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One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea: it wasn
by cjs_ac 2y ago
One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea: it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
- goatlover 2y agoWhat does that mean? Physics is still empirical at the end of the day. Experiments decide what theories best explain the world. Math doesn't have such a requirement. It doesn't need to model natural phenomenon. Your physics lecturer sounds like a Platonist.
- tombert 2y agoI don't think OP is really wrong here. Wasn't there a debate in the late 19th century that basically asked if math had to have some mapping to the natural world, or should it work independently? I though there was some argument about this with Hilbert and Poincaré about this, and Hilbert more or less won.
- mrtesthah 2y agoSee Our mathematical universe : my quest for the ultimate nature of reality by Max Tegmark https://archive.org/details/ourmathematicalu0000tegm https://archive.org/details/ourmathematicalu0000tegm
- goatlover 2y agoThat's metaphysics not science. I'm not against metaphysics, but philosophy is distinct from physics. And it's Tegmark's particular metaphysics. Interesting but hardly a consensus among physicists or philosophers.
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- lupire 2y agoIt's a very weak loose statement, but I think the idea is that leading scientific and mathematical thinkers (think Newton as a quintessential example) were "natural philosophers" who studied whatever caught their interest and took it wherever it went. Astronomers invented lenses and ground them and studied the starts and developed algebra and calculus to model the observations. Some people were more narrowly focused, like Gauss who did mostly math (but an amazing breadth of math!) There was a lot of hesitancy about math that couldn't be empirically illustrated by building out of atoms, like irrational numbers and then transcendental numbers and imaginary numbers and then infinite structures.
- failbuffer 2y agoAdd negative numbers to your list as well. Mathematicians used to rearrange terms specifically to avoid them (e.g. before the concept existed).
- teqsun 2y ago> "Your physics lecturer sounds like a Platonist." I don't understand what this means, but it made me envision a McCarthy-esque witch hunt for "Platonist and Platonist sympathizers" lurking amongst the faculty
- HPsquared 2y ago"In this house we side with Aristotle."
- aeneasmackenzie 2y agoJust say witch hunt. McCarthy was entirely correct that there were a lot of communists and communist sympathizers, so many that many of the people he thought were helping him were themselves communists or communist sympathizers. Witches on the other hand are not real.
- tomrod 2y agoBut Platonists, ironically on many levels, are also real. Sometimes complex. But never fully imaginary.
- jfactorial 2y agoThere are no Platonists, only imitations of the one true heavenly Platonist.
- tomrod 2y agoGenuinely chuckling.
- bee_rider 2y agoHe missed most of the actual Soviet agents, though, right? Both seem to have mostly focused building up a lie to suppress some outside-the-norm element that the guy in charge wanted to hunt. That McCarthy also managed to have some real agents to miss is not a big difference.
- Joker_vD 2y ago> Math doesn't have such a requirement Geometry? Lobachevsky actually proposed a test on measuring sum of angles of a celestial triangle to decide which geometry actually applied to the real world.
- verzali 2y agoThere are multiple geometries though, they don't have to describe the real world. In mathematics you are free to base your geometry on whatever axioms you want, whether they are realistic or not. I'd say the question of which geometry applies in the real world is more a question for physicists (or cosmologists, today).
- Joker_vD 2y agoThis is a very late-XIX century development. Geometry used to be an integral part of physics, vide Newton's Principia.
- meroes 2y agoWondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.
- Joker_vD 2y agoNo, it's trying to prove that Euclid's parallel postulate can be derived from other axioms is what goes back millennia. People were certain it's a) true, b) necessary consequence of other axioms. Gauss was probably the first to consider the possibility that it may be false; others at best tried reductio ad absurdum, arrived to some wildly unusual theorems, decided those were absurd enough to demonstrate the truth of the fifth postulate, and went back to trying to derive it.
- meroes 2y agoIt's either true as an axiom or true as derived from other axioms and/or theorems. In neither case does latching onto Euclid's other common notions/postulates/theorems as the selection it must be proved true from make sense as a 1.5kya long task. I think there must have been a sense that it was true only as an axiom. Proving it from other axioms/theorems was then a goal to secure it's truth "further". But you'd only attempt that if you thought there was something questionable in the first place.
