356: Nerd Sniping

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Nerd Sniping

Title text: I first saw this problem on the Google Labs Aptitude Test. A professor and I filled a blackboard without getting anywhere. Have fun.

Explanation

Nerds have a way of getting distracted easily and focusing on one thing and ignoring the rest, when they feel their specific skills are challenged by an interesting problem. Black Hat has decided to make this into a disturbing game of getting nerds, in this case a physicist, to stop in the middle of a street and get crushed by traffic by showing them an interesting problem to solve. (This may be based on a real event—see the trivia section).

The problem Black Hat shows is an electronics engineering thought experiment to find the resistance between two points. In normal wiring, a one-ohm resistor would result in one ohm of resistance. Two resistors connected in a series, where electricity has to go through each, has two ohms of resistance. Two one-ohm resistors in parallel give the circuit only half an ohm since you have a conductivity (inverse resistance) that is the sum of the conductivities of the path (1 ohm of resistance is 1/1 mho, thus over 2 paths is 2 mho or 1/2 ohms). With an infinite grid of equal resistors, you have an infinite number of paths to take, and for each path an infinite number of both series and parallel paths to consider, so much more advanced methods are needed. The exact answer to the question is (4/π − 1/2) ohms, or about 0.773 ohms. See Infinite Grid of Resistors.

Black Hat explains the concept of his new sport, Nerd Sniping, to Cueball while killing the physicist, but Cueball is appalled and will have no part in this sport, which doesn't make Black Hat give up on him as he suggests it would be fun if he made his own sign. Black Hat finally suggests that "physicists are two points, mathematicians three." This may indicate that he considers a mathematician to be a more difficult target for his game than a physicist would be. It is unclear whether this is meant as a dig on physicists or on mathematicians; it might be because physicists are interested in a wider range of problems, or because mathematicians require a higher-quality problem to hold their interest. Alternatively, he just dislikes mathematicians more, and is thus willing to award more points for sniping one of them.

In the title text, Randall explains that he saw this problem in a Google Labs Aptitude Test. This is a collection of puzzles published by Google as a parody of tests such as the SAT. Google is known for using logic & math puzzles in their job interviews.

Randall explained in a speech at Google five days before this comic was released that he was nerd sniped, in a way, by that problem in this test (see problem 10 on page 2), and got quite irritated when he ultimately found that it was actually a modern physics research problem, requiring very advanced math, far more complicated than the other puzzles. Putting such a problem in an aptitude test can be a way of testing if someone might realize when they cannot solve a problem and remember to move along to the other problems. If they fail to do this, they will never reach the easier problems that come later, and will fail due to their inability to realize when they will come up short. This is also important knowledge to have about yourself. Seen in this context, it is not necessarily a bad idea to have such an impossible problem in an aptitude test, as it is not interesting to have someone who is easily nerd sniped working for you.

Note that the truck should have stopped no matter what, since the nerd was walking on a pedestrian crossing. However, the driver may have seen him walking, then estimated that he would be safe before reaching him and realized too late that he had stopped in the street. Alternatively, the truck driver is part of Black Hat's sport. Or was himself/herself nerd sniped by the sign.

Randall has later referred back to the concept of Nerd Sniping several times in the past, such as in the title text of 730: Circuit Diagram, and in the what if? blog. In Visit Every State (7 years after this comics release), the entire comic was shown at the top and the truck again further down the post—Randall has again been nerd sniped by a paper he read. This also happens to him in Lunar Swimming—see the title text for the second to last picture.

Transcript

[Black Hat is sitting on a chair, Cueball is standing next to him. Across the street, another Cueball-like guy is coming from a building walking towards the pedestrian crossing across from Black Hat.]

Black Hat: There's a certain type of brain that's easily disabled.

Black Hat: If you show it an interesting problem, it involuntarily drops everything else to work on it.

[The Cueball-like man across the street is about to enter a crosswalk, which is seen from right behind Black Hat in his chair, holding onto the sign, which is still pointing down. Cueball is looking on.]

