everything in physics is made up to make the math work out
March 5, 2023 8:07 AM Subscribe
Dr. Katie Mack wrote a short article for Science Focus to talk about what's "real" in physics: "..in practice, physics isn’t built around ultimate truth, but rather the constant production and refinement of mathematical approximations. It’s not just because we’ll never have perfect precision in our observations. It’s that, fundamentally, the entire point of physics is to create a model universe in math - a set of equations that remain true when we plug in numbers from observations of physical phenomena."
Of course, the universe likes to occasionally remind physicists that it wasn’t a math major.
posted by Thorzdad at 8:35 AM on March 5, 2023 [12 favorites]
posted by Thorzdad at 8:35 AM on March 5, 2023 [12 favorites]
Very true of the extremes: particle physics and cosmology, but the stuff that makes airplanes fly and cellphones work seems to be real enough.
posted by OHenryPacey at 9:14 AM on March 5, 2023
posted by OHenryPacey at 9:14 AM on March 5, 2023
You need some quantum physics to figure out cellphones.
posted by ocschwar at 9:16 AM on March 5, 2023 [2 favorites]
posted by ocschwar at 9:16 AM on March 5, 2023 [2 favorites]
yes, of course, and what we know of it has been utilized to make a very practical thing work, and as we continue to delve the practical uses will continue to unfo0ld whether or not we have a TOE at the end of it
posted by OHenryPacey at 9:20 AM on March 5, 2023 [1 favorite]
posted by OHenryPacey at 9:20 AM on March 5, 2023 [1 favorite]
Mack is the best science explainer out there, fun and with much more humility than Neil deGrasse Tyson. Her book, The End of Everything, is a great read.
posted by rikschell at 9:24 AM on March 5, 2023 [5 favorites]
posted by rikschell at 9:24 AM on March 5, 2023 [5 favorites]
I’ve just read a draft manuscript of a book by a physicist friend for non-physicist readers in which there is no math, and despite having a learning disability in math, it was very clear to me that math/formulas are the most economical way of expressing many concepts. (He’s a clear and engaging writer, so the issue is the complexity of communicating physics concepts, not his ability to do so, per se.)
posted by mollymillions at 10:03 AM on March 5, 2023 [3 favorites]
posted by mollymillions at 10:03 AM on March 5, 2023 [3 favorites]
I recently finished Richard Feynman's QED, which is an attempt at an explanation in laymen's terms.
The book includes roughly 20 pages of Feymnan trying to explain vector addition and multiplication along with integration over N-D space, without any mathematical notation, and well, if you needed that explanation, I doubt that explanation worked for you, and I have no alternative to offer.
What is nice about the book, however, is that Feynman gives the classic Feynman stance on QED: the Schrodinger equation is difficult to understand and apply, and counterintuitive, but when used correctly it produces hypotheses that experiments will consistently bear out. There is no need to wax philosophic about semantic interpretations of the Schrodinger equation, because when you're done with your undergrad bull session you're back into mundane reality where the laws of classical physics continue to apply. And if you object to any interpretation, tough shit, because the equation produces hypotheses that bear out.
The same attitude applies to the rest of physics as well, IMO
posted by ocschwar at 10:39 AM on March 5, 2023 [4 favorites]
The book includes roughly 20 pages of Feymnan trying to explain vector addition and multiplication along with integration over N-D space, without any mathematical notation, and well, if you needed that explanation, I doubt that explanation worked for you, and I have no alternative to offer.
What is nice about the book, however, is that Feynman gives the classic Feynman stance on QED: the Schrodinger equation is difficult to understand and apply, and counterintuitive, but when used correctly it produces hypotheses that experiments will consistently bear out. There is no need to wax philosophic about semantic interpretations of the Schrodinger equation, because when you're done with your undergrad bull session you're back into mundane reality where the laws of classical physics continue to apply. And if you object to any interpretation, tough shit, because the equation produces hypotheses that bear out.
