4 ms·

> I was watching the second lecture yesterday, towards the end of which Feynman distinguishes between what he calls a ‘Babylonian’ approach and a ‘Greek’ one. H

> I was watching the second lecture yesterday, towards the end of which Feynman distinguishes between what he calls a ‘Babylonian’ approach and a ‘Greek’ one. His idea here is that mathematicians have a tendency to arrange their theories in the Greek style on an axiomatic basis, while this can’t work in physics, at least in a time of theoretical growth, because it is never clear which approach is basic. For example, one may view a physical theory in terms of forces or field potentials or conservation laws or paths of least action, and unpredictably any one of them might provide new insight as to how to link together physical facts. Okay, so that explains the Greek approach. What's the Babylonian approach? Without that key piece of information I'm pretty lost as to what this is about.

stan_rogers 11y ago
Think of it as having a "flat file" of facts and some basic tools for deriving one from another. It's not the universe of facts that differs, just the hierarchy. Until you have enough knowledge to discern which are fundamental and which are derived, all of the facts have equal stature. That, in turn, allows you to reason from any one point to any other without violating any supposed axioms (which may, on reflection, turn out to have been special case derivations rather than actual axioms). (And the Messenger lectures are publicly available in several places, including YouTube; the one you want is entitled "The Relationship of Mathematics and Physics".)
shas3 11y ago
E. T. Bell [1], a 20th century historian of science writes about the different strains of ancient/medieval mathematics in his book 'Development of Mathematics'. Greek approach to science is roughly represented by Plato and Pythagoras, where they have a disdain for arithmetical computations and a reverence for the beauty of the mathematical proof, particularly in geometry. Mesopotamia/Babylon, India, and China on the other had a more empirical approach to mathematics, with emphasis on arithmetic, number theory, and so on. Obviously, exceptions exist, for example, Archimedes. Greek is the Platonic ideal- math existing in a different realm uncorrupted by the real world, while Babylonian is the mathematics (and beauty therein) of trade and architecture- modeling the real world using mathematics. Edit: Further, the theory is, when Islamic conquest and the Silk Route connected the west and east through Central Asia and Europe, there was syncretism. In addition to Islamic scholars' rediscovery of the Greek philosophers, they also combined this with ideas from India which via Fibonacci and others made its way to Europe in its new integrated form, right before the Renaissance. [1] E. T. Bell, "Development of Mathematics," Dover, 1st ed 1940 / most recent ed 1990 https://books.google.com/books?id=_5KAnw3QMC8C&printsec=frontcover#v=onepage&q&f=false https://books.google.com/books?id=_5KAnw3QMC8C&printsec=fron...

stan_rogers 11y ago

Think of it as having a "flat file" of facts and some basic tools for deriving one from another. It's not the universe of facts that differs, just the hierarchy. Until you have enough knowledge to discern which are fundamental and which are derived, all of the facts have equal stature. That, in turn, allows you to reason from any one point to any other without violating any supposed axioms (which may, on reflection, turn out to have been special case derivations rather than actual axioms). (And the Messenger lectures are publicly available in several places, including YouTube; the one you want is entitled "The Relationship of Mathematics and Physics".)

shas3 11y ago

E. T. Bell [1], a 20th century historian of science writes about the different strains of ancient/medieval mathematics in his book 'Development of Mathematics'. Greek approach to science is roughly represented by Plato and Pythagoras, where they have a disdain for arithmetical computations and a reverence for the beauty of the mathematical proof, particularly in geometry. Mesopotamia/Babylon, India, and China on the other had a more empirical approach to mathematics, with emphasis on arithmetic, number theory, and so on. Obviously, exceptions exist, for example, Archimedes. Greek is the Platonic ideal- math existing in a different realm uncorrupted by the real world, while Babylonian is the mathematics (and beauty therein) of trade and architecture- modeling the real world using mathematics. Edit: Further, the theory is, when Islamic conquest and the Silk Route connected the west and east through Central Asia and Europe, there was syncretism. In addition to Islamic scholars' rediscovery of the Greek philosophers, they also combined this with ideas from India which via Fibonacci and others made its way to Europe in its new integrated form, right before the Renaissance. [1] E. T. Bell, "Development of Mathematics," Dover, 1st ed 1940 / most recent ed 1990 https://books.google.com/books?id=_5KAnw3QMC8C&printsec=frontcover#v=onepage&q&f=false https://books.google.com/books?id=_5KAnw3QMC8C&printsec=fron...