Wednesday 5 November 2014

The puzzle comes before the solution


I incline to the view that the puzzle comes before the solution, and that the solution is often a long time coming. Each puzzle, once solved, can be passed on as a cultural benefit: here be tigers, don’t shit in the drinking water, planets orbit the sun in elliptical orbits. The great library in Alexandria was the old world’s papyrus internet, and for about three centuries before Christ an agreeable stroll through the stacks was the beginning of many an education. A culture which builds a library gives its citizens an advantage, but the primary cause was the wit that caused the scrolls to be written in the first place.

After completing his studies in Athens, in 245 BC Eratosthenes was called to Alexandria to become the third-ever Chief Librarian. Some years later, hearing that there was a well in Aswam where on the summer solstice the sun shone down to the very bottom (such that a person peering down it could see that their shadow blocked the sun from reflecting up from the water) he realised he could calculate the circumference of the earth without leaving Alexandria.  Using the gnomon, the part of a sundial which casts a shadow (some say by observing the shadow cast from an obelisk near his lodgings) he measured the Sun's angle of elevation in Alexandria at noon on the summer solstice, and found it to be 1/50th of a circle south of the zenith. He assumed the well was due south, that the earth was a sphere, and that the camel drivers were right in their estimates of the distance they had to travel to get to Aswam. On that basis he calculated that the circumference of the earth was 5o times that distance, which turned out to be a fair approximation, in that some of the errors in his assumptions cancelled themselves out.

So, what do we make of his achievement? Eratosthenes had benefitted from a good education, and he had an entire library to guide his thoughts. By the standards of the time he was very probably well fed, well housed and of high socio-economic status. One school of cultural thought would argue that it was only a matter of time before any idle reader, no greater than the next, would burst out of the great library into the Alexandrian sunshine, ready to carry out the necessary calculations. Incidentally, in partial support of that cultural perspective, Eratosthenes was nicknamed “Beta” by his contemporaries, because he was great at many things, but always second and never first. The sort of guy who might never have achieved tenure.

However, as far as we know from the fallible written record, he was the first to calculate the circumference of the earth, and did so by using his brain. There were others just as well educated and as well fed who didn’t work it out. He also is credited with being the father of geography; estimated celestial distances, the diameter of the sun, year length and leap year, doubling the cube, and an algorithm for finding prime numbers. Not a bad haul for a librarian.

I think that the cultural explanation for intellectual achievement is partial and limited, and that the puzzle comes before the solution. Some one has to solve the puzzle, and that the more puzzle solvers you have, the more society flourishes, usually becoming healthier and wealthier.

It might be churlish to mention it, but if we resurrected the puzzle now: “There is a well to the south of you where, one day a year, the sun shines right down to the bottom of the well. What do you conclude from that?” I wonder how many modern citizens, given the accumulated wisdom of another two thousand years, would be capable of realising they could determine the circumference of the earth, and calculate it to a fair approximation.


  1. and had their been IQ tests then how would a literate Athenian in the time of Aristotle have scored vs a German?

    would it be due to the Athenian's better genes?

    1. We can only estimate their intellectual ability, within some wide ranges, but on the basis of the problems there were solving for the first time they were very probably equivalent to 3 standard deviations above the current Greenwich Mean IQ, say at about the IQ 145 level.

  2. Eratosthenes was undoubtly very smart. The famous cattle problem was stated by Archimedes in a letter to Eratosthenes. The tone of the letter suggests that Archimedes and Eratosthenes were personal friends. Probably Archimedes studied in Alexandria as a young man and became friends with Eratosthenes there.

    Eventually the Greeks developed a quite accurate notion of the size of the solar system at least relative to the distance between the Earth and the Sun. They had problems exactly determing that distance. Their proposed methods are theoretically correct but difficult to carry out because of the brightest of the sun. But they knew the distance to planets like Jupiter and Saturn pretty accurately relatrive to the distance between the Earth and Sun. They knew the distance between the Earth and Sun well enough to know that the Sum was much bigger than the Earth. They knew the distance to the Moon and the size of the Moon quite well.

    Their unsuccessful attempts to measure steller paralax convinced them that the fixed stars were at enormously greater distances than the planets. They guessed correctly that the stars were distant suns.

    The one thing they got wrong was placing the sun at the center of the solar system and regarding the Earth as being stationary instead of rotating. That the Earth was rotating instead of the heavens revolving was in fact put forward by Aristarchus. I think the basic obstacle to the acceptance of this theory by the Greeks was their intuitive feeling that if indeed we are flying around the center of the Earth at thousands of miles per hour why don't we feel it. People at that time rarely experienced uniform motion at high speeds like modern people do in a jet plane.

    1. Yes, and if you look at the actual debate about the heliocentric model at the time of Galileo (as opposed to later propaganda) it was a difficult argument to prove, with significant counter-arguments which Galileo never totally addressed. However, any child now visiting the Science Museum can offer the visual proof of the earth's rotation.

  3. I should have said "at about a thousand miles per hour".