The real cause of climate change over the last millennium

Posted: July 9, 2017 by tallbloke in Analysis, climate, modelling, Ocean dynamics, solar system dynamics

Fig 1. Integration of solar data departing from long term average as a proxy for OHC

OK, this the last post before I go. This is a comment I made this morning over at Pierre Gosselin’s place.

To understand the effect of solar variation on a large heat capacity mass like Earth’s oceans, you have to integrate the solar data to get a reasonable proxy for ocean heat content. If you look at empirical comparisons of average sunspot number during periods when the ocean temperature is steady, you can derive a value of approximately 40 sunspots per month. This also happens to be the average sunspot number over the period of record from 1749 to today. Integrating the sunspot numbers as a running total departing from this average produces a reasonable proxy for OHC.

Calibrating the Steinhilber et al TSI reconstruction based on 10Be to the same baseline, we obtain a reconstruction which compares well to the Mann et al 2008 millennial temperature reconstruction, as seen in Fig1.

Adding in the detrended AMO and PDO oceanic oscillations and a CO2 value giving around 0.4C per doubling as per Richard Lindzen’s estimate, we obtain a curve which reproduces HADSSTv3 to an R^2 of 0.9 for monthly values since 1870 in Fig 2.


Fig 2. Combining the solar integral with detrended AMO, PDO, and CO2 at 0.4C/doubling to replicate HASsst3 (lower panel)

The continuation of the model in blue in the lower panel is based on our planetary solar model plus a replication of the AMO from the C20th. It shows a moderate drop in global SST to 2050.

  1. tallbloke says:

    Depending on who you believe for the magnitude of solar variability over the last several hundred years (Estimates vary by several W/M^2), the most likely ‘amplification’ of TSI variation comes from the effect of solar magnetic variation on low level cloud cover, whether that works through the ‘Svensmark effect’ or some other mechanism. See Nir Shaviv’s paper ‘using the oceans as a calorimeter’ for details.

  2. AndyG55 says:

    Should also consider the frequency variations in UV band.

  3. Why not speak to Leif Svalgaard.

    [Reply] Oh I did. He averts his eyes from the millennial plot and refuses to discuss it. Then he tries to say the integration is not valid because it uses the long term average SSN. First time he’s ever tried to refute the idea there’s no long term trend in solar activity 🙂

    Solar variability causes less than 1C change

    [Reply] +/-0.7C is about what solar variability supplies. Look at the Y-axis scale

    Why not speak to Willis Eschenbach there is no detectable effect of solar variability in the temperature record

    [Reply] Lol. We debunked the cowboy’s solar ‘analysis’ in this post.

    I thought the osmic ray influec had been disproven by experiment?

    [Reply] Far from it. Josh Kirby at CERN has been making good progress with the experimental work.

  4. Ron Clutz says:

    Tallbloke, thanks for that analysis. It is consistent with a similar analysis by Dan Pangburn that I summarized in a post:

    Figure 10: 5-year running average of measured temperatures with calculated prior and future trends (Data Set 1) using 34 as the average daily sunspot number and with V1 SSN. R2 = 0.978887

    Projections until 2020 use the expected sunspot number trend for the remainder of solar cycle 24 as provided [6] by NASA. After 2020 the ‘limiting cases’ are either assuming sunspots like from 1924 to 1940 or for the case of no sunspots which is similar to the Maunder Minimum.

  5. Solar up to 2005 despite it becoming lower since mid last century was still high and it should have caused warming which is what happened. Only since 2005 has solar activity been in an inactive mode which will promote global cooling.

    I expect global cooling to begin (I think it has ) this year not 5 years from now.

    Solar criteria is now moving to the values I had said would be significant enough to cause global cooling, following 10+ years of sub solar activity(2005-present) in general. Duration is now needed for my low average value solar parameters. I am of the opinion that if solar conditions are extreme enough it could move the terrestrial items which govern the climate to threshold values to one degree or another. This is perhaps part of the reason why abrupt climate change has occurred in the past.


    global cloud cover global

    snow cover/sea ice cover

    volcanic activity major

    sea surface temperatures

    atmospheric circulation








    SOLAR IRRADAINCE OFF .15% not reached yet.

    All given solar effects enhanced by a weakening geo magnetic field.

    My solar /climatic play is very low sustained solar activity will result in an increase in the earth’s albedo ,while at the same time lowering sea surface temperatures the result is global cooling.

  6. Leif is an agenda driven person whose opinions to me are worth zero when it comes to the climate and why/how it changes the same for Eschebach.

