Solar-Planetary recap part one: The 11 year Schwabe cycle.

Posted: May 11, 2020 by tallbloke in Cycles, solar system dynamics
Tags: ,
The Sun’s 11 year cycle is the most well known among many others we’ll cover in this series.

Now we’ve entered the minimum between solar cycles 24 and 25, this seems like a good moment to recap what we’ve discovered about the Sun and the planetary system that revolves around it here on the Talkshop during the last decade. The idea that the Sun’s activity cycles were somehow linked to the motion of the planets didn’t begin here of course. In fact, the idea goes all the way back to Rudolf Wolf, the Swiss astronomer who in the 1800s collated the old, and continued adding new sunspot observations. He was convinced that the orbit of Jupiter modulated sunspot numbers.

Wolf was an admirer of the work of Heinrich Schwabe, who was the first to discover an approximately decadal cyclic variation in sunspot numbers. Wolf refined and extended the observations and found that while some solar cycles were a little over ten years long, others were much closer to Jupiter’s orbital period of just under twelve years. The long term average was found to be around 11.1 years.

In the late 1990s, Finnish solar observer Timo Niroma made a careful study of the historic solar cycle lengths from one minimum to the next and illustrated his findings with this probability distribution diagram on his website. For each solar cycle the central estimate gets 4 x marks. at a tenth of a year either side, 3 x marks, at two tenths either side, 2 x marks and at three tenths of a year either side, 1 x mark. This procedure has the effect of smoothing the data so we can see the emergent pattern more clearly. The tentative data for cycle zero uses 0’s instead of x’s

solar cycle lengths
Figure 1. Probability distribution of solar cycle lengths by Timo Niroma

Study of these data reveals a few important observations. Firstly, the solar cycle length is rarely its long term average of ~11.1 years, but tends to cluster around two attractor periods near 10.3 and 11.9 years.

Secondly, the difference between these two attractor periods is ~1.6 years, which is close to the length of the synodic conjunction period of Earth and Venus. This clue leads us to realise that the two attractors are 6.5 and 7.5 times the 1.5987 year E-V period respectively.

Finally, we can see that over the sunspot record, the shorter ~10.38 year period has occurred more frequently than the longer ~11.99 year period. The ratio is 4:3.

To calculate an accurate figure for the average solar cycle length then, we simply multiply the 10.38 year period by 4, and the 11.99 year period by 3, sum the results, and divide by the total number of cycles, which is 7. This gives us the longer term average of 11.07 years, which agrees with most modern studies of Schwabe cycle length.

Planetary alignment indices have been constructed by researchers Jean Pierre Desmoulins, Ching Cheh Hung (NASA), and Roy Martin to further understand these relationships. A more recent treatment has been made by astrophysicist Ian Wilson in his 2013 PRP paper The Venus–Earth–Jupiter spin–orbit coupling model.

This advances the concept that Jupiter and the terrestrial planets, specifically Earth and Venus, can influence bulk motions in the convective layers of the Sun, and thus the solar cycle itself. In section 2 of the paper (V-E-J tidal torquing model), we learn that Jupiter advances 13 degrees relative to the alignment line of each Venus-Earth (V-E) conjunction. After 7 V-E in 11.1909 years Jupiter has made 91 degrees of advancement, therefore the time taken for 90 degrees is 90/91 of 11.1909 = 11.068 years, very close to the widely accepted mean length of a solar cycle. For full details refer to section 2, and for a summary of the paper see section 4 – Conclusions.

Quoting from the PRP paper (the period in question is 360 Venus-Earth conjunctions): It takes Jupiter 575.518 yr to re-synchronize itself with the penta-synodic Venus–Earth alignment cycle. In addition, it takes two 575.518 yr periods (= 1151.0 yr) for Jupiter to resynchronize itself with the penta-synodic Venus–Earth alignment cycle and also with respect to the stars (Wilson, 2013).

Comments
  1. oldbrew says:

    This post has been pending for a couple of months (blame me). The series referred to is going to be delayed but hasn’t been abandoned.

    Recently a German group has said it just ‘discovered’ the JEV period and the solar link, which is amusing as the PRP paper is about seven yeras old, and JEV was discussed at the Talkshop and probably elsewhere well before that.

    In July last year, scientists at the Helmholtz Centre in Dresden Rossendorf made a little-noticed but exciting discovery. Every 11.07 years, the planets Venus, Earth and Jupiter are aligned quite precisely. At this point in time, their gravitational force acts jointly in one direction on the Sun.

    “The agreement is amazingly accurate: we see a complete parallelism with the planets over 90 cycles,” explains Frank Stefani, one of the authors of the publication published in Solar Physics.

    https://notrickszone.com/2020/05/09/earths-mean-temperature-falling-planetary-alignment-suspected-as-driver-of-the-11-year-solar-cycle/

    “a little-noticed but exciting discovery” – really? 😎

  2. […] über Solar-Planetary recap part one: The 11 year Schwabe cycle. — Tallbloke’s Talkshop […]

  3. tallbloke says:

    Thanks OB, I’d forgotten about this draft while I’ve been busy on other matters. There’s much more to say on this subject. For example JEV and the ~1151yr cycle also feature in Rick Salvador’s 2013 PRP model of solar activity.

