Which do you grasp first in physics?

nesf

The maths or the concept?

I'm a conceptual person. I always had to figure out what was happening first and then look at the maths. The maths itself meant little to me. (I know, ****ing weird)

Just curious, I know from experience that most people get the maths first. The conceptual understand comes later. Am wondering if anyone else on here is like me.

Son Goku

Depends on the area.

Quantum Mechanics: maths first, then concept.

Special Relativity: concept first, then maths.

General Relativity: Both simultaneously as they were almost blurred into one.

Newtonian Mechanics and Thermodynamics: The concept, which is then easily seen in the maths.

nesf

Good point, it does vary from area to area.

Although, you haven't seen enough classical mechanics if you think the maths is clear

I was strange in that I always got the concept first, even in quantum where conceptually it's a nightmare.

Or maybe it might be more accurate to say it was my grasp of the mathematics rather than my grasp of the concepts that was the weaker of the two.

The two do "co-exist". It's impossible to "ignore" the maths in quantum for instance. But then quantum is counter-intuitive at the best of times. You need to "re-train" your mind to think in a certain way to grasp it.

Quite a few people would do this via the maths. I always did it through the "situation" if that makes sense.

Son Goku

nesf wrote:

Good point, it does vary from area to area.

Although, you haven't seen enough classical mechanics if you think the maths is clear

True, I remember seeing the Lagragian for a football and thinking: "Holy **** thats one big equation"

nesf wrote:

I was strange in that I always got the concept first, even in quantum where conceptually it's a nightmare.

With QM I had a conception of it first, but that was a worded conception of it.
When I first learned the Maths of Quantum Field Theory, hell even Quantum Mechanics, there were times when I just looked at the maths and even though I could solve the problems and manipulate it I had no idea what individual terms represented. So I knew what the expression represented, but individual terms gave me trouble. Especially specific operators.

Over time though, I finally understood entire expressions in terms of their components.

Although I never had this problem with General Relativity, its physical meaning was always so clear.

Spear

nesf wrote:

I was strange in that I always got the concept first, even in quantum where conceptually it's a nightmare.

When I was taught quantum mechanics, the concepts were usually. A reasonable enough approach since a lot of the behaviour can only be seen through the mathemtaical aspect, which is a cetain thing, whereas some of the concepts (pilot wave theory, sum over histories) are still contentious. I've heard this approach referred to as "shut up and do the maths".

nesf

Spear wrote:

When I was taught quantum mechanics, the concepts were usually. A reasonable enough approach since a lot of the behaviour can only be seen through the mathemtaical aspect, which is a cetain thing, whereas some of the concepts (pilot wave theory, sum over histories) are still contentious. I've heard this approach referred to as "shut up and do the maths".

There's a subtle and important difference between a conceptual understanding and an explanation of what's happening. If you know what I mean.

You can understand that something happens but not be able to explain why or the relationships etc.

Edit:

A simple example of the way my mind works.

Take quantum tunneling through a barrier. For me it was my favourite example of the counter intuitive behaviour at "quantum" levels. In order for me to make the maths sensible to me I first had to get my head around the fact that particles behaved like this. First comes the realisation of what happens. Then comes the maths. And finally comes the "explanation" of what's happening.

If that makes sense.

Spear

A simple example of the way my mind works.

Take quantum tunneling through a barrier. For me it was my favourite example of the counter intuitive behaviour at "quantum" levels. In order for me to make the maths sensible to me I first had to get my head around the fact that particles behaved like this. First comes the realisation of what happens. Then comes the maths. And finally comes the "explanation" of what's happening.

If that makes sense.

I guess it depends on how you learned. In my case tunneling was a prime example of maths first, exposing the unexpected nature of tunneling, thus knowledge of the phenomena at least, if not understanding.

dudara

It really depends on the area. For a lot of QM, the maths was hard, and obscured the concept for me. Once I grasped the concept, then the maths simplified and became obvious.

Conceptually wise, tunneling is very easy to understand, once you accept the wave explanation.

stevenmu

I've always found the concept easier to grasp first too. Once I have an understanding of the concept I can then understand the maths behind it, which helps me better understand the concept.

I'm just about to read Roger Penrose's Road To Reality which is supposedly pretty maths heavy so I can see myself having to flick back quite a lot to see where particular equations/derivations/proofs came from. 2 years of mathematical physics in college taught me that, no matter how clearly I understand something when I look at it first, the chances are I won't have a clue what it is next time I look at it

Son Goku

Although the final stage in mathematical understanding is the ability to figure out equations or relations based solely on your knowledge of their components.

