Data!

Forward problems are problems with a well-defined answer: throwing a fair die, what’s the probability of getting a 4? Inverse problems look at data and create what necessarily has uncertainty: looking at this data, was it generated with a fair die?

Most problems given in mathematics classes (outside of statistics) are forward problems, with well-defined answers. Yet, most real-life problems are inverse problems. We don’t know the actual equations of the world, and even if we did, our measurement of reality would have uncertainty.

Pure mathematics is important, but I maintain complete allergy to error is unhealthy and gives a distorted view of mathematics. Consider, for instance —

This is my favorite of Dan Meyer’s videos.

If you go through the calculations correctly for working out how long it takes Dan to get up the stairs, the answer comes short by about a second and a…

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