  4. oldbrew says:

    See Ian Wilson’s figure 4 for a diagram of the planetary movements. The 575.5~ year period is about 26 Hale cycles, or 52 Schwabe. The description of how it works is on the same page, and calls for a bit of concentration but it should be worth the effort.

    Click to access prp-1-147-2013.pdf

  5. Paul Vaughan says:

    Even Bollinger in 1952 was who?man y hears be UN-D Mayan’s lot machine…..?
    May UN C my yen $ 1 o 1 IT’s pull ease state-D evil lip meant.

    ….and they call it the “security” counts ill!

  6. JB says:

    Now insert a third component, a mass 3.72x that of E-V combined, with an orbital period of 1681.3 earth days, and you have the sun’s solar cycle variance pre-Holocene. Tends to make Plato’s discussion of weather extremes in the Critias more credible.

  7. stpaulchuck says:

    gawd I love this stuff!! The people who have the time, patience, and income to study the mass of numbers and come up with solutions like this are real science heroes IMHO. Some science requires super computers and teams of researchers, while other science requires an inquiring mind and a handheld calculator. A hat tip to both ends and the middle.

  8. Paul Vaughan says:

    Remember: Bollinger was relying shitty numbers from the navy almanac. The Mayan numbers were only released AFTER the iron curtain fell.

    Even a MINOR tweak wrecks things as sensitive as Mayan 5256. And remember that 5256 ties to 36750 as I outlined on Suggestions-42. The whole package ties together top-to-bottom, hinging on some pretty simple stuff at the core.

    Basically the designer had a couple sieves in mind and tied everything towards them. Stuff can’t quite make it all the way. That’s why it’s necessary at ADVANCED level of analysis not just to consider this-and-that IN ISOLATION but rather to see how the sieves fit together IN CONCERT.

    Otherwise: This little model and that little model require things to be off in OPPOSITE directions and they destroy composite slip-cycle structures like 5256, etc.

    5256 is actually huge diagnostically. I outlined basics over here:
    https://tallbloke.wordpress.com/2020/05/06/net-zero-mania-threatens-to-derail-our-lockdown-recovery-rupert-darwall/

    I post a lot of exploratory stuff. What you see there isn’t exploratory. It’s definitive and it’s Mayan.

  9. oldbrew says:

    Playing catch-up…

    Press release of May 27, 2019

    The Sun follows the rhythm of the planets
    New study corroborates the influence of planetary tidal forces on solar activity

    One of the big questions in solar physics is why the Sun’s activity follows a regular cycle of 11 years. Researchers from the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), an independent German research institute, now present new findings, indicating that the tidal forces of Venus, Earth and Jupiter influence the solar magnetic field, thus governing the solar cycle. The team of researchers present their findings in the journal Solar Physics (doi: 10.1007/s11207-019-1447-1).

    https://www.hzdr.de/db/Cms?pNid=99&pOid=58444

  10. Paul Vaughan says:

    God’s Watch:in stock

    Chinese people are naturally mathematical geniuses ….despite WHOever’s sittin’ near-own-D in the deep states sov. ignorance, weather American or Chinese.

    I’m repeating a few select lines from Suggestions-42.

    — –

    19.8650360864628 = 1/(1/11.8626151546089-1/29.4474984673838)

    The top estimate for J-S is 119 times better than the bottom one.

    19.865035730288 = 4/(Φ(ΦΦ)^e*(1+(13*11)^(1/4))-2/304407)
    19.8649936390493 = 2/((1+(13*11)^(1/4))/4/(13*11*7*5*3)^(1/4)-1/304407)

    – —

    44.2784629967673 = 2 / (3/0.615197263396975-5/1.00001743371442+2/11.8626151546089)

    The top estimate for double-hale is 4 times better than the bottom one.

    44.2784332763321 = 2φ(φφ)^e
    44.2783394595719 = 4*(13*11*7*5*3)^(1/4)

    Note how far off Bollinger was relying on the shitty navy almanac estimates:
    https://ojs.library.okstate.edu/osu/index.php/OAS/article/view/3713/3387

    Needless to say 5256 does not exist for shitty navy almanac estimates.

    (sarc)It’s a miracle(/sarc) : All of a sudden after 11/9 low and behold official western government models PRECISELY match ancient Mayan wisdom. Lol. No fanfare. No announcement. Just some benign numbers appear in some table buried in some document many hundreds of pages long.

    Still sat little read ride D-UN hood:
    More than just riding them EU no. WHO’11 SLAM deep state brakes in UNcivil west turn dis-curse.

    No. won door Desmoulins (late 90s) without see-through eye-run court in hindsight all the way back not just to Bollinger (1952) but sage Mayan in tall luck chew well supplements passed buy O-logic call liberty and freedom.

