Crease: The Great Equations
From Scienticity
(New page: {{BNR-table|scienticity=5|readability=4|hermeneutics=5|charisma=4|recommendation=4}} Robert P. Crease, ''The Great Equations : Breakthroughs in Science from Pythagoras to Heisenberg''. New...) |
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Robert P. Crease, ''The Great Equations : Breakthroughs in Science from Pythagoras to Heisenberg''. New York : W.W.Norton & Company, 2008. 315 pages; illustrated; with notes and index. | Robert P. Crease, ''The Great Equations : Breakthroughs in Science from Pythagoras to Heisenberg''. New York : W.W.Norton & Company, 2008. 315 pages; illustrated; with notes and index. | ||
| - | Relax. This is not a mathematical textbook, nor a mathematical explication of the “great equations” of science and mathematics. Rather they are essays that consider the place of these great equations in history: the intellectual milieu that saw them come into existence, their scientific impact and, | + | Relax. This is not a mathematical textbook, nor a mathematical explication of the “great equations” of science and mathematics. Rather they are essays that consider the place of these great equations in history: the intellectual milieu that saw them come into existence, their scientific impact and, through that, their effect on culture and their cultural meaning. Yes, equations can have cultural meaning: for better or worse the Pythagorean theorem, Einstein’s mass-energy equations, and Heisenberg’s Uncertainty Principle all have cultural meaning. |
There are other less popularly known equations that are still important. Newton’s laws of motion, Newton’s law of universal gravitation, Euler’s equation, the second law of thermodynamics, Maxwell’s equations of electrodynamics, Einstein’s field equation for general relativity, and Schroedinger’s wave equation for quantum mechanics. Even when written down by one person, these equations represent a coming together of scientific currents of their times, and each one has an interesting story to tell. | There are other less popularly known equations that are still important. Newton’s laws of motion, Newton’s law of universal gravitation, Euler’s equation, the second law of thermodynamics, Maxwell’s equations of electrodynamics, Einstein’s field equation for general relativity, and Schroedinger’s wave equation for quantum mechanics. Even when written down by one person, these equations represent a coming together of scientific currents of their times, and each one has an interesting story to tell. | ||
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It’s not by any means a mathematical book, but Crease does display each equation at the head of each chapter in mathematical symbols. That’s obviously important to a book about equations, but I think it’s also very good for the general, non-technical reader. One doesn’t need to understand the equations mathematically, but there’s value in simply seeing what they look like. True, Crease sometimes explains to some extent what an equation means, but understanding an equation in mathematical terms is not his goal. Rather, he would like his readers to appreciate each equation and to have some idea what the equation is expressing. | It’s not by any means a mathematical book, but Crease does display each equation at the head of each chapter in mathematical symbols. That’s obviously important to a book about equations, but I think it’s also very good for the general, non-technical reader. One doesn’t need to understand the equations mathematically, but there’s value in simply seeing what they look like. True, Crease sometimes explains to some extent what an equation means, but understanding an equation in mathematical terms is not his goal. Rather, he would like his readers to appreciate each equation and to have some idea what the equation is expressing. | ||
| - | There is even an aspect of aesthetic appreciation involved. That may sound silly, but mathematicians and | + | There is even an aspect of aesthetic appreciation involved. That may sound silly, but mathematicians and mathematical physicists will tell you that correct equations have a certain "beauty" to them. Looking at these equations in that way gives some non-verbal, non-expository feeling of what it's like to work with mathematical expressions. |
I appreciated Crease's many insights. For instance, I was taught, like many other physics students, that Heisenberg's uncertainty relations told us something about measurements disturbing the measured. This is ingrained in the popular understanding, too ("the observer disturbs the universe"), but it's wrong. The real implication is deeper and much more interesting. | I appreciated Crease's many insights. For instance, I was taught, like many other physics students, that Heisenberg's uncertainty relations told us something about measurements disturbing the measured. This is ingrained in the popular understanding, too ("the observer disturbs the universe"), but it's wrong. The real implication is deeper and much more interesting. | ||