The same attitude applies to the rest of physics as well, IMO
posted by ocschwar at 10:39 AM on March 5, 2023 [4 favorites]
" s f a r a s t h e l a w s o f m a t h e m a t i c s r e f e r t o r e a l i t y , t h e y a r e n o t c e r t a i n ; a n d a s f a r a s t h e y a r e c e r t a i n , t h e y d o n o t r e f e r t o r e a l i t y . "
A l b e r t E i n s t e i n
posted by tspae at 11:16 AM on March 5, 2023 [9 favorites]
A l b e r t E i n s t e i n
posted by tspae at 11:16 AM on March 5, 2023 [9 favorites]
but the stuff that makes airplanes fly
I spent some amateur hours learning about the math of flying airplanes. As it turns out, most of it is hacks and approximations. We've accomplished a lot with those hacks and approximations, yes, but nothing like a beautiful mathematical theory of turbulence or laminar flow separation. Ultimately, you need to put your thing into a wind tunnel and measure what happens very carefully... and even that will only give you numbers that are useful for building an airplane within a narrow range of angles in which the air behaves nicely.
The closest thing we've got to a mathematical "truth" is the Navier–Stokes equations. These aren't nice equations, so the only way to use them is to divide the air into arbitrary chunks and have a computer do the equations a few billion times for you until it hopefully gives you a reasonable approximation of what will happen.
But even then, the answer you get is based on the behaviour of an idealized gas, not on whatever reality might be.
People often use bridges when talking about this stuff - "if the math weren't real, how do you think engineers get bridges to stay up?" - and I always respond, "Have you seen the dirty deeds that engineers do to math?"
posted by clawsoon at 11:17 AM on March 5, 2023 [9 favorites]
I spent some amateur hours learning about the math of flying airplanes. As it turns out, most of it is hacks and approximations. We've accomplished a lot with those hacks and approximations, yes, but nothing like a beautiful mathematical theory of turbulence or laminar flow separation. Ultimately, you need to put your thing into a wind tunnel and measure what happens very carefully... and even that will only give you numbers that are useful for building an airplane within a narrow range of angles in which the air behaves nicely.
The closest thing we've got to a mathematical "truth" is the Navier–Stokes equations. These aren't nice equations, so the only way to use them is to divide the air into arbitrary chunks and have a computer do the equations a few billion times for you until it hopefully gives you a reasonable approximation of what will happen.
But even then, the answer you get is based on the behaviour of an idealized gas, not on whatever reality might be.
People often use bridges when talking about this stuff - "if the math weren't real, how do you think engineers get bridges to stay up?" - and I always respond, "Have you seen the dirty deeds that engineers do to math?"
posted by clawsoon at 11:17 AM on March 5, 2023 [9 favorites]
Excellent article, but definitely written by a theoretician. ;-) Which is to say — as someone who was trained in experimental physics, there’s nothing I disagree with in the article, but a similar article written by an experimentalist would have a very different feel.
A lot of concepts in physics are “made up to make the math work”, but also because they’re the simplest ideas that are both consistent with our observations, and reasonably similar to things that we can more directly measure. Items not all math — physical theories also involve proposing some change to what we think is actually going on. When you see physicists talking about “parsimony”, they’re often referring to making the minimum modification to our understanding of the world to fit the data.
(The trick is that a lot of things can only be observed indirectly, via their effects on other phenomena. A lot of experimental physics is finding tricks for doing indirect measurements we’re confident in.)
Dark matter is a good example: Our observations of objects in the universe didn’t line up with our understanding of gravity and the stuff we saw out there. “Dark matter” is effectively the hypothesis that there’s more stuff out there that we can’t see — and then to work out the limits on where it might be, how it might interact with other things (or not), etc. Other theories have been proposed, such as modifications to how we think gravity works, but they don’t fit the evidence as well, and are in some ways bigger jumps from where we are now than “stuff we can’t find”.
