michaelsullivan comments on Learned Blankness - Less Wrong

130 Post author: AnnaSalamon 18 April 2011 06:55PM

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Comment author: SilasBarta 18 April 2011 07:29:38PM *  28 points [-]

Great article! I didn't realize how I blank on some of those.

When I tutored math, new students acted as though the laws of exponents (or whatever we were learning) had fallen from the sky on stone tablets. They clung rigidly to the handed-down procedures. It didn’t occur to them to try to understand, or to improvise.

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?

Sandra runs helpless to her roommate when her computer breaks -- she isn’t “good with computers”. Her roommate, by contrast, clicks on one thing and then another, doing Google searches and puzzling it out.[4]

Wow, a footnote on this one and not even a link to the xkcd about it? ;-)

Comment author: michaelsullivan 19 April 2011 05:37:25PM 9 points [-]

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.