The Rule of Two, Part I

Do you know how old you were when you first learned to count? You might be thinking 3 or 4. If you were precocious, then your parents might have told you you could count as soon as you could talk, though I doubt you remember. Regardless of your (or your parents’) memories, you have been counting for longer.

Babies imprint — usually on their mother. The first number you learn is actually a pair of numbers, which I call, “Mom” and “Not Mom” but are more recognizable as 1 and 0.

The count of something is a description, and the simplest case of this is presence or absence of some characteristic. Numerically we use 0 and 1 — 0 for absence and 1 for presence.

Why must there be two choices. A characteristic that is universal is frankly not newsworthy. If everything was blue, for instance, we wouldn’t even have names for colors, blue included. So, while there are some categories that literally everything (or nothing) belongs to, you’ll seldom find the need to mention it. (Such statements are also incredibly difficult to verify. Is it necessarily true that everything shares a universe with us?)

The number system with only two digits — binary (or base two) — is therefore the most basic number system for counting. I don’t mean basic in the sense that everyone knows it but basic in the sense that it contains the least number of digits.

How rampant is this sort of binary characterization? How many times have you heard a statement that begins with, “There are two kinds of people…”?

Yes, that’s right, the number two is represented in binary as 10. The system you are most familiar with is decimal or base ten. In base ten, the number 10 is 1 ten (the base) and 0 ones. In base two, 10 means 1 two (the base) and 0 ones.

Isn’t decimal the norm? Base ten is widely accepted on our planet, but historically it has had some competition. The Babylonians used a base 60 (fancy word sexagesimal) number system. The Mayans had a system that was base twenty (vigesimal).

So, how old is this binary thing, anyway?

And God said, “Let there be light,” and there was light. God saw that the light was good, and he separated the light from the darkness.  God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning—the first day. Genesis 1:3-5 NIV

Did you catch that? When Genesis says God created light he got darkness (or absence of light) as a free gift for his troubles. Furthermore, the act of separating them is a characterization — exactly what a young baby does when it distinguishes between the source of food and comfort and everything else.

So, you’ve been using binary for almost your whole life. The underlying notion is as old as creation. And, there are only two symbols to remember (or teach).  As a bonus, learning about other bases improves your own understanding of decimal, in a similar way as learning a foreign language teaches you about the grammar of your native tongue.