Weekend open thread

Posted: February 26, 2016 by tallbloke in Blog

OK ren, this is the place for your interesting comments and graphics.🙂

Comments
  1. ren says:

    In Europe, the winter will not end soon.

    The sun getting quieter.

    Atlantic getting colder.

  2. ren says:

    Due to the location of the polar vortex ice in the Arctic is growing rapidly.

  3. ren says:

    The expected further strong rise in temperature in the stratosphere. The graph shows temperature jump after a decline in solar activity.
    http://acdb-ext.gsfc.nasa.gov/Data_services/met/metdata/annual/merra/t60_90n_30_2015_merra.pdf

  4. Paul Vaughan says:

    Je me souviens…

    25 months ago (January 23, 2014 at 10:53 pm)
    vukcevic quoted:

    “Forgive a child that fears the dark; the tragedy is when men fear the light. -Plato”

    https://tallbloke.wordpress.com/2014/01/23/wuwt-demagoguery-parting-of-the-ways-and-new-beginnings/

    “The old get old and the young get stronger
    May take a week and it may take longer
    They got the guns but we got the numbers…”
    — The Doors 5:1

  5. Paul Vaughan says:

    “Your ballroom days are over baby, night is drawing near…” — The Doors – Five to One

  6. Doug says:

    At first flash of Eden
    We race down to the sea
    Standing there on
    Freedom’s shore

    Waiting for the sun

  7. ren says:

    “Five to one, baby
    One in five
    No one here gets out alive, now”

  8. ren says:

    “Riders on the storm.
    Riders on the storm
    Into this house we’re born
    Into this world we’re thrown ”
    http://pl.sat24.com/pl/sp

  9. tallbloke says:

    http://climateofsophistry.com/2016/02/26/slayer-double-victory/#comment-26210

    0 Responses to Slayer Double Victory

    tallbloke says:
    Your comment is awaiting moderation.
    2016/02/26 at 2:35 PM
    “In other words, you cannot prevent something from emitting at the temperature that it is at. And of course, again, radiant emission from a cooler object does not transfer heat to a warmer object.”

    The cooler object does not transfer heat, it transfers energy. Since it is cooler, it isn’t going to “make the warmer object warmer than it was before”, but it is going to slow the rate it cools at (i.e. the rate it loses energy).

    At this point you need to remember that we are not discussing a closed system. The Sun is pushing energy in continually, and energy is being emitted to space continually. Changing the make-up of the atmosphere won’t alter the amount of energy incoming or outgoing, but it will alter the rate at which energy moves through various parts of the system.

    However, CO2 variation will make very little difference, because there’s far less of it than there is water vapour, which is the much bigger determinant. Variation of water vapour content in the upper atmosphere has a far larger effect than that near the surface, and that has been falling for a decade according to NASA’s NVAP-M data. Here’s why:

    Its the Sun.

  10. chilemike says:

    Congrats on the goal Tallbloke! I tried to donate but I live in Chile and have my billing address for my cards in the US. Send me an email if you still need a few USD for movie related stuff. Love your site and associated mathematics, science , etc.

  11. Paul Vaughan says:

    Remember: One of Jim’s girlfriends was a witch.

    Roger Andrews wrote:

    “Ray:

    “Could it be that the Fibonacci series predicts ‘stability’ for systemic relationships?”

    I think phi might, but every numeric sequence where the next number is the sum of the previous two converges on phi, and the Fibonacci series is just one of an infinite number of them (the Lucas numbers are another). So if the Fibonacci numbers really do control “systemic relationships” they must have some special property that none of the other numeric series that converge on phi does.”

    “This isn’t a unique property of the Fibonacci series. As I noted in my response to Suricat EVERY sequence of numbers where the next number is the sum of the previous two converges on phi.”

    https://tallbloke.wordpress.com/2014/01/22/why-phi-earths-secret-neighbours/

  12. Paul Vaughan says:

    Got that?

  13. Ed says:

    Thanks Paul and Ren, this has been more enjoyable than the last ten topics.

  14. “The Connolley Problem, pt 3: A Time Span Problem”
    http://gelbspanfiles.com/?p=3603

  15. ren says:

    Russell Cook
    ” Our Sun started to warm up soon after its birth 4.5 billion years ago. So far it has only warmed by about 30% but the rate of warming will steadily increase until the red giant stage marks the end of its active life. A 30% warm up doesn’t sound much until you realise that it’s equivalent to about a 25ºC rise of temperature for the Earth’s surface. Or to put it in more familiar terms, seven times the difference between an ice age and now. If the Sun was delivering a third less heat when life started four billion years ago how on earth was it warm enough for it to flourish? alternatively, if it was warm enough then why are we not now intolerably hot?

    One answer to this puzzling question about Earth’s temperature, and why it has always been comfortable for life, is that maybe our planet has the capacity to keep its temperature right for life. Just as we keep our core temperature close to 37ºC regardless of whether it is freezing outside or torridly hot. Temperature is not the only property of Earth that somehow or other stays right for life. Have you ever wondered about the air you breathe and why the oxygen is 21%, not 50% or 10%? It so happens that if the oxygen were above 25% fires would be so fierce that few if any trees would survive and if it were below 15% it would be impossible to start a fire. 21% is just right.

    Many other properties of Earth, like the cloudiness of the skies and the abundance and quality of rain, are uncannily right for life. So many of them in fact that it’s reasonable to ask if all these things can be right by chance?”
    http://web.archive.org/web/20070311212927/http://www.channel4.com/science/microsites/S/science/nature/gaia.html

  16. ren says:

    Because the Earth is not a closed system is able to regulate the temperature.

  17. Paul Vaughan says:

    5 tiles per
    1 scale step
    when the middle class
    bridges the gap

    between neighbors
    above & below…

    ((1/1)+(1/2))^2 = 2.25
    ((2/1)+(2/3))^2 = 7.11111111111111
    ((3/2)+(3/5))^2 = 4.41
    ((5/3)+(5/8))^2 = 5.25173611111111
    ((8/5)+(8/13))^2 = 4.90792899408284
    ((13/8)+(13/21))^2 = 5.03574971655329
    ((21/13)+(21/34))^2 = 4.98643045801683
    ((34/21)+(34/55))^2 = 5.00519555480594
    ((55/34)+(55/89))^2 = 4.99801729361179
    ((89/55)+(89/144))^2 = 5.00075759169983
    ((144/89)+(144/233))^2 = 4.99971066442701
    ((233/144)+(233/377))^2 = 5.00011052200155
    ((377/233)+(377/610))^2 = 4.99995778517579
    ((610/377)+(610/987))^2 = 5.00001612474822
    ((987/610)+(987/1597))^2 = 4.99999384091178
    ((1597/987)+(1597/2584))^2 = 5.00000235256492
    ((2584/1597)+(2584/4181))^2 = 4.99999910140054
    ((4181/2584)+(4181/6765))^2 = 5.00000034323451
    ((6765/4181)+(6765/10946))^2 = 4.99999986889609
    ((10946/6765)+(10946/17711))^2 = 5.00000005007724
    ((17711/10946)+(17711/28657))^2 = 4.9999999808722
    ((28657/17711)+(28657/46368))^2 = 5.00000000730617
    ((46368/28657)+(46368/75025))^2 = 4.99999999720929
    ((75025/46368)+(75025/121393))^2 = 5.00000000106596
    ((121393/75025)+(121393/196418))^2 = 4.99999999959284
    ((196418/121393)+(196418/317811))^2 = 5.00000000015552
    ((317811/196418)+(317811/514229))^2 = 4.9999999999406
    ((514229/317811)+(514229/832040))^2 = 5.00000000002269
    ((832040/514229)+(832040/1346269))^2 = 4.99999999999133
    ((1346269/832040)+(1346269/2178309))^2 = 5.00000000000331
    ((2178309/1346269)+(2178309/3524578))^2 = 4.99999999999874
    ((3524578/2178309)+(3524578/5702887))^2 = 5.00000000000048
    ((5702887/3524578)+(5702887/9227465))^2 = 4.99999999999982
    ((9227465/5702887)+(9227465/14930352))^2 = 5.00000000000007
    ((14930352/9227465)+(14930352/24157817))^2 = 4.99999999999997
    ((24157817/14930352)+(24157817/39088169))^2 = 5.00000000000001

  18. Paul Vaughan says:

    …and of course Roger Andrews was right — it’s 5:1 no matter where you start …for example:

    ((-1012/-15)+(-1012/-1027))^2 = 4685.68465776938
    ((-1027/-1012)+(-1027/-2039))^2 = 2.30584348925079
    ((-2039/-1027)+(-2039/-3066))^2 = 7.02478040329003
    ((-3066/-2039)+(-3066/-5105))^2 = 4.42793511603208
    ((-5105/-3066)+(-5105/-8171))^2 = 5.24321338285508
    ((-8171/-5105)+(-8171/-13276))^2 = 4.91091831907373
    ((-13276/-8171)+(-13276/-21447))^2 = 5.03457042741712
    ((-21447/-13276)+(-21447/-34723))^2 = 4.98687536726413
    ((-34723/-21447)+(-34723/-56170))^2 = 5.00502481054641
    ((-56170/-34723)+(-56170/-90893))^2 = 4.99808239457922
    ((-90893/-56170)+(-90893/-147063))^2 = 5.00073270820733
    ((-147063/-90893)+(-147063/-237956))^2 = 4.99972016657463
    ((-237956/-147063)+(-237956/-385019))^2 = 5.00010689213931
    ((-385019/-237956)+(-385019/-622975))^2 = 4.99995917160657
    ((-622975/-385019)+(-622975/-1007994))^2 = 5.00001559517102
    ((-1007994/-622975)+(-1007994/-1630969))^2 = 4.99999404319113
    ((-1630969/-1007994)+(-1630969/-2638963))^2 = 5.00000227530092
    ((-2638963/-1630969)+(-2638963/-4269932))^2 = 4.99999913091273
    ((-4269932/-2638963)+(-4269932/-6908895))^2 = 5.00000033196185
    ((-6908895/-4269932)+(-6908895/-11178827))^2 = 4.99999987320186
    ((-11178827/-6908895)+(-11178827/-18087722))^2 = 5.00000004843258
    ((-18087722/-11178827)+(-18087722/-29266549))^2 = 4.9999999815004
    ((-29266549/-18087722)+(-29266549/-47354271))^2 = 5.00000000706622
    ((-47354271/-29266549)+(-47354271/-76620820))^2 = 4.99999999730095
    ((-76620820/-47354271)+(-76620820/-123975091))^2 = 5.00000000103095
    ((-123975091/-76620820)+(-123975091/-200595911))^2 = 4.99999999960621
    ((-200595911/-123975091)+(-200595911/-324571002))^2 = 5.00000000015041
    ((-324571002/-200595911)+(-324571002/-525166913))^2 = 4.99999999994255
    ((-525166913/-324571002)+(-525166913/-849737915))^2 = 5.00000000002194
    ((-849737915/-525166913)+(-849737915/-1374904828))^2 = 4.99999999999162
    ((-1374904828/-849737915)+(-1374904828/-2224642743))^2 = 5.0000000000032
    ((-2224642743/-1374904828)+(-2224642743/-3599547571))^2 = 4.99999999999878
    ((-3599547571/-2224642743)+(-3599547571/-5824190314))^2 = 5.00000000000047
    ((-5824190314/-3599547571)+(-5824190314/-9423737885))^2 = 4.99999999999982
    ((-9423737885/-5824190314)+(-9423737885/-15247928199))^2 = 5.00000000000007
    ((-15247928199/-9423737885)+(-15247928199/-24671666084))^2 = 4.99999999999997

    If that doesn’t help people understand why the EOFs are so simple ( https://tallbloke.wordpress.com/2016/02/02/paul-vaughan-noaa-corruption-of-sst-records/ ), I don’t know what will. (Probably nothing …or maybe only personalized divine intervention!)

