Great article, though I’ve always been a bit more of a mathematical realist myself.
the mathematical structure of a physical theory often points the way to furtheradvances in that theory and even to empirical predictions.
The part that still fascinates me is how taking a couple of different mathematical descriptions of certain phenomena and working solely with the numbers under the “laws” of mathematics can lead to mathematical theories and predictions of seemingly unrelated phenomena.
For example, Einstein developed Special Relativity to account for the inconsistencies between classical mechanics and Maxwell’s equations using primarily the observation that the speed of light is absolute regardless of the motion of the light source and the postulate that the laws of physics are the same in all inertial reference frames. He just worked with the numbers under the rules of mathematics to (independently) develop the Lorentz transformations which lead to his Special Relativity.
The key feature here is that Einstein did not perform experiments. He knew form the null-result of the Michelson-Morley experiment that the speed of light is constant, but besides that, the vast amount of the work done was what Richard Hamming called “Scholastic” in its approach. I’ve even heard it said that as far back as Newton, the idea of non-locality was considered preposterous and that in itself gives the idea of a universal speed limit which might have been enough, along with Galileo’s Principle of relativity to get very close to Special Relativity using only the tools of mathematics he had available to him and the current theories of motion and electromagnetism.
Now obviously a lot of work went into that, but so many strange predictions fell out of it that it really is amazing, some might say “unreasonable”. For example, time dilation, mass/energy equivalence, length contraction, and eventually (after GR) black holes, relativistic cosmology, gravitational lensing, and the existence of dark matter.
That we can derive knowledge about how the universe works because of inconsistencies between simpler mathematical descriptions of various phenomena really does seem to suggest that the universe “runs on math”. Now I don’t mean to suggest that the equations are written somewhere in the sky and that some entity “breathes fire” into them; Just that the structure of the universe is isomorphic to the ideal math that we could use to explain and predict it. I would not be at all surprised to find out that somehow, “they are the same thing,” whatever that might mean.
the structure of the universe is isomorphic to the ideal math that we could use to explain and predict it. I would not be at all surprised to find out that somehow, “they are the same thing,” whatever that might mean.
Great article, though I’ve always been a bit more of a mathematical realist myself.
The part that still fascinates me is how taking a couple of different mathematical descriptions of certain phenomena and working solely with the numbers under the “laws” of mathematics can lead to mathematical theories and predictions of seemingly unrelated phenomena.
For example, Einstein developed Special Relativity to account for the inconsistencies between classical mechanics and Maxwell’s equations using primarily the observation that the speed of light is absolute regardless of the motion of the light source and the postulate that the laws of physics are the same in all inertial reference frames. He just worked with the numbers under the rules of mathematics to (independently) develop the Lorentz transformations which lead to his Special Relativity.
The key feature here is that Einstein did not perform experiments. He knew form the null-result of the Michelson-Morley experiment that the speed of light is constant, but besides that, the vast amount of the work done was what Richard Hamming called “Scholastic” in its approach. I’ve even heard it said that as far back as Newton, the idea of non-locality was considered preposterous and that in itself gives the idea of a universal speed limit which might have been enough, along with Galileo’s Principle of relativity to get very close to Special Relativity using only the tools of mathematics he had available to him and the current theories of motion and electromagnetism.
Now obviously a lot of work went into that, but so many strange predictions fell out of it that it really is amazing, some might say “unreasonable”. For example, time dilation, mass/energy equivalence, length contraction, and eventually (after GR) black holes, relativistic cosmology, gravitational lensing, and the existence of dark matter.
That we can derive knowledge about how the universe works because of inconsistencies between simpler mathematical descriptions of various phenomena really does seem to suggest that the universe “runs on math”. Now I don’t mean to suggest that the equations are written somewhere in the sky and that some entity “breathes fire” into them; Just that the structure of the universe is isomorphic to the ideal math that we could use to explain and predict it. I would not be at all surprised to find out that somehow, “they are the same thing,” whatever that might mean.
Tegmark’s Mathematical universe hypothesis is one answer to what that might mean.