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RECENT POSTS IN THIS TOPIC

Shawn Halayka: on 5/8/20 at 23:33pm UTC, wrote Jonathan! Glad to hear from you. Well, I submitted a similar paper to...

Jonathan Dickau: on 5/8/20 at 23:13pm UTC, wrote I like what you have written Shawn... You have presented an interesting...

Steve Dufourny: on 4/5/20 at 19:49pm UTC, wrote Hi, Ok thanks,I will tell you if necessary , I don t know if I will do it ,...

Shawn Halayka: on 4/4/20 at 17:56pm UTC, wrote Well, if you do write an essay, please make sure that it has lots of...

Steve Dufourny: on 4/4/20 at 17:50pm UTC, wrote For the essay, I don t know, maybe I will do it, I have some ideas but I am...

Steve Dufourny: on 4/4/20 at 17:42pm UTC, wrote You are welcome, not really ,3D spheres mainly and we can play in maths...

Shawn Halayka: on 4/4/20 at 17:17pm UTC, wrote P.S. Do you have an essay submission? I can't find you on the page.

Shawn Halayka: on 4/4/20 at 17:15pm UTC, wrote Dear Steve, Thanks again for your words. When you say sphere, you're...


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FQXi FORUM
September 19, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: On the computability of the cosmic matter density from first principles by Shawn Halayka [refresh]
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Author Shawn Halayka wrote on Mar. 9, 2020 @ 22:45 GMT
Essay Abstract

The tessellation of space is considered for the 3-sphere. It is found that there is a matter density $Omega_M = 0.284$ associated with the curvature of the 3-sphere.

Author Bio

Artist and computer software developer.

Download Essay PDF File
Note: This Essay PDF was replaced on 2020-03-19 22:21:26 UTC.

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Author Shawn Halayka wrote on Mar. 10, 2020 @ 01:07 GMT
Equation 5 should be:

K = frac{1}{T} sumlimits_{i=1}^{T} k_i = frac{k_1 + k_2 + ... + k_T}{T}.

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Author Shawn Halayka replied on Mar. 20, 2020 @ 15:27 GMT
This was fixed in version 2.0.

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Yutaka Shikano wrote on Mar. 10, 2020 @ 01:16 GMT
You computed the value as N = 10,000 K = 0.28821, N = 100,000 K= 0.28413, N = 1,000,000 L = 0.28452. However, from N = 100,000 to 1,000,000, the value of K is increasing. Therefore, I could not follow your logic on the finite size scaling $lim_{N to infty} K (N) = 0.284$. Would you tell us the details of your logics?

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Author Shawn Halayka replied on Mar. 10, 2020 @ 01:29 GMT
Dear Yutaka,

Thank you for sharing your thoughts.

To be honest, qhull does not support N larger than 1,000,000. I would not say that it's simply increasing, but more like oscillating.

Even if my number is off, there is still some curvature K, and there is a matter density associated with it.

I hope I've answered your question.

- Shawn

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Author Shawn Halayka replied on Mar. 10, 2020 @ 01:32 GMT
P.S. Do you know of a software that does what qhull does, but without the problems of qhull?

Thanks for your guidance.

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Author Shawn Halayka replied on Mar. 10, 2020 @ 02:04 GMT
P.P.S. Or would you know how to compile qhull, and use long double suppport?

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Author Shawn Halayka wrote on Mar. 10, 2020 @ 02:42 GMT
It occurred to me that this curvature leads to just dark matter. Regular matter is above and beyond dark matter. The rest is dark energy.

- Shawn

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Author Shawn Halayka replied on Mar. 20, 2020 @ 15:28 GMT
This was fixed in version 2.0.

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Manfred U.E. Pohl wrote on Mar. 11, 2020 @ 15:23 GMT
Dear Shawn Halayka,

looks nice. It is not coincidene. I tink it must lead to something ocillating.

As my ToE 12*pi*c^3=1^2 (mapping 2D to 3D-time) is about 0,298233... it is a representation of a ocillation that "looks" like random but is not (if we know how to calculate PI)

Best regards

Manfred U.E. Pohl

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Author Shawn Halayka replied on Mar. 11, 2020 @ 15:36 GMT
Dear Manfred,

Thanks for sharing your observations, and for your confidence that this is not simply a coincidence.

- Shawn

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Author Shawn Halayka wrote on Mar. 15, 2020 @ 17:24 GMT
I've attached a screenshot of a 2-sphere tessellation made out of triangles.

