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[bradrn]

[Coordinate systems are] mathematical abstractions and don't exist. You can create any wacky coordinate system you want, and it won't respond to gravity, or create gravity, because mathematical abstractions are not physical things.

Now we’re getting into philosophical territory. Are mathematical abstractions physical things? I tend to reject such questions entirely as being category errors — that pesky word ‘are’ causes trouble when we’re trying to be precise. I prefer to say that ‘mathematical abstractions describe physical things’, and leave it at that.

Honestly if you're going to nitpick the word "is", you're simply looking to attack, not to converse.

Not at all. I’m simply of the opinion that when our sentences are too ambiguous, we don’t have a hope of conversing in a sensible way.

Nothing you've said acknowledges what I was saying, which is that gravity does not affect mathematical objects. Nothing about the number two changes if it's "near" a large mass... it can't be near anything except another number. That is not how spacetime works.

Indeed, the number two is not affected by gravity. But this is only because the value ‘2’ simply doesn’t fit into the appropriate equations! If you instead take a set of vectors, you can calculate the way gravity affects them just fine. And unsurprisingly, that mathematical object can also be interpreted straightforwardly as a physical system.

No one understands why gravity can affect spacetime itself …

Another category error. Gravity does not ‘affect’ spacetime — gravity is spacetime! (Or at least, part of spacetime.)

That's one way of looking at it, but a) it doesn't deal with why spacetime is deformed by mass

True — though that is somewhat different to your original statement. To model that, you have to bring in some extra mathematical machinery to construct a curved spacetime around your masses — from what I’ve been reading I gather that the relevant objects are the Ricci tensor and the stress–energy tensor, though at this point my understanding becomes a bit fuzzy.

and b) as you agreed, we don't really understand gravity, so saying "what it is" is overblown.

This is fair; I could have added some qualifiers there. (Though note I was responding to a comment of yours about general relativity, so in context I hope it’s understandable.)

Analogies can be misleading, but let's try: if you were a sailor you'd see the ocean as a curved 2-D surface, and the shortest path to your destination is a curve. For purposes of surface navigation, you never need to wonder why all paths are curved— you make your spherical model and you're done. But we can ask why you can't actually go in a straight line, and provide an answer (there's a planet in the way). On another level, we can explain why planets have the shape they do.

I’m not sure what your point is here; could you clarify please?

Math is not physics.

True, but physics is maths. Specifically, physics is merely the mathematics which describes physical phenomena (plus associated experiments, of course).

I understand what you mean, but I hope you realize that math is not philosophy, and when scientists try to do philosophy of science, they're as able to tie themselves in knots as anyone else. E.g. look at the last hundred years of argument over measurement and QM. And you do know that physics is not just math, because you later talk about falsification, which is humanistic procedure, and ultimately ethical.

This is very fair, and I was wrong to say ‘merely’. (For the second time — I should stop using that word…) That being said, my day-to-day physics research certainly involves a lot of mathematics, and from that perspective it feels like physics is mostly applied mathematics.

As I said, I've read physics, so I totally get the feeling that we should forget the words and just grok the underlying equations. But I'm sorry, it's a feeling, not even a philosophical stance.

It’s more than a feeling, though: from personal experience, I can tell you that it’s the only way to do things. Words are fine and very, very useful, particularly when it comes to intuition-building, but they’re not precise. Language in general isn’t precise. So to do physics work — which is by its nature precise — you either have to be very careful and restricted in how you use language, or you need to use something else (in this case mathematics). In practise, physicists tend to do a mixture of both.

Another thing to consider — mathematics is unreasonably effective. We don’t know why, we don’t know how, but mathematics certainly seems to describe the universe in some way. So we might as well use it and understand it, because it’s the closest thing we have to understanding the universe.

Perhaps it might also help if I outline my workflow when learning new physics. I start by deliberately ignoring the mathematics, and focussing on the words involved, to get a coarse overview of the physical phenomenon I’m trying to understand. After that, I can start to seriously look at the equations involved, and try to match them up with the words. I might read a couple of different explanations, to get different words for the same thing. Eventually, after staring at it long enough, I’ll reach a stage where I can read and understand the equations directly — and that’s when I know I’ve understood the words, because the words exist only as a way of teaching the equations. It’s also the point at which I can start to actually make predictions, because words alone don’t suffice for modelling anything on a firm basis.

Once you start saying that the equations "are" anything, you're deep in ontology.

Exactly! This is why I objected so much to your use of the word ‘is’ earlier.

