We have seen that *units* of measurement
and indeed the very nature of the *dimensions*
of measurement are arbitrary models of what is significant,
constructed for the practical convenience of their users.
If this causes you some frustration or disappointment,
you are not alone; most students of Physics initially
approach the subject in hope of finding, at last, some
rigor and reliability in an increasingly
insubstantial and malleable reality.
Sorry.

What most disillusioned Physics students do next is to seek refuge in mathematics. If physical reality is subject to politics, at least the rarefied abstract world of numbers is intrinsically absolute.

Sorry again. Higher mathematics relies on pure logic,
to be sure, but the *representation* used to describe
all the practically useful examples (*e.g.* "arithmetic")
is intrinsically arbitrary, based once again on
rather simpleminded models of what is significant in a
practical sense. The decimal number system,
based as it is upon a number whose only virtue is that
most people have that number of fingers and thumbs,
is a typical example. If we had only thought to distinguish
between fingers and thumbs, using thumbs perhaps for
"carrying," we would be counting in *octal*
and be able to count up to twenty-four on our hands.
Better yet, if we assigned significance to the *order*
of which fingers we raised, as well as the *number*
of fingers, we could count in *binary* up to
31 on one hand, and up to 1023 using both hands!
However, we have already made use of that information
for other communication purposes . . . .

Is mathematics then arbitrary? Of course not.
We can easily understand the distinction between the
*representation* (which is arbitrary) and the
*content* (which is not). Ten is still ten,
regardless of which number system we use to write it.
Much more sophisticated notions can also be expressed
in many ways; in fact it may be that we can only achieve
a deep understanding of the concept by learning to express
it in many alternate "languages."

The same is true of Physics.

Jess H. Brewer - Last modified: Wed Dec 16 11:30:42 PST 2015