natural log raised
negative root one times pi
plus one equals naught
number plus number
thus begins human science
gods rule no longer
Thursday, August 5, 2010
Monday, November 9, 2009
Mathematical Writing as Modern Runes
The symbols of mathematics often appear in American pop culture in writings, movies, posters and T-shirts. In some cases individuals using the symbols understand what they mean and want to show-off their knowledge of the subject. However, in many more cases the terms are simply modern runes that convey the users sense that math is truth and beauty and power and like a magic potion bestows the same on the wearer of the T-shirt, the room in which the poster hangs, or where ever else the conjuror may use them. The most frequently seen such spell is “energy equals mass times the constant of light squared” a short hand form of Albert Einstein’s Special Theory of Relativity. It is difficult to say just why the math-illiterates are drawn to the formula, but, it has become a wide spread icon in popular culture. It appears on posters, coffee mugs, clothing and most anything which someone may feel the need to decorate to show a relationship to science, intelligence or education. Or, maybe it is just the beauty and simplicity of a far reaching idea.
When I say runes of course I make reference to the ancient Germanic writings that may or may not have been real writing. One school of thought explains them, at least early on, as the effort of illiterate people to imitate writings they saw in use by more advanced cultures. Symbols to which the illiterate attributed magical powers which they could not understand, but felt sure had power because the educated among their foes could use them to great effect. They, therefore, developed their own writing which could be inscribed on weapons, clothes, monuments and other objects that may need magic support. Whether that definition is right or not it is the one I use here to describe a concept of use of mathematical symbols and statements which, I believe, many who employ do not, in fact, comprehend.
It is all the more sad because it seems obvious that the math-challenged want to know the language and be let in on its secrets. I hear much in the media about the sad state of art education in public schools and how these are often the first programs to be cut in financial hard-times. The problem with math education is not the same. Most recognize the importance of math to basic education. Few recognize the esthetic appeal of math; the art, not “of math,” but in math.
Maybe, those empty art classrooms could be filled with math theory classes to replace the otherwise lost esthetic. I’m just saying ...
Unfortunately few seem to recognize the profound human need for what are described as “advanced” math. I refer not to applied math, but “pure” math. That word used by math snobs to mean math solely for the sake of math itself, and who, consequently, turn-off all of us not born to the subject. By advanced I mean those math categories usually taught only at college or graduate-school levels. Now that I have delved into “Math Theory” through the dubious realm of popular books on the subject, I can only wonder why I was not taught this most basic of math comprehension very early in my primary schooling? It would be useless in balancing my check book or compiling actuarial tables, but it would be good for the soul. It may have sparked affection for math that would have given me cause to want to learn the multiplication tables. (I learned them at recess as punishment for talking in class.) Not to mention that it is fun, unlike some of the “practical” math I was so bored with as a child. I was an old man before I learned that math is a fun game.
Our education system is so wrapped up with learning the practical stuff we all need to get on in life it relegates the fun stuff to late in our college careers, if at all. I attended a state supported school whose freshman courses, like most, were designed to “wash-out” the lackadaisical and intellectually unfit. (I qualified for both.) It was often said that college gets easier as one rises through the grades. True. Partly because one gets educated to the system, how it all works, what the tricks are, etc. But, mostly the subject matter becomes more enjoyable, more worth while, more applicable, and pertinent.
The survey history course you were forced to endure as a freshman tried to cram a thousand years of human experience into three one hour lectures a week for three months from one book. It was only as a upper classman or graduate that you got down to learning all there was to learn about some specific historical tidbit that you really could spend the time and energy with to see the beauty or truth or power which was what really fired your imagination about history in the first place. Who cares who the emperors of Rome were? Is it not more interesting that the political parties were derived from chariot race teams?
The old academic saw about the PhD; that as you progress through school you learn more and more about less and less until you finally achieve a PhD and know nothing at all. It is funny, especially for those of us jealous of the achievement. The truth is that it is only by getting down to brass tacks (you know, the smallest item) that one can really appreciate the whole.
Energy equals mass times the constant for light squared as math runes may also be a psychological handle on the otherwise incomprehensible universe. Indeed all such popular displays might be a cry for enlightenment; a shout to humanity to see and understand. Nay, condemnations of educators that do not, themselves, comprehend the beauty of Euler’s natural log to the power of the square root of negative one times pi, plus one equals zero. Why did we all not cover this most beautiful of equations in primary school?
