Pythagorean addition in the head! And other things in the head
We learn how to quickly compute the combined variation of two processes without having to go through variance explicitly. We learn a fun technique to test situational awareness e.g. in pilots.
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Pythagorean addition
The length of the hypotenuse is given by c² = a² + b².
The total variation in standard deviations from two sources of variation is given by s² = p² + q².
The energy, mass and momentum of a particle is related as E² = (mc²)² + (pc)².
This is a really freakin' common relationship, and it's kind of annoying to mentally estimate. But not with the alpha-max plus beta-min algorithm, which turns it into a breeze. Find out how today!
Full article (2–5 minute read): Pythagorean addition
Flashcard of the week
I have the following flashcard from Working Minds (Hoffman et al.)
What example is used early in the book for testing situational awareness?
The book is a guide to cognitive task analysis, which is a technique for figuring out what people who are good at something really do. It explains some clever ways we can test what goes on in people's heads. Some of these same techniques are useful for better understanding what opaque AI systems do too.
I am totally going to borrow some of these techniques when teaching my children to drive, although that's still many years away.
The experimenter waits until the subject is in a tricky situation in the simulator, then pauses the simulation, covers the instruments, and asks the subject what the instruments were reading at the moment the simulation was paused.
I think this was phrased in terms of a flight simulator, but it could really be about any form of simulation that relies on instruments for feedback.
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