The Matching Game

Mysticism

Part of the philosophy (epistemology) of mathematics is pondering how numbers came to exist. To imagine that numbers were always there, or that they exist in relation to some ideal numeric form is too mystical for me. Perhaps our brains are wired to group and collect things in a way that naturally leads to mathematical thinking. The matching game is a kind of number origin story that makes this assumption.

The Game

The matching game starts with a named collection of items. Take, for instance, this collection of Xs which has the name “three”:

X X X

The game involves matching up other sets of items, item by item, with “three” and observing the results. Matching with this set of Ys:

Y Y

reveals that not all of the Xs have a match. This condition is called less than. This collection of Ys is less than “three”.

Matching with this set of Zs:

Z Z Z Z

reveals that not all of the Zs have a match. This condition is called greater than. This collection of Zs is greater than “three”.

Matching with this set of Ws:

W W W

reveals that each item from both sets has a match. This condition means that the matching set has the same name as our original set. This collection of Ws is “three”.

After playing the matching game for a while with differently named sets, like “one”, “two”, etc, it becomes obvious that there are some rules about the relationships between sets. For instance:

subtract: take an item away from “three” matches a “two”
add: combine a “two” and a “three” and the result matches a “five”

Basic math follows. This shows how math can be understood as a shortcut for the matching game, in the same way that multiplication is a shortcut for addition.

What This Means

This might be how numbers really work. But I don't know.

What I know is that this explains one way that numbers might be a natural outcome of normal things that our brains do, like recognizing patterns, putting things in groups and comparing things.

←

updated April 2019