0356: "Nerd Sniping"

[iNap]

http://xkcd.com/356/
Alt: I first saw this problem on the Google Labs Aptitude Test. A professor and I filled a blackboard without getting anywhere. Have fun.

What about engineers, though? Should I be worried?

For that matter, I'm majoring in EE. Should I be worried about this guy in particular?

[Cabhan]

I'm Computer Science, but I can imagine this happening. Something about LL(1) languages. I shall now be forever warier.

[Number3Pencils]

Absolutely hilarious. Reminds me of Alan Mendelsohn's "missile whistle" from Alan Mendelsohn, the Boy from Mars. He shoots an incredibly loud whistle right at someone's head, and as they turn in astonishment, they adjust their course just slightly and run smack into a trash can.

[chardish]

Gosh, I want to say that it's infinite. That'd be too easy though, right?

[athelas]

Reaction mechanisms. Actually, I kind of want a really hard problem, just to chew on when I'm bored.

[Lobstrosity]

One thing I never liked about this comic is how it excludes "Literary Nerds", if you will.

i.e. "Which is a better literary work, Stephen Crain's "Open Boat" or Ralph Waldo Emerson's "Self Reliance"?"

[DragonMudd]

I'm a physicist and I had that problem on my Math Methods final... never could figure out what it had to do with anything that we covered in that class (complex analysis, crazy PDEs and other continuous stuff).

[++$_]

I'd be posting in this thread, but I'm busy thinking about the problem instead.

[theyellowhobbit]

One thing I never liked about this comic is how it excludes "Literary Nerds", if you will.

In this case it's a good thing. We're smart enough not to get hit by trucks...

(Though I'm more archaeology/religion nerd, but it's the same principle. Though I suppose a shiny artifact would have the same effect on me...)

[erl137]

It looks like a preturbative problem to me . . . of course, I'm not as clear on the technical end of that as I'd like, so, somebody please feel free to correct me.

[Lobstrosity]

In this case it's a good thing. We're smart enough not to get hit by trucks...

(Though I'm more archaeology/religion nerd, but it's the same principle. Though I suppose a shiny artifact would have the same effect on me...)

Agreed. But I guess this comic just made me think in general, all of the comics. I guess the description of the comic excludes literature though. Only language... (A webcomic of romance, sarcasm, math, and language.)

[Aleril]

Hee

I think I am the only person here who didnt even bother with the problem because I dont know anything about it.

Good comic though

[Trella]

I also didn't even bother

[vwlou89]

Wouldn't the resistance be 0? I actually came up with a number that would satisfy this in my Calculus class: 1-.99999... It comes out to .000...0001 (infinite zeros). It can be represented as "the limit of y such that y=1/x as x goes to infinity". Since it could never really reach zero it would be as close to zero as was possible. Just a thought.

[Jorpho]

Ah, reminds me a lot of this old Story Minute comic. (I first saw it on a professor's door, with the last panel's caption replaced by "And then he went to graduate school...")

I love those old Story Minute bits; a shame the books are out of print.

[Kleppner]

Why can I see my professor making this a question on my final exam.
(Yes, they do actually read XKCD!)

[theyellowhobbit]

Hee

I think I am the only person here who didnt even bother with the problem because I dont know anything about it.

Good comic though

I didn't bother with it either.

[phlip]

Gosh, I want to say that it's infinite. That'd be too easy though, right?

I would say it'd have to be less than three ohms... since there's a 3 ohm path between the two nodes, and adding extra, parallel paths, can only make the resistance less...

Also... is it a bad sign that, despite the entire setup of the strip warning me about it, I still almost stopped reading the strip in the middle and started trying to solve the puzzle, before I realised what I was doing, and finished reading the strip?

vwlou89: Please don't bring up the 0.999... = 1 thing again... I'm still recovering from last time.

[ptveite]

Wow, the more I think about it, the cooler/more disgusting this problem becomes.

[ep103]

w00t its 2/pi ohms!
http://answers.google.com/answers/threadview?id=92564

Now get moving before you all get hit by trucks

[vwlou89]

vwlou89: Please don't bring up the 0.999... = 1 thing again... I'm still recovering from last time.

Will do...i really don't mean to instigate argument (yet it always happens) it just seems like such a convenient but totally hypothetical number and it kind of makes sense in this case.

[DragonHawk]

Oh-oh. This could be dangerous. I suspect this is doing to be one busy thread.

(under breath: Let's see, resistance is cumulative in series, but an inverse ratio in parallel... the grid is infinite, so we've got an unlimited number of both types... though the parallel paths will always also have some series paths, but there are series paths without any parallel elements... I wonder if that could lead to a canceling effect, making for a "neater" answer... but maybe not, and looking for that is red herring... hmmmm.... looks at clock Yikes. Okay, punt.)

I have discovered a truly marvelous answer to this, which this post is too small to contain...

[Chimo]

Hmm... is this by any chance the Classhole? (http://xkcd.com/72/ for those of you who don't remember) I mean, he's got a top hat and everything. This latest endeavor seems to suit him.

