“On one hand, I got seduced by it at an early age because it’s so elegant, this infinite hierarchy of infinites. On the other hand, I think that it’s not real in the sense that I don’t think that there’s anything truly infinite in our physical world.
Moreover, assuming the infinite has caused many of the worst problems in physics right now. One of the biggest problems we have in cosmology is called the measure problem, which prevents us from predicting anything rigorously. It comes from the assumption that space can be stretched out ad infinitum. Space is truly continuous. If that were really true, to even measure the distance between two points, you would need to write out a real number like 5.732… with infinitely many decimals, yet we’ve never measured any number better than 17 decimals. That’s a pretty far cry from infinity!
Most of the stuff I teach at MIT which assumes infinity we even know is wrong. When I calculate why it is that you can hear me by using the equation for sound waves, it assumes that air is continuous, that at infinitely many points in the air there is this pressure you can measure there. But we know it’s wrong because air is made of atoms. It’s much more convenient to make that continuum approximation than to deal with all those pesky atoms.
My guess is that we will ultimately discover some other mathematical description of the Universe which is infinity-free and find that all this infinite math that we’re using today is just a really convenient approximation.
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