Somethings in mathematics are constant, both here and on alpha centauri, like the circumference of a circle divide by its diameter is Π or the hypotenuse squared is the sum of each leg squared in a right triangle etc.
But neither of those facts are true in non-Euclidean geometries like Spherical Geometry or Hyperbolic Geometry. The jury is still out on whether the universe is flat or has some sort of curvature. Meanwhile spherical geometry is fundamentally useful because we live on a sphere, not on a plane, and it is more accurate at modeling the 2-D space that we navigate in.
My point being, assumptions get baked-in to systems in surprising ways. Even something seemingly-objective like math. Especially when you're using it as the basis for communication, then what counts as "basic" or "fundamental" or "standard" reflects a perspective, not a fundamental truth.
It's likely their mathematical systems would eventually reach the same conclusions as ours, but the prominence or significance of fields or results (like circles and triangles) might be radically different. Even though we view those components as absolutely fundamental, it's possible an equivalent system could be built from different primitives.
lmkg|3 years ago
My point being, assumptions get baked-in to systems in surprising ways. Even something seemingly-objective like math. Especially when you're using it as the basis for communication, then what counts as "basic" or "fundamental" or "standard" reflects a perspective, not a fundamental truth.
It's likely their mathematical systems would eventually reach the same conclusions as ours, but the prominence or significance of fields or results (like circles and triangles) might be radically different. Even though we view those components as absolutely fundamental, it's possible an equivalent system could be built from different primitives.