  19. oldbrew says:

    Lucas numbers are all combinations of two alternate Fibonacci numbers e.g.
    7 = 5 + 2
    11 = 8 + 3
    18 = 13 + 5
    etc.

  20. Paul Vaughan says:

    Josh should do a cartoon with the theme: red taped to death by joy-deprived administrative framing

    Flo Rida gives a lesson in harmonious entertainment…

    Exploring the beauty of nature should be less administrative and more like this:

    The key isn’t more red tape!! (and a bunch of old men arguing at wuwt is going to accomplish exactly what!? sweet **** all)

  21. Paul Vaughan says:

    OK OB just swap the start-up order (from (1,2) to (2,1))…

    ((3/1)+(3/4))^2 = 14.0625
    ((4/3)+(4/7))^2 = 3.6281179138322
    ((7/4)+(7/11))^2 = 5.69473140495868
    ((11/7)+(11/18))^2 = 4.76347946586042
    ((18/11)+(18/29))^2 = 5.09428956083372
    ((29/18)+(29/47))^2 = 4.96457393714825
    ((47/29)+(47/76))^2 = 5.0136167618025
    ((76/47)+(76/123))^2 = 4.99481133445967
    ((123/76)+(123/199))^2 = 5.00198371151824
    ((199/123)+(199/322))^2 = 4.99924255494666
    ((322/199)+(322/521))^2 = 5.00028935696842
    ((521/322)+(521/843))^2 = 4.99988948112
    ((843/521)+(843/1364))^2 = 5.00004221527963
    ((1364/843)+(1364/2207))^2 = 4.99998387531823
    ((2207/1364)+(2207/3571))^2 = 5.00000615909792
    ((3571/2207)+(3571/5778))^2 = 4.99999764743649
    ((5778/3571)+(5778/9349))^2 = 5.00000089859967
    ((9349/5778)+(9349/15127))^2 = 4.99999965676552
    ((15127/9349)+(15127/24476))^2 = 5.00000013110391
    ((24476/15127)+(24476/39603))^2 = 4.99999994992276
    ((39603/24476)+(39603/64079))^2 = 5.0000000191278
    ((64079/39603)+(64079/103682))^2 = 4.99999999269383
    ((103682/64079)+(103682/167761))^2 = 5.00000000279071
    ((167761/103682)+(167761/271443))^2 = 4.99999999893404
    ((271443/167761)+(271443/439204))^2 = 5.00000000040716
    ((439204/271443)+(439204/710647))^2 = 4.99999999984448
    ((710647/439204)+(710647/1149851))^2 = 5.0000000000594
    ((1149851/710647)+(1149851/1860498))^2 = 4.99999999997731
    ((1860498/1149851)+(1860498/3010349))^2 = 5.00000000000867
    ((3010349/1860498)+(3010349/4870847))^2 = 4.99999999999669
    ((4870847/3010349)+(4870847/7881196))^2 = 5.00000000000126
    ((7881196/4870847)+(7881196/12752043))^2 = 4.99999999999952
    ((12752043/7881196)+(12752043/20633239))^2 = 5.00000000000019
    ((20633239/12752043)+(20633239/33385282))^2 = 4.99999999999993
    ((33385282/20633239)+(33385282/54018521))^2 = 5.00000000000003
    ((54018521/33385282)+(54018521/87403803))^2 = 4.99999999999999

    …but that’s just another case from the infinite set of possibilities like Roger Andrews wisely emphasized.

    φ’s defined by the relationship with neighbors (for ANY starting pair — no matter how ordered).

    (φ+Φ)^2 = 5
    That’s the bottom line.

    Mysterious physics my *ss. It’s simple geometry and how you aggregate over it (blindly like they do at wuwt …or otherwise empowered with better awareness and freedom from overriding political objectives and low-IQ domineering donor bosses…)

    If you think there’s something extra-extra-extra special about Fib & Lucas, just let us know.

    Meanwhile this Lucas sings the tune that’s on my mind today…

    “They’ll be screamin’ at me ‘fore I even hit 5.” “They don’t wanna hear no speech… been a long week… no time for no talkin’…”

  22. James McGinn says:

    Science is confused about water because they are confused about polarity. They see polarity as a function of “polar’ bonds (a “polar” bond is a covalent bond that has an electronegativity difference). It’s not that simple. Many molecules have “polar” bonds but are not polar (they are not dipoles). A polar molecule is asymmetrical in addition to having electronegativity differences. And where it really gets confusing is when you consider that with water (and only with water) symmetry is variable–AND ACTUALLY VARIES AS A CONSEQUENCE OF HYDROGEN BONDING!

    In water polarity drops to zero when symmetry is achieved through coordinated tetrahedral bonds. The failure to comprehend this and its implications is the reason they are so perplexed by water and its many anomalies. For example, once you understand this it becomes immediately apparent why H2O has its high heat capacity. Strangely, the professionals have no ability to grasp the importance of symmetry to polarity. They write paper after paper and do video after video that demonstrates their ignorance of the intricacies of polarity and then they make lists of water’s anomalies, pretending they have explained something that they have not explained. The following paper tries to get beyond that same ground hog day, over and over again, glossing over, inability to grasp what is really happening at the molecular level that is so typical of the study of water:

    https://zenodo.org/record/37224

  23. oldbrew says:

    Fibonacci gets there faster than all the rest, that’s the point. Check the numbers needed to get a 5.000…. result.

  24. Chic Bowdrie says:

    Tallbloke,

    I saw your comment on the latest Postma post (climateofsophistry.com). I commented with the following and would appreciate feedback on it.

    Tallbloke’s statement that “the cooler object does not transfer heat, it transfers energy” may have been more palatable as “the cooler object does not transfer any net energy.” Arfur Bryant may still object on the grounds that this leaves room for a photon from a cold body actually being absorbed at the surface of a warmer body. Nonetheless, it is obvious to me that a cooler body can slow the rate that a warmer body cools. For example, consider the extreme case of a hot body placed at the South Pole vs. the same hot body placed in a warm humid place. The hot body will undoubtedly cool faster at the pole irrespective of how you hypothesize the cooling occurs.

    The other point of contention is the existence of a greenhouse effect. The problem starts with the term greenhouse which almost everyone agrees is a misnomer. Why do we still use it?

    To avoid being hypocritical, I will refer to the greenhouse effect as the “Temperate Atmosphere Effect (TAE).” The TAE results in an atmosphere warmer than it would be without TAE gases, AKA, IR active gases (IRAGs). Without IRAGs, the planet would still be warmer than without an atmosphere, but it would be subject to much wider diurnal temperature swings than the present atmosphere. Gradually adding IRAGs to an IRAG-free atmosphere will make the days cooler and the nights warmer. Adding sufficient IRAGs to the atmosphere, we arrive at our present day temperate atmosphere.

    Now to consider what happens if additional IRAGs are added to the atmosphere. This is the question Tallbloke raised and what I believe the blogosphere refers to as the “enhanced” greenhouse effect which I would prefer we call the enhanced TAE. I think Tallbloke misspoke by saying “Changing the make-up of the atmosphere won’t alter the amount of energy incoming or outgoing…,” because IRAGs affect SW reaching the surface and how much LW escapes, at least on short time scales. What I think is most important is to determine how much effect [if any!] an incremental increase in any IRAG will have on long term global temperature. IMO, this is the holy grail of climate science.

  25. Paul Vaughan says:

    Hmm…
    So you think you can use a quadrat to aggregate fully-informative samples from a pinwheel tiling do you?…

    The rate of convergence isn’t the unifying property.
    Stability comes from the limit.

    “In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called “analog signals”) and discrete-time signals (often called “digital signals”). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.”https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

    Finally! After all these years — at long last: We’re venturing into the politically-forbidden territory where the “sufficient condition” is NOT met. (Will false gods (you know their initials!) appear and attempt to strike us down? Perhaps not under superior Talkshop cover…)

    Are you limiting your search to integer seeds OB?
    (Φ,1) & (1,φ) converge on and stabilize at exactly 5 instantly.

    (Φ,1):

    ((1.61803398874989/1)+(1.61803398874989/2.61803398874989))^2 = 5
    ((2.61803398874989/1.61803398874989)+(2.61803398874989/4.23606797749979))^2 = 5
    ((4.23606797749979/2.61803398874989)+(4.23606797749979/6.85410196624968))^2 = 5
    ((6.85410196624968/4.23606797749979)+(6.85410196624968/11.0901699437495))^2 = 5
    ((11.0901699437495/6.85410196624968)+(11.0901699437495/17.9442719099992))^2 = 5
    ((17.9442719099992/11.0901699437495)+(17.9442719099992/29.0344418537486))^2 = 5
    ((29.0344418537486/17.9442719099992)+(29.0344418537486/46.9787137637478))^2 = 5
    ((46.9787137637478/29.0344418537486)+(46.9787137637478/76.0131556174964))^2 = 5
    ((76.0131556174964/46.9787137637478)+(76.0131556174964/122.991869381244))^2 = 5
    ((122.991869381244/76.0131556174964)+(122.991869381244/199.005024998741))^2 = 5
    ((199.005024998741/122.991869381244)+(199.005024998741/321.996894379985))^2 = 5
    ((321.996894379985/199.005024998741)+(321.996894379985/521.001919378725))^2 = 5
    ((521.001919378725/321.996894379985)+(521.001919378725/842.99881375871))^2 = 5
    ((842.99881375871/521.001919378725)+(842.99881375871/1364.00073313744))^2 = 5
    ((1364.00073313744/842.99881375871)+(1364.00073313744/2206.99954689615))^2 = 5
    __

    (1,φ):

    ((2.61803398874989/1.61803398874989)+(2.61803398874989/4.23606797749979))^2 = 5
    ((4.23606797749979/2.61803398874989)+(4.23606797749979/6.85410196624968))^2 = 5
    ((6.85410196624968/4.23606797749979)+(6.85410196624968/11.0901699437495))^2 = 5
    ((11.0901699437495/6.85410196624968)+(11.0901699437495/17.9442719099992))^2 = 5
    ((17.9442719099992/11.0901699437495)+(17.9442719099992/29.0344418537486))^2 = 5
    ((29.0344418537486/17.9442719099992)+(29.0344418537486/46.9787137637478))^2 = 5
    ((46.9787137637478/29.0344418537486)+(46.9787137637478/76.0131556174964))^2 = 5
    ((76.0131556174964/46.9787137637478)+(76.0131556174964/122.991869381244))^2 = 5
    ((122.991869381244/76.0131556174964)+(122.991869381244/199.005024998741))^2 = 5
    ((199.005024998741/122.991869381244)+(199.005024998741/321.996894379985))^2 = 5
    ((321.996894379985/199.005024998741)+(321.996894379985/521.001919378725))^2 = 5
    ((521.001919378725/321.996894379985)+(521.001919378725/842.99881375871))^2 = 5
    ((842.99881375871/521.001919378725)+(842.99881375871/1364.00073313744))^2 = 5
    ((1364.00073313744/842.99881375871)+(1364.00073313744/2206.99954689615))^2 = 5
    ((2206.99954689615/1364.00073313744)+(2206.99954689615/3571.00028003358))^2 = 5

    We have a lot of terrain to cover. Please get with the program people. (Or be prepared to eat dirt!)