I’d also note, from the article:
Dark matter, dark energy, cosmic inflation, black hole singularities, and all the other hypothetical denizens of our current cosmology might seem less real than falling apples or electricity or fluid flow because we don’t experience them in our everyday life, but from a physicist’s perspective, they’re all equally good fodder for mathematical abstraction.
This is true as far as mathematical theory-building goes, but not as far as equality in our conceptual understanding of the world. I think we’d be a lot quicker to discard the concept of dark matter if a better mathematical explanation popped up, than we would the concept of gravity itself… precisely because gravity is easier to observe!
posted by learning from frequent failure at 11:23 AM on March 5, 2023 [5 favorites]
A lot of concepts in physics are “made up to make the math work”, but also because they’re the simplest ideas that are both consistent with our observations, and reasonably similar to things that we can more directly measure. Items not all math — physical theories also involve proposing some change to what we think is actually going on. When you see physicists talking about “parsimony”, they’re often referring to making the minimum modification to our understanding of the world to fit the data.
(The trick is that a lot of things can only be observed indirectly, via their effects on other phenomena. A lot of experimental physics is finding tricks for doing indirect measurements we’re confident in.)
Dark matter is a good example: Our observations of objects in the universe didn’t line up with our understanding of gravity and the stuff we saw out there. “Dark matter” is effectively the hypothesis that there’s more stuff out there that we can’t see — and then to work out the limits on where it might be, how it might interact with other things (or not), etc. Other theories have been proposed, such as modifications to how we think gravity works, but they don’t fit the evidence as well, and are in some ways bigger jumps from where we are now than “stuff we can’t find”.
I’d also note, from the article:
Dark matter, dark energy, cosmic inflation, black hole singularities, and all the other hypothetical denizens of our current cosmology might seem less real than falling apples or electricity or fluid flow because we don’t experience them in our everyday life, but from a physicist’s perspective, they’re all equally good fodder for mathematical abstraction.
This is true as far as mathematical theory-building goes, but not as far as equality in our conceptual understanding of the world. I think we’d be a lot quicker to discard the concept of dark matter if a better mathematical explanation popped up, than we would the concept of gravity itself… precisely because gravity is easier to observe!
posted by learning from frequent failure at 11:23 AM on March 5, 2023 [5 favorites]
It was UK philosopher Williamson [his talk should be on YouTube] who 10 years ago also already argued for a model-centric approach to doing science and philosophy. So my problem with the author's argument is how it omits that their very argument isn't necessarily only one physical outlook in the first place, that there is a historical context and meta theorizing regarding the appropriate role of models. The problem is that not only does this argument is conceited because it contains philosophical presuppositions, but also that other physicists don't agree with equating models with approximations and that all there is is this reductive definition of physics.
posted by polymodus at 11:30 AM on March 5, 2023
posted by polymodus at 11:30 AM on March 5, 2023
Also, using math in physics didn't just happen because we felt like it.
Using math in physics was done because *it worked*.
If poetry would predict observations better than F=ma, then physics would be poetry.
posted by NotAYakk at 12:19 PM on March 5, 2023 [6 favorites]
Using math in physics was done because *it worked*.
If poetry would predict observations better than F=ma, then physics would be poetry.
posted by NotAYakk at 12:19 PM on March 5, 2023 [6 favorites]
"All models are wrong; some models are useful"
posted by lalochezia at 1:20 PM on March 5, 2023 [1 favorite]
posted by lalochezia at 1:20 PM on March 5, 2023 [1 favorite]
Observations of physical phenomena....Why science says not to rely on eyewitness accounts. Is that with or without the slide rule? Using Science or math to create a tight net of inviolate measurements, to facilitate speedy implementation of, say nuclear weapons in a time of perceived need, created some highly if not breakneck processes, to advance science, warfare, chemical processes, the business of all of the above. This is light years below celestial activity, and serves more of the above, a sort of self perpetuating disaster, with a basic model, which functions outside even the most basic ethical constructs, made OK by the math equation.