    Anthony will not allow me to post on his site because I was to tough on Leif. lol

  7. tallbloke says:

    Good analysis Salvatore.
    And I don’t post at WUWT any more either. As you say, driven by an agenda, not by a passion for scientific discovery.

  8. Paul Vaughan says:

    We determined years ago that Svalgaard, Mosher, Eschenbach, and a few others are part of a “control the opposition” campaign. Then we moved on.

  9. edhoskins says:

    It seems that, driven by the need to continually support the Catastrophic Anthropogenic Global Warming thesis climate scientists are examining the temperature record at altogether too fine a scale, month by month, year by year.

    Our current, warm, congenial Holocene interglacial has been the enabler of mankind’s civilisation for the last 10,000 years, spanning from mankind’s earliest farming to recent technology.

    Viewing the Holocene interglacial at a broader scale is much more fruitful, on a century by century and even on a millennial perspective.

    According to ice core records, the last millennium 1000AD – 2000AD has been the coldest millennium of our current Holocene interglacial.

    Each of the notable high points in the Holocene temperature record, (Holocene Climate Optimum – Minoan – Roman – Medieval – Modern), have been progressively colder than the previous high point.

    In the ice core record, for its first 7-8000 years the early Holocene, including its high point known as the “climate optimum”, have had virtually flat temperatures, an average drop of only ~0.007 °C per millennium.

    But the more recent Holocene, since a “tipping point” at around 1000BC, 3000 years ago, has seen temperature fall at about 20 times that earlier rate at about 0.14 °C per millennium .

    The Holocene interglacial is already 10 – 11,000 years old and judging from the length of previous interglacial periods, the Holocene epoch should be drawing to its close: in this century, the next century or this millennium.

    But the slight beneficial warming at the end of the 20th century to the Modern high point has been transmuted into the “Great Man-made Global Warming Scare”.

    The recent warming since the end of the Little Ice Age has been wholly beneficial when compared to the devastating impacts arising from the relatively minor cooling of the Little Ice Age, which include:
    • decolonisation of Greenland
    • Black death
    • French revolution promoted by crop failures and famine
    • the failures of the Inca and Angkor Wat civilisations
    • etc., etc.

    As global temperatures have already been showing stagnation or cooling over the last nineteen years or more, the world should now fear the real and detrimental effects of cooling, rather than being hysterical about limited, beneficial or probably now non-existent further warming.

    Warmer times are times of success and prosperity both for man-kind and the biosphere. For example during the Roman warm period the climate was warmer and wetter so that the Northern Sahara was the breadbasket of the Roman empire .

    According to the Ice Core records, each of these successive Holocene warm periods have been cooler than the one previously and a tipping point towards accelerated global cooling occurred at about 1000BC.

    The coming end of the present Holocene interglacial will in due course again result in a mile high ice sheet over much of the Northern hemisphere.

    As the Holocene epoch is already about 11,000 years old, the reversion to a true ice age is almost overdue and would be the real climate catastrophe.

    With the present reducing Solar activity, significantly reduced temperatures, at least to the level of another Little Ice Age are predicted quite soon later this century.

    Whether the present impending cooling will really lead on to a new glacial ice age or not is still in question.

    This point is more fully illustrated here:

  10. Paul Vaughan says:

    TB: CO2 explains 0% of the variance. Rip it out and take a cleansing walk in the hills.

  11. Paul Vaughan says:

    Pareto Principle: naturally divine division of uniformity

    Consider the limiting hypotenuse of the pyramidal face isosceles right-bisector:

    Inscribed in the design are angles encoded as lengths — more specifically angles inversely encoded in a pair of quadratic integer rings (“2 circles”) as complementary lengths. Since the Pareto Principle is ubiquitous in nature, the engineers may have been inspired to construction by anything. The notion that it had to be the solar system (“celes”) or whatever is just a selective provocation. It could have been simple structure noticed in vegetation (or anything else) during an inspiring nature walk. The Pareto Principle is universal. It subsumes statistical mechanics and everything we’ve explored about phi.

  12. Bob Weber says:

    The v1 SSN average since 1749 is 52, not 40, and v2 is 82.

    AMO & PDO are records of prior TSI impact, as it’s adding former TSI influence to the present TSI influence, ie, making the TSI effect on SST time-dependent and layered.


    Salvatore there are times when your general opinion is on the mark, but the continual use of all these thresholds without understanding the real variation in the main important variable, TSI, is bad for us who do understand. You are giving everyone the wrong impressions and expectations of TSI and what the sun is doing and will do:

    “SOLAR IRRADAINCE OFF .15% not reached yet. ” …. is a vacuous statement.

