Not of This Earth! Instagram! Mathematica, Physics, and the Universe — What Can Last Forever Without Being Recreated?
A page can burn. A galaxy may go supernova and shatter. The theorem on it is not thereby false. That's what I mean by 'not of this Earth' i.e. a mathematical truth is not dependent on the survival of the terrestrial object in which it is inscribed.
For over 2,300 years, mathematical theorems have retained their logical validity for centuries. Once rigorously proven, they do not require periodic reconstruction, software updates from time to time, or rediscovery!
Take the Pythagorean theorem. In Euclidean geometry, the proof of it establishes a relationship which doesn't need to be re-proven every year. You can draw another triangle or write the proof all over again but you're just reproducing a representation. You haven't created the truth which is what makes the proof work. Whether or not such truths exist independently of the human mind is a philosophical question and the proof in itself doesn't answer it.
Physics takes us back to observation. We write down equations to describe the universe, and then they become axioms and rules. The planets don't wait for us to publish a theory before they go on moving.
That's the limit I'm after. We can build a model, we can repeat an experiment, we can reproduce a calculation. None of those things in themselves constitutes the recreation of the universe or the bringing into being of the regularities which govern it. What we do is provide axioms and rules. The universe provides the answers to those formulas of math.
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Reference
Physics in History. (n.d.). Physics and mathematics printable posters package [High quality] [Digital poster collection]. Retrieved from https://t.co/zI14dxxWNg