Physical Intuition, Not Mathematics (2011)
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Physical Intuition, Not Mathematics (2011)
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Re: Physical Intuition, Not Mathematics (2011)
#2I would be interested to know more as to how people think in the language of mathematics when deriving and reading mathematical formulas as I really struggle with it if I don't get the intuition.
Re: Physical Intuition, Not Mathematics (2011)
#3While 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 what Scott Aaronson says about probability in quantum mechanics. While Feynman in his famous lectures just says that quantum mechanics is counter intuitive and you are not supposed to truly understand it, Scott Aaronson uses math to explain how to correct your intuition (and I am stressing, this is not just about learning the math, it is about basing your intuition on the math, not on the everyday experience).
Re: Physical Intuition, Not Mathematics (2011)
#4The 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.
Re: Physical Intuition, Not Mathematics (2011)
#5While 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 have an idea what a wavefunction does in certain regions, oscillate? decay? how many nodes, etc.
Re: Physical Intuition, Not Mathematics (2011)
#6I think this is interesting because the implications go beyond just physics and mathematics.
Sometimes we learn things in one domain that could be easily applicable in others, yet since we've never practiced said things in another context, it's hard for us to make this connection. Often, all we need is a little nudge in the right direction, which could open to us a new world of insights that we didn't have before.
Re: Physical Intuition, Not Mathematics (2011)
#7The 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.
I think there are two separate issues here. One is 'just' another way of understanding or visualizing a concept or process: "look the problem over and see if you can understand the way it behaves, roughly, when you change some of the numbers". Isn't this exactly what you do with a debugger when you step through the code? Or if I'm designing a data structure or algorithm, I have to play around in my head, or with pen and paper, before even thinking about going near a keyboard.
The other issue is 'allowing' oneself to imagine and visualize these things (math/physics equations / software). I don't think the point is to restrict yourself to things for which you have physical intuition, it's more that it's easier to go from physical experience -> intuition about physics phenomena that are closely related to physical experience -> intuition about math /physics /software that don't have a counterpart in our physical experience as humans e.g. quantum mechanics
Re: Physical Intuition, Not Mathematics (2011)
#8The 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.
It seems like a common intuition in software is the "code smell", where you can just look at some code and tell if it will be "maintainable" or "good", for some value of that.
I've come to think of it more as a "familiarity" though - where if you're familiar with writing stable and maintainable systems, you'll get the right smells - but some people have opposite feelings about systems, and it seems like they are people that have the opposite type of experience as well.
Other types of intuition I think are based mostly on pattern recognition. If you have a system that makes a set of choices that follows a well known pattern to you, your brain can start predicting what has been done where, and with enough confirmation, can start feeling confident about the behavior of other parts not yet scrutinized. Once again, if things are done in an unfamiliar way, all that evaporates and one needs to fall back to looking at the low level strategies and techniques.
Re: Physical Intuition, Not Mathematics (2011)
#9The 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.
That's what this is about: http://worrydream.com/SeeingSpaces/
Re: Physical Intuition, Not Mathematics (2011)
#10Related 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 forget about the force the table exerts upward back on the books. You can have students get on their hands and knees and put books on their back, or have them lie on their back and hold up books with their hands and arms. They 'embody' the table, in a sense. When you add a second book, you feel that you have to exert more effort (which correlates with force) to hold the books up.