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The hypotenuse of a triangle with unit length sides is real enough.
by sorokod 5y ago
The hypotenuse of a triangle with unit length sides is real enough.
- drdec 5y agoI assume you mean in the physical sense? What if you get down to the quantum level? You don't have a straight line in the Euclidean sense any longer.
- voxl 5y agoYeah instead you have probability theory baked right in, real numbers and all!
- drdec 5y agoYou are conflating a mathematical model with reality, begging the question as it were.
- voxl 5y agoSure, otherwise you're just solipsistic, we have to assume things exist, it's how you make progress. If you think quantum is "the real stuff that exists" then you should assume, for now, that the model actually models something, and our best guess is that it's merely probability theory.
- sorokod 5y agoDo you question the existence of triangles and their mathematical properties?
- drdec 5y agoAbsolutely. There's no reason to believe space is Euclidean, in fact, relativity says it is curved. Quantum mechanics says that it is not infinitely divisible.
- gsinclair 5y agoIt depends what you mean by “existence”. Mathematical triangles are ideal conceptions that exist only in our minds.
- Sharlin 5y agoAlgebraic reals are the easy part, as are the few familiar classes of transcendentals that include numbers like pi and e. There’s only countably many of those. The set of all reals that can be described is countable. It’s the literally undescribable ones that are the problem, ontologically speaking
- sorokod 5y agoOntologically speaking describing members of any uncountable set is a problem.
- marcosdumay 5y agoIs it? Can you measure it? Do distances with arbitrary precision even exist?
- sorokod 5y agoYou probably question the existence of distances with exact precision. Arbitrary distance you get with good old ℚ.