“The Problem in the “Nerd Sniping” xkcd Comic” by peralice

About this episode

The episode discusses solving a problem from an xkcd comic using random processes to analyze circuit resistance.

A few days ago I saw this comic reposted, and I thought: wait! Unlike every prior time I have seen this comic, I actually know how to solve this now! One thing which I often find really cool, and which I don’t think comes up a lot in most people's mathematical education, is when you can learn something about some thing non-random by analysing a random process. So, let me show you a way to find out the resistance between two points in a circuit by instead finding out the number of times someone randomly walking around that circuit will step on those points. Equivalent Resistance Here's a closeup of the problem: You may be familiar with the rules for series and parallel resistors from high school: if there are some resistors in series (one after another), this is “equivalent to” having a single resistor in the circuit which has a resistanceequal to the sum of their resistances. That is, if you replace the resistors with just one of resistance , the behaviour of the rest of the circuit will be the same. Some resistors in series If there are some resistors in parallel, this is “equivalent to” having [...] --- Outline: (00:54) Equivalent Resistance (02:20) Circuit Laws (05:57) A…

People in this episode

Guest: peralice

Topics covered

• circuit analysis
• random processes
• equivalent resistance
• mathematics education
• random walks
• Fourier analysis

Keywords

• nerd sniping
• xkcd
• circuit laws
• system of equations
• potential function

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