Nicola Scafetta: Jupiter’s orbital eccentricity may drive ~60yr and millennial climate cycles.

Posted: September 24, 2020 by tallbloke in solar system dynamics
Figure 3. The 60‐year eccentricity function (blue) of Jupiter (see Figure 2) against: (a) the HadCRUT global surface temperature record (Morice et al., 2012) detrended of its quadratic polynomial fit f(t) ¼ a(t − 1850)2 + b (cf. Scafetta, 2010, 2016) (correlation coefficient r^2 = 0:5, p < 0.01); (b) the 5‐year running average of the Indian summer monsoon rainfall from 1813 to 1998 (Agnihotri & Dutta, 2003) (correlation coefficient r^2 = 0:5, p < 0.01)


 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

Comments
  1. Paul Vaughan says:

    WY$key$how more

    Need “DO!”win(N/A) “hey!” $stack.

    22 = 216-194 = 378 mod 178
    78 = 294-216 = σ(194)-378+ΣΔ(378))
    Sum$sea-moonstarUSine(quality).
    100 = 22+78 = average(-178,378) = s(194) = σ(194)-194

    200 = 378-178 = 600-400 = δ(600)-δ(400) = 440-240; δ(600) = 440; δ(400) = 240
    a1’1iz!’CRamDO!NOR10CA11$ “RialΦbuoy!”

    “$peekin’word$ave.whiz-dem:11ET(IT)B” — B-T(e/11)$ — “there/11 B an answer: 11ET(IT)B”
    735 = ΣΦ(1800); σ(735) = σ(ΣΦ(1800)) = 8*171 = 1368; 13.68 = 4428Φ/(378-178)

    1800.something, 400.something, 600.something
    4426.94099321971 = (378-178)*σ(ΣΦ(1800))*φ/average(-178,378)
    4426.72767880129 = (378-178)*√(geomean(400,600))
    Financial error$in home11and markIT$www(age)$0(CA11)“DO!”late..

    COP
    IRD = Ice Ralph DO!BRI$$ 6000 too 7200 with no. elect trick get tar:
    Φ(401) = 400; Φ(400) = 160; 400 = Φ(1500) = Φ(1000)
    Φ(601) = 600; Φ(600) = 160 = 320/2
    addjustin+1Bound air e^c[a]n”DO!”$yen$topeel ‘why $0men?’ e^bono nos.

    Peer Hid Rowed
    “Caste$seize-dumb!” with22in limITobviUS11y accounts$4+won moon “shy” yen seas-dem:
    Φ(1201) = 1200; Φ(1200) = 320; Σφ(320)=ΣΦ(323); Σφ(323)=ΣΦ(58); 58+158 = 216
    Φ(1801) = 1800; Φ(1800) = 480 = 320+160

    “Well, mine aims$[Jane-wei]pot’em ore…” — $SSTeve ear11

  2. Paul Vaughan says:

    Peaceful MAG Rowe Gate$yen Critter: Ria11y

    WA$sh!in side d(00)r[]ink(cove trade)$seek routes$11UN(US$0)11air:

    Φ(491) = 490
    Φ(401) = 400 = 447-47 = ΣΦ(323)-Σφ(323)
    Φ(601) = 600 = σ(378-ΣΔ(378)) = σ(216) = σ(Φ(494)) = σ(Φ(ΣΦ(323)+Σφ(323)))
    Φ(601) = 600 = σ(447) = σ(ΣΦ(323))

    “done too: terms$ave. ‘DO!’ tee envy ET(no.)” — SSTeveURL

    AuthorIT4seas truth and peace TOGETHER.

  3. Paul Vaughan says:

    Page Won Peace B11inkUN$too C11i.e.MET FR/action :

    RialΦbuoy!” COP Peer Hid Rowed accounts$4+won moon “shy” yen seas-dem.

  4. Paul Vaughan says:

    Ally Caught Highway 601

    What else prime“O Rially??” accounts$Fear the name “monstrous moonshine”?
    378 = (s^2)(360/2) = (s^2)(354) = (s^2)(2*(47+59+71)) = (s^2)(7#)

    aliquot Monster US Hwy 601:
    378,582,594,846,1026,1374,1386,2358,2790,4698,6192,11540,12736,12664,11096,11104,10820,11944,10466,5236,6860,9940,14252,14308,15218,10894,6746,3376,3196,2852,2524,1900,2440,3140,3496,3704,3256,3584,4600,6560,9316,8072,7078,3542,3370,2714,1606,1058,601,1,0

    “more too” “My.My.”NY.“the picture”

  5. Paul Vaughan says:

    Φ11APin(N/A)CO11″add DO!”nos. wwwE$Turnmath
    “can’t derive 55 $SAM.My.H[e^I]g[no]r[e] aim US$how more nos.

    7 = 323-316 = 62-55

    “The efforts of Seven […] have been compared by many writers to the deprogramming […]”

    62 = ΣΔ(55)
    55 = ΣΔ(49) = ΣΔ(7^2) = ΣΔ((62-55)^2) = ΣΔ((ΣΔ(55)-55)^2)

    316 = Σ(Heegner nos.) = 378-ΣΔ(55)
    323 = 196883-196560 = 378-55

    71 = ΣΦ(55)

    “Just11i.e.ca.PR.air” — mmmaid”DO!”N/A

  6. Paul Vaughan says:

    Reports 27 to 28 days May B ‘Cause’

    Let US pray for peace, tranquility, security, and stability.

    “C-aim hone with ABrand(Knew Plan)” — SSTeve ear11

    Sum as$sea$add”DO!”11 miss$story:
    245 = 316-71 = 316-ΣΦ(55); 2*245 = 490 —- ally CAUGHT point “row beers” in chariot
    252 = 323-71 = 323-ΣΦ(55); 2*252 = 504 —– lowOEIS “amicable pair”
    394 = 323+71 = σ(194)+s(194); s(394) = 200 = average(-Σφ(323),ΣΦ(323)) = 378-178; s(200) = 265; s(265) = 59

    7 nos. IT$no “ami” ca.ba111 :
    252 = average(220,284); 111 = ΣΦ(252) = ΣΦ(average(220,284)

  7. Paul Vaughan says:

    amicable“(in no. wei)play “DO!”

    s(s(608)) = s(652) = s(496) = 496; ΣΣΔ(496) = 1690
    Lucy seas Homer ha$good reason too×C11aim “DO!”

    Φ(601) = 600; Φ(600) = 160; Φ(160) = 64
    Φ(401) = 400; Φ(400) = 160; Φ(160) = 64
    Φ(1801) = 1800; Φ(1800) = 480; Φ(480) = 128; Φ(128) = 64
    Φ(1201) = 1200; Φ(1200) = 320; Φ(320) = 128; Φ(128) = 64

    64 = ΣΣΦ(378)-ΣΣΦ(178) —— $sum won in.vest.gate$why$0$simple?series$SAR11eft doubt of OEIS

    Can figureITout, but no. ×plane ace yen$offered :
    s(220) = 284; s(284) = 220; 64 = 284-220
    s(1184) = 1210; s(1210) = 1184; 26 = 1210-1184
    s(2620) = 2924; s(2924) = 2620; 304 = 2924-2620

    s(1690) = 1604; s(1604) = 1210 — ally caught$sum$switchin’ ±26 (13, 104, 208 scale)
    s(1692) = 2676; s(2676) = 3596; s(3596) = 3124; s(3124) = 2924 — aliquot ±304 switch (19, 608, 2432 scale)

    Sum wons$caught[11and in]the middle…
    s(1691) = 109; s(109) = 1; s(1) = 0; 109+1 = 110 = 220/2 = s(284)/2
    109’s twin prime = 107; 107+109 = 3^3+4^3+5^3 = 216

    …tune-note “amicable” modular$scaling:
    s(10744) = 10856; s(10856) = 10744; Σ = 21600 = 3^3*4^3*5^3/Φ(378 mod 178)
    ⌊10744/average(-178,378)⌉ = 107; ⌊10856/average(-178,378)⌉ = 109; 107+109 = 216
    10000 = average(-178,378)^2; 744 = 10744-average(-178,378)^2
    320 = 744-levels sum = 28+163+67+43+19 = 5*(284-220)

    aliquot$sum?psychi11$in≠equal≠IT:
    220 = Φ(378 mod 178)*(378 mod 178) = s(284) = s(Φ(Φ(378 mod 178))*71)
    284 = Φ(Φ(378 mod 178))*71 = s(220) = s(Φ(378 mod 178)*(378 mod 178))
    504 = 284+220 = nom.in.a11y fameUS Joe.putter$at turn psychi11 answer inquest yen:
    64 = s(220)-s(284)

    Summatime Ford Circle $0 Too 11: “$$summatime$$addnos.” — 11ONno.DO!11ray$

  8. Paul Vaughan says:

    “Cure 10” CA11

    “Sporadic and Excepional” 194 was an intriguing source of mystery, but no. more….

    194 = DO!mention of monster care actor$table
    94 = 194 mod s(194)
    Φ(94) = Φ(47) = 46
    Φ(46) = Φ(23) = 22 = 378 mod 178
    71 = 94-23 = ΣΔ(Δ(194))

    Φ(22) = 10 = Φ(378 mod 178)
    Φ(10) = 4 = Φ(Φ(378 mod 178))
    Φ(4) = 2 = Φ(Φ(Φ(378 mod 178)))
    Φ(2) = 1 = Φ(Φ(Φ(Φ(378 mod 178))))
    Φ(1) = 1 = Φ(Φ(Φ(Φ(Φ(378 mod 178)))))

    Σs(194) = 496 —- perfect
    s(s(608)) = s(652) = s(496) = 496; ΣΣΔ(496) = ΣΣΔ(Σs(194)) = 1690

  9. Paul Vaughan says:

    Notation Knew “Next Term” Show More

    (a; q_n)
    (q; q_n)
    φ(q)=(q; q)_∞
    [n]_q
    [n]!_q

    “In number theory, certain special functions have traditionally been studied, such as particular Dirichlet series and modular forms. Almost all aspects of special function theory are reflected there, as well as some new ones, such as came out of the monstrous moonshine theory.”

    q-exponential
    “q-analogs are often found in exact solutions of many-body problems. In such cases, the q → 1 limit usually corresponds to relatively simple dynamics, e.g., without nonlinear interactions, while q [less than] 1 gives insight into the complex nonlinear regime with feedbacks.”

    √φ
    e(^x)(_√φ) at n=∞
    = 2.90723512764398
    ^2
    = 8.45201608740708
    *2
    = 16.9040321748142

    √(9-4/8.45201608740708) =
    2.92005824156182 —————— 22, 1470
    2.92005097731613 ~= seed for prime-generating function

    π/4
    e(^x)(_π/4) at n=∞
    = 2.90810322680047
    ^2
    = 8.45706437772733
    *2
    = 16.9141287554547

    √(9-4/8.45706437772733) —————— Lagrange seas more than Markov nos.
    = 2.9201066141423

  10. Paul Vaughan says:

    70 = ΣΔ(100)

    $$sum hear e^(monster+baby) ‘ADD JUST‘ poll-lure ops$sites$(in green11)and.

    61.0464822565173 = slip(29.4474984673838,11.8626151546089)
    835.546575435631 = slip(61.0464822565173,19.8650360864628)
    “the long s(low) goodbye” — qotsa
    4270.09258127429 = slip(164.791315640078,84.016845922161)
    48590.8284812209 = slip(4270.09258127429,171.406220601552)
    “where’ve you gone again mice s(weet)? everybody wants ’22 no. …” — qotsa
    82461.1077537223 = slip(4270.09258127429,61.0464822565173)
    314418.107917848 = slip(48590.8284812209,835.546575435631)

    “Joe Biden is the duly elected president of the United States. We follow the Constitution in this country,” he said. “Joe Biden is the president of the United States. We went through the electoral votes, we went through that whole process, and Joe Biden is the president.”

    compare:
    3.14460551102969 = 4√Φ
    3.14418107917848 = slip(48590.8284812209,835.546575435631)/10^5
    3.14159265358979 = π

    “Mayan sun” conversion generates primes up to 41:
    2.92005097731622=2.92+10/(196560-394-1/3.14418107917848)

    ” ’11ucky’ C11over: […] 11eaves EU answered with a quest yen-mark” — dr.and[DO!]ran “The Reflex”

    review

    Note nominal slip-structure:
    70 = ⌊69.9482168903912⌉ = ⌊ 4270.09258127429 / 61.0464822565173 ⌉
    58 = ⌊58.1545420802987⌉ = ⌊ 48590.8284812209 / 835.546575435631 ⌉

    Nominal assembly:
    4200 = 4270-70 = s(4370)-70
    42 = 4200/100; 100 = 42+58; 58+4370 = 158+s(4370) = 4428

    fits 70^2 = 4900 & p(19) = σ(σ(194))-194 = 490 scale:
    δ(94) = 49; δ(49) = 7 = δ(δ(94)); δ(δ(94))^2 = δ(94)
    Φ(49) = Φ(δ(94)) = 42

    UN_94
    56 = Σδ(94)
    111 = Σφ(94)
    223 = average(ΣΦ(σ(194)),323); 123 = ΣΦ(294); 294 = σ(194)
    100 = average(-ΣΦ(σ(194)),323) = 4370-s(4370) = 4370-4270

    quick review of coefficients with earned hindsight: 194 = 279-85

    84.0168459218229 = 194/(-85/11.8626151546089+279/29.4474984673838-1/36750.3379015986-1/30031)
    84.016845922161 = 1 / U
    -0.000000000402 = % error

    Still true today: ignorance is bliss. (Each monstrous insight seeds many revelations.)

