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Why space has exactly three dimensions

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"THE ONLY way is up." An earnest student of our physical realities might find room to dispute this jollying phrase. There is also down, and, for that matter, left, right, forwards and backwards. Six ways to go. Then again, the further up you go, the less down you are, and similarly for left and right, forwards and backwards. So that's three independent directions to move in – gravity and local obstacles permitting.

It is a fact so bald that we rarely stop to ask an even balder question: why?

Physicists have wrestled with this perplexing question of space's essential three-ness for a good while now – not, it must be said, with much success. Our best theories of nature supply no clue as to why space might have three dimensions, rather than two, four or 5.2. Even worse, the drive for ever-grander replacements keeps finding hints that the magic ...

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1. Why not? You either gotta stop somewhere (so 3 is a nice selection, imo), or accept that we can only physically engage with the 3 we know, out of a potentially infinite number..

and, as the article sort-of elaborates:

2. Einstein would suggest, if indirectly, that it's not just 3

3. Many new cosmological hypotheses involve more dimensions...

You'll note I offer 3 answers. Spooky.


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I think the wiki has a nice diagram about the ``privileged character of 3+1 spacetime'' here.

Personally, theories involving higher dimensional space always annoy me.

Everybody acknowledges that the ``extra dimensions'' need to be tightly curled up so we can't see them, but I have yet to read an argument that I find convincing about why those particular extra dimensions are curled up - in a sense we are right back to the beginning just with a rephrased question: instead of ``why does space have exactly 3 dimensions?'' we are now asking ``why does space have exactly 3 non-compact dimensions?'' - not very much progress, in my opinion.

Extra dimensional theories (like Kaluza-Klein theory) may be mathematically elegant, but they have to jump through a lot of hoops; like ``why are these extra dimensions so compact that we only see the lowest order matter wave?''.

Any time you increase the number of spatial dimensions beyond 3 you have to immediately - and somewhat arbitrarily, it seems to me - impose some rules to make the Pauli exclusion principle continue to act as if there were only 3 spatial dimensions.

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3+1 is a piece of the puzzle that fits best with the rest of the pieces.

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