UPDATE: My answer to this problem. Which, at the end of the day, isn't really an answer at all.
As part of our explorations of "why this math" for aspects of physics, I pose an obvious and seemingly simple question: which type of numbers is required to describe the world around us?
We use different types of numbers in mathematics. For example, we have the integers, the rational numbers, the real numbers, and the complex numbers. Furthermore, there is a distinct hierarchy among number types - the hierarchy for the four types above is:
\(integers \subset rational ~numbers \subset real ~numbers \subset complex~ numbers\).
There are additional number types such as the hypercomplex numbers (which are fascinating if you've never run across them). Physics, however, should only need to use a certain type of number to describe the universe, and which type should be dictated by nature. Which number type is required for our current physical theories, and why?
A couple comments for this question:
Arguing that one number type is simply more convenient to describe phenomena is not a valid argument, as we are looking for what is required.
On its surface this seems like a very straightforward question, but I warn everyone that it is actually rather subtle.
There are different answers to this question, depending on what you believe about measurement and/or the fundamental structure of our world. Hence I hope everyone will provide a number of interesting viewpoints.
Finally, as always - only if enough interest and discussion is shown by the members of our community will I post my own answer. I and your peers on Brilliant want to hear everyone's thoughts!