A quasi-periodic ~2400-year climate cycle – or not?

Posted: July 29, 2020 by oldbrew in Analysis, climate, Cycles, data


We’ll look here at examples of where a 2400 year period has been identified by researchers in radiocarbon data.
– – –
Part of the abstract below is highlighted for analysis. The original Talkshop post on the paper in question:
S. S. Vasiliev and V. A. Dergachev: 2400-year cycle in atmospheric radiocarbon concentration

Abstract. We have carried out power spectrum, time-spectrum and bispectrum analyses of the long-term series of the radiocarbon concentrations deduced from measurements of the radiocarbon content in tree rings for the last 8000 years. Classical harmonic analysis of this time series shows a number of periods: 2400, 940, 710, 570, 500, 420, 360, 230, 210 and 190 years. A principle feature of the time series is the long period of ~ 2400 years, which is well known. The lines with periods of 710, 420 and 210 years are found to be the primary secular components of power spectrum. The complicated structure of the observed power spectrum is the result of ~ 2400-year modulation of primary secular components. The modulation induces the appearance of two side lines for every primary one, namely lines with periods of 940 and 570 years, of 500 and 360 years, and 230 and 190 years. The bi-spectral analysis shows that the parameters of carbon exchange system varied with the ~ 2400-year period during the last 8000 years. Variations of these parameters appear to be a climate effect on the rate of transfer of 14C between the atmosphere and the the ocean.

Looking at the ‘primary’ numbers:
‘The lines with periods of 710, 420 and 210 years are found to be the primary secular components of power spectrum. The complicated structure of the observed power spectrum is the result of ~ 2400-year modulation of primary secular components.’
[See Figure 3 and Table 1 in the paper]
– – –
Analysing this:
2400-year modulation = Mod-2400
210-year = de Vries cycle
420-year = de Vries pair (21 Jupiter-Saturn conjunctions)

With these periods we can derive as an approximation:
Square root of 2400*210 = 709.93 years
Therefore, the geometric mean of Mod-2400 and de Vries pair = ~710-year

The periods quoted in the abstract are rounded by the authors to the nearest ten years, but the pattern is there.

Substituting more accurate numbers for the de Vries pair:
21 Jupiter-Saturn = 417.16575 years
(via NASA JPL data: https://ssd.jpl.nasa.gov/?planet_phys_par)

Using the formula from this post:
24 * 2503y = 25 * 2402.88y
(24:25 = 2.4:2.5)

Then:
2402.88 * 417.16575 = (1001.1988y)² [geometric mean of the two periods]
2402.88 / 2.4 = 1001.2
417.16575 * 2.4 = 1001.1978

1001.2 * 2.5 = 2503
(2.4 = 12/5)

By the same method for the single de Vries period:
2402.88 * 208.58287 = (707.9545)² [geometric mean of the two periods]
This corresponds to the 710 year period referred to in the paper as a ‘primary secular component’ of the power spectrum.

Cross-check: 707.9545 * √2 = 1001.1988
– – –
Vasiliev and Dergachev cite a NASA-sponsored paper by Hood and Jirikowic:
A Probable Approx. 2400 Year Solar Quasi-cycle in Atmospheric Delta C-14

They say:
The residual record can be modeled to first order as an amplitude modulation of a century-scale periodic forcing function by a approx. 2400 year periodic forcing function.

The caption to their Figure 4 says:
Figure 4. Simple model of amplitude modulation of a 200 year sinusoid (a) by a 2400 year sinusoid (b). The product is shown in (c) and has characteristics that are qualitatively similar to those of the residual 14-C record.

They also refer to:
the empirical evidence discussed here for a dominantly solar origin of both the century-scale and longer-term (~ 2400 year) residual variations in the Conference 14-C record.

Figure 4 is worth a look to get a better idea of what they mean.
– – –
A series of three articles under the title ‘Nature Unbound IV – The 2400-year Bray cycle’ can be found here:
https://judithcurry.com/?s=bray

Finally, Ivanka Charvatova finds a ~2402 year solar inertial motion period in this paper:
Responses of the basic cycles of 178.7 and 2402 yr in solar–terrestrial phenomena during the Holocene

Comments
  1. oldbrew says:

    Another way of looking at it (Fig. 3):
    710² / 210 = 2400 (2400.476)
    (210*2 = 420)
    – – –

  2. Paul Vaughan says:

    Starting Point for Discussion

    J: 11.__________ years
    S: 29.__________ years
    U: 8_.__________ years
    N: 16_.__________ years

    Someone please fill in Charvatova’s model parameters with ALL the decimal places.

  3. Paul Vaughan says:

    clarification:
    in Julian years please

  4. oldbrew says:

    ‘Charvatova (2000) suggests to a possible relation of the ~2400 year period to a similar one discovered in radio-carbon series.’ – Vasiliev & Dergachev.

    See also:
    Recurring variations of probable solar origin in the atmospheric Δ14C time record
    L. L. Hood J. L. Jirikowic
    First published: January 1990
    https://doi.org/10.1029/GL017i001p00085
    Citations: 22

  5. Paul Vaughan says:

    Mayan Queen of Spaades “Beat IT”

    BSfool bell lure in a moon stir US sly helios fear IC OB survey shh! UN:
    No. 1’s eye sees what’s We’11-hood D-UN.

    “No. 1 WW ants-tube. D-feat-D” — MJ

    WHO’s REM main knew Jan. EU wary?
    “EU have too shh!O-theme that Eur.a11y knot[OB]scured…

    IC the climate casino awe weights real ease of just won list honor.