    1 / 178.266850068779 = 19J-47S ——– coefficients Homer: no. thing ‘special luke’ sea

    171.4 = 5^2*√(323-378+178-76) = 25*√47
    76 = average(-171,323) = 19+19+19+19
    320 ~= beat(3337,292)

  11. Paul Vaughan says:

    The “Friendly” Giant Nos().

    We/11hhIDe^UN?Lh’Lhhale$(ally in knew mar qet) :
    1186 = average(1184,1188)

    s(1188) = 2172; s(2172) = 2924; s(2924) = 2620; s(2620) = 2924 — aliquot in
    s(1184) = 1210; s(1210) = 1184 ————————————– “amicable” loop

    22 = 378 mod 178
    139 = average(1184-1210,2924-2620)

    “sum times words ha!VE II-meanin’$”
    (φφ)^e = 22.139 —- the “friendly” limIT if eur. dr.ink.in Lhh’Lhale
    “cos() there’s a sin() : [11] wants 2B sure” — LOD22plan

    278 = (2924-2620)-(1210-1184)
    278 = average(-178,378)

    “with award[11]can get what? shheik aim h”

    (L-Lh)/(L-Lhh)=II

    16.91 = harmean(29.4497209985316,11.86) ——— UNtuned (nominAI)
    16.9122914926352 = harmean(29.4474984673838,11.8626151546089) — Seidelmann (1992)
    No.s(UN)”Ami”Term(in)NATO[] : DO!baiT($)up$side?own^Cos(!$$!)

    Φ(132) = 40 = Φ(100)
    Φ(40) = 16
    Φ(16) = 8
    Φ(8) = 4
    Φ(4) = 2
    Φ(2) = 1; 71 = ΣΦ(132) = ΣΦ(100)
    Φ(1) = 1; repeats define stop (not in Σ = sum)

    Translation, rotation, reflection:
    We/11B11owe, 4●Trump need $too look out(h)more than just Bill(y)|DO|.

  12. Paul Vaughan says:

    000h9$ Lhhale

    (ΣZΣ)φ3-(ΣZΣ)Φ3 = 00h
    (ΣZΣ)Φ3 = Lhh
    (ΣZΣ)φ3 = Lh

    55uperman55$(add)
    Our Lady
    =
    R:EUware?y?DDab out eur. faithh
    weather or not EUs(hh00)DDkneeldowhhandobei?
    orDO!NNair’risejust’NN’oughtgood’enoughh 22day
    [$$00] We/11just11aughhinT($(aid))
    DO!sent∞”Any∞buddy??”∞eveR!NO. the world’s∞A$$sov[www]wei
    =
    Peace SeaRChh: 220,284
    09S96l-Σ8896l=ΣZΣ

    Big Tech-Monster $0 herd: IT’$no. “friendly summatime” G-aim of ln(Dart$).

  13. Paul Vaughan says:

    Ami[]cable[K]new[$]in can’t talk key “LA:EUdowNN22s(11leap!!)” – M

    “brexit life: We raftZZC11everNNever11and” — Metallica
    R-verse/11 B1100[TO]sea ford circles can’t hh mar[11]in folkUSstan.

    120 = average(220-284,2924-2620)
    120 = average(220-s(220),2924-s(2924))
    120 = average(s(284)-284,s(2620)-2620)
    120 = average(-64,304); 120’s 3-perfect
    s(120) = 240 = 304-64; σ(120) = 360 = σ(323) ; 323 = 196883-196560

    22 on the dow((N))low?OEIS T(ally)caught$(sea)((K))(win)$

    139 = average(-26,304)
    139 = average(1184-1210,2924-2620)
    139 = average(1184-s(1184),2924-s(2924))
    139 = average(s(1210)-1210,s(2620)-2620)

    Diamond Ave. or SAM(My.)He ignoreWHO”Can?T(derive)=55″

    278 = 304-26
    278 = (2924-2620)-(1210-1184)
    278 = (2924-s(2924))-(1210-s(1210))
    278 = (s(2620)-2620)-(s(1184)-1184)
    278 = average(178,378)

    VA[]Nhhale!”UNweather” comm.ENSOliz’em $sumbuy0$0$ err pairusITmissm.

    Moon: ssteer55hhout”C11oud55ummattree”

    2eurAI2et CZZ Any-side[C22]why-spin? in-flip Dia11 “US Strait” 55hh!own:
    “Dozens of websites briefly went offline around the globe Tuesday, including CNN […] illustrating how vital a small number of behind-the-scenes companies have become to running the internet.” –ctvnews.ca

    ruNNin the inNNturnn!y!et?
    NN = 378 mod 178
    178 = Σs(hh)
    84 = NN+Σs(NN)

    NNeutr(AI)11artistIC represssentacesun of a11-concerned groups, math theme MET totient playUN$0CR:
    ‘Rock 101’ v[]an CO[up!vert] = 11owesst odd merten socr owe^$inprime; Φ(101) = 100 = Φ(5●5●5)

    RaveUN: every won s(we/11comm.)and a11est$(UN) hh “the voice of God” in aliquots(NNorton).

  14. Paul Vaughan says:

    “Amicable” Hitchhiker’s a11|22 (“all liz”)

    “in Eur. C[11]OS(IT)” MOT0011O[X]ca
    19 = average(284-220,1184-1210)
    Nos.”vvhhoo^^aidvvhhoo”inhhace$$T:seaDC

    “cos(D-err$)a$$ign’non’dowa11” — 11ed22plan
    (11-2)*11 = 11^2-11*2 = 121-22

    hhome mar a11 ego:
    22 = 378 mod 178
    air-ru$$T(00)vert seas “off-tune everNNever11and” – M —- f(UN)!101!writinsong
    22 = 220/110*1210/110
    22 = (284-84)/100*(1184-84)/100
    electric banjo = “G[]ain of 55and” – M
    284 = 220/11*10+84
    1184 = 1210/11*10+84
    have UN ABowe no. knew
    220 = (284-84)*11/10
    1210 = (1184-84)*11/10
    10 $$how??more

    T(ally)C?awe?$$TAmi-ca.B(a11)pairusty

    42 = ΣΔ(178)-ΣΔ(378) ——– quotsAPairus$011VE$(ET(11D$[11]11UN$))
    42 = average(22,Σs(22)) = average((378 mod 178),Σs(378 mod 178))

    BeuroweCRatIC BEAST

    “addjust wanD: EU 2*no. Dat Bei. Bjour db est”
    — 11(N/A)de(11)ray$$sumMOREtime$$addnos.

    2*(ΣΔ(178)-ΣΔ(378)) = mod(284,average(-178,378)) = mod(1184,average(-178,378))
    “T(wwwE$T)UN’yyear-mined’and[C11]!a!sh!in eur. dr.aim$” — METa11owe.ca

    84 = 22+62 = 22+Σs(22) = (378 mod 178)+Σs(378 mod 178)
    178 = Σs(44) = Σs(62) = Σs(Σs(22)) = Σs(Σs(378 mod 178)) —– sea B low: Rially nestUSs(eeries(eeries(eerie)))

    “$spin knit11ike.CAD(y/n)amo(at11andtalk’meltseaDO!Caida11’O[X]$e/11ace$UN)” — ace sea /00vert/ DC

    “Annoys Few” Word: hhUShh11ITa11’AB’:DO!N’T(sea)award”

    84 = (378 mod 178)+Σs(378 mod 178)
    84 = (378 mod Σs(Σs(378 mod 178)))+Σs(378 mod Σs(Σs(378 mod 178)))
    84 = (378 mod Σs(Σs(378 mod Σs(Σs(378 mod 178)))))+Σs(378 mod Σs(Σs(378 mod Σs(Σs(378 mod 178)))))
    et(c).

    “Never mind that noise EU herd — Metallica

    284 = 220/mod(378,178)*(378-178)/Φ(mod(378,178))+2*(ΣΔ(178)-ΣΔ(378))
    1184 = 1210/mod(378,178)*(378-178)/Φ(mod(378,178))+2*(ΣΔ(178)-ΣΔ(378))

    Tar22andJane$wei BIG TECH imageUN ace sh!own 6/LAguesst dawns in the B1100 C.
    Cos SAM: maze in a11 i.e. caught with no. s(in) cook e^monde$store jure.

    220 = (284-2*(ΣΔ(178)-ΣΔ(378)))*mod(378,178)/(378-178)*Φ(mod(378,178))
    1210 = (1184-2*(ΣΔ(178)-ΣΔ(378)))*mod(378,178)/(378-178)*Φ(mod(378,178))

    1100seaDO!n’t D-bait IT’s(UN)ami’tr(AP).
    The mowesstimepeertunesearise R-left doubt $0 v.OEIS.

    Conventionalmic:CO[no.11]mainstream a11|22 Can. ridicule and d!55m!55 what’s wwwe/11hh!dm!
    Meanwwwhhisle Homer dr.ink$44ale.

  15. Paul Vaughan says:

    Ramanujan’s Best Friend

    “God save the queen.” ——— sea B11owe no. won say UN: “$0 much more$(UN)s(poke)UN”

    342 = ΣΣΦ(178) = 2*171

    142 = ΣΔ(220) = Σδ(220)-(378-178) = 342-200
    284 = s(220) = 2*ΣΔ(220) = 2*142 = 2*(342-200) = 2*(Σδ(220)-(378-178))
    342 = Σδ(220) = ΣΔ(220)+(378-178) = 142+200
    200 = Σδ(220)-ΣΔ(220) = 342-142 = 378-178

    amicably us s(eur.) Bet:

    42 = ΣΔ(178)-ΣΔ(378)
    42 = average(22,Σs(22)) = average((378 mod 178),Σs(378 mod 178))
    84 = 22+Σs(22) = (378 mod 178)+Σs(378 mod 178) = 2*(ΣΔ(178)-ΣΔ(378))

    δ(300) = 220

    300 = Σδ(220)+ΣΔ(378)-ΣΔ(178) = 342-42
    300 = ΣΔ(220)+ΣΔ(378)-ΣΔ(178)+(378-178) = 142-42+200

    resolving another longstanding mystery (peacefully as promised) :
    58 = 200-142 = (378-178)- ΣΔ(220) = (378-178)+ΣΔ(378)-ΣΔ(178) = Σδ(220)-s(220) = Σδ(220)-2*ΣΔ(220)
    review of context:
    316 = ΣHeegner = Plato+average(-178,378)
    216 = Plato = 158+58
    158 = Σ”104 levels” = ΣHeegner/2
    320 = Σ”744 levels” = 220+average(-178,378) ————————– hhL!

    s(UN)chained no. more:
    242 = average(142,342)
    110 = Φ(242) = Δ(242)
    132 = φ(242) = δ(242) ———– resolves longstanding Jupiter-Saturn curiosity
    71 = ΣΦ(132) ——————————— top-level climate casino

    484 = 142+342 = s(220)+(378-178) = 284+200
    162 = ΣΔ(484)-(378-178) = 362-200 = Φ(163)
    163 = ΣΦ(484)-(378-178) = 363-200 ———– THE MAGENTA BRIDGE
    163 = ΣΦ(378) = ΣΦ(171) —————————- missed story link
    “…and wash awe way the reign” — Soundgarden

    220 = Φ(484) = Δ(484) = 484-264; 264 = φ(484) = δ(484)
    200 = 484-284 = 363-163 = 362-162

    Summary: Solar system “DO!” simple order$$show more!! (Lucy to Homer: “Triangular numbers integrate to tetrahedral.”)

    Supplementary

    Δ(220) = 80
    Δ(80) = 32
    Δ(32) = 16
    Δ(16) = 8
    Δ(8) = 4
    Δ(4) = 2; 142 = ΣΔ(220)
    Δ(2) = 2; repeats define stop (not in Σ = sum)

    δ(220) = 140
    δ(140) = 92
    δ(92) = 48
    δ(48) = 32
    δ(32) = 16
    δ(16) = 8
    δ(8) = 4
    δ(4) = 2
    δ(2) = 0; 342 = Σδ(220)

    notation, OEIS links

    10 = Φ(22)
    220 = 22*Φ(22)
    22 = 378 mod 178
    220 = (378 mod 178)*Φ(378 mod 178)

    s(220) = 4*ΣΦ(132) = 4*ΣΦ(100) = 4*71; 504 = 220+s(220) ———- again: Σseries NOT in OEIS
    “What sh!out[$F]Buy[11]’11 chew: mineDO!vert manner” hhale’n’vote$ “ink ABout direct$yen won Dair why?” REM

    Numbers are just transformers with more than won function:
    17.2616851219298 = beat(835.546575435631,16.9122914926352)
    131.716392653884 = slip(19.8650360864628,17.2616851219298) ———— 132 ahhazeUN!
    504.413226524327 = slip(131.716392653884,9.93251804323141) ———— 504 rat
    “s(ET) tune s(UN) dials(hanD) $0 V.GOALED” Queens(o11v-ethUStune[C]NNeige)
    16.5767613988929 = axial(835.546575435631,16.9122914926352)
    100.143082519986 = slip(19.8650360864628,16.5767613988929) ———— 100 cheese
    hhomer s(eveUN)$peechL:OEIS, $0 no. DO this time h bid UN

    ca.seaNNO.11owesst amicable number.
    Buy(DO!NNO?)parT(US$UN)imageUNITneeda11(owesst)in!ahaZZ$stack: R=220; D=284; s(R)=D; s(D)=R

  16. Paul Vaughan says:

    beware typos — check above and especially below (assembled in haste) — obvious corrections abound

  17. Paul Vaughan says:

    73 = ΣΦ(323)-average(ΣΣΦ(178),ΣΣΦ(378)) = average(19,43,67,163)
    111 = ΣΦ(73) = ΣΦ(φ(1333))