I do effectively the same thing with the 3-sphere tessellation made out of tetrahedra. Once I have the tessellation, I calculate curvature based on neighbouring tetrahedra.

- Shawb

attachments: 1_2-sphere.png

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Author Shawn Halayka replied on Mar. 20, 2020 @ 15:29 GMT
This was fixed in version 2.0.

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Manfred U.E. Pohl wrote on Mar. 15, 2020 @ 21:11 GMT
Dear Shawn,

i am not sure about the final notation on how to calculate cosmos in Pythagoras style. But effectivly there should be two tessellation-3d-volume spheres in equilibrium of force (surface*surface/distance)

a try attached..

Best, Manfred

attachments: gravity.png

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Author Shawn Halayka replied on Mar. 15, 2020 @ 23:02 GMT
Dear Manfred,

Can you please explain in greater detail how this applies to my model?

- Shawn

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Manfred U.E. Pohl wrote on Mar. 16, 2020 @ 08:41 GMT
i try,

- we talk about cosmic matter denisty

- i don't work with 1,0,1,0,1.. but with 1,-1,1,-1,1..

(coulomb : to each charge -1 must be a charge +1 in universe)

flow of information (m/s (1/-1))

=>

12 pi c^3=1 => c[meter/second] = 0,298233409... (1st constant)

fine structure - constant = 1/137,63 [meter / second] (2nd constant)



(0,298233409..-0,2845...) * 10^-4 = would be approx. fine - structure-constant (mine is 1/137,63)

(my correction factor is 10^4 to project stream of information from one dimension into 4 dimension)

but in detail i can't tell regarding your lim K->infinity N , as i don't have the concept of infinity in my mathematic and i didn't ready your code in detail.

best, manfred

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Author Shawn Halayka replied on Mar. 16, 2020 @ 15:36 GMT
Dear Manfred,

Alright, well thanks for the notes!

- Shawn

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Author Shawn Halayka replied on Mar. 16, 2020 @ 16:02 GMT
P.S. Replace infinity with some large number, like 1x1020.

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Author Shawn Halayka wrote on Mar. 16, 2020 @ 17:23 GMT
It occurred to me that there is some kind of collapse:

The pseudorandomly-placed vertices gravitate, and so their tetrahedra become as regular as possible.

- Shawn

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Author Shawn Halayka replied on Mar. 16, 2020 @ 17:29 GMT
P.S. The edge length histogram collapses from a wave shape into a single spike shape.

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Author Shawn Halayka replied on Mar. 16, 2020 @ 17:31 GMT
P.P.S. The histogram goes from many bins into one bin.

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Author Shawn Halayka replied on Mar. 18, 2020 @ 17:22 GMT
P.P.P.S. The vertices should repulse, not attract.

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Author Shawn Halayka wrote on Mar. 19, 2020 @ 16:37 GMT
I made a short PDF about the collapse of the system-wide edge length histogram:

Link

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Author Shawn Halayka wrote on Mar. 19, 2020 @ 22:21 GMT
Shawn Halayka re-uploaded the file Halayka_bezier_escape.pdf for the essay entitled "On the computability of the cosmic matter density from first principles" on 2020-03-19 22:21:26 UTC.

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Author Shawn Halayka wrote on Mar. 20, 2020 @ 01:08 GMT
The essay has been replaced.

The new title is 'On the computability of the cosmic dark matter density from first principles'.

The new abstract is 'The tetrahedral tessellation of space is considered for the 3-sphere. It is found that there is a dark matter density $Omega_{DM} = 0.284$ associated with the curvature of the 3-sphere.'

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Paul N Butler wrote on Mar. 22, 2020 @ 00:41 GMT
This is a copy of my comment to you in response to your comment to me on my paper’s site on Mar. 16, 2020.

Dear Shawn,

I looked at your paper and in it you express a desire to understand the density of dark matter. I presently concentrate on the structure of normal matter and once that is understood it is then possible to get an understanding of what is actually being detected and...

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Author Shawn Halayka replied on Mar. 22, 2020 @ 00:58 GMT
Dear Paul,

Thank you so much for reading my paper, and for sharing your thoughts.

I will read your post again and again until I fully understand it. Once I understand, I'll send you a reply. :)

- Shawn

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Paul N Butler replied on Mar. 23, 2020 @ 01:32 GMT
This is a copy of my comment to you in response to your comments to me on my paper’s page on Mar. 22, 2020.

