Nicola Scafetta: Solar Oscillations and the Orbital Invariant Inequalities of the Solar System

Posted: March 1, 2020 by oldbrew in Cycles, research, Solar physics, solar system dynamics
Tags: ,
Solar system [credit: BBC]

This new paper from our good friend Nicola Scafetta takes another look at the Sun’s cyclic behaviour and possible planetary influences on it, referencing various researchers whose work has appeared at the talkshop, along the way.
– – –
Abstract
Gravitational planetary lensing of slow-moving matter streaming towards the Sun was suggested to explain puzzling solar-flare occurrences and other unexplained solar-emission phenomena (Bertolucci et al. in Phys. Dark Universe 17, 13, 2017). If it is actually so, the effect of gravitational lensing of this stream by heavy planets (Jupiter, Saturn, Uranus and Neptune) could be manifested in solar activity changes on longer time scales too where solar records present specific oscillations known in the literature as the cycles of Bray–Hallstatt (2100–2500 yr), Eddy (800–1200 yr), Suess–de Vries (200–250 yr), Jose (155–185 yr), Gleissberg (80–100 year), the 55–65 yr spectral cluster and others. It is herein hypothesized that these oscillations emerge from specific periodic planetary orbital configurations that generate particular waves in the force-fields of the heliosphere which could be able to synchronize solar activity.

These harmonics are defined by a subset of orbital frequencies herein labeled as “orbital invariant inequalities” of the solar system that derive from the synodical periods among the Jovian planets. Thus, they are associated with the repeating pattern of planetary alignment relative to the Sun when tidal forcing, interplanetary magnetic couplings and planetary lensing effects could be enhanced. These frequencies are physically relevant also because they are invariant relative to any spinning system centered on the Sun and, therefore, they and their combinations should characterize the spectrum of any forcing able to externally synchronizing the internal dynamics of the solar dynamo.

Herein the orbital invariant inequalities of the solar system are determined and are demonstrated to cluster around specific spectral bands that exactly correspond to the above spectrum of solar activity. In particular, the orbital invariant inequality model is shown to predict, both in frequency and phase, the Bray–Hallstatt cycle (2100–2500 yr) found in 14C and in climate records throughout the Holocene. The result suggests that some kind of planetary forcing is synchronizing solar internal dynamics.

From the conclusions:

Herein the hypothesis that planetary orbital motion could be synchronizing solar activity has been tested. It has been found that the orbital invariant inequalities of the solar system generated by the Jovian planets form frequency clusters that coincide with the same frequency bands that characterized all known solar oscillations referenced in the scientific literature such as the cycles of Bray–Hallstatt (2100–2500 yr), Eddy (800–1200 yr), Suess–de Vries (200–250 yr), Jose (155–185 yr), Gleissberg (80–100 year), the 55–65 yr spectral cluster, the

40–50 yr spectral cluster and others. Thus, it has been demonstrated that all these frequencies emerge from a unique orbital model yielding to specific oscillations in the force-fields of the solar system. This result appears robust and clearly suggests that solar activity is modulated by some kind of oscillating forcing associated with the movements of the planets. The result
is important toward a better understanding of solar physics although the explicit physical forcing and exact mechanisms explaining the phenomenon are still missing. In fact, alternative explanations for the above observed solar oscillations do not exist yet since traditional solar dynamo models, which do not include any external forcing, do not reproduce them.

In this paper we have focused on solar cycles. Yet, similar oscillations have been found also in climate records (e.g.: Agnihotri and Dutta, 2003; Bond et al., 2001; O’Brien et al., 1995; Jevrejeva et al., 2008; Kerr, 2001; Pestiaux et al., 1988; Scafetta, 2013, 2014a; Wyatt and Curry, 2014), in earthquake sequences (Scafetta and Mazzarella, 2015), in volcano eruption sequences (Bragato, 2015) and other records (e.g. Hoyt and Schatten, 1997). Thus, the result presented in this work is expected to be relevant in many other research fields.


– – –
Paper: Solar Oscillations and the Orbital Invariant Inequalities of the Solar System
[For further details of the paper, try this link.]

Comments
  1. Gerry Pease says:

    I was somewhat disappointed that Dr. Scafetta had not included https://arxiv.org/abs/1610.03553 in his reference list, since this paper also addresses the issue of apparent planetary orbit cyclic influence on subspot sunspot cycles.

