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# Dark Energy Related To Golden Mean Values?

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In a set of recent posts I put up on Facebook under various discussion forums, I presented the idea that the amount of dark energy needed to account for acceleration of Hubble expansion might have some relation to the Golden Mean.

That dark energy value, put by some as 1.38x 10^-123, has a numerical coefficient that looks (as far as it goes) for all the world like 2-phi, the latter part being the smaller value of the Golden Mean, 0.618033989...., or (sqrt5-1)/2.   123 is itself a Lucas number, one of the generalized Fibonacci series whose ratios of nearest neighbor terms gives values increasingly close to the Golden Mean.

1.38.... can also be generated approximately using a larger Lucas number divided by the next smaller Fibonacci number (for example 199/144 and so on). Various manipulations of the equations dealing with the Golden Mean seem to show an intimate relationship with base 10 math (if anyone here knows ways to deal with this in other bases I'd be very interested in seeing your work here).

WIth Lucas numbers as 2,1, 3,4, 7,11,18, 29, 47, 76, 123, 199..... and the Fibonacci numbers as 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.... one can align the two series one above the other (Lucas over Fib). If you do this starting with Lucas 2, then 123 is the 11th Lucas term. But one can also upshift Lucas and Fibonacci both so they both start at 1, so the first ratio is 1/1. Then 123 is the 10th Lucas term in the upshifted sequence.

Some years back I had observed that (at least to a first approximation) that the number of dimensions utilized by String Theorists was twice every other Fibonacci number, so starting with 1, 1, 2, 3, 5, 8, 13, 21...., doubling to 2, 2, 4, 6, 10, 16, 26, 42.... we select 2, 4, 10, 26.....

It would be quite amusing if there were something to all this with regard to accelerating Hubble expansion and dark energy....

Jess Tauber

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In a set of recent posts I put up on Facebook under various discussion forums, I presented the idea that the amount of dark energy needed to account for acceleration of Hubble expansion might have some relation to the Golden Mean.

That dark energy value, put by some as 1.38x 10^-123, has a numerical coefficient that looks (as far as it goes) for all the world like 2-phi, the latter part being the smaller value of the Golden Mean, 0.618033989...., or (sqrt5-1)/2.   123 is itself a Lucas number, one of the generalized Fibonacci series whose ratios of nearest neighbor terms gives values increasingly close to the Golden Mean.

1.38.... can also be generated approximately using a larger Lucas number divided by the next smaller Fibonacci number (for example 199/144 and so on). Various manipulations of the equations dealing with the Golden Mean seem to show an intimate relationship with base 10 math (if anyone here knows ways to deal with this in other bases I'd be very interested in seeing your work here).

WIth Lucas numbers as 2,1, 3,4, 7,11,18, 29, 47, 76, 123, 199..... and the Fibonacci numbers as 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.... one can align the two series one above the other (Lucas over Fib). If you do this starting with Lucas 2, then 123 is the 11th Lucas term. But one can also upshift Lucas and Fibonacci both so they both start at 1, so the first ratio is 1/1. Then 123 is the 10th Lucas term in the upshifted sequence.

Some years back I had observed that (at least to a first approximation) that the number of dimensions utilized by String Theorists was twice every other Fibonacci number, so starting with 1, 1, 2, 3, 5, 8, 13, 21...., doubling to 2, 2, 4, 6, 10, 16, 26, 42.... we select 2, 4, 10, 26.....

It would be quite amusing if there were something to all this with regard to accelerating Hubble expansion and dark energy....

Jess Tauber

Pure Crackpottery!

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Call it what you want- the math itself is irrefutable. Or are you ignorant about that?

Jess Tauber

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Call it what you want- the math itself is irrefutable. Or are you ignorant about that?

Jess Tauber

Whatever man, I don't call those nonsense numbers math, as I said before "Pure Crackpottery".

Edited by VictorMedvil
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Here's a link to introduce you, O Great Guru of Stable Geniushood- to the value of 1.38 x 10-123 Planck units: https://medium.com/futuresin/the-number-behind-dark-energy-f1175e20f3b8   The lists of Fibonacci and Lucas numbers are well known, and the dimensional values of 4, 10, and 26 are known to String Theorists. But you must be with our glorious President in knowing better than all these actual specialists working in these areas. Hope you've taken precautions against coronavirus, because IT doesn't give a damn about ideologically-motivated opinions.

