I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.
Right, 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.
In other words, to say we cannot make an object that is π meters is to say we cannot make an object that is any specific length.
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.
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
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.
Right, but you can have exactly a third of some group of particles. You can’t have exactly pi of some group of particles I think is what they were saying
The other guy said good about one out of three known particles. That’s what make it rational!
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
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.
I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.
Right, 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.
In other words, to say we cannot make an object that is π meters is to say we cannot make an object that is any specific length.
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.
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
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.
If you have three particles, 1/3 of that is one particle. No need to divide an indivisible particle.
But if I don’t have three particles, 1/3 requires division.
Right, but you can have exactly a third of some group of particles. You can’t have exactly pi of some group of particles I think is what they were saying
The other guy said good about one out of three known particles. That’s what make it rational!
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
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.
Sure. But how about a plank length instead of width of H atom. That would be great.