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Zero nothings and the curse of an active mind

Ah, the curse of an active mind.

Mine gets me into trouble a lot--like right now. It's 1:15 am (10/01/1999) and I can't fall asleep. Why not? I'm not sure. It could be because I didn't get up this morning until 11:30. Maybe. But I'm betting that I can blame it on my (over) active mind.

Right now I'm thinking about a question that I came up with earlier: What would the unary number system consist of? One or zero?

Where did this come from? I was reading my C++ book and it mentioned 'unary operators', and on another page it had the word 'binary'. That's all my mind neded to get going: "Unary number system... hmmm..."

Other number bases have always fascinated me (like base 36). So I've been thinking about this whole unary number thing.

By the way, for those of you less of the mathematical persuasion, a unary number system is base 1 - unary, uno, one, get it? You're quite familiar with base 10 - decimal, and probaly base 2 - binary, also.

So what then, is base 1? Mathematically it can consist of only one numeral. Okay, so 1 or 0? Base 2 uses 1s and 0s; base 3 uses 1s, 2s and 0s; base 16 even uses the letters A, B, C, D, E and F. So which one do I pick?

The general rule is mantissa (the base of the base) minus one is the highest number. So base one must be all zeros. I guess that explains why there are no negative bases.

But how would that work? What can you count with zeros? Nothing. How many nothing? Zero nothing.

Terry Pratchett once wrote a trilogy of books about the little people who lived in a department store -- think The Borrowers for people a little more grown up. It was anthologized as The Bromeliad -- named for a flower in which rainforest frogs live. They live their entire lives in them, a world in one flower.

It's a great read.

Anyway, in the book, frogs can only count one. One of the frogs looks over the edge of his flower one day and sees one flower, and another one, and one more and more ones: a lot of ones.

That's more like it in my opinion. Unfortunately, since there is only one numeral, there is no zero.

So what can you count then? Anything or nothing?

You know, this is getting rather silly.