    SORCE TSI maximum daily is 1362.2561, so the “off by 0.15%” yields 1360.2127.

    The maximum monthly SORCE value was 1361.8859, for an “off by 0.15%” of 1359.8431.

    Neither of these low-ish TSI levels in reality actually lasts longer than the passage of large area sunspot group(s) that occur at the top of the sunspot cycle, when TSI is generally high. Also, these low levels have yet to be reached in any TSI dataset during the several solar minimums since TSI measurements began, Therefore this threshold as stated is unrealistic, too low.

    The present solar cooling will last for only a few more years until SC25 starts. If you’re lucky, by 2020 there will have been a very minor cooling for the decade 2010-20. Just think of all the people who now have the wrong idea of what the sun does, and all the resistance to the real solar influence that this wrong thinking generated after years of carpet bombing the internet with your unsupported thresholds. Please stop.

  13. Paul Vaughan says:

    Length of face edges =+2*sin(2*pi()/5)
    Shortest slide down face of pyramid =+1/(2*cos(2*pi()/5))
    Height of pyramid =+sqrt(1/(2*cos(2*pi()/5)))
    Area of each face of pyramid =+1/(2*cos(2*pi()/5))
    Area of base of pyramid =+((2*sin(2*PI()/5))^2)+((2*cos(2*PI()/5))^2)

    2*pi()/5 radians = 1/5 cycles

    Pyramid design materially illustrates:
    Divinity (divine stability) based on Pareto Principle division.

    They were thinking in squares.
    The Conway Triangle in the Pinwheel Tiling is the simplest geometric expression of the Pareto Principle. Take the square roots of Pareto Principle pieces (1/5 & 4/5) and by the Pythagorean Theorem you have a Conway Triangle plus Pinwheel Tiling.

    An internet search for Pareto Principle only turned up 1 triangular representation, so maybe society has been a little slow to recognize how Pinwheel Tiling, the Conway Triangle, and the golden mean all derive from the Pareto Principle.

    A superior illustration would represent the fractal properties of the Pareto Principle with scaling. (The triangular image turned up in the internet search (above) fails to represent the fractal scaling.)

    How’s it possible that such extreme simplicity was overlooked? It’s difficult to imagine — just as difficult as it is to believe Pinwheel Tiling was only discovered 22 years ago. I don’t think it was overlooked. More likely it has been rediscovered independently and repeatedly by countless individuals. It’s easy enough to imagine that recorded history is a laughable model of what really happened, based on comically biased samples.

  14. Paul Vaughan says:

    Red, white, and blue are similar Conway Triangles stably proportioned according to the Pareto Principle:

  15. Paul Vaughan says:

    ENSO accounts for 100*((1/(φ+Φ))^2)% of variance.

    Start with any real number.
    Add 1.
    Take the reciprocal.
    Add 1.
    Take the reciprocal.
    Add 1.
    Take the reciprocal.

    Stability’s simpler than your imagination.

  16. stpaulchuck says:

    wait! now you’re trying to tell me the sun has a lot to do with the planet’s temperature? How can that be? I mean it’s 94 million miles away. Manbearpig and Mann tell me it has no effect. Their computer models tell them that. How could a computer be wrong?

  17. Paul Vaughan says:

    Stability’s natural with a Pareto-principled division of unity.

    Consider further the example introduced above (The Pyramids):

    Pole Square:
    1/Φ = 1/2cos(2π/5) = √(φ+1) = φ = 1.618033989

    Face Square
    (1/2cos(2π/5))^2 = φ+1 = φ^2 = φ/Φ = 2.618033989

    Edge Square:
    (2sin(2π/5))^2 = (φ^2)+1 = φ+2 = φ√5 = 3.618033989

    Specific instance:

    (29.44749847)*(11.86261515) / (29.44749847 – 11.86261515) = 19.86503609 = Bi-Decadal Oscillation = BDO

    (29.44749847)*(11.86261515) / (29.44749847 + 11.86261515) = 8.456145746
    (2.618033989)*(8.456145746) = 22.13847698 = Hale cycle = Jupiter-Earth-Venus (JEV) cycle
    22.13847698 / 2 = 11.06923849 = Schwabe cycle

    (19.86503609)*(3.618033989) / (19.86503609 – 3.618033989) = 4.423731549
    2 * 4.423731549 = 8.847463097 = Lunar Apse Cycle = LAC

    (4.423731549)*(1.618033989) / (4.423731549 + 1.618033989) = 1.184711316 = Chandler Wobble = CW

    (4.423731549)*(1.618033989) / ( (4.423731549 + 1.618033989) / 2 ) = 2.369422633 = Quasi-Biennial Oscillation = QBO

    Earth-Moon (immediate) & Earth-Venus (intermediate) are hierarchically rooted couples.
    Jupiter & Saturn (distal origin) shape Earth’s wind field — including QBO & Milankovitch.