    [ :

  26. ren says:

    Strong GCR jump from 25 January and a sharp jump of temperature in the stratosphere.

  27. tallbloke says:

    Paul: We have a lot of terrain to cover. Please get with the program people. (Or be prepared to eat dirt!)

    Hmmm, worms, so tasty.🙂
    Humble pie is more agreeable, so humbly I’ll ask Paul to be just a little less cryptic for us, so we can get with the program(me).

  28. tchannon says:

    Going to be fun watching where these trains are going. Some free rein.

  29. oldbrew says:

    ‘Are you limiting your search to integer seeds OB?’

    Just saying the Fibonacci series is the best at following the phi numbers, patterns, ratios etc.
    Having 1,2 and 5 in its series probably helps😉

  30. oldbrew says:

    PV: ‘(Φ,1) & (1,φ) converge on and stabilize at exactly 5 instantly.’

    Looking at the numbers in brackets below that, they are converging on the Lucas series.
    But – the sum of every 2 alternate Lucas numbers is a multiple of 5 (e.g. 11+29).
    And – dividing that sum by 5 returns a Fibonacci number.
    And – every Lucas number is the sum of two Fibonacci numbers.

  31. tallbloke says:

    CB: I think Tallbloke misspoke by saying “Changing the make-up of the atmosphere won’t alter the amount of energy incoming or outgoing…

    I’ve clarified this in my latest response there (awaiting approval).

  32. tallbloke says:

    OB: Fibonacci gets there faster than all the rest, that’s the point.

    Well, it’s one of the points. Obviously not a point that’s relevant to Paul’s immediate interest, but a point nonetheless.

    Having 1,2 and 5 in its series probably helps

    2+3=5
    13-8=5

    5 is the 5th Fibonacci number

    5 is the usual number in Landscheidt’s ‘big hand’ cycles and fractal derivations of it.

  33. Paul Vaughan says:

    Roger Andrews was right. (The thing that struck me when I reviewed the Toro thread was that no one conceded that.)

    As I’ve outlined in full detail (with numbers rather than cryptic algebra no less), Fib is not the fastest converger.

    Series commencing with the seeds (Φ,1) & (1,φ) converge on and stabilize at exactly 5 instantly. (A faster rate of convergence than “instant” is not possible. More precise convergence than “exactly” is not possible.)

    If something is unclear, it’s crystal unclear what it might be.

    Let me begin stabbing at unclarity with a question to help overcome misunderstandings:
    Why the fixation on only counting numbers?
    (It’s a genuine honest question.)

    I’ve pointed out 2 series with instant exact convergence. What the heck isn’t clear about that? (another genuine honest question; no sarcasm)

  34. Paul Vaughan says:

    The series seeded with (Φ,1):

    0.618033989
    1
    1.61803398874989 = 1 + 0.618033988749895
    2.61803398874989 = 1.61803398874989 + 1
    4.23606797749979 = 2.61803398874989 + 1.61803398874989
    6.85410196624968 = 4.23606797749979 + 2.61803398874989
    11.0901699437495 = 6.85410196624968 + 4.23606797749979
    17.9442719099992 = 11.0901699437495 + 6.85410196624968
    29.0344418537486 = 17.9442719099992 + 11.0901699437495
    46.9787137637478 = 29.0344418537486 + 17.9442719099992
    76.0131556174964 = 46.9787137637478 + 29.0344418537486
    122.991869381244 = 76.0131556174964 + 46.9787137637478
    199.005024998741 = 122.991869381244 + 76.0131556174964
    321.996894379985 = 199.005024998741 + 122.991869381244
    521.001919378725 = 321.996894379985 + 199.005024998741
    842.99881375871 = 521.001919378725 + 321.996894379985
    1364.00073313744 = 842.99881375871 + 521.001919378725
    2206.99954689615 = 1364.00073313744 + 842.99881375871
    3571.00028003358 = 2206.99954689615 + 1364.00073313744
    5777.99982692973 = 3571.00028003358 + 2206.99954689615
    9349.00010696331 = 5777.99982692973 + 3571.00028003358
    15126.999933893 = 9349.00010696331 + 5777.99982692973
    24476.0000408564 = 15126.999933893 + 9349.00010696331
    39602.9999747494 = 24476.0000408564 + 15126.999933893
    64079.0000156057 = 39602.9999747494 + 24476.0000408564
    103681.999990355 = 64079.0000156057 + 39602.9999747494
    167761.000005961 = 103681.999990355 + 64079.0000156057
    271442.999996316 = 167761.000005961 + 103681.999990355
    439204.000002277 = 271442.999996316 + 167761.000005961
    710646.999998593 = 439204.000002277 + 271442.999996316
    1149851.00000087 = 710646.999998593 + 439204.000002277
    1860497.99999946 = 1149851.00000087 + 710646.999998593
    3010349.00000033 = 1860497.99999946 + 1149851.00000087
    4870846.99999979 = 3010349.00000033 + 1860497.99999946
    7881196.00000013 = 4870846.99999979 + 3010349.00000033
    12752042.9999999 = 7881196.00000013 + 4870846.99999979
    20633239 = 12752042.9999999 + 7881196.00000013
    33385282 = 20633239 + 12752042.9999999
    54018521 = 33385282 + 20633239
    87403803 = 54018521 + 33385282

    For comparison, the series seeded with (1,1):

    1
    1
    2 = 1 + 1
    3 = 2 + 1
    5 = 3 + 2
    8 = 5 + 3
    13 = 8 + 5
    21 = 13 + 8
    34 = 21 + 13
    55 = 34 + 21
    89 = 55 + 34
    144 = 89 + 55
    233 = 144 + 89
    377 = 233 + 144
    610 = 377 + 233
    987 = 610 + 377
    1597 = 987 + 610
    2584 = 1597 + 987
    4181 = 2584 + 1597
    6765 = 4181 + 2584
    10946 = 6765 + 4181
    17711 = 10946 + 6765
    28657 = 17711 + 10946
    46368 = 28657 + 17711
    75025 = 46368 + 28657
    121393 = 75025 + 46368
    196418 = 121393 + 75025
    317811 = 196418 + 121393
    514229 = 317811 + 196418
    832040 = 514229 + 317811
    1346269 = 832040 + 514229
    2178309 = 1346269 + 832040
    3524578 = 2178309 + 1346269
    5702887 = 3524578 + 2178309
    9227465 = 5702887 + 3524578
    14930352 = 9227465 + 5702887
    24157817 = 14930352 + 9227465
    39088169 = 24157817 + 14930352
    63245986 = 39088169 + 24157817
    102334155 = 63245986 + 39088169

  35. Paul Vaughan says:

    The series seeded with (1,2):

    1
    2
    3 = 2 + 1
    5 = 3 + 2
    8 = 5 + 3
    13 = 8 + 5
    21 = 13 + 8
    34 = 21 + 13
    55 = 34 + 21
    89 = 55 + 34
    144 = 89 + 55
    233 = 144 + 89
    377 = 233 + 144
    610 = 377 + 233
    987 = 610 + 377
    1597 = 987 + 610
    2584 = 1597 + 987
    4181 = 2584 + 1597
    6765 = 4181 + 2584
    10946 = 6765 + 4181
    17711 = 10946 + 6765
    28657 = 17711 + 10946
    46368 = 28657 + 17711
    75025 = 46368 + 28657
    121393 = 75025 + 46368
    196418 = 121393 + 75025
    317811 = 196418 + 121393
    514229 = 317811 + 196418
    832040 = 514229 + 317811
    1346269 = 832040 + 514229
    2178309 = 1346269 + 832040
    3524578 = 2178309 + 1346269
    5702887 = 3524578 + 2178309
    9227465 = 5702887 + 3524578
    14930352 = 9227465 + 5702887
    24157817 = 14930352 + 9227465
    39088169 = 24157817 + 14930352
    63245986 = 39088169 + 24157817
    102334155 = 63245986 + 39088169
    165580141 = 102334155 + 63245986

    For comparison, the series seeded with (2,1):

    2
    1
    3 = 1 + 2
    4 = 3 + 1
    7 = 4 + 3
    11 = 7 + 4
    18 = 11 + 7
    29 = 18 + 11
    47 = 29 + 18
    76 = 47 + 29
    123 = 76 + 47
    199 = 123 + 76
    322 = 199 + 123
    521 = 322 + 199
    843 = 521 + 322
    1364 = 843 + 521
    2207 = 1364 + 843
    3571 = 2207 + 1364
    5778 = 3571 + 2207
    9349 = 5778 + 3571
    15127 = 9349 + 5778
    24476 = 15127 + 9349
    39603 = 24476 + 15127
    64079 = 39603 + 24476
    103682 = 64079 + 39603
    167761 = 103682 + 64079
    271443 = 167761 + 103682
    439204 = 271443 + 167761
    710647 = 439204 + 271443
    1149851 = 710647 + 439204
    1860498 = 1149851 + 710647
    3010349 = 1860498 + 1149851
    4870847 = 3010349 + 1860498
    7881196 = 4870847 + 3010349
    12752043 = 7881196 + 4870847
    20633239 = 12752043 + 7881196
    33385282 = 20633239 + 12752043
    54018521 = 33385282 + 20633239
    87403803 = 54018521 + 33385282
    141422324 = 87403803 + 54018521

    The series seeded with (1,φ):

