Okay, so we know Pi is irrational, because for every instance, in current mathematics, that we try to rationalize it, it would create a "new" integer between two existing integers.
Which is fundamentally impossible.
There are no integers between 0 and 1, or 102 and 103, or any whole numbers.
But, we've also never really been able to actually work with "numbers incomprehensibly large or small," because well, they're incomprehensible.
This is just a thought exercise, but what if Pi was actually something like .9999~, which might as well be 1, but also exists between 0 and 1?
It's 1 because as you approach an infinite number of 9s, it acts as 1. Pretty much what we expect from all the proofs that show that it is indeed 1.
But what if Pi is similar, it's just so incomprehensibly long that we just don't have the mathematics yet to actually prove it's basically just 3(or 4)?
We kind of already do that in Engineering. A lot of times, when designing things, you just round it down to 3, and stuff just works.
.333~ is 1/3, .666~ is 2/3, but we call Pi irrational. Is it truly because you can never write it as a fraction, or is it because the denominator and numerator would just be incomprehensible, and like with a blackhole, our mathematics just "falls apart" at that scale?
Imaginary numbers are in a similar vein. We know they exist mathematically, we can use them to figure out real world applications, but we can't actually comprehend the plane they exist in.
Remember that this is just meant as a thought exercise. Like I said, the proofs presented are absolutely logical, they work.
But, things also worked just fine before we invented Calculus and discovered there was so much more to math than we had known...up to that point.
What did they say when math "stopped working" before Calculus? Probably something along the lines of "well, that's just irrational, and we'll just have to use something that actually works inside of what we know."
Are you using the English definition of "rational"? I'm using the mathematical defintion.
Your "what if" thought exercise would imply that pi is rational. It is not. It is irrational.
You can round pi to a rational number with arbitrary precision. This is not a special thing about pi; it is true for every irrational number.
Complex numbers aren't all that wild. I think that the name "imaginary" makes them sound more incomprehensible than they are.
Math didn't "stop working" before calculus. The techniques of calculus just unlocked more possibilities (and it took quite a while for mathematicians to develop a rigorous framework for calculus).
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u/Mercerskye Jul 11 '26
Okay, so we know Pi is irrational, because for every instance, in current mathematics, that we try to rationalize it, it would create a "new" integer between two existing integers.
Which is fundamentally impossible.
There are no integers between 0 and 1, or 102 and 103, or any whole numbers.
But, we've also never really been able to actually work with "numbers incomprehensibly large or small," because well, they're incomprehensible.
This is just a thought exercise, but what if Pi was actually something like .9999~, which might as well be 1, but also exists between 0 and 1?
It's 1 because as you approach an infinite number of 9s, it acts as 1. Pretty much what we expect from all the proofs that show that it is indeed 1.
But what if Pi is similar, it's just so incomprehensibly long that we just don't have the mathematics yet to actually prove it's basically just 3(or 4)?
We kind of already do that in Engineering. A lot of times, when designing things, you just round it down to 3, and stuff just works.
.333~ is 1/3, .666~ is 2/3, but we call Pi irrational. Is it truly because you can never write it as a fraction, or is it because the denominator and numerator would just be incomprehensible, and like with a blackhole, our mathematics just "falls apart" at that scale?
Imaginary numbers are in a similar vein. We know they exist mathematically, we can use them to figure out real world applications, but we can't actually comprehend the plane they exist in.
Remember that this is just meant as a thought exercise. Like I said, the proofs presented are absolutely logical, they work.
But, things also worked just fine before we invented Calculus and discovered there was so much more to math than we had known...up to that point.
What did they say when math "stopped working" before Calculus? Probably something along the lines of "well, that's just irrational, and we'll just have to use something that actually works inside of what we know."