What is the distance between A and C?

If you measure the distance between A and C in the right triangle below, then it is shorter via the hypotenuse (b) than via the two other legs (a and c).

Now, imagine that you partition this hypotenuse into an infinite number of legs of right triangles, then the length of these legs will still be just as longer as the legs a and c are than b. It doesn’t matter how many triangles you partition it into, or from which right angle you start. So, what is the length between A and C?

Say that you instead measure the distance by the time it takes for you to travel from A to C. Then, that distance will instead depend on the speed with which you travel – the faster you go, the longer will the distance be (for you, but not for an observer).

The distance between A and C is thus relative. The question is why? The answer is that the figure above (ie, the right triangle) is two-dimensional, whereas the distance between two points in reality is in a three-dimensional space. The figure is thus a reduction of three dimensions into two dimensions, and in such dimensional reductions some measure has to yield into relativity. It is impossible to portray something that exists in X dimensions in X-1 dimensions without turning some measure relative. A reduction of dimensions can’t keep all measures absolute, because it simultaneously reduces the number of measures.

This fact is actually the reason why time is relative to speed in space. The fundamental problem is that every description of something is a dimensional reduction and thus turning at least one measure relative. In this case, it is time that has to yield into relativity when we try to catch our four-dimensional reality in three dimensions.

There are lots of things to say and find out about this relation between reality and our descriptions of reality, but most fundamental is to keep track of which is which. Approaches like cladistics and particle physics (ie, class realistic approaches) actually turns the relation between them up-side-down, ie, believe (and even claim) that our descriptions of reality are real INSTEAD of reality. This track does however lead astray into “an indefinite search for the indefinable”, as Charles Darwin expressed it.

Another contribution to understanding of conceptualization http://menvall.wordpress.com/