[phlip]

w00t its 2/pi ohms!
http://answers.google.com/answers/threadview?id=92564

Now get moving before you all get hit by trucks

Hmm... unless I'm misreading that page, isn't that for just across one diagonal? ie, the diagonal across a 2x2 square of nodes?

The comic has the diagonal across a 2x3 rectangle of nodes...

[DragonMudd]

w00t its 2/pi ohms!
http://answers.google.com/answers/threadview?id=92564

Now get moving before you all get hit by trucks

Good find, but that's not quite the same problem. The one you found was across a single diagonal... this one is from a Knight's move. Maybe 3/pi?

Edit: Dang... just a bit too slow.

[Hit3k]

Ah resistors, thy mortal enemy. I always had trouble working out resistance in physics when doing electricity. but what you've really got to ask yourself is: Are they in series or parallel?

I'm just a bit... drugged up on medicine at the moment.. I don't know if I make any sense or not.

[floyd4one]

It looks like a preturbative problem to me . . . of course, I'm not as clear on the technical end of that as I'd like, so, somebody please feel free to correct me.

Actually this problem is solved using a 2D Fourier series. I'm guessing the answer is between 2/pi Ohms and 8/3pi Ohms (the solutions between 1 diagonal and 2 diagonal points away respectively)

Runs off to play with Mathematica.... Yes I am a physicist.

Edit: Here's the solution if you want to check yourself

Spoiler:

The answer is 4/pi-.5 Ohms == .773 Ohms.
As I predicted the resistance is between the other two cases which are numerically .637 and .849 Ohms.

[aerojad]

in before the group tries to figure it out!

[ep103]

I didn't have time to read the derivation, as I need to get studying for a non-ece final I have in 8 hours, but...
if the solution I did find is only for a single square diagonal, can't we assume that since this is an infinite symetrical grid, with each indidivual box having equivalent resistance, the equivalent resistance of the problem in question should be related by a simple triangle, ie,
taking the triangle formed in the single square to have signs equal to an arbitrary unit of 1,
the hyptoneuse then has a length of sqrt(2).
For the rectangle depicted here, using the same units, the hyptoneneuse will have a length of sqrt(5).
Assuming symmetry, etc, etc, we therefore have the answer here is (2/pi)*sqrt(5)/sqrt(2)...?

edit: this comes out to sqrt(10)/pi ohms

[bjswift]

I had this on my 2nd semester physics class midterm. There's a pretty simple, elegant solution to it but I don't remember what it is. Prolly somewhere on the interwebs.

[AltoidAddict]

Hee

I think I am the only person here who didnt even bother with the problem because I dont know anything about it.

Good comic though

I didn't bother with it because even though I had the electromagnetic unit of physics 3 years ago, I'm still traumatized by it.

[ThatOneRedhead]

Awww... I was working on a take home final in Complex Variables and Analysis. Now, I am imagining infinite resistance networks.

/as an EE, this problem warms my heart

[floyd4one]

I had this on my 2nd semester physics class midterm. There's a pretty simple, elegant solution to it but I don't remember what it is. Prolly somewhere on the interwebs.

Fermat? Is that you??

edit: this comes out to sqrt(10)/pi ohms

Oh so close but not quite right

[chishm]

After a brief look, I can tell you that it is between 0.5 Ohms and 1.0 Ohm. Now to find the exact value...

[Hit3k]

spoiler'd cause it has the answer.

Spoiler:

10. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knight's move away?

R[m_, n_] := 1/(2π) Integrate[1/t (1 - ((t - I)/(t + I))^(m + n) ((t - 1)/(t + 1))^Abs[m - n]), {t, 0, ∞}]

R[1, 2]

(8 - π)/(2 π)

This problem is discussed in J. Cserti's 1999 arXiv preprint. It is also discussed in The Mathematica GuideBook for Symbolics, the forthcoming fourth volume in Michael Trott's GuideBook series, the first two of which were published just last week by Springer-Verlag. The contents for all four GuideBooks, including the two not yet published, are available on the DVD distributed with the first two GuideBooks.

http://mathworld.wolfram.com/news/2004-10-13/google/ Answers to the whole GLAT[Google Labs Aptitude Test] It doesn't look that difficult..

*can now be seen running towards his computer with mathematica to try it out*

[floyd4one]

[quote="Hit3k"]spoiler'd cause it has the answer.
beat ya to it

[Hit3k]

spoiler'd cause it has the answer.
beat ya to it

That was from mathematica. I realise you beat me too it. I thought I'd show the mathematica solution though

[floyd4one]

spoiler'd cause it has the answer.
beat ya to it

That was from mathematica. I realise you beat me too it. I thought I'd show the mathematica solution though

Showing your work is highly overrated

In fact it's that kind of extra split-second dilly-dallying that gets you hit by a bus... *zoom-zoom*

[Hit3k]

spoiler'd cause it has the answer.
beat ya to it

That was from mathematica. I realise you beat me too it. I thought I'd show the mathematica solution though

Showing your work is highly overrated

Thats what I said to my maths teacher[s]!

[floyd4one]

You know if xkcd has this kind of motivating power, Randall ought to put it to good use. For example slip in a subtle problem that is equivalent to a proof of NP-completeness or some other intractable task... within hours of being posted someone on the fora might have a solution!