    Massive Jupiter & Saturn shepherd the Earth-Venus & Earth-Moon couples.

    The major western fault (only superficially stable) is based on unstable proportions. In contrast, the Pentagon and 5-point stars on far-eastern flags symbolize the natural key to stability.

  18. oldbrew says:

    Study: ‘monitoring sunspots is not an adequate means for predicting EUV irradiance—more measurements and study are required to better understand the factors at play.’

    Abstract: ‘Solar EUV irradiance cannot be predicted accurately by sunspot index alone’
    – – –
    Note the title: ‘Global conditions in the solar corona from 2010 to 2017’

    They are monitoring solar conditions at a time of historically very low sunspot activity.

    Full text:

    ‘To our knowledge, this is the first report of its kind that presents global long-term values of coronal conditions over most of a solar activity cycle. This paper is an overview of the main results’

    ‘Although the total solar irradiance at Earth varies very little, the relative variance in the EUV is as large as the mean irradiance (21). This EUV light interacts with Earth’s thermosphere and stratosphere and may affect climate in a “top-down” process in regions such as northern Europe’ — [bold added]

  19. oldbrew says:

    PV: the ratio of the average lunar apogee-perigee time to the lunar nodal cycle period is very close to 21:5 (Fibonacci) which is of course by definition a whole number equivalent ratio to Phi³:1.
    – – –
    Phi and the Great Pyramid of Khufu
    Posted: November 19, 2015

  20. Paul Vaughan says:

    BDO review

  21. Paul Vaughan says:

    Wind Volatility Review

  22. Paul Vaughan says:

    The Fair Far Eastern Star

  23. Paul Vaughan says:

    Pinwheel Tiling is based on the Conway Triangle
    …and the Conway Triangle is based on The Pareto Principle.

    Natural stability is simpler than we imagined.

  24. Paul Vaughan says:

    100*((2/(φ+Φ))^2)% of stability is naturally rooted in harmony with the golden star.

  25. Lit says:

    @Paul Vaughan
    Very nice Posts. “Simpler than we thought”, that is spot on. I would even say: the most simple solution possible is what the universe uses. So let’s go back to the laws of thermodynamics and geometry, we already havet the solutions for everything

  26. oldbrew says:

    Climate models still failing – by grossly overestimating warming, as usual – after all these years…

  27. tallbloke says:

    Wow, lot’s of interesting stuff happened on this thread while I was away. Just to clear up one point for starters before I have to do some physical work today.

    Paul V: TB: CO2 explains 0% of the variance. Rip it out and take a cleansing walk in the hills.

    It’s a gambit to encourage engagement from the CO2 afflicted. The magnitude is very similar to the ‘adjustments’ to the data, so you can simply substitute that label to restore purity. 🙂

  28. oldbrew says:

    From WryHeat by Jonathan DuHamel


    “What physical evidence supports the contention that carbon dioxide emissions from burning fossil fuels are the principal cause of global warming since 1970?”

    (Remember back in the 1970s, climate scientists and media were predicting a return to an “ice age.”)

    I have posed that question to five “climate scientist” professors at the University of Arizona who claim that our carbon dioxide emissions are the principal cause of dangerous global warming. Yet, when asked the question, none could cite any supporting physical evidence.
    . . .
    The outputs from computer models diverge widely from observational evidence because the models attribute too much warming influence to carbon dioxide emissions and too little to natural variation.

  29. oldbrew says:

    Dr Tim Ball: Successful Cover-up and Lack of Accountability in Climate Deception
    July 30, 2017

  30. oldbrew says:

    Another inconvenient truth…

    4,300 Days Since Last U.S. Major Hurricane Strike
    July 31st, 2017 by Roy W. Spencer, Ph. D.
    – – –

  31. Paul Vaughan says:

    TB clarified: “It’s a gambit to encourage engagement from the CO2 afflicted. The magnitude is very similar to the ‘adjustments’ to the data, so you can simply substitute that label to restore purity.”

