Apr 24, 2007 19:25
Thales is the father of philosophy, science and mathematics circa 600 B.C. Because - he did something that changed the way we look at the world. We know that Egyptian mathematics had a pure, theoretical aspect about it that made their cardinal numbers impractical. We have their 'rope stretchers' as an example of them using ordinal numbers to measure. I stipulate that the essential difference between an ordinal number and a cardinal is the degree of exactness. A length of rope blessed by a priest is more prone to change than a yard stick. Greek thoughts on numbers didn't go further than to see that they don't change, (the proof of cardinality). Thales considerable integration was to see that he could relate his cardinal numbers to the Egyptian cardinals and render them practical. This had the effect of showing Greeks how to prove their practical numbers and showing Egypt that their numbers can denote. Thales discovered it possible to overcome the problem of constant change. His demonstration was proved with reason and logic and is the first instance of a man proving a thought without referring to god. Whats the difference? The Greeks had, as a matter of course, assumed that numbers and examples of numbers were related while wherever mysticism was in charge the certainty of numbers couldn't be guaranteed. If god made them he could remake them differently. This is mysticism's way of denying objectivity. Science is not possible except by the relation of ordinal to cardinal number. Its as easy as relating 'first ' to 'one'. It is impossible to conceive of an instance of 'first' that does not imply an instance of 'one'. The way we prove an ordinal number is to point at it. In the case of rope stretchers, if asked the length of said rope, one has only to point and say "that long". The way we prove a cardinal number is to explain how it is related ordinally. Had there been a yard stick at 600 B.C. one could compare religious ropes to yard sticks and draw the appropriate conclusions of longer/shorter, etc.