  6. oldbrew says:

    Charvatova says:
    It was also found that very long (nearly 370 yr) intervals of the solely trefoil orbit of the SIM occurred in steps of 2402 yr. Such exceptional intervals occurred in the years 159 BC–208 AD, 2561–2193 BC, 4964–4598 BC, etc. A stable behaviour of ST phenomena during these long segments is documented.

    There is no mathematical model as such in her paper. The dates quoted are derived from the solar inertial motion diagrams, as documented in Figure 4.

  7. oldbrew says:

    V&D: The complicated structure of the observed power spectrum is the result of ~ 2400-year modulation of primary secular components.

    Main frequency: 2400/710 = 710/210
    (They used multiples of 10 years in the graphic).

  8. Paul Vaughan says:

    Tune Knight: Sci11UNs Communication

    OBacknowledge-D:
    “There is no mathematical model as such in her paper”

    IT exists and IT was US-D.
    IT simply was knot ID-D.

    5 Fathom: UN knew SOS eerie US mind set:

    I will twist the knife and bleed my aching heart
    and tear IT apart
    — Garbage #1 CRush

    “Bury center” is political code weather left or right.

    2400 Q-borg: Tim Channon found no. th’ UN ‘ear IT? (too 2 UN 1 seeks 6 hive 5?)

    Mess Age in the Err Craft: UN Dare Grown-D Miss $Sell Vac Scene

    Bet ER: DO the review. WHO’s BRI11ant ID was IT to knot have IC report numb brrs and their SORCE err or CRaft? Maybe some UN WHO want-D to cause more D-tech-dive “work”.

    Share ring? Knot incline-D UN dare “classified” “intellectual property” of IT‘s “trade secrets”.
    IT has US tie-D in knots. Sea We-D knot free 2’s peek.

    UN of verse AI: trains later. Comp PR UN-D ?
    If knot: tough shh!IT for 5 moor. Then AI of US in no cent loom $ UN eerie.

    With the numbers listed precisely: Green light’s instant (copy/paste/post).
    May Be. butter right to IC with Anon name US. WHO’s Quest UNs AB out IT.

  9. oldbrew says:

    The Vasiliev & Dergachev paper doesn’t rely on Charvatova at all. Neither do any of the other studies they cite, AFAIK.

    But Charvatova’s ~370 year period either exists and repeats or it doesn’t. Obviously she says it does, with supporting SIM diagrams (Fig. 4 in the PRP paper).

    This is 2403 years (53 Saturn-Uranus = 2402.934 years).
    Left and right are about 120 degrees different.

  10. oldbrew says:

    More discussion with Bill Howell:

    An Independent Verification of Ivanka Charvátová’s Solar Inertial Motion (SIM) Curves
    William Neil Howell

    Click to access Howell%20-%20solar%20inertial%20motion%20-%20NASA-JPL%20versus%20Charvatova.pdf


    (version: incomplete, uncorrected second draft 18Jun08)

    Some other Bill Howell stuff here – includes various links:

    Charvatova’s Solar Inertial Motion (SIM) hypothesis – similar SIM curves yield similar solar activity
    http://www.billhowell.ca/Charvatova%20solar%20inertial%20motion%20&%20activity/_Charvatova%20-%20solar%20inertial%20motion%20&%20activity.html

  11. Paul Vaughan says:

    OB: You leave the impression you think Charvatova used the Seidelmann (1992) model.

    I advise that someone write to her and ask for precise verification. I want to run comparative diagnostics at this stage as I have the whole thing cracked and all that’s left is sensitivity testing.

    I’ve already given all of the puzzle pieces. I just haven’t assembled them all in one place. The main reason is I get so incredibly annoyed with that stupid filter that favors paragraphs over blocks of numbers and algebra.

    Lots of things fall out clearly. I’ll list a few now:

    1. 96 & 104 combine to give 100 and this is clear in aa index diagnostics (solves a puzzle I discovered in 2008).
    2. V&D 940 & 570 do not arise from 710 & 2400 but rather 710 and 2900. If you study the figures in V&D carefully there’s no getting around this. They threw a curve-ball in their paper and I’ve figured out what they missed and/or misrepresented: DO (which Tim Channon found).
    3. Landscheidt Cycle (980 years) shows up yet another way: as a base-level UN slip cycle. (This is a new result I turned up while reviewing with analogous extensions.)
    4. There are 4 noteworthy jovian slip cycles bundled around 2300-2400. One of them fits V&D like a glove. Luminaries will find clear scope for further exploration and diagnostics here.

    It’s all algebraically analogous to JEV.
    I’ll share some insights in “climate casino” format, which was chosen to deliberately accent parallels.

