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Physical Intuition, Not Mathematics (2011)

realphysics.blogspot.com

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Re: Physical Intuition, Not Mathematics (2011)

#51

Post by crimsonalucard »

Does anyone have a good theory for what they think intuition is?

I'm interested in process. What is the mapping algorithm that transforms problem into solution? While intuition appears to be magic, I believe that there is a very concrete process happening in our subconscious.

My personal guess is that we're transforming the problem into a format more suited for different modules of our brain to process.

For the table problem we apply 2 transformations. One is referred to as a calculation, the other as intuition.

"Calculation" involves transforming the table into symbols (mathematics) for the language/logical part of our brain to process; the other transformation involves turning the table into a sort of fuzzy 3D visualization for the imaginative/spatial part of our brain to analyze.

Both transformations yield transformed results. Symbols yield a symbolic/numeric solution, a fuzzy 3D visualization yields an equally fuzzy 3D solution.

Funny how two different process that are both seemingly systematic are called different things. Why is one called intuition and the other not?

Re: Physical Intuition, Not Mathematics (2011)

#52

Post by UhUhUhUh »

A problem is that the reverse is also true. Simple example: stretch a rope around the earth that fits tightly and add 1 m to the length. Can a cat go under the rope (it's always a cat). Intuitively that seems like a "No". The simplest of formulae says "Yes" ( 1m/2pis = +/- 15 cm). Here, pretty much everyone has to resist intuition and trust numbers. I think the best way to conceptualize intuition is some sort of unconscious sub-process carried out by the brain at all times that has to be shut down or de-prioritized most of the time to allow for hard, "empirically-validated", processes to dominate the global activity (similar to early life "pruning"). As all neuronal processes, these need to be activated to remain available.

Re: Physical Intuition, Not Mathematics (2011)

#53

Post by marcosdumay »

brak2718 wrote: post #4

The technique served me very well doing physics and engineering in an earlier life. I struggle now with the chaos of software systems because I'm unable to "feel" what's going on.

As hard as the actual calculations may be, the main feature of a mechanics is that it is conceptually simple.

Now, software just isn't. Managing complexity requires a completely different intuition from exploring a simple space.

Re: Physical Intuition, Not Mathematics (2011)

#54

Post by harperlee »

UhUhUhUh wrote: post #52

A problem is that the reverse is also true. Simple example: stretch a rope around the earth that fits tightly and add 1 m to the length. Can a cat go under the rope (it's always a cat). Intuitively that seems like a "No". The simplest of formulae says "Yes" ( 1m/2pis = +/- 15 cm). Here, pretty much everyone has to resist intuition and trust numbers. I think the best way to conceptualize intuition is some sort of unco…

Intuitively it can also be answered: suppose you pinch the rope, so it is tight (you step on it and pull from between your two feet, for example). You'd have a handle for the earth that will go to about just above your knee. A cat fits!

Re: Physical Intuition, Not Mathematics (2011)

#55

Post by [deleted] »

harperlee wrote: post #54
UhUhUhUh wrote: post #52

A problem is that the reverse is also true. Simple example: stretch a rope around the earth that fits tightly and add 1 m to the length. Can a cat go under the rope (it's always a cat). Intuitively that seems like a "No". The simplest of formulae says "Yes" ( 1m/2pis = +/- 15 cm). Here, pretty much everyone has to resist intuition and trust numbers. I think the best way to conceptualize intuition is some sort of unco…

Intuitively it can also be answered: suppose you pinch the rope, so it is tight (you step on it and pull from between your two feet, for example). You'd have a handle for the earth that will go to about just above your knee. A cat fits!

[deleted]

Re: Physical Intuition, Not Mathematics (2011)

#56

Post by noobermin »

jivardo_nucci wrote: post #24
pdpi wrote: post #13

Earlier quoted context omitted.

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…

I think you're calling Aristotelian physics "Galilean mechanics."

Re: Physical Intuition, Not Mathematics (2011)

#57

Post by noobermin »

reagency wrote: post #26
noobermin wrote: post #5

Earlier quoted context omitted.

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)

Sure, but I'm not sure how that is related. What I'm essentially talking about is you have a DE that is of the form -i h\phi_t -b\phi_{xx} + V(x)\phi = 0 and graphing \phi as you vary V(x). That is not obvious unless you know how solutions of the equation behave for different simple cases of V(x) and continuity. That, I argue, is intuition.

Actually, what you mentioned sounds like intuition to me. You didn't make hand plot the polynomial, so that is relying on intuition over rigour, which I think is what the OP's quote from Feynman referred to.

Re: Physical Intuition, Not Mathematics (2011)

#58

Post by fiatjaf »

crimsonalucard wrote: post #50
fiatjaf wrote: post #17

Isn't this obvious? Why does someone have to say it?

The table is obvious because it's used as an example. Developing intuition for something list say... relativity is not as obvious.

Relativity is impossible to imagine and intuit, also particles and quantum phaenomena. Physicists always tell the public to "not try to imagine" these things, because that's the natural and obvious thing to do: to imagine and try to intuit.

This student at the example is probably crazy or fake.

Re: Physical Intuition, Not Mathematics (2011)

#60

Post by amelius »

crimsonalucard wrote: post #51

Does anyone have a good theory for what they think intuition is? I'm interested in process. What is the mapping algorithm that transforms problem into solution? While intuition appears to be magic, I believe that there is a very concrete process happening in our subconscious. My personal guess is that we're transforming the problem into a format more suited for different modules of our brain to process. For the table…

I think intuition is just using (or trying to use) a higher level of abstraction to approach a problem.
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