is it possible to prove a fourth (spatial) dimension?

[klaymen]

is it possible to prove a fourth (spatial) dimension?

[wendy]

Yes

If you can construct four lines at right angles to each other, then you have at least four dimensions. If you can't then you do not have four dimensions. Simple, really.

W

[klaymen]

well, would we be able to see that?

[wendy]

the physicists have a different number of dimensions as you look at the problem. Sometimes we are rumoured to live in 11 dimensions, except for 3 space and 1 time, all the rest are of the order of the plank distance.

On the other hand, the question about proving four dimensions, really is about establishing four free variables. Sometimes you just can't tell, but the general assumption is that we live in what is freely a horochorix.

W

[klaymen]

ok, well the real question i wanted to ask is (this is the one that someone tried to punch me in the face over) has it been proven that there are at least 4 spatial dimensions?

[houserichichi]

There are 4 spacetime dimensions, no less (3 space, 1 time). As for more than that nothing has been "proven" but there exist theories that require them. Of course this is assuming by "exist" you mean "physically exist" or, more succinctly, "outside the realm of mathematics."

[jinydu]

ok, well the real question i wanted to ask is (this is the one that someone tried to punch me in the face over) has it been proven that there are at least 4 spatial dimensions?

As far as we know, there are only 3 spatial dimensions. However, relativity relies on four-dimensional spacetime vectors.

[jinydu]

Perhaps a quote from my new Linear Algebra textbook ("Linear Algebra with Applications" 3rd edition, by Otto Bretscher) would be helpful:

"Definition: Dimension
Consider a subspace V of R^n. The number of vectors in a basis of V is called the dimension of V, denoted by dim(V).

This algebraic definition of dimension represents a major advance in the development of linear algebra, and indeed of mathematics as a whole: It allows us to conceive of spaces with more than three dimensions. This idea is often poorly understood in popular culture, where some mysticism still surrounds higher-dimensional spaces. The German mathematician Hermann Weyl (1855-1955) puts it this way: "We are by no means obliged to seek illumination from the mystic doctrines of spiritists to obtain a clearer vision of multidimensional geometry" (Raum, Zeit, Materie, 1918).

The first mathematician who thought about dimension from an algebraic point of view may have been Frenchman Jean Le Rond d'Alembert (1717-1783)...."

[houserichichi]

There are, however, many other kinds of dimensions completely disjoint from the vector space one...for instance fractal dimension.