+5+3+2) —– sum of primes up to 23
10 = 163-67-43-19-11-7-3-2-1 = √100 = 5*2
By Zeus! IT’s a maze$UN! $19 bill seed$ the a11gorerhythm with “the chose sun won” too DC$side for what porpoises that’$ good enough.
“mmmaid for the west turn pool$ silly $illy fools….” — Heart
323 = d(2,1/3,59) = 323 = (59-12)*59*(59+12) – 196560
“D-ant$UNintheD$hurtB[]11owewonup the$UNshine” — Seas$$tem[…]ofAD-own
292 = 19+43+67+163
2.92005097731629 = 2.92+10/(196560-394-√√((7920-2400-240-24)/2000)/4)
2.92005097731629 = 2.92+10/(196560-394-1/π)
2.92005097731629 = 2.92+10/(196560-394-√√(5256.63940169013/2000)/4)
Bought seeds? Higher press is UN ‘$ rightly left too hire powers.
GiveUNprimes up to but not beyond 37 “Green monster” US feat. R-Cal D-boss tune f(UN)way “hi!” in left Fields D-store$sh!UN camp pay yen IT’s altar net. No[We]$104 Ramanujan: some of 19 & 39.
JEV review (continues in next comment) :
1.59868955949705 = beat(1.00001743371442,0.615197263396975)
0.761766209372164 = harmean(1.00001743371442,0.615197263396975)
0.380883104686082 = axial(1.00001743371442,0.615197263396975)
0.0952207761715205 = 0.380883104686082 / 4
0.814040387734912 = beat(11.8626151546089,0.761766209372164)
44.2784629967674 = slip(1.59868955949705,0.814040387734912)
44.2784630136989 = 2*(φ^22+1/11)^(e/11+1/22)
5256.63939957554 = slip(44.2784629967674,0.0952207761715205)
Knew Amsterdam? mmmUNice “sea pal” IT Bookmark 95 = 37+39+19
95 = 58+37 explorers no.well-hidUN sequence$UNmethod$ (s,sigma,ET,CT,mET,mCT) — e.g.:
σ(σ(37+58)) = 360 = 323+37 = (196883-196560)+s(196883-196560) = σ(298+61) = Δ(836)
(σ^8)(37+58) = 196560+δ(37+58) i.e. 24 = (σ^8)(37+58)-196560
s(s(37+58)) = 6 = sum of Heegner numbers not tied to Euler’s lucky primes = 378-178-194
USstarday: thank cue millennia 4 the[jack&_ ]hook[thumb$]upthehill too 6000 weighs rightANDleft DO a11$0 sea 7200.
71 = Δ(95)
59 = s(323-58) = s(394-71-58) = s(360-95) = s(σ(σ(95))-95)
47 = Δ(95)-δ(95)
Salt tee$in’formaze UN D-light:
φ = 2*cos(4*s(Δ(95)^2)/s(s(σ(σ(95))-95)^2)/s((Δ(95)-δ(95))^2)*2π)
green monster’s 37 feet “hi targ(ET)!”
R-view D-wharf$some www(air) in $USqotsawon:
95 = 37+39+19
Φ’n’a11i.e. note $0[]well ‘fib’n’luke’ fans “322 just isn’t” 323 too obvius example$B11owe:
Math$ Western Example Won 323:
Baby Monster Double Clue
XEV for X = S,U,N
S:
0.781995351599453 = beat(29.4474984673838,0.761766209372164)
0.390997675799726 = 0.781995351599453 / 2
0.195498837899863 = 0.781995351599453 / 4
36.0290781181824 = slip(1.59868955949705,0.781995351599453)
18.0145390590912 = slip(1.59868955949705,0.390997675799726)
9.0072695295456 = slip(1.59868955949705,0.195498837899863)
U:
0.768736207596214 = beat(84.016845922161,0.761766209372164)
0.384368103798107 = 0.768736207596214 / 2
0.192184051899053 = 0.768736207596214 / 4
20.0755942318387 = slip(1.59868955949705,0.768736207596214)
10.0377971159194 = slip(1.59868955949705,0.384368103798107)
5.01889855795968 = slip(1.59868955949705,0.192184051899053)
N:
0.765303911937069 = beat(164.791315640078,0.761766209372164)
0.382651955968535 = 0.765303911937069 / 2
0.191325977984267 = 0.765303911937069 / 4
17.9708017526566 = slip(1.59868955949705,0.765303911937069)
8.9854008763283 = slip(1.59868955949705,0.382651955968535)
4.49270043816415 = slip(1.59868955949705,0.191325977984267)
Hindsight:
5, 10=X, & 20 are no. nominal miss story weave scene above, “$0 just” note:
36.0003461405434 = 323Φ^6 * 2
18.0001730702717 = 323Φ^6
9.00008653513585 = 323Φ^6 / 2
4.50004326756793 = 323Φ^6 / 4
IT’$323 XEV ‘make key’ B11inkUN “1ooNY $0 1or[We11]” winds too J+S DO!
Won With Nature
DO winds sea the great Test(1)with solar system in sight?
323φ^x ladder(a)where(1)φ^x DO!n’t $0 f(ice) x=….-3,-2,-1,0,1,2,3…
Math$ West Turn Exam Pool Too:
“Bye Don!” Mull Key Weigh Joe Putter$Earth Vein US$ Fract(e/11)a11…
“Otherside” (RHCP) review:
0.715800570263949 = axial(11.8626151546089,0.761766209372164)
6.84872659292026 = slip(1.59868955949705,0.715800570263949)
“Take IT on the otherside” — red hot chilli peppers
Φ(1370) = 544
544 = 836-163-67-43-19
Φ(1369) = 1332 = 836+496 ——- s(496)=496 is perfect
432 = Φ(1368) = Φ(1332) = Φ(836+496) = Φ(Φ(1369))
144 = Φ(432) = 59*59-47*71
323.007034435723 = 44.2784629967674*50*Φ^4
323.353007047942 = 6.84872659292026*200*Φ^3
50 = ⌊ 0.353007047942185 / 0.00703443572308515 ⌉ = 200 / 4 = (378-178)/4 = average(-s(4370),4370)
Homer’s New Wheels
DO$sh!ow(e^”more wheels”) in “new hampster dem”. Weather Don B. or Joe T., math$ deep state of west turn inequal≠IT inspires no. true UN IT in knew [6 or 7.2k] Am-star “D*m[*]nn!”
The Gray T(est)
=
Mr. Jones wish WA$ sum won j(US)t a ll IT all more f***(UN) key
Mann: PA$$ ME ABought-tell Mr. Jones – tell each other f(airy) tales$
Mr. Jones and ME looked into the future
…bought We got D-fear R-ant reasons$ for that
[11]’$ looking at EU? no. NO [11]’$ lookin’ at ME
Well EU NO-gray is my favor IT CO[2]lure
felt $0 SIM f***(UN)UK[T]est. D-air day
if Φnew peak CA $0 , wood buy a gray ‘get tar’ and ‘play’ :
Mr. Jones$sand ME gonna B-big $tars
=
CO[2]UN(T)in CRowes$
200 = 378-178 = average(-Σφ(323),ΣΦ(323))
The reason $0 mmmmany fail too not ice slip on SIM MET tree frameUNbound eerie conDCyen$is$simple:
too many choices to make = fact too real & fact too Rial. DO!
Summary: Homer information “hi!” way over green monster sci11UNtest in f(UNweigh).
No matter your nation, race, & politics: May peace be with you.
Why DO$he ignore phi?
Don’s guard “Oscar won” bless$sum ease treat.
