The precision of our manufacturing capabilities might be limited as QM has this discreete nature. It might be limited in this universe. So pi may only exist theoretically
Comment on Irrational
themeatbridge@lemmy.world 3 months agoRight, by my point is that your accuracy and precision are the same whether you are making a 1 meter length object or a π meter length object. Your meter stick is not accurate to the width of a hydrogen atom, either.
But if we accept the precision of our manufacturing capabilities as “close enough,” then it is equally as close to exactly π as it is to exactly 1.
mexicancartel@lemmy.dbzer0.com 3 months ago
themeatbridge@lemmy.world 3 months ago
But you could make that same argument for a lot of fractions. 1/3 doesn’t exist because you cannot divide a quantum in three. 0.333 repeating means that eventually you have to divide an indivisible foundational particle in thirds.
rbits@lemm.ee 3 months ago
If you have three particles, 1/3 of that is one particle. No need to divide an indivisible particle.
themeatbridge@lemmy.world 3 months ago
But if I don’t have three particles, 1/3 requires division.
mexicancartel@lemmy.dbzer0.com 3 months ago
Yes. I would argue 1/3 does not exist in quantum either.
The problem is that something that doesn’t exist in our universe or reality doesn’t disprove anything in mathematics. Mathematics is abstract. It is rules built up on rules. It does not care about reality or anything
barsoap@lemm.ee 3 months ago
You can divide a thing made up of any multiple of 3 number of things into three. Say, divide twelve eggs by three that’s four eggs, rational division is justified by “I could have multiplied some numbers beforehand so now I can divide”, it’s the inverse of multiplication, after all.
But that only applies to rationals: The issue is that there’s no integer you could multiply pi with that would result in an integer… otherwise pi would be a rational number which it isn’t.
Donkter@lemmy.world 3 months ago
Not to reiterate what other people have said here. But you can make an object 1 meter long by defining that object as 1 meter (hell, you don’t have to, but you can define 1 meter as the length that light travels in a specific amount of time or something silly). Then, to create something two meters long, you can have two of those one-meter lengths. To make something π meters long, you would need infinite precision, that is not true for 1 meter or even 1/3 as you mention later in this thread. There is no way to divide anything into exactly π length. There is an easy way to divide something into a number that can be expressed as a fraction, such as 1/3, or any fraction you care to come up with, even if it can be represented as .3 repeating.