Date: Around 1993
I hear that some people claim that they can imagine
4-dimensional objects. I wonder how this can be since our universe only
has three physical dimensions - is it really possible to imagine these
things and do these people have any proof? I myself find it impossible to
imagine anything but projections of these objects onto 3-dimensions.
With some practice in mathematics it is not, in principle,
difficult to imagine objects in any dimension. It is a little harder to
think about what they would look like. The reason that four dimensions
seems to be important is that space (3) and time (1 dimension) are clearly
linked by relativity. The large number of experiments in relativistic
speeds verify this quite well. So, if our world is fundamentally four
dimensional, it means that time and space can be mixed when we make
measurements of quickly moving objects. For most of our everyday
experience it simply means that we should consider time as our fourth
dimension. This means that we are moving through a four dimensional
space, but does not mean that there are four dimensional objects in the
usual sense. Objects are still only three dimensional at a given
time. Their path through four dimensional space time can be represented
by a four dimensional volume.
Four-dimensional objects do not exist in our universe because it has
three dimensions. I do not know how people can imagine a Four-dimensional
object. We live in three dimensions, and it is difficult to imagine another
"direction" that is perpendicular to our existing dimensions. Perhaps
people with special imaginations can do it. There are some speculations
about more dimensions in string theory, but these are only speculations and
in any case the size of the other dimension is microscopic.
This difficulty would be analogous to color vision. Humans usually see
three primary colors, and the brain is able to "see" the full spectrum of
colors from these primaries. Some creatures, like insects, have a fourth
primary color receptor. They might "see" colors that humans cannot
imagine, or at least I cannot imagine.
In terms of mathematics, there is no problem with four dimensions or any
On the other hand, physics equations describe our reality in three
dimensions and usually do not work when extended to four and higher
dimensions. That is because physics equations describe physical reality
and our reality is three dimensional.
One can think about four-dimensional moons orbiting four-dimensional
earths, but the equations do not work properly. And if you have a
four-dimensional sun, do the nuclear reactions still operate that keep the
sun generating heat?
Or one can think about four-dimensional atoms and molecules forming a
four-dimensional piece of salt, metal, or wood, but what structure and
bonding would they have? In four-dimensions, would atoms even exist? At
the center of an atom, protons and neutrons that are bound together into
the nucleus. In four-dimensions, does this binding still take
place? Nobody knows.
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Update: June 2012