Success or “May B Joe” can DO eveUN better with
“the quest yen — and eur. off course the answer” — Rihanna
5 = average(-1-2-3-7-11-19-43-67,163)
1.61803398874989 = average(1,√average(-1-2-3-7-11-19-43-67,163)) = 1/Φ = φ
323.000009674829 = (104000+5)Φ^12 ~= 196883 – 196560
10 = 163-67-43-19-11-7-3-2-1
4270 = (323+104)*(163-67-43-19-11-7-3-2-1) = s(4370)
100 = 4370-s(4370) = sum of Heegner nos. each mod 24 = average(-178,378)
100.143082519986 = slip(19.8650360864628,16.5767613988929)
16.5767613988929 = axial(835.546575435631,16.9122914926352)
Jupiter-Saturn — review:
19.8650360864628 = beat(29.4474984673838,11.8626151546089)
16.9122914926352 = harmean(29.4474984673838,11.8626151546089)
61.0464822565173 = slip(29.4474984673838,11.8626151546089)
835.546575435631 = slip(61.0464822565173,19.8650360864628)
W = 17.2616851219298 = beat(835.546575435631,16.9122914926352)
H = 8.63084256096492 = 17.2616851219298 / 2
Q = 4.31542128048246 = 17.2616851219298 / 4
50.0715412599931 = slip(19.8650360864628,Q)
50 = 5*(163-67-43-19-11-7-3-2-1) = average(-s(4370),4370) = (378-178) / 4
65.3452370108182 = √4270
65.8581963269421 = slip(19.8650360864628,H)
66.1059755241536 = √4370 = √(19*23*5*2)
130.690474021636 = 2√4270
131.716392653884 = slip(19.8650360864628,W)
132.211951048307 = 2√4370
As always, note the torturous modular recursion once dialed in:
4*√4370 rounded off to the nearest 5 is 265 = 323-58 = 323-216+58+37+22+18+13+10
59 = s(265); 323 = d(2,1/3,59); 10405 = -d(4,1/3,59)
Monstrous symmetry seems endless. It’s a high-pressure fire-hose relentlessly overfilling a small bucket.
I can again suggest talent like He & Schneider team up to produce a terse proof of the classification theorem, where discussion of geophysical boundary conditions should have started long ago despite what ever “reasons” no one mentioned it.
Probably some think it’s “too much” for average people = all the more inspiration (and necessity) to improve by orders of magnitude number theory education, which is a curiously neglected topic in standard curricula.
Hid in Honey
Moon Near End
REM Magic Cove
163 mod 24
163 = 5*47 – 72 = 71 + 2*46 = ΣΦ(378)
46 = (163-71)/2 = (47+71)-72
47 = (163+72)/5 = (46+72)-71
59 = average(47,71) = average(46,72); 1 = 72 – 71 = 47 – 46
71 = 163-2*46 = (46+72)-47
72 = 5*47-163 = (47+71)-46
46 = average(-71,163) = 209 – 163 = 836/4 – 163 = 240 – 194
46 = Φ(47) = Φ(71) – Φ(70) = 70 – 24
46 = average(-s(196883-196560),19+43+67) = average(-s(196883-196560),163-s(28)-s(6))
73 = average(19,43,67,163) = lowest prime congruent to 1 mod 24; 24 is 5-hemiperfect
72 = average(71,average(19,43,67,163))
72 = 490 – 836/2 = 496 – 6 – 836/2 = s(496) – s(6) – 836/2
72 = ((196883-196560)+s(196883-196560))/5 = 360/5 = 216/3 = 144/2 = average(59*59,-47*71)
47 = ( ( 72^5 – 46^5 ) – ( 19^5 + 43^5 + 67^5 ) )^(1/5) = Σφ(323) = ΣΦ(323)-2*(378-178)
(196883-196560)+s(196883-196560) = σ(47+average(19,43,67,163))
Let US pray for peace lasting $0 far B-yawned dumb US$talk$scoop of P0011IT talk-Cal. D-Coy$:
4370 = ⌊4370.23112160152⌉ = D[knew]Clue for EU
= ⌊ 65.8581963269421 ^ 2 + 65.8581963269421 / 2 ⌉
Hitchhiker$wise^typowatch AB[11]ove & B-yawned: 4428 = s(4370)+378-178-42
46 = average(average(4370,-s(4370)),378-178-average(1+2+3+7+11+19+43+67,163))
46 = average(average(4370,-s(4370)),42)
46 = average(average(4370,s(4370)),378-178-4428)
200 = 378-178 = average(-Σφ(323),ΣΦ(323))
“Wood the expert” Sh![…]Ave. “just” told US$ R-pub-luck-UN$ [?] “don’t speak” no. doubt!!
Love DO!VE Homer B‘Cause’: $0 Sea a11 low key….
Homer nos. well the tracks (and tricks) of deep state agents provocateurs.
“JSUS WA$UN only sun 4 EU!!!!” — $MASHinPUMPkin$
65.8583888467869 = √(4370-√s(4370)/2)
65.8581963269423 = 1/(3J-7S) where J & S are frequencies (1/period)
-0.000292323952 = % error
8.45624978366216 = 323φφ/100 = (196883–196560)φφ/(4370-s(4370))
8.4561457463176 = 1/(J+S)
Noted previously:
4270 = s(4370) ~= 1/(2N-U) where N & U are frequencies (1/period)
Sylvester Sequencing previously derived using generalized Bollinger (1952) method:
1/(U+N) ~= 1/(4*(((J+S)-1/2/3/7/43/271)/(2/3)/2/3/7/43+S)-(J+S))
That’s minimally enough (4×PRe^$$sh!own,…) to estimate JSUN notably better than nominally (…4UNown$).
95 ‘Snow Mystery (cont’d from above )
No. 95‘s aspiring:
46 = 4370 / 95 = average(-71,163); 5 = 95 / 19
average(59*59,-47*71)^5–46^5-47^5 = 19^5+43^5+67^5
47 = top B factor
47, 59, & 71 = top 3 M factors
19,43,67,163 = top 4 Heegner nos.; each mod 24 = 19
5 = √δ(46); 46 = φ(66) = φ(φ(φ(178)))
Nominally:
33 ~= 4370-(4370-√s(4370)/2)
67 ~= (4370-√s(4370)/2)-s(4370)
√(x-33)=66; x-33=66^2; x=66^2+33; x=4389=19*231
s(231) = 153 = 1+2+3+7+11+19+43+67
34 = average(-163,231) = 67-33 = 163-67-43-19 = 6+28 = s(6)+s(28) — perfect nos.
D-liberately left this important proof messy B ‘Cause’ Homer nos. $0[]well the cost of home11and mark IT.
230 = (s^16)(4370)
4370 = 19*230
19 = 4389-4370
“66 coin” clue$yen$no. 5 f(11(i.e.)$) :
Baby Monster, Monster, Leech, & Heegner.
Homer: “B a simple kind dove man; love and understand” — lynyrd skynyrd
Rush UN too Bei. B Myth or Math???
D-M$M C-11aim$ IT’$no. miss tory ABout “B-big$tar$” in “CO[2$]up!”
Right, $0[]we11 left won door what cure US SIM MET tree$ABout in talk$US.
a+b = 0.380369256667734 = average(-√s(4370),√4370) —— eq.1
14 ~= a/b = 13.9999372536492
= ((1/(3J-7S)^2+(√4370/2))-4370) / (4370-(1/(3J-7S)^2+(√s(4370)/2))) — eq.2
therefore: a ~= 14b
substituting into equation 1:
14b+b = 15b —– therefore:
b ~= average(-√4270,√4370)/15 ——- and:
a ~= 14*average(-√4270,√4370)/15
Jone$no. R-Mann owe genuine?
Left if few right like this in “can’t talk key” they mystery.