    1
    1.618033989
    2.61803398874989 = 1.61803398874989 + 1
    4.23606797749979 = 2.61803398874989 + 1.61803398874989
    6.85410196624968 = 4.23606797749979 + 2.61803398874989
    11.0901699437495 = 6.85410196624968 + 4.23606797749979
    17.9442719099992 = 11.0901699437495 + 6.85410196624968
    29.0344418537486 = 17.9442719099992 + 11.0901699437495
    46.9787137637478 = 29.0344418537486 + 17.9442719099992
    76.0131556174964 = 46.9787137637478 + 29.0344418537486
    122.991869381244 = 76.0131556174964 + 46.9787137637478
    199.005024998741 = 122.991869381244 + 76.0131556174964
    321.996894379985 = 199.005024998741 + 122.991869381244
    521.001919378725 = 321.996894379985 + 199.005024998741
    842.99881375871 = 521.001919378725 + 321.996894379985
    1364.00073313744 = 842.99881375871 + 521.001919378725
    2206.99954689615 = 1364.00073313744 + 842.99881375871
    3571.00028003358 = 2206.99954689615 + 1364.00073313744
    5777.99982692973 = 3571.00028003358 + 2206.99954689615
    9349.00010696331 = 5777.99982692973 + 3571.00028003358
    15126.999933893 = 9349.00010696331 + 5777.99982692973
    24476.0000408564 = 15126.999933893 + 9349.00010696331
    39602.9999747494 = 24476.0000408564 + 15126.999933893
    64079.0000156057 = 39602.9999747494 + 24476.0000408564
    103681.999990355 = 64079.0000156057 + 39602.9999747494
    167761.000005961 = 103681.999990355 + 64079.0000156057
    271442.999996316 = 167761.000005961 + 103681.999990355
    439204.000002277 = 271442.999996316 + 167761.000005961
    710646.999998593 = 439204.000002277 + 271442.999996316
    1149851.00000087 = 710646.999998593 + 439204.000002277
    1860497.99999946 = 1149851.00000087 + 710646.999998593
    3010349.00000033 = 1860497.99999946 + 1149851.00000087
    4870846.99999979 = 3010349.00000033 + 1860497.99999946
    7881196.00000013 = 4870846.99999979 + 3010349.00000033
    12752042.9999999 = 7881196.00000013 + 4870846.99999979
    20633239 = 12752042.9999999 + 7881196.00000013
    33385282 = 20633239 + 12752042.9999999
    54018521 = 33385282 + 20633239
    87403803 = 54018521 + 33385282
    141422324 = 87403803 + 54018521

  36. Paul Vaughan says:

    Any number in any of these series fills the gap between it’s neighbors — i.e. it’s the difference between it’s richer & poorer neighbors.

    The series (Φ,1) & (1,φ) are special. Any number in these series equals the difference, beat, AND geometric mean of its richer & poorer neighbors. (The other series listed only have that property in the limit as n goes to infinity.)

  37. Paul Vaughan says:

    Noteworthy: The sequence of axial periods of richer & poorer Lucas neighbors converges to Fib.

  38. Paul Vaughan says:

    Noteworthy: The sequence of (Φ,1) axial periods (of richer & poorer neighbors) equals (φ^(n-2))/√5 and converges to Fib.

  39. oldbrew says:

    PV: isn’t everything in Lucas Fib-related in the end?

    Only Phi can claim its square equals itself plus one.

  40. Paul Vaughan says:

    Both Lucas & Fibonacci are subsumed by something more general. I think I’m starting to see why conventional focus stopped at Lucas & Fibonacci rather than following through. It was a good enough approximation of something more fundamental. Lucas was “close enough” on the difference side and Fibonacci was “close enough” on the sum side. A little more digging would have revealed the fundamental geometric roots. I’ll aim to devote a little more time to algebraic formalization, perhaps generously supplementing that with some tabulated aid for the algebraically impaired.

  41. oldbrew says:

    We still have 8 Earth orbits = ~13 Venus = 5 conjunctions and
    3 Neptune = ~2 Pluto = 1 conjunction

    1,2,3,5,8 and 13 are Fibonacci numbers.
    Any Lucas equivalents in our planetary system?

  42. oldbrew says:

    ‘The heliospheric current sheet separates regions of the solar wind where the magnetic field points toward or away from the Sun. The complex field structure in the photosphere simplifies with increasing height in the corona until a single line separates the two polarities at about 2.5 solar radii. That line is drawn out by the radially accelerating solar wind to form a surface similar to the one shown in this idealized picture. The surface is curved because the underlying magnetic pattern rotates every 27 days with the Sun.’
    http://web.archive.org/web/20060901124602/http://quake.stanford.edu/~wso/gifs/HCS.html

    2 x 2.5 = diameter = 5 (solar radii)

    Also: ‘During most of the solar cycle the current sheet is basically a tilted dipole with varying degrees of quadrupole distortion. Near solar maximum the dipole decays leaving a much more complicated structure.’

    Artist’s Conception of the Heliospheric Current Sheet

  43. tallbloke says:

    Paul: Why the fixation on only counting numbers? (It’s a genuine honest question.)

    As I noted two years ago, just two comments below the Roger Andrews comment that Paul highlights:

    “Observations show that the most common ratios where clusters of small bodies such as TNO’S form are at Fibonacci ratios such as 2:3, 3:5, 5:8, etc. So it may well be that Fibonacci is ‘special’ because it fulfils both the stability and energy transfer functions.”

    The ‘counting numbers’ of the Fibonacci series form resonant ratios between real objects in the real world. Resonance transfers energy, and we’re very interested in energy transfer. As I have already noted many times over the last several years, the golden ratio is remarkably un-resononant, yet lies very close to those whole ‘counting number’ Fibonacci ratios.

    I think this is what makes the Fibonacci series unique, and is the reason why most of the ‘near whole counting number’ orbital ratios between planet pairs are Fibonacci number pairs, as OB noted above.

    Hypothesis:
    Nature is efficient, and being able to shift planet pair orbital ratios from maximally resonant whole ‘counting number’ Fibonacci ratios to minimally resonant phi ratios with the minimum of time and energy enables the most efficient maintenance of system stability.

  44. Paul Vaughan says:

    JEV dies with insistence on counting numbers. In other words E does not determine V nor does V determine E. Rather the larger system bodies determine the nature of the E & V relationship …and JEV lives.

    I’ve organized a table that should help sort conceptualization without any potentially encumbering algebra.

    Note from the table that:
    Lucas Fibonacci ~= axial period of richer & poorer nearest-neighbors on φ power ladder
    Fibonacci Lucas ~= beat period of richer & poorer nearest-neighbors on φ power ladder
    • (φ+Φ)Fibonacci = (√5)Fibonacci ~= Lucas
    • (φ+Φ)axial = (√5)axial = beat = difference = geometric mean for richer & poorer nearest-neighbors on φ power ladder, all equaling φ^n
    • ( (φ+Φ)Fibonacci + Lucas ) / 2 = φ^n

    +0	0.00000000	axial_____	(φ+Φ)axial	1.00000000	geomean___	difference	beat______	2.00000000	1.00000000
    +1	1.00000000	0.72360680	1.61803399	1.61803399	1.61803399	1.61803399	1.61803399	1.00000000	1.61803399
    +2	1.00000000	1.17082039	2.61803399	2.61803399	2.61803399	2.61803399	2.61803399	3.00000000	2.61803399 = 1.61803399 + 1.00000000
    +3	2.00000000	1.89442719	4.23606798	4.23606798	4.23606798	4.23606798	4.23606798	4.00000000	4.23606798 = 2.61803399 + 1.61803399
    +4	3.00000000	3.06524758	6.85410197	6.85410197	6.85410197	6.85410197	6.85410197	7.00000000	6.85410197 = 4.23606798 + 2.61803399
    +5	5.00000000	4.95967478	11.0901699	11.0901699	11.0901699	11.0901699	11.0901699	11.0000000	11.0901699 = 6.85410197 + 4.23606798
    +6	8.00000000	8.02492236	17.9442719	17.9442719	17.9442719	17.9442719	17.9442719	18.0000000	17.9442719 = 11.0901699 + 6.85410197
    +7	13.0000000	12.9845971	29.0344419	29.0344419	29.0344419	29.0344419	29.0344419	29.0000000	29.0344419 = 17.9442719 + 11.0901699
    +8	21.0000000	21.0095195	46.9787138	46.9787138	46.9787138	46.9787138	46.9787138	47.0000000	46.9787138 = 29.0344419 + 17.9442719
    +9	34.0000000	33.9941166	76.0131556	76.0131556	76.0131556	76.0131556	76.0131556	76.0000000	76.0131556 = 46.9787138 + 29.0344419
    10	55.0000000	55.0036361	122.991869	122.991869	122.991869	122.991869	122.991869	123.000000	122.991869 = 76.0131556 + 46.9787138
    11	89.0000000	88.9977528	199.005025	199.005025	199.005025	199.005025	199.005025	199.000000	199.005025 = 122.991869 + 76.0131556
    12	144.000000	144.001389	321.996894	321.996894	321.996894	321.996894	321.996894	322.000000	321.996894 = 199.005025 + 122.991869
    13	233.000000	232.999142	521.001919	521.001919	521.001919	521.001919	521.001919	521.000000	521.001919 = 321.996894 + 199.005025
    14	377.000000	377.000531	842.998814	842.998814	842.998814	842.998814	842.998814	843.000000	842.998814 = 521.001919 + 321.996894
    15	610.000000	609.999672	1364.00073	1364.00073	1364.00073	1364.00073	1364.00073	1364.00000	1364.00073 = 842.998814 + 521.001919
    16	987.000000	987.000203	2206.99955	2206.99955	2206.99955	2206.99955	2206.99955	2207.00000	2206.99955 = 1364.00073 + 842.998814
    17	1597.00000	1596.99987	3571.00028	3571.00028	3571.00028	3571.00028	3571.00028	3571.00000	3571.00028 = 2206.99955 + 1364.00073
    18	2584.00000	2584.00008	5777.99983	5777.99983	5777.99983	5777.99983	5777.99983	5778.00000	5777.99983 = 3571.00028 + 2206.99955
    19	4181.00000	4180.99995	9349.00011	9349.00011	9349.00011	9349.00011	9349.00011	9349.00000	9349.00011 = 5777.99983 + 3571.00028
    20	6765.00000	6765.00003	15126.9999	15126.9999	15126.9999	15126.9999	15126.9999	15127.0000	15126.9999 = 9349.00011 + 5777.99983
    21	10946.0000	10946.0000	24476.0000	24476.0000	24476.0000	24476.0000	24476.0000	24476.0000	24476.0000 = 15126.9999 + 9349.00011
    22	17711.0000	17711.0000	39603.0000	39603.0000	39603.0000	39603.0000	39603.0000	39603.0000	39603.0000 = 24476.0000 + 15126.9999
    23	28657.0000	28657.0000	64079.0000	64079.0000	64079.0000	64079.0000	64079.0000	64079.0000	64079.0000 = 39603.0000 + 24476.0000
    24	46368.0000	46368.0000	103682.000	103682.000	103682.000	103682.000	103682.000	103682.000	103682.000 = 64079.0000 + 39603.0000
    25	75025.0000	75025.0000	167761.000	167761.000	167761.000	167761.000	167761.000	167761.000	167761.000 = 103682.000 + 64079.0000
    26	121393.000	121393.000	271443.000	271443.000	271443.000	271443.000	271443.000	271443.000	271443.000 = 167761.000 + 103682.000
    27	196418.000	196418.000	439204.000	439204.000	439204.000	439204.000	439204.000	439204.000	439204.000 = 271443.000 + 167761.000
    28	317811.000	317811.000	710647.000	710647.000	710647.000	710647.000	710647.000	710647.000	710647.000 = 439204.000 + 271443.000
    29	514229.000	514229.000	1149851.00	1149851.00	1149851.00	1149851.00	1149851.00	1149851.00	1149851.00 = 710647.000 + 439204.000
    30	832040.000	832040.000	1860498.00	1860498.00	1860498.00	1860498.00	1860498.00	1860498.00	1860498.00 = 1149851.00 + 710647.000
    31	1346269.00	1346269.00	3010349.00	3010349.00	3010349.00	3010349.00	3010349.00	3010349.00	3010349.00 = 1860498.00 + 1149851.00
    32	2178309.00	2178309.00	4870847.00	4870847.00	4870847.00	4870847.00	4870847.00	4870847.00	4870847.00 = 3010349.00 + 1860498.00
    33	3524578.00	3524578.00	7881196.00	7881196.00	7881196.00	7881196.00	7881196.00	7881196.00	7881196.00 = 4870847.00 + 3010349.00
    34	5702887.00	5702887.00	12752043.0	12752043.0	12752043.0	12752043.0	12752043.0	12752043.0	12752043.0 = 7881196.00 + 4870847.00
    35	9227465.00	9227465.00	20633239.0	20633239.0	20633239.0	20633239.0	20633239.0	20633239.0	20633239.0 = 12752043.0 + 7881196.00
    36	14930352.0	14930352.0	33385282.0	33385282.0	33385282.0	33385282.0	33385282.0	33385282.0	33385282.0 = 20633239.0 + 12752043.0
    37	24157817.0	24157817.0	54018521.0	54018521.0	54018521.0	54018521.0	54018521.0	54018521.0	54018521.0 = 33385282.0 + 20633239.0
    