And just to be clear, gazing at the equations can keep you out of some trouble— that was one of Feynman's points. If you start reifying Ψ, you end up confusing probabilities with actual particles and may end up believing Everett. (Apologies if you're an Everettian— but if you are, many-worlds is not math, it's philosophy.)

I think I do count myself as an Everettian, after reflection. But, as it happens, I only began to do so once I learnt the maths of quantum mechanics — ‘many-worlds’ sounds obviously stupid when presented in layman’s terms, but less so when you realise that the ‘worlds’ referred to are just superposed quantum states. If you interpret them as sci-fi multiverse-style things, it stops corresponding to physical reality. This is the sort of thing I mean by saying that you can only be sure you understand the words if you understand the maths behind them.

But, you know, Feynman was also very good at using words, at relating the math to actual things in the world (something students memorizing the equations don't always grasp), and for that matter invented what he called a "dippy process" to make QED actually calculable. (Renormalization is more difficult for your "physics is math" position than Ψ, because the whole point is that there is a whole series of possible renormalizations, depending on what you use as a lower bound on distance— and if you try to extrapolate to infinitesimals, the whole things blows up. Which renormalization process is "real"?)

Yeah, renormalisation is something I’m suspicious of. From what I hear, a lot of mathematicians are suspicious of it too.

This is actually a really important point, because it allows us to talk about falsification. I could never say that, for instance, ‘serial verb clauses do not exist’, because ‘serial verb clause’ never referred to any one specific thing in the first place.

You should really know more about linguistics by this point! Linguists also talk, possibly way too much, about philosophy of science. Now, it's highly questionable to try to treat all science as if it's physics— see Ernst Mayr, a biologist, on this. But yes, linguistics can make predictions, and those can be verified or not. And if you think the problem is that terms are not defined, you obviously haven't read Chomsky. I mean, that's probably a good life choice, but on the plus side Chomskyans usually do have definitions of their terms, expressed in structural terms.

Yes, I do agree that Chomskyans are much better at defining the meaning of their terms (and in fact considered mentioning that in my earlier post; not sure why I didn’t). That’s why their theories are falsifiable. That being said, I think treating linguistics as physics, with all the precision that entails, is the wrong choice — which is why I tend to prefer theories along the lines of Construction Grammar, insofar as I use adhere to any one theory at all.

Thank you for showing my point so exactly. Physicists could have adopted Einstein's redefinition; if they did, all your books would talk about ether rather than (or in addition to) spacetime, and they'd say that Einstein redefined how the ether was understood, and all the underlying math would be the same.

But they didn’t. Because like I said, physicists tend to avoid redefinition.

---

At this point I feel like this conversation is getting into the weeds a bit, so let me try to summarise and condense the general points I’ve been trying to make. First and foremost, physicists like to use terms precisely, because they’re merely verbal reflections of the mathematics, which is fundamental. As a consequence of this, redefinitions are dispreferred to new coinages, unless the mathematics is sufficiently similar. Secondly, it isn’t necessarily the case that mathematical abstractions are physical things, but it’s certainly true that mathematical abstractions correspond to physical things, and can describe their behaviour near-exactly. Finally (and somewhat tangentially to everything else), gravity in general relativity is a reflection of curvature in spacetime, in such a way that it’s fair to call them the same thing.

(And if anything in that summary seems to contradict stuff I’ve said elsewhere in this conversation, it’s probably because I wasn’t sufficiently precise earlier, so please let me know as early as possible if you’re confused about something! Or it might be because you changed my mind, but I don’t think that’s happened yet… )

[Raphael]

That being said, my day-to-day physics research certainly involves a lot of mathematics, and from that perspective it feels like physics is mostly applied mathematics.

Obligatory xkcd:

[Rounin Ryuuji]

On the other end, do you get anthropology, history, literature, and linguistics?

[zompist]

On the other end, do you get anthropology, history, literature, and linguistics?

chomsky-view.jpg (96.63 KiB) Viewed 833 times

[Raphael]

Neat! Did you make that yourself?

[Raphael]

On the other end, do you get anthropology, history, literature, and linguistics?

<troll mode>
Those are just subdivisions of sociology.
</troll mode>

[zompist]

Brad— I think we're agreeing more than we're disagreeing, so I will just respond to your summary.

At this point I feel like this conversation is getting into the weeds a bit, so let me try to summarise and condense the general points I’ve been trying to make. First and foremost, physicists like to use terms precisely, because they’re merely verbal reflections of the mathematics, which is fundamental.

That's fine.

As a consequence of this, redefinitions are dispreferred to new coinages, unless the mathematics is sufficiently similar.