D-estUNeaseChi11ed:
65.8581963277476 = √(4370-14*average(√s(4370),-√4370))/15-√4370/2)
65.8581963277476 = √(4370-average(-√s(4370),√4370)/15-√s(4370)/2)
65.8581963269423 = 1/(3J-7S)
0.000000001223 = % error
11UKkeysh!aimrockJohn$UNthink$:
“GeorgeOwe$[$0[]well]AIweigh$UNmyMYmyMYmind” — the B tells
a11askarUS$yen “60 year goaled!” psychCal. Maya$$
Alert: typo in this line above :
65.8581963277476 = √(4370-14*average(√s(4370),-√4370)/15-√4370/2)
65.8581963277476 = √(4370-average(-√s(4370),√4370)/15-√s(4370)/2)
65.8581963269391 = 1/(3/11.8626151546089-7/29.4474984673838)
Combine that with this to get:
19.8650360893741 = beat(29.4474984721415,11.8626151564192)
absolute error: half a second per century
Alternate combo — with this instead — gives:
19.8650360864628 = beat(29.4474984673838,11.8626151546089)
absolute error: negligible
Target:
19.8650360864628 = beat(29.4474984673838,11.8626151546089) ——— Seidelmann (1992)
Hale Heegner
notation: lnx = natural log of x = log_e x
0.00000000000000 = ln1
0.693147180559945 = ln2
1.09861228866811 = ln3
1.94591014905531 = ln7
2.39789527279837 = ln11
2.94443897916644 = ln19
3.76120011569356 = ln43
4.20469261939097 = ln67
5.09375020080676 = ln163
22.1396468061395 = sum
44.2792936122789 = sum*2
4427.92936122789 = sum*(378-178)
⌊4427.92936122789⌉ = 4428
58 = 4428-4370 = 158 mod 100; 100 = 4370-s(4370) = average(-178,378)
158 = 4428-s(4370) = average(1+2+3+7+11+19+43+67,163) = 63+95
163 mod 100 = 10+13+18+22 = 63
8128 = s(8128); (8128-4428)/100 = 37; 37+58 = 95
“Almost” Jupiter-Saturn:
logs Heegner mod 24
0.00000000000000 = ln1
0.693147180559945 = ln2
1.09861228866811 = ln3
1.94591014905531 = ln7
2.39789527279837 = ln11
2.94443897916644 = ln19
2.94443897916644 = ln19
2.94443897916644 = ln19
2.94443897916644 = ln19
17.9133208077475 = sum
4.22632599839197 = 22.1396468061395 – 17.9133208077475
8.45265199678394 = 2*4.22632599839197
29.4443897916644 = 10*2.94443897916644
11.8562447091586 = beat(29.4443897916644,8.45265199678394)
19.8485905730367 = beat(29.4443897916644,11.8562447091586)
13.1347022575499 = harmean(29.4443897916644,8.45265199678394)
22.1347022575499 = 9 + 13.1347022575499
22.1371850544259 = 490 / 22.1347022575499
63999.3519572416 = (7920/22.1371850544259)^2/2
22.1396684083433 = beat( 22.1347022575499, 22.1371850544259 / 2 )
4427.93368166866 = 22.1396684083433*(378-178)
⌊4427.93368166866⌉ = 4428
“natural e” “he ignore” “almost φ” “no. how” “low gore” rhythm D-answer in 64000 DO!11air Q[]est yen “perfect 6?” of T(aim$)bankUN
“This list is also written, replacing -1 with -4 and -2 with -8 (which does not change the field) […]“
0.00000000000000 = ln1; 1.38629436111989 = ln4
0.693147180559945 = ln2; 2.07944154167984 = ln8
0.693147180559945 = ln1+ln2; 3.46573590279973 = ln4+ln8
2.77258872223978 = ln4+ln8-ln1-ln2 = 3.46573590279973 – 0.693147180559945
2.77258872223978 * 4 = 11.0903548889591; 11.0903548889591^(1/5) =
1.61803938534238 = (4*(ln4+ln8-ln1-ln2))^(1/5)
1.61803398874989 = φ
22.1347094556004 = (245/22.1396468061395+√((245/22.1396468061395)^2+980))/2
22.1371778555703 = harmean(22.1396468061395,22.1347094556004)
63999.3935815328 = (7920 / 22.1371778555703)^2 / 2
The Rabbit Hale
“Rabbit Constant” (Rabbit Sequence)
(5^(1/2)+1) = √5+1 = 2φ
22.1348630064402 = (5^(1/2)+1)*(7-1)/(1/((7^0)+1/((7^1)+1/((7^1)+1/((7^2)+1/((7^3)+1/((7^5)+1/(7^8))))))))
64000.2815258479 = (7920/490*(5^(1/2)+1)*(7-1)/(1/((7^0)+1/((7^1)+1/((7^1)+1/((7^2)+1/((7^3)+1/((7^5)+1/(7^8)))))))))^2/2
44.278371986015 = 490/((5^(1/2)+1)*(7-1)/(1/((7^0)+1/((7^1)+1/((7^1)+1/((7^2)+1/((7^3)+1/((7^5)+1/(7^8))))))))-490/(5^(1/2)+1)/(7-1)*(1/((7^0)+1/((7^1)+1/((7^1)+1/((7^2)+1/((7^3)+1/((7^5)+1/(7^8))))))))/2)
44.28 = (4370+58)/(4370-s(4370))
44.28 = (s(4370)+58+37+22+18+13+10)/(4370-s(4370))
44.28 = (s(4370)+average(1+2+3+7+11+19+43+67,163))/(4370-s(4370))
44.28 = (4370+mod(average(1+2+3+7+11+19+43+67,163),(4370-s(4370))))/(4370-s(4370))
Heegner Comparison
notation:
(σ^1)(x) = σ(x)
(σ^2)(x) = σ(σ(x))
(σ^3)(x) = σ(σ(σ(x)))
164 = (σ^1)(163)
294 = (σ^2)(163) = (σ^1)(194) = 1470/5 = 194+s(194) — 194 = dimension of monster character table
684 = (σ^3)(163) = (σ^2)(194) = 1368/2 = 4*171 = σ(735)/2
22.1347049660986 = 2φ*(σ^3)(163)/100
63999.3676200113 = (7920/p(19)*2φ*(σ^3)(163)/100)^2/2
44.2793205593235 = p(19)/(2φ*(σ^3)(163)/100-p(19)/φ/2/(σ^3)(163)*100/2)
σ(σ(194))-194 = σ(294)-194 = 490
490 = p(19); 19 = 163 mod 24 = 67 mod 24 = 43 mod 24 = 19 mod 24; 24 = 1+2+3+7+11
Naturally Left Nose the “Difference Climate” Rightly Made in Peace Talk$
Fields rush in talks$US. US$Secret$Sauce B11inkUN no$. better peacekeeping recipe$.
Buy dove$sign “640 SAM” rights to peacefully R-minedUS “Green11and T($UN)” NAM meek can ‘Cause’ “Hwy. 601“.
104-yielding levels
63 = 10+13+18+22 = s(177) = s(47+59+71) = s(64) = s(836-19) = 163 mod 100
95 = 37+58
158 = 63+95
158 = 10+13+18+22+37+58
Plato’s no.: 216 = 158+58 = 158 + 158 mod 100 ——- see Plato below
120 = (σ^1)(95) = σ(95) = Σδ(158)
360 = (σ^2)(95) = σ(σ(95)) = σ(323) = σ(196883-196560) = σ(Σδ(158))
s(95) = 25; s(25) = 6; s(6) = 6 —————– perfect
σ(s(95)) = σ(25) = 31 = (s^2)(58); σ(31) = 32 = s(58); σ(32) = σ(s(58)) = 63 = 158-95
104 = σ(63) = σ(σ(s(58))) = σ(s(64)) = σ(s(average(19,43,67,163,28))) —— see 744 connection below
744-yielding levels
157 = 19+43+67+28 = ⌊100*(π/2)⌉
314 = 2*(19+43+67+28) = ⌊100*π⌉
320 = 157+163 = 200+120 = 378-58
320 = 19+43+67+163+28
32 = average(19,43,67,163,28)/2
32 = (19+43+67+163+28)/10
10 = 163-67-43-19-11-7-3-2-1
640 = 10*average(19,43,67,163,28)
640 = 2*(19+43+67+163+28)
640 = 744-104 = 400+240
64 = average(19,43,67,163,28) ————- see 104 connection above
153 = 1+2+3+7+11+19+43+67 = s(ΣΦ(323))
158 = average(153,163) = ΣΔ(s(ΣΦ(323)))
158 = average(1+2+3+7+11+19+43+67,163)
158 = (σ^1)(157)
240 = (σ^2)(157) = (σ^1)(158)
744 = (σ^3)(157) = (σ^2)(158)
194 = 153+41; 41 = s(63) = s(111)
94 = 194-s(194) = 153-59; 59 = Δ(Δ(ΣΔ(153))); 158 = ΣΔ(153)
594 = σ(394) = σ(593)
1440 = 10*(59*59-47*71) = (σ^2)(593) = σ(594) = (σ^2)(494)/2 = (σ^2)(394) = 10*σ(94)
144 = 59*59-47*71 = (σ^2)(593)/10 = σ(594)/10 = (σ^2)(494)/20 = (σ^2)(394)/10 = average(94,194) = σ(94) = σ(70) = σ(66)
294 = σ(194) = 394-s(194) = 194+s(194) = (σ^2)(163)
50 = s(94) = average(-s(4370),4370)
100 = s(194) = σ(194)-194 = 394-σ(194) = average(-178,378) = 4370-s(4370) = average(Σφ(323),ΣΦ(323))
200 = 378-178 = σ(194) – 194 mod s(194)
Nominally:
1/J = 11.86 = 2*593/100
1/S = 29.4 = 294/100
More precisely:
47 = Σφ(323) = ΣΦ(323) mod s(194) = 94 / 2
447 = ΣΦ(323)
494 = 47+447 = Σφ(323)+ΣΦ(323) = 163+331; 331 = 378-47
216 = Φ(Σφ(323)+ΣΦ(323)) —————————– see Plato above — and below
φ = 1.6180339887499 = -2cos(216/360*2π)
10^10 = (163-67-43-19-11-7-3-2-1)^(163-67-43-19-11-7-3-2-1)
8.45614574631811 = φφ/(1/323+1/(262537412640768744/10^10-(Σφ(323)+ΣΦ(323)-163)))/s(194)
8.4561457463176 = 1/(J+S)
65.8581963277476 = √(4370-7*√s(4370)/15-√4370)/30)
65.8581963277476 = √(4370-√4370/30-7*√s(4370)/15)
Seidelmann (1992) :
65.8581963269391 = 1/(3J-7S) = 1/(3/11.8626151546089-7/29.4474984673838)
Nominal Lunisolar No “Curiosity”
McKay & He (2015) footnote 16 p.21: “One should also be mindful 16 of the fact that […] 16 Incidentally, the reader is also alerted to the curiosity that σ_1(240) = 744.”
