On the computability of the cosmic matter density from first principles by Shawn Halayka

Shawn Halayka

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.

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Shawn Halayka

Equation 5 should be:

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

Shawn Halayka

This was fixed in version 2.0.

Yutaka Shikano

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?

Shawn Halayka

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

Shawn Halayka

P.S. Do you know of a software that does what qhull does, but without the problems of qhull?

Thanks for your guidance.

Shawn Halayka

P.P.S. Or would you know how to compile qhull, and use long double suppport?

Shawn Halayka

P.P.P.S. Where N = 1,100,000, K = 0.284381 +/- 0.136794. Oscillating.

Shawn Halayka

This was fixed in version 2.0.

Shawn Halayka

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

Shawn Halayka

This was fixed in version 2.0.

Manfred Pohl

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

Shawn Halayka

Dear Manfred,

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

- Shawn

Shawn Halayka

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.

- ShawbAttachment #1: 1_2-sphere.png

Shawn Halayka

This was fixed in version 2.0.

Manfred Pohl

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, ManfredAttachment #1: gravity.png

Shawn Halayka

Dear Manfred,

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

- Shawn

Manfred Pohl

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

Shawn Halayka

Dear Manfred,

Alright, well thanks for the notes!

- Shawn

Shawn Halayka

P.S. Replace infinity with some large number, like 1x1020.

Shawn Halayka

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

Shawn Halayka

P.S. The edge length histogram collapses from a wave shape into a single spike shape.

Shawn Halayka

P.P.S. The histogram goes from many bins into one bin.

Shawn Halayka

P.P.P.S. The vertices should repulse, not attract.