Teachable Moment:This TED video discusses the invention of the GPS as a perfect example of open innovative systems where "chance favors the connected mind". I also like it because it provides a good example of how innovation can be as simple as merely the inversion of our thinking... in this case, one group of scientists had discovered how to track a moving object in space from a fixed point on the ground... and another one pushed them to think about tracking a moving object on the ground from a fixed point in space.
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Only on TV, could a teacher find a teachable moment in a locked storage room with a gang member. And of course, if you're going to challenge a gang member to anything, it might as well be explaining to them how an atom works!
In 1935, Schrodinger wrote a paper about the state of Quantum Physics wherein he posited the following:
"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts"
Great video from Stand and Deliver
Your arm is about ten times longer than the distance between your eyes. That fact, together with a bit of applied trigonometry, can be used to estimate distances between you and any object of approximately known size.
Imagine, for example, that you're standing on the side of a hill, trying to decide how far it is to the top of a low hill on the other side of the valley. Just below the hilltop is a barn, which you feel reasonably sure is about 100 feet wide on the side facing you.