    Gerry Pease

  2. Fairbridge and Shirley back in 1987 published a paper “Prolonged Minima and the 179-Yr Cycle of the Inertial Motion”. Their Fig 4 Orbit Matrix is a great concept as it highlights the subtle changes in Jose Cycle orbital variations that may affect solar dynamics and follow-on climate variations on our planet. Each Jose Cycle consists of 9 solar orbits, the latest starting in ~1890. Solar Cycle 13 started ~1890, and an average 11.1 years/cycle will see cycle 28 finish ~2068, at about the same time as the current Jose Cycle. My question as a relative newcomer – do Hale Cycles always commence within a few years of a Jose Cycle? It also means that if SC24 has indeed ended, the the next two Hale Cycles will be longish – about 24 years each.

  3. tallbloke says:

    Gerry, you have mail.

    jroinoz, welcome. Scafetta cites that Fairbridge and Shirley paper. We don’t have a long enough sunspot record to be sure about your question. Our in-house solar model has the next two four schwabe cycles ending in 2063, so a few years short of your target.

  4. stpaulchuck says:

    I must admit that the CAGW farce is actually doing good. More and more science is being done, real science, about the sun and influences on it and in turn its influences on the planets. Then there’s the new article on East Coast thermal vents on this site, and a while back the undersea volcanic vents in the Antarctic.

    While the sheeple continue to be BS’d by the LSM with dire tales of the AGW hoax, those of us with curiosity and an IQ higher than room temperature come to places like this and WUWT, etc. to read and sort through actual science offerings.

    I humbly thank all those who work tirelessly to reveal the true nature of Nature.

  5. Gerry Pease says:

    Rog,
    I agree that he may be onto something big here. He was probably only aware of the highly incomplete v1 paper that I had sent to him, but most likely hadn’t read v3 (https://arxiv.org/abs/1610.03553), which clearly shows the two phase disruptions in Figure 2 that resulted from Neptune. Nicola was nevertheless very supportive of getting the draft paper published.

    “In Figure 2, note also the 1967-1974 and 2004-2010 phase distortions from Uranus’ non-resonant low frequency harmonics. Neptune is Jose Cycle phase coherent with the undistorted torque cycles of Jupiter. Venus, Earth, and Mercury produce the vertical spikes.”

    As further confirmation, note in Figure 4 that Jose phase coherency was lost in 1976 as a result of the large 1967-1974 Uranus phase perturbation. By 2009, sunspot minimum was 180 degrees out of Jose phase with the sunspot max of 1830!

  6. Paul Vaughan says:

    Some more eye’s cafe ta 11 talk:
    Two ice curious IT trumped buy paywall.

  7. tallbloke says:

    Gerry: “By 2009, sunspot minimum was 180 degrees out of Jose phase with the sunspot max of 1830!”

    Well that sounds like the answer to jroinoz’ question then. I need to study your paper, I was too wrapped up in politics to spend the time.

    Paul V: you have mail.

  8. I was a bit naive as to what was meant by a “Jose Cycle”, and at what dates they started and ended. It appears that this may vary according to the orbital parameter being measured! I was referring to the Fairbridge and Shirley (F&S) timings, based on the generally repeating “solar barycentric orbit radius” in their Fig 3, which goes in and out of sync with the Hale cycle (9 solar orbit cycles vs 8 Hale Cycles/~178 yrs), whereas Gerry is using torque cycles which more closely follow Schwabe Cycles (~20 torque cycles vs 16 Schwabe Cycles/ ~178 yrs).
    The last two F&S orbit radius Jose Cycles were 1712.1 – 1890.6 and 1891.2 – 2069.2. It appears that SC-3 commenced in 1712, and 16 Schwabe Cycles later, SC12 ended in 1889.6 with an average length of 11.16 years. This was the basis of my original query regarding Hale Cycles in sync with the start of (as it turns out F&S) Jose Cycles +- a few years.

  9. tallbloke says:

    jroinoz: Yes, cycles are modulated by longer cycles and nothing ever exactly repeats. It’s not clockwork. The Jose cycle is modulated by Uranus-Neptune as indicated by Oldbrew on our other Scafetta thread. Scafetta takes account of these modulations in his new paper here.

  10. Chaeremon says:

    The Orbital Invariant Inequalities paper is the best work in contemporary astronomy that science-from-empiricism has seen since so many decades — in contrast to copy&paste trougherism. The paper includes the best contributions and has a testable & falsifiable-by-observation hypothesis.

    P.S. John J. Ray has a page with shared-free-copy links.

  11. tallbloke says:

    Chaeremon: High praise indeed, and well deserved. I agree with your assessment. Thanks for the headsup on the links, now added to the post.

