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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s