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| - | The uncertainty principle is incomplete | + | The uncertainty principle is incomplete in a different sense. It is a mathematical relation, and a feature of the statistical interpretation of the wave function in quantum mechanics. It makes no reference to any underlying physical picture; there are no references to waves or particles, nor to physical experiments. It is not obvious what it refers to, except possibly the clicks of a detector. yet it is ''about'' gaps ''in'' the world itself. These gaps are not epistemological but ontological; having to do not with our knowledge but with the world. |
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This is strange, but why? It is important to see what the strangeness is ''not'' due to. The strangeness of the uncertainty principle is not due to the measurement process disturbing the object measured, which would be a feature of any Newtonian theory involving exchange of particles. Nor is it due to the presence of statistics. Rather, the strangeness of quantum mechanics is that quantum formulations are not "about" a real or ideal object in the conventional sense. [p. 264] | This is strange, but why? It is important to see what the strangeness is ''not'' due to. The strangeness of the uncertainty principle is not due to the measurement process disturbing the object measured, which would be a feature of any Newtonian theory involving exchange of particles. Nor is it due to the presence of statistics. Rather, the strangeness of quantum mechanics is that quantum formulations are not "about" a real or ideal object in the conventional sense. [p. 264] | ||
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Each of the chapters, one each to an equation, is followed by an "interlude", a rumination on some topic that came up in the chapter and deserves its own essay. The remarks quoted above about the lack of science in history books came from such an interlude. So does the following about how science works, and how all the bits of science fit together to create a model of something that we call "reality". | Each of the chapters, one each to an equation, is followed by an "interlude", a rumination on some topic that came up in the chapter and deserves its own essay. The remarks quoted above about the lack of science in history books came from such an interlude. So does the following about how science works, and how all the bits of science fit together to create a model of something that we call "reality". | ||
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| - | Yet another thing we learn from these journeys is about the nature of scientific concepts. It is tempting to think that there is some pre-existing structure embedded in nature that we are only discovering and translating into mathematical language—that equations are descriptions rather than interpretations or creations. But how we translate depends on the journey we have already taken, on our dissatisfactions with it, and on how we responded to those dissatisfactions. We "fall up," to adapt a phrase of George Steiner. It is thus misleading to picture science as proceeding solely by scientists producing new concepts, then testing and revising them. Two things are wrong with this picture. One is that the meaning of one concept depends on the meaning of all the others; a concept is one element of that fishbowl-like world that Newton discovered at the heart of the world we live in, and needs everything | + | Yet another thing we learn from these journeys is about the nature of scientific concepts. It is tempting to think that there is some pre-existing structure embedded in nature that we are only discovering and translating into mathematical language—that equations are descriptions rather than interpretations or creations. But how we translate depends on the journey we have already taken, on our dissatisfactions with it, and on how we responded to those dissatisfactions. We "fall up," to adapt a phrase of George Steiner. It is thus misleading to picture science as proceeding solely by scientists producing new concepts, then testing and revising them. Two things are wrong with this picture. One is that the meaning of one concept depends on the meaning of all the others; a concept is one element of that fishbowl-like world that Newton discovered at the heart of the world we live in, and needs everything else in that fishbowl for its meaning. Testing one concept thinking you are testing it and not everything else is like asking, Is New York to the right or left of Boston? without knowing where you are; without having the rest of the map. And we not only need the rest of the fishbowl, but the rest of our experience of the world as well. A scientific concept that we trust is really a concept plus that experience, and when our experience changes—new practices, new technologies—so does how the concept applies to the world. That's why concepts never stay put, and always change or are being elaborated; a concept that tests right at one time can be inadequate at another. There is no right way to say something that does not include our experience with it. [pp. 268—269] |
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