The Man Who Knew Infinity | Hacker News Reader

The Man Who Knew Infinity

math.columbia.edu

131 pointschmaynard32 comments

Completely offtopic, except for math and title, but highly recommended while waiting for the movie:

"How To Count Past Infinity" https://www.youtube.com/watch?v=SrU9YDoXE88

Thank you. I really needed something to counter the horror of "The Imitation Game". The fact that the latter had got universal acclaim and many awards really scares me. A lot.

It's one of my favorite recent (say, >=2013) movies actually, perhaps even my favorite.

I would ask why you call it a 'horror' but I suppose opinions just differ and there might be a great many things one could list about it being bad. Instead, I would like to know why do you say it scares you that it received awards. Like, would you rather contentless movies like Divergent or The Hunger Games got all the awards?

From the same blog, here's what's wrong with The Imitation Game.

http://www.math.columbia.edu/~woit/wordpress/?p=7365

Because it has almost nothing to do with actual life and passion of Alan Turing, who was infinitely more interesting person than that cliché Asperger type depicted in the movie.

Nothing to do with the movie, but I thought his autistic aspects to be violently hilarious when reading more about him. He seemed to be at times completely oblivious of social implications and rules, which gave many great anecdotes to punctuate his life.

Seriously, those are not content-free movies. You're just not the target market.

But you want to look at what got no awards while The Imitation Game cleaned up? Selma, a movie with way more relevance to America than TIG.

But I'm guessing you're not in the target market for that either.

(And also, as others have already pointed out, the content is bad.)

Selma looks like an interesting movie, not sure I'm not the target market, aside perhaps from not being American.

Selma's historical gravity weighed down the movie making like concrete shoes.

To rephrase you question, do you prefer something stupid, or something stupid that pretends to be clever (and sully something you like)?

Also, false dichotomy.

I've always understood Ramanujan to be known less for "knowing infinity" than for "knowing" all the positive integers: https://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Hardy.E2.8...

OK, I'm blushing, because at first I thought it was going to be about Georg Cantor. I can still hope, I guess.

At least based on Wikipedia, Cantor's life would make a lousy movie. The first half of his career was consumed by petty academic politics, and in the second half he lost interest in mathematics. Curiously, if we believe Wikipedia, Kronecker came up with the idea of constructive mathematics specifically in order to stymie Cantor. I always had the suspicion that constructivism was all about a distinction without a difference.

That's pretty far from what I get from the Wikipedia article. Kronecker sounds genuinely concerned about constructivism, not like he was disingenuously plotting the downfall of Cantor, which seems to be what you got from it.

Constructivism has an important difference from non-constructivist math: it is computable. The math you can do with assistance from a theorem prover such as Coq is constructivist math. In fact, one of the labs in Pierce's _Software Foundations_, you get to show for yourself how various formulations of classical logic create problems.

https://www.cis.upenn.edu/~bcpierce/sf/current/Logic.html#la...

I think (in constrast to my friend teaching the class on theorem proving) that there is still room for non-constructivist math, but I can see why one would prefer constructivist math. We have computers.

I see non-constructivist math not much different from theology. That is assume something that cannot be experimentally observable or constructable and then apply logic.

Suppose God doesn't exist. Then ... middle, middle, middle,...Contradiction. Thus by "excluded middle", God does exist. I have never seen theology do that.

Theology proceeds by saying God exists with no proof, constructive or otherwise. Then it derives whatever it wants from that. Logic applies only when it's convenient and if you start from false premises, you can prove anything correct.

Nonconstructive proofs usually tell you something exists, but don't give you an example of it. Theology asserts something exists(with no proof), gives you examples(which don't support the assertions). Quite a difference here.

Consider medieval consideration about number of angels that can fit on a pin. Those were often pretty sofisticated deductions that are not much different in spirit from modern deductions from Continuum hypothesis.

You're not addressing these sorts of arguments, which is what fpoling is referring to:

https://en.wikipedia.org/wiki/Existence_of_God#Deductive_arg...

Can you, please, give me an example of a nonconstructive mathematical concept that's close to what you linked?

You said

> Suppose God doesn't exist. Then ... middle, middle, middle,...Contradiction. Thus by "excluded middle", God does exist. I have never seen theology do that.

Here is a summary of Anselm's argument for the existence of God:

> 1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).

> 2. God exists as an idea in the mind.

> 3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.

> 4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).

> 5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)

> 6. Therefore, God exists.

(Emphasis mine.)

https://en.wikipedia.org/wiki/Ontological_argument#Anselm

But really, you don't even need something with such a close 1-to-1 mapping for fpoling's comment to be reasonable. Consider the Banach–Tarski paradox. In both cases, you're talking about "something that cannot be experimentally observable or constructable" -- a perfect being, or a certain disjoint decomposition of the 3-ball -- "and then apply logic".

i think cantor would be more appropriately described as the man who knew finity

Infinity's pretty big, there's lots of room for people to know it.

Maybe Cantor would be The Man Who Knew Infinities.

I also highly recommend the book: http://www.amazon.com/gp/product/B00BW4VEGM/ref=dp-kindle-re...

Can't wait to watch this when it comes out.

As a side note - I had the chance to take a class with the author of this blog, Professor Woit, and would highly recommend his blog even for those not actively studying math.

The book was great! I am so excited we're getting to see this made into a movie. Very excited it's coming soon to the states. Coming from a similar cultural context as Ramanujan, I appreciated some of the details given by Kanigel in his book.

I read a book about his life, it was a cool insight into life of a brahmin boy under british rule.

Using "infinity" in the place of a number in mathematical formulas is, in my view, a kind of hack made by mathematicians. Infinity is a concept, not a number.

As long as you're careful, you can treat infinity as a number. It lacks some nice properties but can allow you to clean up a lot of statements. For instance if you want to define a measure on some sigma algebra, it's useful to be able to let some sets have infinite measure. Analogously, you may have a function that has an integral, but one which does not converge.

Anyway, numbers aren't real. They're all "concepts", so, as long as our statements are consistent, we can do what we want!

what is an example of a mathematician using infinity as a number?

I was kinda disappointed by the book, but the movie sounds really awesome.

Not Cantor I guess.

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