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Interactive math textbooks

There is no excuse for Ron Larson‘s Calculus, the textbook I used in high school. It’s over 1,000 pages long and it’s printed on paper. This may have been acceptable in 1998 when it was first printed, but today I am amazed that it remains in print. That’s because textbooks should be electronic and interactive.

You have to be suspicious of exisitng “interactive” math content, because it may be interactive in a very shallow sense. For example, if you get a hard question wrong then it shows you an easier question. What I’d like to see are interactible examples and figures: Move a point around on the figure and see how things change in real-time.

Strom et al. have done a very good job of this with Immersive Math, an interactive linear algebra textbook. (A paper textbook cannot update its figures in real-time.) They also have hover-tips for referenced theorems and definitions, which is a nice touch. (In a paper textbook you’d have to flip back.)

I made my own demo for solids of revolution, a difficult topic for many students. You can move a slider to see the differential volume element change. But you can also hover over a term, like dA, in the equations to highlight the geometrical interpretation corresponding to the term. Click the animation to be redirected to the demo and try it yourself.

rev3

Artificial consciousness

I think it’s only a matter of time before somebody builds a consciousness in the laboratory. If you don’t believe in souls, then a brain is just an organic computer. Here are some numbers to illustrate the plausibility:

Take the number of neurons in the cerebral cortex of a mouse (4E6) and multiply it by the number of stars in the galaxy (1E11). Now multiply it by the price of gold in USD per gram (1E3). Incredibly, the resulting number is still less than the number of transistors in the world (3E21).

Luddites may leave angry rants in the comments.