Monday - November 16, 2009

Proof: Teachers Are Lazy

Did you ever have one of those “Ah ha!!” moments, and perhaps say “Eureka!” out loud?

And you know the story behind eureka. [εὕρηκα] It’s Greek for “I found it!” And you were taught the story in school, whether you got any of the details or not. Some old king (Hiero III, king of Syracuse) way back in the day (265 BC) thought that his crown wasn’t made of pure gold. So he hired Archimedes to prove him right, without melting the thing down for assay. One day Archi was taking a bath, and noticed that the water level in the tub went up when he stuck his leg in. “Eureka!” he cried, and went running off to the palace without even stopping to put on a towel.

And teachers use this little story to teach the basic concepts of mass and volume. End of story.



Except, well, while that thesis is factually sound, the Greeks didn’t have the technology to carry out the experiment to a reliable degree of proof. Given a pot big enough to put an actual crown in, the difference in water level between one made of pure gold and one made of a lesser alloy would have been less than half a millimeter. Barely visible to the naked eye, and well within the margin of error caused by any air bubbles, changes in temperature, evaporation, etc.

The real way Archimedes could have found that the crown wasn’t pure was to balance it against a measure of pure gold, then to put both pans of the balance under water. The pan with the less pure gold in it would rise up.

420 years ago Giambattista della Porta wrote about this, and showed how dipping the scales would do the job. 3 years before that Galileo had written a similar treatise, but he had figured out a way to read the scales to prove exactly what the impurity level was. That method and that knowledge may have been old hat even then.

So the world has known that the Archimedes story is pretty weak for an awfully long time. This is what author Terry Pratchett calls “lies to children”; teaching a highly simplified story to kids that at face value seems to work, so that later on you can teach them the details without their little heads being in danger of popping. Except that the actual real method of proof is pretty simple, and makes for a wonderful demonstration, and expands the kid’s minds to encompass 2 other natural laws that old Archi is credited with discovering. But that takes a bit more effort. And who knows if most kids are ever given the more advanced part of the story anyway. See? Teachers really are lazy.

Read all about it if you want. Here (easy), here (medium), and here (hard).

Ok, the obvious pun here is about “lies in the balance”, so you witty types will have to do better than that in the comments.

Posted by Drew458     on 11/16/2009 at 03:24 PM   
Filed Under: • Amazing Science and Discoveries •  
• Comments (1) • Trackbacks(0)  Permalink •  

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