I don't think that's a given. It's just like there are different sizes of infinite, and more numbers between 0 and 1 than there are real numbers, or something.
That’s really interesting, and matches my completely groundless intuition. Just because it could happen, even on an infinite scale, doesn’t mean it would. That makes sense to me at least.
Yeah, I mean math and even science aren't always intuitive, so we have to have rules and theories to go by that demonstrate repeatability. Subatomic physics doesn't even really work like our models say, it's just that the models give the best results in predicting what we'll find.
Another example is randomness. Not all random numbers are the same, it depends on how you derive them as to what you'll get. I guess in some way that's related to what numbers will pop up for an irrational number. It's said with enough monkeys randomly typing on typewriters eventually you'll get a Shakespeare work. It already happened a number of times... since we're in sense monkeys and got a number of Shakespeare works. Didn't even need typewriters.
So it basically still boils down to a question of determinism vs, well, not free will but, I guess “indeterminism” would be a word for it. Semantics kind of break down at explaining the nature of existence at some point. I wonder if that is true for mathematics as well.
It’s like that quote of Alfred Korzybski’s, “the map is not the terrain”. The explanation is not reality, it must by necessity be something less, or something different from it.
Rhaedas@fedia.io 1 day ago
I don't think that's a given. It's just like there are different sizes of infinite, and more numbers between 0 and 1 than there are real numbers, or something.
tomiant@piefed.social 1 day ago
That’s really interesting, and matches my completely groundless intuition. Just because it could happen, even on an infinite scale, doesn’t mean it would. That makes sense to me at least.
Rhaedas@fedia.io 1 day ago
Yeah, I mean math and even science aren't always intuitive, so we have to have rules and theories to go by that demonstrate repeatability. Subatomic physics doesn't even really work like our models say, it's just that the models give the best results in predicting what we'll find.
Another example is randomness. Not all random numbers are the same, it depends on how you derive them as to what you'll get. I guess in some way that's related to what numbers will pop up for an irrational number. It's said with enough monkeys randomly typing on typewriters eventually you'll get a Shakespeare work. It already happened a number of times... since we're in sense monkeys and got a number of Shakespeare works. Didn't even need typewriters.
tomiant@piefed.social 1 day ago
So it basically still boils down to a question of determinism vs, well, not free will but, I guess “indeterminism” would be a word for it. Semantics kind of break down at explaining the nature of existence at some point. I wonder if that is true for mathematics as well.
It’s like that quote of Alfred Korzybski’s, “the map is not the terrain”. The explanation is not reality, it must by necessity be something less, or something different from it.