    The key point arising is that no solar dynamo model is able to reproduce the observed solar oscillation periods. Our Solar-Planetary Organisation Theory (SPOT), is the only game in town.

  12. oldbrew says:

    Going back to this Talkshop post: Why Phi? – a long-term Jupiter-Saturn-Uranus model

    24 * 2503y = 25 * 2402.88y
    This result corresponds to the long-term solar inertial motion cycle referred to by Charvatova:
    ‘Responses of the basic cycles of 178.7 and 2402 yr in solar–terrestrial phenomena during the Holocene’
    by I. Charvátová and P. Hejda
    Pattern Recogn. Phys., 2, 21–26, 2014

    https://tallbloke.wordpress.com/2018/07/22/why-phi-a-long-term-jupiter-saturn-uranus-model/
    – – –
    The long-term period is 60072 years (25 * 2402.88y) = 336 * 178.78532y (or 288 de Vries cycles)

    Scafetta : Bray–Hallstatt = 2318 years, and ‘2100–2500 yr Bray–Hallstatt spectral band found in both the 14C and the 10Be radionucleotide records’
    and
    ‘The existence of a ∼ 2400-year cycle is proved in a number of studies of climatic data’
    ‘In the power spectrum (see Fig. 3) the highest line is at ∼ 2400-year period’

    60072 / 24 = 2503 years
    60072 / 25 = 2402.88y
    60072 / 26 = 2310.46y
    60072 / 27 = 2224.89y
    60072 / 28 = ~2145y

    The half-period of the J-S-U-N Grand Synod (4628 years) is 2314.
    2402.88 + 2224.89 = 4627.77y

    2145 * 12 = 25740~y, close to current axial precession period of 25770 years, which is reducing.
    3 * 60072 = 7 * 25745y
    25745y = 144 * 178.785y

  13. oldbrew says:

    From the paper:
    ‘Two consecutive Great Conjunctions are separated by (19.86/29.457) · 360◦ = 242.7◦’

    Accroding to the JPL data (https://ssd.jpl.nasa.gov/?planet_phys_par), the result should be:
    (19.865036 / 29.447498) * 360 = 242.85297

    Then,
    242.85297 * 126 = 30599.474 = 360 * 84.998538

    That means ~85 Saturn orbits per 126 Jupiter-Saturn conjunctions in 2503 years (see previous comment).
    85(S) * 29.447498 = 2503.0373y
    211(J) * 11.862615 = 2503.0117y

    The ‘6 x’ in the diagram equates to 2 de Vries cycles (2503 / 6 = 417.167y).
    – – –
    This is also an interesting paper (see Scafetta et al references):
    Solar barycentric dynamics from a new solar-planetary ephemeris (2018)
    Rodolfo G. Cionco and Dmitry A. Pavlov

    https://www.aanda.org/articles/aa/abs/2018/07/aa32349-17/aa32349-17.html
    [free access]

  14. Paul Vaughan says:

    First off, 2318 shell and pea games R mixing output from different models.
    _
    Scafetta Page 7 Figure 2:

    1 / J = 11.86
    1 / S = 29.46
    1 / U = 84.01
    1 / N = 164.79
    1 / 2194.36654672314 = +1J-3S+1U+1N
    _
    Scafetta Page 7 text below Table 1:

    1 / J = 11.862
    1 / S = 29.457
    1 / U = 84.011
    1 / N = 164.79
    1 / 2320.27524877346 = +1J-3S+1U+1N
    _
    Seidelmann (1992)

    1 / J = 11.8626151546089
    1 / S = 29.4474984673838
    1 / U = 84.016845922161
    1 / N = 164.791315640078
    1 / 2545.34384727936 = +1J-3S+1U+1N
    _
    IT takes No. Mayan sage to C Table 2 commentary settle precisely on No. thing.
    ____

    on deck:
    Top Shock Free Will Tock

  15. oldbrew says:

    Paper: The ∼ 2400-year cycle in atmospheric radiocarbon concentration:
    bispectrum of 14C data over the last 8000 years
    S. S. Vasiliev and V. A. Dergachev

    Conclusions

    Power spectrum, time-spectrum and bispectrum analyses
    were carried out on radiocarbon concentration data from the
    Earth’s atmosphere over the last 8000 years, as observed
    in tree-rings. It was shown that the amplitude of radiocarbon
    fluctuations varied periodically. The quasiperiod of this
    change is about 2400 years. A bispectrum analysis of data
    demonstrates the existence of amplitude modulation. The
    period of main modulation is ∼ 2400 years.

