michaelsullivan comments on Learned Blankness - Less Wrong
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Great article! I didn't realize how I blank on some of those.
I'd like to self-centeredly bring up a similar anecdote, which forms part of my frustration how people give unnecessarily-complex explanations, typically based on their own poor understanding.
In chemistry class, when we were learning about radioactive decay and how it's measured in half-lives, we were given a (relatively) opaque formula, "as if from the sky on stone tablets". I think it was
mass_final = mass_initial * exp(-0.693 * t / t_halflife)
And students worked hard to memorize it, not seeing where it came from. So I pointed out, "You know, that equation's just saying you multiply by one-half, raised to the number of half-lives that passed."
"Ohhhhhhhhhhhh! It's so much simpler that way!" And yet a test question was, "What is the constant in the exponent for the radioactive decay formula?" Who cares?
Wow, a footnote on this one and not even a link to the xkcd about it? ;-)
It looks like that formula is a lot like cutting the ends off the roast.
The answer to "who cares?" is most likely "some 1930s era engineer/scientist who has a great set of log tables available but no computer or calculator".
I am just young enough that by the time I understood what logarithms were, one could buy a basic scientific calculator for what a middle class family would trivially spend on their geeky kid. I remember finding an old engineer's handbook of my dad's with tables and tables of logarithms and various probabilistic distribution numbers, it was like a great musty treasure trove of magical numbers to figure out what they meant.
I don't know where that ended up, but I still have his slide rule.
Of course, even in the day, it would make more sense to share both formula, or simply teach all students enough math to do what Gray does above and figure out for yourself how to calculate the model-enlightening formula with log tables. Since you'd need that skill to do a million other things in that environment.