Four-dimensional Objects

[circa 1991]

Question:
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.
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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.

Sam Bowen
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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 
number dimensions.

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.

Bob Erck
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