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enthusiastickThere was a physics teacher at my high school named Mr. Cahalan. During my time there many of his students affectionately nicknamed him Captain Cahalan, because in addition to teaching science he also taught a senior English course called Literature of the Sea, which was more or less an excuse for a bunch of guys to sit around reading Moby Dick and The Old Man and the Sea and, near as I can tell, not work very hard. Captain Cahalan was such a strong and influential personality that my friend Horowitz actually named his rock band Cahalan in his honor.
Its worth noting in all of this that I never actually had Mr. Cahalan as a teacher. There were too many great teachers at K-O for me to be so lucky as to study under them all, and this was one I missed. But I heard stories.
Captain Cahalan first came to my attention when a friend of mine was in his class, and reported that he seemed inordinately fond of decrying his own teachings as being "not physics," which seemed odd. According to the story he would spend twenty minutes walking the class through the solution to some particularly thorny physics dilemma, and when he was through, he would turn to them and smile.
"But that's not physics," Captain Cahalan would announce cryptically, with what I imagine to be a mischievous twinkle in his eye. "That's just algebra."
This confusing statement mystified my friend at first, and so she shared it with me and we spent a while trying to puzzle out just what the Hell he was talking about. The answer seems obvious to me now, upon reflection: a great deal of what is taught in high school as being physics (and some chemistry) is in fact simple algebra. If you're really lucky and very smart it might even be calculus, but that's still not necessarily physics. You learn to correctly apply and manipulate the formulae that have been laid out in order to come up with an answer.
In the true pursuit of physics, however, it is the formula themselves which are the answer, and rather than making the data fit into them you are attempting to make them fit the data. You don't try and calculate how fast a weight will fall from a certain height or how far it will slide across a surface before friction stops it. You know these things already. Instead you measure them as precisely as possible and try to back-engineer the equations we now take for granted. Isaac Newton is a genius not for being good at manipulating what we knew to be true but instead for finding mathematical ways of describing the world as it was, and accurately predicting how the universe would behave.
Incidentally these two qualifiers for good physics, that it be both descriptive and predictive, is part of where we get into trouble with String Theory, and why its arguably not a theory at all. String Theory is descriptive as you like; it provides wonderful, almost poetic characterizations of the world as it is. But it predicts nothing, and thus the rigorous testing that makes up the scientific method cannot be applied to it. And since it can be neither proven nor disproven through experiment, its not much of a theory at all, and there's a movement in physics to stop discussing it and teaching it entirely, because it encourages lassitude. A whole generation of scientists is being raised to believe that we know the answer and simply can't find a way to prove it, rather than striving to find a better, more useful answer. But I digress.
I got to thinking about all of this because of work. In my current job at a research company I spend a lot of time working with statistics. And statistics bother me, not just because they're damned lies. Statistics is one of several field of mathematics that I almost completely failed to grasp. Alongside geometry I am forever puzzled by statistics because I cannot get my hands around it. Lacking an intuitive grasps of the fundamental concepts I never quite get comfortable, and am forever struggling, adrift in a sea of terms I must look up again and again, because I never developed an index in my brain, and so even when I have the definitions in mind I can't properly file them away.
Whereas, by contrast, I'm happy to do algebra until the cows come home. Or simple arithmetic by hand, for that matter. These things I understand on some fundamental level, probably because they were taught to me a great deal more slowly and laboriously. And so where any number of my contemporaries and coworkers will throw up their hands and flail in despair at having to solve a simple one-variable formula, or perform long division, I will delight, since its one of the few mathematical tasks I still remember how to do. Give me a pencil and some scratch paper and I will work out whatever you like "the long way." And a willingness to do so, an understanding of how its done, can occasionally be fantastically useful. When working with Microsoft Excel, for example, sometimes the thing to do is write out your formula on a piece of paper and solve it for X, then plug that formula into your cell (replacing A1 or whatever for X) and you're off.
Its a pity, really. I'm not especially a math person, and I grew up believing that meant that I could never really be a science person, either. I'm fascinated by science -- some science, anyway -- I'm curious and I'm engaged, but in high school at least I walked away embarrassed by the fact that these things alone did not translate into good grades. And perhaps that was true for me, but computers are getting better and better at doing our algebra and calculus for us, and there will come a time when the only qualifications required for science will be interest and passion, and the value of qualities like insight and inspiration will shine through even the most mathematically challenged student.
Its worth noting in all of this that I never actually had Mr. Cahalan as a teacher. There were too many great teachers at K-O for me to be so lucky as to study under them all, and this was one I missed. But I heard stories.
Captain Cahalan first came to my attention when a friend of mine was in his class, and reported that he seemed inordinately fond of decrying his own teachings as being "not physics," which seemed odd. According to the story he would spend twenty minutes walking the class through the solution to some particularly thorny physics dilemma, and when he was through, he would turn to them and smile.
"But that's not physics," Captain Cahalan would announce cryptically, with what I imagine to be a mischievous twinkle in his eye. "That's just algebra."
