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Tallbloke will snow in the UK in early March.

http://earth.nullschool.net/#2016/03/02/0300Z/wind/isobaric/500hPa/overlay=temp/orthographic=-348.60,54.17,1201

In Europe, the winter will not end soon.

The sun getting quieter.

Atlantic getting colder.

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

Sorry.

http://ocean.dmi.dk/arctic/icecover.uk.php

The expected further strong rise in temperature in the stratosphere. The graph shows temperature jump after a decline in solar activity.

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— The Doors 5:1May take a week and it may take longer

They got the guns but we got the numbers…”

“Your ballroom days are over baby, night is drawing near…”— The Doors – Five to OneAt first flash of Eden

We race down to the sea

Standing there on

Freedom’s shore

Waiting for the sun

“Five to one, baby

One in five

No one here gets out alive, now”

“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

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.

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.

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/

Got that?

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

“The Connolley Problem, pt 3: A Time Span Problem”

http://gelbspanfiles.com/?p=3603

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

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

5tiles per1scale stepwhen the

middle classbridges 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

…and of course Roger Andrews was right — it’s

5:1no 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!)Lucas numbers are all combinations of two alternate Fibonacci numbers e.g.

7 = 5 + 2

11 = 8 + 3

18 = 13 + 5

etc.

Josh should do a cartoon with the theme: red taped

to deathby joy-deprived administrative framingFlo Rida gives a lesson in harmonious entertainment…

Exploring the beauty of nature should be

less administrativeand 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)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 casefrom theinfinite set of possibilitieslike Roger Andrews wisely emphasized.φ’s defined by

the relationship with neighbors(for ANY starting pair — no matter how ordered).(φ+Φ)^2 = 5That’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

thisLucas sings the tune that’s on my mind today…“They’ll be screamin’ at me ‘fore I even hit5.”“They don’t wanna hear no speech… been a long week… no time for no talkin’…”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

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

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.

Hmm…

So you think you can use a

quadratto aggregate fully-informative samples from apinwheeltiling 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_theoremFinally! After all these years — at long last: We’re venturing into the

politically-forbiddenterritory where the“sufficient condition”isNOTmet. (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

integerseeds OB?(Φ,1) & (1,φ) converge on and stabilize atexactly5instantly.(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!)

[ :

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

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).

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

‘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 😉

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.

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).

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 helps2+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.

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

fulldetail (withnumbers rather thancryptic algebra no less), Fib isnotthe fastest converger.Series commencing with the seeds (Φ,1) & (1,φ) converge on and stabilize at

exactly5instantly. (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 exactconvergence. What the heck isn’t clear about that? (another genuine honest question; no sarcasm)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

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

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

differencebetween 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 propertyin the limitas n goes to infinity.)Noteworthy: The sequence of axial periods of richer & poorer Lucas neighbors converges to Fib.

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

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

Only Phi can claim its square equals itself plus one.

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.

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?

‘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

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.

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

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

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

Earth & Venus are coupled (

accidentalmisinterpretations 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!

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/

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?

It’s a bit too abstract for me.

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?

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

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

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

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

criticallyonblindaudience buy-in to thealways well-hiddenuniformity assumption. They never address it squarely. They just evade. They pretend the physics can be realistically conceivedwithoutattention 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.

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

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’.

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

TB: ‘Four JS axial is ~(8 x phi³)’

That would make 1 J-S axial = ~2 x phi³.

(5 V-E = ~8 years)

http://earthsky.org/space/why-space-bodies-come-in-different-sizes

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.

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 joviansin 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

wholeright demands attention tolimits & 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

simpletable 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

falseassumptions (hence the quotation marks in “physical”) about boundaries & limits).The image that summarizes the table is this one.

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

One more try…

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?

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’?

