Last night on public television a program titled "The Great Math Mystery" was not as clear as it could have been.
Let's begin with the question, What are numbers? Numbers are imagined abstractions that we use to label or to count specific things, or to measure. Abstractions exist in our mind. I venture to say that abstractions do not exist outside the mind of humans or some clever animals. Abstractions are not attached to anything physical.
Consider the following. A few people walk by your house every workday morning. You count them: one, two, three, etcetera. The fourth person doesn't consider herself as embodying anything such as four-ness. That is something in your mind. It's your subjectivity, not hers.
The ancient philosopher Pythagoras was confused and associated numbers with real things outside our heads. Plato followed suit. (Both were discussed in last night's broadcast.) With theological certitude, Pythagoras held to the nonsense that the number 1 embodied reason, 2 was female, 3 was male, 5 (2+3) was marriage, and 6 (marriage plus 1) was creation.
The question What is Math remains. We can imagine various kinds of numbers: odd numbers, even numbers. We can add numbers, divide them by other numbers (10 divided by 2 = 5), put them in different kinds of sequences, or put them into equations (2 of an unknown = 10, dividing both sides of the equal sign equally produces 5 in place of the unknown). This is algebra.
Equations are redundant arrangements. Equations add nothing to the world outside of our head. But, through simplification, working with equations helps us measure relationships.
Mathematics has a vocabulary that one needs to learn in order to communicate with professional mathematicians. There are in nature, curves to be measured, accelerations and decelerations, randomness and other patterns to be considered. Scientists applying math to motion and matter outside the mind find amazing patterns. Mathematicians can arrange formulas and equations with great complexity, and it has significance when measuring relationships outside their head. But this need not involve a leap into metaphysics. It is metaphysics to assume that math exists not only in the heads of mathematicians but also in that which they are measuring.
One person interviewed in last night's broadcast said that mathematics (in our head) is absolute and that engineers and scientists measuring nature are working with approximation. As we delve into greater complexity, our measurements become more difficult and out of reach. Our ability to measure, in other words, has limitations, hence the approximation.
Copyright © 2016 by Frank E. Smitha. All rights reserved.