Another thing physicists are not is historians of language. I think you're going by your idealized image of scientists. Off the top of my head:

-- are fields the same thing Maxwell talked about?
-- are atoms the same thing imagined by Heisenberg pre-QM?
-- is gravity the same thing for Newton, for Einstein, or for that matter string theorists?
-- would Newton and the standard model define light the same way? How about force?
-- what about elements for Lavoisier and today?
-- is the meter defined the same way as in 1799?
-- is a nebula or galaxy the same thing as in 1900?

You can't simultaneously maintain that scientists never redefine terms, and that the math is primary, because the math has changed over hundreds of years. (And will change again if certain theorists get their way.)

You can certainly point to hundreds of terms that haven't changed, but that's not the point: my position is not that physicists (like other language users) are in a rush to change everything, but that they (like other language users) do make changes, either from new understanding or on a whim.

When the theories (and math) change, scientists can redefine old terms, and they can replace them; I don't think the process is as pure and principle-driven as you suggest. In the case of "ether", we've already seen evidence that Einstein and other physicists considered redefinition.

Secondly, it isn’t necessarily the case that mathematical abstractions are physical things, but it’s certainly true that mathematical abstractions correspond to physical things, and can describe their behaviour near-exactly.

Fair enough, but I think you underestimate the difference between math and physics, and that makes you take strange positions such as that mathematical objects respond to gravity. I mean, if you really think vectors have mass, you should see a doctor. But I think you're just being careless, out of over-reifying the equations. The statement above is better.

Finally (and somewhat tangentially to everything else), gravity in general relativity is a reflection of curvature in spacetime, in such a way that it’s fair to call them the same thing.

Fine as stated, but that shows, rather than undermines, my point that spacetime is not just a coordinate system.

[zompist]

Neat! Did you make that yourself?

Yep!

[bradrn]

-- are fields the same thing Maxwell talked about?

Not entirely familiar with how he used the term, but from what I can find online the answer is ‘yes’. Maxwell’s equations haven’t changed in the past 150 years.

-- are atoms the same thing imagined by Heisenberg pre-QM?

Can’t speak to Heisenberg specifically, but we did have several different models of the atom before QM. They all had obvious problems or were quickly disproved, though. And people have understood the basic properties of the atom since Mendeleev, so I’m comfortable with calling them ‘the same thing’ — we might think of a carbon atom as being a plum pudding, a set of orbits or a collection of wavefunctions, but the carbon atom stays the same all along.

-- is gravity the same thing for Newton, for Einstein, or for that matter string theorists?

If you substitute Earth-like conditions into General Relativity, you can rederive Newtonian mechanics, complete with the nicely-behaved Newtonian gravity we all know and love. Same with string theory. So, as with atoms, I’m comfortable with saying that they were describing the same thing, even though they thought about it differently.

(In fact I already made this point, though for particles: ‘when the traditional meaning of ‘particle’ gives a sufficiently close approximation to the actual behaviour we’re happy to use it’.)

-- would Newton and the standard model define light the same way?

Same thing as for gravity and atoms. They may not define it in the same way, but we know that what Newton meant by ‘light’ is the same as how we use the term — and again, you can rederive all Newton’s observations of light from quantum optics (though it’s difficult — but see e.g. https://oceanopticsbook.info/view/radia ... r-equation to get an idea of how one does something like this).

How about force?

Quantum mechanics doesn’t have forces. Even modern Classical Mechanics abandons that notion — I recall reading a book which explicitly commented on that fact, saying that the way we think about things in modern formulations is just too different for the word to be of any use. ‘Force’ in modern physics is a specifically Newtonian concept.

-- what about elements for Lavoisier and today?

According to Wikipedia, Lavoisier’s definition of an element is ‘a single substance that can't be broken down by chemical analysis and from which all chemical compounds are formed’. That sounds entirely accurate to me, and matches how modern chemists think about elements most of the time.

-- is the meter defined the same way as in 1799?

I’ll admit this one has changed — though not very much! And in my experience, people tend to complain about standards endlessly when they change.

-- is a nebula or galaxy the same thing as in 1900?

I’m not an astronomer, so I really wouldn’t have a clue. But I can ask the astronomers in my department if you want. I’d guess it’s a similar situation to the above: they thought about it differently, but it’s the same object either way. (Literally the same, in this case, since there’s only so many nebulae!)

You can't simultaneously maintain that scientists never redefine terms, and that the math is primary, because the math has changed over hundreds of years. (And will change again if certain theorists get their way.)

Of course the maths has changed! But it can only change in such a way that previous experimental observations remain valid — which means that in almost all cases, you can re-derive the previous theory from the new theory. Both GR and QM satisfy this criterion, as will any successful string theory.

