Howdy! I’m in a hyper and surreal state of mind. I’ve just returned from a Barnes and Noble binge. Something about that place, man, makes me feel like I can do anything! Especially when I have a sizable birthday gift card… I just realized I walked out with the equivalent of a semester’s worth of college course work. Bought a book on Macromedia Dream Weaver, so that maybe someday I can spice up the ol’ blog a little bit. Then I found “The Globalization Reader” which should bring me up to date on the state of the world. I think I’ve been needin’ that. Kansas State at Salina was a little light on the humanities. I’ve also been feeling like I got out of calculus too soon. I know, people say that all the time. I’ve just kinda been feeling like my brain is turning to putty, so I bought a full calc textbook in paperback. Its like Tae Bo for the mind, baby!
Speaking of… I’m just finishing up “Zen and the Art of Motorcycle Maintenance” by Robert Pirsig. Talk about a head trip. One of the best books I’ve ever read. That may also have something to do with my rekindled interest in math. He describes the odd situation of different systems of geometry being logically sound individually, but contradictory of each other. Pirsig credits French mathematician Poincare (1854-1912) with the following line of thought…
Euclid’s postulate of parallels, which states that through a given point there’s not more than one parallel line to a given straight line, we usually learn in tenth grade geometry. It is one of the basic building blocks out of which the entire mathematics of geometry is constructed.
…in the first quarter of the nineteenth century, and almost at the same time, a Hungarian and a Russian- Bolyai and Lobachevski- established irrefutably that a proof of Euclid’s fifth postulate is impossible.
Lobachevski assumes at the start that through a given point can be drawn two parallels to a given straight. And he retains besides all Euclid’s other axioms. From these hypotheses he deduces a series of theorems among which it’s impossible to find any contradiction, and he constructs a geometry whose faultless logic is inferior in nothing to that of the Euclidian geometry.
A mathematics that admits internal logical contradictions is no mathematics at all. The ultimate effect of non-Euclidian geometries becomes nothing more than a magician’s mumbo jumbo in which belief is sustained purely by faith!
A German named Riemann appeared with another unshakable system of geometry which throws overboard not only Euclid’s postulate, but also the first axiom, which states that only one straight line can pass through two points. Again there is no internal contradiction, only an inconsistency with both Lobachevskian and Euclidian geometries.
According to the Theory of Relativity, Riemann geometry best describes the world we live in.
So is Euclidean geometry true or is Riemann geometry true? [Poincare] answered, The question has no meaning. As well ask whether the metric system is true or the avoirdupois system is false; whether Cartesian coordinates are true and polar coordinates are false. One geometry cannot be more true than another; It can only be more convenient.
So instead of math being part of the universe, it just describes it, and depending on which aspect of the universe you’re looking at, different sets of rules may apply. Rock On.
Warning: Cynicism to Follow
Got me wondering how often we confuse truth with convenience. A close friend once relayed to me a bit of advice he received from a mentor. “There will be many loves of your life, but only one will be convenient.” Thought it was a crock at the time. I mean if its really love, I thought, don’t you make it convenient? But now I can sort of see what he meant. Take two free spirited people, for example. They may fall totally in love with each other, but the very reason they love each other is the reason they don’t end up together. Someday they’ll change or just calm down or wear out of being so free and lonely, and they’ll settle down with someone. Wouldn’t be that the former free spirit loved the new person more, just that they happened to come along when (s)he was ready to jump off the marriage cliff.
Speaking of… I’m just finishing up “Zen and the Art of Motorcycle Maintenance” by Robert Pirsig. Talk about a head trip. One of the best books I’ve ever read. That may also have something to do with my rekindled interest in math. He describes the odd situation of different systems of geometry being logically sound individually, but contradictory of each other. Pirsig credits French mathematician Poincare (1854-1912) with the following line of thought…
Euclid’s postulate of parallels, which states that through a given point there’s not more than one parallel line to a given straight line, we usually learn in tenth grade geometry. It is one of the basic building blocks out of which the entire mathematics of geometry is constructed.
…in the first quarter of the nineteenth century, and almost at the same time, a Hungarian and a Russian- Bolyai and Lobachevski- established irrefutably that a proof of Euclid’s fifth postulate is impossible.
Lobachevski assumes at the start that through a given point can be drawn two parallels to a given straight. And he retains besides all Euclid’s other axioms. From these hypotheses he deduces a series of theorems among which it’s impossible to find any contradiction, and he constructs a geometry whose faultless logic is inferior in nothing to that of the Euclidian geometry.
A mathematics that admits internal logical contradictions is no mathematics at all. The ultimate effect of non-Euclidian geometries becomes nothing more than a magician’s mumbo jumbo in which belief is sustained purely by faith!
A German named Riemann appeared with another unshakable system of geometry which throws overboard not only Euclid’s postulate, but also the first axiom, which states that only one straight line can pass through two points. Again there is no internal contradiction, only an inconsistency with both Lobachevskian and Euclidian geometries.
According to the Theory of Relativity, Riemann geometry best describes the world we live in.
So is Euclidean geometry true or is Riemann geometry true? [Poincare] answered, The question has no meaning. As well ask whether the metric system is true or the avoirdupois system is false; whether Cartesian coordinates are true and polar coordinates are false. One geometry cannot be more true than another; It can only be more convenient.
So instead of math being part of the universe, it just describes it, and depending on which aspect of the universe you’re looking at, different sets of rules may apply. Rock On.
Warning: Cynicism to Follow
Got me wondering how often we confuse truth with convenience. A close friend once relayed to me a bit of advice he received from a mentor. “There will be many loves of your life, but only one will be convenient.” Thought it was a crock at the time. I mean if its really love, I thought, don’t you make it convenient? But now I can sort of see what he meant. Take two free spirited people, for example. They may fall totally in love with each other, but the very reason they love each other is the reason they don’t end up together. Someday they’ll change or just calm down or wear out of being so free and lonely, and they’ll settle down with someone. Wouldn’t be that the former free spirit loved the new person more, just that they happened to come along when (s)he was ready to jump off the marriage cliff.
How about religion? In general, I don’t think people shop around for religions too critically. If you’re a Christian or a Muslim or a Hindu, its probably principally due to where you are from and who raised you. Pretty convenient, huh? But they all insist that theirs is THE truth about God and how God wants us to live. Is it so far fetched that they are (at best) different cultural manifestations of similar spiritual relationships with the all-pervasive-energy-of-the-universe or (at worst) different ways humans take advantage of other humans’ relationships with said energy?
But hey, what do I know? I’m just an aerial lawn boy.
End Cynicism.
But hey, what do I know? I’m just an aerial lawn boy.
End Cynicism.
1 comment:
Great post. I wouldn't call it cynical as much as I would call it a realistic take on how much timing and convenience play such a huge part in our lives. It's good to know someone thinks about this stuff other than myself.
Post a Comment