  12. Paul Vaughan says:

    Jovial Game of Celestial Hearts

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

    C = 1 / 835.546575435631 ____ Card Players Shuffled with Deck
    C = Challenger of Harmonic Means = Queen of Spades
    = Contestant Rocking Hearts 4 Calendar Mayan-D Count Roll

    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 / 16.5767613988929 = +0.5J+0.5S+1C ____ Splitting the Deck
    R-C = 1 / 17.2616851219298 = +0.5J+0.5S-1C

    1B = ⌊1(R-C)/B⌉B = harmonic of B slipping nearest 1(R-C) ____1 Whole
    |1(R-C)-1B| = |W-| = 1 / 131.716392653884 = -0.5J+1.5S-1C __|Solar Core|
    2B = ⌊2(R-C)/B⌉B = harmonic of B slipping nearest 2(R-C) ____2 Halves
    |2(R-C)-2B| = |H-| = 1 / 65.8581963269422 = -1J+3S-2C __|Solar Opposition|
    5B = ⌊4(R-C)/B⌉B = harmonic of B slipping nearest 4(R-C) ____4 Quarters
    |5B-4(R-C)| = |Q-| = 1 / 50.071541259993 = +3J-7S+4C __|Solar Rights|

    1B = ⌊1(R+C)/B⌉B = harmonic of B slipping nearest 1(R+C) ____1 Whole
    |1(R+C)-1B| = |W+| = 1 / 100.143082519986 = -0.5J+1.5S+1C __|Galactic Core|
    2B = ⌊2(R+C)/B⌉B = harmonic of B slipping nearest 2(R+C) ____2 Halves
    |2(R+C)-2B| = |H+| = 1 / 50.0715412599931 = -1J+3S+2C __|Galactic Opposition|
    5B = ⌊4(R+C)/B⌉B = harmonic of B slipping nearest 4(R+C) ____4 Quarters
    |5B-4(R+C)| = |Q+| = 1 / 96.1829470900284 = +3J-7S-4C __|Galactic Rights|

  13. Paul Vaughan says:

    19.8650360864628 = (29.4474984673838)*(11.8626151546089) / (29.4474984673838 – 11.8626151546089)
    8.4561457463176 = (29.4474984673838)*(11.8626151546089) / (29.4474984673838 + 11.8626151546089)
    16.9122914926352 = (29.4474984673838)*(11.8626151546089)/((29.4474984673838+11.8626151546089)/2)

    ⌊ 29.4474984673838 / 11.8626151546089 ⌉ = ⌊2.4823783022197⌉ = 2
    29.4474984673838 / 2 = 14.7237492336919
    61.0464822565173 = (14.7237492336919)*(11.8626151546089) / (14.7237492336919 – 11.8626151546089)

    ⌊ 61.0464822565173 / 19.8650360864628 ⌉ = ⌊3.07306173473895⌉ = 3
    61.0464822565173 / 3 = 20.3488274188391
    835.546575435631 = (20.3488274188391)*(19.8650360864628) / (20.3488274188391 – 19.8650360864628)

  14. Paul Vaughan says:

    ⌊ 131.716392653884 / 19.8650360864628 ⌉ = ⌊6.63056397585119⌉ = 7
    131.716392653884 / 7 = 18.8166275219835
    356.533700137559 = (19.8650360864628)*(18.8166275219835) / (19.8650360864628 – 18.8166275219835)

    ⌊ 65.8581963269421 / 19.8650360864628 ⌉ = ⌊3.31528198792559⌉ = 3
    65.8581963269421 / 3 = 21.9527321089807
    208.886643858908 = (21.9527321089807)*(19.8650360864628) / (21.9527321089807 – 19.8650360864628)

    ⌊ 50.0715412599931 / 19.8650360864628 ⌉ = ⌊2.52058647374493⌉ = 3
    50.0715412599931 / 3 = 16.690513753331
    104.443321929454 = (19.8650360864628)*(16.690513753331) / (19.8650360864628 – 16.690513753331)

  15. Paul Vaughan says:

    ⌊ 131.716392653884 / 9.93251804323141 ⌉ = ⌊13.2611279517024⌉ = 13
    131.716392653884 / 13 = 10.1320302041449
    504.413226524327 = (10.1320302041449)*(9.93251804323141) / (10.1320302041449 – 9.93251804323141)

    ⌊ 65.8581963269421 / 9.93251804323141 ⌉ = ⌊6.63056397585119⌉ = 7
    65.8581963269421 / 7 = 9.40831376099173
    178.266850068779 = (9.93251804323141)*(9.40831376099173) / (9.93251804323141 – 9.40831376099173)

    ⌊ 100.143082519986 / 19.8650360864628 ⌉ = ⌊5.04117294748986⌉ = 5
    100.143082519986 / 5 = 20.0286165039972
    2432.25439579341 = (20.0286165039972)*(19.8650360864628) / (20.0286165039972 – 19.8650360864628)

    ⌊ 356.533700137559 / 50.0715412599931 ⌉ = ⌊7.12048583218722⌉ = 7
    356.533700137559 / 7 = 50.9333857339369
    2959.13381403679 = (50.9333857339369)*(50.0715412599931) / (50.9333857339369 – 50.0715412599931)

    ⌊ 504.413226524327 / 131.716392653884 ⌉ = ⌊3.82954024446897⌉ = 4
    504.413226524327 / 4 = 126.103306631082
    2959.13381403688 = (131.716392653884)*(126.103306631082) / (131.716392653884 – 126.103306631082)

  16. Paul Vaughan says:

    ⌊ 504.413226524327 / 65.8581963269421 ⌉ = ⌊7.65908048893794⌉ = 8
    504.413226524327 / 8 = 63.0516533155409
    1479.56690701844 = (65.8581963269421)*(63.0516533155409) / (65.8581963269421 – 63.0516533155409)

    939.447668560927 = (2959.13381403679)*(713.067400275117) / (2959.13381403679 – 713.067400275117)
    574.604095118134 = (2959.13381403679)*(713.067400275117) / (2959.13381403679 + 713.067400275117)