Secondly, it isn’t necessarily the case that mathematical abstractions are physical things, but it’s certainly true that mathematical abstractions correspond to physical things, and can describe their behaviour near-exactly.

Fair enough, but I think you underestimate the difference between math and physics, and that makes you take strange positions such as that mathematical objects respond to gravity.

I’m not entirely sure what position do I take here, though I don’t recall saying anywhere that ’mathematical objects respond to gravity’.

On reflection, perhaps I’m influenced by the fact that I do a lot of simulations. Which means that I can take some maths, translate them fairly literally into a computer program, and — hey presto! Suddenly you have what looks like reality, running on a screen! And it’s more than ‘looks like’, too: a good enough simulation can actually predict experimental results, or at least replicate them. From this perspective, it doesn’t matter that there’s (say) no literal photons bouncing around the computer; the entities in question behave the same way whether they’re actual photons in the lab or simulated photons made up of maths. And when you see that, it becomes very hard to believe that mathematical abstractions have no reality at all, at least in some sense of the word.

I mean, if you really think vectors have mass, you should see a doctor.

Vectors in general don’t have mass, of course. A momentum vector, on the other hand… well, it doesn’t ‘have’ a mass either, but it does have some relation to mass.

Finally (and somewhat tangentially to everything else), gravity in general relativity is a reflection of curvature in spacetime, in such a way that it’s fair to call them the same thing.

Fine as stated, but that shows, rather than undermines, my point that spacetime is not just a coordinate system.

This whole discussion strikes me as being a bit pointless, because we’re debating imprecise words, when we should just be looking at the precise mathematics of it. And the mathematics of GR states that spacetime is a… Lorentzian manifold, apparently. At this point it starts to get into stuff I don’t understand well, but it appears that you can map coordinate systems onto open subsets of that manifold using its coordinate chart, so I don’t feel particularly uncomfortable calling this a ‘coordinate system’ at an intuitive level, even if it is somewhat more complex than the ‘coordinate systems’ we learn about in high school.

[zompist]

Sigh... this is an elaborate exercise in missing the point. I said I was talking about history of language, and you want to talk about equations or physical things. I don't get it-- later on you explicitly admit "Vectors in general don’t have mass, of course." So you know perfectly well that language is not math, and math is not physics. So why backtrack?

[re fields]
Not entirely familiar with how he used the term, but from what I can find online the answer is ‘yes’. Maxwell’s equations haven’t changed in the past 150 years.

Narrowly-- you're wrong about the math; see here.

Maxwell originally presented 20 equations using partial differentials. Using vectors, Heaviside needed four equations to express the same ideas. Now, using tensors and 4D "relativistic" notation, only two equations are needed.

Secondly, I'm talking about language, because this is where you made a claim I disagree with (that physics don't redefine their terms). Maxwell understood electromagnetism as waves propagating in ether. In QED fields, except gravity, are understood as originating in particles (with of course their weird wavefunction-based QM behaviors).

— we might think of a carbon atom as being a plum pudding, a set of orbits or a collection of wavefunctions, but the carbon atom stays the same all along.

If I say the word has changed, it's not a response to say that the thing is the same. This covers most of the rest of your responses.

(If you really want to assert that the physics is the same because the physical objects remain the same, what you're actually doing is denying all scientific progress. Atoms were atoms in ancient Greek, but Lucretius was wrong about how they worked. We understand things better precisely because we understand them differently.)

[re nebulas]
I’m not an astronomer, so I really wouldn’t have a clue. But I can ask the astronomers in my department if you want. I’d guess it’s a similar situation to the above: they thought about it differently, but it’s the same object either way. (Literally the same, in this case, since there’s only so many nebulae!)

Again, "it's the same physical object" is not relevant to the changes in word meaning. In 1900 people thought the galaxies were clouds (Latin nebulae) within the Milky Way.

On reflection, perhaps I’m influenced by the fact that I do a lot of simulations. Which means that I can take some maths, translate them fairly literally into a computer program, and — hey presto! Suddenly you have what looks like reality, running on a screen! And it’s more than ‘looks like’, too: a good enough simulation can actually predict experimental results, or at least replicate them. From this perspective, it doesn’t matter that there’s (say) no literal photons bouncing around the computer; the entities in question behave the same way whether they’re actual photons in the lab or simulated photons made up of maths.

Confusing a model for the reality is a fallacy. But I understand the enthusiasm for modeling and the wonder of a good model.

This whole discussion strikes me as being a bit pointless, because we’re debating imprecise words, when we should just be looking at the precise mathematics of it.