It is not just the observation of physical phenomena, but the willful misuse of all of existence, for base, callous, opportunism. The term callous is used as a substitute for screaming.
Scientific American
posted by Oyéah at 1:20 PM on March 5, 2023 [1 favorite]
It is not just the observation of physical phenomena, but the willful misuse of all of existence, for base, callous, opportunism. The term callous is used as a substitute for screaming.
Scientific American
posted by Oyéah at 1:20 PM on March 5, 2023 [1 favorite]
Newton’s maths explains a vast mass of observations with just a few really simple equations. Some modern physics seems to explain fairly marginal observations at the cost of a huge mass of complex theory and unbelievably huge ontological commitments.
Newton did have to create a lot of math involving infinitesimals in ways that weren’t viewed as simple at the time. It’s tempting to look at the present and say that it’s messy and uncertain and then look at the past and say that it’s clean and elegant, ignoring the refinement that happened over that time. My graduate research was in a physics sub-field that was hotly contested, involved multiple groups trying to figure out how to make Bose Einstein condensates work, and took up years and years. It resulted in Nobel prizes. Now it’s a common undergrad physics experiment.
It’s possible that we don’t have the right math framework to describe the problems we’re tackling now. It’s possible that the more obvious to describe physics and math problems, the low hanging fruit, has been done and now we’re reaching farther and farther to understand more and more. I dunno, I find it exciting.
posted by sgranade at 1:58 PM on March 5, 2023 [8 favorites]
Newton did have to create a lot of math involving infinitesimals in ways that weren’t viewed as simple at the time. It’s tempting to look at the present and say that it’s messy and uncertain and then look at the past and say that it’s clean and elegant, ignoring the refinement that happened over that time. My graduate research was in a physics sub-field that was hotly contested, involved multiple groups trying to figure out how to make Bose Einstein condensates work, and took up years and years. It resulted in Nobel prizes. Now it’s a common undergrad physics experiment.
It’s possible that we don’t have the right math framework to describe the problems we’re tackling now. It’s possible that the more obvious to describe physics and math problems, the low hanging fruit, has been done and now we’re reaching farther and farther to understand more and more. I dunno, I find it exciting.
posted by sgranade at 1:58 PM on March 5, 2023 [8 favorites]
People often use bridges when talking about this stuff - "if the math weren't real, how do you think engineers get bridges to stay up?" - and I always respond, "Have you seen the dirty deeds that engineers do to math?"
Years ago, one of my kids and I watched a Great Courses class called Understanding The World's Greatest Structures. Highly recommended; we learned so much from it.
One thing I remember is that thousands of years ago, before the mathematics of the way forces are carried to the ground was understood, people build semi-circular arches that worked just fine. But they worked because the entire parabolic arch that is the most efficient for carrying the force was "hidden" inside the thick structure (engineers and others more knowledgeable will forgive the wrongness of my retelling of this thing from ten years ago). They didn't have the math, but they had an ugly real-world approximation that contained and took advantage of the math.
posted by Well I never at 3:08 PM on March 5, 2023 [2 favorites]
Years ago, one of my kids and I watched a Great Courses class called Understanding The World's Greatest Structures. Highly recommended; we learned so much from it.
One thing I remember is that thousands of years ago, before the mathematics of the way forces are carried to the ground was understood, people build semi-circular arches that worked just fine. But they worked because the entire parabolic arch that is the most efficient for carrying the force was "hidden" inside the thick structure (engineers and others more knowledgeable will forgive the wrongness of my retelling of this thing from ten years ago). They didn't have the math, but they had an ugly real-world approximation that contained and took advantage of the math.
posted by Well I never at 3:08 PM on March 5, 2023 [2 favorites]
Years ago, one of my kids and I watched a Great Courses class called Understanding The World's Greatest Structures. Highly recommended; we learned so much from it.