This confusing statement mystified my friend at first, and so she shared it with me and we spent a while trying to puzzle out just what the Hell he was talking about. The answer seems obvious to me now, upon reflection: a great deal of what is taught in high school as being physics (and some chemistry) is in fact simple algebra. If you're really lucky and very smart it might even be calculus, but that's still not necessarily physics. You learn to correctly apply and manipulate the formulae that have been laid out in order to come up with an answer.
In the true pursuit of physics, however, it is the formula themselves which are the answer, and rather than making the data fit into them you are attempting to make them fit the data. You don't try and calculate how fast a weight will fall from a certain height or how far it will slide across a surface before friction stops it. You know these things already. Instead you measure them as precisely as possible and try to back-engineer the equations we now take for granted. Isaac Newton is a genius not for being good at manipulating what we knew to be true but instead for finding mathematical ways of describing the world as it was, and accurately predicting how the universe would behave.
Incidentally these two qualifiers for good physics, that it be both descriptive and predictive, is part of where we get into trouble with String Theory, and why its arguably not a theory at all. String Theory is descriptive as you like; it provides wonderful, almost poetic characterizations of the world as it is. But it predicts nothing, and thus the rigorous testing that makes up the scientific method cannot be applied to it. And since it can be neither proven nor disproven through experiment, its not much of a theory at all, and there's a movement in physics to stop discussing it and teaching it entirely, because it encourages lassitude. A whole generation of scientists is being raised to believe that we know the answer and simply can't find a way to prove it, rather than striving to find a better, more useful answer. But I digress.
I got to thinking about all of this because of work. In my current job at a research company I spend a lot of time working with statistics. And statistics bother me, not just because they're damned lies. Statistics is one of several field of mathematics that I almost completely failed to grasp. Alongside geometry I am forever puzzled by statistics because I cannot get my hands around it. Lacking an intuitive grasps of the fundamental concepts I never quite get comfortable, and am forever struggling, adrift in a sea of terms I must look up again and again, because I never developed an index in my brain, and so even when I have the definitions in mind I can't properly file them away.
Whereas, by contrast, I'm happy to do algebra until the cows come home. Or simple arithmetic by hand, for that matter. These things I understand on some fundamental level, probably because they were taught to me a great deal more slowly and laboriously. And so where any number of my contemporaries and coworkers will throw up their hands and flail in despair at having to solve a simple one-variable formula, or perform long division, I will delight, since its one of the few mathematical tasks I still remember how to do. Give me a pencil and some scratch paper and I will work out whatever you like "the long way." And a willingness to do so, an understanding of how its done, can occasionally be fantastically useful. When working with Microsoft Excel, for example, sometimes the thing to do is write out your formula on a piece of paper and solve it for X, then plug that formula into your cell (replacing A1 or whatever for X) and you're off.
Its a pity, really. I'm not especially a math person, and I grew up believing that meant that I could never really be a science person, either. I'm fascinated by science -- some science, anyway -- I'm curious and I'm engaged, but in high school at least I walked away embarrassed by the fact that these things alone did not translate into good grades. And perhaps that was true for me, but computers are getting better and better at doing our algebra and calculus for us, and there will come a time when the only qualifications required for science will be interest and passion, and the value of qualities like insight and inspiration will shine through even the most mathematically challenged student.
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(no subject)
Date: 2007-01-11 07:51 pm (UTC)I revel in Geometry and I comprehend Statistics well enough. Algebra and the things that follow from it, however, make me want to poke out my eyeballs and the eyeballs of others.
I often wish I could have been a Sociobiology major. But, it's not really an undergrad major and I wouldn't want to wade through all that real biology (and more importantly chemistry and physics) to get to this thing at the end that's more Evolutionary Psychology than anything else. It falls into that category of things like Archaeology that, though though they sound incredibly interesting to me, I will probably never really wind up involved with.
(no subject)
Date: 2007-01-11 09:19 pm (UTC)Geometry is actually very similar (though I won't be able to convey my point as easily nor as eloquently as you might). In high school physics, they give you the pre-derived equations and have you do the labs in hopes that you can prove to yourself that the equations work. Why the equations work is often left on the back burner and forgotten about while waiting for everyone to meet the first objective. Now, with geometry, they show you all the shapes and hand you the boiled-down, algebraic equations for area, volume, etc with the same expectations. The hows and whys aren't presented until you get to calculus 2. Then they show you where the equations come from and how to perform the calculations faster using integrals.
As far as statistics goes, the only thing I understand is averaging test data in order to model that property in a much larger population. Especially if it were a destructive test. Then you'd have no product left.
(no subject)
Date: 2007-01-13 03:19 am (UTC)(no subject)
Date: 2007-01-13 03:35 am (UTC)(no subject)
Date: 2007-01-13 03:37 am (UTC)(no subject)
Date: 2007-01-15 07:43 pm (UTC)