    I figured as much, played along, and very much enjoyed several purifying walks in the hills. Nature is so beautiful …and exercise outdoors is healthier than useless debate, which can be efficiently skipped on the streamlined path to discovery!

    Like always I’ve got a bunch more to say but no time. So far as I’ve observed, nature sets the pace of commentary …and I’m more than content to let nature be our trusted guide!

    Best Regards as always

  32. tallbloke says:

    My thanks to Paul Vaughan for the beautiful diagram of ‘The Pareto Principled division of unity’ he posted in his comment back on July 9th
    I find that visually expressed geometry comes to me more naturally than algebra so I investigated this diagram and found that with a simple fractal rescaling to set the smallest conway triangles in his diagram to their ‘natural’ 2:1 ‘size’, several of the numerical identities we frequently find and use in our investigations dropped into place within his ‘golden circle’ very easily and naturally.

    Note that:
    φ + Φ + Φ/φ = φ^2.

    φ + Φ = √5
    The hypotenuse of the 2:1 conway triangle = √5
    The diameter of the circle = √5

    The chord of length 2 intersects at right angles the point of division between φ and Φ on the diameter. Is this telling us something about the relationship between φ and Pi? Is it exact, or does it derive from the close similarity between the numerical values of Pi and 4/√φ ?

    The solid orange triangle is something of a curiosity. It’s quite close to being a Kepler triangle, but isn’t. The squares of the hypotenuse and other longer side, (√5/2)^2 and (2(√5/5))^2 are reciprocal. It seems remarkable to me that their values (1.25 and 0.8) are such simple numbers. The reciprocal of the square of the short side is 2.22 recurring.

    Intriguingly, the sum of the reciprocals of the squares on the hypotenuse and ‘middle’ side of a Kepler triangle equals the reciprocal of the square of the shortest side. 1/φ^2 + 1/φ = 1/1

    I think the kepler triangle will be the only right angled triangle to exhibit this symmetry, but I’ll leave these numerical puzzles to the mathematicians to ponder.

  33. Sphene says:

    Paul has shown an interesting relationship between φ and π in his research, here:,

    In Paul’s equations there is the term 2cos(2π/5), which in degrees is 2*cos(72), and is = 2*0.309016994 = 0.618033988.

    Φ = [2*cos(2π/5)] = 1/φ = [(√5-1)/2].

  34. tallbloke says:

    Sphene: many thanks for the reminder, I come across the [2*cos(2π/5)] expression myself and posted it on the talkshop long ago. It had slipped out of my ruptured memory cell.

  35. oldbrew says:

    ‘We will learn to find the exact value of cos 72 degrees using the formula of sub-multiple angles.’
    – – –
    Looks like climate models will need an update…

    Study reinforces the Amazon forest’s importance in regulating atmospheric chemistry
    August 1, 2017

    Airborne measurements made as part of the Green Ocean Amazon experiment (GOAmazon) show that the Amazon rainforest emits at least three times more isoprene than scientists had previously thought.
    . . .
    According to Paulo Artaxo at the University of São Paulo’s Physics Institute (IF-USP) in Brazil and a co-author of the study, isoprene is one of the main precursors of ozone in the Amazon, and it indirectly influences the balance of greenhouse gases in the atmosphere.
    . . .
    According to Artaxo, the Amazon forest was already considered the world’s largest source of isoprene even before these new discoveries. “These findings reinforce the importance of this ecosystem to the regulation of the planet’s tropical atmospheric chemistry,” he said. “Now, we need to include the results in global climate models to see exactly what effect these new values for isoprene emissions have on the climate.”
    [bold added]

    Read more at:

  36. tallbloke says:

    OB: Whoah, that’s neat!

    cos72 = sin18 = (√5-1)/4

    Now where have I seen an equation that looks a lot like that before? 🙂


    “Now, we need to include the results in global climate models to see exactly what effect these new values for isoprene emissions have on the climate finger pressure required on the scales to ensure the output of the climate models is still scary .”

    There, fixed it for them.

  37. tallbloke says:

    I can feel some talkshop heraldry coming on…

    A globe, Aurum, floats on a field, Azure, half masked by a diagonal field of Albino Albedo. The fields are proportioned Vaughan-Conway-Pareto style.

    The Sun illuminates our clear blue sky, the field which is seen. The cloud obscures the Sun, hiding half its light – the unseen field. The clear sky and cloudy areas are in a harmonious dynamic balance. The ‘missing’ chevron forming the pennant tails represents the ‘unknown-unknowns’, which we estmate by ratio between the fields of the Pennant, whose geometry speaks of the principles and proportions which guide our enquiry.