  45. oldbrew says:

    PV: Earth:Venus semi-major axis ratio corresponds to line ‘+1’ i.e. 1:0.72333
    http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html

  46. Paul Vaughan says:

    The E & V relationship is more than the sum & difference of its parts!

    Earth & Venus are coupled (accidental misinterpretations that I’m suggesting otherwise here maybe?), but they’re also constrained by something bigger …and that something just happens to be universal.

    We’ll keep working on improving mutual understanding….

    Cheers!

  47. oldbrew says:

    We’re told that magnetospheres provide planets with a protective shield against the force of the solar wind.
    Funny how Venus, the planet with no magnetism to speak of, also has the thickest atmosphere😉
    http://sci.esa.int/venus-express/50246-a-magnetic-surprise-for-venus-express/

  48. Paul Vaughan says:

    Typo:

    “• Lucas ~= axial period of richer & poorer nearest-neighbors on φ power ladder
    • Fibonacci ~= beat period of richer & poorer nearest-neighbors on φ power ladder”

    should read:

    • Fibonacci ~= axial period of richer & poorer nearest-neighbors on φ power ladder
    • Lucas ~= beat period of richer & poorer nearest-neighbors on φ power ladder

    (Note that Lucas & Fibonacci swapped locations.)

    Did the table help?

  49. oldbrew says:

    It’s a bit too abstract for me.

  50. tallbloke says:

    It certainly gives me more insight into the relationship between orbital params, Lucas and Fibonacci numbers, thanks Paul. I did an in-page search for ‘richer’ to find its first use and got this:

    “The series (Φ,1) & (1,φ) are special. Any number in these series equals the difference, beat, AND geometric mean of its richer & poorer neighbors.”

    I’m struggling a bit with this. It can’t just mean ‘higher and lower’ can it? If it does, then why not just say higher and lower?

  51. tallbloke says:

    OB: Funny how Venus, the planet with no magnetism to speak of, also has the thickest atmosphere

    Well maybe that’s because, with no magnetosphere to defend it, the Sun induced a big field in Venus’ core and made it bloody hot, which caused lots of volcanic outgassing, producing the thick atmosphere.

  52. tallbloke says:

    Paul: You asked a question I tried to answer here:
    https://tallbloke.wordpress.com/2016/02/26/weekend-open-thread/comment-page-1/#comment-114206
    It may help improve mutual understanding if you’d respond directly to my reply, so I can see where you’re coming from.
    Thanks

  53. oldbrew says:

    TB: shouldn’t the solar wind have ‘blown’ all that thick volcanic atmosphere far away according to magnetosphere theories?

  54. Paul Vaughan says:

    Sequence matters.
    They know that people trying to model the “physics” without first getting the geometry right will never succeed.
    It’s a campaign. There’s not even a snowball’s chance in h*ll of getting the “physics” right (in quotes to remind of assumptions lazily made to make the math tractable) if geometric central limits are ignored. They know this. That’s why they thought police to such excessive extent.
    Their whole strategy depends critically on blind audience buy-in to the always well-hidden uniformity assumption. They never address it squarely. They just evade. They pretend the physics can be realistically conceived without attention to geometric limits & boundaries. They’ve succeeded in brainwashing people we’d expect to be far less naive. It’s a dead-ending trust-burner.

    __

    OB: I think I can distill the table further. I’ll give an update when possible (probably no more than days from now, but competing interests are forcefully escalating…)

    __

    TB: higher & lower if you prefer (nearest-neighbors either side of the middle class either way)

    It’s just mind-boggling that this equivalence criterion isn’t widely well-known. It’s like the pinwheel tiling. How is it even possible that no one noticed that before 22 years ago?? It’s a sobering reminder (super sobering in this case) that simple things get overlooked. Our culture is so obsessed with complexity. It doesn’t even value the simple. That’s one of the things that causes me to appreciate far eastern values. There’s a more profound respect for the power of vacuous simplicity in far eastern culture. But Hollywood doesn’t know how to celebrate vacuous simplicity …and so off has gone western culture, lusting and lurching mindlessly for complexity, accepting even complex illusion over simple truth.

  55. oldbrew says:

    5 V-E (‘pentagram period’) x phi³ = 4 J-S axial

  56. oldbrew says:

    PV: ‘I think I can distill the table further’

    Thanks. We can see that alternate axial (Fib.) columns sum to the ‘in-between’ right-hand (Lucas) column e.g. axial cols. ‘+1’ and ‘+3’ sum to right col. ‘+2’.

  57. tallbloke says:

    OB: 5 V-E (‘pentagram period’) x phi³ = 4 J-S axial

    Now that’s quite nice because it’s also quite close to 3 solar cycles (~3.05). One solar cycle is itself (very) close to phi^5. Four JS axial is ~(8 x phi³).

  58. oldbrew says:

    TB: ‘Four JS axial is ~(8 x phi³)’

    That would make 1 J-S axial = ~2 x phi³.
    (5 V-E = ~8 years)

  59. oldbrew says:

    Here’s one problem with internal planetary dynamos – Lenz’s law.
    http://regentsprep.org/Regents/physics/phys08/clenslaw/

    Wilf James explains:
    ‘The theories that refer to moving metal within the Earth as the source of the Earth’s magnetism directly conflict with a very basic law of electricity and magnetism. It is known as Lenz’s Law.

    It can be paraphrased as:
    If a conductor that is in a complete (closed) circuit moves in a magnetic field, a current will be induced in the conductor. The induced current will have its own magnetic field that is opposite in polarity to the magnetic field that induced the current in the conductor in the first place. This means that it is impossible to have a self-sustaining magnetic field as the basis for the Earth’s magnetism.

    For those whose knowledge of electricity and magnetism is weak I offer an explanation based on an item that most people will have some acquantance with – an electric motor.’
    http://homepage.ntlworld.com/wilf.james/Earth%27s%20Magnetism.html

    Magnetic reversals may also be a bit tricky for conventional theory.

  60. Paul Vaughan says:

    Again: No model looking at V & E in isolation can work. I again suggest broader perspective: Think not just of a here-&-now freeze-frame but rather of evolution at Milankovitch timescale. As I pointed out in the why phi thread: JEV is extraordinarily sensitive and dies with the slightest change if not coupled to the jovians in model equations. Perhaps I have not made the point with sufficient force.

    It’s fine to look at puzzle pieces in isolation to develop awareness & insight, but to get the whole right demands attention to limits & boundaries.

    _

    While waiting for me to have time to refine the tabulation, I’m confident that anyone who copies/pastes (paste special as text) into an Excel worksheet will immediately be able to see the main bullet points I listed above the table (February 29, 2016 at 8:54 pm).

    The “.0000000″s and decimal point lengths I have to force (I perhaps unwisely expended time automating the cosmetic decisions) to make the columns line up make it more difficult than necessary to notice the pattern (an instance of (rather unhelpfully) competing objectives) that’s dead simple when I look at the same numbers in Excel in their original format.

    It’s too bad there’s no “excel” tag or something like that in html. After all these years of web development you’d think it would be easy enough to post a simple table (but it’s not).

    I could get it all perfect on an image, but then people can’t copy/paste the numbers. Given the complexity of other things that have been developed for the web, the lack of web development to support communication of a simple table seems pretty ridiculous …but it is what it is and communication work-arounds (possibly/probably less efficient than optimal) will have to be found…

    (just another example of an important simple thing pushed beneath a series of complex interests in a corrupted hierarchy of priorities…)

    The table’s intended as an aid for learning geometry fundamentals overlooked by the mainstream when aggregating samples and specifying “physical” models (based on false assumptions (hence the quotation marks in “physical”) about boundaries & limits).

    The image that summarizes the table is this one.

