discrete numbers

9 10 2011

Had more of an idea about this a few days ago, but never got down to writing it. So, here is the vestiges of it.

The very act of numbering cuts up the world. Two as distinct from three. It is less a distinction, between this and that, and more of a boundary. Drawing a boundary around a thing, much in the same way a word might be used to package a thing perceived.

The structuralist might necessitate a distinction, of opposites. And there is, of course, a difference between two and three apples.

I’ve already remarked on sameness as being important for counting, or multiplying. There was something in here about multiplication…

3×7       7×3

Three times seven. Three groups of seven. Seven times three. Seven groups of three. Quite different descriptions of reality, or indeed different situations in reality. When calculated to the “answer”, 21, there is a further loss of information. Three boxes of matches with 7 matches in each, versus seven boxes of matches with 3 matches in each… same number of matches, different numbers of boxes.

It wasn’t this… it was a different tack. I just can’t remember… it was something very very simple about this notion of discrete numbers. What this means in terms of our mind’s processing. What the last observation seems to be about, is our mapping of number to “things”, discrete mental objects that might match some material situation, eg matches and boxes. This is happening at a slightly… later, or higher… aspect of consciousness; what comes first, is the discrete mapping of number like a word to a thing. One, two, three…

Wait a mo — another thought. Counting is one, two, three… the pointing at a new thing and including the old… two includes one, three includes two and one. Whereas, there is the whole-image form of counting (can’t remember the correct name for this… it’s not “counting”), where eg 7 things are immediately recognised as seven things even if the perceiver doesn’t have a word for “seven”. Hmmm three as in third…

For some reason, this makes me come round to music. Thinking about counting in time. Counting objects, I think, comes later. It’s a combination of this pattern matching, immediately taking in a pattern, and noticing a pattern in time. Combine those, and you get counting things.

But this is miles away from my initial thought about discrete numbers.

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