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SilasBarta comments on Learned Blankness - Less Wrong
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Comments (186)
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? ;-)
When I teach College Algebra at the community college where I work, one of the standard applications in the chapter on exponents and logarithms is half-life. The required text doesn't give the half-life formula above, but instead gives
mass_final = mass_initial * exp(k * t)
and shows how to calculate k by using t_halflife for t (and 1/2 mass_initial for mass_final).
This is a useful general method, but in the course of explaining why radioactive decay is exponential and what half-life means, I naturally derive
mass_final = mass_intial * (1/2) ^ (t / t_halflife),
so I just tell them to use that.
Maybe I'm cheating them because I'm making them do less work, but I like to think that some of them leave the class understanding what the heck a half-life is.
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.
I was going to ask where the constant for the exponent came from, but with a calculator and the Wikipedia page on exponentiation, I figured it out myself. This site is good for me.
I really think that strip should be in the Related To list at the top...
I have to say, if I saw anyone write the equation that way I'd question how much they understood the concept themselves!
EDIT: Let me also add, if I saw anyone asking that "what's the constant" question, I'd conclude they didn't understand it unless I saw good evidence otherwise...
Just to brighten your day, that would be most teachers and probably most textbook editors.