People tell me they have trouble understanding the concept of multiple dimensions. We supposedly live in a 4 dimensional world (the 4th being time).
Dimension
as mathematicians use the term means orthogonal. Each orthogonal means
90 degrees away. Each higher dimension is orthogonal to the lower
dimension. A line is one dimension a square is two dimensions and a
cube is three dimensions. The square has two lines that are 90 degrees
off of the original line. The cube has sides that are 90 degrees off
the square. Higher spaces can be drawn but are harder to envision.
For me, I think of dimensions and orthogonality as meaning 'really different.' My conception has us living in a high level of dimensions. In addition to the three standard dimensions I add color, sound, smell, touch, vibration, temperature, uprightness, concepts and infra-red radiation.
In my conception, people who lack any of these dimensions live in a slightly different world than I do. A blind person doesn't perceive a bell the way I do if I can see it, except that the blind person uses many other dimensions to approximate my standard American perception.
Many animals and insects have very different senses than I and they live in other dimensions as a consequence. Elephants can feel vibrations that are much lower than we can feel and many insects can see in the infra-red and ultra-violet spectrum. Sharks can detect small fluctuations in electricity and birds can sense fluctuations in gravity.
I put concepts
in the list of dimensional senses. That is because without words, I
doubt that the world around us is perceived the same way. If you know
that the Japanese and other linguistic groups have two words for blue
compared to our own, you will not be surprised to see that a rainbow
has a blue and light blue region that are each the same size as our one blue...we only see
blue as having a slightly wider region in the rainbow because we have
rainbow words that are not as distinct as the Japanese. So concepts, as
embodied in words constitute a dimensionality.
The image above right shows five dimensions of a rectilinear object as shown to you in two dimensions.