Why 0 and 1, of All Things?

Can you count with two? You can. The rule is exactly the one you know: when a column is full, carry. Base ten carries at 9; base two carries immediately, at 1.

0, 1 — and then? Only two symbols, so carry: 10. Then 11, then carry again: 100. To our eyes they read 'ten, eleven, one hundred', but they mean two, three, four.

The beacon fire was already binary

It feels foreign, but humanity has used this trick for ages. Beacon fires: lit or unlit. One beacon can only say 'the enemy came / did not', but five in a row can send thirty-two different messages.

Morse code likewise: short, long. Two signals carried the world's telegrams. Given enough of them, on and off can carry anything.

But why settle for two?

Here is the kernel of this piece. Electricity could be divided into ten steps — one volt means 1, two volts mean 2, and so on. That would save a lot of columns. So why do computers insist on two?

So the real reason computers use binary is not mathematics but sturdiness. Two states is not the way to hold the most; it is the way to be wrong the least. Billions of switches clicking billions of times a second and almost never erring — the secret is this plainness.

A little further in

And not only numbers go in

What about letters? Simple: assign every letter a number. A is 65, B is 66. The world agreed on one numbering, and Korean script and emoji have their numbers too. The sentence you just read is, inside the machine, a long parade of numbers.

A photograph is chopped into tiny dots, three numbers per dot — so much red, so much green, so much blue. Sound is the air's trembling measured tens of thousands of times a second, each height written down. Video is those photographs flipped dozens of times a second.

Now read on and off as true and false. Then not only numbers but judgements become calculable. 'It is raining: true.' 'I have an umbrella: false.' The man who built the rules for adding and multiplying such things is the self-taught mathematician from the end of the first piece.

Tool The Binary Board — Counting with Eight Switches Eight switches to flip yourself. Press +1 and watch the carry happen; build a target number; see your own name become a row of on and off. Knowing by reading and knowing by pressing are different things.

How to hold numbers in on and off, how to swap the world for numbers, how to calculate a judgement. The ingredients are assembled. The next piece is about giving the machine its orders — computer languages.

The question that remainsLetters, pictures and sound all go in as numbers. Is there anything that cannot be?