    47 = 28+19
    71 = 28+43
    95 = 28+67
    191= 28+163
    191 = 73+2*59 = 73+47+71
    191 = Σφ(158) = ΣΦ(145) = ΣΦ(290)

  18. Paul Vaughan says:

    sidereal & tropical
    25757.05496809 = beat(0.615197263396975,0.61518257)
    25763.987503107 = beat(1.00001743371442,0.99997862)
    25902.4692609995 = beat(1.88084761346252,1.88071105)
    23094.6280196825 = beat(11.8626151546089,11.85652502)

    Mars
    4819052.73659072 = beat(25902.4692609995,25763.987503107)
    4588072.54235821 = beat(25902.4692609995,25757.05496809)

    nodes
    2409526.36829536 = 4819052.73659072 / 2
    2294036.2711791 = 4588072.54235821 / 2

    Jupiter
    222903.550976462 = beat(25763.987503107,23094.6280196825)
    223423.821534848 = beat(25757.05496809,23094.6280196825)

    nodes
    111451.775488231 = 222903.550976462 / 2
    111711.910767424 = 223423.821534848 / 2

    408057.954160484 = harmean(2409526.36829536,222903.550976462)
    407190.049947398 = harmean(2294036.2711791,223423.821534848)

    153330.53308891 = beat(408057.954160484,111451.775488231)
    153947.018386359 = beat(407190.049947398,111711.910767424)

    306661.06617782 = 2 * 153330.53308891
    307894.036772718 = 2 * 153947.018386359

  19. Paul Vaughan says:

    220 = Φ(ΣΔ(220)+Σδ(220))
    220 = Δ(ΣΔ(220)+Σδ(220))
    100 = average(-s(220),ΣΔ(220)+Σδ(220)) = average(-178,378) = 4370-s(4370) = s(194)
    132 = φ(average(ΣΔ(220),Σδ(220)))
    132 = δ(average(ΣΔ(220),Σδ(220)))
    71 = ΣΦ(100) = ΣΦ(average(-178,378)) = ΣΦ(average(-s(220),ΣΔ(220)+Σδ(220)))
    71 = ΣΦ(132) = ΣΦ(φ(average(ΣΔ(220),Σδ(220)))) = ΣΦ(δ(average(ΣΔ(220),Σδ(220))))
    163 = ΣΦ(ΣΔ(220)+Σδ(220))-(378-178) = ΣΦ(378) = ΣΦ(171)
    163 = ΣΦ(100+ΣΦ(100)) = ΣΦ(ΣΦ(132)+ΣΦ(average(-178,378)))

    s(220) = 4*ΣΦ(132) = 4*ΣΦ(100) = 4*71; 504 = 220+s(220)

    158 = 378-178+ΣΔ(378)-ΣΔ(178) = 316/2
    220 = 178+ΣΔ(178)-ΣΔ(378) = 178+42 = 378-158
    284 = s(178+ΣΔ(178)-ΣΔ(378)) = 378-94 = s(378-158)
    220 = s(4*ΣΦ(132)) = s(4*ΣΦ(100)) = s(4*71) = 504-s(220) = s(284)
    284 = 4*ΣΦ(132) = 4*ΣΦ(100) = 4*71 = 504-220 = s(220)

  20. Paul Vaughan says:

    4428 ~= (378-178)√√(1/(93/1.00001743371442+93/y-30/0.0754402464065708-63/0.0745030006844627)/(93/1.00002638193018+93/y-30/0.0754402464065708-63/0.0745030006844627))

    0.0808503462976957 = 29.5305889852334 / 365.25
    0.0808503463381246 = 29.530589 / 365.25
    -0.000000050005 = % error
    -1.57802424 seconds/century = absolute error

    980 = 323+average(7920,-2400,-240,-24)/2
    1000 = average(7920,2400,240,24)/2-323

  21. Paul Vaughan says:

    name origin no. where? “monstrous moonshine“.

  22. Paul Vaughan says:

    16.9122914926352 = harmean(29.4474984673838,11.8626151546089) — sidereal
    16.9021472081198 = harmean(29.42351935,11.85652502) ——————— tropical
    16.9072178287419 = harmean(16.9122914926352,16.9021472081198)
    2.9072178287419 = 16.9072178287419 – 14
    ^2 =
    8.45191550375478
    √(9-4/8.45191550375478) =
    2.92005727717672 ———— seeds:

    2,3,5,7,11,13,17,22,31,52,76,108,158,247,300,481,608,997,1604
    2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73 — see prime-generating function

    481 = Δ(11#) = Σs(4370/Φ(22)) = 5 * 96.2
    481 = Σs(437); 437 = 378+Σφ(378)-Σδ(378)
    s(1690) = 1604; s(1604) = 1210; s(1210) = 1184; s(1184) = 1210

  23. Paul Vaughan says:

    323±58=(265,378)
    58=Φ(59); 59=s(265)
    437±59=(378,496); 496=s(496)

    58 = Σφ(378)-Σδ(378)+ΣΔ(378)-ΣΦ(378)
    59 = Σφ(378)-Σδ(378)
    437 = 378+Σφ(378)-Σδ(378)
    323 = 378-Σφ(378)+Σδ(378)-ΣΔ(378)+ΣΦ(378) = 196883-196560
    360 = σ(378-Σφ(378)+Σδ(378)-ΣΔ(378)+ΣΦ(378))

    378 = ΣΔ(378)+Φ(378)+Δ(378)

    478 = (28+163+67+43+19)+(58+37+22+18+13+10)
    478 = 320+158 = 316+162
    478 = (1+2+3+7+11+19+43+67+163)+Φ(163)
    478 = (1+2+3+7+11+19+43+67+ΣΦ(378))+Φ(ΣΦ(378))
    478 = (1+2+3+7+11+19+43+67+ΣΦ(378))+ΣΔ(378)

    270 = φ(378) = δ(378) = 162+108 = 378-108
    163 = ΣΦ(378)
    162 = ΣΔ(378) = Φ(163) = 378-Φ(378)-Δ(378)
    108 = Φ(378) = Δ(378) = 378-φ(378) = 378-δ(378)
    216 = Φ(378) + Δ(378)
    271 = ΣΦ(378)+Φ(378) = ΣΦ(378)+Δ(378)

  24. Paul Vaughan says:

    22 = ΣΣΦ(378)-ΣΣΦ(178)+ΣΔ(378)-ΣΔ(178)
    22 = ΣΦ(323)-Σφ(323)-378 = 378 mod 178
    Φ(22) = 10 = 163-67-43-19-11-7-3-2-1

    10^10 = (163-67-43-19-11-7-3-2-1)^(163-67-43-19-11-7-3-2-1)
    10^10 = Φ(22)^Φ(22) = Φ(378 mod 178)^Φ(378 mod 178)
    10^10 = Φ(ΣΦ(323)-Σφ(323)-378)^Φ(ΣΦ(323)-Σφ(323)-378)

    8.456145746318 = φφ/(1/323+1/(262537412640768744/10^10-(Σφ(323)+ΣΦ(323)-163)))/s(194)
    8.456145746318 = 1/(J+S)

  25. Paul Vaughan says:

    25757.05496809 = beat(0.615197263396975,0.61518257)
    23094.6280196825 = beat(11.8626151546089,11.85652502)
    11547.3140098413 = 23094.6280196825 / 2
    20931.0502252768 = beat(25757.05496809,11547.3140098413)
    111711.910767424 = beat(25757.05496809,20931.0502252768)

    1.00001743371442 = 1/E
    1.00002638570363 = beat(111711.910767424,1.00001743371442)
    1.00002638193018 = 365.259636 / 365.25
    0.000000377335 = % error; absolute error ~= 11.9 seconds / century

    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)
    1.00002638589293 = beat(111711.910767424,1.00001743390371)
    1.00002638193018 = 365.259636 / 365.25
    0.000000396264 = % error; absolute error ~= 12.5 seconds / century

  26. Paul Vaughan says:

    478 = ΣΦ(216)+Σφ(216) = (28+163+67+43+19)+(58+37+22+18+13+10)
    162 = Φ(163) = ΣΔ(378) = (28+163+67+43+19)-(58+37+22+18+13+10)
    216 = 378-ΣΔ(378) = Φ(ΣΦ(323)+Σφ(323))

    608 = Σφ(836)-ΣΦ(836) ——- another longstanding curiosity resolved
    s(s(608)) = s(652) = s(496) = 496; 496 = Σs(194)
    ΣΣΔ(496) = 1690

  27. Paul Vaughan says:

    Σs(608) = 1756 = 608+s(608)+s(s(608)) = 608+652+496 = 1260+496 = Φ(1333)+496
    Σs(28) = 28
    1728 = 1756-28

  28. Paul Vaughan says:

    323 = 196883-196560
    836 = ΣΦ(323)-Σφ(323)+ΣΔ(323)-Σδ(323)
    1216 = -ΣΦ(836)+Σφ(836)-ΣΔ(836)+Σδ(836)
    0 = ΣΦ(836)-Σφ(836)-ΣΔ(836)+Σδ(836)

  29. Paul Vaughan says:

    0 = ΣΦ(4)-Σφ(4)+ΣΔ(4)-Σδ(4) = ΣΦ(4)-Σφ(4)-ΣΔ(4)+Σδ(4)
    0 = ΣΦ(8)-Σφ(8)+ΣΔ(8)-Σδ(8) = ΣΦ(8)-Σφ(8)-ΣΔ(8)+Σδ(8)
    0 = ΣΦ(16)-Σφ(16)+ΣΔ(16)-Σδ(16) = ΣΦ(16)-Σφ(16)-ΣΔ(16)+Σδ(16)
    0 = ΣΦ(32)-Σφ(32)+ΣΔ(32)-Σδ(32) = ΣΦ(32)-Σφ(32)-ΣΔ(32)+Σδ(32)
    0 = ΣΦ(64)-Σφ(64)+ΣΔ(64)-Σδ(64) = ΣΦ(64)-Σφ(64)-ΣΔ(64)+Σδ(64)
    0 = ΣΦ(128)-Σφ(128)+ΣΔ(128)-Σδ(128) = ΣΦ(128)-Σφ(128)-ΣΔ(128)+Σδ(128)
    0 = ΣΦ(256)-Σφ(256)+ΣΔ(256)-Σδ(256) = ΣΦ(256)-Σφ(256)-ΣΔ(256)+Σδ(256)
    0 = ΣΦ(512)-Σφ(512)+ΣΔ(512)-Σδ(512) = ΣΦ(512)-Σφ(512)-ΣΔ(512)+Σδ(512)
    0 = ΣΦ(1024)-Σφ(1024)+ΣΔ(1024)-Σδ(1024) = ΣΦ(1024)-Σφ(1024)-ΣΔ(1024)+Σδ(1024)
    0 = ΣΦ(2048)-Σφ(2048)+ΣΔ(2048)-Σδ(2048) = ΣΦ(2048)-Σφ(2048)-ΣΔ(2048)+Σδ(2048)
    0 = ΣΦ(4096)-Σφ(4096)+ΣΔ(4096)-Σδ(4096) = ΣΦ(4096)-Σφ(4096)-ΣΔ(4096)+Σδ(4096)

  30. Paul Vaughan says:

    The Wizard Davo$

    36 = -ΣΦ(323)+Σφ(323)+ΣΔ(323)-Σδ(323)
    836 = ΣΦ(323)-Σφ(323)+ΣΔ(323)-Σδ(323)

    “left all ‘the people’ feel ENSO find” — BS

    608 = -ΣΦ(836)+Σφ(836) = -ΣΔ(836)+Σδ(836)
    s(s(608)) = s(652) = s(496) = 496

    “The crux of it is that […] is selling you the […] and the cure […]” “The […] still won’t have access to […] features without handing over even more […] to the same company that created this[…]sinkhole.”

    average(496,836) = 36+35+34+33+32+31+30+29+28+27+26+25+24+23+22+21+20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1

  31. Paul Vaughan says:

    Nominally Deterrent (“west word lead: instill preceding”) Weigh$well DCompetition

    Build$sum comparative D-light seas Framanujan: ΣΦ, Σφ, ΣΔ, & Σδ.
    Δ(n) & δ(n) are at most 1 from Φ(n) & φ(n), respectively, but: not so for ΣΔ(n) & Σδ(n) versus ΣΦ(n) & Σφ(n). (Myth or math?)

    concise description of sorting & classification method (that balances for powers of 2 with noteworthy alternation & exceptions) :
    comparative aggregation of recursive structure

    478 = sum of 104 & 744 levels = (10+13+18+22+37+58)+(28+163+67+43+19)
    194 = ΣΦ(478)-Σφ(478)+ΣΔ(478)-Σδ(478)
    496 = Σs(194)
    ΣΣΔ(496) = 1690

    interdisciplinary+intercultural explorer traversing Fields$ perspective notes:
    Curiously and/or mysteriously, specialist tribes appear too withhold (perhaps an accident, perhaps not) some of the best cards.
    Let’s D-lightfully observe how long it takes noteworthy characters too build the OEIS (too be even more incluesieve).

    59 = average(47,59,71)
    “when the wizard f(11OX)$ buy” — BS
    163 = ΣΦ(59)-Σφ(59)+ΣΔ(59)-Σδ(59)

    When asked “what is the physical mechanism?” the answer is always “the one($) you believe in”, but that doesn’t excuse supersingular ignorance of Boundary Conditions (in≠equal≠IT) shaping (in cons$art with top e.g. rough fee) heterogeneous physical aliasing (as in discrete $sir cue la tory TOpoll owe G$shift). Remedial prescription: $superior number theory (& concrete math) education for the masses begin$now$0 future generation$sea better dynamic TO$$elation of nonlinear processes$simply adjustin’big tent’ UN IT as follows$ less time for D-bait + more time for peace and tranquility.