    Suggestions for improvement welcome

    Maybe the white field needs to be made more interesting by covering it in mystical looking equations with lots of phi and square root symbols in them? 🙂

  38. oldbrew says:

    If you join the two right-hand corners with a vertical line is that another Conway triangle?
    – – –
    ‘There, fixed it for them.’


  39. tallbloke says:

    Yes, 20% of the area of the Blue one, which is in turn 80% the area of the white one.

  40. oldbrew says:

    OK, so the Pareto principle 80:20 is represented by the ratio of the two smallest of three Conway triangles and the ratio of the long:short sides of the rectangle is 2:1

  41. tallbloke says:

    You’ve got it. The 80-20 is the blue vs the ‘missing’ triangle. The White vs Blue is 100-80 which is similar to the cloud vs blue sky fraction on Earth. The Sun’s effect on cloud cover is what causes the centennial scale variance in surface temperature. So the pennant summarizes the state of climate knowledge as well as working in some of our ratios and principles.

  42. oldbrew says:

    cos72 = sin18 = (√5-1)/4

    Now where have I seen an equation that looks a lot like that before?
    – – –
    Well, yes obviously we have (√5-1)/2 = 1/Phi

    Note also that 72:18 fits the Pareto Principle (80%:20%)

  43. Paul Vaughan says:

    Sea-kayaking’s the primary goal today, but there’s enough time to sharpen things up a little:

    Hale = ΦT/φ^(2e) = 1 / 22.1387431832142
    J+S = φT/φ^(2e) = 1 / 8.45624742778278
    S = [ΦΦT/φ^(2e)+1/(5•5)]/2 = 1 / 29.4479688047631
    J = [(√5+Φ)T/φ^(2e)-1/(5•5)]/2 = 1 / 11.8627389334436
    V = [5E-√5T/φ^(2e)+1/(5•5)]/3 = 1 / 0.615196915778351
    J-S = 2ΦT/φ^(2e)-1/(5•5) = 1 / 19.8651691565795



    Further reminder:

    √5 = φ+Φ = φφ-ΦΦ = φ/Φ-Φ/φ

    Yet further reminder (in case that wasn’t enough!):

    = (√5)^2
    = (Φ+φ)^2
    = (Φ+φ)(Φ+φ)
    = ΦΦ+Φφ+φΦ+φφ
    = ΦΦ+φφ+Φφ+φΦ
    = (ΦΦ+φφ)+(Φφ+φΦ)
    = 3+2

    Even further reminder (in case that STILL wasn’t enough!!):

    = 1/[(√5)^2]
    = 1/[(Φ+φ)^2]
    = 1/[(Φ+φ)(Φ+φ)]
    = 1/[ΦΦ+Φφ+φΦ+φφ]
    = 1/[ΦΦ+φφ+Φφ+φΦ]
    = 1/[(ΦΦ+φφ)+(Φφ+φΦ)]
    = 1/[3+2]

    …and for anyone (perhaps somewhere along the major western fault) who really needs it spelled out in full detail to see the ladder of powers fractal resulting from a Hierarchically Pareto Principled Division of Unity:

    5•5 = 5^2 = ((Φ+φ)^2)^2
    = ΦΦΦΦ+ΦΦΦφ+ΦΦφΦ+ΦΦφφ+ΦφΦΦ+ΦφΦφ+ΦφφΦ+Φφφφ+φΦΦΦ+φΦΦφ+φΦφΦ+φΦφφ+φφΦΦ+φφΦφ+φφφΦ+φφφφ
    = ΦΦΦΦ+φΦΦΦ+ΦφΦΦ+ΦΦφΦ+ΦΦΦφ+φφΦΦ+ΦφφΦ+ΦΦφφ+φΦφΦ+ΦφΦφ+φΦΦφ+Φφφφ+φΦφφ+φφΦφ+φφφΦ+φφφφ
    = ΦΦΦΦ+ΦΦ+ΦΦ+ΦΦ+ΦΦ+1+1+1+1+1+1+φφ+φφ+φφ+φφ+φφφφ
    = (ΦΦΦΦ+φφφφ)+(ΦΦ+φφ)+(ΦΦ+φφ)+(ΦΦ+φφ)+(ΦΦ+φφ)+1+1+1+1+1+1
    = (ΦΦΦΦ+φφφφ)+3+3+3+3+1+1+1+1+1+1
    = 7+3+3+3+3+1+1+1+1+1+1
    = 25

    Piece of cake if you’re a far-eastern tiger-mom’s 5-star offspring ready — due to decisively superior math education — to recognize both the stability of the Pentagon and the instability of the major western fault.