    228.511660883048 = (2432.25439579341)*(208.886643858908) / (2432.25439579341 – 208.886643858908)
    192.365894180056 = (2432.25439579341)*(208.886643858908) / (2432.25439579341 + 208.886643858908)
    504.413226524332 = (2432.25439579341)*(417.773287717816) / (2432.25439579341 – 417.773287717816)
    356.533700137555 = (2432.25439579341)*(417.773287717816) / (2432.25439579341 + 417.773287717816)

  17. Paul Vaughan says:

    ⌊ 208.886643858908 / 100.143082519986 ⌉ = ⌊2.08588190619376⌉ = 2
    208.886643858908 / 2 = 104.443321929454
    2432.25439579362 = (104.443321929454)*(100.143082519986) / (104.443321929454 – 100.143082519986)

    8.63084256096492 = 17.2616851219298 / 2
    4.31542128048246 = 17.2616851219298 / 4

    ⌊ 19.8650360864628 / 17.2616851219298 ⌉ = ⌊1.15081673348482⌉ = 1
    19.8650360864628 / 1 = 19.8650360864628
    131.716392653884 = (19.8650360864628)*(17.2616851219298) / (19.8650360864628 – 17.2616851219298)

    ⌊ 19.8650360864628 / 8.63084256096492 ⌉ = ⌊2.30163346696964⌉ = 2
    19.8650360864628 / 2 = 9.93251804323141
    65.8581963269421 = (9.93251804323141)*(8.63084256096492) / (9.93251804323141 – 8.63084256096492)

    ⌊ 19.8650360864628 / 4.31542128048246 ⌉ = ⌊4.60326693393928⌉ = 5
    19.8650360864628 / 5 = 3.97300721729256
    50.0715412599931 = (4.31542128048246)*(3.97300721729256) / (4.31542128048246 – 3.97300721729256)

    8.28838069944647 = 16.5767613988929 / 2
    4.14419034972324 = 16.5767613988929 / 4

    ⌊ 19.8650360864628 / 16.5767613988929 ⌉ = ⌊1.19836653303036⌉ = 1
    19.8650360864628 / 1 = 19.8650360864628
    100.143082519986 = (19.8650360864628)*(16.5767613988929) / (19.8650360864628 – 16.5767613988929)

    ⌊ 19.8650360864628 / 8.28838069944647 ⌉ = ⌊2.39673306606072⌉ = 2
    19.8650360864628 / 2 = 9.93251804323141
    50.0715412599931 = (9.93251804323141)*(8.28838069944647) / (9.93251804323141 – 8.28838069944647)

    ⌊ 19.8650360864628 / 4.14419034972324 ⌉ = ⌊4.79346613212144⌉ = 5
    19.8650360864628 / 5 = 3.97300721729256
    96.1829470900285 = (4.14419034972324)*(3.97300721729256) / (4.14419034972324 – 3.97300721729256)

  18. Paul Vaughan says:

    Jovial Game of Celestial Hearts

    U = 1 / 84.016845922161 ____ Cards Featured
    N = 1 / 164.791315640078
    C = 1 / 48590.8284812209 ____ Card Players Shuffled with Deck
    C = Challenger of Harmonic Means = Queen of Spades
    = Contestant Rocking Hearts 4 Calendar Mayan-D Count Roll

    B = 1 / 171.406220601552 = +1U-1N = beat __________________ Dealer’s Time Table
    R = 1 / 111.292543528394 = +0.5U+0.5N = harmonic mean
    I = 1 / 55.6462717641972 = +1U+1N = axial period

    R+C = 1 / 111.038221334937 = +0.5U+0.5N+1C ____ Splitting the Deck
    R-C = 1 / 111.548033396551 = +0.5U+0.5N-1C

    2B = ⌊1(R-C)/B⌉B = harmonic of B slipping nearest 1(R-C) ____1 Whole
    |2B-1(R-C)| = |W-| = 1 / 369.89908519333 = +1.5U-2.5N+1C __|Solar Core|
    3B = ⌊2(R-C)/B⌉B = harmonic of B slipping nearest 2(R-C) ____2 Halves
    |2(R-C)-3B| = |H-| = 1 / 2340.74786894369 = -2U+4N-2C __|Solar Opposition|
    6B = ⌊4(R-C)/B⌉B = harmonic of B slipping nearest 4(R-C) ____4 Quarters
    |4(R-C)-6B| = |Q-| = 1 / 1170.37393447185 = -4U+8N-4C __|Solar Rights|

    2B = ⌊1(R+C)/B⌉B = harmonic of B slipping nearest 1(R+C) ____1 Whole
    |2B-1(R+C)| = |W+| = 1 / 375.617889254102 = +1.5U-2.5N-1C __|Galactic Core|
    3B = ⌊2(R+C)/B⌉B = harmonic of B slipping nearest 2(R+C) ____2 Halves
    |2(R+C)-3B| = |H+| = 1 / 1962.57776108677 = -2U+4N+2C __|Galactic Opposition|
    6B = ⌊4(R+C)/B⌉B = harmonic of B slipping nearest 4(R+C) ____4 Quarters
    |4(R+C)-6B| = |Q+| = 1 / 981.288880543385 = -4U+8N+4C __|Galactic Rights|

  19. Paul Vaughan says:

    171.406220601552 = (164.791315640078)*(84.016845922161) / (164.791315640078 – 84.016845922161)
    55.6462717641972 = (164.791315640078)*(84.016845922161) / (164.791315640078 + 84.016845922161)
    111.292543528394 = (164.791315640078)*(84.016845922161)/((164.791315640078+84.016845922161)/2)