  11. Interesting discussion on solar activity, which brought to my mind the views presented by a rather old geologist, unfortunately passed away, but his leagacy remains. I refer to Rhodse Fairbridge and his views on solar activity, Schwabe cycles and the solar jerk still available:

    Best regards

    Boris

  12. Sorry, I forgot the link to Fairbridge:

  13. Paul Vaughan says:

    Life’s a port.

    Eye-D DOn’t w’han tune O.
    Ignore isUNs bliss.

    “W’hen Eur. blowin’Hide O” — T———–ip

    _JEV-: 22.14
    _SEV-: 18.015 ~= 2 * 22.14 / 2.458
    JSEV+: 12.805 ~= 2 * 22.14 / 3.458
    JS___: 19.865 ~= 4 * 22.14 / 4.458

    “Thor O sov. pass UN
    Mow V-E so fast
    into that wed UN ring
    out at the speed wei”

    √√13√√11 + 1
    √√13√√11 ± 0 : meet O-Bei. ware
    √√13√√11 – 1

    “sum kind DO V-E E11Vis thing” — Tragically Hip

  14. Paul Vaughan says:

    Taxi Driver: Less UN is morse sun

    “out at the speed wei
    sum kind DO V-E E11Vis thing”

    – — – — – — – — – — – — – — – — – — – — – — – — – —
    “O-Bei. bee
    eye feel phiiii√(Φ-φ)iiiii ‘n’
    numb. pretty sure IT’s 8675309 EU wine”

    – — — — — — — — — — — — — — — — — — — — — —
    22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
    22.1392314983836 = 1/(3/0.615197263396975-5/1.00001743371442+2/11.8626151546089)
    “MAKE SNOW cents”
    0.000000038239 = %error
    – — — — — — — — — — — — — — — — — — — — — —
    “sum times the faster IT gets
    the less EU need to No.”
    — Tragica11y‘ip

  15. Paul Vaughan says:

    “We R the PReasts of the temp-pols of C-ER inks” — Rush

    22.1392315068494 = (φ^(2*(396-(13*11*7*5*3)/(13+11+7+5+3)))+1/(396-(13*11*7*5*3)/(13+11+7+5+3)))^((2e+1)/(2*(396-(13*11*7*5*3)/(13+11+7+5+3))))

    “the less UNeed to know” — Tragica11y ‘ip

  16. Paul Vaughan says:

    Human Writes Gen-UN-D√(Φ—φ)yen

    Imagine Chinese and American people free of satUN’s deep state chains 2 be BFF.

    With insight-full guard down ease deep state,
    IT Can. fall right in from UN door to ROC Eur. Mayan-D.

    2.61803453508785 = (φ^22+1/11)^(1/11)
    ^
    2.71828182845905 = e
    =
    13.6827961283553 = (φ^22+1/11)^(e/11)
    ×
    1.6180341575776 = (φ^22+1/11)^(1/22)
    =
    22.1392315068494 = (φ^22+1/11)^(e/11+1/22)

    Antarctic Borg luck D-own check mate a weights only D-vine bellief in God’s real ease.

    “Wan weigh or UN other” — Blondie

    39602.9999747494 = φ^22
    0.0909090909090909 = 1/11
    39603.0908838403 = (φ^22+1/11)

    — – — — – — — – — — – — — – — — – —

  17. Paul Vaughan says:

    Homing in
    on Backs Eat
    Tax C-driver

    9 = 3^2
    16 = 4^2
    25 = 5^2

    3600 = 9*16*25 = 3^2 * 4^2 * 5^2
    39600 = 11*3600 = 11 * 9*16*25 = 11 * 3^2*4^2*5^2

    657 = 3*(4*5*11-1)
    5256 = 3*8*(4*5*11-1)

    Won Too 3-4-5: try angle homes in on buy no. meal.

    Square UN both sides equa11y:
    1/(φ+Φ)^4 + 8/(φ+Φ)^4 + 16/(φ+Φ)^4 = 1
    Grew pin BRI Ta11y:
    9/(φ+Φ)^4 + 16/(φ+Φ)^4 = 1
    Simpl√(Φ-φ)phi yen:
    9/25 + 16/25 = 1
    Spot UN square read:
    (3^2 / 5^2) + (4^2 / 5^2) = 1
    Mu11 tip p11y yen bye five square red:
    3^2 + 4^2 = 5^2

    3-4-5 Try UN Gall of Naive Bellief.
    Left luck D-own in deep state isn’t right.

    Weather American, Chinese, or whatever, IT’s right to love the people UN left lost in deep state-lust.

    With the right people-loving Mayan-D set E-V UN-weak can flips witches absolute powers plan-D lock-D D-own for trust sting naive AB use.

    SatUN lured the naive with promises of climate agreement only to turn on a D-ieme. No justice after fire red agreements cool-D the naive Who were left believing absolute secure IT wasn’t D-bait-UN-D-switch for only just ice.