I watched that series during my civil engineering undergrad, and it was super helpful!
posted by curious nu at 3:14 PM on March 5, 2023
I watched that series during my civil engineering undergrad, and it was super helpful!
posted by curious nu at 3:14 PM on March 5, 2023
> "Now it’s a common undergrad physics experiment."
Glimpses beyond infinity are now given to freshmen math students as homework assignments
posted by kyrademon at 4:18 PM on March 5, 2023 [2 favorites]
Glimpses beyond infinity are now given to freshmen math students as homework assignments
posted by kyrademon at 4:18 PM on March 5, 2023 [2 favorites]
This is a nice article and a good explanation. I do have one quibble with her discussion of epicycles, but I think it's an important quibble. When the Copernican and then Keplerian models of orbital motion were first introduced, they actually weren't more accurate than epicyclic models. (The Copernican model places the Sun at the center of the solar system, but still has the planets moving in circular orbits. The Keplerian model replaces the circles with ellipses with the Sun at one focus.) In fact, I think I recall that epicycles were quickly added back into the Copernican model in order to make it fit the data as well as the previously-existing epicyclic models. Keplerian orbital motion in fact can't predict observations as well as epicyclic motion can, because it has some flawed assumptions (the big one being that the Sun isn't stationary at the foci of the planetary elliptical orbits, but in fact the Sun and planets both orbit their common center of mass; the more minor flaw being that it doesn't account for interactions between planets). Yet despite this, most physicists would probably agree that Kepler's model is a superior physical theory to the epicyclic model.
The thing is, the epicyclic model of orbital motion can be tuned arbitrarily to fit the data, so it was already quite good at making predictions. In fact, it turns out that epicyclic orbits can be used to model any periodic motion, because epicycles are a perfectly good set of mathematical basis functions for periodic motion. So epicycles are potentially a powerful way of describing orbits, but a terribly way of explaining them. Kepler's laws of orbital motion are a superior physical theory to epicycles, not because they fit the data better or make better predictions, but because they provide a more satisfying explanation for the observations. The arbitrarily fine-tuned epicycles are discarded in favor of a few satisfying, mathematically simple statements about how any planet should move given a few simple parameters, plus fitted values of those parameters for each planet (primarily size and eccentricity of the ellipse describing its orbit, but also other geometric parameters describing its orientation in three dimensions). And in turn, Newton's Law of Universal Gravitation is a superior physical theory to Kepler's laws of motion, by explaining elliptical orbits using the same mechanics that are used to explain terrestrial motion.
So my quibble is mostly about the idea that the point of physics is primarily to come up with mathematical models that keep doing a better job of fitting and predicting observations. That is definitely a thing that physics does, and it's an important thing. But in my opinion the more fundamental thing is that it comes up with mathematical models that keep doing a better job of explaining observations.
posted by biogeo at 4:23 PM on March 5, 2023 [14 favorites]
The thing is, the epicyclic model of orbital motion can be tuned arbitrarily to fit the data, so it was already quite good at making predictions. In fact, it turns out that epicyclic orbits can be used to model any periodic motion, because epicycles are a perfectly good set of mathematical basis functions for periodic motion. So epicycles are potentially a powerful way of describing orbits, but a terribly way of explaining them. Kepler's laws of orbital motion are a superior physical theory to epicycles, not because they fit the data better or make better predictions, but because they provide a more satisfying explanation for the observations. The arbitrarily fine-tuned epicycles are discarded in favor of a few satisfying, mathematically simple statements about how any planet should move given a few simple parameters, plus fitted values of those parameters for each planet (primarily size and eccentricity of the ellipse describing its orbit, but also other geometric parameters describing its orientation in three dimensions). And in turn, Newton's Law of Universal Gravitation is a superior physical theory to Kepler's laws of motion, by explaining elliptical orbits using the same mechanics that are used to explain terrestrial motion.