  32. Paul Vaughan says:

    Dr. One Left Owe Vert 601

    Duke bri11D plot top US nos. the write trumpet air serves only what’$11oft over.

    292 = average(ΣΦ(314),Σφ(314)) = 163+67+43+19

    $πLhhwy601heignorealiquotsumwon

    314 = 601-ΣΦ(601)-Σφ(601)+ΣΔ(601)+Σδ(601) = ⌊100π⌉
    314 = 316-ΣΦ(316)-Σφ(316)+ΣΔ(316)+Σδ(316)

    aCADemIC$ paid hh D-vote$UN ZZ form AI IT, canu$sumarizze what’s D-liberately left doubt of volUNtieroxp[11]eer ace sun?

    447 = 314-ΣΦ(314)-Σφ(314)+ΣΔ(314)+Σδ(314) = ΣΦ(323)

    316 = 2*(104 level sum) = 2*(10+13+18+22+37+58) = ΣHeegner nos.
    320 = (744 level sum) = (28+163+67+43+19)

    318 = average(316,320)
    318 = 320-ΣΦ(320)-Σφ(320)+ΣΔ(320)+Σδ(320)
    318 = 378-ΣΦ(378)-Σφ(378)+ΣΔ(378)+Σδ(378)

    Homer’$a11oonNY, $0 lure “DO!” can. hh ave. IT’$ best US e^$ in D-sky$.
    600 = Φ(601)

  33. Paul Vaughan says:

    Perfectly Amicable Sing-Along, with Ally Caught Tool in a Round

    We CO2*ll’$ mi$$ s(UN) IT’$hhistoric B11ink con$sumETtree: ΣΦ(323)-Σφ(323)-378 = 378 mod 178

    11ETUS$note we11 $sum Boundary Conditions “up north”:
    447 = ΣΦ(608) = ΣΦ(323) = 314 – ΣΦ(314) – Σφ(314) + ΣΔ(314) + Σδ(314)
    223 = ΣΦ(304)
    111 = ΣΦ(152) —– ⌊UN harmean⌉
    55 = ΣΦ(76)

    Balancing aggregation criteria well, just in time 2 review the base.

    4 = –76-ΣΦ(76)+Σφ(76)-ΣΔ(76)+Σδ(76) = 2^2
    8 = -152-ΣΦ(152)+Σφ(152)-ΣΔ(152)+Σδ(152) = 2^3
    16 = -304-ΣΦ(304)+Σφ(304)-ΣΔ(304)+Σδ(304) = 2^4
    32 = -608-ΣΦ(608)+Σφ(608)-ΣΔ(608)+Σδ(608) = 2^5
    64 = -1216-ΣΦ(1216)+Σφ(1216)-ΣΔ(1216)+Σδ(1216) = 2^6
    128 = -2432-ΣΦ(2432)+Σφ(2432)-ΣΔ(2432)+Σδ(2432) = 2^7

    Myth or math?

    80 = -ΣΦ(76)+Σφ(76)-ΣΔ(76)+Σδ(76) = 5 * 2^4
    160 = -ΣΦ(152)+Σφ(152)-ΣΔ(152)+Σδ(152) = 5 * 2^5 = 323-163
    320 = -ΣΦ(304)+Σφ(304)-ΣΔ(304)+Σδ(304) = 5 * 2^6
    640 = -ΣΦ(608)+Σφ(608)-ΣΔ(608)+Σδ(608) = 5 * 2^7
    1280 = -ΣΦ(1216)+Σφ(1216)-ΣΔ(1216)+Σδ(1216) = 5 * 2^8
    2560 = -ΣΦ(2432)+Σφ(2432)-ΣΔ(2432)+Σδ(2432) = 5 * 2^9

    Heegner nos. perfectly well: 19 = x mod (1+2+3+7+11) for x = 19,43,67,163; 19+19+19+19 = 76

    2432 = 5*2^9-2^7 = 2560-128 = 19*2^7
    1216 = 5*2^8-2^6 = 1280-64 = 19*2^6
    608 = 5*2^7-2^5 = 640-32 = 19*2^5; s(608) =4*163= 652; s(652) = 496; s(496) = 496
    304 = 5*2^6-2^4 = 320-16 = 19*2^4
    152 = 5*2^5-2^3 = 160-8 = 19*2^3
    76 = 5*2^4-2^2 = 80-4 = 19*2^2
    38 = 5*2^3-2^1 = 40-2 = 19*2^1
    19 = 5*2^2-2^0 = 20-1 = 19*2^0

    Homer’$pie in a⌊round⌉ “up
    north” $11each moon$star “DO!”

    323 = 1470-ΣΦ(1470)-Σφ(1470)-ΣΔ(1470)+Σδ(1470) = 196883-196560
    157 = -ΣΦ(1470)+Σφ(1470)+ΣΔ(1470)-Σδ(1470) = 314 / 2
    000 = -ΣΦ(980)+Σφ(980)+ΣΔ(980)-Σδ(980)
    157 = -ΣΦ(490)+Σφ(490)+ΣΔ(490)-Σδ(490)) = ⌊100π⌉ / 2

    314 = ⌊100π⌉ =
    -ΣΦ(490)+Σφ(490)+ΣΔ(490)-Σδ(490))
    -ΣΦ(980)+Σφ(980)+ΣΔ(980)-Σδ(980)
    -ΣΦ(1470)+Σφ(1470)+ΣΔ(1470)-Σδ(1470)

    Knot$(orrery)
    BC0$ perfect
    weather$ami[-ΣΦ(220)+Σφ(220)-ΣΔ(220)+Σδ(220)-378ON]caba11canuck$hhown:

    284 = -608+ΣΦ(608)-Σφ(608)+ΣΔ(608)+Σδ(608)
    1210 = ΣΦ(304)+Σφ(304)+ΣΔ(304)+Σδ(304)
    220 = ΣΦ(152)-Σφ(152)+ΣΔ(152)+Σδ(152)
    1184 = -378-ΣΦ(378)+Σφ(378)+ΣΔ(378)+Σδ(378)

    478 = (28+163+67+43+19)+(58+37+22+18+13+10) —- 744+104 levels
    478 = 84+ΣΦ(84)+Σφ(84)+ΣΔ(84)+Σδ(84) —————- U+
    478 = -ΣΦ(1210)+Σφ(1210)+ΣΔ(1210)-Σδ(1210)
    3456 = 1210-ΣΦ(1210)+Σφ(1210)-ΣΔ(1210)+Σδ(1210) = 2 * 1728 —— j-invariant
    1690 = 1210+ΣΦ(1210)+Σφ(1210)-ΣΔ(1210)-Σδ(1210) ——————- JSharmean

    My. CR owe sov. DO!N’T $peek a⌊round⌉ 193:
    1470 = 1186 + 284 = 1186 + s(220) = 5*σ(193); 193.385594895064 = slip(22.1392314983837,19.8650360864628)
    735 = average(1186,284) = average(1186,s(220))
    Sum th11ng monster US22hharp.ABout, NO. DOUBT: 378 = ΣΦ(194)+Σφ(194)-ΣΔ(194)+Σδ(194)
    1186 = -378+ΣΦ(378)+Σφ(378)-ΣΔ(378)+Σδ(378)

    IT’$ SAM ON SST URLeach 11ET US$ play DO! amicably:
    216 = -ΣΦ(323)+Σφ(323)+ΣΔ(323)+Σδ(323)
    220 = ΣΦ(216)-Σφ(216)+ΣΔ(216)+Σδ(216) = s(284)
    284 = ΣΦ(220)-Σφ(220)+ΣΔ(220)+Σδ(220) = s(220)
    504 = 220+ΣΦ(220)-Σφ(220)+ΣΔ(220)+Σδ(220) = 220+284 = 220+s(220) = s(284)+284

    11owe$SST2 sea are pairUS$ami CO2B11y:
    220 = 2*(2*5*11); s(220) = 284
    1210 = (2*5*11)*11; s(1210) = 1184

    =
    […] Sanders often advocates for things that are “common sense.”

    The president gave a nod to Sanders, who noted their past rivalry and yet spoke with similar urgency about the moment before them — how the future of democracy rests with how well they can connect with people who feel the government has forgotten them.

    Ask Sanders any question, on almost any topic, and his answers are almost always the same — it’s time for the government to stop catering to the rich and powerful and instead focus on the working people of this country.

    Once seen as outlandish, Sanders’ views have captivated millions of Americans who filled arenas to hear him speak, particularly after the Great Recession and amid a growing awareness of the nation’s gaping inequality.

    “The president may have won the nomination, but Bernie Sanders won the argument,” Senate Republican leader [mmmC022e/11] said recently back home in [can’t talk key…]

    But in developing the investment package with the president, Sanders showed another side of his skill set: that of a pragmatic legislator.
    =

  34. Paul Vaughan says:

    Left Over 986…

    …in can aid y’no. how MP “$sure!” :

    5256 = 7920-2400-240-24 —-(M11,E8)
    4270 = s(4370) ———————(B)

    986 = 5256-4270 ————–JSlip

    986.377938012414 = slip(304.031799474187,131.716392653884); *3/2:
    1479.56690701844 = slip(504.413226524327,65.8581963269421); *2:
    2959.13381403688 = slip(504.413226524327,131.716392653884)
    2959.13381403679 = slip(356.533700137559,50.0715412599931)

    Certain11y peephhi!11 who-think they “no. $SUM thing” ABout 980 could misunderstand, misinterpret, and misrepresent 986 (a different but functionally-related $pace “yell symmetry!”) weather buy typor,we11,DC$sign.

    inC”DO!”n’t!foo11hh”DO!”bait: eve “UN B-art” 11earns22stay peacefu11 & tranqui11 when “DO! buy into11jaune$” D-liberately provokes$withh LODZZplane, BO$$ ON f(UN) 22 $$sea hhi! 11and washh in tune “[11] nos. hhowe22 get what$$shheik aim hh”. Notes$SAM IC AB11y nos.:

    504 = 220+284
    504.413226524327 = slip(131.716392653884,9.93251804323141)
    504.413226524325 = slip(208.886643858908,131.716392653884)
    504.413226524329 = slip(131.716392653884,104.443321929454)
    504.413226524326 = slip(178.266850068779,131.716392653884)
    504.413226524332 = slip(131.716392653884,104.443321929454)

    put in DCoy$11ingo vert mont star:

    252 = average(220,284)
    252.206613262163 = slip(65.8581963269421,4.9662590216157)
    252.206613262164 = slip(104.443321929454,65.8581963269421)
    1479.56690701844 = slip(252.206613262163,65.8581963269421)
    2959.13381403688 = slip(252.206613262163,131.716392653884)

    UNdoorSSTooD-atoll$singahhLong, PRsumAB11y in220cent11y (22 rightly spin) Rush (AB-born ease?) “workin’ man.” NN0$we11 PC hhair peer when can talk key Fri. D-Chi11 kin: withh_care no.11$s(and)D-hheirs$.

  35. Paul Vaughan says:

    Amicable Circles CO22a11US

    “21st century’s yesterday” — inxs
    IT$syncan’t talk key do!or[we11]B:
    “The wwwURL11? DO!VE 0$ s(umPiRe) s(cent.) 22 dr.reign” — s(mass)hh’n’DpumpCan$

    1184 = -378-ΣΦ(378)+Σφ(378)+ΣΔ(378)+Σδ(378)
    1186 = -378+ΣΦ(378)+Σφ(378)-ΣΔ(378)+Σδ(378)

    Image UN 22 mass caught history: bernie and don united in peace and tranquility.