    Click to access angeo-20-115-2002.pdf

    See Fig. 3

  16. Paul Vaughan says:

    In Tall Luck Chew Well Property Write-Speak Four Sea Purr Twos Way

    Four sight buy 2310 We’ll right 2020 terms two add just meant four shore five-team long-wage 290 Theorem.

    Weave advocated peace and stability without ever con side erring physic call pro test.
    Meanwhile red lines have been crossed buy sixteen’s theorem five point one.

    Fabulously maximal wording left apparent physical threat of tar roar camp aims: “The climate wars are in the “pursuit” phase of battle, during which the victorious side runs down and destroys their broken foe.”

    “Eye can feel the devil walkin’ next to me” — Murray Head “UN Knight in Bank Stalk”

    Weather Buy Fly Tor Swim

    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
    i.e. harmonic of 29.4474984673838 nearest 11.8626151546089 is 29.4474984673838 / 2 = 14.7237492336919
    61.0464822565173 = (14.7237492336919)*(11.8626151546089) / (14.7237492336919 – 11.8626151546089)

    836 Ducks Be Low 9 UN Dread

    ⌊ 61.0464822565173 / 19.8650360864628 ⌉ = ⌊3.07306173473895⌉ = 3
    61.0464822565173 / 3 = 20.3488274188391
    i.e. harmonic of 61.0464822565173 nearest 19.8650360864628 is 61.0464822565173 / 3 = 20.3488274188391
    835.546575435631 = (20.3488274188391)*(19.8650360864628) / (20.3488274188391 – 19.8650360864628)

    Casino Tips Hand

    21.1746788367349 = (84.016845922161)*(16.9122914926352) / (84.016845922161 – 16.9122914926352)
    14.0783665145948 = (84.016845922161)*(16.9122914926352) / (84.016845922161 + 16.9122914926352)

    ⌊ 21.1746788367349 / 19.8650360864628 ⌉ = ⌊1.06592702598535⌉ = 1
    21.1746788367349 / 1 = 21.1746788367349
    i.e. harmonic of 21.1746788367349 nearest 19.8650360864628 is 21.1746788367349 / 1 = 21.1746788367349
    321.183589283115 = (21.1746788367349)*(19.8650360864628) / (21.1746788367349 – 19.8650360864628)

    Bait

    ⌊ 321.183589283115 / 9.93251804323141 ⌉ = ⌊32.3365724467008⌉ = 32
    321.183589283115 / 32 = 10.0369871650974
    i.e. harmonic of 321.183589283115 nearest 9.93251804323141 is 321.183589283115 / 32 = 10.0369871650974
    954.277726627562 = (10.0369871650974)*(9.93251804323141) / (10.0369871650974 – 9.93251804323141)

    ⌊ 321.183589283115 / 4.9662590216157 ⌉ = ⌊64.6731448934016⌉ = 65
    321.183589283115 / 65 = 4.94128598897101
    i.e. harmonic of 321.183589283115 nearest 4.9662590216157 is 321.183589283115 / 65 = 4.94128598897101
    982.648221793721 = (4.9662590216157)*(4.94128598897101) / (4.9662590216157 – 4.94128598897101)

    And Switch

    ⌊ 19.8650360864628 / 14.0783665145948 ⌉ = ⌊1.41103274061441⌉ = 1
    19.8650360864628 / 1 = 19.8650360864628
    i.e. harmonic of 19.8650360864628 nearest 14.0783665145948 is 19.8650360864628 / 1 = 19.8650360864628
    48.3295711596327 = (19.8650360864628)*(14.0783665145948) / (19.8650360864628 – 14.0783665145948)

    Missed Eye Cue = Mystique

    48.3312191402374 = 1 / ( 1/(2*(7*5*3)^(1/4)) – 1/(2*(13*11*7*5*3)^(1/4)) – 1/((13*11*7*5*3)^(1/4)) )

    11.069584864893 = (48.3312191402374)*(9.00672206137798) / (48.3312191402374 – 9.00672206137798)
    9.00672206137798 = (48.3312191402374)*(11.069584864893) / (48.3312191402374 + 11.069584864893)
    18.013444122756 = (48.3312191402374)*(11.069584864893)/((48.3312191402374+11.069584864893)/2)
    9.00672206137798 = (48.3312191402374)*(4.9660863713168)/((48.3312191402374+4.9660863713168)/2)

