21–30 of 223 posts
Why not?
Is it impossible to calculate infinite values in general? I suspect not, My understanding is that a lot of calculus is in fact on how to calculate infinite values.
And a computer is a universal machine, this means that while it can not calculate everything, it can calculate anything that is calculable.
Earlier quoted context omitted.
Huh? Mathemathical proof is not a social construct. This makes no sense.
The proof is not a social construct. The truth is. The proof is a mechanism to reach that consensus, by convincing other mathematicians of a specific truth. That is all it is. There is a naive idea that a proof is a purely mechanical series of steps that provides access to truth. Last I checked, this isn't so for the vast majority of proofs in math. Such a proof would be way too tedious to construct or check by mathe…
> The truth is.
Yeah, that is how it feels like nowadays, however the truth is bound in a narrow set of assumptions. These assumptions are bound in reality even in mathematics (One apple is one apple, you add another one, you have two). And while there is an epistemologic level to reality, you would dismiss reality entirely by calling it a social construct.
The details of how a truth is communicated is in a sense a social contruct, because communication as a whole is, however nobody would call it like that. It is maybe a small reminder that meddling with language for no apparent reason is a warning sign, but this is going a bit off-topic.
> Hou and Luo’s work was suggestive, but not a true proof. That’s because it’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity, but it can’t actually reach it — meaning that the solution might be very accurate, but it’s still an approximation. I feel certain that if you run a process that approaches infinity using ordinary floating-point numbers, you will actually…
But more likely, the program would have to be built where it understands the symbolic forms involved, more like a proof solver than simple cfd math.
"That’s because it’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity, but it can’t actually reach it" Why not? Is it impossible to calculate infinite values in general? I suspect not, My understanding is that a lot of calculus is in fact on how to calculate infinite values. And a computer is a universal machine, this means that while it can not calculate everythin…
A "computer" is just a function from {0,1}^N -> {0,1}^M
Earlier quoted context omitted.
> and that nothing was true until a social consensus had been reached between mathematicians. So how do calculators and computers work then?
1+1=2 is a social construct. It’s simple, repeatable and therefore programable - but still a social construct.
I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
There are such reachable truths, but every mathematical system has a non empty set of axioms - or assumptions- which are 'given'.
> Hou and Luo’s work was suggestive, but not a true proof. That’s because it’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity, but it can’t actually reach it — meaning that the solution might be very accurate, but it’s still an approximation. I feel certain that if you run a process that approaches infinity using ordinary floating-point numbers, you will actually…
"That’s because it’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity, but it can’t actually reach it" Why not? Is it impossible to calculate infinite values in general? I suspect not, My understanding is that a lot of calculus is in fact on how to calculate infinite values. And a computer is a universal machine, this means that while it can not calculate everythin…
Almost all functions aren't computable, as they aren't discrete. A "computer" is just a function from {0,1}^N -> {0,1}^M
Earlier quoted context omitted.
Double precision floats have a maximum value of 1.7976931348623158 E + 308
That is not correct; they have a maximum value of positive infinity. See what you get when you square 1.7e+307.
The "Inf" interpretation, of, eg., 11111111111111111 isnt infinity.
And, in general, almost every function isnt representable on the discrete domain above.
floats are a hacky interpretation of discrete bit patterns
I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…