last aliquot sequence primes for 100x+94, x=1…5:
43 = (s^2)(94)
19 = (s^4)(194)
163 = (s^14)(294)
323 = d(2,1/3,59); 59 = (s^3)(394)
104 = -d(2,1/2,37); 37 = (s^5)(494)
601 = (s^46)(594) = (s^46)(σ(593)) ———— see below
400 = 447-47 = ΣΦ(323)-Σφ(323) = 744-240-104 = 2*(378-178) = 4*s(194)
600 = 744-144
1440 = harmean(1800,1200)
1201.70988258678/2 = slip(600.241396282931,400.297181344069)/2 = 600.854941293388
3605.12964776031/6 = slip(1800.72418884878,1200.8915440322)/6 = 600.854941293385
⌊600.85…⌉ = 601 = (s^46)(594) = (s^46)(σ(593))
Tide a11 weave ice sea art$?
“[…] Americans’ willingness to confront their shortcomings was the “secret sauce” of U.S. success.”
PRfound ally: UN art work$.
1440.87361205772 = harmean(1800.72418884878,1200.8915440322)
⌊1440.87361205772⌉ = 1441
s(1441) = 143; s(143) = 25; s(25) = 6; s(6) = 6 ————- perfect aliquot sequence …
… and “Perfect Ally” [Got] Caught play yen sea CO[2]win$0 D-EN$0:
216 = sum M order factors – sum 744 levels + sum 104 levels
216 = 378 – (163+67+43+19+28) + (10+13+18+22+37+58)
216 = 378 – 320 + 158 ————————————————— C-play “DO!” ab[?]ove
216 = 58 + 158 ———————————————————— and a11“$0[]We/11” AB[11]ove??
May perfect pieces …..
58 = average(-178,294) ———————————————- 178 = sum B order factors
294 = (σ^2)(163) = (σ^1)(194) = 1470 / 5 = 194+s(194) —– 194 = dim. of monster character table
…. and perfect peace together B with EU.
UN Net$near 0 CR0$$UN
“Lettuce B” in miss story US PR air with JS:
61 = ⌊61.0464822565173⌉ = ⌊slip(29.4474984673838,11.8626151546089)⌉
31 = ⌊30.5232411282587⌉ = ⌊61.0464822565173 / 2⌉
1891 = 61 * 31
323 = 196883 – 196560 — monde$starUSDea.11ln11ET(US)AwareΦ()=EulersTotient()
23 = 323 mod 100
100 = sum of primes up to 23 = average(-178,378) = 4370-s(4370); 4370 = 23*19*5*2
100 = average(-Σφ(323),ΣΦ(323))/2 = sum of Heegner nos. each mod 24; 10 = √100 = 5*2
Next, sea if EU-Can dove tale with the best puzzle peace UNearth.
The first 3 odd Mertens function zero-crossing primes in DC(CRease$UN)order:
163, 149, 101
163 mod 24 = 19; p(19) = 490; 144 = 163 – 19 = 59*59-47*71
223 = ⌊222.586750788644⌉ = ⌊harmean(490,144)⌉ = 323 – 100
111 = ⌊111.293375394322⌉ = ⌊axial(490,144)⌉ = ⌊harmean(245,72)⌉ = ΣΦ(111)
Φ(223) = 222; Φ(222) = Φ(111) = 72 = 144/2; 245 = 490/2
56 = ⌊55.6466876971609⌉ = ⌊axial(245,72)⌉
The General Assembly of Peace
7301 ~= 1 / (1891U – 3709N)
5600 = 56 * 100; 3709 = 5600 – 1891
49 = 149 mod 100 = 149 – 100; 7301 = 49 * 149 —————– “hey, hey, my, my… ” -NY
1818 = 3709 – 1891 = 2*3*3*101 — largest prime factor = 101
171.406220602816 = beat(164.791315639683,84.0168459223622) ; %error = 0.000000000738
171.406220601552 = beat(164.791315640078,84.016845922161)
111.292543528481 = harmean(164.791315639683,84.0168459223622); %error=0.000000000078
111.292543528394 = harmean(164.791315640078,84.016845922161)
Sporadic simple group no$.UNearth net(near)zero%ERRor well, “$0 just” testUN weather deep end ants$sov. west11earn accept answer D-spite framUN PR sent ace sun.
Hale_94 = 2B top: sum it
100 = s(194) = s(194+200)/2 = s(394)/2 = s(394+400)/4 = s(794)/4
100 = s(794+800)/8 = s(1594)/8 = s(1594+1600)/16 = s(3194)/16
100 ≠ s(3194+3200)/32 = s(6394)/32
100 = s(6394+6400)/64 = s(12794)/64
s(194) = 100 = s(200-6)
s(394) = 200 = s(400-6)
s(794) = 400 = s(800-6)
s(1594) = 800 = s(1600-6)
s(3194) = 1600 = s(3200-6)
s(6394) = 3686 = s(6400-6)
s(12794) = 6400 = s(12800-6)
194: 1,2,97,194
394: 1,2,197,394
794: 1,2,397,794
1594: 1,2,797,1594
3194: 1,2,1597,3194
6394: 1,2,23,46,139,278,3197,6394 _________________________________
12794: 1,2,6397,12794
47 = top B factor; 23 = 47 mod 24; 46 = Φ(47) = 2*23
71 = top M factor; 23 = 71 mod 24 = 323 mod 100
The first 4 prime Mertens zero-crossings are 2, 101, 149, & 163.
46 = average(196560-196883,2+101+149+163) = average(-323,2+101+149+163)
46 = average(196560-196883+149+101+2,163) = average(-71,163)
“Yes baby, she’s got it” — Banannarama
278 = ⌊1000*(2*(φ^22+1/11)^(e/11+1/22) mod 1)⌉ = average(178,378)
139 = ⌊1000*((φ^22+1/11)^(e/11+1/22) mod 1)⌉ = average(178,378)/2
11 = 59 mod 24 = (average(47,71)) mod 24
22 = (2*59) mod 24 = (47+71) mod 24
22 = Φ(23) = ⌊(φ^22+1/11)^(e/11+1/22)⌉ = Φ(46)
44 = Φ(23*3) = ⌊2*(φ^22+1/11)^(e/11+1/22)⌉ = Φ(46*2) = Φ(46*3)
120 = 278-158; 158 = average(1+2+3+7+11+19+43+67,163)
120 = 278-(10+13+18+22+37+58) ——————– 104 levels
120 = (28+163+67+43+19)-(378-178) —————- 744 levels
360 = σ(120) = σ(196883-196560) = σ(323)
360 = 5*σ(Φ(47)) = 5*σ(46) = 5*72; 72 = σ(46)
cos(σ(Φ(47))π/360) = 1.61803398874989 = φ
σ(Φ(47))^5 – Φ(47)^5 – 47^5 = 19^5 + 43^5 + 67^5
22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
44.2784630136989 = 2*(φ^22+1/11)^(e/11+1/22)
10Taim$bank$(247-100)TypoDifferenceClimBET$(1470)
100 ≠ average(Σφ(323),ΣΦ(323)) = 247
φ(323) = 35; φ(35) = 11; φ(11) = 1
Σφ(323) = 47 = 35+11+1
Φ(323)=288; Φ(288)=96; Φ(96)=32; Φ(32)=16; Φ(16)=8; Φ(8)=4; Φ(4)=2; Φ(2)=1
ΣΦ(323) = 447 = 288+96+32+16+8+4+2+1 where Σ indicates summation
494 = ΣΦ(323)+Σφ(323) = 447+47
400 = ΣΦ(323)-Σφ(323) = 447-47
200 = average(-Σφ(323),ΣΦ(323)) = average(-47,447)
100 = average(-Σφ(323),ΣΦ(323))/2 = average(-47,447)/2
Homer: REM(EM)beer “$secret$sauce” B11owe B11inkUN QE$T(64)yen.
