I wonder how much of this is just a function of what math you've ended up working with a lot.

Humans have really bad intuition about math. This shouldn't be that surprising. We evolved in a context where selection pressure was on finding mates and not getting eaten by large cats.

Speaking from personal experience as a mathematician (ok a grad student but close enough for this purpose) it isn't that uncommon for when I encounter a new construction that has some counterintuitive property to look at it and go "huh? Really?" and not feel like it works... (Read more)(Click to expand thread. ⌘F to Expand All)Cmd/Ctrl F to expand all comments on this post


All the axioms of ZF seem reasonable.

The axiom of foundation seems pretty ad hoc to me. It's there to patch Russell's paradox. I see no reason not to expect further paradoxes.

We arrived at the axiom of infinity from a finite amount of experience, which seems troubling to me.

This is an extremely finite, weird statement.

It's a very cool construction, but it's a finite one that we can verify by hand or with computer assistance. Of the things that ZF claims exist, some of them have this "verifiability" property and some don't. At the very ... (Read more)(Click to expand thread. ⌘F to Expand All)Cmd/Ctrl F to expand all comments on this post

5XiXiDu8y Here is another page [http://singingbanana.com/dice/article.htm] dealing with non-transitive dice that I liked.
1Eliezer Yudkowsky8y I would be interested in knowing if there is any second-order system which is strong enough to talk about continuity, but not to prove the existence of a first uncountable ordinal.

Harry Potter and the Methods of Rationality discussion thread, part 8

by Unnamed 8y25th Aug 20111 min read658 comments


Update: Discussion has moved on to a new thread.

The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread.  This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.

The first 5 discussion threads are on the main page under the harry_potter tag.  Threads 6 and on (including this one) are in the discussion section using its separate tag system.  Also: one, two, three, four, five, six, seven.  The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.

As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.

Spoiler Warning:  this thread is full of spoilers.  With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13.  More specifically:

You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).

If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.