Sunday, April 1, 2012

quote for the day

"If I were at the outside, say at the heaven of the fixed stars, could I stretch my hand or my stick outwards or not? To suppose that I could not is absurd; and if I can stretch it out, that which is outside must either be body or space(it makes no difference which it is, as we shall see). We may then in the same way get to the outside of that again, and so on, asking on arrival at each new limit the same question; and if there is always a new place to which the stick may be held out, this clearly involves extension without limit. If now what so extends is body, the proposition is proved; but even if it is space, then, since space is that in which body is or can be, and in the case of eternal things we must treat that which potentially is as being, it follows equally that there must be body and space(extending) without limit." - Archytas

We even have a bust of Archytas(from roman times to be sure; these are suppose to be Roman copies of Greek origins; you can take it or leave it I suppose!).

I remember thinking of these problems of whether space is infinit or not and thinking much the same thing when young(as Archytas clearly did in the quote above). I find the quote interesting because it shows 1) consciousness to wonder, and 2) reasoning ability.  This wonder at whether space in infinit or not also goes to the general building of Pyramids of all kinds.

Well, maybe the Egyptian pyramids were built more for the King to go to heaven, but the Ziggurats and the Mayan pyramids seem to me to be about people trying to build the highest structure they can to maybe reach out with their bare hands and touch the heavens!  I wonder what they thought when they reached the top, reached out and found out that, well, things are not so simple!


I should say more about Archytas.  He was considered by Vitruvius(a Roman engineer; not a mathematician; note, there seems to be no roman mathematicians in their thousand years; if they needed one, they just went to the Greeks) the first mechanical engineer; legend says he made a flying machine(a questionable statement!  Not to mention, considered the tunnel at the Island of Samos built long before his time; well, clearly there were some mechanical engineers before Archytas time). 

Archytas major contribution was a mathematical one; he found a way of doubling the cube(one of the three delian problems; squaring the circle, trisection of an angle, and doubling of the cube). 

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