  61. Paul Vaughan says:

    Not sure how this reworked formatting will display, but let’s see…

    n 	Fibonacci 	n-1 ,  n+1	(φ+Φ)Fib  	n-1 ,  n+1	n-1 ,  n+1	n-1 ,  n+1	n-1 ,  n+1	φ^n       	Lucas     	sum of preceding 2, seeded with (1,φ)
    0 	0         	axial     	0	(φ+Φ)axial	geomean   	difference	beat      	1         	2         	1         
    1 	1         	0.72360680	2.23606798	1.61803399	1.61803399	1.61803399	1.61803399	1.61803399	1         	1.61803399
    2 	1         	1.17082039	2.23606798	2.61803399	2.61803399	2.61803399	2.61803399	2.61803399	3         	2.61803399 = 1.61803399 + 1         
    3 	2         	1.89442719	4.47213595	4.23606798	4.23606798	4.23606798	4.23606798	4.23606798	4         	4.23606798 = 2.61803399 + 1.61803399
    4 	3         	3.06524758	6.70820393	6.85410197	6.85410197	6.85410197	6.85410197	6.85410197	7         	6.85410197 = 4.23606798 + 2.61803399
    5 	5         	4.95967478	11.1803399	11.0901699	11.0901699	11.0901699	11.0901699	11.0901699	11        	11.0901699 = 6.85410197 + 4.23606798
    6 	8         	8.02492236	17.8885438	17.9442719	17.9442719	17.9442719	17.9442719	17.9442719	18        	17.9442719 = 11.0901699 + 6.85410197
    7 	13        	12.9845971	29.0688837	29.0344419	29.0344419	29.0344419	29.0344419	29.0344419	29        	29.0344419 = 17.9442719 + 11.0901699
    8 	21        	21.0095195	46.9574275	46.9787138	46.9787138	46.9787138	46.9787138	46.9787138	47        	46.9787138 = 29.0344419 + 17.9442719
    9 	34        	33.9941166	76.0263112	76.0131556	76.0131556	76.0131556	76.0131556	76.0131556	76        	76.0131556 = 46.9787138 + 29.0344419
    10	55        	55.0036361	122.983739	122.991869	122.991869	122.991869	122.991869	122.991869	123       	122.991869 = 76.0131556 + 46.9787138
    11	89        	88.9977528	199.010050	199.005025	199.005025	199.005025	199.005025	199.005025	199       	199.005025 = 122.991869 + 76.0131556
    12	144       	144.001389	321.993789	321.996894	321.996894	321.996894	321.996894	321.996894	322       	321.996894 = 199.005025 + 122.991869
    13	233       	232.999142	521.003839	521.001919	521.001919	521.001919	521.001919	521.001919	521       	521.001919 = 321.996894 + 199.005025
    14	377       	377.000531	842.997628	842.998814	842.998814	842.998814	842.998814	842.998814	843       	842.998814 = 521.001919 + 321.996894
    15	610       	609.999672	1364.00147	1364.00073	1364.00073	1364.00073	1364.00073	1364.00073	1364      	1364.00073 = 842.998814 + 521.001919
    16	987       	987.000203	2206.99909	2206.99955	2206.99955	2206.99955	2206.99955	2206.99955	2207      	2206.99955 = 1364.00073 + 842.998814
    17	1597      	1596.99987	3571.00056	3571.00028	3571.00028	3571.00028	3571.00028	3571.00028	3571      	3571.00028 = 2206.99955 + 1364.00073
    18	2584      	2584.00008	5777.99965	5777.99983	5777.99983	5777.99983	5777.99983	5777.99983	5778      	5777.99983 = 3571.00028 + 2206.99955
    19	4181      	4180.99995	9349.00021	9349.00011	9349.00011	9349.00011	9349.00011	9349.00011	9349      	9349.00011 = 5777.99983 + 3571.00028
    20	6765      	6765.00003	15126.9999	15126.9999	15126.9999	15126.9999	15126.9999	15126.9999	15127     	15126.9999 = 9349.00011 + 5777.99983
    21	10946     	10946     	24476.0001	24476     	24476     	24476     	24476     	24476     	24476     	24476      = 15126.9999 + 9349.00011
    22	17711     	17711     	39602.9999	39603     	39603     	39603     	39603     	39603     	39603     	39603      = 24476      + 15126.9999
    23	28657     	28657     	64079     	64079     	64079     	64079     	64079     	64079     	64079     	64079      = 39603      + 24476     
    

  62. Paul Vaughan says:

    One more try…

    n 	Fibonacci 	n-1 & n+1 	(φ+Φ)Fib  	n-1 & n+1 	n-1 & n+1 	n-1 & n+1 	n-1 & n+1 	φ^n       	Lucas     	sum of preceding 2, seeded with (1,φ)
    0 	0         	axial     	0         	(φ+Φ)axial	geomean   	difference	beat      	1         	2         	1         
    1 	1         	0.72360680	2.23606798	1.61803399	1.61803399	1.61803399	1.61803399	1.61803399	1         	1.61803399
    2 	1         	1.17082039	2.23606798	2.61803399	2.61803399	2.61803399	2.61803399	2.61803399	3         	2.61803399 = 1.61803399 + 1         
    3 	2         	1.89442719	4.47213595	4.23606798	4.23606798	4.23606798	4.23606798	4.23606798	4         	4.23606798 = 2.61803399 + 1.61803399
    4 	3         	3.06524758	6.70820393	6.85410197	6.85410197	6.85410197	6.85410197	6.85410197	7         	6.85410197 = 4.23606798 + 2.61803399
    5 	5         	4.95967478	11.1803399	11.0901699	11.0901699	11.0901699	11.0901699	11.0901699	11        	11.0901699 = 6.85410197 + 4.23606798
    6 	8         	8.02492236	17.8885438	17.9442719	17.9442719	17.9442719	17.9442719	17.9442719	18        	17.9442719 = 11.0901699 + 6.85410197
    7 	13        	12.9845971	29.0688837	29.0344419	29.0344419	29.0344419	29.0344419	29.0344419	29        	29.0344419 = 17.9442719 + 11.0901699
    8 	21        	21.0095195	46.9574275	46.9787138	46.9787138	46.9787138	46.9787138	46.9787138	47        	46.9787138 = 29.0344419 + 17.9442719
    9 	34        	33.9941166	76.0263112	76.0131556	76.0131556	76.0131556	76.0131556	76.0131556	76        	76.0131556 = 46.9787138 + 29.0344419
    10	55        	55.0036361	122.983739	122.991869	122.991869	122.991869	122.991869	122.991869	123       	122.991869 = 76.0131556 + 46.9787138
    11	89        	88.9977528	199.010050	199.005025	199.005025	199.005025	199.005025	199.005025	199       	199.005025 = 122.991869 + 76.0131556
    12	144       	144.001389	321.993789	321.996894	321.996894	321.996894	321.996894	321.996894	322       	321.996894 = 199.005025 + 122.991869
    13	233       	232.999142	521.003839	521.001919	521.001919	521.001919	521.001919	521.001919	521       	521.001919 = 321.996894 + 199.005025
    14	377       	377.000531	842.997628	842.998814	842.998814	842.998814	842.998814	842.998814	843       	842.998814 = 521.001919 + 321.996894
    15	610       	609.999672	1364.00147	1364.00073	1364.00073	1364.00073	1364.00073	1364.00073	1364      	1364.00073 = 842.998814 + 521.001919
    16	987       	987.000203	2206.99909	2206.99955	2206.99955	2206.99955	2206.99955	2206.99955	2207      	2206.99955 = 1364.00073 + 842.998814
    17	1597      	1596.99987	3571.00056	3571.00028	3571.00028	3571.00028	3571.00028	3571.00028	3571      	3571.00028 = 2206.99955 + 1364.00073
    18	2584      	2584.00008	5777.99965	5777.99983	5777.99983	5777.99983	5777.99983	5777.99983	5778      	5777.99983 = 3571.00028 + 2206.99955
    19	4181      	4180.99995	9349.00021	9349.00011	9349.00011	9349.00011	9349.00011	9349.00011	9349      	9349.00011 = 5777.99983 + 3571.00028
    20	6765      	6765.00003	15126.9999	15126.9999	15126.9999	15126.9999	15126.9999	15126.9999	15127     	15126.9999 = 9349.00011 + 5777.99983
    21	10946     	10946     	24476.0001	24476     	24476     	24476     	24476     	24476     	24476     	24476      = 15126.9999 + 9349.00011
    22	17711     	17711     	39602.9999	39603     	39603     	39603     	39603     	39603     	39603     	39603      = 24476      + 15126.9999
    23	28657     	28657     	64079     	64079     	64079     	64079     	64079     	64079     	64079     	64079      = 39603      + 24476     
    

  63. Paul Vaughan says:

    OB, if anything remains unclear — anything at all — please say so.
    TB, please let me know what you are able to discern from this clearer tabulation.

    Let’s make sure this gets understood.

    I regard the φ^n & “sum of preceding 2, seeded with (1,φ)” columns to be the most fundamental columns. I don’t look at these columns as converging on Lucas, but rather I look at Lucas as converging on these columns.

    Similarly I do not regard the axial period as converging on Fibonacci, but rather I regard Fibonacci as converging on the axial period (which I regard as more fundamental than Fibonacci).

    I suspect there may be some resistance to looking at it from this more deeply fundamental perspective. With a lot of formality we could probably define away this initial difference in introductory level perspectives, but for the purposes of the type of discussion we’re having, I don’t think that’s necessary. Probably (at this stage) it’s better for us to focus first only on what relates to what, what converges to what in the limit as n goes to infinity, and what exactly equals what both initially and at every step of the way as n goes to infinity, etc.

    Remember that φ+Φ = √5.
    Fib = Fibonacci
    (φ+Φ)Fib = √5 times Fibonacci

    working from either of the fundamental columns
    φ^n & “sum of preceding 2, seeded with (1,φ)” (which are equal):
    axial = axial period = xz/(z+x)
    beat = beat period = xz/(z-x)
    where x comes from row n-1
    and z comes from row n+1
    (and y (not used in the calculation) comes from row n for comparison)

    I suspect that’s probably enough notes to help almost everyone sort this out and make sense of it.

    With each rung in the φ power ladder (as n increases one step at a time) this illustration scales up by the amount illustrated in this simpler illustration.

    We’ve already covered most of this (more vaguely), but what’s clarified here is:
    a) inclusion of (φ+Φ)axial = (√5)axial period in the equivalence criterion.
    b) how Lucas & Fibonacci fall on opposite sides of the same nearest-neighbor φ coin (remember that we’re working our way towards less naive, more clear perception of coupling & aggregation criteria (to be continued)).

    Is it all (or is at least some of it) starting to make a little (or a lot) more sense?

  64. oldbrew says:

    PV: if I look at row 2, the n-1 and n+1 values are rows 1 and 3.

    The number in row 2 is the geometric mean of rows 1 and 3 but the column says ‘axial’?

