In my view nonnegative real numbers have good physical representations: amount, size, distance, position. Even negative integers don't have this types of models for them. Negative numbers arise mostly as a tool for accounting, position on a directed axis, things that cancel out each other (charge). But in each case it is the structure of <R,+> and not <R,+,*> and the positive and negative values are just a convention. Money could be negative, and debt could be positive, everything would be the same. Same for electrons and protons.

So in our everyday reality I think -1 and i exist the same way. I also think that complex numbers are fundamental/central in math, and in our world. They just have so many properties and connections to everything.

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Someone 3 hours ago | parent [-]

> In my view nonnegative real numbers have good physical representations

In my view, that isn’t even true for nonnegative integers. What’s the physical representation of the relatively tiny (compared to ‘most integers’) Graham’s number (https://en.wikipedia.org/wiki/Graham's_number)?

Back to the reals: in your view, do reals that cannot be computed have good physical representations?

	▲	bmacho 3 hours ago \| parent [-]
		Good catch. Some big numbers are way too big to mean anything physical, or exist in any sense. (Up to our everyday experiences at least. Maybe in a few years, after the singularity, AI proves that there are infinite many small discrete structures and proves ultrafinitist mathematics false.) I think these questions mostly only matter when one tries to understand their own relation to these concepts, as GP asked.