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When good pseudorandom numbers go bad

Multivariate normal sampling can be wildly irreproducible if you’re not careful. Sometimes more than others. There are eldritch horrors, ill-conditioned matrices, and floating point nightmares in here. Teaching sand to do linear algebra was a mistake

There’s one key idea here: there are a lot of row operations that go into solving this problem, and if the divisor on one of these steps turns out to be very very small, the computation error due to floating point nonsense can be very large. Linear algebra was perfectly willing to destroy itself, and frankly we didn’t have to try very hard, all we had to do was feed it one ill-conditioned matrix, compute the wrong fucking condition number, and the entire hubristic edifice crashes to the ground like a second-rate Death Star. In practice then, defining condition numbers for a specific computing problem is a bit of a trade-off, trying to find something that a human being can make sense of without throwing away so much information as to render the whole exercise pointless.

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