Not really, because we're not disagreeing over anything mathematical.

[bradrn]

Sigh... this is an elaborate exercise in missing the point. I said I was talking about history of language, and you want to talk about equations or physical things. I don't get it-- later on you explicitly admit "Vectors in general don’t have mass, of course." So you know perfectly well that language is not math, and math is not physics. So why backtrack?

I have a feeling we’re talking past each other — it feels a bit like the point you’re trying to make is very different to the point I think you’re trying to make (and vice versa). That being said, let me continue on in the hope of reaching some sort of understanding…

[re fields]
Not entirely familiar with how he used the term, but from what I can find online the answer is ‘yes’. Maxwell’s equations haven’t changed in the past 150 years.

Narrowly-- you're wrong about the math; see here.

Maxwell originally presented 20 equations using partial differentials. Using vectors, Heaviside needed four equations to express the same ideas. Now, using tensors and 4D "relativistic" notation, only two equations are needed.

You’re quite right; my apologies.

— we might think of a carbon atom as being a plum pudding, a set of orbits or a collection of wavefunctions, but the carbon atom stays the same all along.

If I say the word has changed, it's not a response to say that the thing is the same.

How is this not a response‽ Semantic change occurs when the referent of a word changes. If a word refers to the same thing as it did previously, its meaning can’t have changed. Perhaps our understanding of how it relates to other words has improved, but by that logic e.g. ‘bird’ must have suddenly changed its meaning when people discovered it was a subset of ‘dinosaur’, which to me seems clearly wrong.

Atoms were atoms in ancient Greek, but Lucretius was wrong about how they worked. We understand things better precisely because we understand them differently.

Yes, exactly. (Though to some extent I take issue with that word ‘differently’, since it’s rare for new understanding to completely invalidate previous understanding. Even Aristotelian physics is OK-ish as an approximation in the right circumstances — and Newtonian physics suffices for almost everything we need at human scales.)

On reflection, perhaps I’m influenced by the fact that I do a lot of simulations. Which means that I can take some maths, translate them fairly literally into a computer program, and — hey presto! Suddenly you have what looks like reality, running on a screen! And it’s more than ‘looks like’, too: a good enough simulation can actually predict experimental results, or at least replicate them. From this perspective, it doesn’t matter that there’s (say) no literal photons bouncing around the computer; the entities in question behave the same way whether they’re actual photons in the lab or simulated photons made up of maths.

Confusing a model for the reality is a fallacy.

Of course; I’m not doing that at all. I’d rather say I’m doing the reverse: because the results of the model are close to experiment, we can deduce that the principles underlying the model have some kind of physical validity.

This whole discussion strikes me as being a bit pointless, because we’re debating imprecise words, when we should just be looking at the precise mathematics of it.

Not really, because we're not disagreeing over anything mathematical.

Then what exactly are we disagreeing over?

[zompist]

How is this not a response‽ Semantic change occurs when the referent of a word changes. If a word refers to the same thing as it did previously, its meaning can’t have changed.

Meaning is not reference! This is basically Ling 101, but I know I covered this in the SCK, which you read!

Simple, silly example: Batman and Bruce Wayne have the same referent. If meaning is reference, then "Batman is Bruce Wayne" is a tautology (x = x) and "Joker knows that Batman is Bruce Wayne" is also a tautology (and is true for everyone, not just Joker.) But it's simply not true that "Batman is Bruce Wayne" is like "x = x". And Joker does not know that "Batman is Bruce Wayne" unless he knows that Batman is a secret identity, and who that identity is.

We could say similar things about "The Andromeda Nebula." Andromeda is visible to the naked eye and has been known for a millennium. But through the 1800s people thought it was a gas nebula, or a stellar system in formation, in any case a relatively nearby object. It wasn't until 1925 that it was recognized as what we now call a galaxy, like the Milky Way.

The referent was the same, but almost all people who talked about Andromeda literally didn't know what they were seeing, and it did not mean to them what it means to us.

The birds are not a very good example since they remain a valid cladistic class. Quite a few taxonomic categories are quite a mess, and have been reinterpreted, often multiple times, in ways that diverge from ordinary language. "Fish" would be a better example of a traditional term that doesn't really survive in modern taxonomy. You can use it informally, but it's not a taxon any more.

Then what exactly are we disagreeing over?

You tend to delete the bits where I state my point, but as I keep saying, it's about history of language, and philosophy of science.

