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(posting this because of the invitation morning CCC below)
First let me say that you should take anything I say with a grain of salt. I am not a physicist or mathematician. My interest in sphere packing came after Ukrainian mathematician Марина В'язовська published the solution for the sphere-packing problem in 24 dimensional space[^].
With that being said I make the following postulate:
Our Milky Way galaxy (and therefore all other galaxies) appears to be a single object. In other words, the matter outside of the singularity appears to share the same space. The 'extra mass' required to explain the rotational speed is not necessary. You don't need a PhD in mathematics to explore this idea. And apparently I am not the first person to discover this strange property of n-spheres[^].
However I can't find anyone else making the claim that galaxies might be single objects. It only requires two assumptions:
1.) That the particles that make up the atom are moving in higher dimensional space.
2.) That atoms are tightly packed at the maximum density[^] within the singularity at our galactic center.
If that is true then you can use simple geometry to calculate that some of the particles inside the singularity also exist outside of the Schwarzschild radius at our galactic center.
TL;DR:
There is no dark matter. The 'extra mass' required to explain galaxy rotational speed is not necessary. Galaxies appear to be a single objects.
I invite criticism and opinions. But I am leaving in a few minutes and will not be back for several hours.
Best Wishes,
-David Delaune
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Randor wrote: I invite criticism
Your momma was a snow blower!!
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Your mother was a hamster and your father smells of elderberries!
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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The problem with this is that we have plenty of evidence (gravity, electromagnetic radiation, ...) that on the macroscopic level, space-time has 3 space dimensions and 1 time dimension. It is possible that at extremely small scales (much smaller than a proton) there are more space dimensions, but this has yet to be proven.
I have not checked the math in the article that you linked, but even if it is correct - your theory requires that macroscopic objects must have more than 4 dimensions. As I said above, there is no evidence for this whatsoever.
Sorry. 
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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Daniel Pfeffer wrote: your theory requires that macroscopic objects must have more than 4 dimensions.
This doesn't make any sense to me. Could you better describe what you are trying to say?
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One of the theories attempting to explain why gravity is so weak is that at tiny scales, the universe has more than 3 space dimensions. These are not the dimensions that we are familiar with (in which a line may be billions of light-years long), but are tiny (orders of magnitude smaller than a proton). They could only be detected directly with extremely powerful accelerators.
The idea is that while gravity in the macroscopic universe follows an inverse square law, in these tiny dimensions it follows an inverse cube (or higher) law. This means that gravity starts out strong, and gets much weaker before it starts following an inverse square law.
Your idea requires that the universe have more than 3 macroscopic space dimensions, which would mean that (a) gravity, electromagnetic radiation, etc. would follow an inverse cube (or higher) law, and (b) stable planetary orbits, atoms, etc. could not exist.
EDIT: fixed typos
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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Daniel Pfeffer wrote: Your idea requires that the universe have more than 3 macroscopic space dimensions
You are just repeating the same thing without explaining why you believe the extra spatial dimensions would need to be macroscopic. Keep in mind that I am not presenting a physical theory but rather a geometric postulate.
From a geometry perspective the math is correct. The question here isn't whether the mathematics is wrong. I am looking for reasons why it wouldn't represent the physical world.
Btw, other than the recent theory by Sir Roger Penrose (Twister) nearly all of the other GUT are using extra spatial dimensions. So the idea of extra dimensions is not exactly controversial.
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If we look at the exterior spheres in your n-dimensional example, and assuming hyper-spheres of unit radius, the centre of the sphere closest to the origin is at (1, 1, 1, ...). The centre of the sphere diagonally opposite in the hyper-cube is at (3, 3, 3, ...). The distance (assuming a Euclidian space) between the centres is d2 = 22 + 22 + 22 + ... = n * 22.
We have d = 2*n0.5. The largest diameter would be dsphere = 2*(n0.5 - 1), with the largest radius being rsphere = n0.5 - 1. So far, so good.
The hidden assumption is that all dimensions are Euclidean - any line may be extended to any length, only one parallel may be drawn through a point outside a line, etc.
The problem with this is that at the macroscopic (Cosmological) level, the Universe appears to follow General Relativity, which requires a non-Euclidean space-time (3 space dimensions, 1 time dimension). If you add dimensions at the macroscopic level, you must first get rid of General Relativity. Astronomers and physicists are very reluctant to do this, because so far - General Relativity has passed every test thrown at it.
General Relativity fails when dealing with tiny objects, or space-time singularities. Quantum Mechanics rules in the tiny object range. We therefore cannot rule out the existence of additional microscopic (much smaller than a proton) dimensions. It is these microscopic dimensions that may play a part in unifying gravity with the other 3 forces.
In order to unify all forces (GUT), we will have to come up with a theory of Quantum Gravity. While we don't know the exact form that the GUT theory will take, we do know that it must:
- Give General Relativity in the "large mass, no singularity" limit
- Give Quantum Mechanics in the "small mass" limit
- Give new results in the "large mass, singularity" limit (which cannot be explained by either General Relativity or Quantum Mechanics)
"Dark Matter" is indeed a mystery, but I would be very reluctant to throw out all of our current theories just because there is one fact that doesn't fit. I would wait until a theory comes along that explains "dark matter" as well as all the other phenomena explained by our current theories.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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You are doing the same thing once again. You are giving some simple Cartesian math describing the topology of 4-spheres in relation to a tesseract without describing how this relates to your statement that extra dimensions would need to be be macroscopic.