Jess Tauber

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Here's a link to introduce you, O Great Guru of Stable Geniushood- to the value of 1.38 x 10-123 Planck units: https://medium.com/futuresin/the-number-behind-dark-energy-f1175e20f3b8   The lists of Fibonacci and Lucas numbers are well known, and the dimensional values of 4, 10, and 26 are known to String Theorists. But you must be with our glorious President in knowing better than all these actual specialists working in these areas. Hope you've taken precautions against coronavirus, because IT doesn't give a damn about ideologically-motivated opinions.

Jess Tauber

Slightly less crank, you see I thought you didn't have any evidence to back this up however it seems you do, so I was wrong, continue. You don't know how many wack-jobs I have heard make claims proving different cranky things. It sounded like a crank conclusion however it seems it wasn't after reading that article. Yes in Planck units it is that.

Edited by VictorMedvil
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Generalized Fibonacci numbers (different series all of which have ratios of nearest neighbor terms converging on Phi) are also well known from studies in biological systems. They deal with growth and packing. At least the growth part might have some connection to accelerating Hubble expansion. Packing, on the other hand, would have to deal with the density of matter and/or dark matter, wouldn't it?  Some years back I had looked at the professionally produced estimates of the relative amounts of these components in the observable universe and had observed that they seemed to fall into another Fib-like sequence. I just can't remember offhand the particulars so will have to reexamine my original findings.

As an aside you might consider amusing, consider the way Fibonacci and Lucas numbers pattern in the PERIODIC TABLE, when they are taken as ATOMIC NUMBERS. Up to 89 inclusive, ALL the Fib atomic numbers map to positions in periods that are leftmost within orbital half-rows. Remember that in orbital filling sequences, all lobes in the orbital must be filled singly before they start to take on partners, producing spin-opposed pairs of electrons per orbital lobe. ALL the ODD Fib atomic numbers map to the leftmost positions of the left half of the orbital row- that is to where there is only a single electron occupying one lobe. And ALL the EVEN Fib atomic numbers map to the leftmost positions of the right half of the orbital row, where there is the first DOUBLET. Up to 89 there are NO exceptions. A hell of a mathematical coincidence, don't you think? And as the next Fib atomic number would be 144, which is unlikely to ever see synthesis, this pretty much covers the entire knowable Periodic Table. One should also note that after 89 all the Fibonacci numbers are also misplaced positionally relative to the orbitals in their periods.

As for the Lucas atomic numbers, on the other hand, THEIR patterning is less perfect. Up to 18 (that is, 2, 1, 3, 4, 7, 11, 18, still a good run), they pattern to RIGHTMOST positions in half orbital rows- that is to either half-filled or completely-filled orbitals. Problems start to occur with copper (atomic number 29). Here the positional mapping is one left of where it needs to be, and ideally (from the way the PT has its electronic configurations laid out positionally within periods) it SHOULD have a d9 configuration (10 electrons filling the d orbital completely). But in actuality it HAS a d10 configuration. It does this by internally abstracting one s electron from a filled (s2) orbital and moving it to the nearly filled d orbital, which is more stable (lower energy configuration). Thus it DOES preserve the Lucas atomic number trend configurationally even though the mapping is off positionally within the Periodic Table itself. And then 47 (silver), the system uses exactly the same sort of 'fix'- an internal abstraction of one s electron and reassignment to the d orbital. 76, osmium, would under the above schemes fit the FIBONACCI atomic number pattern, since it has a d6 configuration. But in its monatomic gaseous state osmium is well known to present highly reduced chemical reactivity, nearly as much as an actual noble gas such as xenon, which has a p6 configuration. d6 vs. p6. Almost 'as if' the orbital itself were being reinterpreted in some way.   It is also interesting that while the positional mappings within periods of copper and silver are moved one step left of where they *should* be for orbital filling, osmium is actually one step RIGHT of where it should be (though copper and silver, with odd Luc atomic numbers, ideally should be at the end of the FIRST half orbital, not the second). In generalized Fibonacci sequences there are always TWO odd numbers for every even- (1,1,2)(3,5,8 )(13,21,34)(55,89,144)... and so on for Fib, and then (2,1,3)(4,7,11)(18,29,47)(76,123,199)... and so on for Luc. Note that the even term comes at the right side of the triplet for Fibonacci numbers, and at the left side of the triplet for the Lucas numbers. I have wondered whether there is something about this that has affected the anomalous Lucas atomic number patterning after 18.

