This past week we've been working on diffusion.
I get my kids up into a corner, then tell them to pick a direction, walk in that direction until they hit something, then ricochet as though you were a billiard ball.
After a few moments, I ask them to stop and note their positions. I tie their motion to the "Whoever Smelt It, Dealt It" hypothesis of fart diffusion--silly but effective--then ask them to keep moving again. The students are interspersed throughout the room, but two critical ideas emerge:
1) They are not evenly dispersed, and
2) Their positions keep changing even when they are at equilibrium. (Equilibrium is a dynamic state--true equilibrium, in the sense that every part of a system has the same concentration of particles, does not hold in tiny volumes.)
I have a box of balls--yellow on one side, black on the other, with a free agent blue ball (yes, sophomores giggle at "blue ball") randomly tossed in the mix. I shake them up until the blacks and yellow balls are reasonably interspersed.
"Will this arrangement of balls ever happen again if I keep shaking the box?"
Most say no.
"Is this arrangement possible?"Well, yeah, Dr. D, duh--it just happened."Will this arrangement of balls ever happen again."It could, maybe..."Will it?"
Most think not, and I agree with them. I think. Playing with an infinite number of possible arrangements over an infinite number of trials scrambles the mind.
A child muttered in class this week that she keeps knowing less than she thought she knew.
I stole this exercise from Ms. Rinaldi here at BHS--I steal from a lot of folks.
Leslie makes a good point--Michael Franti rocks!