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- tines 2y ago> it wasn't made during the nineteenth century That's because people were totally focused on physics, and math was just a useful tool sometimes. Doing physics was the true goal and observation the final arbiter of truth. Nowadays, that distinction is blurred but for the opposite reason; people think that anything conceived by sound math must be true, and observation has taken a back seat.
- selectodude 2y agoTo some extent, observation has taken a back seat because we're at the point in our physics journey where we pontificate about things that are too small or too dark and far away to see. We simply can't observe this stuff anymore.
- LeifCarrotson 2y agoFurthermore, we might not be able to observe it but we can observe simulations of it. If it was not possible to simulate, I think we'd be less invested in the math and physics of it.
- TheRealPomax 2y agoFurthermore, even if you can write down the math, it might not even be solvable (sometimes provably so) and simulations (or more accurately, numerical analysis and the finite element method) are our only option.
- dizzant 2y agoThis is an interesting take, the article touches on it too. > “Physicists are much less concerned than mathematicians about rigorous proofs,” says Timothy Gowers, a mathematician at the Collège de France and a Fields Medal winner. Sometimes, he says, that “allows physicists to explore mathematical terrain more quickly than mathematicians.” GP is right that the currently observed physical laws go far beyond our ability to observe them in reality because of the cost of observations. International effort over decades is required to create facilities capable of making helpful new observations: think of LHC, LIGO, James Webb, etc. On the other hand, once the facilities are built and ground-breaking observations appear, we suddenly have a debt of theoretical and simulated exploration to understand all their implications. The low cost of computation greatly extends the value we can take from every truly new observation of reality. In order to observe something new, we must be able differentiate it from something already understood. It seems like the physics and math communities are currently in a season of increasing our understanding of the existing models well enough to motivate trying to break them.
- tech_ken 2y agoWell also the idea of physics as the field we currently have didn't exist much before the 17th century. Movement of bodies, astronomy, fluid dynamics, electromagnetics, optics, etc. all kind of were their own thing (if they existed at all). Fundamental developments in calculus in the late 1600s enabled these subjects to be collected under one method of study/analysis which we now call physics. As much of modern math follows from the lineage of calculus the border between the things being modeled and the tools for modeling them is naturally kind of blurry, however the distinction did still exist quite strongly throughout this entire period. Look at ex. probability or algebra, although often researchers were pursuing both physics and math, they were aware that the subjects were distinct.
- nobodyandproud 2y agoIt—that is, science at the time—all fell under the umbrella term of natural philosophy.
- waterhouse 2y agoMathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. — V.I. Arnold: "On teaching mathematics" (1997)
- janalsncm 2y agoPhysics is the subset of mathematics with physical application. However mathematics need not have physical applications in order to be valid math.
- trashtester 2y agoPure Calculus is not Physics even though it has applications in Physics. Just like English isn't Physics even if you can have describe aspects of Physics using English. For Math and English to be Physics, it needs to specifically define what physical meaning the variables and parameters involved have. Typically, you recognize it as Physics when it comes with units.
- naasking 2y agoMath probably split off a bit because of the attempts at formalization. That was a useful tangent though, arguably giving us computer science via the lambda calculus, Turing machines, etc.
- SkiFire13 2y agoI would argue that in the twenty-first century the distinction is even greater thanks to computer science.
- namaria 2y agoI think you don't understand enough physics, maths or cs if you think there's a way to draw a neat line between any pair of them.
- SkiFire13 2y agoSaying that there's a distinction between them is different than drawing a neat line. Surely you aren't arguing that they're the same discipline instead?
- FromTheSteppe 2y agoHaha in my country half the computer science degrees are titled "Applied Mathematics".
- hirvi74 2y agoSuch a title makes me feel like I might come off smarter than I actually am -- I like it. Especially when considering my mathematically understanding and abilities.
- speedchess 2y ago> One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea: It's actually a 19th century idea. The discovery or acceptance of non-euclidean geometry in the 19th century untethered math from physics or physics from math. > and it seems to be disappearing in the twenty-first. It can't disappear because math is no longer tied to the physical world. Math is simply theorem generation regardless of whether the axioms and theorems apply to the physical world. The math used in physics is only a tiny subset of possible math.