Take the Divergence Theorem for example, many people can work it out, but few can interprate what it means based on the physicality of Volume integrals, Surface integrals and vector calculus.

nesf

Son Goku wrote:

Take the Divergence Theorem for example, many people can work it out, but few can interprate what it means based on the physicality of Volume integrals, Surface integrals and vector calculus.

Very nice example


I think most of my problems with pop-science comes from the belief that you can understand the concepts when they are spelt out in english and not need to see any maths.

The problem is, that for a lot of physics, an awful lot is lost in translation.

When I talk about conceptual understanding I'm talking about where I see the physical data if you know what I mean. Where I know what's detected.

I most definitely do not mean an "explanation in English" which pretty much amounts to the same thing as a mathematical formula.

I'm not sure if I'm making much sense here.

Son Goku

One thing a lot of people fail to understand is that being good at mathematics does not make you good a physics.

Take Edward Witten, the father of current superstring theory, he is a brilliant mathematician, but I wouldn't be confident that he is actually a brilliant physicist.

Spear

Son Goku wrote:

One thing a lot of people fail to understand is that being good at mathematics does not make you good a physics.

Take Edward Witten, the father of current superstring theory, he is a brilliant mathematician, but I wouldn't be confident that he is actually a brilliant physicist.

But the opposite is definitely true. I was and remain crappy at maths, and only barely got through my degree as a result.

nesf

Spear wrote:

But the opposite is definitely true. I was and remain crappy at maths, and only barely got through my degree as a result.

Agreed. "fluency in maths" is a necessary part of Physics.

I found that it was the most neglected part of Physics at college. They assumed that you could just "accept" the maths. This is not condusive to an open mind in my opinion.


Whether an open mind is a hinderance at undergraduate level is a different argument though

David19

Thats interesting. I would have thought that being a good mathematician would generally = being a good physicist. I imagined that would be true at the top level of theoretical physics anyway, since it becomes very mathematical.

Also Nesf, I always wondered whether physics undergraduates got enough maths. I'm doing a maths degree and share plenty of maths classes with theoretical physics students. I was thinking that this gives them a huge advantage over physics graduates.

nesf

David19 wrote:

Thats interesting. I would have thought that being a good mathematician would generally = being a good physicist. I imagined that would be true at the top level of theoretical physics anyway, since it becomes very mathematical.

Also Nesf, I always wondered whether physics undergraduates got enough maths. I'm doing a maths degree and share plenty of maths classes with theoretical physics students. I was thinking that this gives them a huge advantage over physics graduates.

You're confusing physics and maths.

Theoretical physics is a subset of physics. As is experimental physics and applied physics.

Theoretical physics is seperated from philosophy by the existence of experimental physics.


Being a good mathematician most definitely does not make you a good at physics. It makes life easier with regard to the mathematics. But that is all.

Plus pure maths is not really of a lot of use, applied maths is. Different disciplines entirely Different thinking and "frames of mind" are needed in them.

I've seen many a good mathematician fall to pieces when faced with physics and conversly many a good physicist fall to pieces when faced with abstract maths.

The two are most definitely not the same. That said the line between physics and maths is blurred. But the forefront of physics is at the experimental side. The theoretical side is only playing catch-up.

ecksor

nesf wrote:

Plus pure maths is not really of a lot of use, applied maths is.

A lot of use to physics or a lot of use in general? I suppose you'd define applied maths as "maths that's useful to physics" ?

nesf

ecksor wrote:

A lot of use to physics or a lot of use in general?

I thought that the post taken in the context of the thread would answer that.

ecksor wrote:

I suppose you'd define applied maths as "maths that's useful to physics" ?

Originally it's roots could be defined as such, but it's grown very broad as a discipline and also covers the study of mathematical constructs beyond their direct use as applied in physics.

It's essentially more than "maths that's useful to physics". I'd phrase it as "the study of maths that happens to be useful in science and engineering".

There is more to applied maths than physics and vice versa.

ecksor

nesf wrote:

I thought that the post taken in the context of the thread would answer that.

That seems to imply the answer is the former, but then you say:

nesf wrote:

There is more to applied maths than physics and vice versa.

Which seems to imply the latter. If that's the case I'm curious to know what areas of pure mathematics you're thinking of.

nesf

Well it all depends on what you consider "to be a lot of use" means.

Personally my opinion is that maths is a language and to study mathematics is to study the language of maths and the complex concepts that it's capable of representing with a clarity lacked by spoken languages.

If that makes sense.

I think of applied maths as a subset of maths rather than something seperate. There is a huge amount of cross-over.