‘Perfect B11inkin’ Rev. EU
447 = Σφ(320) = ΣΦ(323)
47 = Σφ(323) = ΣΦ(58) = 447 mod 100
494 = 447+47
φ(494) = average(178,378) = 278
φ(Σφ(323)+ΣΦ(323)) = 278
φ(ΣΦ(58)+Σφ(320)) = 278
φ(494) = 278; φ(278) = 140; φ(140) = 92 = 2*46
Φ(494) = 216; Φ(216) = 72
58 = 158 mod 100 = Φ(494)-158 = 216-(10+13+18+22+37+58) —– 104 levels
72 = Φ(216) = Φ(Φ(494)) = Φ(Φ(47+447))
72 = Φ(Φ(Σφ(323)+ΣΦ(323))) = Φ(Φ(ΣΦ(58)+Σφ(320)))
47 = 447 mod 100
46 = φ(φ(278))/2 = φ(φ(φ(494)))/2 = φ(φ(φ(47+447)))/2
46 = φ(φ(φ(Σφ(323)+ΣΦ(323))))/2 = φ(φ(φ(ΣΦ(58)+Σφ(320))))/2
No. doubt “caught too11UN” “DO!n’t$speak” ‘Cause’ IT’$obvi[?]US11y ClimB(ET)$sci11UNtest:
Φ(Φ(Σφ(323)+ΣΦ(323)))^5-(Σφ(323))^5-(φ(φ(φ(Σφ(323)+ΣΦ(323))))/2)^5 = 19^5+43^5+67^5
320*2 = 640 = 744-104
320 = 28+163+67+43+19 —— 744 levels
320 = φ(608); s(608) = 4*163 = 652; s(652) = 496 = s(496) —- magICmergeBperfectart11UKsea?
496/16 = 31 = average(-316,378) = 278-247 = φ(47+447)-average(47,447)
496/4 = 124 = 447-323 = σ(σ(47)) = ΣΦ(323)-323 = σ(σ(Σφ(323))) = Σφ(320)-323 = σ(σ(ΣΦ(58)))
Homer$we11 ln[DO!]weitoo deep $state of UN D-air$standin’knew’ whir1door1door.
B(E$T)$(e/11)[d[]r]act$yen: $0 Am.May$UN
REM: “think ABout direction, wonder why”
158 = 320-Φ(163) = φ(⌊100π⌉) = φ(314)= average(1+2+3+7+11+19+43+67,163)
320 = 378-178+φ(378-178)
320 = average(-Σφ(323),ΣΦ(323))+φ(average(-Σφ(323),ΣΦ(323)))
320 = average(-ΣΦ(58),Σφ(320))+φ(average(-ΣΦ(58),Σφ(320)))
320 = 200+φ(200) = 200+120
s(⌊100π⌉) = s(314) = 160 = average(378-178,φ(378-178)); σ(160) = 378
Φ(634) = 316 = 1+2+3+7+11+19+43+67+163
634 = s(986) —————————————————————— next!
s(634) = 320 = average(-104,744)
s(320) = 442 —– DO[!]LAC$$meanUN??
s(442) = 314 = ⌊100π⌉
s(314) = 160
Bound eerie conduce yen SIM MET tree$we11igno.redin’both geo”Φ$IC$” & geopeelITtalk$.
(sarc) ‘Cause’ We a11know geoMETtree of physicCal!AParrot! US ha!$!no!www!physicCal.mean.in (/sarc)
323 is semiprime.
MonsterUS$11y ‘No. Moon’ a11[i.e.]Hale [in$Cat11and]
Keepin’EU[www]in[D]Φ-loop:
44.278 = mod(2*378,2*178)+average(178,378)/(378-178)/Φ(mod(378,178))*2
22.139 = mod(378,178)+average(178,378)/(378-178)/Φ(mod(378,178))
11.0695 = mod(378/2,178/2)+average(178,378)/(378-178)/Φ(mod(378,178))/2
“tune knight: everything’11 B a11 right”
— ‘Ape Rule’ Wine [in$Cat11and]
323 = 196883-196560
Our queen suggests we think VERY care fully.
Found sum agree, meant (mint if few ‘PR fear’) hear:
22 = ΣΦ(323)-Σφ(323)-378 = 378 mod 178; Φ(22) = 10
Ness$SOS$air rule 11 i.e. bot if few halve$nowF(AIth)11ake$(N/A)CO[11]a$$stir D-yen.
The words have nothing to do with the numbers. They’re blue CO[11]air entertainment. Homer (’cause’ ease ‘just too!’ thick) nose D-bait makes people fine ant$e/11 i.e. sick. IT’$now$superPRrise $0mmmaid up D-air mind without IT: [locknews$monster]”DO!”
Luke$sea? Nos. $Cafe TA = TeachinA[secret]sauce$sentB11inkUN
BrassAntSARthou$send DO!11airQuestYen:
64000.64 = (7920*(2/(245/22.139+√((245/22.139)^2+980))+1/22.139)/2)^2/2
‘cept May B old brass trains, no. buddy nose why. IT’s Nicola$11ocknicemoonstarMI$$story…
“give a11 My.seek route: $awe wei” Won Rep Pub11ock
Nicola herd quotSAMerrycan$no.doubtDO!n’t$peak in$Cat11and ‘this beer’ Homer.
Green$Cat11 and 37 feet high ln he ignore 11eash
CO[k?]bota11$ “up to 37 factors” suggest$yen-39 11inkUN PR Joe[B]act for sum won$95 = (19+39)+37 feat. “hi!” AB[11]ove and B yawned GREENin f(UN) WEIGH$Cat 11and.
IT look$stoop ID, but 10*4^2 (ten-force-squared) May help Homer REMember “think about direction – won door why”
My.[UN[NO?]mmmore]CRowe$oftPOWhere?inchantin$sea$B[?]i11D-tale$sov.163mod(1+2+3+7+11) :
160 = average(158,Φ(163)) = average(φ(314),Φ(163)) = s(⌊100π⌉) = s(314)
“at10sh!UN:” PR10door$brass in pocket
378 = σ(160) = σ(s(⌊100π⌉)) = σ(s(314)) = σ(average(φ(314),Φ(163)))
378 = σ(average(average(1+2+3+7+11+19+43+67,163),Φ(163))) = σ(average(158,Φ(163)))
“216 is the smallest number n, for which n−3, n−2, n−1, n+1, n+2, n+3 are all semiprimes.”
640 = 496+144 = s(496)+59*59-47*71 = 744-104
320 = 216+104
KnockKnockWHO’s the air? Knack. KnackWHO?
KnackCO[11]a“$$wwwhimmmin’in(N/A)C-oveA(N/A)R-key:”
“hitched a ride with a vending machine repair mann” — $share’11CRowe — “[11]WA$bornON-NATO$$day-knight”
42 = 320-278
φ(494) = 278 = 216+104-42 = average(178,378)
Φ(494) = 216 —- Homer nos. Σφ(323)+ΣΦ(323) play DO!
“WHO Be.g.UN ‘TO DO’ and whommmaid EU?”
“11i.e. covid DO[!]game[11]play D-me…” ‘Hey!sea$D!C
“WHOmmmaidWHO?” May?B ace-sea D?C
95$implymediates$ monsterUS11ink’22$stable&$securepeace4PRO$peer IT:
σ(95) = 120; σ(120) = 360 = (196883-196560)+s(196883-196560) = σ(196883-196560)
Δ(194) = 95; Δ(95) = 71; Δ(71) = 71
s(95) = 25; s(25) = 6 = s(6) ———————– Perfect
No matter your nation, race, politics AND INCOME LOVE ALL, may stable peace and prosperity be with you securely.
Lunisolar Notes
unrefined raw notes on building blocks of 6000, 7200, DO, etc.