Black Hat: This has led me to invent a new sport: Nerd Sniping.

Black Hat: See that physicist crossing the road?

[Black Hat lifts up the sign when the physicist is in the middle of the street, halfway across the pedestrian crossing.]

Black Hat: Hey!

[A close-up of Black Hat's sign is shown in a frameless panel. There is text above and below an image of a four-by-five grid of nodes with resistors (shown as wiggly lines) between every node and also continuing away from the 16 outer nodes. A total of 5 columns with 5 and 4 rows with 6 resistors for a total of 20 nodes and 49 resistors. Two nodes, a knight's move apart, are marked with red circles in the 3rd row 2nd column and the 2nd row 4th column.]

Sign: On this infinite grid of ideal one-ohm resistors,

Sign: what's the equivalent resistance between the two marked nodes?

[The Cueball-like physicist has stopped pondering the questions, a hand to his chin.]

Physicist: It's... Hmm. Interesting. Maybe if you start with... No, wait. Hmm... You could—

[In another frameless panel, a ten-wheeled truck is zooming past from the right, apparently going through the spot where the physicist just stood.]

Truck: Foooom

[Cueball looks down on Black Hat, who looks back up from his chair at the curb, again holding the sign down. He lifts one hand up while replying.]

Cueball: I will have no part in this.

Black Hat: C'mon, make a sign. It's fun! Physicists are two points, mathematicians three.

Trivia

• It could be that Randall was inspired by a story from John H. Conway about when he was involved in a "near" nerd snipe event that was a perfect match for this comic.
  • The story can be read in the book Candid Science Five from 2005 (two years before this comics release), specifically on page 22:

"[Donald] Coxeter came to Cambridge and he gave a lecture, then he had this problem ... I left the lecture room thinking. As I was walking through Cambridge, suddenly the idea hit me, but it hit me while I was in the middle of the road. When the idea hit me I stopped and a large truck ran into me ... So I pretended that Coxeter had calculated the difficulty of this problem so precisely that he knew that I would get the solution just in the middle of the road ..."

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Discussion

Just because the problem contains an infinite series (or parallel) doesn't mean that it's unsolvable. It's tricky, certainly, and getting the "true" answer involves some rather heavy math, but it's not impossible. Indeed, Google shows that it's already been answered. 76.122.5.96 20:42, 20 September 2012 (UTC)

I've always had an issue with this problem for one simple reason. In an infinite set of resistors, there is no space to apply a charge, thus there is no resistance. Ohm's law states Resistance = Voltage / I(current). So, in a system where there is no current (creating a divide by zero error), and there is no voltage (no change in electron work capacity, because we don't have a way to excite the electrons, because there is no power) Resistance is incalculable. lcarsos (talk) 22:22, 20 September 2012 (UTC)

We live in 3 dimensions, just place a battery above the grid with wires going to the 2 points. --84.197.34.154 22:59, 24 October 2012 (UTC)

Not everybody does... --FlatlandDweller 11:08, 15 November 2012 (UTC)

baDumpBump! 172.68.142.89 16:22, 28 June 2018 (UTC)

I believe the OP is referencing the issue that an infinite circuit could not hold a current. Connecting a battery would only work for a finite grid. In addition, the orientation of the battery in physical space has no relation to its behavior in a circuit, only the points of connection matter. Think about what the battery is doing to generate a current. How does electric potential apply over an infinite grid? Even moving it through a magnetic field won't work as the flux will be uniform across each cross section. You can't rotate an infinite grid either... -- Flewk (talk) (please sign your comments with ~~~~)

This is an idealized version of the general problem of determining the resistance between two points in a volume of some material. Like, say, two electrode tips in a liquid electrolyte? Getting a mathematically exact solution in this situation requires integrating over an infinity of paths, even when the liquid volume is finite. Add in the fact that there are no perfect insulators, and you'll have to consider arbitrarily long paths, too. 162.158.203.15 03:46, 19 April 2021 (UTC)