I guess I shouldn't have bothered posting about this on codeproject. 
I should have posted a Haiku instead. 
Need to get some work done today so can't continue on this topic. I'd like to hear more from you if you can assemble something I can understand. You can sometimes find me (in the evenings) in the intellectual dark web on discord and also the Wolfram channel. I am also in the C++ channel on discord.
Best Wishes,
-David Delaune
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What happens when galaxies collide? If the atoms are already packed at the maximum density, wouldn't this create a real big boom? Or maybe they should bounce off each other? 
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When they collide I can envision a lot of options:
- They're mostly empty space and can pass through one another (with gravitational distortions)
- The combined gravitation from both galaxies will cause them to combine into a new galaxy with a new density
Were they composed of charged "star" particles than they could bounce off one another in a manner similar to that in which we give material objects the property of "solid" when in fact they're mostly empty space.
| Ravings en masse^ |
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| "The difference between genius and stupidity is that genius has its limits." - Albert Einstein | | "If you are searching for perfection in others, then you seek disappointment. If you seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010 |
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Marc Clifton wrote: What happens when galaxies collide?
I have absolutely no idea.
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Well, they act like big clumps of smaller items: Antennae Galaxies - Wikipedia[^]
And several dwarf galaxies (such as the Sagittarius Dwarf Spheroidal Galaxy) are currently colliding with the Milky Way and merging with it.
I think that means that the galaxy can only be considered as a single object in aggregate - on a finer scale it's clearly an assemblage of smaller independent objects held together with a "glue" we call gravity, but which seems to be a distortion of "flat" spacetime.
But I'm no astronomer, no large object physicist: it just seems to me that somebody is trying to ignore fine scale objects to make calculations easier (in the same way that ignoring electrons, protons, and neutrons in favour of indivisible atoms does on a smaller scale).
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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Just as an aside:
I stopped smoking that particular stuff some years ago.
| Ravings en masse^ |
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| "The difference between genius and stupidity is that genius has its limits." - Albert Einstein | | "If you are searching for perfection in others, then you seek disappointment. If you seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010 |
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W∴ Balboos, GHB wrote: I stopped smoking that particular stuff some years ago.
But clearly moved on to smoking something else. 
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Randor wrote: There is no dark matter
Lots of alternative theories. Black holes can provide the mass, as well as stars that are made up of nothing but bosons.
Randor wrote: If that is true then you can use simple geometry to calculate that some of the particles inside the singularity also exist outside of the Schwarzschild radius at our galactic center.
"Simple"?
My chilli is, yes. Anything involving gravity isn't, usually.
Randor wrote: 1.) That the particles that make up the atom are moving in higher dimensional space.
Which higher dimensional space? It that theory, math, or something one can prove?
Bastard Programmer from Hell 
"If you just follow the bacon Eddy, wherever it leads you, then you won't have to think about politics." -- Some Bell.
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Eddy Vluggen wrote: Which higher dimensional space? It that theory, math, or something one can prove?
To my knowledge nobody has been able to design an experiment for determining if higher dimensional space exists. The closest thing we've got is the recent discoveries by Dan Shechtman[^] where aperiodic crystals found in nature hint at a possible projection from higher dimensional space.
Dan Shechtman | Quasi-Periodic Crystals - YouTube[^]
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Quote: "Oh freddled gruntbuggly,
Thy micturations are to me
As plurdled gabbleblotchits on a lurgid bee.
Groop, I implore thee, my foonting turlingdromes,
And hooptiously drangle me with crinkly bindlewurdles,
Or I will rend thee in the gobberwarts
With my blurglecruncheon, see if I don't!"
... not you ... wikipedia.
modified 25-Feb-21 12:38pm.
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Hmmm,
Shechtman won the 2011 Nobel prize in chemistry.
I am beginning to see why out of ~22 million software developers in the world only 15 members post regularly in the Lounge.
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Randor wrote: only 15 members post regularly in the Lounge.
Only 15?
I would have said we are at least 35 to 40...  
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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and most probably reach it accidently ...
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OK - today I do that deed (having been fully "prepped") by submitting myself to the whims of a gastroenterologist. I need some advice due to the following observations:
He wears a pith helmet[^] during procedures
There were the heads of several gerbils stuffed and mounted on his wall
I have the feeling he sees his job as gerbil-hunting and am afraid what will happen if he's disappointed.
Special Note to Chris M: I just thought up an enhancement for the "Type" category for here, in the Lounge. The "Too Much Information" selection, along with an appropriate icon of warning.
| Ravings en masse^ |
|---|
| "The difference between genius and stupidity is that genius has its limits." - Albert Einstein | | "If you are searching for perfection in others, then you seek disappointment. If you seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010 |
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Bring a samurai sword and insist on remaining awake during the procedure.
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you actually can stay awake for the procedure. However you will then feel most of the procedure. Depends upon your comfort level with said procedures process. Which would explain the gerbil heads on the walls. HAHAHAHA.
Be prepared to toot your horn for a few days with all the extra air they use to expand the region so they have a better excursion.
To err is human to really elephant it up you need a computer
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