This blog is not about music, unless it be the 'music of the spheres'.


It is a sad fact that, throughout recorded history, many books have been irretrievably lost. In many cases, had these books survived, they may have given some insight into the life and character of their authors. Such is the case with all but one of the books of the geometer Hipparchus.

If people think of ancient geometers at all, they usually think of Euclid or Pythagorus. If they think of ancient astronomers at all, they usually think of Plato or Ptolemy. Poor Hipparchus! What did he ever do to deserve such obscurity?


Hipparchus built a foundation in astronomy and geometry on which Ptolemy (Claudius Ptolemaeus), some three centuries later, would build an intellectual edifice to last a thousand years. It is entirely plausible that Hipparchus drew from Babylonian sources in building his geometry. This does not in any way detract from his genius. Hipparchus' table of chords was incredibly accurate for its day, and formed the basis of the table of chords in Ptolemy's Almagest.


I wonder what Hipparchus might have made of Bertrand's paradox. Perhaps he would have resolved the paradox by making a random choice from a discrete set of pre-calculated chords, somewhat akin to Bertrand's random radius method.


Caveat: I am not a mathematician. I study the ancients from a linguistics / philosophy perspective. If I understand any of the math without the intervention of a severe headache, I count myself extremely fortunate.