I think you have a reductive, idealistic view of philosophy of science. You tend to walk back the wilder claims when challenged, but you seem really invested in treating physics as mathematics and vice versa, skipping over the non-mathematical aspects of science, and assuming that scientists use language with a precision and invariability that, well, isn't how language works and isn't supported by the history of science.

As I've said, I think your position is contradictory: you want to dismiss the language entirely in favor of math, but at the same time you take really strong positions about certain words (e.g. "gravity", "ether", even "is").

I guess my point is the basic linguistic one about language change: it's always there, even when people deny it or deplore it, and scientists aren't immune. And that's a good thing! If scientific language was as unchanging as you (sometimes) think it is, it would be far more confusing and less useful. Flexibility and redefinition are nice tools to have.

[bradrn]

How is this not a response‽ Semantic change occurs when the referent of a word changes. If a word refers to the same thing as it did previously, its meaning can’t have changed.

Meaning is not reference! This is basically Ling 101, but I know I covered this in the SCK, which you read!

Yeah, well, maybe it’s not coincidental that that’s still the book of yours I comprehend the least well…

Simple, silly example: Batman and Bruce Wayne have the same referent. If meaning is reference, then "Batman is Bruce Wayne" is a tautology (x = x) and "Joker knows that Batman is Bruce Wayne" is also a tautology (and is true for everyone, not just Joker.) But it's simply not true that "Batman is Bruce Wayne" is like "x = x". And Joker does not know that "Batman is Bruce Wayne" unless he knows that Batman is a secret identity, and who that identity is.

We could say similar things about "The Andromeda Nebula." Andromeda is visible to the naked eye and has been known for a millennium. But through the 1800s people thought it was a gas nebula, or a stellar system in formation, in any case a relatively nearby object. It wasn't until 1925 that it was recognized as what we now call a galaxy, like the Milky Way.

The referent was the same, but almost all people who talked about Andromeda literally didn't know what they were seeing, and it did not mean to them what it means to us.

Interesting point. Intuitively I feel that the case of Andromeda is not comparable to the case of Batman, but I can’t quite explain why. Let me reflect on this.

The birds are not a very good example since they remain a valid cladistic class. Quite a few taxonomic categories are quite a mess, and have been reinterpreted, often multiple times, in ways that diverge from ordinary language. "Fish" would be a better example of a traditional term that doesn't really survive in modern taxonomy. You can use it informally, but it's not a taxon any more.

Weeell, I do happen to think that paraphyletic taxa should be considered valid… (But that’s a discussion for another time!)

Still, I accept that ‘fish’ has changed since we discovered that cetaceans etc. are mammals. That makes this a rare case of a scientific term which genuinely did change its meaning.

Then what exactly are we disagreeing over?

You tend to delete the bits where I state my point, but as I keep saying, it's about history of language, and philosophy of science.

Apologies for the deletions; I genuinely thought I was keeping all the bits where you stated your point. Could you quote some places where I wrongly did that please?

I think you have a reductive, idealistic view of philosophy of science. You tend to walk back the wilder claims when challenged, but you seem really invested in treating physics as mathematics and vice versa, skipping over the non-mathematical aspects of science, and assuming that scientists use language with a precision and invariability that, well, isn't how language works and isn't supported by the history of science.

Re ‘physics as mathematics’: I do believe this is true. If it wasn’t in at least some sense, I wouldn’t be in the same university department as the mathematicians! My day-to-day research involves a lot of mathematics; the day-to-day work of the other physicists I know also involves a lot of mathematics. The main difference from ‘mathematics’ per se is that experimental work also plays a role. A summary of my position might be that I define physics as that portion of mathematics which directly describes the real world.

Re scientists’ use of language: perhaps it’s not perfect, but it’s pretty darn precise! Compare it to the situation in linguistics: no two linguists can exactly agree on the definition of terms, grammar-writers freely use well-established terms in new ways as long as it sort of relates to how that word has been used previously, and precise definitions of anything are rare, usually in terms of prototypes and often controversial in any case. This, to me, feels a lot more similar to ‘how language works’ than the way physicists use language. And I find it unsurprising that the two most physics-like fields of linguistics, in terms of word use, are acoustic phonetics (closely related to experimental physics) and Chomskyan formal grammar (similar in approach to theoretical physics / mathematics).

(If you want an example of this, I submit Unterladstetter 2019, which spends ~50 pages outlining the various definitions of a ‘serial verb construction’ before giving up: ‘serialisation as a theoretical concept is too laden with features that are hard to put to the test, while at the same time the phenomenon, as a whole, continues to have fuzzy boundaries’. I cannot recall seeing anything like this in any physics writing, with the possible exception of textbooks which need to teach students to avoid thinking about concepts in too fuzzy a way.)