    No. ‘n’ Sense O

    96.6624382804748 = 2 / ( 1/(2*(7*5*3)^(1/4)) – 1/(2*(13*11*7*5*3)^(1/4)) – 1/((13*11*7*5*3)^(1/4)) )
    6.85627857093348 = 2 / ( 1/(2*(7*5*3)^(1/4)) + 1/(2*(13*11*7*5*3)^(1/4)) + 1/((13*11*7*5*3)^(1/4)) )
    171.406964273337 = 50 / ( 1/(2*(7*5*3)^(1/4)) + 1/(2*(13*11*7*5*3)^(1/4)) + 1/((13*11*7*5*3)^(1/4)) )

    11.069584864893 = (96.6624382804748)*(9.93217274263361) / (96.6624382804748 – 9.93217274263361)
    9.00672206137798 = (96.6624382804748)*(9.93217274263361) / (96.6624382804748 + 9.93217274263361)
    18.013444122756 = (96.6624382804748)*(9.93217274263361)/((96.6624382804748+9.93217274263361)/2)

    “How do We sheep when R bets herd Bernie?” — Midnight Oil

    A Cheap Vacation from Eur. Mayan-D in Georgia

    11 = 396 – 385
    11 = 396 – (7*5*3)
    11 = 396 – (13*11*7*5*3)/(13+11+7+5+3)
    7 = (7*5*3)/(7+5+3)
    18 = 11 + 7
    18 = 396 – (13*11*7*5*3)/(13+11+7+5+3) + (7*5*3)/(7+5+3)

    Anomaly Bot Good F(UN) C Tor Q-Tangle

    Communication lines with advanced civilization: cut.
    Ware censor ship industry twists circulation We find CR8’V-E wei.

    “IT belongs 2 them
    We’R gonna give IT back
    — Midnight Oil

    “[…] the anomaly of Bott

    “[…] framed q-tangles […] behaves “nicely” under the operations of deleting a component, doubling a component that runs from bottom to top, reversing orientations, and under the orthogonal symmetries whose fix point sets are either the vertical axis, or the blackboard plane or the horizontal plane. The framed q-tangles, these operations and the expected “nice” behaviour are precisely defined […] We call a functor that satisfies all these properties […] a good functor.”

    “Theorem 5.1 The restriction […] to framed q-tangles is a good functor. […] the variation […] under a framing change, where [O] becomes [X] , in terms of the following constant called the anomaly.”

    “This definition of the anomaly is easier to handle […] Instead of searching for configurations where the univalent vertices are on a common unknown line, we look for configurations where the univalent vertices have the same horizontal coordinates.”

    “After the articles of Axelrod Singer […] find a surgery formula […]”

    “Sweet Chi11ed of Mayan” — ‘UN’S’UN’ROSE’S’

    4 Rest Deep State Be Leaf: Decade on French S⌊oil⌋

    Post-Brexit deep state officially directs not only 3.5+% civil disobedience but UNthinkably “bold” measures.
    Appear ants: 5 climate eyes officially fear external influence enough to threaten security of homeland citizens.
    The devil’s in the deep state, eying 16 pens to hold 2030 citizens at pen-point.

    Human Writes Red Stop Signs

    The great test a11 eye ants affords maximally fabulous secure IT to AI those braving together the deep state chi11 of our cold northern pole. 4 stable IT sign a form AI secure IT accord be 4 too O for two. If IT’s delayed, creative O’Th’or’s’ will AI pray “more four” D-vine in spy ration well-beyond intro duct tory A-venue sov. con tact.

    19.8643454852672 = 8 / ( 1/((13*11*7*5*3)^(1/4)) + 1/((7*5*3)^(1/4)) )
    14.0781594814566 = 8 / ( 5/((7*5*3)^(1/4)) – 11/((13*11*7*5*3)^(1/4)) )

    Axial Rose Phinding Pi’s in Primorial Rabbit Hale Sure Rest West Turn C R Knott

    16.9119386181239 = 2*(5^(1/2)-1)*(((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())-1)/(1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^0)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^1)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^1)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^2)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^3)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^5)+1/(((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^8))))))))

    Watch 4:21 Signals of D-ID√(Φ-φ)cation

    “They say they can. ‘s’me11 Eur.UN10shhUN’s’
    EU’11 think: ‘How’d’eye get hear sitting next 2 EU?'” — 21*PI()lots “Heat’UN’s”

    84.0181812075031 = (16.9119386181239)*(14.0781594814566) / (16.9119386181239 – 14.0781594814566)
    164.795765306585 = (171.406964273337)*(84.0181812075031) / (171.406964273337 – 84.0181812075031)