Physics on the otherhand is not maths, it's about data and finding a logical explanation for the way the data behaves.

To paraphrase horribly:

"Physics is the study of nature, and maths is the language it's written in."


"Pure" mathematics.... Well, mathematicians often complain when their lovely pure maths is "sullied" by someone finding a "use" for it. Number theory used to be the lovely and pure, but now it isn't.

I'm unsure exactly what you are trying to ask me. If you are asking me to draw a solid line seperating useful and "pure" mathematics then I'm afraid I can't.

If you want me to talk about maths thats useful with regard physics and "pure" maths then yes, yes I can. But what purpose would that serve?

ecksor

nesf wrote:

I'm unsure exactly what you are trying to ask me. If you are asking me to draw a solid line seperating useful and "pure" mathematics then I'm afraid I can't.

Right. Your post above seemed to imply that this was possible.

nesf

ecksor wrote:

Right. Your post above seemed to imply that this was possible.

How so?

I never limited the "usefulness" of maths to a certain aspect of study.

What's not applicable to any real world concept today might be tomorrow. It's a blurred boundary between the abstract and the real.

The entirety of maths could be considered useful as an exercise in logic if you want to look at it that way.

It's all a matter of perspective. As usual.

Son Goku

nesf wrote:

Whether an open mind is a hinderance at undergraduate level is a different argument though

It most certainly is a hindrance.

Also Nesf, I always wondered whether physics undergraduates got enough maths. I'm doing a maths degree and share plenty of maths classes with theoretical physics students. I was thinking that this gives them a huge advantage over physics graduates.

It can be both an advantage and disadvantage.
On one hand, yes they are taught a lot of mathematics.
On the other hand the become "masters of methods".
In other words they know how to find Lagrangians and Hamiltonians, e.t.c., but don't really have developed physical intuition.
The become more mathematicians than physicists.*

This is a big problem with physics at the moment. A lot of the people being trained in physics are really more gifted at mathematics than physics.
They can solve equations but really can't see the physical reality of the situation being described.

Although a much bigger problem in physics at the moment is "fashion trends", appeal to authority and the "wine and cheese intelligentsia", but I won't go into that.

*This only applies to purely theoretical physics degrees. I'm not talking about degrees with the title "Theoretical Physics".
For instance Trinity have a degree with this title, but they still do experimentation.

ecksor

nesf wrote:

How so?

Well, if you didn't mean it to imply that then we don't have any disagreement, but I think I explained where that came from. The original sentence I quoted didn't refer to anything in particular, just a concept of "usefulness".

nesf wrote:

I never limited the "usefulness" of maths to a certain aspect of study.

In which case I don't see how it makes sense to try to categorise pure mathematics as mathematics that isn't useful (and I think we both mean practically useful). If you had been restricting to physics then I think you would have a better chance of making that divide although I'd still be a bit sceptical. That's why I asked you to clarify.

nesf wrote:

What's not applicable to any real world concept today might be tomorrow. It's a blurred boundary between the abstract and the real.

Agreed.

nesf wrote:

The entirety of maths could be considered useful as an exercise in logic if you want to look at it that way.

That's not what I'm getting at. I've not studied a gigantic amount of pure mathematics, but of the algebra, analysis, geometry, number theory and mathematical logic I've studied I'm aware of practical applications for all of it. They're still very definitely pure mathematics courses I've been taking though.

nesf

Fair points ecksor.


My original statement was referring to maths with respect to physics. Only a small portion of mathematics is relevant in physics, as I'm sure you know. I was questioning the poster's assertation that by somehow studying more mathematics rather than doing experiments made someone a better physicist.

That simply isn't true. Plus the reality of the situation is that only a small percentage of physical research is on "high level theoretical" topics like string theory.

Most of it is concerned with experiments and reality, not with trying to fit maths onto something that we have no data on. Not that this isn't relevant or useful. It's just that it isn't the real meat of physics.


Back to what you were saying. I used to think in terms of "useful" and "pure" mathematics. I don't anymore. I know what's useful with regards physics. But I'm constantly suprised by the ways other disciplines find ways to impliment "abstract" maths into their studies.

David19

nesf wrote:

Agreed. "fluency in maths" is a necessary part of Physics.

I found that it was the most neglected part of Physics at college. They assumed that you could just "accept" the maths.

I made my post in reference to this. Are you not implying that physics undergraduates don't do enough maths?

Also, wouldn't a theoretical physicis graduate be much better prepared to study say quantum mechanics or string theory than a physics graduate? I'm just curious, I don't really know what physicists study. I'm just making presumptions.

Also, I should point out I'm aware there's more to physics than topics like string theory.