Jess Tauber

Edited by pascal
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OK- so one online source lists the components of our visible universe as approximately 68% dark energy, 27% dark matter, and less than 5% normal matter. I'm not sure how the latter is segregated into normal matter versus energy.  Well 68 is twice 34, a Fibonacci number. And 27 is one more than 26, twice the Fibonacci number two moves back in the sequence (similar in execution to using every other doubled Fibonacci number in DIMENSIONAL specifications in String Theories). So extending this pattern logically backwards we would have 2, 4, 10, 26, 68.... for dimensions, and similarly for relative proportions of components in terms of percentages. I don't see any relation before 26, but perhaps there's something we haven't accounted for? And where does the @5% normal matter fit in here?

Jess Tauber

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OK- so one online source lists the components of our visible universe as approximately 68% dark energy, 27% dark matter, and less than 5% normal matter. I'm not sure how the latter is segregated into normal matter versus energy.  Well 68 is twice 34, a Fibonacci number. And 27 is one more than 26, twice the Fibonacci number two moves back in the sequence (similar in execution to using every other doubled Fibonacci number in DIMENSIONAL specifications in String Theories). So extending this pattern logically backwards we would have 2, 4, 10, 26, 68.... for dimensions, and similarly for relative proportions of components in terms of percentages. I don't see any relation before 26, but perhaps there's something we haven't accounted for? And where does the @5% normal matter fit in here?

Jess Tauber

Is it not more likely any numerical relationship is a coincidence ?

I am having a slow day what is phi, supposed to represent? How does a golden mean https://en.wikipedia.org/wiki/Golden_mean_(philosophy) even link into maths.

Edit I wouldnt bank on dark matter existing to prove your theory.

Edited by Flummoxed
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https://en.wikipedia.org/wiki/Golden_ratio

This is essentially the simplest possible recursive relationship, referring only to itself (and thus needing no prior referent- which comes in handy if your universe is starting from nothing),

Jess Tauber

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Today I was reminded that in 10-dimensional String Theory there is 1 time dimension, 3 extended spatial dimensions, and 6 compactified dimensions. Well, it is probably as meaningless as the every-other-doubled Fibonacci number of dimensions across String Theories, but the sequence of 1, 3, 6... consists of the first three terms of the TRIANGULAR NUMBERS.

Jess Tauber

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Today I was reminded that in 10-dimensional String Theory there is 1 time dimension, 3 extended spatial dimensions, and 6 compactified dimensions. Well, it is probably as meaningless as the every-other-doubled Fibonacci number of dimensions across String Theories, but the sequence of 1, 3, 6... consists of the first three terms of the TRIANGULAR NUMBERS.

Jess Tauber

T5he nu5mbers 0,1,2,3,4,5,6,7,8,9,0 are what we u5se for coun5t5ing . T5here is no myst5ery, Perhap5s t5he only myst5ery i see t5his mori=ning is why my nu5mber  five key is st5u5ck. New keybpo5ard req5u5ired?

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I can't remember whether you were also down on earlier posts I put up about how Pascal Triangle combinatorics operate with atomic nuclear and electronic shells. Its easy to shoot people down when you haven't got a clue- witness our President going out of his way to shut the pandemic response team a couple of years back, yet now blaming the Dems (and especially Obama) for the crisis now that he finally was forced to admit it actually is a crisis- one that 'some miracle' isn't likely to happen for. We have a viral pandemic sweeping the world- but we also have a long-standing epidemic of self-satisfied ignorance. But you are entitled to your opinion. Just remember though that the Pascal Triangle can be used to generate the Golden Mean, pi, the base of the natural logarithm e, and lots of other stuff. The universe doesn't give a damn about personal biases against numerical patterning- in a few years we'll all be equally dead.

Jess Tauber

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I am having a slow day what is phi, supposed to represent? How does a golden mean even link into maths.[?]

Among other things, the ratio is a feature in the geometry of a pentagram and geometry is a discipline of mathematics ala Descartes.

https://en.m.wikipedia.org/wiki/File:Pentagram-phi.svg

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You can get + or - half the larger or smaller Golden Ratio (so 0.618033989 or 1.618033989, which are also respectively (sqrt5-1)/2 and (sqrt5+1)/2) using polygons of ANY multiple of 18 degrees, either under sines or cosines of these angles (alternatively) in a repeating pattern. The Pentagon is just the most popular one.