    Right now God loves people watchin’:
    We’re left pray yen to exit the deep state of UNcontrolled government abuse.

    We’re right to love the people weather Chinese, American ….or otherwise we may be left permanently in a deep state of absolute luck D-own.

    (ΦΦ+φφ)V+(φφ-ΦΦ)(ΦΦ-φφ)E+(φΦ+Φφ)J

    0.615197263399154 = 3/((φ^22+1/11)^(-e/11-1/22)+5/E-2/J)
    0.615197263396975 = 1/V
    0.000000000354 = %error
    -0.000000000729 = %error logscale

  18. Paul Vaughan says:

    Zero One Two 3-4-5 Triangle

    The invitation for tea deeply state-D: no. UN over five tee.

    The strictly obsessed, absolutely assaulting mindset with witch satUN’s army relentlessly and viciously attacks innocents with below-median income is straight-up terrifying savage-works:

    “UN.wei.or.UN.O-Thor.img.UN.nugget.ch.ill.get.ch.” — Blondie “One way or Another”

    657 = 0+3*(4*5*11-1)
    657 = 1+4*(5*3*11-1)
    657 = 2+5*(3*4*11-1)

    It would have been more humane to just offer us all euthanasia, but that X-act lie defines satUN WHO’s maximal pressure camp aim is suffer ring:

    “ill-dr.hive pass-D Eur. house
    ill-C WHO’SAR O UN-D
    ill fall O Eur. bus D-own town
    C WHO’s’hang UN out
    ill wok D-own them all
    lead EU to the sue poor more kit check[sh]out
    ill trick ya – give ya the slip
    some specials and rat food “get lost” in the CR-owe-D
    C IT AI ware eye can. find out WHO ya cull – May be nex-D weak

    Stand over!!!
    Buy the wall!” — Blondie

    Deep States of Cynicism

    Weather IT’s the deep state of China or America, the beautiful Chinese and American people will find a way to be BFF.

    5256 = 8 * (0+3*(4*5*11-1))
    5256 = 8 * (1+4*(5*3*11-1))
    5256 = 8 * (2+5*(3*4*11-1))

    Aftermath class reminds us that life without freedom is a dead end.

    It’s vita11 to UN door stand deeply state-D aftermath.
    Hence the graph f**k mess aging.

    We strictly cannot trust authority at this time. They will stoop to any level in their drive to torment below the median income. They’re possessed by a savagely fierce relentless in tent UN to get us one way or another.

    A borg cube in Anarctica gives mandatory welcome for lockdown enthusiasts. This’ll free up homes and land for more homeland parks and trails, which will always remain open to the free since all the lockdown freaks from everywhere in the world will be observing glaciers from their borg cube lockdown, confidently knowing their supply lines are managed only from below the median with tables turned in favor of just ice.

    Recent events have clarified that climate belief polarization is deeper and more stable than peoples lives. Militant pushing leads to fatalities (including 3 billion financial fatalities) that entrench beliefs more deeply than we’re even able to fathom.

    However, fair trade may be feasible (like roots with leaves or between organs more generally).

    “In God We Trust”

    Strong AND flexible — dynamic beyond just static stability — is a more potent combination for party package deal vitality (minus the poison pills) to whether pressure weather godly or imagined so.

    Freedom is many orders of magnitude more important to people than climate belief.

    Torch in agree meant I can’t be left naively trust sting that EU know WHO = wanna-be dictator satUN will not turn on dime and take candy from a baby after signing each deal, weather sooner or later.

    Turning on a dime is what dictators do, weather with Eur. trust or without it.

    The less UN recently reinforced: a secure life is a dead end without secure freedom. Stabilizing freedom from tyranny is hard-wired into our nature as some kind of incomprehensibly deep imperative. We fathom neither the depth of our nature nor its free will.

  19. tallbloke says:

  20. Paul Vaughan says:

    Taking a Little Stock

    22.1391697297859 = 2*(13*11*7*5*3)^(1/4)
    22.1392314983836 = 1/(3/0.615197263396975-5/1.00001743371442+2/11.8626151546089)
    -0.000279000640 = %error

    22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
    22.1392314983836 = 1/(3/0.615197263396975-5/1.00001743371442+2/11.8626151546089)
    0.000000038239 = %error

    It’s 7296 times better than primorial.

    – — – – — – – — – – — – – — – – — – – — – – — – – — –

    limit of (φ^x+2/x)^(2e/x+1/x) as x goes to infinity:
    φ(φφ)^e

    22.139216638166 = φ(φφ)^e
    22.1392314983836 = 1/(3/0.615197263396975-5/1.00001743371442+2/11.8626151546089)
    -0.000067121650 = %error

    It’s only 4 times better than primorial.

    With x = 22
    (φ^x+2/x)^(2e/x+1/x) = (φ^22+1/11)^(e/11+1/22)
    It does 1755 times better than the limit φ(φφ)^e.
    The integer x = 22 very near exactly optimizes the fit with JEV.