  65. Paul Vaughan says:

    To repeat:

    =
    working from either of the fundamental columns
    φ^n & “sum of preceding 2, seeded with (1,φ)” (which are equal):
    axial = axial period = xz/(z+x)
    beat = beat period = xz/(z-x)
    where x comes from row n-1
    and z comes from row n+1
    =

    Reminder:
    The series we’re exploring is the following one:

    1
    1.618033989
    2.61803398874989 = 1.61803398874989 + 1
    4.23606797749979 = 2.61803398874989 + 1.61803398874989
    6.85410196624968 = 4.23606797749979 + 2.61803398874989
    11.0901699437495 = 6.85410196624968 + 4.23606797749979
    17.9442719099992 = 11.0901699437495 + 6.85410196624968
    29.0344418537486 = 17.9442719099992 + 11.0901699437495
    46.9787137637478 = 29.0344418537486 + 17.9442719099992
    76.0131556174964 = 46.9787137637478 + 29.0344418537486
    122.991869381244 = 76.0131556174964 + 46.9787137637478
    199.005024998741 = 122.991869381244 + 76.0131556174964
    321.996894379985 = 199.005024998741 + 122.991869381244
    521.001919378725 = 321.996894379985 + 199.005024998741
    842.99881375871 = 521.001919378725 + 321.996894379985
    1364.00073313744 = 842.99881375871 + 521.001919378725
    2206.99954689615 = 1364.00073313744 + 842.99881375871
    3571.00028003358 = 2206.99954689615 + 1364.00073313744
    5777.99982692973 = 3571.00028003358 + 2206.99954689615
    9349.00010696331 = 5777.99982692973 + 3571.00028003358
    15126.999933893 = 9349.00010696331 + 5777.99982692973
    24476.0000408564 = 15126.999933893 + 9349.00010696331
    39602.9999747494 = 24476.0000408564 + 15126.999933893
    64079.0000156057 = 39602.9999747494 + 24476.0000408564
    103681.999990355 = 64079.0000156057 + 39602.9999747494
    167761.000005961 = 103681.999990355 + 64079.0000156057
    271442.999996316 = 167761.000005961 + 103681.999990355
    439204.000002277 = 271442.999996316 + 167761.000005961
    710646.999998593 = 439204.000002277 + 271442.999996316
    1149851.00000087 = 710646.999998593 + 439204.000002277
    1860497.99999946 = 1149851.00000087 + 710646.999998593
    3010349.00000033 = 1860497.99999946 + 1149851.00000087
    4870846.99999979 = 3010349.00000033 + 1860497.99999946
    7881196.00000013 = 4870846.99999979 + 3010349.00000033
    12752042.9999999 = 7881196.00000013 + 4870846.99999979
    20633239 = 12752042.9999999 + 7881196.00000013
    33385282 = 20633239 + 12752042.9999999
    54018521 = 33385282 + 20633239

    All calculations are based on this column (or alternatively the φ^n column which is equal …but if people look at it only that way they may miss Roger Andrews’ key point …and the learning opportunity would be missed).

    If something is still unclear, just say so. This is fundamental.

  66. oldbrew says:

    What does n-1, n+1 refer to? To me it suggests alternate rows but the whole table is based on the sum of consecutive rows.

    If I take row 1 as x and row 3 as z the axial is a number < x, and not one of the numbers listed.

  67. oldbrew says:

    So ‘(φ+Φ)axial’ column / √5 (i.e. φ+Φ) gives the ‘axial’ column value.
    (φ+Φ)axial and geomean columns both return powers of φ.

    Where Earth’s semi-major axis is 1(AU), Venus AU is φ/√5 (99.92% accurate).
    And Mercury’s SMA in AU is close to 1/φ² (98.67%).

  68. Paul Vaughan says:

    Let’s go through a few examples:
    __

    For row n=1:

    axial = (2.618033989)*(1) / (2.618033989 + 1) = 0.723606798
    (φ+Φ)axial = (√5)*(0.723606798) = (2.236067977)*(0.723606798) = 1.618033989
    geomean = √( (1)*(2.61803398874989) ) = 1.61803398874989
    difference = 2.61803398874989 – 1 = 1.61803398874989
    beat = (2.61803398874989)*(1) / (2.61803398874989 – 1) = 1.61803398874989
    φ^1 = 1.61803398874989
    __

    For row n=5

    axial = (17.94427191)*(6.854101966) / (17.94427191 + 6.854101966) = 4.959674775
    (φ+Φ)axial = (√5)*(4.959674775) = (2.236067977)*(4.959674775) = 11.09016994
    geomean = √( (6.85410196624968)*(17.9442719099992) ) = 11.0901699437495
    difference = 17.9442719099992 – 6.85410196624968 = 11.0901699437495
    beat = (17.9442719099992)*(6.85410196624968) / (17.9442719099992 – 6.85410196624968) = 11.0901699437495
    φ^5 = 11.0901699437495
    __

    The key property:
    Different operations give the same result.

    (You can safely bet your house, your family, & your job that most mainstream climate scientists aren’t aware of this, never mind the implications for sampling & aggregation.)

    If it isn’t clear how to successfully do the same calculations for other rows, please say so.

    Regards

  69. Paul Vaughan says:

    Once TB & OB acknowledge that they get this much, we’ll take insight to the next level.
    (We’re not done the lesson yet. We’re only part-way through it.)

  70. oldbrew says:

    ‘Different operations give the same result.’ – aka a formula.

    Yes that’s OK for me.

    Hartmut Warm is on to this to some extent at least. His book is big on golden and silver sections, geometric means, harmonics, pentagons and other geometric shapes, etc. Worth ordering and they’re almost giving it away – or they were when TB and I bought it.

  71. oldbrew says:

    If we say: 5 = φ² * n²
    then: 5 – n = φ² * n
    and: 5 – 2n = √5
    and: 5n = n² + 5
    and: maybe some other stuff too.

  72. oldbrew says:

    Then there are the Pell numbers.

    ‘In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2.’

    ‘In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number and the Pell number before that. The first few terms of the sequence are
    0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, … (sequence A000129 in OEIS).
    http://en.wikipedia.org/wiki/Pell_number

    There are also Pell-Lucas numbers.
    http://en.wikipedia.org/wiki/Pell_number#Pell-Lucas_numbers

  73. Paul Vaughan says:

    “Conversely, notice that if α is rational then this sequence is not equidistributed modulo 1, because there is only a finite number of options for the fractional part of aj = jα. […] However it is known that the sequence {αn} is not equidistributed mod 1 if α is a PV number.”
    https://en.wikipedia.org/wiki/Equidistributed_sequence
    https://en.wikipedia.org/wiki/PV_number

    quadratic & algebraic integers, plastic numbers…

    The Regulator — this is where the lesson goes next:
    https://en.wikipedia.org/wiki/Dirichlet's_unit_theorem#The_regulator

    Math is such a disorganized world conceptually??… Everything’s connected but mathematicians don’t bother constructing a road map. They have a “I know where it is, so that’s good enough” attitude …and perhaps rightly so because their lifetime is too short to even finish exploration (and road-mapping’s orders of magnitude beyond that time-consumption-wise).

    Everyone can do their best to see as many of the sights as possible.
    The Regulator: I think we can at least get everyone that far — at least the basics of it.

  74. Paul Vaughan says:

    The image is from wiki’s roots of unity page.

  75. oldbrew says:

    The red points are the outline of a pentagon.

  76. Paul Vaughan says:

    Yes, the fifth roots of unity define the pentagon in the complex plane. (That’s how I’ve been drawing the pentagons I’ve illustrated in recent weeks.)

    OB suggested:
    “If we say: 5 = φ² * n²
    then: 5 – n = φ² * n
    and: 5 – 2n = √5
    and: 5n = n² + 5
    and: maybe some other stuff too.”

    Better check your algebra there.

    Btw those other series you mention have special properties, but they don’t have the same special beat properties.

  77. Paul Vaughan says:

    n 	Fibonacci 	(φ+Φ)Fib  	log((φ+Φ)Fib,φ)
    0 	0         	0         	          
    1 	1         	2.23606798	1.67227594
    2 	1         	2.23606798	1.67227594
    3 	2         	4.47213595	3.11269603
    4 	3         	6.70820393	3.95528777
    5 	5         	11.1803399	5.01682781
    6 	8         	17.8885438	5.99353621
    7 	13        	29.0688837	7.00246365
    8 	21        	46.9574275	7.99905820
    9 	34        	76.0263112	9.00035962
    10	55        	122.983739	9.99986262
    11	89        	199.010050	11.0000525
    12	144       	321.993789	11.9999800
    13	233       	521.003839	13.0000077
    14	377       	842.997628	13.9999971
    15	610       	1364.00147	15.0000011
    

    n 	Lucas     	log(Lucas,φ)
    0 	2         	1.44042009
    1 	1         	0
    2 	3         	2.28301183
    3 	4         	2.88084018
    4 	7         	4.04377043
    5 	11        	4.98303480
    6 	18        	6.00644375
    7 	29        	6.99753342
    8 	47        	8.00094138
    9 	76        	8.99964031
    10	123       	10.0001374
    11	199       	10.9999475
    12	322       	12.0000200
    13	521       	12.9999923
    14	843       	14.0000029
    15	1364      	14.9999989
    

    n 	φ^n       	log((φ^n),φ)       
    0 	1         	0 
    1 	1.61803399	1 
    2 	2.61803399	2 
    3 	4.23606798	3 
    4 	6.85410197	4 
    5 	11.0901699	5 
    6 	17.9442719	6 
    7 	29.0344419	7 
    8 	46.9787138	8 
    9 	76.0131556	9 
    10	122.991869	10
    11	199.005025	11
    12	321.996894	12
    13	521.001919	13
    14	842.998814	14
    15	1364.00073	15
    

    log((φ^n),φ) = n
    but
    log(Lucas,φ) does NOT exactly equal n (only approximately and converging in limit).
    log((φ+Φ)Fib,φ) does NOT exactly equal n (only approximately and converging in limit).

    On a LOG scale what's an integer is NOT the same.
    (This is what I meant above about φ^n being the more fundamental series.)

    I hope these tables help overcome some of the miscommunications about Fibonacci & Lucas. On a base φ log scale they only approximate integers whereas φ^n hits integers exactly.

  78. oldbrew says:

    PV says:
    OB suggested:
    If we say: 5 = φ² * n²
    then: 5 – n = φ² * n
    and: 5 – 2n = √5
    and: 5n = n² + 5
    and: maybe some other stuff too
    .

    Better check your algebra there.”

    n = 1.381966 or: 3 – φ
    I’ve checked it again. Is there a problem?

  79. Paul Vaughan says:

    TB: JEV is profoundly sensitive (its a total dealbreaker — check the numbers firsthand to see) and completely ruined by any other way of looking at it. I suggest you reconsider “constructal law”. I suggest its much simpler than Bejan seems to contend. It’s not so mysterious as to necessitate conjecture of a consciousness pursuing efficiency.

    φ^n defines the landscape and stuff just rocks around the attractor.
    Why resist this more parsimonious explanation that actually preserves the observed order?

    Maybe in cross-disciplinary exchange its a matter of people not having some missing foundation and I’m not able to identify exactly what key piece of background they’re missing. I don’t know. I just don’t understand the resistance to not only acknowledging the coupling of JEV to the jovians at some instant in time, but also keeping it in mind.

    You know on some level I think people realize it, but then we see again and again considerations of E & V in isolation popping up (as if there’s still an unsolved problem, but there isn’t), so maybe it’s more a matter of people just haven’t finished sorting out their thinking and we’re just observing vacillations back and forth and around due to not-yet-mature fragmented &/or intermittent conceptualization.