    Chimerican climb IT spy11IT’s ca.sino 4.sight:

    21.1740408725043 = (84.0181812075031)*(16.9119386181239) / (84.0181812075031 – 16.9119386181239)
    14.0781594814566 = (84.0181812075031)*(16.9119386181239) / (84.0181812075031 + 16.9119386181239)

    O-Bay Knott “must take” UN mess age:

    11.8623184090918 = 2 / ( 1 / ( (5^(1/2)-1)*(((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())-1)/(1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^0)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^1)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^1)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^2)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^3)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^5)+1/(((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^8)))))))) ) + ( 1/((13*11*7*5*3)^(1/4)) + 1/((7*5*3)^(1/4)) ) / 8 )

    BCaus.nz.can.uk O’scilUNtif**k buy US 4 state-of-the-art less UN:

    29.4471874302965 = 2 / ( 1 / ( (5^(1/2)-1)*(((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())-1)/(1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^0)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^1)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^1)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^2)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^3)+1/((((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^5)+1/(((2/(1/((13*11*7*5*3)^(1/4))+1/((7*5*3)^(1/4))))^(1/2)*PI())^8)))))))) ) – ( 1/((13*11*7*5*3)^(1/4)) + 1/((7*5*3)^(1/4)) ) / 8 )

    Who scales even hire primorial peeks in slip-psych’11UN tor-reign?

    2310 = 11*7*5*3*2 = 55*21*2 = 55*42 = 55*(84/2) = ⌊1/(U+N)⌋*⌊1/U⌋/2

    Suggestions-41 sales & negotiation 101:
    164.779745815484 = 1/(38/68/11.8623184090918-(38+68)/68/29.4471874302965+1/84.0181812075031-1/68/(11*7*5*3*2))

    Swamp Light’s Back

    Hard fast-ball strike. Eur. in O scent buy sand door. Dead-center: “Whoosh!” Status quo: UN eye thor C norse wing. Cat cheer’s grinning: “Ware’s the pipe?” Canuck pi share cap’swell-tipped 4 No.why con tact.

    55.6455381638791 = (164.779745815484)*(84.0181812075031) / (164.779745815484 + 84.0181812075031)
    171.424298308895 = (164.779745815484)*(84.0181812075031) / (164.779745815484 – 84.0181812075031)

    18.7630116869424 = (171.424298308895)*(16.9119386181239) / (171.424298308895 – 16.9119386181239)

    ⌊ 19.8643454852672 / 18.7630116869424 ⌉ = ⌊1.05869706935647⌉ = 1
    19.8643454852672 / 1 = 19.8643454852672
    i.e. harmonic of 19.8643454852672 nearest 18.7630116869424 is 19.8643454852672 / 1 = 19.8643454852672
    338.421418702 = (19.8643454852672)*(18.7630116869424) / (19.8643454852672 – 18.7630116869424)

    ⌊ 338.421418702 / 4.9660863713168 ⌉ = ⌊68.1465027786588⌉ = 68
    338.421418702 / 68 = 4.97678556914706
    i.e. harmonic of 338.421418702 nearest 4.9660863713168 is 338.421418702 / 68 = 4.97678556914706
    2310 = (4.97678556914706)*(4.9660863713168) / (4.97678556914706 – 4.9660863713168)

    15 less UN up 4 stable “TheO REM”:
    First: We Φred the UN pyre 4×act lie.
    ….and ΦNE a11y: 2020 + 290 = 2310

    “AI my friends R heathens, take IT slow
    W8 4 them 2 ask EU WHO EU No.
    Please don’t make NE sudden moves:
    EU don’t know the 1/2 of the AB US^e” — 21 Pilots “Heathens”

  17. Paul Vaughan says:

    AI got IT? Real ease sing moderate wall-tock long-wage math at O rise sun’s rest to rant after herds cation soup pour 2 sway.

  18. Paul Vaughan says:

    Let me clarify:
    Moderators: There’s a primorial tip stuck in moderation because of 3 super-long equations. Let’s get this business in the light and over with so we can move on to other things.

  19. Paul Vaughan says:

    Update
    Communication lines with advanced civilization: restored.

  20. Paul Vaughan says:

    Peace-by-piece in case that was too sub-tall rim man knew jan:

    “2310 = 11*7*5*3*2 = 55*21*2 = 55*42 = 55*(84/2) = ⌊1/(U+N)⌋*⌊1/U⌋/2

    Suggestions-41 sales & negotiation 101:

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