Maybe the Universe is a 4 spatial dimension Hypersphere

[Gibsense]

Misunderstanding of n-Spheres
While it's true that the "surface" of an nnn-sphere is an (n−1)(n-1)(n−1)-sphere, the post conflates the mathematical definition of hyperspheres with physical cosmology. A 3-sphere is a higher-dimensional construct with no direct physical analogy to our observable universe's 3D spatial structure.

Interesting opens the door for debate. I don't conflate it. I suggest that there is a whole different way of interpreting the reality of time and space and the 3 sphere is not a suggested analogy but a fact. A cross section of a 3 sphere is a 2 sphere and consequently the mathematics of a sphere are valid (used later). I need to quit to do other stuff right now but will be back as I disagree with much of your response.
I am not trying to describe conventional views here but to point out some alternative and real alternatives. see you later.

 

[Gibsense]

Oh I see Jim has been restricted at this time. Anyway, his response to Hypersphere... was good standard stuff and I was about to try and demolish it. Whatever I think that his recent post deserves to be addressed even if it is a bit cut and paste teaching mode. If Jim remains absent maybe someone else can pick up the veteran's banner.
Just a note for Jim if you still read here:
Some of your responses need updating. For example, earlier you stated that entangled particles were linked at the speed of light. This is not so, they link instantly. Just pointing out that updating is useful.

Misunderstanding of n-Spheres
While it's true that the "surface" of an nnn-sphere is an (n−1)(n-1)(n−1)-sphere, the post conflates the mathematical definition of hyperspheres with physical cosmology. A 3-sphere is a higher-dimensional construct with no direct physical analogy to our observable universe's 3D spatial structure.

What would have been correct is to say "Current cosmology theory does not confirm a 3-sphere is the right model for the shape of the Universe." Note: things move on and a Torus may be a good contender

Undefined Hypersphere Radius
The claim that the radius of a hypersphere is "undefined" is incorrect. In mathematics, the radius of any nnn-sphere is well-defined. The formula - Surface Area=2π2r3 for a 3-sphere demonstrates this. The reference to π.2r is a non-sequitur and applies only to circles, not hyperspheres.

I am trying to describe relationships between 3spheres and 2spheres. In this context "undefined" means that the concept of radius doesn't apply in the way it does for regular spheres in three-dimensional space, that's all. Moving on to some facts:

• It is valid to remove a dimension or two to try to understand how things might work so we drop a dimension from a 3-sphere to a 2-sphere (equivalent to taking a cross-section of a hypersphere). We take a further deduction to illustrate 'on paper' dropping from a 2-sphere to a 1-sphere. That is a cross-section of a 2 sphere is a circle. All members of the same 'family' and a valid procedure
• Dropping dimensions can help us visualize and understand complex shapes like hyperspheres. When you go from a 3-sphere to a 2-sphere, you're just looking at a "slice" of it, e.g. how a circle is a slice of a sphere. We can see relationships and properties in a more relatable way. It breaks down a big problem into smaller, more manageable pieces.

 

[Atlan0001]

Hypercube:

"Menger sponge"
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Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal | Quanta Magazine

Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge.

www.quantamagazine.org

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"Tesseract"
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Tesseract - Wikipedia

en.wikipedia.org

=================

 

[Gibsense]

Conflation of Time and Distance:
Equating one second with 299,792,458 meters conflates units of time and space. This equivalence arises from the speed of light but doesn’t imply they are interchangeable in the way the post suggests. Using time as a "radius" is not physically meaningful without additional justification.

I am not conflating anything; I am stating it as a fact. It lies at the heart of most of my posts and is a basic axiom in most of my suggestions. Quote ex Spacetime Physics by E F Taylor and J A Wheeler: " What used to be understood as a measure of the speed of light is understood today as 2 ways to measure separation in Spacetime." Further statements (chapter 3) talk of the unification of measurements of distance and time.

Obviously care is needed in discussions to avoid misunderstanding and especially where relativity is king. As for additional justification: Reinterpretation of the 'Age of the Universe' as Light Years rather than Years results in a value for the Hubble Constant that matches the current best guess of about 70. It relies on an assumption that the age can be regarded as a radius and our expanding space as a circumference. A simple fact.

 

[Gibsense]

Universe’s Age as Radius:
The claim that the age of the universe can be considered its "radius" is speculative and unfounded. The universe’s scale is described by the scale factor in cosmology, not simply by its age. Furthermore, the concept of the universe as a 2-sphere (implying a 3D surface in 4D space) is a speculative hypothesis, not established science.

Speculative yes. Perhaps a bit more than that - maybe a hypothesis when other people's supportive calculations are taken into account. Many of my posts as Threads are (logical) speculations intended to cause a 'pause for thought' to shake up the atrophied, lol, establishment. ( helping out Penrose's speculation maybe) .

Anyway, the lessons learned here could be transferred to a Torus (in Part)
PS I am surprised you find it so difficult considering the efforts of Timescape Cosmology

 

[Gibsense]

Hubble Constant Calculation:
Using 2πr to estimate the Hubble constant misrepresents its derivation. The Hubble constant is determined empirically by observing the redshifts of galaxies and their distances, not by geometric assumptions about the universe’s shape.

This has already been addressed above. That's the point of Geometry. The shape of the Universe is key to understanding how the Engineering of the Universe works. Disputing a valid input is not a useful teaching mode

 

[Gibsense]

Black Hole Universe Hypothesis:
While some theorists have explored the universe-as-a-black-hole idea, it remains speculative and lacks empirical support. The post leaps to conclusions without providing credible evidence for why this model would explain the observed expansion rate or galaxy formation.

I have never, in the last few years, pretended that the universe is a black hole. i have however suggested that a black hole may cause the birth of a new universe under certain conditions (a White Hole).
Please quote me if you have time and we can sort out the misunderstanding

 

[Gibsense]

Early Galaxies and Local Galaxies:
Observations of high-redshift galaxies show significant differences in structure, size, and composition compared to local galaxies. The post’s claim contradicts well-established astronomical evidence.

Please be a bit more specific. You may be correct in offering this sweeping statement but I cannot tell with this arm-waving statement

 

[Gibsense]

Quantum Mechanics and Cosmology:
The assertion that the ideas solve "quantum mechanic issues" is vague and unsupported. Quantum mechanics and general relativity remain distinct frameworks, and speculative cosmological models do not inherently solve quantum problems without a specific mechanism.

Yes this is true except for the statement implying that only teaching professors can offer up ideas for discussion

 

[Gibsense]

Hypercube:

"Menger sponge"
=================

Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal | Quanta Magazine

Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge.

www.quantamagazine.org

=================

"Tesseract"
=================

Tesseract - Wikipedia

en.wikipedia.org

=================

The Menger Sponge is only vaguely related to Hyperspheres.
The tesseract might apply in the 4D Ball inside a hypersphere in a modified form (perhaps) but I do not think it works for the hypersphere which is 3D (in a 4D embedding space)

 

[Atlan0001]

The Menger Sponge is only vaguely related to Hyperspheres.
The tesseract might apply in the 4D Ball inside a hypersphere in a modified form (perhaps) but I do not think it works for the hypersphere which is 3D (in a 4D embedding space)

They both work for me because I interpret both differently than you do, probably! Just as I interpret the below differently than you have, again probably :

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Riemannian manifold - Wikipedia

en.wikipedia.org

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