Just crocodidoodle the battery to the pencil lines as and where required for an infinity of varieteediddly. I used Google News BEFORE it was clickbait (talk) 18:51, 20 January 2015 (UTC)

This problem is "unsolvable" only if you try to just use the basic methods for finite networks. There is a page on this at http://mathpages.com/home/kmath668/kmath668.htm that reports that the cited points have a resistance of 4/pi - 1/2 ohms (.773234... ohms). The 1/2 ohm resistance between adjacent nodes is actually well known. Divad27182 (talk) 05:05, 5 October 2012 (UTC)

Solution here as well: http://mathworld.wolfram.com/news/2004-10-13/google/ Potie15 (talk) 03:50, 18 March 2013 (UTC)

Nowhere it is said that the problem is unsolvable, just that it is interesting. Of course, the sniping is more effective if the problem is also difficult to solve, because otherwise the victim would get over it quickly. Dargor17 (talk) 17:47, 16 June 2013 (UTC)

That method for parallel resistors is wrong. You don't divide resistances by the number of paths, you sum the reciprocals and then take the reciprocal of that. The method described only works if every resistor has the same value. While that's true in this problem, it's misleading to pass that off as a method that works for all cases. --173.245.55.60 03:32, 1 April 2014 (UTC)

Good point. I made some slight alterations to clarify that we are assuming the resistors are equal. It seems a better solution than getting into the more complex version of the problem. --BlueMoonlet (talk) 12:20, 1 April 2014 (UTC)

The real question is: why did the physicist cross the road? --Alcatraz ii (talk) 00:53, 29 September 2014 (UTC)

to get to the other sine. Or if you want a punchline specific to physics (sine is a math concept technically)... Brownian motion--Twisted Code (talk) 20:25, 30 March 2023 (UTC)

Amazing. From the first comment the discussion is diverted from discussing the comic, to discussing the problem presented in the comic. The commentators have been nerd sniped by a demonstration of nerd sniping. Randall is just that good. 108.162.216.86 17:55, 30 April 2014 (UTC)

"Sniping" might also be a pun or have a deliberately dual meaning in this context, referring to both a sniper and a snipe hunt (do kids still practice the latter?). The former makes sense if Black Hat's purpose is to actually rid the world of physics and math nerds (consistent with his characteristic misanthropy and cynicism), but the latter also fits the theme of merely distracting a nerd with an impossible task, which the title text suggests may have been Randall's motivation for the strip. (On a side note, the Wikipedia article reveals that the terms sniper and snipe hunt have a common origin, which makes twice in the last month it's resolved a long-standing etymological puzzle for me. The other case united the multiple, seemingly unrelated meanings of minute ["tiny" vs. time] and second [ordinal vs. time]; see sexagesimal.) 173.245.54.182 01:40, 18 June 2014 (UTC)

I've been led to believe that 'minute' means 'tiny amount of time', 'second' is 'secondary tiny amount of time', and , I quote "Real snipe (a family of shorebirds) are difficult to catch for experienced hunters, so much so that the word "sniper" is derived from it to refer to anyone skilled enough to shoot one." from the snipe hunt wiki page. 141.101.104.4 23:45, 27 September 2014 (UTC)

Why doesn't someone solder together a thousand one ohm resistors into a grid then use an ohmmeter to measure the resistance? Then repeat with smaller and smaller grids to see if there's any effect on the measurement. If the resistance does not change, or at least doesn't change until the grid size gets quite small, then the "infinite" term in the problem is a 'red herring' to mislead. Pointless, useless, irrelevant etc information in problems is a common tactic for gauging the ability to recognize and reject such data. 199.27.133.122 00:35, 18 November 2014 (UTC)

Incidentally, should this page mention that what if 113 (I don't know how to do links, sorry) contains a picture of this comic? 108.162.216.65 23:36, 24 February 2015 (UTC)

Yes I will do so. Have just referred to another what if where he is mentioning nerd sniping. --Kynde (talk) 11:40, 16 February 2016 (UTC)

