> If you throw away real numbers, then you lose major things in physics. I think for example you lose the wave function in QM. Then again, have you ever observ

> If you throw away real numbers, then you lose major things in physics. I think for example you lose the wave function in QM. Then again, have you ever observed a non-computable number as a component of the value of a wave function in nature? Real numbers add a lot of cruft which can never be practically observed (due to not being computable). One of the main reasons we lose things is that our results have been built upon the real numbers since they were easier to conceptualize and to work with, but it's possible that a lot can be recovered (maybe even everything we care about) using only the computable numbers. For instance, see https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis for some results in recovering analysis (limits, differentiation, integration, etc) using the computable numbers.