    ⌊ 164.791315640078 / 84.016845922161 ⌉ = ⌊1.96140802277619⌉ = 2
    164.791315640078 / 2 = 82.395657820039
    4270.09258127429 = (84.016845922161)*(82.395657820039) / (84.016845922161 – 82.395657820039)

    ⌊ 4270.09258127429 / 171.406220601552 ⌉ = ⌊24.9121214287811⌉ = 25
    4270.09258127429 / 25 = 170.803703250972
    48590.8284812209 = (171.406220601552)*(170.803703250972) / (171.406220601552 – 170.803703250972)

    55.7740166982756 = 111.548033396551 / 2
    27.8870083491378 = 111.548033396551 / 4

    55.5191106674687 = 111.038221334937 / 2
    27.7595553337344 = 111.038221334937 / 4

    85.7031103007758 = 171.406220601552 / 2
    42.8515551503879 = 171.406220601552 / 4

    27.8231358820986 = 55.6462717641972 / 2
    13.9115679410493 = 55.6462717641972 / 4

    9.93251804323141 = 19.8650360864628 / 2
    4.9662590216157 = 19.8650360864628 / 4

    4.2280728731588 = 8.4561457463176 / 2
    2.1140364365794 = 8.4561457463176 / 4

  20. Paul Vaughan says:

    ⌊ 171.406220601552 / 111.548033396551 ⌉ = ⌊1.53661355904147⌉ = 2
    171.406220601552 / 2 = 85.7031103007758
    369.89908519333 = (111.548033396551)*(85.7031103007758) / (111.548033396551 – 85.7031103007758)

    ⌊ 171.406220601552 / 55.7740166982756 ⌉ = ⌊3.07322711808295⌉ = 3
    171.406220601552 / 3 = 57.1354068671839
    2340.74786894369 = (57.1354068671839)*(55.7740166982756) / (57.1354068671839 – 55.7740166982756)

    ⌊ 171.406220601552 / 27.7595553337344 ⌉ = ⌊6.17467457748694⌉ = 6
    171.406220601552 / 6 = 28.5677034335919
    981.288880543382 = (28.5677034335919)*(27.7595553337344) / (28.5677034335919 – 27.7595553337344)

    ⌊ 369.89908519333 / 171.406220601552 ⌉ = ⌊2.15802602668191⌉ = 2
    369.89908519333 / 2 = 184.949542596665
    2340.74786894369 = (184.949542596665)*(171.406220601552) / (184.949542596665 – 171.406220601552)

    ⌊ 171.406220601552 / 111.038221334937 ⌉ = ⌊1.54366864437174⌉ = 2
    171.406220601552 / 2 = 85.7031103007758
    375.617889254102 = (111.038221334937)*(85.7031103007758) / (111.038221334937 – 85.7031103007758)

    ⌊ 375.617889254102 / 85.7031103007758 ⌉ = ⌊4.38278013406827⌉ = 4
    375.617889254102 / 4 = 93.9044723135256
    981.288880543382 = (93.9044723135256)*(85.7031103007758) / (93.9044723135256 – 85.7031103007758)

    ⌊ 171.406220601552 / 27.8870083491378 ⌉ = ⌊6.1464542361659⌉ = 6
    171.406220601552 / 6 = 28.5677034335919
    1170.37393447185 = (28.5677034335919)*(27.8870083491378) / (28.5677034335919 – 27.8870083491378)

    ⌊ 1170.37393447185 / 111.292543528394 ⌉ = ⌊10.5161936044102⌉ = 11
    1170.37393447185 / 11 = 106.397630406532
    2419.09562407727 = (111.292543528394)*(106.397630406532) / (111.292543528394 – 106.397630406532)

    2385.623964918 = (2432.25439579341)*(2340.74786894369)/((2432.25439579341+2340.74786894369)/2)
    2402.24320580332 = (2419.09562407727)*(2385.623964918)/((2419.09562407727+2385.623964918)/2)

  21. Paul Vaughan says:

    ⌊ 104.443321929454 / 19.8650360864628 ⌉ = ⌊5.25764571858129⌉ = 5
    104.443321929454 / 5 = 20.8886643858908
    405.375732632252 = (20.8886643858908)*(19.8650360864628) / (20.8886643858908 – 19.8650360864628)

    ⌊ 96.1829470900285 / 19.8650360864628 ⌉ = ⌊4.84182090943057⌉ = 5
    96.1829470900285 / 5 = 19.2365894180057
    608.063598948375 = (19.8650360864628)*(19.2365894180057) / (19.8650360864628 – 19.2365894180057)

    1216.12719789677 = (608.063598948375)*(405.375732632252) / (608.063598948375 – 405.375732632252)

    2432.25439579355 = (208.886643858908)*(192.365894180057) / (208.886643858908 – 192.365894180057)

    ⌊ 208.886643858908 / 19.8650360864628 ⌉ = ⌊10.5152914371626⌉ = 11
    208.886643858908 / 11 = 18.9896948962643
    430.953071338593 = (19.8650360864628)*(18.9896948962643) / (19.8650360864628 – 18.9896948962643)

    ⌊ 192.365894180057 / 19.8650360864628 ⌉ = ⌊9.68364181886114⌉ = 10
    192.365894180057 / 10 = 19.2365894180057
    608.063598948375 = (19.8650360864628)*(19.2365894180057) / (19.8650360864628 – 19.2365894180057)

    1479.5669070184 = (608.063598948375)*(430.953071338593) / (608.063598948375 – 430.953071338593)

  22. Paul Vaughan says:

    Mods: Something like 4 calculation-laden comments are caught in the filter.

