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Comment by whatshisface | Hacker News Reader

The reason that it is difficult to write physics knowledge in English is because physics knowledge is math, in that really what it boils down to is a bunch of relationships between things we can measure and other things that are studied by mathematicians. That's what we've been building up over these thousands of years. That's what it is.

You absolutely can explain a physical law in English, but it's either going to be 1. directly correspondent to the equations or 2. inaccurate.

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There is a '3' here, too. Which is that the explanation is more abstract than the equations, i.e. it carries less information but is still accurate in what it says.

>... physics knowledge is math

This would be hard to justify in the face of the fact that many alternate formulations often exist with identical predictive power of the same physical phenomena. So we can't say the phenomenon is the mathematical formulation, because it's equally some other formulation too. The best we can say is all of the most precise descriptions we've found so far have been given in terms of mathematical statements.

I think the reason many physicists feel the temptation to communicate their work without equations is that the most interesting and creative part of their work is likely prior to equations in which their results are codified. And that abstract idea that led to the equations, which may now be just a simple image in the physicists mind, seems like something shareable and interesting.

At least that's been my experience doing abstract math and programming work and feeling a desire to share the 'key idea' behind certain things with non-technical friends.

> So we can't say the phenomenon is the mathematical formulation

That's true, but our knowledge of the phenomenon is exactly equivalent to our knowledge of the math. Our knowledge of the math consists of knowing that it fits experiment (the part that makes it physics,) and also knowing how we can manipulate it symbolically (this part is math and captures the equivalent formulations.)

>There is a '3' here, too.

You're right, I had missed that option. Although this is very rarely possible and when so very difficult.

One of the problems with English is a poor control of ambiguity: it's never clear about which parts of what has been stated were meant. Ideally we would be writing our vague physics explanations in an oligosynthetic language where we could append phenomes until a word had reached exactly the level of specificity intended - instead we have to wave our hands and hope that people don't make the wrong guesses about which interpretations were intended and which weren't.

>... but our knowledge of the phenomenon is exactly equivalent to our knowledge of the math.

I agree with that.

> Ideally we would be writing our vague physics explanations in an oligosynthetic language where we could append phenomes until a word had reached exactly the level of specificity implied.

I imagine each of those phonemes is an additional 'qualification', adding more constraints to what is being said?

I also feel like it should be mentioned that mathematical statements about physical phenomena carry a kind of ambiguity and aren't exact either. For instance, classical mechanics fails to take into account the curvature of spacetime in its predictions; so it may be accurate enough, but 'exact' isn't correct (even though everyone considered it to be for a long time). So then, is General Relativity 'exact'? It's an improvement, but calling it exact is unjustified. Then we have multiple candidate theories hoping to unify the domains of quantum and relativistic phenomena, but 1. it hasn't been done and 2. we still won't know if it's exact or just a better approximation.

It may seem pedantic, but I think the distinction between 'exact' and 'ridiculously close' is important. 'Exact' tempts people into making an identification between the two things.

Yes, it's critically important to make sure people understand that propagation of errors is as much a part of scientific knowledge as the ideal equations. (That's still math, though. ;) I'm not talking about platonic ideals, just symbols and practical considerations.)

That's fair, I think I read your initial comment too quickly. And I should know better, I think we've spoken on here in the past :)

Not sure what your background is. Mine is physics. I spent a long time in academia before moving to software and machine learning. I agree that in some sense mathematical models are the most efficient means to communicate something about much of physics, and certainly the most important method by which physics is used in applications (e.g. engineering). I would hesitate to go further. There's the empirical part of physics which even as a theoretician I always viewed as more important, and often more subtle, and at least as profound. There is a lot of heuristics, art and intuitive leaps embedded in physics that are not adequately captured by the math.

I think the intuitive leaps (How was this discovered? How do we think about this in practice? How should we arrange the concepts in our heads so that we can be useful with them?) are as much about the human brain and the way it works as they are about physics. It's no surprise that math isn't the best notation for them - in an alternate universe, perhaps their study is considered to be a branch of the humanities!

If you asked a hyperinteligent dolphin, "how do you think about the universe?" you would receive and answer totally different from what we'd expect and probably involving a lot of fish. If you asked it how to calculate the period of a pendulum, its answer would be equivalent to ours!

So in that sense I think the "profound statements," might actually be a lot less profound than the calculations themselves.

> physics knowledge is math

OpenGL is even better. J

My teacher said that, I wil know physics well when I can derive my own formulas to calculate solution by looking at problem, but not opposite.

BTW. Can you help me with formula, if you know math so well?

See https://mathoverflow.net/questions/291185/name-of-equation-f...

There are physical phenomena that do not readily become math. "Positive and minus attract" for instance does not have an obvious mathematical basis as the inverse square law.

I'm not sure what you mean by that. Charges q1 and q2 will experience forces (all else being equal) proportional to q1*q2. This captures the way attraction/repulsion scales with amount of charge, and gives you the sign rule for "free."

Here is a fairly in-depth page about it: http://farside.ph.utexas.edu/teaching/em/lectures/node28.htm...

Those pages have some interesting observations - for example, it begins with an action-at-a-distance model, but then it goes on to say that this is inconsistent with Newton's third law in a universe in which information cannot propagate instantaneously. This is presumably implicit in the math, but does making the point in natural language go beyond that?

More generally and abstractly, does the math have anything to say about causes, and if not, is that a limitation or a profound insight?

Propagation delays are missing from Columb's law, which is what you get from Maxwell's equations when you assert that everything is static (meaning, in a practical sense, that you think everything is slow-moving enough.) This can be written in either math or English - and don't think that it's never "aesthetic" to write math in English. People do it sometimes.

>More generally and abstractly, does the math have anything to say about causes, and if not, is that a limitation or a profound insight?

The most reductive way of looking at it is that physical laws are the file-compressed versions of lots and lots of lab spreadsheets. The odd part about this picture? The compression ratio is mind-boggilingly high; and even more amazingly it can often (essentially always) predict the contents of lab spreadsheets that have not already been filled. Information theory probably has something to say about how this works out but I don't know what it would be.

It has no obvious basis because the two aren't related. The phenomenon you describe might as easily have been some other power. Several exercises in my undergrad and graduate E&M courses explored what might classical E&M look like under different models, in fact.

> physics knowledge is math

You make it sound like we know what mathematics is, or what knowledge is. We don't. Things are much more mysterious than that.

And as for your statement about physics, I don't care if you can write down an equation such as "f=ma" and manipulate it. You are not doing physics.

I was actually trying to carefully avoid any excessively profound statements - my claim is that since our knowledge of physics is recorded in math symbols, then any other expression of that knowledge has got to be equivalent to math symbols.

Secondly, I fear that we might be looking at a Chinese room problem. If I gave you a sheet of paper with someone's correct homework on it, could you really know for sure if they had a clue what they were doing?

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