alt Hacker NewsAll the transcendental numbers are "manufactured in a mathematical laboratory somewhere".
In fact we can tighten that to all irrational numbers are manufactured in a mathematical laboratory somewhere. You'll never come across a number in reality that you can prove is irrational.
That's not necessarily because all numbers in reality "really are" rational. It is because you can't get the infinite precision necessary to have a number "in hand" that is irrational. Even if you had a quadrillion digits of precision on some number in [0, 1] in the real universe you'd still not be able to prove that it isn't simply that number over a quadrillion no matter how much it may seem to resemble some other interesting irrational/transcendental/normal/whatever number. A quadrillion digits of precision is still a flat 0% of what you'd need to have a provably irrational number "in hand".
Replies
It appears quantum phenomena are accurately described using mathematics involving trig functions. As such we do encounters numbers in reality that involve transcendental numbers, right?
> You'll never come across a number in reality that you can prove is irrational.
If a square with sides of rational (and non-zero) length can exist in reality, then the length of its diagonal is irrational. So which step along the way isn't possible in reality? Is the rational side length possible? Is the right angle possible?