    Massively amicable giant weather myth or math:
    1186 = 1184+ΣΦ(1184)+Σφ(1184)-ΣΔ(1184)-Σδ(1184)

    Sum homework help for Homer, who’s DO!win the massively giant math amicably:

    Φ(378) = 108
    Φ(108) = 36
    Φ(36) = 12
    Φ(12) = 4
    Φ(4) = 2
    Φ(2) = 1; 163 = ΣΦ(378)
    Φ(1) = 1 — repeat, not in sum

    φ(378) = 270
    φ(270) = 198
    φ(198) = 138
    φ(138) = 94
    φ(94) = 48
    φ(48) = 32
    φ(32) = 16
    φ(16) = 8
    φ(8) = 4
    φ(4) = 2
    φ(2) = 1
    φ(1) = 0; 811 = Σφ(378)

    Δ(378) = 108
    Δ(108) = 36
    Δ(36) = 12
    Δ(12) = 4
    Δ(4) = 2; 162 = ΣΔ(378) = Φ(163)
    Δ(2) = 2 — repeat, not in sum

    δ(378) = 270
    δ(270) = 198
    δ(198) = 138
    δ(138) = 93
    δ(93) = 34
    δ(34) = 19
    δ(19) = 0; 752 = Σδ(378)

    1184 = -378-ΣΦ(378)+Σφ(378)+ΣΔ(378)+Σδ(378) = -378-163+811+162+752
    1186 = -378+ΣΦ(378)+Σφ(378)-ΣΔ(378)+Σδ(378) = -378+163+811-162+752

    378 = sum of supersingular primes = ΣΦ(323)-Σφ(323)-22

  36. Paul Vaughan says:

    2360489.30436563 = beat(44.2792936122789,44.2784630136989)

    2360489.30437277 = 2/(1/(φ^22+1/11)^(e/11+1/22)-1/ln(163*67*43*19*11*7*3*2*1))
    1180244.65218639 = 1/(1/(φ^22+1/11)^(e/11+1/22)-1/ln(163*67*43*19*11*7*3*2*1))

    405375.147994516 = 1/((1/(φ^22+1/11)^(e/11+1/22)-1/ln(163*67*43*19*11*7*3*2*1))/2+1/271/43/7/3/2)

    g4-g3, s4-s3, g2-g5

  37. Paul Vaughan says:

    5*σ(193) = typo above
    “1470 = 1186 + 284 = 1186 + s(220) = 5*σ(193); 193.385594895064 = slip(22.1392314983837,19.8650360864628)”

    5*σ(σ(193)) = correction
    1470 = 1186 + 284 = 1186 + s(220) = 5*σ(σ(193)); 193.385594895064 = slip(22.1392314983837,19.8650360864628)

    194 = σ(193) = 1+193
    294 = σ(194) = σ(σ(193)) = 1+2+97+194
    100 = s(194) = 2+97+194 = σ(194)-σ(193)

  38. Paul Vaughan says:

    22 = 735-713 = 378 mod 178
    601 = 1314-713 = (7920-2400-240-24)/4 – 713
    84 = average(713-601,average(713,-601))
    M11,B,M with E8

    V&D (2400 thread)
    713.067400275117 = 4*178.266850068779
    713.067400275117 = 2*356.533700137559
    378 = ΣΦ(713)-Σφ(713)-ΣΔ(713)+Σδ(713) = sum of supersingular primes

    939 ~= beat(2959,713) — both JS & lunisolar

  39. Paul Vaughan says:

    JEV slip on JS:

    46.7562353908971 = beat(835.546575435631,44.2784629967674)
    42.0500855356652 = axial(835.546575435631,44.2784629967674)

    132.193670214152 = slip(46.7562353908971,19.8650360864628)
    360.052437637012 = slip(42.0500855356652,19.8650360864628)

    720.109976797377 = slip(132.193670214152,16.9122914926352)
    1600.05985446962 = slip(720.494098826682,132.193670214152)

    notice scaling:
    40 = √1600
    1600 = 40^2
    64000 = 40^3

    generalize:
    1 = 2^0*5^0 = 40^0
    40 = 2^3*5^1 = 40^1
    1600 = 2^6*5^2 = 40^2
    64000 = 2^9*5^3 = 40^3

    supplementary:
    21 = average(22.14,19.86)
    21.0021337924233 = average(22.1392314983837,19.8650360864628)
    42.0042675848465 = 2 * 21.0021337924233
    84.0085351696931 = 2 * 42.0042675848465

  40. Paul Vaughan says:

    237 = 400-163 = ΣΦ(323)-Σφ(323)-163
    237 = average(158,316)
    237 = 4370/Φ(378 mod 178)-(378-178)
    237 = 2*beat(640,average(-178,378))

    supplementary:
    316 = ΣHeegner = 1+2+3+7+11+19+43+67+163
    323 = 196883-196560; 447 = ΣΦ(323); 47 = Σφ(323)

  41. Paul Vaughan says:

    “Can’t Talk Key” Numbers

    Observe weather OEIS (eventually) reflects the name.

    Simple example:
    ———–
    δ(12) = 8
    δ(8) = 4
    δ(4) = 2
    δ(2) = 0; 14 = Σδ(12)
    ———–
    δ(14) = 9
    δ(9) = 3
    δ(3) = 0; 12 = Σδ(14)
    ———–
    Summary:
    Σδ(12) = 14 — 1
    Σδ(14) = 12 — 2
    Σδ(12) = 14 — 1
    Σδ(14) = 12 — 2; etc.

    Seed with sum of supersingular primes:
    Σδ(378) = 752
    Σδ(752) = 894 — 1
    Σδ(894) = 902 — 2
    Σδ(902) = 894 — 1
    Σδ(894) = 902 — 2; etc. — endless loop, like amicable numbers

    Merge recursive dynamical systems (the preceding and the lowest amicable pair) :
    1186 = 902+284 = 1470-284 = average(902,1470); 284 = s(220); 902 = Σδ(Σδ(Σδ(378)))

    Smallest untouchable weird number founds sociable chain including 744:
    Σδ(836) = 1126 — 1
    Σδ(1126) = 744 — 2
    Σδ(744) = 1534 —- 3
    Σδ(1534) = 1334 —– 4
    Σδ(1334) = 1293 —— 5
    Σδ(1293) = 740 ——– 6
    Σδ(740) = 1126 — 1
    Σδ(1126) = 744 — 2
    Σδ(744) = 1534 —- 3
    Σδ(1534) = 1334 —– 4
    Σδ(1334) = 1293 —— 5
    Σδ(1293) = 740 ——– 6
    Σδ(740) = 1126 — 1
    Σδ(1126) = 744 — 2; etc.

  42. Paul Vaughan says:

    323 = 196883-196560
    836 = ΣΦ(323)-Σφ(323)+ΣΔ(323)-Σδ(323)
    1216 = -ΣΦ(836)+Σφ(836)-ΣΔ(836)+Σδ(836)

    Σδ(744) = 1534 = Σδ(1216)
    Σδ(1534) = 1334
    Σδ(1334) = 1293
    Σδ(1293) = 740
    Σδ(740) = 1126 = Σδ(836) = Σδ(600)
    Σδ(1126) = 744

  43. Paul Vaughan says:

    Punt a (2020 Hindsight) Gone!

    Reviewing 104 & 744 levels (leaving perfect 28 aside as an isolated case since only s(28) goes there), errors are scale-invariant for 0 congruent to n mod 5 (e.g. 147, 294, 735, etc.).

    0 = (0+0+0)/316 = 0/316
    1 = (5+147+164)/316 = 316/316
    2 = (10+294+328)/316 = 632/316
    5 = (25+735+820)/316 = 1580/316
    10 = (50+1470+1640)/316 = 3160/316
    20 = (100+2940+3280)/316 = 6320/316

    Some (maybe not all) lovers sov. 49^2 = 2401 in a deep state of 2432 ignorance missed the scenic route to perfection:
    s(s(292+316)) = 496

    292 = 163+67+43+19 —– 744 levels (omitting 28 = s(28) as a perfectly isolated case)
    316 = 2*(10+13+18+22+37+58) —– double the 104 levels
    316 = 163+67+43+19+11+7+3+2+1 —- Heegner nos.

    608 = 292+316 = 2432/4
    s(608) = 652 = 163*4
    s(652) = 496 ————————— “rhyme without a reason?”
    s(496) = 496 ——- perfect no. (USA inverted totalitarianism’s theme song)

    Sum DO!n’t no. weave been right here SSTringin’ the bass.
    NATO states “sing-along left” in “can talk key diss” belief: “Teach me? EU will sea…” -Metallica

  44. Paul Vaughan says:

    Perfect Trade icehhLace sh!own!

    Write 28 trade mysteries, so far left no. doubt comm.:
    2317.99883398204 = 80*(√28+√163+√43+√19) ~= 2318
    1469.97105093686 = 50*(√10+√13+√18+√22+√37+√58)

    Know peace and tranquility, weather left, AND right clues:
    164.007196265537 = 5*(√28+√163+√67+√43) —————— what is missing?

  45. Paul Vaughan says:

    “Be a simple kind dove man. Love and understand” -Lynyrd Skynyrd

    29.3999997224409 = (1/1728+√10+√13+√18+√22+√37+√58)
    489.999995374015 = (1/1728+√10+√13+√18+√22+√37+√58)*50/3
    734.999993061023 = (1/1728+√10+√13+√18+√22+√37+√58)*25
    979.999990748031 = (1/1728+√10+√13+√18+√22+√37+√58)*100/3
    1469.99998612205 = (1/1728+√10+√13+√18+√22+√37+√58)*50
    36749.9996530511 = (1/1728+√10+√13+√18+√22+√37+√58)*1250
    73499.9993061023 = (1/1728+√10+√13+√18+√22+√37+√58)*2500

    29.4 = ⌊10*29.3999997224409⌉/10
    490 = ⌊489.999995374015⌉
    735 = ⌊734.999993061023⌉
    980 = ⌊979.999990748031⌉
    1470 = ⌊1469.99998612205⌉
    36750 = ⌊36749.9996530511⌉
    73500 = ⌊73499.9993061023⌉

    σ(193) = 194; 193 ~= slip(22.14,19.86)
    σ(194) = 294 = ⌊293.999997224409⌉ = ⌊(2/3456+√10+√13+√18+√22+√37+√58)*10⌉
    σ(294) = 684 = σ(735) / 2 = σ(ΣΦ(1800)) / 2

    σ(220) = 504
    σ(110) = 216; σ(216) = 600

  46. Paul Vaughan says:

    “and if you do this sun it’ll help you sum sunny day” — Lynyrd Skynyrd “Simple Man”

    Recall…
    36750.3379015986 = 8/(g_2 + 5*g_3 + 5*g_4 + g_6 + s_2 + s_3 + s_4 + s_6)

    in deeper state of scrutiny:

    1728 ~= 1727.91176140242 = average(1727.17161033091,1728.65191247393)
    = -average(
    1/((√10+√13+√18+√22+√37+√58)-29.4) ,
    -2*(√10+√13+√18+√22+√37+√58)^2 )

    1728.65191247393 = 2*(√10+√13+√18+√22+√37+√58)^2
    29.3994210187372 = (√10+√13+√18+√22+√37+√58)
    0.000578981262787437 = 29.4-(√10+√13+√18+√22+√37+√58)
    1727.17161033091 = 1/(29.4-(√10+√13+√18+√22+√37+√58))
    29.4000000575328 = (1/1727+√10+√13+√18+√22+√37+√58)
    5.75328122920382E-08 = (1/1727+√10+√13+√18+√22+√37+√58)-29.4
    17381385.685163 = 1/((1/1727+√10+√13+√18+√22+√37+√58)-29.4)
    173813.85685163 = 1/((1/1727+√10+√13+√18+√22+√37+√58)-29.4)/100

    La2011 Table 6 La2004a
    173913.043478261 = 1 / g_2 = 360*60*60/7.452
    173813.85685163
    0.057064855719 = % error

    La2011 Table 6 La2010a
    173889.708842077 = 1 / g_2 = 360*60*60/7.453
    173813.85685163
    0.043639783284 = % error

    La2011 Table 5
    173804.240903943 = 1 / g_2 = 360*60*60/7.456665
    173813.85685163
    -0.005532325133 = % error

  47. Paul Vaughan says:

    Chandler’s Amicable Divisor Sum (no taxicab included)

    σ(690) = 1728
    30.602899672346 = √28+√163+√67+√19
    30.6000011216214 = √28+√163+√67+√19-2/690
    29.3999997224409 = 1/1728+√10+√13+√18+√22+√37+√58
    60.0000008440623 = 1/1728+√10+√13+√18+√22+√37+√58+√28+√163+√67+√19-2/690
    8.44062280349125E-07 = -60+1/1728+√10+√13+√18+√22+√37+√58+√28+√163+√67+√19-2/690
    1184746.69853316 = 1/(-60+1/1728+√10+√13+√18+√22+√37+√58+√28+√163+√67+√19-2/690)
    1184 = s(1210); 1210 = s(1184) ——- amicable nos.

    1.18474669853316 = 1/1000000/(-60+1/1728+√10+√13+√18+√22+√37+√58+√28+√163+√67+√19-2/690)
    2.36949339706633 = 1/500000/(-60+1/1728+√10+√13+√18+√22+√37+√58+√28+√163+√67+√19-2/690)
    432.728731639238 = 365.25/1000000/(-60+1/1728+√10+√13+√18+√22+√37+√58+√28+√163+√67+√19-2/690)
    43 is not left doubt in assembly he ignores:

    153.000005608107 = 5*(√28+√163+√67+√19-2/690)
    153 = 1+2+3+7+11+19+43+67

  48. Paul Vaughan says:

    2318 Ways to Sea “2400”

    exec cue dove summary:
    42 11ink$ 104 & 744

    hitchhiker, Plato – quick review:
    42 = ΣΔ(178)-ΣΔ(378) = average(22,Σs(22)); 22 = 378 mod 178
    216 = 378-ΣΔ(378) = 378-Φ(163)

    “isle$shh!owe EU ‘how too’ fined $sanctuary” — the CO[II]T

    28.9749854247756 = √28+√163+√43+√19

    Σδ(42) = 29 (saturn)
    Σδ(29) = 0; 29 = ΣΣδ(42)

    Σδ(104) = 118 = 47+71 = 2*59 (jupiter)
    Σδ(118) = 61 (jupiter&saturn)
    Σδ(61) = 0; 179 = ΣΣδ(104) = 323+47*71-59^2 (11UNaTALK$shh!op)

    179 = Δ(209) = 58+(10+13+18+22+58) = 58+(11^2) = 216-37
    Just white collar readers can sea what’s politics and what’$knot?

    40	1159	1158.99941699102	10.74
    80	2318	2317.99883398204	9.74
    120	3477	3476.99825097307	9.16
    160	4636	4635.99766796409	8.74
    200	5795	5794.99708495511	8.42
    240	6954	6953.99650194613	8.16
    280	8113	8112.99591893716	7.94
    320	9272	9271.99533592818	7.74
    360	10431	10430.9947529192	7.57
    

    last column = measure of alignment quality =
    log of reciprocal absolute error (log base 2 to ease interpretation)

    Adjusting error tolerance to be less exclusive:

    1	29	28.9749854247756	5.32
    2	58	57.9499708495511	4.32
    3	87	86.9249562743267	3.74
    
    36	1043	1043.09947529192	3.33
    37	1072	1072.07446071670	3.75
    38	1101	1101.04944614147	4.34
    39	1130	1130.02443156625	5.36
    40	1159	1158.99941699102	10.74	local max
    41	1188	1187.97440241580	5.29
    42	1217	1216.94938784057	4.3
    43	1246	1245.92437326535	3.72
    
    76	2202	2202.09889228294	3.34
    77	2231	2231.07387770772	3.76
    78	2260	2260.04886313249	4.36
    79	2289	2289.02384855727	5.39
    80	2318	2317.99883398204	9.74	local max
    81	2347	2346.97381940682	5.26
    82	2376	2375.94880483160	4.29
    83	2405	2404.92379025637	3.71
    

    PET $SSTrue “DO!”

