[ainar-g]

It will be really funny if there is some bit of new, undiscovered physics, that went undiscovered for so long just because it's best described using some esoteric maths like complex base numbers.

Highly unlikely, but fun to think about.

[throwaway37585]

Are there any examples where the representation of a number matters in physics?

[jfoutz]

I recall some effort in moving from imperial measurement to metric. Reality itself does not care, but the math sure gets easier if you carefully select units.

Actually, another neat example is analog vs digital computation. your models can get very different answers. I recall some Mandelbrot guy talking about that.

[retzkek]

See Gaussian (cgs) units for an example, compare Coulomb's law in cgs and SI: https://en.wikipedia.org/wiki/Gaussian_units#Unit_of_charge