Thursday, May 26, 2005

The foundation of arithmetic

Math is a language. It is easier to compare to music then English as both are fairly limited and standardized so anyone can understand them. But really it is not different from even English.

The most basic part of arithmetic is counting and numbers.

Counting is the organization of quantities. *** means something different then *****. Counting one of the oldest recorded skills we have. The Lebombo Bone
proceeds the Agricultural Revolution and the domestication of animals.

Quantities are physical things: blocks, Cheerios, beans, or anything else. Young children also happen to respond best to physical things that they can see, touch, smell, taste and hear. All you have to do is give them a certain number of things and let them play with them. "Here are 10 Cheerios," or "Here are 7 blocks." over a fairly short period of time children will pick up on that.

Quantities are good, but are severely limited in scale. Counting 10-20 objects is easy enough but beyond that things fall apart. So we use numbers as a shortcut to represent any quantity we want. 1, 2, 3 are what we us instead of *, **, ***.

It is far easier to write 793,284,104,849,290,328,953,427,394 then it is to carry that many countable objects around or even to say it. Seven hundred and ninety-three septillion, two hundred and eighty--four sextillion, one hundred and four quintillion, eight hundred and forty--nine quadrillion, two hundred and ninety trillion, three hundred and twenty--eight billion, nine hundred and fifty--three million, four hundred and twenty--seven thousand, three hundred and ninety--four, by the way, in case you were wondering.

Our number system actually Indian, not Arabic as most people think, I was surprised too. The earliest known record comes from Monday 25 August 458 A.D. the date written on an Jaina cosmological text; the oldest known text to use zero and the place value system with word symbols.

Some primitive cultures had only words for one and two and could only get to four by saying one-two and two-two, to count beyond those quantities they devised various ingenious ways around the language, including counting the fingers and toes of groups of people. Primitive isn't the same as dumb.


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