Comment by anon291
4 days ago
> computer science with the finite
um... no... computer science is very concerned with the infinite. I'm surprised quanta published this. I always think highly of their reporting.
4 days ago
> computer science with the finite
um... no... computer science is very concerned with the infinite. I'm surprised quanta published this. I always think highly of their reporting.
I think this is pretty common for Quanta, and it might be sticking out more because it's a field we're familiar with.
I'm really torn about this, because I think they're providing a valuable service. But their general formula doesn't diverge a whole lot from run-of-the-mill pop-science books: a vague, clickbaity title and then an article that focuses on personalities and implications of discoveries while glancing over a lot of important details (and not teaching much).
I agree with our assessment of Quanta. I used to enjoy reading their articles, but the clickbait title formula has put me off. Also their status as a mouthpiece of the Simons foundation grantees.
I feel like I’m being a bit curmudgeonly, but I don’t read them much any more.
Initially I too thought - but we try to approximate infinity in CS all the time.
But I have come to think, well actually, approximate is doing some heavy lifting there AND I have never used infinity for anything except to say "look I don't know how high this should go, so go as far as you can go, and double that, which is really saying, you are bound by finite boundaries, you'll have to work within them, and the uncountable thing that I was thinking about is really finite.
Edit: Think of it like this
We know that it's most likely that the universe is infinite, but we can only determine how big it is by how far we can see, which is bounded by the speed of light, and the fact that we can only see matter emitting light (I'm being careful here, if the big bang theory is right, and I am understanding it correctly, there is a finite amount of matter in the universe, but the universe itself is infinite)
Asymptotics is a good example of CS using infinity practically.
Also, a small aside: there’s a finite amount of matter in the visible universe. We could have infinite matter in an infinite universe.
Computer science isn't concerned with the uncountable infinite though, which is what measure theory is mostly concerned with as countable sets all have measure zero.
Every non halting program with partial results correlates to a real number, and this sort of thing is talked about in theoretical C's all the time. Broadly speaking program analysis is akin to statements on the reals. The fields are the same. Even most day to day computer programming is ultimately reliant on the same kind of reasoning
What? You can find tons of textbook examples when dealing with the uncountable sets from non-deterministic finite automata. Those frequently deal with power sets (like when you have an infinite alphabet) which are quintessentially uncountable
Another glaring example:
> Set theorists use the language of logic, computer scientists the language of algorithms.
Computer science doesn’t use logic? Hello, Booleans.
So lazy, especially when you can ask an AI to tell you if you’re saying something stupid.