    The Doors to stability (5:1) are open.

  44. tallbloke says:

    Paul V: Hale = ΦT/φ^(2e) = 1 / 22.1387431832142

    Maybe I missed something while I was away but I don’t know what T is.
    Solving for T:
    T = (1/22.138743 * φ^(2e))/Φ = 1.0000213858

    I’m none the wiser and probably did something wrong. Can anyone help?

  45. Paul Vaughan says:

    Tip: Milankovitch

  46. tallbloke says:

    T is a correction factor for a long term precession?

    I hate having to guess the definition and origin of undefined variables.

  47. Sphene says:


    Paul’s comment on May 23, 2017 at 8:57 am, has computations of T = tropical year frequency here:

  48. Sphene says:

    Paul on May 23, 2017 at 6:53 pm has further discussion and development here:

    “…terrestrial year frequencies
    T = tropical
    L = anomalistic
    lunar month frequencies
    D = draconic (nodal)
    A = anomalistic
    Y = synodic…”

  49. tallbloke says:

    Thanks again Sphene. I actually searched suggestions 27 for ‘T space equals-sign’ but I don’t think the browser search routine liked it.

  50. Sphene says:

    Glad to help. I am slowly plodding my way through Paul’s formulas and calculations, and I have various comments bookmarked to help me refer back to specific items.

  51. tallbloke says:

    I’m glad someone has time to be organised.
    Would you like a job constructing the talkshop index? 🙂

    I jest of course. Good stuff, I can now proceed with working through the rest of Paul’s comment.

  52. Paul Vaughan says:

    (J+S)/(φ/Φ) = (J-S+5^(-2))/2 = ΦT/φ^(2e) = 3V-5E+2J

    Chop a Conway Triangle on the Pareto Principle.

    Do it again — i.e. chop the 1/5 littler Conway Triangle into 5 more even littler Conway triangles.

    E-T is part of Milankovitch (Does anyone really think a realistic solar system model would ignore Milankovitch cycles??? I sure hope not!)

    Remember E & T are frequencies. The periods are 1/E & 1/T.

  53. Paul Vaughan says:

    “This is the end, beautiful friend, the end.” — The Doors

    ΦΦ(J+S) = (J-S+[(φφ+ΦΦ)+(φΦ+Φφ)]^(-2))/2 = ΦT/φ^(2e)
    = (φφ+ΦΦ)V-[(φφ+ΦΦ)+(φΦ+Φφ)]E+(φΦ+Φφ)J

    years in days:
    tropical = 365.242189
    anomalistic = 365.259636
    sidereal = 365.256363
    express all in Julian years = 365.25

    0.240846697327135 = 1/Me
    0.615197263396975 = 1/V
    1.00001743371442 = 1/E
    1.88084761346252 = 1/Ma
    11.8626151546089 = 1/J
    29.4474984673838 = 1/S
    84.016845922161 = 1/U
    164.791315640078 = 1/N

    1/T = 365.242189 / 365.25
    compare 1/E with 365.256363 / 365.25

    previously calculated (in some other thread) from…
    …to verify Seidelmann (1992)

  54. tallbloke says:

    Aha, the light dawns. 1/75 = [1/(5•5)]/3
    Amazing stuff.
    I shall continue pondering the physical meaning of Euler’s number (e)

  55. oldbrew says:

    3² Neptune = 5³ Jupiter (orbits) — about 99.98% accurate

  56. tallbloke says:

    I realised the mainstream theory of why the solar system orbital distances are what they are (“It’s collisions innit!”), was a load of horse feathers a few years ago when I got the general insight that it’s the synodic conjunction periods that set the orbits via resonance. When I worked through the system from the outside to the centre using that time dimension instead of orbital distances, I discovered the connectedness hidden in the, solar cycles, orbital periods and conjunction periods, and the thing that connected them all was the Fibonacci series. That’s what started us down the ‘why phi?’ path to understanding.

    Paul’s expert contribution has now taken us to the forefront of accurately derived knowledge of the system. One day in the (I hope) not too distant future, current mainstream perturbation theories will be seen for the ragtag bag of epicycles they are…

    You can capture many of the relevant threads by using ‘why phi?’ as a search term., and, as you already know, following Paul V’s comments on the suggestions pages.

    Looking at the song title intro to Paul’s last comment, it may soon be time for a summary post, where we can pull together what we’ve discovered so far.

