I don’t agree with you that traditional math is extremely effective in predicting the physical world. It is in fact very bad at predicting anything that isn’t an extremely isolated situation. It’s -theoretically- very good at predicting the physical world, but by the same token, you can -theoretically- use fourier transforms of aperiodic waves instead of trigonometric functions.
And mathematical systems exist without -any- concept of quantity. Set theory and category theory, for example, both exist without an internal representation of quantity.
To say, based on that we’ve had success with our particular brand of mathematics, that we should expect similar mathematical systems in use by aliens—why, this is to ignore entirely the implications of the UTM Theorem. There are an infinite number of analogous mathematical systems with analogous predictive powers.
I don’t agree with you that traditional math is extremely effective in predicting the physical world. It is in fact very bad at predicting anything that isn’t an extremely isolated situation. It’s -theoretically- very good at predicting the physical world, but by the same token, you can -theoretically- use fourier transforms of aperiodic waves instead of trigonometric functions.
And mathematical systems exist without -any- concept of quantity. Set theory and category theory, for example, both exist without an internal representation of quantity.
To say, based on that we’ve had success with our particular brand of mathematics, that we should expect similar mathematical systems in use by aliens—why, this is to ignore entirely the implications of the UTM Theorem. There are an infinite number of analogous mathematical systems with analogous predictive powers.