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> Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. Can you elaborat

• 5xz41s0P8T5N 14y ago
  That argument confuses 'loving math' with 'loving things made of math'. I enjoy eating cake and playing video games, that does not make me a chemist and developer. Your parent comment missed the point of his parent.
  • walrus 14y ago
    Maybe. I'd like to hear back from lutusp before I jump to that conclusion.
  • lutusp 14y ago
    > That argument confuses 'loving math' with 'loving things made of math'. That might be a fair objection if they could be separated. If I say y = cos(x) * e^-x^2, when expressed in two dimensions I get this: http://i.imgur.com/MePPy.png http://i.imgur.com/MePPy.png And in three dimensions I get this: http://i.imgur.com/9gr4u.jpg http://i.imgur.com/9gr4u.jpg But I'm still looking at y = cos(x) * e^-x^2 -- the picture only confirms the mathematical identity. So it is with Avatar -- when we watch Avatar, we're looking at math. And much of nature is defined using math -- note that I said, not described, but defined. Here's an example -- there are species of locusts (cicadas, actually) that reproduce at 13-year and 17-year intervals. Until recently, no on knew why. It turns out that both 13 and 17 are prime numbers, and this ties into a survival strategy hatched by natural selection (quite by chance). All explained here: http://arachnoid.com/prime_numbers/index.html#Mathematical_Locusts http://arachnoid.com/prime_numbers/index.html#Mathematical_L... In other words, the locust survival strategy is math speaking out loud. If you read a book in which a seashore is described, do you argue that the description isn't germane to the thing being described? If the writer isn't skilled, or the reader is lacking in the capacity for visualization, then that is perhaps a legitimate objection, but for most people, words convey meaning. So does math. Math is a language in much the same way that words are a language. The distinction between "loving math" and "loving things made of math" is dubious at best. When P.A.M. Dirac wrote his now-famous equation that describes how relativistic electrons behave, he noticed that it had two solutions -- sort of like a quadratic equation. At first he doubted that there could really be two kinds of matter, as his equation suggested. But within a few years antimatter was observed, and Dirac forever afterward wished he had been willing to take his own equation at face value and predict antimatter himself. My point? The math told him something about reality that no one knew, even him. To put it another way, the math was reality.
• lutusp 14y ago
  > To me, the interesting part of mathematics is the process of manipulating expressions, not the expressions themselves. I think most mathematicians and physicists would disagree. I think such people wouldn't want distinguish between generating equations and studying them and their effects, especially with physical equations that must reflect reality to have any value. For example, I can make elaborate predictions about a lot of physical reality with: f = G M_1 M_2 / r^2 (gravitational force) And if I want to study tidal forces, all I need to do is take the first derivative of the above: f = 2 G M_1 M_2 / r^3 (tidal force) I have just "manipulated" an equation, but with an awareness of the equation's physical consequences and effects, and I can now use the second equation to make predictions about ocean tides, the future position of the moon, and the temperature of the volcanoes on Io (which arise from the energy of tidal forces). So for me, the equation itself is immensely valuable for modeling reality -- it's more than a case of manipulating terms. > For example, the number pi would be pretty boring if it weren't for the theorems related to it. Pi, as it turns out, may serve as a source for random sequences of digits. So apart from its geometric meaning, Pi stays interesting.
  • walrus 14y ago
    > Pi, as it turns out, may serve as a source for random sequences of digits. So apart from its geometric meaning, Pi stays interesting. Right, but the fun part (for me) is finding out how and why pi can be used as a source of random sequences of digits, not the fact itself. > I think most mathematicians [...] would disagree. I would be surprised to meet a mathematician who enjoyed learning theorems/proofs more than finding theorems and proving things on their own. That's why I said the interesting part is the process of manipulating expressions rather than the expressions themselves. Based on your gravity/tides example, I think you would take the same stance (Do you?). I just wasn't clear enough in my previous comment.
    • lutusp 14y ago
      > I would be surprised to meet a mathematician who enjoyed learning theorems/proofs more than finding theorems and proving things on their own. One must crawl before one can walk. Reading the work of others is quite enjoyable. And not everyone yearns to reinvent the wheel -- for many problems, understanding the prior work gives one more than enough satisfaction. > That's why I said the interesting part is the process of manipulating expressions rather than the expressions themselves. A finished equation can stand alongside the finest art, and garner the same kind of appreciation. People still read Einstein's relativity equations, and Maxwell's electromagnetic equations, with a deepening appreciation of their beauty, quite apart from the degree to which they describe reality. Also, there is the interesting task of applying equations to real-world problems. I don't need to rewrite the gravitational and tidal equations to discover new things while applying them. > Based on your gravity/tides example, I think you would take the same stance (Do you?). Not really. It would be like asking someone whether they prefer reading, or writing. Obviously the full experience of literacy involves both. Here's a comparison -- a common problem for student writers, usually pointed out by someone with more experience, is that they haven't read enough to be able to write effectively. There's a parallel in mathematics -- those who take the trouble to read enough mathematics, by so doing learn how to express themselves more efficiently. For me, the two equations I posted earlier, one that describes the gravitational force, and the other the tidal force, the mathematically interesting thing is the relationship between them, not so much the equations themselves -- the fact that a simple derivative operation produces the second equation (in physical terms it's because the tidal force is felt by any two adjacent masses placed arbitrarily close together). For physical equations, working with them means either imagining their consequences, or modeling them, usually with a computer. In that case, you don't manipulate the equations, you use them to model reality. So having an equation that's known to represent some aspect of reality is just the beginning of a research program that models the consequences of the equation and compares the model to reality. Here's an example. Observations of Jupiter's moon Io revealed the possibility of a large, static tidal force on its mass. You may be aware that a static force doesn't require any energy expenditure (imagine a book lying on a table). Then someone pointed out that Io has an elliptical orbit, which means Io is constantly moving toward, and away from, Jupiter. This would have the effect of changing the tidal force, and a changing tidal force would perpetually change the moon's shape -- and changing the moon's shape would require energy. This would generate a lot of heat. Shortly thereafter, volcanoes were observed on Io, a moon too small to have the kinds of volcanoes we have here, and the explanation was the elliptical orbit and tidal force. That's mathematics.