| Math Mojo - Making Math Meaningful |
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Who Made this Site, Anyway? |
OK, so this atrocity committed against the commutative law is a stupid joke, and not exactly a MathMojo Multiplication Method, but I'm including it to make a point. We all "get" the joke, because we've experienced the universal phenomenon of drawing false conclusions. There are so many opportunities to reach false conclusions when learning math. Why is that? Well, of course, as usual, I don't know. But I have some Ideas about it that have been kicking around my head since my youth. As loyal readers of Math Mojo and the Math Mojo Chronicles know, I have a been a practicing magician (illusionist) since I was a kid. I spend a lot more time thinking about the meaning of magic than I do performing or practicing (and I've spent a lot of time doing those things). Naturally that lead me to thinking about why people make false conclusions. My thoughts about them are too complex to go into detail here, but I'd like to talk about one of them - and that's "voodoo." What the heck do I mean by "voodoo"? Well, as an example, let's take the case of the ancient superstition that lead people to believe that to appease the "volcano gods" you'd have to throw a virgin into the steaming lava-crater every year or so. Let's face it, those people had no clue what caused or prevented volcanos. But the things didn't erupt every year, so each year they were quiet, the people could tell themselves that their "virgin-volcano-pre-emption-plan" was working. Then, when the volcano finally erupted and blew the village into the next time-zone, they could say, "Well, for 20 years it worked, and it only failed once. Looks like a good system to us. And hey, maybe there was something that conspired against it. Yeah! That's the ticket! Maybe that harlot wasn't a virgin after all. That's why it didn't work. So... the system was good after all!" I know that this example sounds facetious, but I think it is closer to the truth as any other characterization of this phenomenon. And it still goes on today. "Look, the terrorists haven't blown up another set of World Trade Towers since 2001. So throwing the Constitution and the Bill of Rights into the toilet has been working after all!" When you study math, and learn how to model the way things work, by using as accurate data as you can find, and as in-depth analyses as you can come up with, and by being ruthlessly honest as you can be, you become a kind of "BS Detector." That doesn't mean that you never get fooled, it just means that you have better systems in place so you get fooled less often than people who rely on "voodoo thinking." Just like locking your car is no guarantee that it won't get stolen, but never locking it is almost a guarantee that it eventually will. "Voodoo thinking" is the sign of a very immature mind. That is why young children are so prone to it. The above joke pretty much only works when you tell it about young students. Just like 1+ 1 + 1 "must equal 111," or "twenty times one is twenty-one." What is happening is that the simplest answer to understand (the one that requires the least amount of thought) is taken as the actual answer. Sometimes people don't like to think. (Imagine that!) It is interesting that there is actually a similar way of thinking that is much more sophisticated, and actually makes sense. It is: "the simplest answer that works (often the one that requires the most amount of thought) is usually the best answer." This is a paraphrase of the famous "Occam's Razor." Usually the part about the answer working is not included in the quote, because it is assumed that you know that. Otherwise you could just say something inane, like, "Because the devil made me do it." "Why is the sky blue?" "Because" may be the simplest answer, and on some great Zen level it might work, but until we reach that great level, "because" is just idiotic. As an answer, it accomplishes nothing. Some simple answers, like twisting the commutative law to get 6 times 7 to equal 24, do more than nothing, they lead to total misunderstanding of the concept, and into a pit of more and more confusion until the misunderstanding is corrected. Have you ever heard the new age (rhymes with "sewage") concept that, "Since Einstein proved that quantums can be in two places at one time, that proves that some people can time travel, and that astral projection is true, and that you can go faster than the speed of light and that the law of attraction...blahblahblah." It is beyond hope to reason with simplistic pap like this. Many people only know the name of one physicist - that's why so many people erroneously associate Einstein with Quantum Theory. Those same people don't have a clue as to what the theory is about, or that the plural of quantum is "quanta," or even of what the word "quantum" means. But the main problem is that they take one concept and somehow magically assume they can extrapolate that to anything they find convenient. It is very much like our bad multiplication logic from the joke, only this time the fallacy is an atrocity committed against the associative law. It's like saying, "Well, since cars can travel at 200 mph, why can't they invent a dog that runs 200 mph?' The answer isn't that "they can't," the answer is, "What the hell kind of question is that? What does one have to do with the other?" I used to teach math at Job Corps facility. Many of the students there never had a decent education before (and Job Corps did all it could to make sure they never would at Job Corps, either, which is why I resigned..but I digress). Since a lot of the students never had the chance to develop their logic skills in school, I tried to introduce some logic concepts into the trivial math curriculum they were expected to learn by rote. I began with the old chestnut of, "If all firemen wear red suspenders, and my uncle is a fireman, what color are his suspenders?" Will it surprise you to hear that instead of realizing within nanoseconds that the answer is "red," most of those 16-22 year old students came up with remarks like, "Hey, I've seen firemen without red suspenders, so you're lying man," or "Why do they all wear red suspenders?" People like to overlook details about questions and statements if it makes it easier for them to think about the problem. In this case, the particle "if" was overlooked, and it turned the sentence from a syllogism (an "if-then" statement) into a statement of fact to these students. So now they could feel like they could make statements about it and judgments about me that made them feel like they had some control. But it kept them from understanding what I'd actually said, and it kept them from learning anything from it. I understand that insecure, immature minds feel like they need to do that. And I am not blaming some of those kids (many of whom were tragically deprived of most chances to develop their intellectual maturity) for lacking that maturity. It's not a value judgment. But I do think there is something fundamentally wrong with a society whose education system, mainstream media and political process value simple solutions for complex problems more than it values teaching deep, meaningful concepts to every one of its citizens. A person who is deprived of chances to understand his world is at a grave disadvantage. He may develop defense mechanisms to deal with his situation. It's the same way that many dumb people feel that "might makes right." They think that what they lack in brains, they can make up in violence. The answer is not to punish people for not having had the advantages that we may have had. That would only increase the spiral of deprivation. There but for fortune go you or I. The answer is for everyone to be enfranchised to understand what can be understood, wonder at what can't, and have the wisdom to know the difference. |
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Math Mojo is part of Magic and Learning - a company which uses methods of magicians to teach thinking skills.