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:

11.6180339892.61803398874989= 1.61803398874989 + 14.23606797749979= 2.61803398874989 + 1.618033988749896.85410196624968= 4.23606797749979 + 2.6180339887498911.0901699437495= 6.85410196624968 + 4.2360679774997917.9442719099992= 11.0901699437495 + 6.8541019662496829.0344418537486= 17.9442719099992 + 11.090169943749546.9787137637478= 29.0344418537486 + 17.944271909999276.0131556174964= 46.9787137637478 + 29.0344418537486122.991869381244= 76.0131556174964 + 46.9787137637478199.005024998741= 122.991869381244 + 76.0131556174964321.996894379985= 199.005024998741 + 122.991869381244521.001919378725= 321.996894379985 + 199.005024998741842.99881375871= 521.001919378725 + 321.9968943799851364.00073313744= 842.99881375871 + 521.0019193787252206.99954689615= 1364.00073313744 + 842.998813758713571.00028003358= 2206.99954689615 + 1364.000733137445777.99982692973= 3571.00028003358 + 2206.999546896159349.00010696331= 5777.99982692973 + 3571.0002800335815126.999933893= 9349.00010696331 + 5777.9998269297324476.0000408564= 15126.999933893 + 9349.0001069633139602.9999747494= 24476.0000408564 + 15126.99993389364079.0000156057= 39602.9999747494 + 24476.0000408564103681.999990355= 64079.0000156057 + 39602.9999747494167761.000005961= 103681.999990355 + 64079.0000156057271442.999996316= 167761.000005961 + 103681.999990355439204.000002277= 271442.999996316 + 167761.000005961710646.999998593= 439204.000002277 + 271442.9999963161149851.00000087= 710646.999998593 + 439204.0000022771860497.99999946= 1149851.00000087 + 710646.9999985933010349.00000033= 1860497.99999946 + 1149851.000000874870846.99999979= 3010349.00000033 + 1860497.999999467881196.00000013= 4870846.99999979 + 3010349.0000003312752042.9999999= 7881196.00000013 + 4870846.9999997920633239= 12752042.9999999 + 7881196.0000001333385282= 20633239 + 12752042.999999954018521= 33385282 + 20633239All calculations are based on this column (or alternatively the φ^n column

which is equal…but if people look at itonlythat way theymay missRoger Andrews’keypoint …and the learning opportunity would be missed).If something is still unclear, just say so. This is fundamental.

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.

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%).

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

Once TB & OB acknowledge that they get this much, we’ll take insight to the

nextlevel.(We’re not done the lesson yet. We’re only part-way through it.)

‘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.

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.

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

“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

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

The red points are the outline of a pentagon.

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 * n²then: 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.

log((φ^n),φ) = n

but

log(Lucas,φ) does NOT

exactlyequal n (only approximately and converging in limit).log((φ+Φ)Fib,φ) does NOT

exactlyequal 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.

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?

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

observedorder?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 thereisn’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.)

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.

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).

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.

Refining expression even further: Even if they manage to get the central limit modeled right, they may not recognize its nature (a

trivialconsequenceof geometry). So we shouldn’t conflate model accuracy with conceptual accuracy is what I’m cautioning.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.

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.

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.

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

“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_numberφ^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 = Lucasφ^n

–(-Φ)^n = (φ+Φ)FibonacciHow does the Hale core relate to the duration of the solar cycles (or vice versa)?

http://en.wikipedia.org/wiki/List_of_solar_cycles

long run central limit

And as I also pointed out on the why phi thread:

Deviations from thatare defined by the SCL (solar cycle length) differintegral.So the next question might be: what factors determine the length of individual solar cycles?

http://www.sonicwater.org/sonicwater.html

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.

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

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)

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

[ :

Many ways to say the same thing, for sure.

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. 🙂

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 thevariable solar windto 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

TB wrote:

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

A wise eastern cutie sees

no western acuityfor 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.htmlAnother 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(bold added)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 thematter of fact; this, for Aristotle, is the beginning of scientific knowledge.”“Plato emphasized this in the analogy ofthe sun(Republic VI), where he comparedthe chief Form of all, the Form of the Good, with the sun, which as thelight-giving and life-giving agentin the physical world isthe prime material causeof 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).