Regarding Archimedes (a philosophy of math anecdote)

post by KyriakosCH · 2019-10-13T21:25:27.271Z · score: 2 (4 votes) · LW · GW · None comments

Regarding tales told of Archimedes, other than those about his enthusiasm when he managed to conceive of the law of flotation, his contempt for the Roman soldier who demanded he would cease his calculations on those circles he had drawn on sand and the epigram on his tomb where his discovery of the relation between the volumes of a sphere, a cone and a cylinder was accounted for, there is one other worth of mentioning:

He once met, in a beach near Syracuse, a young boy and a slightly older and much taller youth. It was a warm day and those two were wearing white himatia without chitons underneath, as was usual for poorer people. Both left the right shoulder bare, with the fabric rising diagonally to the left shoulder where a pin held it in place, yet Archimedes noticed that in the way they had positioned themselves right next to each other the upper part of the child’s clothes was reaching exactly to the height of the lower part of the youth’s next to him. This formed an elegant, straight line, starting at the lower edge of the first cloth and ending to the upper edge of the other, and from a distance one would get the impression that it was all one continuous material instead of two distinct himatia.  

Despite his surprise, he immediately became aware that while he could notice the effect due to standing opposite those two, their position naturally rendered it impossible for them to witness and enjoy this harmonious sight.  

That they remained there, immobile, because they were indeed aware of the effect and meant for anyone coming near to observe it, was readily obvious; yet Archimedes couldn’t refrain from walking closer and asking just why they went into so much trouble so as to produce something they themselves weren’t allowed to observe, given that if they’d even attempt to steal a glance at it the delicate balance instantly would be ruined and therefore nothing would remain to be seen...

The youth kept silent, but the child, being more impulsive, replied that Archimedes was wrong. It wasn’t at all true that they stood there in this manner out of an intention to present to others the form he saw. To be precise, they were fully oblivious that anyone would be seeing such a thing when coming from afar. They were standing so close to each other out of mere habit. Lastly, they weren’t moving at all because they had been waiting there for their father to return from the beach.  

It is said that then, as he was walking away, he thought that it isn’t as much that nature seamlessly presents us with mathematical symmetries, but that the overall number of elements which, unbeknownst to us, are woven together into any image is so vast that a small number of our own interests is always also contained within it.  

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