  57. Paul Vaughan says:

    Summary is at least 5 years away. Let’s stay harmonized with nature’s lead.

  58. Paul Vaughan says:

    Maybe more like 2040, 2050, or 2070. Nature will decide.

  59. tallbloke says:

    Well if that’s so, we need to leave something coherent for others to pick up and run with. Maybe instead of a summary, we should call it a progress report and get on with it?

  60. tallbloke says:

    Apropos nothing in particular; some triangles:

  61. oldbrew says:

    Date: 03/08/17 GWPF TV

    The Met Offices’s model-based rainfall forecasts have not stood up to empirical tests, and do not seem to give better advice than observational records
    . . .
    …does not give any better information than what could be obtained using a piece of paper, rather than a £97 million super computer.

  62. Paul Vaughan says:

    Nature sets the path and pace.
    The time is ripe for exploration, not summary.
    This is a matter of principle — Pareto Principle to be specific.
    All that’s left to observe is whether the core principle is respected in harmony with nature.

    – –

    “remarkable limit”

    Golden quantum oscillator and Binet-Fibonacci calculus

  63. oldbrew says:

    For any four consecutive Fibonacci numbers – f1, f2, f3, f4:
    f3² – f2² = f4 * f1

    The sum of the squares of any two consecutive Fibonacci numbers is another Fibonacci number.
    The difference between the squares of any two alternate Fibonacci numbers is another Fibonacci number.

  64. tallbloke says:

    I skimmed the theoretical quantum physics paper paul linked above and it’s way over my head. I can vaguely see why he flagged up the “remarkable limit” though.

    There’s Euler’s number (e) again, sitting alongside φ and √5.

    An interesting sentence in the conclusions reads:
    “In a stereographic projection picture of these states, the argument of Fibonacci polynomials has interpretation of a distance between symmetric points in a unit circle.”

    “As above so below” is an ancient maxim. Perhaps if e, φ and √5 bring order to the chaos of sub-atomic theory, that’s why they are also bringing order to the chaos of supposedly random planetary orbits.

  65. tallbloke says:

    With regard to e, getting points to lie on unitary circles at the limit, and logarithmic spirals, this 15 minute youtube video was quite enjoyable. It sets out to explain Euler’s identity with the aid of animated graphical representation, and succeeds quite well.

  66. oldbrew says:

    Is the Universe Made of Math? [Excerpt]

    In this excerpt from his new [2014] book, Our Mathematical Universe, M.I.T. professor Max Tegmark explores the possibility that math does not just describe the universe, but makes the universe

    Lecture (45 mins.)

    – – –

    Critique: Not Even Wrong

  67. tallbloke says:

    Hmmm. Got as far as 7 mins in where the learned prof’s narration was in total denial of Halton Arp’s discoveries of ‘juvenile galaxies’ linked by bridges of matter to ‘mature galaxies’ with totally different redshifts.

    [Edit] Just read the critique OB linked and it pretty much sums up why I steer well clear of cosmology and stick to working on the solar system and other stuff we can actually see and measure properly. I suppose that wanting to be the one to discover the best theory of everything is a natural trait for the scientifically curious megalomaniac, but I think we’ve found more of substance in our own investigations than Tegmark has in the speculative outer reaches of the unknowable.

    Mind you, he’s attracted a $9million funding chunk, so maybe he’s not so daft, even if he is a bullshit artist…

  68. oldbrew says:

    ‘he’s attracted a $9million funding chunk’

    Does he need any research assistants 😎

  69. oldbrew says:

    December 9, 2014

    Dr. Jan Boeyens at the University of Pretoria and Dr. Francis Thackeray of the University of the Witwatersrand in South Africa have researched the many ways that the golden ratio can be seen ‘related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time.’ The researchers believe that geometric shapes found in the natural world throughout the Universe ultimately succumb to the same mathematical property of 1.618.

  70. Frank Mlinar says:

    Tallbloke: Will you provide the sources of your data and a sample of your calculations of your original post on July 9?

  71. The present solar cooling will last for only a few more years until SC25 starts. If you’re lucky, by 2020 there will have been a very minor cooling for the decade 2010-20. Just think of all the people who now have the wrong idea of what the sun does, and all the resistance to the real solar influence that this wrong thinking generated after years of carpet bombing the internet with your unsupported thresholds. Please stop.

    Based on what Bob? A total rebound in solar activity after 2020 which I doubt. You have to be kidding if you think global temperatures which are high now are going to remain so. Not going to happen BOB.

    My thresholds are based on past prolonged solar minimums.