As I've said, I think your position is contradictory: you want to dismiss the language entirely in favor of math, but at the same time you take really strong positions about certain words (e.g. "gravity", "ether", even "is").

I think you misunderstand my position. What I think is that language, in physics, takes its meaning only from maths. If you deleted all the equations from a physics textbook, it would become impossible to comprehend or apply, in a way which wouldn’t occur if you deleted all the words. In fact, many sentences in physics writing can be converted without too much difficulty into mathematics, without changing the meaning. And this is why I take such a strong position about words: when it comes to physics, the words take their meaning only from the mathematics, so if words are used in a way which differs too much from the mathematics, it makes things confusing.

So, given that the maths changes when new theories are introduced, does this contradict my position that physicists generally avoid redefining words? I believe it does not: when a word corresponds to two different equations, usually the one reduces to the other in certain circumstances. For instance, ‘gravity’ may be used in both a relativistic and a Newtonian sense, but the former reduces to the latter in the limit of Lorentz factor near 1.

[zompist]

I think you have a reductive, idealistic view of philosophy of science. You tend to walk back the wilder claims when challenged, but you seem really invested in treating physics as mathematics and vice versa, skipping over the non-mathematical aspects of science, and assuming that scientists use language with a precision and invariability that, well, isn't how language works and isn't supported by the history of science.

Re ‘physics as mathematics’: I do believe this is true. If it wasn’t in at least some sense, I wouldn’t be in the same university department as the mathematicians! My day-to-day research involves a lot of mathematics; the day-to-day work of the other physicists I know also involves a lot of mathematics. The main difference from ‘mathematics’ per se is that experimental work also plays a role. A summary of my position might be that I define physics as that portion of mathematics which directly describes the real world.

You seem to picture yourself way to the right in that xkcd cartoon. And as I said, this is a reductive and over-idealized view; . It's fine to love the math you do, to feel that it's beautiful and deep and admire how it reflects the world. And I totally get the feeling that if you don't understand the math you don't understand the physics.

But it's not good philosophy of science, because it doesn't recognize how physics is not math. Math stands on its own: you can have some absolutely beautiful math with absolutely no real-world application. That's part of its beauty, in fact.

Physics seeks to model the world, which means it's enmeshed in the messiness of the world. You can't judge a theory by its mathematical beauty alone; it has to fit the facts. Ideally it has to make predictions; ideally those can be tested. And just as in other sciences, a lot of day-to-day work is pure description, from cataloguing stars to combing through particle tracks to measuring isotope weights. I think you know this, you just leave it out when you want to rhapsodize about the equations.

Physics is also an interpretation of the world. I disagree with what you say later about taking all the words out of the physics books. You have to explain, at least, what the symbols in the equations refer to! And-- just as in other sciences-- there are theories and interpretations of the data. Naturally there's less consensus in this area, but the very vehemence of the discussions shows that many physicists take these very seriously. And again, I'd note that some physicists are very good at using language to get their ideas across-- cf. Einstein and his thought experiments.

Re scientists’ use of language: perhaps it’s not perfect, but it’s pretty darn precise! Compare it to the situation in linguistics

And I've never said that physics language is "imprecise." I talked about flexibility and redefinition-- which by the way is an example of where you just didn't respond to the point I was actually making. The non-linguist often has the naive attitude that words are and should be fixed in meaning, with no edge cases or fuzzy boundaries. But all those things are features of language, not bugs. And physicists have, properly, used that flexibility when it suits them.

[bradrn]

You seem to picture yourself way to the right in that xkcd cartoon. … you want to rhapsodize about the equations.

Harsh, but probably fair!

And as I said, this is a reductive and over-idealized view; . It's fine to love the math you do, to feel that it's beautiful and deep and admire how it reflects the world. And I totally get the feeling that if you don't understand the math you don't understand the physics.

But it's not good philosophy of science, because it doesn't recognize how physics is not math. Math stands on its own: you can have some absolutely beautiful math with absolutely no real-world application. That's part of its beauty, in fact.

Physics seeks to model the world, which means it's enmeshed in the messiness of the world. You can't judge a theory by its mathematical beauty alone; it has to fit the facts. Ideally it has to make predictions; ideally those can be tested. And just as in other sciences, a lot of day-to-day work is pure description, from cataloguing stars to combing through particle tracks to measuring isotope weights. I think you know this, you just leave it out when you want to rhapsodize about the equations.

Of course experimentation is important! I I’ve spent a lot of time over the past year or two working in various labs (in both chemistry and physics), sometimes quite intensively, and I’m very familiar with what goes on there. My current research group is mostly experimental, too. (As a matter of fact I helped out in the lab just today.) And personally I enjoy experiment quite as much as theory, if not more.