    Wizard davo$seas$e[XC]11USieve method sov. B11ooCO[II]11ure musst!dr.ravePopE^T$he ignore.

    √67-omission alignment-quality clusters.
    Contrast: Other omissions regularly space isolated instances.

    1159 = ⌊29/(29-√28-√163-√43-√19)⌉
    2318 = 2*⌊29/(29-√28-√163-√43-√19)⌉

    Can almost-integer-sea what he ignore?
    VAST opportunity to improve blue collar math and computer science education.

    0.0250145752244419 = 29-√28-√163-√43-√19
    89.4003703719118 = slip(28.9749854247756,0.0250145752244393)
    ⌊1/0.0003703719118⌉ = ⌊2699.9887627188⌉ = 2700 = 3^3*2^2*5^2
    89.4000000015415 = 89.4003703719118-1/3^3/2^2/5^2

    Peace and tranquility threw recursive dynamical systems fram above:

    Σδ(378) = 752
    Σδ(752) = 894 — 1
    Σδ(894) = 902 ——– 2
    Σδ(902) = 894 — 1
    Σδ(894) = 902 ——– 2; etc. — just an endless loop, like amicable numbers

    640 = 744-104 = 2*(28+163+67+43+19)

    Σδ(902) = 894 = Σδ(Σδ(378)) = Σδ(640)
    Σδ(894) = 902 = Σδ(Σδ(Σδ(378))) = Σδ(Σδ(993))
    378 & 993 are Σδ-untouchable

    $SSTringUN the bass ever-so amicably:
    σ(894) = 1800 = 3*600; 600 = Φ(601); 601 = aliquot sequence prime s(378)
    980 = 1216+600-836 —- 1216,600,836 are Σδ-untouchable

    284 = s(220) = Σδ(Σδ(4270)) = Σδ(Σδ(s(4370)))
    220 = s(284) = s(Σδ(Σδ(4270))) = s(Σδ(Σδ(s(4370))))
    s(4370) = 4270 is Σδ-UNtouchable (uranus-neptune)

    Sea? Just inVAsst tune norT(hh)folk bot tour-math red(UKshh!own)word R. “DO!” We:
    “The study of cycles reveals to us our ignorance and is therefore very disturbing to people whose ideas are crystallized.”

  49. Paul Vaughan says:

    Led Amicable ” ‘Cause…”

    “…UN no. sum times “ 220plan

    8.4561457463176 = axial(29.4474984673838,11.8626151546089)
    55.6462717641972 = axial(164.791315640078,84.016845922161)
    9.97142885566705 = beat(55.6462717641972,8.4561457463176)

    16.9122914926352 = harmean(29.4474984673838,11.8626151546089)
    111.292543528394 = harmean(164.791315640078,84.016845922161)
    19.9428577113341 = beat(111.292543528394,16.9122914926352)
    9.97142885566705 = 19.9428577113341 / 2

    2545.34384727959 = slip(19.8650360864628,9.97142885566705)
    2545 = ΣΣδ(220); 2*ΣΣδ(220) = 5090

    midpoint of lowest amicable pair: 252
    sum of lowest amicable pair: 504 = 220+284 = 220+s(220) = σ(220)
    378 = average(252,504) = Σ(supersingular primes) = Σ(unique monster factors)
    42 = 220-178; 178 = Σ(unique baby monster factors)
    Σδ(42) = 29

    71 = -Σδ(42)+100 = top monster factor = highest supersingular prime
    100 = average(-ΣΦ(220),Σφ(220)) = average(-178,378) = s(194)
    100 = average(-Σφ(323),ΣΦ(323))/2 = Σ(primes up to 23) = 4370-s(4370)

  50. Paul Vaughan says:

    Chuck Weather 220

    “Integer Fram”
    “DO!” $scores?

    On the XR thread I introduced a totally new line of commentary. What I considered (at that time) to be the most important comment I ever submitted got stuck permanently in the filter and never appeared.

    He Ignore (p.8 = pdf p.36) Scafetta?…

    2317.56010498444 = 1/(1/11.8622257815013-3/29.4577438277309+1/84.0137716722452+1/164.791884843631)

    …or amicably sharp Sylvester sequencing of Seidelmann (1992)?

    2545.34384727789 = 1/(1/11.8626151546089-3/29.4474984673838+1/84.016845922161+1/164.791315640078)

    In 2005, B. C. Kellner proved E. W. Weisstein’s conjecture that denom(B_n) = n only if n = 1806. – Jonathan Sondow, Oct 14 2013″

    “B. C. Kellner, The equation denom(B_n) = n has only one solution, preprint 2005.”

    a-lot-tell parameter(T’We’)king he(“$sure!”lead DO!n’t)ignore. 4(Σamicable)treat$seas on the river bank sov. IT$$Thhime$…

  51. Paul Vaughan says:

    (902-894)^2 = 8^2 = 64 = 284-220

    peaceful source
    1114 = 894+220
    1186 = 902+284
    of multitudinous puzzling
    1122 = 902+220
    1178 = 894+284
    hhomer seas solar system merge

    2300 = 894+902+220+284
    200 = 14+86+22+78
    100 = 14+86 = 22+78 = 23+19+17+13+11+7+5+3+2
    50 = average(14,86,22,78)

    1100 = 11*100
    11 = (2300-100)/200
    22 = (2300-100)/100 = 11+11
    44 = (2300-100)/50 = 11+11+11+11

    2200 = 894+902+220+284-100
    220 = (2300-100)/Φ((2300-100)/100) = s(284) —– left-right loop$not icing what?

  52. Paul Vaughan says:

    s(220) = 284
    s(284) = 220
    s(220) = 284
    s(284) = 220
    s(220) = 284
    s(284) = 220
    s(220) = 284
    s(284) = 220

    504 = 220+284
    252 = average(220,284)
    378 = average(252,504) = 2+3+5+7+11+13+17+19+23+29+31+41+47+59+71

    Σδ(378) = 752
    Σδ(752) = 894
    Σδ(894) = 902
    Σδ(902) = 894
    Σδ(894) = 902
    Σδ(902) = 894
    Σδ(894) = 902

    4428 = (2214+1986)+(2214-1986)

  53. Paul Vaughan says:

    scrutinizing and differentiating methods a little more deeply

    Comparison:
    2402, 2545
    2258, 2318

    Seidelmann (1992)

    2402.49013653277 = 1/(5/2/11.8626151546089-5/2/29.4474984673838-43/2/84.016845922161+43/2/164.791315640078)

    Substituting the periods used in the 2016 Scafetta paper:

    2258.02531711108 = 1/(5/2/11.8622257815013-5/2/29.4577438277309-43/2/84.0137716722452+43/2/164.791884843631)

    Heegner numbers relate to both models but in different ways. Have Charvatova’s and V&D’s model parameters ever been clarified precisely? The official answer may still be no, but that doesn’t stop sensible people from making careful inference.

    It’s clear there were folks in Seidelmann’s group with a working knowledge of simple sporadic groups.

  54. Paul Vaughan says:

    980 = 902+78 = 894+86 = 323+(7920-2400-240-24)/8

    Unique factors shared by M & B:
    100 = 2+3+5+7+11+13+17+19+23
    78 = 31+47

    Unique to M:
    100 = 41+59 = 29+71
    200 = 41+59 + 29+71

    Note:
    78 = 178 mod 100 = 378 mod 100
    22 = 378 mod 178

    100 = 78+22

  55. Paul Vaughan says:

    11•11 Puttin’ D-Fram Strait in Too•L Eur. Image UN Nation

    “a11y wanna no. is: Can. EU comm. a11 IT a11 C11owe? ‘$sure!’ “ — T&S

    Nominal “1500 years” & “2400 years” with Seidelmann (1992) :

    19.8650360864628 = beat(29.4474984673838,11.8626151546089)
    171.406220601552 = beat(164.791315640078,84.016845922161)

    461.436873121447 = slip(171.406220601552,19.8650360864628)
    85.7031103007758 = 171.406220601552 / 2
    1201.24506826813 = slip(461.436873121447,85.7031103007758)

    60.47 = 1201.24506826813 / 19.8650360864628 is nearer opposition
    7.008 = 1201.24506826813 / 171.406220601552 is nearer conjunction

    2402.49013653625 = 2 * 1201.24506826813

    121 = 11*11
    120.94 = 2402.49013653625 / 19.8650360864628 is nearer conjunction
    14.016 = 2402.49013653625 / 171.406220601552 is nearer conjunction
    14 = 2*7

    1498.49318185589 = slip(461.436873121447,171.406220601552)

    With the parameters used in Scafetta (2016) these cycles (which are coherent with tropical and lunisolar cycles in the Seidelmann (1992) framework) do not exist.

    Myth or math?

    Note$sum “UNnecessary math?” $SSTring$m?th 504.645070973208 = slip(230.718436560724,4.9662590216157) neither con fuse-D[ig!]nor conflated with 504.413226524327.

    Similarly 2432.25439579341 has a different (knew miracle?) interpretation than (IC: from same model) 2402.49013653625.

    2432 weather tropical & sidereal “bass is perfect” Fram UN he ignore$in s(US$)Pence. Sov. white CO[II]air blue mET a11 ICa 11 “mass D-air of popePET$” $ware!ABout m=mob!USE=Euler, weather T = Totient or Time for UN no. T(heir) Beer.

    Butter Write Sea Lift 24

    Peace together quality ingredients of knew a11 i.e. UN$ :
    Pay attention too miss$tory “bye don!!” (44 owe “$sing left rights” withh doubt-elite?sea cure in≠comm.=IT’11…)

  56. Paul Vaughan says:

    Ever One Door

    D-spite D$HR weather for or fear “us vs. them”, what if elite$seas-awe “DO! NNO!” 11y there$ just US SAM IC AB11y?

    First, why is the alternative name “friendly giant”?
    378 = average(σ(220),average(s(220),220))
    378 = (σ(220)+(s(220)+220)/2)/2 = (σ(220)+σ(220)/2)/2 = σ(220)*3/2/2

    Next, DO “experts” miss $simple things while chasing image UN nation?
    252 = 71+ΣΦ(71)+Σφ(71)+ΣΔ(71)

    220 = 2*( ΣΦ(71)+Σφ(71) ) = s(284); 284 = s(220)
    216 = 2*( ΣΦ(71)-Σφ(71) )

    121 = ΣΣφ(178)-ΣΣδ(178) = 11^2
    242 = ΣΣΔ(178)-ΣΣφ(178) = average(ΣΔ(220),Σδ(220)) = 2*121

    more challenging, but delectably understood in M11 context:
    504 = 713-209; 209 = 836 / 4

  57. Paul Vaughan says:

    331 Sea 42

    Left doubt the right guides to American unity?

    “You’ve got to B all Mayan” — H:NDRIX

    26 = ΣΣδ(12) = ΣΣδ(14) = ΣΣδ(15) = ΣΣδ(16) = ΣΣδ(27)
    42 = 16+ΣΣδ(16)

    “I’m tired of wastin’ all my precious…”

    0.999978318672834 = 4270*(-1/u+2/n) = joe
    0.999978649995051 = harmean(joe,don); u = 84.016845922161 (Seidelmann 1992)
    0.999978649995161 = average(joe,don); n = 164.791315640078 (Seidelmann 1992)
    0.999978981317488 = (1/41.6-3/4270)/(1/u-1/n)/4 = don
    84.0185412922146 = 2 * beat(4270,41.6) = donT
    164.794507839317 = 2 * harmean(4270,41.6) = $peek

    171.40616380965 = beat(donT,$peek) * average(joe,don); -0.000033132929 = % error
    4270.09116646754 = 4270 / harmean(joe,don); -0.000033132929 = % error

    164.791261039888 = axial(4270.09116646754,171.40616380965); -0.000033132929 = %error
    84.016818084919 = axial(171.40616380965,164.791261039888); -0.000033132929 = % error

    111.292506653915 = harmean(164.791261039888,84.016818084919); -0.000033132929=%error
    55.6462533269574 = axial(164.791261039888,84.016818084919); -0.000033132929 = %error

    41.5991637550128 = axial(84.016818084919,164.791261039888/2); -0.000033132929=%error

    “…time — J:mi h:ndrix

    4270 = s(4370)
    416 / 4 = 104 = 4 * 26
    416 = 16 * 26
    41.6 ~= 42; 42.0092706461073 = beat(4270,41.6)

    331 corrects “the bias snowed out”: ΣΣδ(42) = ΣΣδ(26) = 29 = peace
    means, weather arithmetic or harmonic, d.j. nos. 365.2422 and tranquil(IT)

  58. Paul Vaughan says:

    8.45614574631759 = φφ/(1/323+1/(26253741+0.2640768744/2-331))/100
    8.4561457463176 = axial(29.4474984673838,11.8626151546089)

    16.9122914926352 = φφ/(1/323+1/(26253741+0.2640768744/2-331))/50
    16.9122914926352 = harmean(29.4474984673838,11.8626151546089)

    absolute error relative to Seidelmann (1992) : ~0 seconds/century
    262537412640768744 = Ramanujan’s constant

  59. Paul Vaughan says:

    980 = σ(178+378) = 602+378

    331±47 = (284,378) = (s(220),378)
    2545 = ⌊1/(J+S-1/2/3/7/43/271)⌉ = ΣΣδ(220)
    (U+N) = (J+S)-2*(J-S)+(J+S-1/2/3/7/43/271)/301
    (U+N)/2 = (J+S)/2-(J-S)+(J+S-1/2/3/7/43/271)/602
    602 = σ(601); 601 = (s^48)(378); 1 = (s^49)(378); 0 = (s^50)(378)
    σ(178) = 601-331
    178 = 331-67-43-19-11-7-3-2-1

    (Σφ(323)+ΣΦ(323))±163 = (331,(7920-2400-240-24)/8)

  60. Paul Vaughan says:

    Equivalence

    6.56961471832961 = axial(29.4474984673838/2,11.8626151546089)

    10.7425999608459 = beat(16.9122914926352,6.56961471832961)
    5.37129998042294 = 10.7425999608459 / 2
    2.68564999021147 = 10.7425999608459 / 4

    4.73161071816289 = axial(16.9122914926352,6.56961471832961)
    2.36580535908144 = 4.73161071816289 / 2
    1.18290267954072 = 4.73161071816289 / 4

    generates exact same slip cycles as…

    17.2616851219298 = beat(835.546575435631,16.9122914926352) , 1/2 , 1/4
    16.5767613988929 = axial(835.546575435631,16.9122914926352) , 1/2 , 1/4

    …at this review link (perfect jupiter-saturn framing)

    example:
    131.716392653884 = slip(19.8650360864628,10.7425999608459)
    131.716392653884 = slip(19.8650360864628,17.2616851219298)

  61. Paul Vaughan says:

    The “No. Reflect” SSTrade IT$ shh!own

    Right hherd what $sum-won “DO!” no.?