  23. Paul Vaughan says:

    Alternating Strategy

    Warning: On the last DO thread I flooded the discussion with a lot of water.

    (Aside: That was deliberate. I’ve been choked about intolerable Western — and especially Five Eyes moves — e.g. lockdowns, double-standards on racism that attack beautiful Chinese people, aggressive campaigns of financial terror now not only on “rogue” foreign nations but on millions of homeland citizens, Boris back-stabbing hardcore volunteer supporters and thus reminding us to remain absolutely cynical about lending trust, incomprehensibly Orwellian climate psy-ops, the creepy shift in our society towards supporting big tech monopolies, the list goes on – the times are running savage interference on better ways.)

    Some of the stuff buried in that DO flood is pure signal. Other stuff is a flood of subharmonics and harmonics. Those with key intuition will know the difference.

    HERE I have NOT watered anything down. Until better avenues for the greater good open up I’m balancing protest of “democratic” psy-ops with solid contribution.

    After the moderator clears the backlog, 2 steps remain.

    Above JS & UN were given separate treatment.

    So the next step is to review how JS & UN slip past one another.
    We’ve covered this before. It’s review with sharpening perspective.

    Then a review of JEV will underscore parallel structure.

    Each of the recipes has 3 ingredients. The procedure stays the same.
    There’s only 1 theme: how the meeting points slip on an axially-locked frame.

    Alert readers see that I give this hierarchical treatment to measure the rate at which nested geometric features slip past one another.

  24. Paul Vaughan says:

    Jovial Game of Celestial Hearts

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

    C = 1 / 171.406220601552 ____ Card Players Shuffled with Deck
    C = Challenger of Harmonic Means = Queen of Spades
    = Contestant Rocking Hearts 4 Calendar Mayan-D Count Roll

    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 / 15.3934519460015 = +0.5J+0.5S+1C ____ Splitting the Deck
    R-C = 1 / 18.7636626447678 = +0.5J+0.5S-1C

    1B = ⌊1(R-C)/B⌉B = harmonic of B slipping nearest 1(R-C) ____1 Whole
    |1(R-C)-1B| = |W-| = 1 / 338.432743555957 = -0.5J+1.5S-1C __|Solar Core|
    2B = ⌊2(R-C)/B⌉B = harmonic of B slipping nearest 2(R-C) ____2 Halves
    |2(R-C)-2B| = |H-| = 1 / 169.216371777979 = -1J+3S-2C __|Solar Opposition|
    4B = ⌊4(R-C)/B⌉B = harmonic of B slipping nearest 4(R-C) ____4 Quarters
    |4(R-C)-4B| = |Q-| = 1 / 84.6081858889894 = -2J+6S-4C __|Solar Rights|

    1B = ⌊1(R+C)/B⌉B = harmonic of B slipping nearest 1(R+C) ____1 Whole
    |1(R+C)-1B| = |W+| = 1 / 68.3854913151666 = -0.5J+1.5S+1C __|Galactic Core|
    3B = ⌊2(R+C)/B⌉B = harmonic of B slipping nearest 2(R+C) ____2 Halves
    |3B-2(R+C)| = |H+| = 1 / 47.4074465992974 = +2J-4S-2C __|Galactic Opposition|
    5B = ⌊4(R+C)/B⌉B = harmonic of B slipping nearest 4(R+C) ____4 Quarters
    |4(R+C)-5B| = |Q+| = 1 / 122.665716840277 = -3J+7S+4C __|Galactic Rights|

  25. Paul Vaughan says:

    9.38183132238388 = 18.7636626447678 / 2
    4.69091566119194 = 18.7636626447678 / 4

    7.69672597300077 = 15.3934519460015 / 2
    3.84836298650038 = 15.3934519460015 / 4

    ⌊ 122.665716840276 / 4.9662590216157 ⌉ = ⌊24.6998226041719⌉ = 25
    122.665716840276 / 25 = 4.90662867361105
    408.644083615556 = (4.9662590216157)*(4.90662867361105) / (4.9662590216157 – 4.90662867361105)

    ⌊ 408.644083615556 / 84.6081858889895 ⌉ = ⌊4.82984098195556⌉ = 5
    408.644083615556 / 5 = 81.7288167231111
    2401.54232383281 = (84.6081858889895)*(81.7288167231111) / (84.6081858889895 – 81.7288167231111)

  26. Paul Vaughan says:

    ⌊ 169.216371777979 / 19.8650360864628 ⌉ = ⌊8.51830175598286⌉ = 9
    169.216371777979 / 9 = 18.8018190864421
    351.291236535953 = (19.8650360864628)*(18.8018190864421) / (19.8650360864628 – 18.8018190864421)

    ⌊ 338.432743555958 / 9.93251804323141 ⌉ = ⌊34.0732070239314⌉ = 34
    338.432743555958 / 34 = 9.95390422223406
    4622.9545388013 = (9.95390422223406)*(9.93251804323141) / (9.95390422223406 – 9.93251804323141)

    ⌊ 338.432743555958 / 4.9662590216157 ⌉ = ⌊68.1464140478629⌉ = 68
    338.432743555958 / 68 = 4.97695211111703
    2311.47726940065 = (4.97695211111703)*(4.9662590216157) / (4.97695211111703 – 4.9662590216157)

    ⌊ 338.432743555958 / 16.9122914926352 ⌉ = ⌊20.0110519442818⌉ = 20
    338.432743555958 / 20 = 16.9216371777979
    30622.009569219 = (16.9216371777979)*(16.9122914926352) / (16.9216371777979 – 16.9122914926352)

  27. Paul Vaughan says:

    Humility, not Hubris

    Here’s a fun one. Some insights are really satisfying. Most of this is review, but here I wrap it up and tie on the ribbon.

