Nobody before the Pythagorean had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.
In the index to the six hundred odd pages of Arnold Toynbee's A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur yet their cosmic quest destroyed the medieval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
The real achievement in discoveries... is seeing an analogy where no one saw one before... The essence of discovery is that unlikely marriage of cabbages and kings — of previously unrelated frames of reference or universes of discourse — whose union will solve the previously insoluble problem.
In my youth I regarded the universe as an open book, printed in the language of equations, whereas now it appears to me as a text written in invisible ink, of which in our rare moments of grace we are able to decipher a small segment.
Wherever we find orderly, stable systems in Nature, we find that they are hierarchically structured, for the simple reason that without such structuring of complex systems into sub-assemblies, there could be no order and stability- except the order of a dead universe filled with a uniformly distributed gas.
It is impossible to decide whether a particular detail of the Pythagorean universe was the work of the master, or filled in by a pupil a remark which equally applies to Leonardo or Michelangelo . But there can be no doubt that the basic features were conceived by a single mind; that Pythagoras of Samos was both the founder of a new religious philosophy, and the founder of Science, as the word is understood today.
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