Imagine the following simple setup: there are two switches (X and Z) and a lamp (Y). Both switches and the lamp are ‘On’. You want to know what switch X does, but you have only one try to manipulate the switches. Which one would you choose to switch off: X, Z or it doesn’t matter? These are the results of the quick Twitter poll I did on the question: Two switches X and Z control lamp Z. Both switches & the lamp are On. You wanna learn what X does. You have one try. Which switch to press? — Dimiter Toshkov (@DToshkov) September 4, 2017 Clearly, almost half of the respondents think it doesn’t matter, switching X is the second choice, and only 2 out of 15 would switch Z to learn what X does. Yet, it is by pressing Z that we have the best chance of learning something about the effect of X. This seems quite counter-intuitive, so let me explain. First, let’s clarify the assumptions embedded in the setup: (A1) both switches and the lamp can be either ‘On’ [1 ] or ‘Off’ [0]; (A2) the lamp is controlled only by these switches; there is nothing outside the system that controls its output; (A3) X and Z can work individually or in combination (so that the lamp is ‘On’ only if both switches are ‘On’ simultaneously). Now let’s represent the information we have in a table: Switch X Switch Z Lamp Y 1 1 1 0 0 0 We are…
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