    2500.20304503681 = (30622.009569219)*(2311.47726940065) / (30622.009569219 – 2311.47726940065)
    2149.24339501203 = (30622.009569219)*(2311.47726940065) / (30622.009569219 + 2311.47726940065)
    2402.13901582301 = (2500.20304503681)*(2311.47726940065)/((2500.20304503681+2311.47726940065)/2)

    2450.19021822768 = (2500.20304503681)*(2402.13901582301)/((2500.20304503681+2402.13901582301)/2)

    OB: Note that 15 * 2450 = 36750.

    Note the parallel structure with our old primorial (as in number theory) mnemonic device, which doubles here as a suggestion that event series and slip cycle aggregation criteria differ fundamentally.

    2502.5 = (30030)*(2310) / (30030 – 2310)
    2145 = (30030)*(2310) / (30030 + 2310)
    2402.4 = (2502.5)*(2310)/((2502.5+2310)/2)

    2451.42857142857 = (2502.5)*(2402.4)/((2502.5+2402.4)/2)

    Also recall that simple sporadic groups tie into monstrous moonshine via primorials.

  28. Paul Vaughan says:

    Moderators: 2 more calc.-laden comments have been trapped in the filter, bringing the total to 6.

    Supplementary note for readers working their way through the V&D calculations:
    2959 = 2 * 1479.5
    713 = 2 * 356.5

    V&D fits the JS slip-cycle frame flawlessly. Note that UN and JS-slip-on-UN aren’t even needed — which really underscores the dominance of JS in the strongest level of windowing.

    I’m very curious about the 1 misrepresentation V&D made. There’s probably some delectable history there, but it may be difficult to expose.

    They’ve done such beautiful work I would choose to let them save face. They carried the ball quite far and the one loose end they left was easy to figure out.

    Getting really technical: Look at the peak just to the right of 0.001 in Figure 3. Take the reciprocal. It’s a number less than 1000. They say it’s 940 and that is consistent with that peak in Figure 3.

    If anyone tries to tell you 940 should be 1000 or 1010 (6 or 7% off) remind them that we often hit below 0.00001% and tend to not even look at things with errors above 0.01%.

    Something around 1000 or 1010 may be wonderfully meaningful in some other way, but it isn’t consistent with V&D’s well-illustrated summary of 940.

    I showed in detail above what accounts for 940 and 570. That suggests a nice diagnostic avenue for further exploration. The world doesn’t have enough people I would trust with that sort of work.

    The last thing I plan to do here is review JEV so readers have a more familiar parallel structure that might help them comparatively ground their orientation in JS & UN slip cycles.

  29. Paul Vaughan says:

    96

    I bring this up because readers not comparing the decimal digits may conflate their thinking about 96 year cycles of different origins.

    Never forget the 96 year lunisolar cycle to which I’ve had to point repeatedly. It is VERY close to the the JS slip cycle outlined above (which means challenging — and interesting — diagnostics).

    There are 2 other 96 year JS cycles of entirely different natures.
    All of these 96 year cycles tie into a monstrous bundle in such a way that they differentiate precisely.
    The number 96^3 is a building block for all of them. Don’t worry about that, but take this seriously:

    Minimalism:

    I wouldn’t trust any climatologist who can’t at least follow and deeply understand the simple derivation of 96 in the lunisolar context. If this isn’t ringing a bell, you’ve missed something important — maybe repeatedly.

  30. Paul Vaughan says:

    Mods: There are still 2 calculation-laden comments caught in the filter.

  31. Paul Vaughan says:

    Lunisolar 96 Review

    The 96 year lunisolar slip-cycle was derived years ago from time-height sections of quasibiennial, annual, and semi-annual oscillations.

    http://ugamp.nerc.ac.uk/hot/ajh/qbo.htm — includes animation

    Here’s a clean, simple outline I shared with talkshop reader Ed:
    https://tallbloke.wordpress.com/suggestions-18/#comment-116526

    ⌊ 0.999978614647502 / 0.0745030006844627 ⌉ = ⌊13.421991134057⌉ = 13
    0.999978614647502 / 13 = 0.0769214318959617
    2.36966735541038 = (0.0769214318959617)*(0.0745030006844627) / (0.0769214318959617 – 0.0745030006844627)

    ⌊ 2.36966735541038 / 0.499989307323751 ⌉ = ⌊4.73943606533166⌉ = 5
    2.36966735541038 / 5 = 0.473933471082076
    9.0943796900619 = (0.499989307323751)*(0.473933471082076) / (0.499989307323751 – 0.473933471082076)

    ⌊ 9.0943796900619 / 0.999978614647502 ⌉ = ⌊9.09457418073658⌉ = 9
    9.0943796900619 / 9 = 1.0104866322291
    96.1613372617316 = (1.0104866322291)*(0.999978614647502) / (1.0104866322291 – 0.999978614647502)

  32. Paul Vaughan says:

    Let’s throw this here right beside that:

    100.143082519986 = (104.443321929454)*(96.1829470900285)/((104.443321929454+96.1829470900285)/2)

    2432.25439579362 = (104.443321929454)*(100.143082519986) / (104.443321929454 – 100.143082519986)
    2432.25439579349 = (100.143082519986)*(96.1829470900285) / (100.143082519986 – 96.1829470900285)
    2432.25439579355 = (208.886643858908)*(192.365894180057) / (208.886643858908 – 192.365894180057)

    In 2008 I estimated 105 and 97 from the drift of seasonal patterns in annual aa index. At the time I didn’t know 96 so well.

