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Physical Intuition, Not Mathematics (2011)

realphysics.blogspot.com

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Re: Physical Intuition, Not Mathematics (2011)

#21

Post by abdullahkhalids »

jrapdx3 wrote: post #11

The problem in discussing this subject is the idea of "intuition" itself because the term doesn't have an unambiguous definition. Meaning varies from one instance to another, even one moment to the next, and disputes arise from imprecise communication. In the example, I think what Feynman is describing, we commonly call "visualization", to be able to "see" the problem in imagination. That is no less a form of abstrac…

I agree that there are various patterns of thought that can be labelled intuition. I would like to add on that you have to practice to develop any of these different types intuition. This is I think what Feynman is saying and he is emphasizing the type of intuition (run the experiment in your head) that is very useful for physicists.

In every field there is probably a different type of intuition that is useful. In abstract math maybe 'getting used to it' very fast is very useful. In geometric math maybe being able to visualize objects in space is useful. In programming maybe seeing the run of the code in your head is useful.

Re: Physical Intuition, Not Mathematics (2011)

#22

Post by stiff »

Feynman also said the following (in the "The Character of Physical Law" lectures):

Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics. Newton's statement of the law of gravitation is relatively simple mathematics. It gets more and more abstruse and more and more difficult as we go on. Why? I have not the slightest idea. It is only my purpose here to tell you about this fact. The burden of the lecture is just to emphasize the fact that it is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics.

Re: Physical Intuition, Not Mathematics (2011)

#23

Post by marincounty »

I had a bad anxiety attack one time. The room I was in felt like it was undulating. Everything started to become fluid like. I can't explain it, and should probally draw it, but years later I still wonder if that's the way the real world actually looks?

Never told anyone--out of fear it could happen again.

Re: Physical Intuition, Not Mathematics (2011)

#24

Post by jivardo_nucci »

pdpi wrote: post #13
krastanov wrote: post #3

While this is a lovely sentiment and a perfectly fine way to approach the sciences (and also engineering oriented disciplines), not all physicist think that way. There is a lot of beauty in deriving laws of nature without relying on physical intuition. A lot of beautiful results are based on purely requiring laws to be self-consistent and seeing that only one possible law is self-consistent. For instance check out wh…

QM is counter-intuitive only insofar as your intuition is naturally wired for a classical mechanics world. Given enough practice, QM eventually becomes second nature too. You pretty much _need_ to go through that process to function at the highest levels. There's a good post by Terrence Tao about this topic, I think it was posted here some time ago: https://terrytao.wordpress.com/career-advice/there%E2%80%99s...

Wrong on two levels:

Our physical intuitions are Galilean, not classical, mechanics (that is, they are non-Newtonian). For example, our intuitions tell us that an object set in motion eventually slows down and stops. That's Galilean (also termed "folk physics" or "naive physics", usually by cognitive scientists).

Most of us had to study formal physics to advance to Newtonian classical mechanics.

Quantum mechanics (QM) is completely non-intuitive, at least as far as intuition about either folk physics or Newtonian classical physics is concerned. IIRC Feynmann says as much in his book "QED: The Strange Theory of Light and Matter", Chapter 28 beginning:

"I think I can safely say that nobody understands quantum mechanics. —Richard Feynman

The quantum theory is not explicable in commonsense terms..."

Of course Feynman used his real-world physical intuition all the way through to his most abstract work. In one case he characterised the internal structure of the proton as being like "marbles inside a tin can." Try and write those equations!

Re: Physical Intuition, Not Mathematics (2011)

#25

Post by reagency »

stiff wrote: post #22

Feynman also said the following (in the "The Character of Physical Law" lectures): Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics. Newton's statement of the law of gravitation is relatively simple mathematics. It gets more and more abstruse and more and more difficult as we go on. Why? I have not the slightest idea. It is only my purpose here to tell you about this…

This is very important. Many students hit a wall when physics passes beyond lay intuition and whatever may they already know well. Advancing in mathematics is essential to feeling comfortable in advanced physics.

Re: Physical Intuition, Not Mathematics (2011)

#26

Post by reagency »

noobermin wrote: post #5
krastanov wrote: post #3

While this is a lovely sentiment and a perfectly fine way to approach the sciences (and also engineering oriented disciplines), not all physicist think that way. There is a lot of beauty in deriving laws of nature without relying on physical intuition. A lot of beautiful results are based on purely requiring laws to be self-consistent and seeing that only one possible law is self-consistent. For instance check out wh…

There is a way to use physical intuition in QM too, although it obviously isn't the physical kind (tables and flipping them over). It tends to be mathematical, but it certainly isn't rigorous chugging through equations. The canonical example of this are the test questions you see in undergraduate QM courses that show you a space potential graph then ask you sketch the wavefunction in different regions. You have to ha…

I can sketch you a graph of (x-1)(x-2)(x-3)(x-4), but it isn't because of intuition. It is because I know how to measure key characteristics of a polynomial (roots and asymptotes) and can smoothly interpolate (simple interpolation is maybe intuitive)

Re: Physical Intuition, Not Mathematics (2011)

#27

Post by reagency »

abdullahkhalids wrote: post #21
jrapdx3 wrote: post #11

The problem in discussing this subject is the idea of "intuition" itself because the term doesn't have an unambiguous definition. Meaning varies from one instance to another, even one moment to the next, and disputes arise from imprecise communication. In the example, I think what Feynman is describing, we commonly call "visualization", to be able to "see" the problem in imagination. That is no less a form of abstrac…

I agree that there are various patterns of thought that can be labelled intuition. I would like to add on that you have to practice to develop any of these different types intuition. This is I think what Feynman is saying and he is emphasizing the type of intuition (run the experiment in your head) that is very useful for physicists. In every field there is probably a different type of intuition that is useful. In ab…

You don't see the code run in your head, though. You get a feel for how this design pattern works at a glance (intuition), or you carefully step through the code like a debugger.

Re: Physical Intuition, Not Mathematics (2011)

#28

Post by reagency »

21p wrote: post #19
edtechdev wrote: post #10

Related to this, there's a fair amount of research on the connection between embodied cognition and the learning of physics (and mathematics), as well as examples of 'embodying' physical forces and laws. An example from Hans Freudenthal is from a standard physics question. If there are books on top of a table, what are the forces acting on the books? Most all students draw the downward force of gravity, but some forg…

The problem I have always had with the analogy of a person holding up the books with their back is that a table doesn't have to do "work" to hold up the books, but a person does. They table isn't burning any calories.

The table has tension, though. Ad opposed to a table made of paper which would not exert force on the book--the book would overcome the table's tension and set the table in motion until the floor exerted an upward force.

Re: Physical Intuition, Not Mathematics (2011)

#29

Post by reagency »

dschiptsov wrote: post #18

Intuitions are insights (hints) from so-called ancient, non-verbal (pre-linguistic) instinctive "knowledge" or "genetic memory". It is not only the kind of knowledge of how birds "know" how to make nests or men know to run out of building when earthquake happen (without any prior training), but also intuitive knowledge about the nature of reality, properties of physical environment, which has been "trained" before an…

That is "instinct", a different concept from "intuition", thought overlapping in some aspect.
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