The duality that is {x:o}

OK, so first thing. At this point everybody says ‘Binary’ or ‘Set Theory’ depending on their training.

It may surprise some to know that neither of those were the first use.

For that you have to go back to Bill Tutte and Tommy Flowers. Who are they you say? Well there is a post on this blog about them, Turing and the computer. Worth reading IMHO. And they deserve at lot more praise than they ever got and a Bust somewhere too. Turing is well known, the others almost nothing.

So what did {x:o} turn into, why {1:0} as you would expect. That old system of Baudot Code (hence bit in binary), not even with holes down the centre of the tape at first, was the first non-stored-program computer.

And its name was ‘Heath Robinson’.

It was the first ever machine decryption of a ‘computer’ cipher in the world. The Germans (and later the Russians) were to fatally believe that a simple XOR against a pseudo-random number generator was cryptographically secure.

Bill Tutte, with a day dreaming pencil in his hand, purely by the thought of his mind alone, visualised how the machine was probably built without even seeing one or knowing how it worked! And shortened the Second World War by 2 years. From just before D-Day on.

And you possibly would never have heard of them. Before 2006 anyway.

So lets get back to {1:0}

It is not unary arithmetic, that old barter system of stones in a pot, not much good for maths.

So other system came into use, based on 3, 10, 12, etc. and of course binary.

And that last one can represent all the others (but rarely uses ratio maths)

But at heart a duality too, present in all modern computers, phones, watches, etc.

But always remember, the Universe (always?) works in Unary.

And that phrase about so many, so few surely applies to Tutte and Flowers even through to today.



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