Math Links

1. Marvin Minsky on "What makes mathematics hard to learn?"

There is a popular idea that, in order to understand something well, it is best to begin by getting things right—because then you'll never make any mistakes.  We tend to think of knowledge in positive terms—and of experts as people who know exactly what to do.  But one could argue that much of an expert’s competence stems from having learned to avoid the most common bugs.

2. A Poker-based primer on p-hacking

It is easy to get impressive results if you are selective about what you tell people. If you have two groups of people who are equivalent to one another, and you compare them on just one variable, then the chance that you will get a spurious 'significant' difference (p < .05)  is 1 in 20. But with eight variables, the chance of a false positive 'significant' difference on any one variable is 1-.95^8, i.e. 1 in 3.

3. A readable assessment of roundoff errors in floating point computation (pdf)

Error-analysis attracts few students and affords fewer career paths. Therefore almost all users and programmers of floating-point computations require help not so much to perform error-analyses (they won’t) as to determine whether roundoff is the cause of their distress, and where.