    11^2 ~= axial(378,178)
    378 ~= beat(178,11^2)
    178 ~= beat(378,11^2)
    22 = 378 mod 178

    Generalized Bollinger (1952) “set-up 58” review:

    22.4690784131689 = beat(171.406220601552,19.8650360864628)
    11.2345392065845 = 22.4690784131689 / 2
    5.61726960329223 = 22.4690784131689 / 4

    17.8018946320197 = axial(171.406220601552,19.8650360864628)
    8.90094731600986 = 17.8018946320197 / 2
    4.45047365800493 = 17.8018946320197 / 4

    hherd seas at bass 1eve1 peace and tranquil IT…

    461.436873121448 = slip(171.406220601552,22.4690784131689)
    666.75261738989 = slip(171.406220601552,11.2345392065845)
    352.798308528103 = slip(171.406220601552,5.61726960329223)

    461.436873121449 = slip(171.406220601552,17.8018946320197)
    666.752617389887 = slip(171.406220601552,8.90094731600986)
    352.798308528101 = slip(171.406220601552,4.45047365800493)

    …left 16+ΣΣδ(16) a bought tale of 16*ΣΣδ(16) whisky:

    6055.74085167653 = slip(352.798308528103,171.406220601552) —– Pump few C11ues$ ($States$seaCRowe$$Torrery)

    36728.0311930377 = slip(6055.74085167753,352.798308528103)
    36728 + 22 = 36750

    Weather or math wonT(EU-tie) “swan myth”? Blue white CO[II]air a C[11]ue$ either (buy “Any hhowe”) wei:

    73456.0623873729 = slip(6055.74085167653,666.75261738989)
    73456 + 44 = 73500 (merge seas on finale with hhomer$DO)

  62. Paul Vaughan says:

    supplementary:
    7^2 = 49
    36728 – 1728
    73456 – 3456 = 70000 (fractal)

    slip cycles on axially-locked frame nearly-confounded with slip-cycles on barycentric-frame (never bothered to do the barycentric calculations until a few days ago)

    at August 4, 2021 at 10:26 am above skip all the calculations between the song-quotes.

  63. Paul Vaughan says:

    clarification: at August 4, 2021 at 10:26 am above
    structures noted between the 1st & 2nd song-quotes are fascinating analogs of amicable numbers (well-worthy of careful study), but
    skip all the calculations between the 2nd & 3rd song-quotes (after I led off track there I realized something bigger was due for contrast)
    _

    a quick sample of barycentric analogs of things long-discussed in other frames:
    130.709519917277 = axial(352.798308528103,207.638115475262)
    147.1093990625 = axial(504.645070973208,207.638115475262)
    207.638115475262 = axial(504.645070973208,352.798308528103)
    705.596617056206 = 2 * 352.798308528103
    1172.48418457888 = beat(504.645070973208,352.798308528103)

    i never gave this any attention until a few days ago, but right away i wondered why no one ever mentioned this:
    1186.69038826437 = axial(2402.49013653625,2344.96836915777)
    2373.38077652875 = harmean(2402.49013653625,2344.96836915777)

    surprise, surprise: i never even did the calculations years ago

    73500 ~= 44+1/(604*(U-N)-70(J-S))
    70000 ~= 1/(604*(U-N)-70(J-S))-3456
    35000 ~= 1/(604*(U-N)-70(J-S))-1728

    i never knew

    to save trouble for those of you puzzling over the 2300-2400a range:
    48970.7082573589 = axial(146912.124772077,73456.0623860383)
    1201.24506826813 = beat(48970.7082573589,1172.48418457932)
    that’s with doubles or halves of things already noted above

    this stuff all just pours out of what I used to call the “climate casino” — a very useful and instantly-adaptable generalization of Bollinger 1952 — (all i had to do was copy/paste 171.4 & 19.86)

    some time i’ll automate a frequency algebra generator — i’ve ignored the coefficients all these years and surely that is another big source of intriguing curiosities to add to a list that has already grown so long it could easily consume 70 lifetimes

  64. Paul Vaughan says:

    using 2402 instead of 2345 for comparison:
    65.7055139702805 = 131.411027940561 / 2
    131.411027940561 = axial(355.35840719613,208.522259703125)
    147.552651419944 = axial(504.645070973208,208.522259703125)
    177.679203598065 = 355.35840719613 / 2
    208.522259703125 = axial(504.645070973208,355.35840719613)
    355.35840719613 = axial(1201.24506826813,504.645070973208)
    710.716814392259 = harmean(1201.24506826813,504.645070973208)
    3 sets of frequencies are ~shared: axial, barycentric, lunisolar
    misinterpretation of records still appears to be the dominant norm
    can you imagine sporadic simple groups as a universal generator of spatiotemporal confounding? can you point to a concise, classic paper on the subject, with good examples based on observation?

    _

    separate note:
    11.8626151546089 = 1/J
    378 ~= 377.930028831452 = 2 * beat(1186.26151546089,163)
    1186.69038826437 = axial(2402.49013653625,2344.96836915777)
    378 ~= 377.908272861772 = 2 * beat(1186.69038826437,163)
    same for Chandler — curious we don’t see the fractal formally addressed by the academic community — there are methods for modular forms that can pin such things exactly even where the slip-cycle periods go locally unstable with input tweaks

  65. Paul Vaughan says:

    2373.38077652875 = harmean(2402.49013653625,2344.96836915777) = 2 * 1186.69038826437
    frames examples for comparative study:
    131.059335212915
    208.07924839476
    354.073730281071
    708.147460562142

    Stay aware: These frames exist using Seidelmann’s (1992) JSUN parameters (which are listed on a nice NASA summary page) but not with the JSUN parameters used by Scafetta (which are posted seperately on scattered NASA pages and derived with numerical methods curiously (and rather suspiciously) coinciding with Heegner numbers at 2318).

    Resolution of Halstatt demands attention to number theory with numerical methods scrutiny.

    Motivation threw quotes for the truest of nature lovers:

    • “Rational functions of j are modular, and in fact give all modular functions.”
    • “The inversion applied in high-precision calculations of elliptic function periods even as their ratios become unbounded.”
    • “A related result is the expressibility via quadratic radicals of the values of j at the points of the imaginary axis whose magnitudes are powers of 2 (thus permitting compass and straightedge constructions). The latter result is hardly evident since the modular equation of level 2 is cubic.”

    I suspect monstrous moonshine resonates quite easily for the right mathematicians, even if others are feeling left doubt of greater unity …threw “knew miracle” puzzling:

  66. Paul Vaughan says:

    Sustainability of PC Ignorance Abounds

    1465.66451612903 = slip(601,378)
    1477.63636363636 = slip(602,378)

    602 = σ(601)

    601.363636363636 = harmean(1470,378)

    1806 = slip(378,43) = 42*43 = 3*602 = product of sylvester sequence

    “The study of cycles reveals to us our ignorance and is therefore very disturbing to people whose ideas are crystallized.”
    — Edward R. Dewey

    331 = 1986 / 6
    Φ(601) = 600

  67. Paul Vaughan says:

    1/600.622534133192 = 10(J-S)-86(U-N)
    1/1201.24506826638 = 5(J-S)-43(U-N)
    1/2402.49013653277 = (5/2)*(J-S)-(43/2)*(U-N)
    where J,S,U,N are frequencies

    600.622534133192 = 1/(10/11.8626151546089-10/29.4474984673838-86/84.016845922161+86/164.791315640078)
    1201.24506826638 = 1/(5/11.8626151546089-5/29.4474984673838-43/84.016845922161+43/164.791315640078)
    2402.49013653277 = 1/(2.5/11.8626151546089-2.5/29.4474984673838-21.5/84.016845922161+21.5/164.791315640078)

    Multiplying 1201 by 2 as a way to match an Earth season is a change in aggregation criteria. Working in the axial frame instead of this barycentric frame is in some senses superior and more appealing than trying to match fractions of an Earth year. In some of the examples I gave not far above I mixed frames to gain a sense of the scale of scatter. Which frame is most useful depends on what features are being explored.

    When I first explored the barycentric frame more than a decade ago I had not yet encountered Seidelmann (1992). I had other summaries from NASA and I knew with absolute certainty they were badly imbalanced. Then I explored other things for years. This is the first time I’ve come back to the subject, this time familiar with Seidelmann (1992) and Bollinger (1952) method generalization.

    Something I wonder: For how long was the model we know as Seidelmann (1992) (or something very nearly equal to it (hair-splittingly close)) shared around privately before 1992?

    Noteworthy: Charvatova did not cite Seidelmann (1992) in her 2010 trefoil paper.
    Referees: Explicit statement of parameters please. Copy/paste is not an onerous request. No rounding off of parameters — none whatsoever — all of the original detail is needed for sound audits. Looking at the 2318 year example was a real eye-opener about how extremely naive some commentators are when they compare periods from different models.

    I want to underscore this again: I think 10Be, 14C, IRD, and many other records are being seriously misinterpreted. I would not be surprised if the recorded variations are variations of things totally different from what people imagine.

  68. Paul Vaughan says:

    Curiously: Peaceful Course to Unity

    209 = 11*19 = 836/4

    3950.1 = slip(836,378) = 7900.2 / 2
    “and it makes me wonder” — led zeppelin
    7900.2 = slip(slip(378,19),slip(378,11)) — supplementary: 3591=slip(378,19); 1039.5=slip(378,11)

    316.008 = 7900.2 / 5^2
    316 = sum of Heegner nos.

    Seidelmann (1992)
    61.0464822565173 = slip(29.4474984673838,11.8626151546089)
    835.546575435631 = slip(61.0464822565173,19.8650360864628) ~= 836

    Using the other set of NASA parameters that were used in the Scafetta (2016) paper (the one highlighting 2318) :
    60.9470469878813 = slip(29.4571389459274,11.8619822039699)
    883.192112166325 = slip(60.9470469878813,19.8588772513307)

    836 is the smallest untouchable weird number.
    378 is the sum of supersingular primes.

    Our discussions a decade ago were in ignorance of symmetry and boundary conditions. Search engines and those attempting to guide those discussions failed to direct our learning about solar system structure (and numerical methods used to summarize it) towards simple sporadic groups — a suspicious failure.

    Towards superior unity: First, there should be a concise, widely-accessible article from an eminently sensible source outlining key highlights. Then: some widely-digestible concise forays into adjacent territory.

    Accessibility: To reach a wide audience, use numbers instead of cryptic algebra that is concisely-keyed and quickly-searchable nowhere for the uninitiated. Monstrous moonshine can be a topic of widespread interest, but mathematicians don’t generally communicate inclusively. The standard notation conventions are horrible. Maybe in the future newcomers will be able to click on weird-looking notation (conventions they have never seen) to link to spreadsheets efficiently clarifying exactly what the notation means with several numerical examples. Technocracy isn’t as inclusive as it could be. A primary mission for genuine unity agents: superior math education.

    To illustrate further the utility of the generalized Bollinger (1952) method, here it is with the JSUN parameters used in Scafetta (2016) to automate discovery of 2318:

    JS:
    19.8588772513307 = beat(29.4571389459274,11.8619822039699)
    16.9132376600574 = harmean(29.4571389459274,11.8619822039699)

    UN:
    171.389290439286 = beat(164.788501026694,84.0120465434634)
    111.287690909751 = harmean(164.788501026694,84.0120465434634)

    joint axial frame:
    19.9443292139205 = beat(111.287690909751,16.9132376600574)
    9.97216460696023 = 19.9443292139205 / 2
    4.98608230348011 = 19.9443292139205 / 4

    resultant analog of the famous JEV cycle summarized neatly by Bollinger:
    4635.02503296546 = slip(19.9443292139205,19.8588772513307)
    2317.51251648273 = slip(19.8588772513307,9.97216460696023) ~= 2318 —– slip(definition)
    1158.75625824137 = slip(19.8588772513307,4.98608230348011)

    …whereas Seidlemann (1992) points to Sylvester’s sequence and amicable numbers, raising floods of interesting (and some downright fascinating) questions about number theory and numerical methods.