So my quibble is mostly about the idea that the point of physics is primarily to come up with mathematical models that keep doing a better job of fitting and predicting observations. That is definitely a thing that physics does, and it's an important thing. But in my opinion the more fundamental thing is that it comes up with mathematical models that keep doing a better job of explaining observations.
posted by biogeo at 4:23 PM on March 5, 2023 [14 favorites]
Also, I think you could just as strongly make the same argument in the opposite direction: math is made up to make the physics work out. Though we also make up math for other reasons, aesthetics being a big one, playfulness being another.
posted by biogeo at 4:25 PM on March 5, 2023 [3 favorites]
posted by biogeo at 4:25 PM on March 5, 2023 [3 favorites]
At first, photons and electrons were more akin to dark matter, a hypothesis invented to make models that agreed with confusing statistics from observations. Nowadays, you can “see” them arriving one by one in a detector, and following little obstacle courses you set up to steer them, etc. They are definitely on a firmer ontological footing than 100 years ago, although it may be reductively true that all physics does is build models. (The same is true of the human mind, if you want to get all epistemological about everyday life.)
posted by mubba at 5:07 PM on March 5, 2023 [4 favorites]
posted by mubba at 5:07 PM on March 5, 2023 [4 favorites]
epicyclic orbits can be used to model any periodic motion, because epicycles are a perfectly good set of mathematical basis functions for periodic motion
Fourier transform, or just very like one?
posted by clew at 5:57 PM on March 5, 2023 [1 favorite]
Fourier transform, or just very like one?
posted by clew at 5:57 PM on March 5, 2023 [1 favorite]
More or less exactly the Fourier transform for the maps from R to R^2, subject to some additional constraints if you're enforcing that the epicycles are indeed circles. There's a 3blue1brown video on the topic, I'll try to find it in a bit.
posted by biogeo at 7:23 PM on March 5, 2023 [3 favorites]
posted by biogeo at 7:23 PM on March 5, 2023 [3 favorites]
The really good mathematical theories don't just fit existing observations, they make predictions of new, previously unexpected aspects of reality that can then be confirmed by observations.
So Newtonian gravity predicted the return of comets and the discovery of the planet Neptune, Maxwell's electrodynamic equations predicted radio waves, Einstein's general relativity predicted black holes and gravity waves, Dirac's quantum equations predicted antiparticles etc.
This happens when the theories aren't just arbitrary mathematical expressions, but they express some insight into physical reality: Newton's equations express the gravitational forces among planets, comets and the sun; Maxwell's equations express how fields are created by electric charges and magnets; general relativity describes how mass bends space; etc. That is, they express the explanations biogeo mentioned upthread.
Cue The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
posted by JonJacky at 7:50 PM on March 5, 2023 [6 favorites]
So Newtonian gravity predicted the return of comets and the discovery of the planet Neptune, Maxwell's electrodynamic equations predicted radio waves, Einstein's general relativity predicted black holes and gravity waves, Dirac's quantum equations predicted antiparticles etc.
This happens when the theories aren't just arbitrary mathematical expressions, but they express some insight into physical reality: Newton's equations express the gravitational forces among planets, comets and the sun; Maxwell's equations express how fields are created by electric charges and magnets; general relativity describes how mass bends space; etc. That is, they express the explanations biogeo mentioned upthread.
Cue The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
posted by JonJacky at 7:50 PM on March 5, 2023 [6 favorites]
If poetry would predict observations better than F=ma, then physics would be poetry.
My Physics Teacher.
posted by storybored at 8:57 PM on March 5, 2023
Maxwell's equations are also invariant under Lorenz transformation, which foreshadows Einstein's special theory of relativity. This invariance was noticed before Einstein's work, but its significance was not. I don’t know when Einstein himself became aware of it.
