Since then, I've learned a thing or two from readers (wonderful readers!) that turns my thinking completely upside down. I experienced an "ah ha!" moment. You know, when the light bulb clicks on over your head (the new cool squiggly kind, not the old Easy-Bake Oven heat source kind). I was thinking about the problem of counting trees in the exact opposite way I should have been. The experience reminded me of a chapter in the history of science:
"Around 1752, Benjamin Franklin developed his theory on the flow of electricity. Franklin believed that electricity flows like a fluid, and this fluid flows from areas of positive charge to areas of negative charge. It would be over 100 years before it was understood that current flow was actually the movement of charged particles.
"By the time science understood that electric current was the movement of negatively charged electrons, it was too late to change the standards, the textbooks, the schematic diagrams, and the generally accepted theory. The direction of current flow was set as opposite to the actual flow of the charge carriers, which we now know flow from areas of negative charge to areas of positive charge."
-- Everything2.com
Today, it's best to think of electric current not as a flow of electrons in one direction, but as a flow of "holes" left behind as electrons move in the opposite direction.
After the jump, why Ben Franklin's mistake is like the challenge of counting trees.