But given this, I still think the mathematics is fundamental to physics, in a way that it isn’t to other subjects. In chemistry, for instance, experiments very often have qualitative goals: things like ‘aim to create X molecule in the lab’, or ‘find a chemical that glows blue’. (Both being areas in which I’ve done research, by the way.) Measurements are important to figure out how well you’ve achieved your aim, but mathematics per se is often not. And you can easily design experiments using no more complex mathematics than basic algebra — chemistry knowledge is essential, but that’s not a particularly mathematical sort of knowledge. (And incidentally, may I point out at this point that chemists strike me as being somewhat laxer in how they use language, and reinterpret words more often than physicists do.)

By contrast, when physicists do experiments… well, on reflection, I guess the day-to-day experience of physics experimentation actually isn’t so different to chemistry. Nonetheless, I find physicists are much more interested in theory-building — there’s a reason you don’t hear much about ‘theoretical chemistry’! (And when it does get developed people tend to call it ‘physical chemistry’, or sometimes ‘er, I dunno, I guess it’s sorta like physics’.) Physicists tend to be very interested in taking their experiments, trying to explain them with mathematics, playing around with the maths to make new predictions about the world, and then trying to make experiments to realise those new predictions. And to do that, you have to understand the maths. Anecdotally, I often hear people—physicists, usually!—talk about ‘understanding the physics of X’, when they mean ‘understanding the mathematical underpinnings of X’.

Physics is also an interpretation of the world. I disagree with what you say later about taking all the words out of the physics books. You have to explain, at least, what the symbols in the equations refer to! And-- just as in other sciences-- there are theories and interpretations of the data. Naturally there's less consensus in this area, but the very vehemence of the discussions shows that many physicists take these very seriously. And again, I'd note that some physicists are very good at using language to get their ideas across-- cf. Einstein and his thought experiments.

On rereading, perhaps I didn’t make myself clear. Of course, words are important! I never intended to dispute that! And for physics education a good explanation is invaluable (I like Mermin’s essay on Writing Physics). My point was more that they’re not core to the subject: in a good physical theory, the mathematics should explain the physical world completely. There’s a reason that one of the most popular interpretations of QM is called ‘shut up and calculate‘ — it’s because you can ‘shut up and calculate‘, and it still works absolutely fine. Note also that there are many well-known physical theories which are nothing but mathematics at the moment (e.g. string theory). By contrast, you can’t do any sensible physics by ignoring the maths and ‘shutting up and thinking about words’, since that rapidly leads you down the road into pseudoscience: stuff that sounds very much like real physics, but falls apart when you try to work out the maths or attempt to get it working experimentally.

Re scientists’ use of language: perhaps it’s not perfect, but it’s pretty darn precise! Compare it to the situation in linguistics

And I've never said that physics language is "imprecise." I talked about flexibility and redefinition-- which by the way is an example of where you just didn't respond to the point I was actually making. The non-linguist often has the naive attitude that words are and should be fixed in meaning, with no edge cases or fuzzy boundaries. But all those things are features of language, not bugs. And physicists have, properly, used that flexibility when it suits them.

I still maintain that physicists deliberately tend to avoid using that flexibility as much as other fields do, by rigorously defining their terms mathematically. But as I said previously, I’m still reflecting on what ‘flexibility‘ involves, and how it relates to the status of the referent.

[Raphael]

Fun fact: I went to school with some people who were a lot better at math than me, but who, at the same time, seemed to have very serious problem understanding even what looked to me like very simple concepts in physics.

[Man in Space]

My sister’s dog wanted to hang out with me today. This is rare.

[Raphael]

My sister’s dog wanted to hang out with me today. This is rare.

Congratulations!

[Raphael]

Today in News of the Weird:

https://edition.cnn.com/2023/03/02/asia ... index.html

Why do I never get to find an island I didn't know I had?

[zompist]

But given this, I still think the mathematics is fundamental to physics, in a way that it isn’t to other subjects.

I don't think we need to argue about how fundamental is is, but just to tease you, I'll mention one discipline where mathematics is central, and it sucks: economics.

Oh, and if you listen to Hossenfelder, string theory. OK, to be fair, she doesn't think it's as bad as economics.

I still maintain that physicists deliberately tend to avoid using that flexibility as much as other fields do, by rigorously defining their terms mathematically. But as I said previously, I’m still reflecting on what ‘flexibility‘ involves, and how it relates to the status of the referent.

Fair enough.