    On Milankovitch & higher timescales for example as E & V rock around the attractor they’re sometimes off by enough to hit integer resonance on a NON-log scale, but that does NOT mean they are free to stay there INDEFINITELY. There seems to be a tendency in discussion for some to fixate on time-freeze-frames, but in the long run it’s not integer resonance on a NON-log scale, but rather integer ANTI-resonance on a LOG scale that defines the attractor.

    That’s just geometry — no “constructal law” romantic notions about pursuit of efficiency needed.

    Are we moving towards better mutual understanding? (I hope so.)

  80. tallbloke says:

    Paul, your comment demands a well considered reply, and you’ll get it a few hours from now. Thanks for taking on the conversational discussion.

  81. Paul Vaughan says:

    Roger, I suspect we’re actually in close agreement about how “downhill” is defined as the system rocks around φ. It hits this non-log integer and flow is facilitated this way, but then it rocks arcoss the long-run LOG-integer attractor to the OTHER SIDE and hits another non-log integer and flow goes the other way. And so on. There’s no missing “physics”, just ignorance of geometry. The false assumptions about the central limit are missing from the boundary conditions in the “physical” models (“physics” in quotes because I can’t and won’t regard it as physics if its proponents are insisting on false assumptions about boundary conditions, sampling, & aggregation).

  82. Paul Vaughan says:

    I’ve screwed up my wording there:
    “The false assumptions about the central limit are missing from the boundary conditions in the “physical” models (“physics” in quotes because I can’t and won’t regard it as physics if its proponents are insisting on false assumptions about boundary conditions, sampling, & aggregation).”

    What I meant to say is that the assumptions are false or that the truth is missing. They may get the integration basically right nonetheless as everything washes out in the integral, but they (currently) appear conceptually blind to the central limit at shorter timescales. (Or at least I never see them pointing it out explicitly.) I don’t doubt that this will change in the future. Once they get on the case they’ll go well past where we are.

  83. Paul Vaughan says:

    Refining expression even further: Even if they manage to get the central limit modeled right, they may not recognize its nature (a trivial consequence of geometry). So we shouldn’t conflate model accuracy with conceptual accuracy is what I’m cautioning.

  84. tallbloke says:

    Paul, lets get this one out of the way to start with:

    It’s not so mysterious as to necessitate conjecture of a consciousness pursuing efficiency.

    I agree. I think it’s autonomic. It goes under several names. ‘Principle of least action’, ‘Parsimony of nature’ etc.

    Newton: “Nature is pleased with simplicity, and affects not the pomp of superfluous causes”
    Galileo: “Nature does not multiply things unnecessarily; that she makes use of the easiest and simplest means for producing her effects; that she does nothing in vain.”
    Aquinas: “If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices”

    φ^n defines the landscape and stuff just rocks around the attractor.

    This just begs the question “Why φ ?”. Now, each of us has been inching towards the answer to this question, and recently, you’ve been making giant strides. The rest of us are still catching up, and we thank you for your patient explanation, much of which I for one will need to re-read and re-read again.

    Stuff just rocking around the attractor, whyever it’s φ, is easier to understand. All true systems contain cybernetic feedback, and in meta-stable chaotic systems, everything oscillates either side of the attractor as perturbations push and shove stuff slightly out of equilibrium.

    It seems to me that what you’re saying is things stuff tends to the least perturbative state, which φ represents. I came to a similar conclusion with my “why phi pi slice” post where I showed that φ, in the round, represents the minimum possibility of orbital resonance.

    But I think there’s a danger of misunderstanding in the use of the mathematical and physics term “attractor”. It’s not that stuff is attracted to φ by some mysterious physical ‘force of φ’, but that stuff is pushed towards φ from anywhere else it happens to be, by the real physical force of gravity (not that we know exactly how gravity works!).

    My (admittedly intuitive) hypothesis of how it comes about that the straight-line force of gravity can force stuff towards the φ ‘attractor’ is that gravity acts on stuff in more than one way.

    There’s the straight-line simple force. Then there’s the effects of the orbitally resonant gravitational force. These two scale differentially, and that’s why it is that they can act in concert to push stuff towards a central limit, which is the unresonant φ condition.

    I’ll stop there for now and ask if I’m still on the same page as you are.

  85. tallbloke says:

    Perhaps something fundamental to consider about the conway triangle and its relationship to the power law of gravity is that 2^2=4 and a 2:4 =1:2 geometry establishes the basic outline of the conway triangle. 1:2 in an orbital period ratio also establishes the strongest orbital resonance there can be.

  86. Paul Vaughan says:

    We don’t need any of this ‘Principle of least action’ stuff (that personifies nature, as lazy quite interestingly).

    It’s simpler.

    How many of these are there…
    https://en.wikipedia.org/wiki/Equidistributed_sequence
    …that meet the equivalence criterion?

    The system can only cumulatively alias itself so far out before it goes over a hill and rolls back.

    Tweak it away from the basin of attraction any which way and check (φ+Φ)axial, geometric mean, difference, & beat. You’ll see that whichever way you tweak it there will be an opposite reaction pulling the other way (in centrally limiting aggregate).

    It’s the geometry that does this to the timing.

    I perceive nothing missing in our understanding of the simple physics. Conceptual ignorance of the timing implications of the simple geometry rather is the cultural obstacle.

    In the solar system case once the Hale Core is defined everything else is just coupled to it.

    By western cultural standards it’s vacuously unpalatable. But it is what it is and simple’s what it is.

  87. tallbloke says:

    OK, I’ll chew on that for a day or so. Sleep now, big action day tomorrow.

  88. Paul Vaughan says:

    “The main interest in PV numbers is due to the fact that their powers have a very “biased” distribution (mod 1). […] A characteristic property of PV numbers is that their powers approach integers at an exponential rate. […] The smallest of them is the golden ratio.”https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number

    φ^n miss Lucas by (-Φ)^n
    (φ^n)/(φ+Φ) miss Fibonacci by ((-Φ)^n)/(φ+Φ)

    Lucas = φ^n + (-Φ)^n
    Fibonacci = (φ^n)/(φ+Φ) – ((-Φ)^n)/(φ+Φ) = (φ^n – (-Φ)^n) / (φ+Φ)

    φ^n + (-Φ)^n = Lucas
    φ^n (-Φ)^n = (φ+Φ)Fibonacci

  89. oldbrew says:

    How does the Hale core relate to the duration of the solar cycles (or vice versa)?
    http://en.wikipedia.org/wiki/List_of_solar_cycles

  90. Paul Vaughan says:

    long run central limit

  91. Paul Vaughan says:

    And as I also pointed out on the why phi thread:
    Deviations from that are defined by the SCL (solar cycle length) differintegral.

  92. oldbrew says:

    So the next question might be: what factors determine the length of individual solar cycles?

  93. Paul Vaughan says:

    It’s not a new question. In phase it relates to JEV at multidecadal (~60 year) timescale, but I haven’t stumbled upon any good clues about the amplitude yet.

  94. oldbrew says:

    PV: 37 V-E, 54 J-E and 91 J-V all come in at about 59 years = ~8/3 Hale?
    5 J = 59.313y
    96 V = 59.059y
    7 J+S = 59.193y

    Good match between 1 J+S and 13 J-V: about 99.75%.
    240 J-Merc = 59 years.
    186 E-Merc = 59.01y
    149 V-Merc = 58.974y

  95. oldbrew says:

    Also J-Merc:E-Merc:V-Merc ratio = 161:100:61
    Very close to φ:1:Φ or 8:5:3 in Fibonacci (= 160:100:60)

  96. Paul Vaughan says:

    1 = -(-1) = 0+1 = 1+0

    [ :

    Many ways to say the same thing, for sure.

  97. tallbloke says:

    Many years ago I came to the realisation that the ultimate ‘grand unification theory’ would be expressed in the equation ∑=1+0
    The problem lies in understanding it.🙂

  98. oldbrew says:

    Clues to solar wind variability.

    ‘NASA’s IBEX observations pin down interstellar magnetic field’

    ‘”Voyager 1 crossed the termination shock at 94 astronomical units, or AU, from the sun, and Voyager 2 at 84 AU,” said Zirnstein. One AU is equal to about 93 million miles, the average distance between Earth and the sun. “That difference of almost 930 million miles was mostly explained by a strong, very tilted interstellar magnetic field pushing on the heliosphere.”

    But that difference may be accounted for by considering a stronger influence from the solar cycle, which can lead to changes in the strength of the solar wind and thus change the distance to the termination shock in the directions of Voyager 1 and 2. The two Voyager spacecraft made their measurements almost three years apart, giving plenty of time for the variable solar wind to change the distance of the termination shock.’ [bold added]

    Read more at: http://phys.org/news/2016-02-nasa-ibex-pin-interstellar-magnetic.html

    Termination shock crossing dates
    Voyager 1: Dec. 2004
    Voyager 2: Oct. 2007
    http://en.wikipedia.org/wiki/Interstellar_probe#Existing_interstellar_probes

  99. Paul Vaughan says:

    TB wrote:
    “Many years ago I came to the realisation that the ultimate ‘grand unification theory’ would be expressed in the equation ∑=1+0
    The problem lies in understanding it.🙂 “

    A wise eastern cutie sees no western acuity for vacuity.

    “Thus, experience does not directly provide us with new apprehensions (of universals) or with new knowledge of necessary truths (connections between universals) but acts as a stimulus to remind us of what we already know but have hitherto in this life forgotten.” — Universals, a Historical Survey – http://cutiesome.blogspot.ca/2012/05/universals-historical-survey.html

  100. Paul Vaughan says:

    Another quote from “Universals, a Historical Survey”:

    “By a process of induction, namely intuitive induction, the first primitive awareness of a universal (necessary to any perception) becomes stabilized in the mind, leading ultimately to a clear and articulate concept of it. Thus, for Aristotle, as for Plato, grasp of universals is by the intellect, but it is by the intellect gradually working on what it is at first dimly and indeterminately conscious of in the data of sense perception.

    A simple example from arithmetic will illustrate his point. As children we learn to count. We get the idea of 2 from being faced with pairs of objects, and we learn that 2 + 2 = 4 from coming to “see,” for instance, that two apples plus two other apples are equal in number to four other apples.

    But we also come, sooner or later, to “see” that the number 2 characterizes any pair of objects, and that 2 + 2 = 4 is a necessary truth, applicable to any two pairs compared with a quartet. We have the power, which becomes actualized in experience, of intuiting clearly the universal in the particular and of intuiting the necessary in the matter of fact; this, for Aristotle, is the beginning of scientific knowledge.” (bold added)

    “Plato emphasized this in the analogy of the sun (Republic VI), where he compared the chief Form of all, the Form of the Good, with the sun, which as the light-giving and life-giving agent in the physical world is the prime material cause of natural life as well as of our awareness, through our senses, of the material world.”

    ….and in a cycle we’ve looped right back to where we started (with vukcevic quoting Plato).

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 )

Twitter picture

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

Facebook photo

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

Google+ photo

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

Connecting to %s