Jess Tauber

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Let phi (lower case p)=0.618033989... and Phi (upper case p)= 1.618033989.... Then...

sin     0=  0, cos     0=1

sin   18= phi/2

cos  36= Phi/2

--------------------

sin   54= Phi/2

cos  72= phi/2

for the first quadrant of the circle

sin  90= 1, cos 90= 0

cos 108= -phi/2

sin  126=  Phi/2

--------------------

cos 144= -Phi/2

sin  162=  phi/2

for the second quadrant of the circle

sin  180= 0, cos  180= -1

sin  198= -phi/2

cos 216= -Phi/2

sin  234= -Phi/2

cos 252= -phi/2

for the third quadrant of the circle

sin  270= -1, cos  270= 0

cos 288=  phi/2

sin  306= -Phi/2

cos 324=  Phi/2

sin  342= -phi/2

for the fourth quadrant of the circle.

Note the highly symmetrical layout of the + or - values, of phi versus Phi, and of the use of the sines versus the cosines.

A further note-  The Pascal Triangle's generation of the Golden Mean/Ratio/Section by first summing shallow diagonal terms and then taking ratios between successive resultant Fibonacci numbers has interesting parallels in the decimalizations of the shallow diagonal terms.

To produce a decimalization you take successive terms from some straight-line relation in the Pascal Triangle and pattern them so that each successive number is at a further negative (or where relevant positive) power of ten.  For example the ROWS of the Pascal Triangle have terms 1 (apex), 11, 121, 1331, and so on. These are also (if one allows for summing when digits cover more than one power of ten) POWERS OF 11. The ratios of any successive decimalization will always be exactly 11.

Decimalization of the side-parallel diagonals (only as a decimal value, since otherwise strings grow out of control) yields ratios of successive decimalizations that are always exactly 9.

But the shallow diagonal terms also decimalized yield ratios that are 5+sqrt35.  And the column terms give decimalizations whose ratios are 5+sqrt15.

I worked all this out on paper using nothing more than a hand calculator a decade ago.

Now the square of the Golden Ratio 1.618033989... simply adds 1, yielding 2.618033989....  The reciprocal of 1.618033989... is 0.618033989....

Interestingly, if you start with 5+sqrt35, or 10.91607878  and take its reciprocal, you get 0.091607978...  In other words if you multiply the reciprocal by 10 and add 10 you get the original term. Then the SQUARE of the original term is 119.1607978....

And if you start with 5+sqrt15, or 8.872983346 and square IT, the result is 78.72983346.   The reciprocal of 5+sqrt15 is 0.112701665, and ITS square is 0.012701665...

The relations are a bit more complex than those of the Golden Ratio, but clearly are related.

The reciprocal of 2-phi, or 1.381966011 is 0.7236067978..., and so it looks like it is related in some way to 5+sqrt35.

Finally, 35 is one less than 36, the square of 6. and 15 is one less than 16, the square of 4. One can recast 11 (ratios of successive decimalizations of Pascal Triangle rows) as 5+sqrt36, and 9 (ratios of successive decimalizations of Pascal Triangle side-parallel diagonals) as 5+sqrt16. These recastings then link the columns and side-parallel diagonals of the Pascal Triangle on the one hand, and the rows and the shallow diagonals on the other.

It all hangs together.

Jess Tauber

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Now, consider the relative proportions supposedly making up the known (and unknown) universe: 68% dark energy, 27% dark matter, and 5% normal matter (but is normal energy subsumed under normal matter?)

68 is 2x 34 (Fibonacci), 27 is 2x 13 (plus one), and 5 is 2x 2 (plus one). The sequence of every other doubled Fibonacci number is 2, 2, 4, 6, 10, 16, 26, 42, 68...And with the relative proportions of components of the universe we have 2, 4, 10, 26, 68..., which match for the most part the dimensions of the universe as proposed by String Theories.

There are two discrepencies- first up to 68, the total sum is 110, not 100. The second is that 10 is missing from the components list, which is why the total sum is 100 and not 110. So perhaps there is something else that we're not taking into account.

I mentioned at the top that the 5% doesn't say anything about normal energy, just mass. At least from the published sources I've seen online. Is THAT the missing 10%?

Jess Tauber

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