# What is dimension? What is the size of dimension?

Recently I heard a TED talk by Brian Greene where he was speaking about String Theory working on $$(10+1)$$ dimensions. Plus he said that we live in only in $$(3 +1)$$ dimensions. So where are others?

He explains that it is crippled to small sizes which we cannot perceive. Also, he gives the analogy of an ant and a man walking on the rope.

So my doubt is, what do physicists mean by saying word dimension? What do you mean by size of dimension? Thanks in advance for your help and support.

Edit: Any link to papers discussing philosophical aspects of the above mentioned is greatly welcome.

• I've deleted a comment (and some replies) that seemed to be starting a debate rather than suggesting improvements to the question. – rob Jun 26 '19 at 0:36

The number of dimensions of space is the number of coordinates required to specify a point in space. The space we see is three-dimensional because we can specify a point in it as $$(x, y, z)$$. If we needed $$(x,y,z,v,w)$$ there would be five dimensions.

Each dimension is different, independent direction in which we can move: forwards/backwards, left/right, up/down for 3D. The size of a dimension can be loosely thought of as how far you could go in that direction before you come back to where you started. For each of the three directions we see, you can go at least many billions of light-years. These may well be dimensions of infinite size. We’re not sure whether they are infinite in size or just really, really big.

Extra dimensions would have to be microscopically tiny, so that we are constantly going “all the way around” in them without even realizing it. If they were macroscopic in size, we would have noticed them.

• for almost 40 yrs it’s been known that such an answer is only partially correct. the extra dimensions in string theory need not have any geometrical interpretation whatsoever. all that’s required is that the total central charge vanishes and that there are at least one space and one time dimension. it’s also possible that even these latter restrictions can be relaxed. in popular accounts string theorists simplify things because they couldn’t be bothered to get into details .. at least that’s my understanding. – Wakabaloola Jun 25 '19 at 18:23
• I didn’t mention string theory. The OP did, but his question was not specifically about dimensions in string theory. What parts of my answer do you think are “partially correct”? – G. Smith Jun 26 '19 at 0:19
• Your last paragraph, e.g., we could live on a D3 brane where the extra dimensions are in the bulk and arbitrarily large. The question is specifically about the 10+1 dimensions in string theory (not Kaluza-Klein theory), and in string theory the answer (as I mentioned above) is more involved. – Wakabaloola Jun 26 '19 at 4:31
• @Wakabaloola Thanks for clarifying the situation in string theory. – G. Smith Jun 26 '19 at 4:34
• @Wakabaloola What is the reasoning behind particles being specifically strings out of a choice of all kinds of objects? What justifies focusing the research investment only on strings? – safesphere Jun 26 '19 at 16:26