## Re: Calling All Nerds

1

When you can't find an academic job, there's always work in TV writing. The referees are cake, too.

Posted by: Sifu Tweety | Link to this comment | 08-22-10 8:20 PM
2

I'm a little confused about what exactly is being proved. The line, "with enough people switching, eventually everyone will end up in their rightful form." makes it sound something like the question of whether a drunkard's walk will return to the origin. But the proof seems to merely show that it is possible for an arbitrarily large group to return to it's original configuration:

"each can be inverted as above in sequence after which x and y can be switched if necessary via , as was desired." (bold mine)

But I may be misunderstanding the proof.

Posted by: NickS | Link to this comment | 08-22-10 8:46 PM
3

2: I think the explanation in the geekwhateveritis post is inexact. The proof is that it's possible to construct a chain such that the group will return to its original configuration. The task of actually constructing such a chain is a separate issue.

Posted by: Sifu Tweety | Link to this comment | 08-22-10 8:50 PM
4

2: They don't seem to state it anywhere, but after reading some synopses of the episode I think I know what the point is. There's a machine that swaps the minds of pairs of people. The catch is that it can never re-switch the same pair (it can switch them with still more people, but never with the same person they've been switched with before). So the problem is, given a set of people whose minds have been switched in some way, is it possible to restore them to their original bodies? And the claim is that by adding two more people to the set, it's always possible to perform a set of switches that restores every mind (including the two new ones) to their original body.

Posted by: essear | Link to this comment | 08-22-10 8:50 PM
5

Calling it a "theorem" seems a little pompous.

Posted by: essear | Link to this comment | 08-22-10 8:52 PM
6

5: you know TV writers.

Posted by: Sifu Tweety | Link to this comment | 08-22-10 8:53 PM
7

6: It seems a little presumptuous to assert that essear knows TV writers, Tweety.

Posted by: Stanley | Link to this comment | 08-22-10 8:56 PM
8

Maybe if I lived in SoCal it would be a plausible assumption.

Posted by: essear | Link to this comment | 08-22-10 8:57 PM
9

You people have no sense of history.

Posted by: Sifu Tweety | Link to this comment | 08-22-10 8:59 PM
10

9: It's true. I don't even remember what comment I'm commenting on right now.

Posted by: Stanley | Link to this comment | 08-22-10 9:01 PM
11

10->9->7->6->5->OP->10.

Posted by: Awl | Link to this comment | 08-22-10 9:10 PM
12

I think I was still just lurking when Moira was around, so to say I know Moira would be a stretch.

Posted by: essear | Link to this comment | 08-22-10 9:17 PM
13

So the problem is, given a set of people whose minds have been switched in some way, is it possible to restore them to their original bodies? And the claim is that by adding two more people to the set, it's always possible to perform a set of switches that restores every mind (including the two new ones) to their original body.

The solution for 4 people is simple. Given a pair (a,b) that have been switched, and a pair of cooperating friends (x,y) you can just do

Swap a * x
Swap b * y
Swap a * y
Swap b * x

at this point both pairs have been swapped relative to their original positions. So just

Swap x * Y

and you will have put a, b back in their correct bodies, and x, y will also be back in their correct bodies.

Posted by: NickS | Link to this comment | 08-22-10 9:21 PM
14

I was told there would be no math.

Posted by: Stanley | Link to this comment | 08-22-10 9:26 PM
15
The proof is that it's possible to construct a chain such that the group will return to its original configuration. The task of actually constructing such a chain is a separate issue.

Well, if you know who is in what body, you can describe the permutation. You then break it up into cycles, and apply the procedure in the proof, no?

Also, has the display here changed for anyone else, or is it just me?

Posted by: Awl | Link to this comment | 08-22-10 9:29 PM
16

15: Right, the proof is constructive.

Nothing looks different to me....

Posted by: essear | Link to this comment | 08-22-10 9:32 PM
17

I'd rather have a constructive proof in front of me than a procrustean affront to comity.

Posted by: JP Stormcrow | Link to this comment | 08-22-10 9:39 PM
18

17: De crustibus non est disputandum.

Posted by: Stanley | Link to this comment | 08-22-10 9:44 PM
19

I find the idea of a non-constructive proof highly counterintuitive.

Posted by: nosflow | Link to this comment | 08-22-10 9:45 PM
20

15.last: I see no change in the display here, if by that you mean the fonts and text layout and whatnot.

Posted by: parsimon | Link to this comment | 08-22-10 9:55 PM
21

16,20: Thanks, I just now smacked the screen and everything's all right again.

Posted by: Awl | Link to this comment | 08-22-10 9:58 PM
22

21: I just now smacked the screen and everything's all right again.

"Don't worry honey, the new monitor you got me isn't broken after all. It's working just like the other one now."

Posted by: JP Stormcrow | Link to this comment | 08-22-10 10:02 PM
23

What's counterintuitive about proofs that aren't constructive? Think about any application of the pigeonhole principle ever.

Posted by: essear | Link to this comment | 08-22-10 10:04 PM
24

Well I mean for that matter the law of the excluded middle is counterintuitive when you get right down to it.

Posted by: nosflow | Link to this comment | 08-22-10 10:16 PM
25

Can I watch this episode on arxiv.org?

Posted by: fake accent | Link to this comment | 08-22-10 10:16 PM
26

I guess my intuitions don't accord with those of the intuitionists.

Posted by: essear | Link to this comment | 08-22-10 10:21 PM
27

Nerds are extremely common among TV writers -- probably a majority -- and "syndicated show" is used innaccurately here, since Futurama was produced for a network and the episode in question isn't in syndication at all. I can't speak to the math.

Posted by: Robert Halford | Link to this comment | 08-23-10 4:29 AM
28

I kind of knew "syndication" wasn't right, but I wanted to get the post up and go watch TV with Jammies.

Also I assumed someone would point out that plenty of TV writers are nerds.

But that such a person would give themselves away as fastidiously nerdy.

Posted by: heebie-geebie | Link to this comment | 08-23-10 5:52 AM
29

Even without the math proof that episode of Futurama is probably one of my all time favorites.

Posted by: CJB | Link to this comment | 08-23-10 6:27 AM
30

When I saw the episode, I was pretty sure we proved (or rather our teacher worked us through a proof of) a very similar theorem in a circus hour maths class once.

Posted by: Ginger Yellow | Link to this comment | 08-23-10 6:43 AM
31

Also, to echo CJB's point, the new Futurama is awesome. Miles better than the "movies". I'm still not too keen on the way they're handling the Fry/Leela relationship, and some of the single note parody episodes have been weak, but generally the writing has been top notch.

Posted by: Ginger Yellow | Link to this comment | 08-23-10 6:44 AM
32

K-sky is a writer in Hollywood too, no?

Posted by: rob helpy-chalk | Link to this comment | 08-23-10 9:59 AM