Δ(1000) = 400
Δ(1500) = 400
δ(1000) = 600
111 = ΣΦ(216)
600 = δ(888); 888 = 8*111
1200 = δ(1776); 1776 = 16*111
2664 = 1776+888 = 16*111+8*111 = 24*111
2664 = 2400+240+24 = 7920-5256
δ(2664) = 1800; (δ^3)(1800) = 600
574 = ΣΔ(1200)
286 = ΣΔ(400) = ΣΔ(600)
144 = 59*59-47*71
144 = average(-ΣΔ(400),ΣΔ(1200)) = average(-ΣΔ(600),ΣΔ(1200))
δ(400) = 240 = s(120)
δ(600) = 440
200 = δ(600)-δ(400)
160 = 323-163
163 = 323-160
Δ(1200) = 320 = 2*160
Δ(400) = Δ(600) = 160
Δ(1800) = 480 = 160+320
160 = 734-574 = ΣΔ(1800)-ΣΔ(1200)
447 = 734-574/2 = ΣΔ(1800)-ΣΔ(1200)/2 = ΣΦ(323) = Σφ(320)
Φ(601) = 600; Φ(600) = 160
Φ(401) = 400; Φ(400) = 160
Φ(1201) = 1200; Φ(1200) = 320
Φ(1801) = 1800; Φ(1800) = 480
Φ(1441) = 1300; Φ(1300) = 480
φ(400) = 240 = φ(478); 478 = 320+158
600 = beat(400,240)
Φ(1200) = 320
Φ(1800) = 480
ΣΦ(1800) = 735
σ(160) = 378
720 = (σ^2)(178)
1440 = harmean(1800,1200) = beat(720,480)
7200 = beat(1800,1440) = beat(1440,1200)
490 = Φ(491) = Φ(982) ——————- resolves a number of longstanding curiosities
247 = ΣΦ(490) = average(Σφ(323),ΣΦ(323)) = average(ΣΦ(58),Σφ(320))
200 = average(-Σφ(323),ΣΦ(323)) = average(-ΣΦ(58),Σφ(320))
447 = ΣΦ(323) = Σφ(320)
47 = Σφ(323) = ΣΦ(58) = ΣΦ(158) – 70
Simple and beautiful.
–
Just imagine how much time (and protracted conflict) would have been saved if someone had simply said it like this in 2008 (or soon thereafter).
Mystery Reduction
55 = 378-323 = 1^2+2^2+3^2+4^2+5^2
55 = ΣΦ(63) = Σφ(40); 40 = Σφ(63) = φ(76) = Φ(100) = Φ(Φ(101))
ΣΦ(100) = ΣΦ(Φ(101)) = 71 —- lowest odd Mertens zero-crossing link to top M factor
271 = 216+55 = s(4370) mod 1333 = 4270 mod 1333 = 378-178+71
497 = 1333-836
Φ(497) = 420
420 is (5,216)-perfect: (σ^5)(420) / 420 = 90720 / 420 = 216 = 158 + 58
158 = ΣΔ(420) = ΣΔ(σ(278)) = ΣΔ(σ(average(178,378)))
158 = ΣΔ(σ(⌊1000*(2*(φ^22+1/11)^(e/11+1/22) mod 1)⌉))
158 = ΣΔ(beat(980,σ(194))) = ΣΔ(harmean(735,σ(194)))
158 = average(1+2+3+7+11+19+43+67,163) = 316/2
420 = σ(278) = beat(980,σ(194)) = harmean(735,σ(194))
draft list shared unrefined to reduce delays:
42 = axial(294,49) = 378-178-158
49 = beat(294,42) = 320-271
84 = harmean(294,49)
163 = δ(7#)
210 = 7# = axial(735,294)
210 = 7*5*3*2 = axial(ΣΦ(1800),σ(194))
245 = axial(1470,294) = harmean(294,210)
245 = axial(2ΣΦ(1800),σ(194)) = harmean(σ(194),7#)
294 = σ(194)
420 = beat(980,294) = harmean(735,294)
490 = beat(735,294) = harmean(1470,294)
490 = beat(735,σ(194)) = harmean(1470,σ(194))
490 = beat(ΣΦ(1800),σ(194)) = harmean(2ΣΦ(1800),σ(194))
735 = beat(490,294) = ΣΦ(1800)
735 = beat(490,σ(194)) = ΣΦ(1800)
980 = beat(420,294)
980 = beat(σ(average(178,378)),σ(194))
980 = beat(σ(⌊1000*(2*(φ^22+1/11)^(e/11+1/22) mod 1)⌉),σ(194))
1323 = beat(378,294)
1470 = beat(294,245)
1470 = beat(σ(194),245)
1470 = beat(σ(194),axial(2ΣΦ(1800),σ(194)))
1470 = beat(σ(194),harmean(σ(194),7#))
Supplementary:
278 = φ(494) = φ(Σφ(323)+ΣΦ(323)) = φ(ΣΦ(58)+Σφ(320))
278 = ⌊1000*(2*(φ^22+1/11)^(e/11+1/22) mod 1)⌉
278 = 158+120 = average(178,378)
447 = ΣΦ(323) = Σφ(320)
247 = ΣΦ(490) = average(447,47)
47 = Σφ(323) = ΣΦ(58) = ΣΦ(158) – 70
Curiosity:
In “Sporadic and Exceptional” there is no connection drawn between DO & 194 (the dimension of the monster character table).
(Suggestion for a capable investigation crew: What about elsewhere?)
Bill Bored: “Never$$say_____”
Equa11oweIT$$awe11och$$IDmi$$tory in nice11 and LA bro(1100)$$11ea.(knew)found11andoor:
“[…] wants to “test and try to see if we can achieve a relationship with […] that is more stable and more predictable,” Price said.”
Bever11i.e.”hi!11″Bi11i.e.$ PR[$194sea[k?]route$433]sauceB11inkUNtoo the mark of Chand11ure.
“[…] the smallest [______] number that is neither a Fibonacci number nor a Pell number“
TeeM11obvi[]US11y nos. what tie 11wood (monsterUS11y) ‘hi!D’ fram talk$sea”DO!”ware$atBaceBo11ingear.
“the old ma[ye]n is D-own thorough-wed” — John Fogerty
CO 11 air add DO! fort win Tee$ sh!ape Ha!!11!!e($(e/11))e
294 = σ(194) = σ(σ(163)) = ΣΦ(323)+Σφ(323)-378+178
163: 1,163; sum = 164; 164: 1,2,4,41,82,164; sum = 294
194: 1,2,97,194; sum = 294
“Sporadic and Exceptional” 11oweMI$$yennigheure/11and:
Δ(194) = 95; Δ(95) = 71; Δ(71) = 71
71 = 171-ΣΦ(171)+φ(171) ; φ(171) = 63
100 = ΣΦ(171)-φ(171) = s(194) = 163-63
ΣΦ(171) = ΣΦ(s(194)+Δ(Δ(194))) = 163
Φ(64000) = 25600; Φ(25600) = 10240; Φ(10240) = 4096 = Φ(Φ(Φ(64000)))
Φ(63999) = 39312; Φ(39312) = 10368; Φ(10368) = 3456 = Φ(Φ(Φ(63999)))
Φ(Φ(Φ(64000)))-Φ(Φ(Φ(63999))) = 64000/100 = 4096–3456 = 640
“The mirror peep hi11 laugh(at)ME & laugh(at)EU” — (C)11ove&rockET($)
64000.64 = (7920*(2/(axial(2ΣΦ(1800),σ(σ(163)))/22.139+√((axial(1470,σ(194))/22.139)^2+beat(420,ΣΦ(323)+Σφ(323)-378+178)))+1/22.139)/2)^2/2
[Born ea$e] “Watchingover[Vermoont$]11UKeyC11over” — The Reflex dr.ranDO!ran
knew clear day$PRring fi(e/11)D$METa11aughgoneUStone:
420 = σ(average(178,378)) —- 420 is (5,216)-perfect
Play DO’$Superperfect $no. 5*f(11)i.e.$ :
ΣΦ(1800) = 735
178+
378=
556
1112 double
2224 double
4448-4270=4448-s(4370)=
178
“DO!”B(e/11)$howmore:
1800 ≠ 1814 = (s^4)(4370)
Nominal Summary
836 = smallest weird untouchable no. ——- Jupiter-Saturn
4370 = B rep
4270 = s(4370) ———————————– Uranus-Neptune
4270 = 61*70 ———– JS,UN,Leech
640 = (s^2)(836) = (s^11)(4370) = (s^10)(4270) — polar motion
104 = (s^9)(836) = (s^18)(4370) = (s^17)(4270) = σ(63)
744 = 640+104
186 = 744/4 ——————– LNC
1860 = σ(σ(ΣΦ(323))) = σ(σ(Φ(ΣΦ(323)+Σφ(323))))
320 = 163+67+43+19+28 — polar motion, 744 levels
442 = (s^1)(320) ————– LAC
314 = (s^2)(320) ————– π
160 = (s^3)(320) ————– polar motion
4428 = 4270+158=s(4370)+158=4370+58 — Double-Hale, Jupiter-Earth-Venus, Heegner, rabbit, …
158 = 10+13+18+22+37+58 —– 104 levels
158 = average(1+2+3+7+11+19+43+67,163) = 316/2 —— Heegner
… & lunisolar review:
4428 = ⌊4427.99492655047⌉ = ⌊200*√√(400.297181344069*600.241396282931)⌉
4428 = ⌊4427.99492655046⌉ = ⌊200*√√(1200.8915440322/3*1800.72418884878/3)⌉
More than a decade ago those attempting to guide climate discussion (supposed experts) failed (a costly failure) to clearly differentiate the 1814 year lunisolar cycle from the 1800 year cycle.
