A computational perspective on set theory | Hacker News Reader

A computational perspective on set theory

terrytao.wordpress.com

37 pointsjlhamilton10 comments

What a fascinating article - rarely do you run across such well written math material! I've got to disagree on the intuitiveness of Cantor's diagonal theory, though; that was one of the most beautiful and intuitive proofs in set theory for me: make a list (denumerable) of decimally expanded reals; change the digit on the diagonal of each; you've now created a number not on the list: QED. Bam.

Really curious about the downvote—did I do something gouche?

Is there a way to view vote history, or are people actually watching the number of votes their comments get?

The only such view is linked as "threads" in the header and as "comments" in profiles.

Individual votes on items are always hidden, especially since they aren't summed consistently (hellbanning, disenfranchisement) and the total displayed is not the number used for ranking (time-decay, demerit heuristics).

There's the "saved: many" link in your profile that lets you see what stories you've personally voted up, but it's been timing out for a while.

I started a new account just the other day (wanted to use my actual name, and participate more) and as a result of that have little karma (not that it matters much), so I noticed when it took a downtick. Seeing as all the stories I'd commented on were still on the front page, I found the offending comment and was surprised there was no reasoning behind it. I like a good argument!

EDIT: ach! It should be gauche*!

The down vote isn't visible now, if that's what you're wondering.

I came into the thread just after it had started and the only comment was ihodes. I thought it was interesting in that after reading the article I shared some of the same thoughts but at this point that single comment was down voted and with zero as the score.

I up voted it back to one and ihodes had already replied asking why it was down voted.

So there's no visible history and he's not seeing down votes, just the final score. It's just that the first vote was a down and he responded to that.

He has a fair question though on down vote policy. It's very hard to see why it should've been down voted.

My policy is to up vote everything worthy of up voting but to only ever down vote the really irrelevant, off topic and rude posts. Others do seem to down vote really random things.

Maybe people should be asked for a reason when they down vote so that they stop and think about it for a moment.

Any random nitwit could have downvoted you; I don't think you should comment on that, unless you get multiple downvotes over at least 5 hours of time.

I think it's gauche? I upvoted you though for trying to use a nice french word :)

Agreed about the diagonalization method, but that's not what he said was unintuitive. He said the statement was unintuitive.

Too bad the article didn't go all the way into computation-land, so I can't readily believe the "finitariness" of the insights contained there. For example, is the function E() actually implementable in Haskell? If it isn't, the whole premise kind of collapses... One way to make sense of this question would be to skip the red herring of constructibility and define reals as lazy streams of bits, then try to write actual code and stuff. (But how in the flying hell do you implement a rationality predicate on reals-as-streams?) There are probably other, non-equivalent ways. This stuff isn't trivial at all.

For a more enlightening perspective on such topics, see the blog "Mathematics and Computation", especially those articles:

http://math.andrej.com/2007/09/28/seemingly-impossible-funct...

http://math.andrej.com/2008/02/06/representations-of-uncompu...

Reply on news.ycombinator.com