So, display those un-intelligible math statements proudly! Care not that you can not fully explain Fourier’s transformation, or construct Gauss’ seventeen-sided polygon, or catch the humor in ”there are 10 types of people, those who understand binary …,” well, not without the internet. It is all good. Rejoice in what you can! I still don’t get Jackson Pollock, but I am impressed with some of his colors.
P.S. I purposefully did not use mathematical symbols to arouse in the reader a yearning for their simplicity and clarity. Miss them, don’t you?
October 17, 2009
When I say runes of course I make reference to the ancient Germanic writings that may or may not have been real writing. One school of thought explains them, at least early on, as the effort of illiterate people to imitate writings they saw in use by more advanced cultures. Symbols to which the illiterate attributed magical powers which they could not understand, but felt sure had power because the educated among their foes could use them to great effect. They, therefore, developed their own writing which could be inscribed on weapons, clothes, monuments and other objects that may need magic support. Whether that definition is right or not it is the one I use here to describe a concept of use of mathematical symbols and statements which, I believe, many who employ do not, in fact, comprehend.
It is all the more sad because it seems obvious that the math-challenged want to know the language and be let in on its secrets. I hear much in the media about the sad state of art education in public schools and how these are often the first programs to be cut in financial hard-times. The problem with math education is not the same. Most recognize the importance of math to basic education. Few recognize the esthetic appeal of math; the art, not “of math,” but in math.
Maybe, those empty art classrooms could be filled with math theory classes to replace the otherwise lost esthetic. I’m just saying ...
Unfortunately few seem to recognize the profound human need for what are described as “advanced” math. I refer not to applied math, but “pure” math. That word used by math snobs to mean math solely for the sake of math itself, and who, consequently, turn-off all of us not born to the subject. By advanced I mean those math categories usually taught only at college or graduate-school levels. Now that I have delved into “Math Theory” through the dubious realm of popular books on the subject, I can only wonder why I was not taught this most basic of math comprehension very early in my primary schooling? It would be useless in balancing my check book or compiling actuarial tables, but it would be good for the soul. It may have sparked affection for math that would have given me cause to want to learn the multiplication tables. (I learned them at recess as punishment for talking in class.) Not to mention that it is fun, unlike some of the “practical” math I was so bored with as a child. I was an old man before I learned that math is a fun game.
Our education system is so wrapped up with learning the practical stuff we all need to get on in life it relegates the fun stuff to late in our college careers, if at all. I attended a state supported school whose freshman courses, like most, were designed to “wash-out” the lackadaisical and intellectually unfit. (I qualified for both.) It was often said that college gets easier as one rises through the grades. True. Partly because one gets educated to the system, how it all works, what the tricks are, etc. But, mostly the subject matter becomes more enjoyable, more worth while, more applicable, and pertinent.
The survey history course you were forced to endure as a freshman tried to cram a thousand years of human experience into three one hour lectures a week for three months from one book. It was only as a upper classman or graduate that you got down to learning all there was to learn about some specific historical tidbit that you really could spend the time and energy with to see the beauty or truth or power which was what really fired your imagination about history in the first place. Who cares who the emperors of Rome were? Is it not more interesting that the political parties were derived from chariot race teams?
The old academic saw about the PhD; that as you progress through school you learn more and more about less and less until you finally achieve a PhD and know nothing at all. It is funny, especially for those of us jealous of the achievement. The truth is that it is only by getting down to brass tacks (you know, the smallest item) that one can really appreciate the whole.
Energy equals mass times the constant for light squared as math runes may also be a psychological handle on the otherwise incomprehensible universe. Indeed all such popular displays might be a cry for enlightenment; a shout to humanity to see and understand. Nay, condemnations of educators that do not, themselves, comprehend the beauty of Euler’s natural log to the power of the square root of negative one times pi, plus one equals zero. Why did we all not cover this most beautiful of equations in primary school?
So, display those un-intelligible math statements proudly! Care not that you can not fully explain Fourier’s transformation, or construct Gauss’ seventeen-sided polygon, or catch the humor in ”there are 10 types of people, those who understand binary …,” well, not without the internet. It is all good. Rejoice in what you can! I still don’t get Jackson Pollock, but I am impressed with some of his colors.
P.S. I purposefully did not use mathematical symbols to arouse in the reader a yearning for their simplicity and clarity. Miss them, don’t you?
October 17, 2009
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