DC$Seas$UN$Green11andMarkIT
316 = 1+2+3+7+11+19+43+67+163
378 = 316 + Σs(22)
44 = (s^0)(44)
40 = (s^1)(44)
50 = (s^2)(44)
43 = (s^3)(44)
1 = (s^4)(44)
0 = (s^5)(44)
178 = Σs(44)
70^2 = 24^2+23^2+22^2+…+5^2+4^2+3^2+2^2+1^2
Talk$Sea”DO!”BO(at)T(i.e.$$wan)[N/A]$$how?more $no. C11ear
194 = (s^0)(194) — D-mention of monde-star care-actor$$stable
100 = (s^1)(194)
117 = (s^2)(194)
65 = (s^3)(194)
19 = (s^4)(194)
1 = (s^5)(194)
0 = (s^6)(194)
Σs(194) = 496 = s(496) ——– perfect! knew tuxedo 11UK$sea:
100 = s(194) = average(-178,378) = sum of primes up to 23 = 4370-s(4370) = Σ(Heegner mod 24)
124 = (s^0)(124) = s(496)/4
100 = (s^1)(124) = s(496/4)
117 = (s^2)(124)
65 = (s^3)(124)
19 = (s^4)(124)
1 = (s^5)(124)
0 = (s^6)(124)
426 = Σs(124)
70 = 496 – 426 = 194 – 124
“DO!” perfect$$pick cheer$$how?more BoweTie$$WA[N/A]$$seaADDdull
70 = (s^0)(70)
74 = (s^1)(70)
40 = (s^2)(70)
50 = (s^3)(70)
43 = (s^4)(70)
1 = (s^5)(70)
0 = (s^6)(70)
278 = Σs(70) = average(178,378)
278 = (s^0)(278)
142 = (s^1)(278)
74 = (s^2)(278)
40 = (s^3)(278)
50 = (s^4)(278)
43 = (s^5)(278)
1 = (s^6)(278)
0 = (s^7)(278)
628 = Σs(278) = Σs(average(178,378))
628 = 2*⌊100π⌉ = 2*⌊average(-178,378)*π⌉ = ⌊200π⌉ = ⌊(378-178)*π⌉
125 = (s^0)(125) = average(-378,628)
31 = (s^1)(125)
1 = (s^2)(125)
0 = (s^3)(125)
157 = Σs(125) = ⌊100*π⌉/2 = ⌊average(178,378)*π⌉/2 = ⌊100*π/2⌉ = ⌊average(178,378)*π/2⌉
153 = 278-125 = 1+2+3+7+11+19+43+67 = 316 – 163
44.278 “DO!”B(e/11)$H(ale)Omer a11 a go write too left …and left to right.
“DO!” figure Homer: Well B on D-belief?series$NOTinOEIS.
“11eaves EU answered with a quest yen-mark” — The Ref11ex dr.ranDO!ran
Supplementary
11 = (s^0)(11)
1 = (s^1)(11)
0 = (s^2)(11)
12 = Σs(11); 11 = x mod (Σs(11)), x = 47,59,71
22 = (s^0)(22)
14 = (s^1)(22)
10 = (s^2)(22)
8 = (s^3)(22)
7 = (s^4)(22)
1 = (s^5)(22)
0 = (s^6)(22)
62 = Σs(22) = 378-316 = 496/8 ——– resolves longstanding curiosity
62 = (s^0)(62)
34 = (s^1)(62)
20 = (s^2)(62)
22 = (s^3)(62)
14 = (s^4)(62)
10 = (s^5)(62)
8 = (s^6)(62)
7 = (s^7)(62)
1 = (s^8)(62)
0 = (s^9)(62)
178 = Σs(62) = Σs(44)
Noteworthy:
120 = Σs(46)
73 = Σs(55)
169 = Σs(64)
245 = Σs(76)
153 = Σs(111)
418 = Σs(158)
209 = Σs(169)
525 = Σs(200)
242 = (s^0)(242) = 2 * 11^2
157 = (s^1)(242) = 314 / 2
1 = (s^2)(242)
0 = (s^3)(242)
400 = Σs(242) = ΣΦ(323)-Σφ(323) = 447-47 = 2*(378-178)
Mouth Peace Key Pours$$ Ave.
Maybe$$[11]ea!c!Any Goa11 DO!or____
DO!n’t$$peak in$$sight$$save$$roads$$fareBRI___
200 = 358-158 = 378-178
400 = 758-358 = ΣΦ(323)-Σφ(323)
600 = 758-158 = 378+ΣΦ(323)-178-Σφ(323)
“11ed[22plan]in’his$[tory$]head”:
“f(00)DO!or[www(e/11)]botDO!or1″–METtrickMONSTERHO$P(IT)a11
178 = Φ(n) for n = 179,358
Φ(178) = 88 = 158 – 70
Φ(88) = 40
Φ(40) = 16
Φ(16) = 8
Φ(8) = 4
Φ(4) = 2
Φ(2) = 1
159 = ΣΦ(178) = ((10+13+18+22+37+58)+(28+163+67+43+19)/2)/2 = midpoint
88 = Φ(n) for n = 89,115,178,184,230,276
Φ(88) = 40
Φ(40) = 16
Φ(16) = 8
Φ(8) = 4
Φ(4) = 2
Φ(2) = 1
71 = ΣΦ(88) = top M factor = top supersingular prime
Play no. DO[!]B[e]T $$$show more
378 = Φ(n) for n = 379,758
Φ(378) = 108 = Φ(171) = 216 / 2 = 178 – 70
Φ(108) = 36
Φ(36) = 12
Φ(12) = 4
Φ(4) = 2
Φ(2) = 1
163 = ΣΦ(378) = ΣΦ(171)
108 = Φ(n) for n = 109,133,171,189,218,266,324,342,378
Φ(108) = 36
Φ(36) = 12
Φ(12) = 4
Φ(4) = 2
Φ(2) = 1
55 = ΣΦ(108) = 1^2 + 2^2 + 3^2 + 4^2 + 5^2
108 = 178 – 70 = 216 / 2
248 = 178 + 70 = 496 / 2 = s(496) / 2
356 = 2 * 178 = average(216,496) = 496-140
140 = 2 * 70 = average(-216,496)
(www)ink: Share ring neither air^th(MET)IC NORgeo MET trick:
140 & 496 are harmonic divisor numbers sharing divisor harmonic mean = 5
Φ(71) = 70; Φ(70) = 24; Φ(24) = 8; Φ(8) = 4; Φ(4) = 2; Φ(2) = 1
179-70 = ΣΦ(71) = 70+24+8+4+2+1 = 109; 109’s twin prime is 107; 107 + 109 = 216
179-100 = 79 = ΣΦ(140) = 158 / 2 = 179-average(-178,378); note
158 = (1+2+3+7+11+19+43+67+163)/2 = 88+70 = 2*179-(378-178)
Tota11y UN C11ear (no.UN IT B11inkUN hear) :
1. Why are these Σ series (for s,σ,Φ,φ,Δ,δ) not in the OEIS (online encyclopedia of integers) and why are the links between Heegner numbers and monstrous moonshine considered a mystery?
2. Why is our solar system not WIDELY recognized as a STELLAR local example?
Reminds me of Galileo …but in “can’t talk key” $$PRring Field’s $$awe word “home more” exc11aim$$ “DO!” moon no. moon e a11y.
