Limits of the mind:
I watch little television but I got a Christmas present of DVD’s of the program “Big Bang Theory.” I found it utterly delightful. The principle characters are young physics faculty members and engineers at a big technology university. The apartment in which most of the action takes place sort of reminds me of home, tube radio, telescope, filing system, favorite couch and so forth. The characters are all brilliant and successful but rather socially inept. That part I can identify with as well.
One episode involved a sort of “Physics Bowl” competition. Questions were offered in the field of physics, and of course our heroes did right well. But on reflection most of the questions were one-word answer questions, factoids that the young men had well memorized. The American education system has been criticized for training students for that sort of exercise and just about nothing else. My own experience is consistent with the suggestion.
At the climax of the competition they are offered a Feynman diagram and an associated equation to be solved. They were totally at sea as of course was the viewing audience, myself included. But in fact it was the only time they were actually asked to think. For them it might not have been easy, but at least it should have prompted a lot of cerebration. In other words they did a caricature of the American student who can retain facts but cannot use them.
When I pick up a new fact or idea I generally busy myself with figuring out how it is related to other things I have been taught and then going on to see what other ways the new notion can be applied. It is almost a vice for me, as you may be able to tell from my essays. How in the world you would teach it is beyond me.
But I take it as axiomatic that you cannot think about something you know until you know something that you can think about. So I am not all that unhappy with the fact based approach. Give me the facts and ways they have been combined in the past and let me run with it.
But the fact is … or I think it is … that there are only so many ideas you can harbor. It has been established (Rodrigo Quian Quiroga et al. Brain Cells for Grandmother SCIENTIFIC AMERICAN vol. 308 no. 2, February 2013 page 31) that certain cells in the brain will respond to certain ideas. Sometimes it is medically necessary to put electrodes directly into a patient’s brain. If the patient is interested then this offers the opportunity to see under what circumstances that cell will change its rate of electrical discharge. One study involved presenting the patient with a number of pictures. Something familiar, like a familiar face, might stimulate the cell. Since the number of cells in the area was enormous and the number of pictures presented limited by the endurance of patient and examiner to a number very much smaller it is assumed that there are many cells that respond in about the same way. Then it was found that, at least sometimes, the cell would respond not only to that picture but any recognizable picture of the same person and even respond to the person’s name. In short they had caught the cell entertaining an idea.
It is all very interesting and much more sophisticated than years ago when cutting edge was being able to put an electrode into a neuron in the lateral geniculate body of a cat’s brain (part of the visual circuitry) and discover that this cell responded to a line presented in a particular orientation so as to fall on a particular place on the retina of the cat.
None of this helps you prepare for an exam unless of course the exam involves the very subject. But the bottom line I draw is that one can entertain only a finite number of concepts. 100,000 is probably not a bad estimate. That I seem to recall is the biggest vocabulary a person can have. In fact, again harking back to ancient recollection, if a person learns two languages that person will probably never learn either as well as if there had only been one. Some brilliant scholar was once described as being able to speak seven languages, but he had a peculiar accent in every one. You can approach the limit of just how many concepts your mind can handle.
I have groused before about such follies as the move to change the name starfish to sea star – right, it’s no fish and it’s no star either. That is utter waste of a precious and limited resource, my mind. Yes I have squandered any amount of time on the occult, not with the thought it could be used but with the thought that it might contain habits of mind that could be turned to good use. No luck, there. So that was not just wasted effort but wasted resource. Sure, “sea star” is not a concept. The starfish is the concept. “Sea star is only an extraneous bit of extra fluff, but the principle holds.
So how in the world does one communicate a concept? You can communicate facts, that’s easy. It’s just have a vocabulary and a grammar and if you have a fact you can transmit it efficiently to someone with the same resources. There must be a grammar of concepts.
Indeed there is such a grammar in specific fields. The Feynman diagram is an excellent example. If someone can formalize the grammar of consanguinity and fertility I shall be all ears.
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