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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^ |
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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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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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I remember, in the recovery room six years ago, producing such a blast as to have easily taken down the Walls of Jericho. Strangely odorless. And then it was done.
Many years ago I experienced this without anesthetic. There's an expression used when one has eaten a lot whereby they exclaim "I could bust". That feeling can be real. A definite once-is-too-many experience.
Before long I'll know my weight sans any digestive content. This allows two interesting observations:
- I can actually time the duration of digestion for that first meal afterwards
- At any given moment I can weigh myself and know precisely "Just How Full of It" I am.
| 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 remember, in the recovery room six years ago, producing such a blast as to have easily taken down the Walls of Jericho. Strangely odorless.
They use air to inflate the bowels so they can see more. You're "prepped", so your intestines nearly empty, not much there that can generate smells.
W∴ Balboos, GHB wrote: Many years ago I experienced this without anesthetic
Ditto. They also extracted 12 small pieces to test, by grabbing the instestines with a hook and simply pulling that part out.
Nowadays, before the procedure begins, I get a sedative, a painkiller, a sleep-aid and get strapped to the bed. Legs and hands.
As for the prep; it used to be a small sip of magnesium done easily, and it changed to 2 liters of salt water. The price difference is small, but on a large amount it adds up.
Hope that the results are at least good.
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: small sip of magnesium
Drinking molten metals? They really wanted you cleaned out.
They took three trophies for analysis. Probably a week before I know.
He also said he found a hemorrhoid - thank goodness I'm not a perfect a**hole.
| 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: Drinking molten metals? They really wanted you cleaned out.
Magnesium sulfite, IIRC; not a metal, but a "salt". Is not a salt in my kitchen.
W∴ Balboos, GHB wrote: They took three trophies for analysis. Probably a week before I know.
If something serious, you be told within a day. I'm "checked" every year. Just glad I'm a developer, not an arse-looking doctor. Imagine doing eight of those each day.
W∴ Balboos, GHB wrote: He also said he found a hemorrhoid - thank goodness I'm not a perfect a**hole.
He *found* one? Meaning you didn't even notice if there? They can get rid of those easily, although you do a Monthy Python walk for a day.
Have something good to eat.
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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Well, you said drink magnesium and, since it's a metal, I presumed they melted it so it could be quaffed. MgSO4, commonly called Epsom Salts, is quite different. Eddy Vluggen wrote: Just glad I'm a developer, not an arse-looking doctor. Imagine doing eight of those each day.
In order to relieve the work pressure (a pun?) these guys often have another office next door where they practice dentistry. There is a certain danger if they get confused.Eddy Vluggen wrote: Meaning you didn't even notice if there?
Internal (sneaky little critter). Current recommended treatment: leave it alone.
And all readers will be thankful to know that no gerbils or ferrets were injured during the procedure.
| 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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W∴ Balboos, GHB wrote: Well, you said drink magnesium and, since it's a metal, I presumed they melted it so it could be quaffed. MgSO4, commonly called Epsom Salts, is quite different.
They didn't call it Epsom salt, but magnesium-something. Tasted like lemons, but only required one swallow. Compare that to some liters of seawater.
W∴ Balboos, GHB wrote: these guys often have another office next door where they practice dentistry. There is a certain danger if they get confused.
Dentists; I often joked at both practices how the denstist digs in more bacteria and has a dirtier job than the one doing hemmoroids.
W∴ Balboos, GHB wrote: And all readers will be thankful to know that no gerbils or ferrets were injured during the procedure.
Gerbils can't survive in a colon, despite the claims on Google. They'd suffocate while biting a way out. Both Gerbil and host would be dead in minutes.
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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Epsom Salts = Magnesium Sulfate.
My "stuff" was about 70% Sodium Sulfate and 15% each of Potassium Sulfate and Magnesium Sulfate.
Being an ingredients reader since I learned to read, I looked at the other contents - which included a lemon flavoring and sweetener. I suppose it was more palatable. Just not possible to drink it quickly enough as it seems to fill the mouth, throat, and all, very quickly. Anyway, your stuff tasted like lemon because the lemon'ed it for you.
There really important thing about dentists and proctologists is to never mix up their office locations when in need of their services.
You are mistaken as the gerbils in question were hatched in-situ.
| 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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