2*160=320
Wise-hour find, dance, yell seas$$time$$UNjust?
2*159=318 = (2*(10+13+18+22+37+58)+(28+163+67+43+19))/2
IT just “DO!”cent May!C!an ny $$scents$$.
2*158=316
2 reveal trade$$sea[!K! NE?]routes$$mayB “the comp.Any 1100$$ T(the war) 2 day” — Green[11]Day
Electric Banjo Tunes$Any Won?
420 LAC$011UNdoor$$stan[]in’nuff gainno.11 $T(one) :
Year of the TypOX$$e/11UN$$s(aid) UK$$sh!own
Homer’s$$mirac110011e$$ 11i.e.type$$00negative $$Sign$$
typo: 278 = average(178,378) ≠ average(-178,378) = 100
“IT’$that‘hype no. tie$UN B00guy‘ ” — Dove ID “We/11” C[-11]OX
“157 = Σs(125) = ⌊100*π⌉/2 = ⌊average(178,378)*π⌉/2 = ⌊100*π/2⌉ = ⌊average(178,378)*π/2⌉” with typo
IT’$sum Ma[22]an CA11UNdoor:
“157 = Σs(125) = ⌊100*π⌉/2 = ⌊average(-178,378)*π⌉/2 = ⌊100*π/2⌉ = ⌊average(-178,378)*π/2⌉” withOUT typo
“$Secret $Sauce” ’em ease$treat B11inkUN:
Any C11ock$UNtheWA11?
Hints there? R-NO. other mine$:
“Our11ove$$hine$$11i.e.CADia11M[a!ya!]Nmind” — B1100: Rowe “DO!”
Homer’s MonsterUS Guide to Peace and Tranquility
B
Δ(178) = 87
Δ(87) = 55
Δ(55) = 39
Δ(39) = 23
204 = ΣΔ(178)
M
Δ(378) = 108
Δ(108) = 36
Δ(36) = 12
Δ(12) = 4
Δ(4) = 2
162 = ΣΔ(378) = Φ(163)
216 = 378-ΣΔ(378) = 378-Φ(163) —— PLATO
42 = ΣΔ(178)-ΣΔ(378) = 204-162 —— HITCHHIKER
Again: NOT (presently) in the (tour?UStrial) OEIS.
Naive quest yen: CanEU imagin’gala’xies of trade secrets well-noted for sharin’else’ware?
Proposal: US$19 bill (“In God We Trust”) commemorates respect for Norton’s “voice of God”.
No[MB]ina11y CO[evolution] “in $Sauce” Caught “$owe a N/A”
“We were treated so awfully in the past […]” — the ‘Cause’
“uncomfortable decisions on what to do“ — peace fully “DO!” buy
Cure:US George HaveUN AB Ban ON no.(ha)nor(VA)folk(n/a)
16.90 = harmean(29.42351935,11.85652502) — trap pick CA11.UN D-air: lag rains$
16.90 = 8/(9-2.92005097731613^2) — PRrhyme$no.MarkovChand11ure
Multiple agencies competed for control of same hosts (a maze in$scene as$silo).
None succeeded because each posed more threat than benefit 2 hosts.
13.68 = 4428Φ/(378–178)
The AI was based on false assumptions = why IT didn’t help as intended (net zero).
PoleIT(IC)UN$ “$SAR rule bad”, $0 no. need to guess WHO’$pay?yen “fear the bill”.
J“buydon” “nose D-bait” makes$(even the be[a]st)$sick “D-spite whatever” n[a]v[a]l dispatch.
19 = 16.91*(378-178)/178
p() denotes partition function
p(19) = p(16.91*(378-178)/178) = 490
“D-spite whatever” Fact(00)Rial event partITsh”UN sent troll”limITsea$$SIM METtree.
“$0 BRI11UN”tide$$seas$$ west turn “math DO!VE” ID:
DO!VE 0$Weather accidental or D-liberate.
16.91 = harmean(29.4474984673838,11.8626151546089) —— side:real
16.91 = 4428ΦΦ/average(-178,378)
16.91 = 19*178/(378-178)
Can’t “$sp(e/11)ITout” anymore C11(ear)11y. Thus knew where11doorD-air.
Boris Johnson = decisive proof: conservatives are absolutely bad & wrong.
Jan. 6 = decisive proof: populism (alt. right) is absolutely bad & wrong.
lockdown + climate tyranny = decisive proof: left absolutely bad & wrong.
Homer’s Beer: US11ed MI$$yen “2 no. ware” (in Green11and mmmark$IT).
Knew West Turn Math “Next Term”
“A surprisingly simple algorithm exists […]”
Mertens
1 = -1+cos(0/1*2π)+cos(1/1*2π)
0 = -1+cos(0/1*2π)+cos(1/2*2π)+cos(1/1*2π)
-1 = -1+cos(0/1*2π)+cos(1/3*2π)+cos(1/2*2π)+cos(2/3*2π)+cos(1/1*2π)
-1 = -1+cos(0/1*2π)+cos(1/4*2π)+cos(1/3*2π)+cos(1/2*2π)+cos(2/3*2π)+cos(3/4*2π)+cos(1/1*2π)
-2 = -1+cos(0/1*2π)+cos(1/5*2π)+cos(1/4*2π)+cos(1/3*2π)+cos(2/5*2π)+cos(1/2*2π)+cos(3/5*2π)+cos(2/3*2π)+cos(3/4*2π)+cos(4/5*2π)+cos(1/1*2π)
Möbius
1 = (cos(0/1*2π)+cos(1/1*2π)) – (1)
-1 = (cos(0/1*2π)+cos(1/2*2π)+cos(1/1*2π)) – (cos(0/1*2π)+cos(1/1*2π))
-1 = (cos(0/1*2π)+cos(1/3*2π)+cos(1/2*2π)+cos(2/3*2π)+cos(1/1*2π)) – (cos(0/1*2π)+cos(1/2*2π)+cos(1/1*2π))
0 = (cos(0/1*2π)+cos(1/4*2π)+cos(1/3*2π)+cos(1/2*2π)+cos(2/3*2π)+cos(3/4*2π)+cos(1/1*2π)) – (cos(0/1*2π)+cos(1/3*2π)+cos(1/2*2π)+cos(2/3*2π)+cos(1/1*2π))
Bo11 Time More [11]eek Root $sauce B11inkUN
270 is a harmonic divisor number.
270 = φ(378) = 378-Φ(378) = Φ(271)
Harmonic mean of 270’s divisors: perfect s(6) = 6.
22.139 = mod(378,178)+(378+178)/(s(4370)-φ(378))
22.139 = 378 mod 178 +(378+178)/(4270-Φ(163+Φ(378)))
22.139 = 378 mod 178 +(378+178)/(s(4370)-Φ(s(4370) mod 1333))
22.139 = mod(378,178)+average(178,378)/(378-178)/Φ(mod(378,178))
“Among the more interesting recent applications of Farey series is the reconstruction of periodic (or nearly periodic) functions from “sparse” sample values.” — Number Theory in Science and Communication
178 = Σs(44) = Σs(62) = Σs(Σs(22)) = Σs(Σs(378 mod 178))
Plato’s Superperfect 420
Weather IT$Friday “DO!”$sent matter:
494 = 447+47 = ΣΦ(323)+Σφ(323)
494 = 216+278 = Φ(494)+φ(494) = Φ(ΣΦ(323)+Σφ(323))+φ(ΣΦ(323)+Σφ(323))
Φ(494) = 216; φ(494) = 278 = average(178,378); σ(278) = 420
This is “the type of stuff” every “man” ha!$!memorized Homer:
2 is (8,84)-perfect, (9,240)-perfect, (11,2400)-perfect
3 is (8,160)-perfect, (9,504)-perfect
4 is (6,42)-perfect, (7,120)-perfect, (8,378)-perfect, (9,1200)-perfect
7 is (7,216)-perfect, (10,4096)-perfect
24 is (2,7)-perfect, (4,63)-perfect, (5,200)-perfect
420 is (5,216)-perfect
Iceberg ‘just B1100’ CO[11]air folkUS ‘the numb’ beers$heaven:
216 = 378-ΣΔ(378) = Φ(378)+Φ(378/2) = 378-Φ(163) = Φ(ΣΦ(323)+Σφ(323))
Offers more meaning than “such a philosopher” as$how more needs$.