141.101.98.34 12:17, 22 May 2015 (UTC) Am I the only one concerned with the fact that this poor guy was still on a crosswalk? The truck should have stopped. 141.101.98.34 12:17, 22 May 2015 (UTC)

No you are not, and good point --Kynde (talk) 11:40, 16 February 2016 (UTC)

When the number of parallel resistors increase, the equivalent resistance decreases. So, in an infinite grid, wouldn't it approach zero? UrubuSelvagem (talk) 03:43, 28 September 2015 (UTC)

They are also in series. For each parallel group, there is, in fact a corresponding group in series. -- Flewk (talk) (please sign your comments with ~~~~)

It is not directly relevant to the discussion of the comic, but this needs to be posted here. Perhaps the best nerd snipe ever actually achieved and a nearly perfect match for the comic (my professor put it in the lecture notes for my group theory class): "Coxeter came to Cambridge and he gave a lecture, then he had this problem ... I left the lecture room thinking. As I was walking through Cambridge, suddenly the idea hit me, but it hit me while I was in the middle of the road. When the idea hit me I stopped and a large truck ran into me ... So I pretended that Coxeter had calculated the difficulty of this problem so precisely that he knew that I would get the solution just in the middle of the road ... One consequence of it is that in a group if a^2=b^3=c^5= (abc)^-1, then c^610=1." (J.H. Conway, Math. Intelligencer v. 23 no. 2 (2001)) I did a search, and the entire passage can be read here perhaps it is even possible that this event is the inspiration for this comic? The inclusion of the "large truck" is almost too perfect. 108.162.240.217 23:45, 2 October 2015 (UTC)

I have now added this story in a new trivia section. --Kynde (talk) 11:40, 16 February 2016 (UTC)

I know a solution that use random walks. :) 141.101.95.153 (talk) (please sign your comments with ~~~~)

I really like this comic. It says a lot about Black Hat, but so much more about Randall :-) --Kynde (talk) 11:40, 16 February 2016 (UTC)

So, *that's* how they did Gaudi in! I always suspected a plot; now I see the method. 172.68.142.89 16:30, 28 June 2018 (UTC)

Solution: ~0.7729906038309804 ohm. GcGYSF(asterisk)P(vertical line)e (talk) 20:36, 4 September 2021 (UTC)

Can't speak for Black Hat's (or Randall's) jurisdiction, but over here a vehicle not stopping for someone on a zebra crossing (especially, but also not taking some basic actions to avoid any unexpected hazard in any road, including not going too fast to do so) would be an actual driving offence. Obviously someone stepping out from behind parked vehicles, or wildlife randomly crossing busy roads without regard for 'human' common sense, would be mitigation and probably become a no-fault situation, but someone clearly stood in an empty road (let alone upon a marked crossing point) should not be a surprise to even a looming juggernaut being responsibly driven. The regressive anti-pedestrian laws in the US might somehow excuse this hollywood trope, but it still always bothers me when a character (gloating antagonist/doomed love-interest/whoever) gets suddenly side-slammed by a vehicle that nobody (we, they, the 'safe on the sidewalk' observers) had seen/heard until the moment before the impact (if that), but whose driver also appears to have been oblivious. And where there's no obvious sign of brakes used, vehicle and victim usually dissapearing just as rapidly off the opposite side of the shot, possibly remains so. (Does not apply to malicious side-swipes, obviously, where vehicle-as-a-weapon is invoked by whoever has gained off-screen control of the 'weapon', either to kick off a villainous attack or for a co-protagonist to interupt an attempted pre-mortem evil gloat...) 172.70.90.48 09:38, 23 January 2024 (UTC)

I created some YouTube Video that details how the problem can be solved (also exploring some paths that do not work): Here is the gitlab page for that https://gitlab.com/mooond/grid-of-1ohm-resistors and here is the youtube playlist (the solution is mostly in chapter III): https://www.youtube.com/playlist?list=PLoGRr8ff1uXESrWh6z0BNTYpc4Y-hlBOm