Dear Shawn,

I looked at the papers at the link that you provided to me, but they did not mention time. They were all different iterations on the topic “The curvature and dimension of a closed surface”.

I may be somewhat familiar with the “light clock experiment”, but tell me how you understand it to be done and the outcome results and your interpretation of what the results tell us.

With Love,

Paul

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Paul N Butler replied on Mar. 24, 2020 @ 22:55 GMT
This is a copy of my comment to you in response to your comments to me on my paper’s page on Mar. 23, 2020.

Dear Shawn,

It is true that there was no time at the beginning of the universe because time is a measure of motion through a distance (D= MT, Where D= distance, M= motion content or speed, and T=time, so, T=D/M. Instead of using a rate such as D/T like miles per hour, which...

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Steve Dufourny wrote on Apr. 3, 2020 @ 14:34 GMT
Hello Mr Halayka,

Interesting that you speak about the spheres, you could like my theory of spherisation, an optimisation evolution of the universal sphere or future sphere with coded 3D quantum spheres and cosmological spheres, don t hesitate to ask details, I have improved a lot my theory since more than 10 years and mainly here on FQXi, I have shared it on Facebook also. I formalise all this puzzle with the mathematics also that I study all Days. These 3D spheres, spheroids, ellipsoids seem foundamental at all scales and it become relevant when we superimpose 3 E8 with finite series of 3D spheres replacing the points or strings of the geometrical algebras, one main coded E8 for the vacuum space, and the two others for the fuelds if I can say, the photons and the Dark matter cold, that permits to create all geonetries, topologies, properties of matters with the poincare conjecture, the lie derivatives, the thurston geometrisation conjecture, the Ricci flow, the Hamilton Ricci flow, the assymetric Ricci flow that I have invented for the unique things, the topological and euclidiam spaces, this and that in maths. The deformations of 3D spheres seem relevant like their properties , angles, senses of rotations, densities, volumes, motions, moments, this and that, we can rank them when we consider specific finite series at this planck scale, coded having the same finite number than our cosmological spheres, they play between the zero absolute and the planck temperature for me and they distribute in function of coded insider the particles, see the difference with the strings at this planck scale and the 1D main Cosmic field creating the physicality, I dont consider that all is Waves but that the codeds are inside the particles in a superfluid aether gravitationa vacuum, the Waves particles duality is respected also because they oscillate and are in a superfluid in contact.

Regards

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Author Shawn Halayka replied on Apr. 3, 2020 @ 14:57 GMT
Dear Steve,

Thank you for your comments.

I'm not really familiar with the mathematics of which you speak. I'm afraid that I"m at a loss for words about some of the more complicated maths that you write about. :(

In any case, thanks again for reading my essay. I really appreciate it.

- Shawn

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Steve Dufourny replied on Apr. 3, 2020 @ 16:39 GMT
You are welcome,

these Tools are not very complicated generally. The E8 is an exceptional Lie Group, you can see its geometry on internet, it is relevant. It is a geometrical algebras in fact and a good tool to rank. It is utilised in strings theory also and for the geometrodynamics with points, they permit to better understand the topologies and geonetries.

The poincare conjecture...

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Author Shawn Halayka replied on Apr. 3, 2020 @ 20:52 GMT
Hi Steve,

Thanks for your enlightening words. I am interested in these things that you talk about. Why a sphere? Why not a string; isn't that what string theorists do is make sure that a particle has some extent at the most fundamental level?

This is kind of what my model is. If the string is of the Planck scale in diameter, then the waves upon that string must be sub-Planckian. My math is good for modelling these waves, because my model is specifically designed to tessellate sub-Planckian detail.

- Shawn

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Jonathan J. Dickau wrote on May. 8, 2020 @ 23:13 GMT
I like what you have written Shawn...

You have presented an interesting result that proves something relevant to the essay question. But the connection is abstruse. The significance might pop out for Renate Loll or Lee Smolin, but most people would miss it. So given that you did not build a stronger bridge between early universe stuff and uncertainty or unpredictability in the current era, nor did you explain why that significance might be model-independent; I can only give you partial credit.

A good exposition for what you did set out, in any case.

Warm Regards,

Jonathan

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Author Shawn Halayka replied on May. 8, 2020 @ 23:33 GMT
Jonathan! Glad to hear from you. Well, I submitted a similar paper to Foundations of Physics, but it was rejected. C'est la vie.

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