Scientific exploration reveals the hole truth
Much of science involves counting things. So why is it that accountants are called ac-count-ants and scientists are not? I think if I had it to do it over again, I might be an accountant instead of a scientist. Counting money has accounted for much of the time I spend anyway. Also, accountants seem to have more of it to count than I do.
But if I had been an accountant, I’d have missed counting so many other interesting things. Over the years I have counted nematode eggs, scavenging ants, mosquitoes, eggs laid by solitary bees, mites on flies and even how many degrees centigrade must accumulate for a mosquito to hatch. Great interesting stuff!
One thing about counting is especially interesting. Scientists often count things that aren’t there. How do we do that? Of course, accountants do the same thing. How do accountants account for the number of people who are unemployed? Even more peculiar, how do they know how many people have “quit” looking for a job? How do they count the money that wasn’t spent during last year’s Christmas season?
Did you know that counting things that aren’t there is a very ancient tradition? Robert Hooke was a brilliant scientist in the 1600s. He invented air pumps, diving bells, rain gauges and even a mechanical adding machine. He wasn’t particularly well-liked because he had a nasty temper. We are told that he and Sir Isaac Newton had a running feud for years. (That brings up another question: Why are so many scientists such odd characters? I am about the only normal one I know.)
But back to Hooke. One time he was examining a piece of cork under a microscope. (Let’s hear of an accountant doing something interesting like that!) He could see that the cork was made up of tiny perforations, or holes, so he decided to count them. Here is a quote from his paper on the subject. “I told (counted) several lines of these pores and found that there were usually about three score of these small cells placed end ways in an eighteenth part of an inch, whence I concluded that there must be near eleven hundred of them ... in the length of an inch, and therefore ... about 1200 million (in a cubic inch).” His experience reminds me of a line from a Beatles’ song: “Now they know how many holes it takes to fill the Albert Hall.” I mean he was counting holes for Pete’s sake! There’s nothing there. It’s like asking how many nothings fit into nothing.
Still, the quote above is important because it was the first known use of the word “cell” to refer to the structure of living things. It was another two centuries before Theodor Schwann proposed the cell theory that all living things are composed of cells. I guess this means we’re mostly holes. This whole concept is, more or less, the root of our understanding of living systems today.
Maybe even stranger than “counting holes” are the physical scientists who count things that can’t even be seen. I was suspicious when I first learned that chemists counted atoms. Now they count electrons and quarks. Come on! And physicists count calories, lumens and magnetic forces.
In my mind, though, mathematicians account for the strangest counting. They count numbers that are nothing more than an idea to begin with. This leads them to count such things as groups of ideas, which are simply the idea of a group of ideas. For example, do you know how many numbers are “even prime numbers”? Just one. It’s two.
There are five “platonic solids,” whatever those are.
I’m not totally clear on the advantage of knowing the number of Archimedean solids (13. )But how many grains of pollen a bee can carry in its pollen sac? Now that’s something you can count on.
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Gary McCallister is professor of biology at Mesa State College.