    — — — — — — — — — — — — — — — — — — —

    Switch-flipping perspective-review of a few sights we’ve seen along the primorial trail:

    JSEV+
    6.40217174588736 = 1 / ( 0/(2*(7*5*3)^(1/4)) + 1/(2*(13*11*7*5*3)^(1/4)) )
    SEV-
    18.013444122756 = 2 / ( 1/(2*(7*5*3)^(1/4)) – 1/(2*(13*11*7*5*3)^(1/4)) )
    J-S
    19.8643454852672 = 4 / ( 1/(2*(7*5*3)^(1/4)) + 1/(2*(13*11*7*5*3)^(1/4)) )
    JEV-
    22.1391697297859 = 1 / ( 0/(2*(7*5*3)^(1/4)) + 1/(2*(13*11*7*5*3)^(1/4)) )

    U-N
    171.406964273337 = 50 / ( 1/(2*(7*5*3)^(1/4)) + 3/(2*(13*11*7*5*3)^(1/4)) )

    φ & e give far tigther fits for the top 4.

    Guard D-own easin’ sight: U-N’s the UNlie one in this group that’s too high. It’s over the limit. The others are a11 UN door the limit.

    Conclusion: The limit of pry more reality is divinity.
    Let us pray to God that we do not become satUN’s prey.

  21. Paul Vaughan says:

    The best insights come out of nowhere.

    22.139216638166 = φ(φφ)^e
    22.139216638166 = (φ^60+1/30)^(e/30+1/60)
    22.1392181913429 = (φ^26+1/13)^(e/13+1/26)
    22.1392214103847 = (φ^24+1/12)^(e/12+1/24)
    22.1392314983836 = 1/(3/0.615197263396975-5/1.00001743371442+2/11.8626151546089)
    22.1392315068494 = (φ^22+1/11)^(e/11+1/22)
    22.1392637394281 = (φ^20+1/10)^(e/10+1/20)
    22.1623822704417 = (φ^10+1/5)^(e/5+1/10)
    24.7952395626488 = (φ^4+1/2)^(e/2+1/4)
    62.7079143931356 = (φ^2+1/1)^(e/1+1/2)

    I had spent the day working on a nuisance problem. I was quite annoyed.
    I went for a hike, overcame the disgust, sat down, and this just fell out of the sky into my head like nothing. These types of discoveries are always purely effortless. The only way I could describe it is that they must come from God.

  22. Paul Vaughan says:

    The next day I easily worked this out in my head while hiking.

    657 = 0+3*(4*5*11-1)
    657 = 1+4*(5*3*11-1)
    657 = 2+5*(3*4*11-1)

    5256 = 8 * (0+3*(4*5*11-1))
    5256 = 8 * (1+4*(5*3*11-1))
    5256 = 8 * (2+5*(3*4*11-1))

    The Mayan sages were fond of deep, memorable simplicity — stuff you could teach a child to do in their head while sharing a hike.

    Anyone thinking Ramanujan’s irrelevant is missing the core point.

    The simple “Ramanujan8tor” tool I built months ago yielded key insights that dovetailed discretely with derivations of generalized NUSJEV slip cycles. I recognized the 3-4-5 triangle in 5256 a day after effortlessly pinpointing 22.1392315068494 = (φ^22+1/11)^(e/11+1/22) from the same triangle.

    Something far more important than any of this has also been on my mind while hiking and I’m taking this very seriously. I’ve come to the conclusion that we should make it illegal to ever suggest locking down people and the economy. I would support a law that would result in instant death penalty for anyone admitting in front of qualified witnesses that they even suggested lockdown of people and/or economy. They would always be free to change their mind when questioned by the qualified witnesses. “Did you suggest lockdown?” If they answer “no”, no penalty. This is a human rights issue. I will never trust a government again. It’s impossible now.

  23. Paul Vaughan says:

    For lion Deep state luck D-own CRaims against human rights,
    EMBed 3-4-5 try UN ga11 in May UN whither dye agnostics:

    For n = 1 and n = 2:
    (n^2+1)^3*(1/n*2*5-1)/2*(7^2*3-(-n+2))
    = n*(n^2+1)^3*(((n-1)^2+1)^3*(0+3*(4*5*11-1))/36^(n-1)+(n-1))
    = n*(n^2+1)^3*(((n-1)^2+1)^3*(1+4*(5*3*11-1))/36^(n-1)+(n-1))
    = n*(n^2+1)^3*(((n-1)^2+1)^3*(2+5*(3*4*11-1))/36^(n-1)+(n-1))

    n = 1
    5256
    = (1^2+1)^3*(1/1*2*5-1)/2*(7^2*3-(-1+2))
    = 1*(1^2+1)^3*(((1-1)^2+1)^3*(0+3*(4*5*11-1))/36^(1-1)+(1-1))
    = 1*(1^2+1)^3*(((1-1)^2+1)^3*(1+4*(5*3*11-1))/36^(1-1)+(1-1))
    = 1*(1^2+1)^3*(((1-1)^2+1)^3*(2+5*(3*4*11-1))/36^(1-1)+(1-1))

    n = 2
    36750
    = (2^2+1)^3*(1/2*2*5-1)/2*(7^2*3-(-2+2))
    = 2*(2^2+1)^3*(((2-1)^2+1)^3*(0+3*(4*5*11-1))/36^(2-1)+(2-1))
    = 2*(2^2+1)^3*(((2-1)^2+1)^3*(1+4*(5*3*11-1))/36^(2-1)+(2-1))
    = 2*(2^2+1)^3*(((2-1)^2+1)^3*(2+5*(3*4*11-1))/36^(2-1)+(2-1))