    These comparative outlines should reduce some of the nuisance cross-talk on Halstatt (for sensible parties at least).

  69. Paul Vaughan says:

    “DO!” Beyond Least Squares $

    Comparing and contrasting symmetries of classical keplerian orbital elements with those of fits will help immensely with the sorting and classification at this stage.

    The 2402 year trefoil — along with a lot other very neat math noted during the last year (still leaving an extraordinarily long rich vein to finish exploring) — is in the classical elements, not the fits.

    Based on Seidelmann (1992) Table 15.6 column “Synodic Period (d)”: 2320.97373292704. (To compare with 2318 he ignore what fits?)

    It’s becoming quite clear why model parameters are left opaque and authors dodge questions about them. This is fantastic.

    Suggested assignment for the ephemerides community:
    1. Please fit with a wide variety of methods beyond least squares.
    2. Then please share detailed parameter estimates (no rounding — all detail needed for sound audits).

    I’ll study symmetry properties comparatively. I’ve got all of the needed tools sufficiently prototyped and I have enough experience with the problem now to say we can start a nice project that will benefit humanity (weather left, right, or whatever).

    We’ll get to the bottom of Halstatt.

    It feels pretty rare to have an idea that might be palatable to the mainstream. It will take a big team with reps from astronomy, surveying engineering, stats, physics, and several braches of math. (Lots of opportunity for conventional mainstream hog-troughing governments can feel proud to support.)

    Seidelmann (1992) section 5.8 intro:
    “Lower accuracy formulas for planetary positions have a number of important applications […]”
    “Classical Keplerian orbital elements […] The errors of the approximate formulas may be compared to those of the integrated ephemerides […] which are less than 1 arcsecond throughout 1800-2050, often much smaller.”
    “The errors made when extrapolating outside this interval can be substantially greater.”

    Focus: both properties of elements and fits to soundly explore sensitive slip cycles in Halstatt range. (Note: Slip cycles in lower ranges are not highly sensitive to parameter tweaks.)

  70. Paul Vaughan says:

    With Jupiter-Saturn fits (instead of keplerian elements) :

    1st column: https://nssdc.gsfc.nasa.gov/planetary/factsheet/
    2nd column: Seidelmann (1992) Table 15.6 column “Synodic Period (d)”

    2314.165996556 2310.96650283341
    1798.25390532363 1800.67427686554
    704.058145756998 703.835620486719
    505.962199892567 506.038605913273
    352.029072878499 351.917810243359
    208.461875842482 208.502970529009
    208.026777519043 208.034259549341
    207.593491673279 207.567651151046
    147.634763269245 147.661880027493
    130.929216699757 130.930028534414
    100.987377272676 100.986836079756
    93.0543888034915 93.0569482000189
    65.4646083498784 65.4650142672068
    50.493688636338 50.4934180398781

    With J, S, U, & N fits:
    2317.51251648273 2320.97373292704

    Notice that the lower periods don’t change much.

    The top period (~2310) is 2432 (net-zero recall) with keplerian elements. The period with J, S, U, & N moves over 200 years (underscoring number theoretic properties of keplerian elements (appearance of sylvester sequence was already fantastic — now spectacular)).

    Backstory: AFTER noticing Heegner 2318 I searched “2318 year cycle” and was immediately reminded of something that came up for discussion at the talkshop a few years ago. That’s what started this fantastic round of review (a refreshing change).

  71. Paul Vaughan says:

    NASA Beats Kepler’s Elementary Classic

    Sylvester’s sequence seas at least “knew miracle” peace:
    1806 is the only solution.

    25479.725512125 = beat(2545.34384727948,2314.165996556)
    25891.3741327569 = beat(2545.34384727948,2317.51251648273)
    25683.9005041663 = harmean(25891.3741327569,25479.725512125)
    25685 = p (Laskar)
    25683.9005041663 = beat(2545.34384727948,2315.83804754128)
    2315.83804754128 = harmean(2317.51251648273,2314.165996556)
    2315.84698617384 = axial(25685,2545.34384727948)
    2315.95930765286 = harmean(2320.97373292704,2310.96650283341)

  72. Paul Vaughan says:

    The “Country Folk” Goalpost

    Lower periods are stable, but reluctant city folks sea the challenge to look around for “a better country” narrative.

    2364963.50364963 = beat(74619.9907876555,72337.575351641) —— explore countryside, scattering hail stat:

    2313.22691399978 = beat(2364963.50364963,2310.96650283341)
    2316.43267412608 = beat(2364963.50364963,2314.165996556)
    2319.78575770643 = beat(2364963.50364963,2317.51251648273)
    2323.25377275563 = beat(2364963.50364963,2320.97373292704)

    2308.71050495714 = axial(2364963.50364963,2310.96650283341)
    2311.9037506318 = axial(2364963.50364963,2314.165996556)
    2315.24372615857 = axial(2364963.50364963,2317.51251648273)
    2318.69816397012 = axial(2364963.50364963,2320.97373292704)

    To point for MAGA, here “bye don!” AP parrot US diversifies too in clued “what’s numerical?”

    25760.4349434063 = beat(1.00001743371442,0.999978614647502)
    25763.987503107 = beat(1.00001743371442,0.99997862)

    2315.84698617384 = axial(25685,2545.34384727948) ————————— seams
    2316.45859565675 = axial(25760.4349434063,2545.34384727948) ——- elementary
    2316.4873186425 = axial(25763.987503107,2545.34384727948) ———enough

    Fit offsets (from Kepler’s classics) don’t look as mysterious as conventional mainstream hesitation to clarify precisely for civilization exactly what Halstatt is. (Maybe they’re trying to force us to buy the book because someone with $200billion “needs” more income?)

    Recall (from 2400 thread) a curious distinction of 25685 from 25760:
    5221.17476429629 = slip(2432.25439579341,131.716392653884)
    20884.6990571851 = 4 * 5221.17476429629
    0.999978499752023 = axial(20884.6990571851,1.00002638193018)
    25684.4120517011 = beat(1.00001743371442,0.999978499752023)

    That’s beyond the patience of most and this is even more so: 25683.9369504749 (tropical review)

    Far from 25685, 25684 is sensitive as conventional mainstream tunes number theory, numerical methods, theoretical physics, and systematic deviations of theoretical physics (kepler classics) from “measured physics” “throwing fits” 2311 & 2321 in silence to “post knew goals” 2314 & 2318 (“grand midpoint” 2316 with no. explanation). Thus$skew$stepUN$stone$sea$spice.sh!own: “What hail stat mystery he ignore?

    US politicians$sea Halstatt “redneck budget” line item (overdue “win decimal” points)$.

    Classic Review

    19.8650360864628 = beat(29.4474984673838,11.8626151546089)

    8.4561457463176 = axial(29.4474984673838,11.8626151546089)
    55.6462717641972 = axial(164.791315640078,84.016845922161)

    9.97142885566705 = beat(55.6462717641972,8.4561457463176)

    “won’t treat you like you’re o so typical” T&S

    2545.34384727959 = slip(19.8650360864628,9.97142885566705)

    Mix myth and math so few can tell “the difference is elementary”.

  73. Paul Vaughan says:

    Seidelmeann (1992) keplerian mean elements
    2432.25439577557 = 1/(27/2/11.8626151546089-67/2/29.4474984673838)

    NASA “factsheet” fits
    1184.58746101992 = 1/(27/2/11.8619822039699-67/2/29.4571389459274)

    Seidelmeann (1992) fits
    1185.0768783208 = 1/(27/2/11.8619993833167-67/2/29.4571726091513)

    1184.8321191296 = harmean(1185.0768783208,1184.58746101992)

    432.670570135933 = 1184.58746101556/1000*365.25
    432.759931511403 = 1184.83211912773/1000 * 365.25
    432.76050078182 = Chandler wobble period in days
    432.779105769231 = 1184.88461538462/1000 * 365.25
    432.849329806901 = 1185.07687832143/1000*365.25

    1184.88461538462 = slip(378,163)

  74. Paul Vaughan says:

    Left Too Write “2318 Mystery”

    Looking at Scafetta’s “Orbital Invariant Inequalities” paper (2020), a question arose:
    Did 0+0 referees notice in equation 7 (top of p.10) sum (Table 2 p.11) thing (U-N)usual?

    55.7553207256706
    57.129763479762
    58.5723667046309
    58.5736825996179
    60.0910975757072
    61.6906837130628
    63.3777586414549; 59.214324604619 = harmean = 1/0.0168878055551105

    82.6389068978088
    85.694645219643
    88.9820076327135
    88.9850446352389
    92.534930803792
    96.3833800978328
    100.565827577768; 90.4720674734613 = harmean = 1/0.0110531352706551

    159.587182057353
    171.389290439286
    185.063293323604
    185.076430357824
    201.123897329472
    220.237032653919
    243.364347556611; 191.627231886105 = harmean = 1/0.00521846498619965

    0.00583467028445541 = 0.0168878055551105 – 0.0110531352706551
    1/0.00583467028445541 = 171.389290439286 179.2

    0.00583467028445541 = 0.0110531352706551 – 0.00521846498619965
    1/0.00583467028445541 = 171.389290439286 179.2

    1/179.2 ~= 0.00558 ≠
    1/171.4 ~= 0.0058
    Opportunity appears left for author(s) to write (U-N)other paper, filling in (more) D-tales….

  75. Paul Vaughan says:

    Halstatt Wisdom Line (Shows Respect)

    Scafetta (2020) underscored that orbitally invariant combos are invariant.
    Beats of adjacent invariants on Scafetta’s list (skipping gaps) draw attention to:

    2607198.3328798 = beat(2319.57436292963,2317.51251648274)
    (using fits, not keplerian)

    Look a step further either of 2 ways:

    2315.45433228986 = axial(2607198.3328798,2317.51251648274)
    2316.48296721465 = harmean(2317.51251648274,2315.45433228986)

    2316.48296721465 = axial(5214396.6657596,2317.51251648274)

    Cross with Keplerian and wonder why no one ever mentioned it:

    25763.3359964344 = beat(2545.34384727948,2316.48205165173)

    Compare with:

    25763.8618611039 = beat(1.00001743390371,0.99997862)

    “Expert” guidance failed us very seriously a decade ago.
    The costs of this failure have been too high.

  76. Paul Vaughan says:

    NASA “factsheet” fits (oak root)

    [omitted: simple backstory prelude]

    16.9132376600574 = harmean(29.4571389459274,11.8619822039699)
    111.287690909751 = harmean(164.788501026694,84.0120465434634)
    171.389290439286 = beat(164.788501026694,84.0120465434634)

    735.00668955291 = 11.8619822039699 + φφ(111.287690909751 + 171.389290439286) – 16.9132376600574
    “came through through the night that our flag was still there — star spangled banner

    36750.3344776455 = 50 * 735.00668955291
    36750.3379015986 = 8 / (g_2 + 5*(g_3 + g_4) + g_6 + s_2 + s_3 + s_4 + s_6) (taxi cabin sing-song)

    DOshhow?mar a11 lag “o no. what?” 11ink$too?

    73500 ~= 44+1/(604*(U-N)-70(J-S))
    70000 ~= 1/(604*(U-N)-70(J-S))-3456
    35000 ~= 1/(604*(U-N)-70(J-S))-1728

    COP lure UN class IC (D-meanor bot a11 “mint snow” thing “or[We/11]22”)

    DO!n’t take D-bait. Our supreme allies: peace, tranquil IT, & serene IT.

  77. Paul Vaughan says:

    Solar system fits NASA’s simply sporadic “factsheet”.

    193 = 593-ΣΦ(323)+Σφ(323)
    593 = C+220-284 = C-ΣΣΦ(378)+ΣΣΦ(178) = C-(902-894)^2
    993 = C+220-284+ΣΦ(323)-Σφ(323) = C-ΣΣΦ(378)+ΣΣΦ(178)+ΣΦ(323)-Σφ(323)

    C = (7920-2400-240-24)/8; 8 = 902-894 = √(284-220) = √(ΣΣΦ(378)-ΣΣΦ(178))
    C = 163+ΣΦ(323)+Σφ(323) = 163+ΣΔ(1470)

    846 = 323+323+378-178 = ⌊2214ΦΦ⌉ = ⌊845.672748907733⌉
    1186 = 902+284 = 1470-284 = average(902,1470); 284 = s(220); 902 = Σδ(Σδ(Σδ(378)))
    1368 = 2214-846 = ⌊2214Φ⌉ = ⌊1368.32725109227⌉
    1691 = 2214-323-378+178 = ⌊4428ΦΦ⌉ = ⌊1691.34549781547⌉

    2100 = average(1986,2214)
    2946 = 4279-1333 = 2100+846
    4200 = 1986+2214

  78. Paul Vaughan says:

    (won hundred for [too) * (70 won)]

    437 = C-220 = 4370 / 10
    504 = 220+284 = C-67-43-19-11-7-3-2-1

    237 = 894-C = Σδ(Σδ(378))-C
    245 = 902-C = Σδ(Σδ(Σδ(378)))-C
    490 = average(C,323)
    980 = 220+284+323+67+43+19+11+7+3+2+1
    980 = 163+ΣΦ(323)+Σφ(323)+323 = 163+ΣΔ(1470)+323

    400 = ΣΦ(323)-Σφ(323)
    494 = ΣΦ(323)+Σφ(323) = 447+47 = ΣΔ(1470)

    323 = 196883196560

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