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Phillip Cunio's Commentary:
Math and Abstraction
1-27-2004 Let's discuss
another science-related topic today. How, exactly, does science
and math relate to the real world? After all, scientific theory is
often rooted in math, and math, as we know, is naught but trickery and
foolishness. Know why? Show me two. Take me anyplace
in the universe and show me "two." You can't. "Two" doesn't
exist physically. It's a concept, not a thing. Of course, two
of any thing are unchanged by anything we say about the concept of two.
Why? They never cared about it in the first place. All of our
concepts about numbers are just that, and they exist only for us. Everything,
from 2 + 2 = 4 to complex integrals mapped as images in the w-plane, are
only concepts. (If you know what that second thing I just mentioned
is, good for you. If not, do a little dance and be glad. Better
for you.) So why then, is 2 + 2 = 4 a correct statement, while 2
+ 2 = 5 is not?
Answer: Because we say it is or is not so. We define not only the concepts of numbers (which can actually be represented by any symbol, not necessarily "2") but also the concepts of fixed relationships between numbers. This means that, if we define these relationships however we please, then we might theoretically assign any number of meanings to the symbolic phrase 2 + 2 = 4; the traditional meaning being not least among them. What this means is that any random or semi-ordered scribbling of numbers on a math test can have the proper meaning. When the symbols we use are arbitrarily designated, based only on traditional meanings, why not just assign newer, better, and in the case of the math test, more correct meanings as needed? This means anything I write down on that test could just as easily be considered correct as anything else. And that means I want some of those points back. Are you listening, Dr. Cristescu? |