  24. Paul Vaughan says:

    Mayan-D Palace Tragica11y C ENSO R shH!p

    Since factors 11 & 13 show up everywhere in primorial contrast,
    note well that (12-n+1)*(12+n-1)+3 = (7^2*3+n-2) reformulates for EU too a wake UN.

    Mayan sages flew only the simplest symbolic consciousness high over government heads why’11 out for a walk. They linked whole chains of thought at no. more than the cool sight of a numb brrr. IT’s not a cold war because we’d rather knot C a cold door. The only way they could think to censor US vampire sent to dr.reign bank accounts homeless with know amaze sin pair of internet goggles left by satUN. No. access = sci11UNs communication.

    147 = 12*12+3 = 144+3 = 29-3-0
    146 = 11*13+3 = 143+3 = 29*3-1 “the whorled is a vampire” (smash sin pomp kin)

    always differentiating between the beautiful peoples
    ….and the terrifying deep states = every government everywhere at every level now

    from now on you cannot post the number 147 on the internet because a censor will dangerously misrepresent you in a database for doing so …. = what I figure they mean by US.stab.bullishh.UN new normal C”

  25. Paul Vaughan says:

    Knot Too Sub-Ta11 Tipi

    Shelter ring dynamic weave tabulated 4 species 5256 NUSJEV.

  26. Paul Vaughan says:

    Jovial Game of Celestial Hearts

    J = 1 / 11.8626151546089 ____ Cards Featured
    S = 1 / 29.4474984673838

    C = Challenger of Harmonic Means = Queen of Spades
    = Contestant Rocking Hearts 4 Calendar Mayan-D Count Roll

    C = U = 1 / 84.016845922161 ____ Card Player Shuffled with the Deck

    B = 1 / 19.8650360864628 = +1J-1S = beat __________________ Dealer’s Time Table
    R = 1 / 16.9122914926352 = +0.5J+0.5S = harmonic mean
    I = 1 / 8.4561457463176 = +1J+1S = axial period

    R+C = 1 / 14.0783665145948 = +0.5J+0.5S+1U ____ Splitting the Deck
    R-C = 1 / 21.1746788367349 = +0.5J+0.5S-1U

    1B = ⌊1(R-C)/B⌉B = harmonic of B slipping nearest 1(R-C) ____1 Whole
    |1B-1(R-C)| = |W-| = 1 / 321.183589283115 = +0.5J-1.5S+1U __|Solar Core|

    1B = ⌊1(R+C)/B⌉B = harmonic of B slipping nearest 1(R+C) ____1 Whole
    |1(R+C)-1B| = |W+| = 1 / 48.3295711596327 = -0.5J+1.5S+1U __|Galactic Core|

    – —– – — – —– – — – —– – — – —– – — – —– – —

    Be aware that things are getting quite discrete.

    Here’s a CRumb trail: _1_ _2_ _3_ _4_ _5_

    Digest the 33052 derivation at the DO links above.

    It’s from the hierarchy of UJS slip cycles, with derivations exactly analogous to JEV — substituting J & S for E & V and U for J …and studying structures (already well-known to others) that fall out discretely.

    Note that 33052 / 2 = 162526 in calculations below.

    Primorial Review
    — — — — — — — — –
    30031 = 13*11*7*5*3*2+1
    30030 = 13*11*7*5*3*2
    510510 = 17*13*11*7*5*3*2
    — — — — — — — — –

    Here’s a warm-up before we hit the really heavy stuff below:

    33052.629138671 = (36750.3379015986)*(30031)/((36750.3379015986+30031)/2)
    33052.6240615815
    0.000015360625 = % error

    30030.9916175238 = (36750.3379015986)*(16526.3120307908) / (36750.3379015986 – 16526.3120307908)
    30031.0000000000
    -0.000027912744 = % error

    The next 2 are to coarsely raise awareness of overlap in the hierarchy — for now just note quickly and keep moving:

    ⌊ 19865 / 980 ⌉ = ⌊20.2704081632653⌉ = 20
    19865 / 20 = 993.25
    i.e. harmonic of 19865 nearest 980 is 19865 / 20 = 993.25
    73463.0188679245 = (993.25)*(980) / (993.25 – 980)
    36731.5094339623 = 73463.0188679245 / 2
    36730.5294184333 = (74619.9907876555)*(72337.575351641) / (74619.9907876555 + 72337.575351641)

