See https://computingbiology.github.io/docs/hamming1998.pdf "Mathematics on a Distant Planet" for more thinking. Many physicists think that math is instrinsic and absolute (objective) in the universe, not "merely a mutual agreement"
See https://computingbiology.github.io/docs/hamming1998.pdf "Mathematics on a Distant Planet" for more thinking. Many physicists think that math is instrinsic and absolute (objective) in the universe, not "merely a mutual agreement"
Except circles don’t exist in the real world. They are an abstraction that mankind created that are similar enough to many natural objects as to be a useful abstraction of them.
In order for two alien races to communicate about pi, they’d have to first agree on the definition of a circle as a set of points equidistant from a central point.
That’s one of the axioms they’d have to agree on before they could even get to pi.
Then again, maybe a circle (and all other geometric abstractions) are too tied specifically to visual perception. Maybe, for example, intelligent aliens who only have auditory perception, would have no concept of a circle but would have gotten to the Doppler effect. Or intelligent aliens who only have tactile perception, would have no concept of a circle but would have gotten to the laws of thermodynamics.