Hi,
Often in a pre-calculus physics course, the instructor will say something like, "The force is the mass times the acceleration, which has the equation:" and go on to write 'F = ma' on the blackboard. To one sufficiently expert in mathematics, that has a jarring sound. Indeed, the English expression is simply a translation from 'math'. The version in the language of math immediately 'pays it's way' by clearly indicating some operations that could be performed, some conclusions that could be drawn. And it has the beauty that, when later one meets 'V=IR' in learning about electricity, one already knows a plethora of properties because this is the same equation -- to this extents the systems are isomorphic. So, one doesn't need to learn electricity from scratch, just those parts that don't map into mechanics (and that is a lot less than you might think ;) ).
And the reason that it becomes more so in modern physics is because the domains we are studying there are more remote from our ordinary experience. Our experience is linear, Euclidean, with a constant flow of time, etc. etc. Anything that I say in trying to describe an electron using any spoken language is wrong, either by omission or by commission. It either gives too vague an idea or one that is too solid. Yes it is a particle, and you imagine a grain of sand on the beach. But it is a wave, and you imagine the water just over the sand. People have proposed 'waveticle' and other non-sense words to name the concept. But what does that accomplish? Can one point to a macroscopic waveticle and say, "an electron is just like that, only smaller and negatively charged."? So, just as defining one unknown in terms of another does no good, so does trying to speak of modern physics in any language but mathematics do no good.
Ultimately, an electron is just an entity defined by a handful of mathematical properties, some of which defy translation into the language of primates who evolved in a 10 eV world. Beings from the center of a star (assuming there are any) would probably be as perplexed in trying to describe a solid object, like a cue ball.
And, of course, there's the irony that we really do, like the drunk who lost his keys in the dark but searched for them near the light, study that which we can. Perhaps, had we taken a different turn millenia ago, we would have an intuitive understanding of their properties. It is that which makes some Eastern religions so intriguing to physicists -- that some of their concepts from ages ago are distorted shadows of modern findings. Perhaps, one day someone will search the shadows undisturbed for eons and we will come out of the cave.
But for now, math's the best we can do.
--Pete
PS I'm following normal practice in this post of blurring the distinction between the map and the terrain. But to have said things like "Ultimately, our model of an electron is . . ." gets too pedantic even for me after a while. :rolleyes:
Ghostiger,Dec 24 2005, 06:25 AM Wrote:Too many modern physicists seem to forget this.Perhaps to some extent it is. However, mathematics is something beyond what I stated in my previous post. It is the ultimate language for expressing relationships between quantities in a clear and precise way. I don't know how else to explain this, but when I speak English, I think in English; when I speak Italian, I think in Italian; and when I'm 'speaking' math, I think in math.
They approach and write about theoretical physics as if it were math but too often still call it science.
I think its Eisnstein envy driving it.
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Often in a pre-calculus physics course, the instructor will say something like, "The force is the mass times the acceleration, which has the equation:" and go on to write 'F = ma' on the blackboard. To one sufficiently expert in mathematics, that has a jarring sound. Indeed, the English expression is simply a translation from 'math'. The version in the language of math immediately 'pays it's way' by clearly indicating some operations that could be performed, some conclusions that could be drawn. And it has the beauty that, when later one meets 'V=IR' in learning about electricity, one already knows a plethora of properties because this is the same equation -- to this extents the systems are isomorphic. So, one doesn't need to learn electricity from scratch, just those parts that don't map into mechanics (and that is a lot less than you might think ;) ).
And the reason that it becomes more so in modern physics is because the domains we are studying there are more remote from our ordinary experience. Our experience is linear, Euclidean, with a constant flow of time, etc. etc. Anything that I say in trying to describe an electron using any spoken language is wrong, either by omission or by commission. It either gives too vague an idea or one that is too solid. Yes it is a particle, and you imagine a grain of sand on the beach. But it is a wave, and you imagine the water just over the sand. People have proposed 'waveticle' and other non-sense words to name the concept. But what does that accomplish? Can one point to a macroscopic waveticle and say, "an electron is just like that, only smaller and negatively charged."? So, just as defining one unknown in terms of another does no good, so does trying to speak of modern physics in any language but mathematics do no good.
Ultimately, an electron is just an entity defined by a handful of mathematical properties, some of which defy translation into the language of primates who evolved in a 10 eV world. Beings from the center of a star (assuming there are any) would probably be as perplexed in trying to describe a solid object, like a cue ball.
And, of course, there's the irony that we really do, like the drunk who lost his keys in the dark but searched for them near the light, study that which we can. Perhaps, had we taken a different turn millenia ago, we would have an intuitive understanding of their properties. It is that which makes some Eastern religions so intriguing to physicists -- that some of their concepts from ages ago are distorted shadows of modern findings. Perhaps, one day someone will search the shadows undisturbed for eons and we will come out of the cave.
But for now, math's the best we can do.
--Pete
PS I'm following normal practice in this post of blurring the distinction between the map and the terrain. But to have said things like "Ultimately, our model of an electron is . . ." gets too pedantic even for me after a while. :rolleyes:
How big was the aquarium in Noah's ark?