    ⌊ 19865.0360864628 / 980.009010709296 ⌉ = ⌊20.2702586092399⌉ = 20
    19865.0360864628 / 20 = 993.251804323141
    i.e. harmonic of 19865.0360864628 nearest 980.009010709296 is 19865.0360864628 / 20 = 993.251804323141
    73503.8049012778 = (993.251804323141)*(980.009010709296) / (993.251804323141 – 980.009010709296)
    36751.9024506389 = 73503.8049012778 / 2 (see 1800 de Rop thread)

    36751.9537223031 = (510510)*(39602.9999747494) / (510510 + 39602.9999747494)
    36751.8230142953 = (30030)*(16526.3120307908) / (30030 – 16526.3120307908)
    0.000355650406 = % error

    The last one and the next 2 should be studied carefully.

    28361.6666666667 = (510510)*(30030) / (510510 + 30030)
    39602.8482007479 = (28361.6666666667)*(16526.3120307908) / (28361.6666666667 – 16526.3120307908)
    39602.9999747494 = φ^22
    -0.000383238648 = %error
    From above in the discussion recall comparatively:
    39600 = 11 * 3^2*4^2*5^2 (i.e. 11 times squares of sides of 3-4-5 triangle)

    Sages master Mayan D-ID place marks in a hierarchy of sharp penning precious sun, easing the climb for students and masters a11like.

    36750.3253483715 = (30031)*(16526.3120307908) / (30031 – 16526.3120307908)
    36750.3379015986 (key shown a dozen ways on Suggestions-42 and 1470 DO thread)
    -0.000034158127 = % error

  27. Paul Vaughan says:

    5256 & 836 links: Interconnections aren’t beyond the right imagination. It’s a fractal.

  28. Paul Vaughan says:

    For those who didn’t follow the crumb trail above, here’s a review of 33052:

    ⌊ 321.183589283115 / 19.8650360864628 ⌉ = ⌊16.1682862233504⌉ = 16
    321.183589283115 / 16 = 20.0739743301947
    i.e. harmonic of 321.183589283115 nearest 19.8650360864628 is 321.183589283115 / 16 = 20.0739743301947
    1908.55545325512 = (20.0739743301947)*(19.8650360864628) / (20.0739743301947 – 19.8650360864628)

    ⌊ 1908.55545325512 / 321.183589283115 ⌉ = ⌊5.94225706710308⌉ = 6
    1908.55545325512 / 6 = 318.092575542521
    i.e. harmonic of 1908.55545325512 nearest 321.183589283115 is 1908.55545325512 / 6 = 318.092575542521
    33052.6240615815 = (321.183589283115)*(318.092575542521) / (321.183589283115 – 318.092575542521)

    Remember: I worked as a botanist in the 90s. One of my degrees is in biology. One of my jobs involved extensive use of detailed identification keys. The method of compare and contrast is used extensively in biology.

    Here’s the analogous derivation for JEV so you can compare and contrast from more familiar territory:

    ⌊ 44.2784629967671 / 1.59868955949705 ⌉ = ⌊27.6967236908067⌉ = 28
    44.2784629967671 / 28 = 1.58137367845597
    i.e. harmonic of 44.2784629967671 nearest 1.59868955949705 is 44.2784629967671 / 28 = 1.58137367845597
    146.000401793801 = (1.59868955949705)*(1.58137367845597) / (1.59868955949705 – 1.58137367845597)

    ⌊ 146.000401793801 / 44.2784629967671 ⌉ = ⌊3.29732316599293⌉ = 3
    146.000401793801 / 3 = 48.6668005979337
    i.e. harmonic of 146.000401793801 nearest 44.2784629967671 is 146.000401793801 / 3 = 48.6668005979337
    491.049532942454 = (48.6668005979337)*(44.2784629967671) / (48.6668005979337 – 44.2784629967671)

    Remember that 5256 / 146 = 36. Everyone should have simple facts like that memorized by now.

    5256 = 72*73. Remember maxima:
    https://oeis.org/A154363
    https://oeis.org/A002267

    Here’s the analogous derivation for SEV:

    ⌊ 36.0290781181824 / 1.59868955949705 ⌉ = ⌊22.5366318958868⌉ = 23
    36.0290781181824 / 23 = 1.56648165731228
    i.e. harmonic of 36.0290781181824 nearest 1.59868955949705 is 36.0290781181824 / 23 = 1.56648165731228
    77.7547651604955 = (1.59868955949705)*(1.56648165731228) / (1.59868955949705 – 1.56648165731228)

    ⌊ 77.7547651604955 / 36.0290781181824 ⌉ = ⌊2.15811142614986⌉ = 2
    77.7547651604955 / 2 = 38.8773825802477
    i.e. harmonic of 77.7547651604955 nearest 36.0290781181824 is 77.7547651604955 / 2 = 38.8773825802477
    491.77195509448 = (38.8773825802477)*(36.0290781181824) / (38.8773825802477 – 36.0290781181824)

    Things to note:
    5256 / 36 = 146.
    UJS 33052 is analagous to JEV & SEV’s 491.

