How many dimensions are there and what are they?

SDStaff Dex replies:

This is a collaboration, between me (the mathematician) and Karen (the physicist and penguinist), to try to cover a question that spans all three disciplines.

If you mean “dimensions” in the sense of “universes,” as in “a creature from another dimension,” come to wreak havoc on earth … well, forget it, there’s only this one universe as far as anyone knows. The use of the word “dimension” in that sense is a crutch for lamer science fiction writers.

If you mean “dimensions” in the sense commonly used by mathematicians and physicists, these are a human concept, invented to simplify mathematical descriptions of the physical world. Customarily we use three dimensions:

• length or back-and-forth (where back is just negative forth)
• width or side-to-side (left is just negative right)
• height or up-and-down (down is just negative up).

You need all three of these directions to definitely locate a point in space. For example, if you wanted to go to the top of the Gateway Arch in St. Louis, you wouldn’t head in just any old direction and expect to get there. No, you have to go a very specific amount of back/forth, a specific amount of side/side, and a specific amount of up/down.

This three dimensional model works pretty well for most things. But there are times when a lesser dimensional model is just fine. If you’re running along a track, you measure your motion in one direction/dimension only. If you’re mowing your lawn, you may want to come up with a more efficient path through two dimensions. If you’re flying a traffic helicopter, you need to worry about all three dimensions.

You may have heard that time is the fourth dimension. Again, this is simply a convenient concept. For instance, if you’re flying a spacecraft to Mars, you need to get it to the right point in space at the right time, otherwise you’ll miss Mars (a moving target).

As dimensions go, time is quite different from space. For one thing, you can only go forward in time and not backward. Does that bother physicists? Nope, it’s all just numbers.

In relativity, where things are going at close to the speed of light, weird physical phenomena occur, namely, length gets contracted (shortened) and time gets dilated (slower). If you do your mathematics in a particular way, you can write one physics equation to take care of both the spatial stuff and the time stuff. Fewer equations, happier physicists.

Then there’s the Fifth Dimension, which was a cool band in the 60s.

Some cosmologists claim that at the instant of the Big Bang, there were 20 or more dimensions, but they all went away except for the three space and one time dimension we have now. We dunno about that, it just means that cosmologists were able to cram 20 or more variables into one big mongo equation, no small feat, but more of a mathematical trophy than anything of practical use to mere mortals.

Footnote: In mathematics, there is no difficulty whatsoever in dealing with n-dimensional spaces, where n can be whatever you’d like. These can be dimensions in the sense of directions in some non-visual hyperspace model, or they can be (more properly) “degrees of freedom.” For instance, if you were trying to model weather patterns, you might find it convenient to identify a point not only by its location in space and at a point of time, but by its barometric pressure, wind velocity, temperature, etc. That would give you a seven dimensional-model. Similarly, physicists dealing with electrons have quantum numbers like spin, isospin, charge, twist, baryon number, etc. For mathematical purposes, these can be used in multi-dimensional formulae, for a convenient model.

So what we’re telling you is, there’s nothing magical or mysterious about dimensions. They’re just notions scientists dreamed up to help them describe the world.

SDStaff Dex, Straight Dope Science Advisory Board

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