    Some years later Vukcevic and I had a different take on an ENSO clustering pattern.
    He suggested 104, but 96 was a better fit.

  33. Paul Vaughan says:

    96: Review of Chandler, QBO, & Polar Motion Definitions

    Lunar Draconic = Nodal Month
    0.0745030006844627 = 27.212221 / 365.25
    0.0372515003422313 = 13.6061105 / 365.25

    Terrestrial Tropical Year
    0.999978614647502 = 365.242189 / 365.25
    0.499989307323751 = 182.6210945 / 365.25

    Chandler Wobble
    ⌊ 0.499989307323751 / 0.0372515003422313 ⌉ = ⌊13.421991134057⌉ = 13
    0.499989307323751 / 13 = 0.0384607159479808
    1.18483367770519 = (0.0384607159479808)*(0.0372515003422313) / (0.0384607159479808 – 0.0372515003422313)

    QBO = Quasibiennial Oscillation
    ⌊ 0.999978614647502 / 0.0745030006844627 ⌉ = ⌊13.421991134057⌉ = 13
    0.999978614647502 / 13 = 0.0769214318959617
    2.36966735541038 = (0.0769214318959617)*(0.0745030006844627) / (0.0769214318959617 – 0.0745030006844627)

    Polar Motion (Group Wave)
    ⌊ 0.999978614647502 / 0.0372515003422313 ⌉ = ⌊26.843982268114⌉ = 27
    0.999978614647502 / 27 = 0.0370362449869445
    6.40939079526111 = (0.0372515003422313)*(0.0370362449869445) / (0.0372515003422313 – 0.0370362449869445)

    Also note:
    ⌊ 835.546575435636 / 6.40939079526111 ⌉ = ⌊130.36286944048⌉ = 130
    835.546575435636 / 130 = 6.42728134950489
    2302.60937468698 = (6.42728134950489)*(6.40939079526111) / (6.42728134950489 – 6.40939079526111)

  34. Paul Vaughan says:

    Moderators: 2 sets of calculations stuck in the filter derive quantities used in other calculations listed above. Are you able to find them? Or do I need to post them again?

  35. Paul Vaughan says:

    Q:SST UN on Corporate Seas of ITees Mono Pole Lie?

    If few are puttin’ the V&D truffle with IC IT’s a 50 year slide across theme agen[t]a bridge.

    X$marks the control verse see AI Luke Duke slide across the hood in Hazard County.

    CC: Causun Caughter clean-SJ!VE!UN Trains Later

    “First pass-D the post”:
    Then SCroll-D up past “16 Figures“.

    This is cleans h!ave UN sci11UNs comm. on C[ENSO]Rship.

  36. oldbrew says:

    Dergachev and Vasiliev claim to have found a ~2300 year dipole period in their 2018 paper…

    Long-term changes in the concentration of radiocarbon and the nature of the Hallstatt cycle

    In the second case (AM-2), the modulation of ∼210-year variations of the SMP is absent. But the existence of ∼2300-year oscillations of the dipole moment is allowed. In the second case, unlike AM-1, the amplitude of the 210-year oscillations in the production rate depends on the phase of the 2300-year variations in the dipole moment, which agrees with the observations.

    Based on the comparison of AM-1 and AM-2 models of amplitude modulation, it can be concluded that changes in the dipole moment of the geomagnetic field are responsible for the observed ∼2300-year variations in the concentration of radiocarbon.

    https://www.sciencedirect.com/science/article/abs/pii/S1364682617306168

    But before that:
    Highlights

    • Analysis of the radiocarbon series shows that there is an amplitude modulation of the ∼210-year cycle.

    • Two models of amplitude modulation of radiocarbon variations are considered: solar and geomagnetic.

    • The geomagnetic field are responsible for the observed ∼2400-year variations in the concentration of radiocarbon.
    – – –
    09 November 2019
    One Hundred Thousand Years of Geomagnetic Field Evolution – open access
    https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019RG000656

  37. Paul Vaughan says:

    96 is simple with QBO, annual, and semi-annual, but years later ERSSTv3b2 has not been restored.

    The primorials 2310 & 210 come into focus when jovian harmonic means are aggregated.

    I haven’t shared that yet.

    There is no community where these things can be discussed sensibly. The climate propaganda has saturated the minds of highly intelligent elite. It’s remarkable how unsuspecting they are that they’ve been duped. Worse: They interpret propaganda as “unbiased news”. I declare them a lost cause. It is not reasonable to think they can be reached. Together they constitute a truly monstrous obstacle to justice and integrity.

    With humility we know the removal or persistence of these justice and integrity barriers is in God’s hands. We are not here to be regarded as members of a fringe cult. Shifts in “climate” power structures would be most welcome, should they occur.

    What would it take to engineer a truly productive climate dialogue? Many things that don’t presently exist and many things that may not exist anytime soon. For sure God is the only negotiator who could make the needed arrangements.

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