356: 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.
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 disadvantageous 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 also 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.
- [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.
- 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.
- "[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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