    The way we’re doing this it’s like going fishing ….as increasingly experienced fishermen. Now we’re scoring some good catches pretty much every time we go out. It’s more fun this way than presenting the generalized formula and ruining all the fishing fun.

  29. Paul Vaughan says:

    Sit-UN: 11 Awe ‘n’ Mow Hour

    Sew image UN EU’V-E a sit-on lawn-mower.
    You C others sti11 USing push-mowers.

    Limit of binomial recursion’s exponential.

    For example repeat-binomial smoothing exactly matches Gaussian smoothing and there’s a normal approximation to binomial in statistics which can be algebraically refined (with reduced ease of application) to be exact.

    Binet formula’s binomial.
    Binet formula’s connection to phi’s in the definition.
    We see it hitting e in limits.

    A simple formula for the geometry of everything we’ve ever discussed should exist, generalized to n-bodies and with switches to flip representation of stable states.

    It would elucidate the spatiotemporal boundary conditions shaping dynamic attractors. Stable states aren’t flukes. Spatiotemporal chaos isn’t random.

    Those who choose to be naive rather than cynical (it’s like choosing to be soft-minded rather than hard-minded) are led to believe that a lot of models are allowed to evolve with blackbox (user blind) approach to stable states. This isn’t good enough for security and public trust of authority.

    Transparent C

    Surely there are classified and patented models. Meanwhile weave become fantastic fishermen — anglers if few prefer — by heeding my yen guidelines.

    Eye’V-E a who’11 base kit of se11 less tee y’a11 heart catchUS and fish UN store ease to tall. Maybe counts I’11 share some later today. Once you see what’s approaching limits from UN other side, a sharp cast can hook quickly.

  30. Paul Vaughan says:

    Primorial e: Break Kin[Luck]D-own with P-DO’or’Pawn

    The UN seize Eur. needs a break.

    Can.UK.Aus.NZ = “canoe cousins” — or “can nuke O sins” if we fail to heed security lessUNs as in clean shave UN Cousin Cooter from the Dukes of Hazard — R EU watchin’ with US to C-the-deep-state of guard D-own’ease (can. ID UN singer for Tragica11y[C ENSO R s]Hip)?

    “out at the speed wei — some kind of E11Vis thing” — TH

    Pi22a Tech Knew CRays e-Key Phine-a11y

    O = OrWe11
    ‘or’ = gold
    “We” is a dis-top√(Φ-φ)un novel.
    In tech no. crew see talk it’s a11 be on say “comm.UN at EU so crazy in lo V-E May kin a foo11oV-E me”

    3.45807182445672 = √√11√√13
    3.45770789871694 = e√φ

    2.71856792918077 = √Φ√√11√√13
    2.71828182845905 = e

    e/11vis√(Φ-φ)UN
    right got IT

  31. Paul Vaughan says:

    Anyone who followed through carefully with the comparisons suggested in my last comment should have discovered something very precise (alongside failed alternatives).

    – — — – — —– – — —

    Here’s a noteworthy UEV slip-cycle:

    ⌊ 10.0377971159193 / 1.59868955949705 ⌉ = ⌊6.27876566547245⌉ = 6
    10.0377971159193 / 6 = 1.67296618598655
    i.e. harmonic of 10.0377971159193 nearest 1.59868955949705 is 10.0377971159193 / 6 = 1.67296618598655
    36.0080108822137 = (1.67296618598655)*(1.59868955949705) / (1.67296618598655 – 1.59868955949705)

    5256 / 36 = 146

    Another noteworthy JSEV slip cycle (beyond the famous 260 ones) :

    ⌊ 22.0589172625393 / 0.399672389874261 ⌉ = ⌊55.1924972087241⌉ = 55
    22.0589172625393 / 55 = 0.401071222955259
    i.e.harmonic of 22.0589172625393 nearest 0.399672389874261 is 22.0589172625393 / 55 = 0.401071222955259
    114.593439607505 = (0.401071222955259)*(0.399672389874261) / (0.401071222955259 – 0.399672389874261)

    ⌊ 114.593439607505 / 11.0294586312696 ⌉ = ⌊10.389761042543⌉ = 10
    114.593439607505 / 10 = 11.4593439607505
    i.e.harmonic of 114.593439607505 nearest 11.0294586312696 is 114.593439607505 / 10 = 11.4593439607505
    294.009475292454 = (11.4593439607505)*(11.0294586312696) / (11.4593439607505 – 11.0294586312696)

    36750 / 294 = 125

    All of the slip cycles point to limits. That’s the connection with Ramanujan’s work. By probing what’s approaching from sides (inequalities) we map corral shapes. It’s not as much fun as it used to be when everything was a mystery, but I’ll persevere to post a few more 5256 highlights. Beyond that my attention may escalate hard in some totally and completely different direction soon enough.

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