Editing 356: Nerd Sniping

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 [https://www.allaboutcircuits.com/technical-articles/resistors-in-parallel-circuit-analysis-with-parallel-resistance/ 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 {{w|Siemens_(unit)#Mho|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 [http://oeis.org/A211074 0.773]  ohms.  See [http://www.mathpages.com/home/kmath668/kmath668.htm Infinite Grid of Resistors].

Randall explained in [http://www.youtube.com/watch?v=zJOS0sV2a24 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 [https://3.bp.blogspot.com/_Ap14FtNN91w/Rll5oF8Px0I/AAAAAAAAAHo/cHG6a83cmlI/s1600-h/GLAT_3.jpg 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)|what if?]]'' blog. In [https://what-if.xkcd.com/113/ 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 [https://what-if.xkcd.com/124/ Lunar Swimming]—see the title text for the second to last picture.

**The story can be read in the book ''[https://books.google.ca/books?id=aFHyUfFUVIwC&printsec=frontcover&hl=da#v=onepage&q&f=false Candid Science Five]'' from 2005 (two years before this comics release), specifically on [https://books.google.ca/books?id=aFHyUfFUVIwC&pg=PA22&lpg=PA22&dq=Coxeter+came+to+Cambridge+and+he+gave+a+lecture,+then+he+had+this+problem+...++Ileft+the+lecture+room+thinking.+As+I+was+walking+through+Cambridge,+suddenly+theidea+hit+me,++but+it+hit+me+while+I+was+in+the+middle+of+the+road.++When+the+ideahit+me+I+stopped+and+a+large+truck+ran+into+me+...++So+I+pretended+that+Coxeter+hadcalculated+the+difficulty+of+this+problem+so+precisely+that+he+knew+that+I+would+getthe+solution+just+in+the+middle+of+the+roa&source=bl&ots=CgmxTG2n0w&sig=ohqqBGtJrpuQFeiCPPusMVsQUV4&hl=en&sa=X&ved=0CB0Q6AEwAGoVChMIy4KdnPakyAIV0ZeICh2OGghP#v=onepage&q=%22in%20the%20middle%20of%20the%20road%22&f=false pages 21–22]:

::"{{w|Harold Scott MacDonald Coxeter|[Donald] Coxeter}} is my hero. I remember a story at one of the conferences in Coxeter's honor and people were telling how this wonderful man had turned them into mathematicians. I thought I must say something different. So when I got up, I said, “Lots of people have come here to thank Coxeter; I've come here to forgive him.” I told them that Coxeter once very nearly succeeded in murdering me. His murder weapon was something that even Agatha Christie would never have thought of: a mathematical problem. Then I told the story, which is actually true.

:: Coxeter came to Cambridge and gave a lecture. Then he had this problem for which he gave proofs for selected examples, and he asked for a unified proof. 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 and bruised me considerably and the man considerably swore at 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. In fact I limped back after the accident to the meeting. Coxeter was still there, and I said, “You nearly killed me.” Then I told him the solution. It eventually became a joint paper. Ever since, I've called that theorem “the murder weapon”. One consequence of it is that in a group if a² = b³ = c⁵ = (abc)⁻¹, then c⁶¹⁰ = 1."