One of the videos in the Kathy Loves Physics series (which is truly outstanding, by the way) features a frustrated-sounding snippet of a letter from Einstein which implies that Einstein put a lot of time and effort into discovering transformations which would do the same for general relativity in some sense, but I don’t know how fruitfully.
posted by jamjam at 11:51 PM on March 5, 2023
One of the videos in the Kathy Loves Physics series (which is truly outstanding, by the way) features a frustrated-sounding snippet of a letter from Einstein which implies that Einstein put a lot of time and effort into discovering transformations which would do the same for general relativity in some sense, but I don’t know how fruitfully.
posted by jamjam at 11:51 PM on March 5, 2023
Fourier series are a mathematical trick to facilitate computation. In some cases, it mirrors the physical reality closely, in some cases approximately, in some cases not at all.
posted by SemiSalt at 4:44 AM on March 6, 2023
posted by SemiSalt at 4:44 AM on March 6, 2023
Maxwell's equations are also invariant under Lorenz transformation, which foreshadows Einstein's special theory of relativity. This invariance was noticed before Einstein's work, but its significance was not. I don’t know when Einstein himself became aware of it.
He was a personal friend of Lorenz. Einstein's novelty was in the semantic interpretation of Lorenz transformations, something Lorenz himself was baffled by.
posted by ocschwar at 5:34 AM on March 6, 2023 [1 favorite]
He was a personal friend of Lorenz. Einstein's novelty was in the semantic interpretation of Lorenz transformations, something Lorenz himself was baffled by.
posted by ocschwar at 5:34 AM on March 6, 2023 [1 favorite]
Fourier series are a mathematical trick to facilitate computation.
I have to disagree with this statement very strongly. Fourier series and their continuous cousins Fourier series, are just a transformation to a new basis. It’s a mathematical trick, yes.
But it’s also more than that; choosing the right basis can elucidate the physics of a problem. Quantum mechanics doesn’t care if you use position space or momentum space, but some problems are so much easier to understand in one or the other.
Same goes for Mellin transforms or Hankel transforms or even just plain matrix basis changes. Changing the mathematical language you write in is not (necessarily) an approximation, and it certainly can give you insight into otherwise opaque phenomena.
posted by nat at 7:16 AM on March 6, 2023 [5 favorites]
I have to disagree with this statement very strongly. Fourier series and their continuous cousins Fourier series, are just a transformation to a new basis. It’s a mathematical trick, yes.
But it’s also more than that; choosing the right basis can elucidate the physics of a problem. Quantum mechanics doesn’t care if you use position space or momentum space, but some problems are so much easier to understand in one or the other.
Same goes for Mellin transforms or Hankel transforms or even just plain matrix basis changes. Changing the mathematical language you write in is not (necessarily) an approximation, and it certainly can give you insight into otherwise opaque phenomena.
posted by nat at 7:16 AM on March 6, 2023 [5 favorites]
The article risks making the reader think that Physics is an endless process of overfitting. I think the game is more to be as minimal as possible without underfitting.
It doesn't really make sense to me to argue that,
say, "group theory was made up to fit the data" any more than it makes sense to say "numbers were just made up to describe what happens when you trade sheep for coins." I mean, I suppose it could be true, but it doesn't tell me anything about the reality of sheep or coins.
It can take an enormous amount of time to learn the mathematical techniques needed to describe the world accurately. Humans seem to be fastest at it, but they also seem prone to reifying the concepts as they learn them.
I think the "reality" is that a shockingly small number of core principles seem to explain almost everything we have ever seen in great detail, and routinely predict things we've never seen. It's a damn useful thing.
posted by dsword at 4:33 PM on March 6, 2023 [1 favorite]
It doesn't really make sense to me to argue that,
say, "group theory was made up to fit the data" any more than it makes sense to say "numbers were just made up to describe what happens when you trade sheep for coins." I mean, I suppose it could be true, but it doesn't tell me anything about the reality of sheep or coins.
It can take an enormous amount of time to learn the mathematical techniques needed to describe the world accurately. Humans seem to be fastest at it, but they also seem prone to reifying the concepts as they learn them.
I think the "reality" is that a shockingly small number of core principles seem to explain almost everything we have ever seen in great detail, and routinely predict things we've never seen. It's a damn useful thing.
posted by dsword at 4:33 PM on March 6, 2023 [1 favorite]
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