Number of Dimensions
How many dimensions are there?
This is still a very hot subject of debate. Most everyone agrees there are
at least 4 (three spatial, and time), but in trying to understand certain
physical problems, some researchers have proposed 10, 11, and even 26
dimensions. There is still much work left to be done before the
scientific community comes to consensus on this question.
In our everyday experience it is easy to describe 3 dimensions - length (1
dimensional space), area (2 dimensional space) and volume (3 dimensional
space). If you add time, you can imagine a 4 dimensional space: your
location within some sort of volume at some particular time. (Imagine you
are in an auditorium in the bucket of a cherry picker crane that you can
set to any height you want and drive to any place in the auditorium at some
particular time.) In mathematics you can have "n" dimensional spaces where
n is any number you can think of. An example of n-dimensional space could
come from the physics of gases. A liter of air contains a HUGE number of
molecules, roughly 30,000,000,000,000,000,000,000 (3 followed by 22 zeros
or in scientific notation 3 times 10 to the 22nd power). If you knew where
every single one of those molecules was at a particular time, you could
define that as a 3 times 30,000,000,000,000,000,000,000 or
90,000,000,000,000,000,000,000 dimensional space, that is the location in 3
dimensional space for 30,000,000,000,000,000,000,000 molecules.
Now what I just described is a physics example of a larger dimensional space
. In pure mathematics, you can work with such spaces even if no one has
thought up or discovered something in the real world that this describes.
Kinda cool, huh?
Hope that helps.
You have to be careful whenever using the term "dimension(s)", because the same
word has several meanings in science.
1. "Dimension(s)" can mean "size" like, "How many centimeters is the piece of
string?" I do not think that is what you want.
2. In classical geometry there are three spatial "dimension" usually designated
(x, y, z). Of course as one generalizes to dynamic problems one has to take time
into account, so then there are four (x, y, z, t).
3. Mathematically, the concept of "dimensions" is generalized to mean "the number
of variables". So this abstract definition: (X1, X2, X3, ..., Xi, ...) there is
no limit to the number of variables, i.e. "dimensions" (which are not necessarily
physical quantities). So the number of "dimensions" can be 1 to an infinite number.
4. Modern cosmological theories talk about multi-dimensional "spaces" up to 11
and counting. These are better called "variables" because these added variables
are necessary to solve the complicated mathematics of those cosmological
The answer depends on whom you ask. We see three normally. Some people
count time as a fourth. People who adhere to "string theory" claim
there are 11 or even 13. No one has yet to firmly prove the existence
of more than 4, but the mathematics used to describe the Universe and
events such as the "Big Bang" need those extra dimensions to work.
Another good question is how many Universes are there?
Unfortunately, Physicists are not in agreement as to the number of spatial
dimensions. There are three observable spatial dimensions (plus time),
however some Physicists who advocate String Theory think there might be
between 10 and 26 spatial dimensions. We cannot observe these dimensions
because they are very small. For example, our universe may be very large in
the three spatial dimensions we are familiar with, but thinner than a proton
in the other 7 dimensions. So as far as our senses are concerned, all those
extra dimensions do not exist.
Scott P. Smith
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Update: June 2012