How Far with Intuition
Inspired by quasi426's thread :shy:
http://www.physicsforums.com/showthread.php?t=84972, :shy: I wonder How far can one advance intuitively into physics...before he/she must accept/rely entirely on mathematics to predict/form conclusions on matters? 
Not very...

Oh, you can reach the highest levels of handwaving without knowing a thing about math; in fact, you can progress so far that you actually become firmly convinced you understand physics a lot better than the professionals.

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I suppose it depends on what area of physics. I wrote an essay titled "Why is Quantum Mechanics SO Difficult" that essentially said that relying on "intuition" based on what we have already understood in classical physics is the major source of misunderstanding, misinterpretation, and bastardization of quantum mechanics. This is why QM is not easily understood especially by the general public.
Zz. 
I would think that not only could you advance pretty far in math and science with intuition, but a high degree of intuition is absolutely essential!
Otherwise, what would you do when you came to the part of the problem where the instructor says, "and it should be intuitively obvious that the three and a half foot equation on the left side simplifies to 2x ......" :rolleyes: :rofl: Of course, Pierre LaPlace is the patron saint of mathematics professors. When Nathaniel Bowditch was translating LaPlace's work into English, he noted, "I never came across one of Laplace's 'Thus it plainly appears' without feeling sure that I have hours of hard work before me to fill up the chasm and find and show how it plainly appears". Edit: Added smilie. Of course, it's really only half kidding, since it certainly helps if the problem seems intuitively obvious in hindsight, at least. But that's going on the assumption that intuition is really just an accumulation of past experience. 
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It is the mathematical formalism that saves us from dangling in midair by providing a link to forms we are familiar with. Once we understand this, we then reformulate our "intuition" based on new set of ideas and allows our intuition to grow and encompass this new set. But it comes out of an understanding of the mathematical formalism first and not simply an expansion out of a current intuition. It is due to this that I disagree that one can go far in learning physics simply based on intuition alone. There's a very BIG roadblock in the form of Quantum Mechanics. Zz. 
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you do realize that as you learn anything in school, you are taking for granted that the infromation that you are receiving is true. Some students will need to take a leap of faith in hopes to understand the concepts with practice, while others will immediately have a basis for understanding due to a path of reason that derives from observed and transfered experience (intuition). In most higher levels of science, you are riding on the intuitive ideas of the lineage of scientists before you. You did not come up with these ideas or theorem. Someone with intuition bridged the gaps for you to walk over. Since science is all about solid proof, pure intuition will not drive take a person very far as there is no proof of intuition (they try to prove it with IQ tests I think). I believe intuition, if you are able to tap into it, will help you progress in learning... hmmm... let's say it's an xfactor :smile: ask me how I come up with my responses to these threads! :biggrin: 
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But this isn't learning in the truest sense, and if one wishes to "go far" in physics, this will NEVER do. Note that I never said that intuition isn't useful. As a practicing physicist, I RELY on my intuition almost every single day to tell me what I should and should not spend time on. However, I am completely aware that I go through the rigors of my education system JUST so I can rely on my intuition when the time comes. But can one actually LEARN physics by simply using one's intuition? I disagree. I have brought up several examples just from QM alone. If we buy into the notion that for one to truly understand something, one must build one's knowlege on top of what one already understands, then QM will present a major discontinuity of that flow. There's nothing intuitive about QM  the names, words, and phrases may sound the same (spin, angular momentum, orbital, observable, measurment, etc.), but they have such a different meaning in QM, you simply cannot use what you already know in the classical world even as analogies! I can explain what a "spincharge separation in a 1D Lutinger Liquid is" and make it sound reasonable, but this will be nothing more than a set of information that you gather without ANY connection or reference to anything else that you have already understood. This is not the way to understand and comprehend anything, at least not in physics. So what is familiar with QM? The mathematics! It is the only connection we have with something that we have a prior understanding of! Look at the timedependent Schrodinger equation, and then look at a generic wave equation. Look at the solution to the hydrogen atom wavefunction and then look at the spherical harmonic expansion of a loop of charge. The intuitive concepts of QM may be very strange and unfamiliar, but the mathematics look damn familiar. You build a new set of intuition based on what you understand from the mathematics. You don't build this set of intuition based on classical intuitions. Zz. 
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Zz. 
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The very fact that physics, or any discipline, has to be formally taught is just about a guarrantee that it's counterintuitive. Most people can hear, understand, and accept Newton's first in a minute, which makes it seem vastly more intuitive than it is, because none of them could ever have arrived at it themselves. 
Intuition's contribution would most likely be zero.
Why? I'm not born with knowledge of mathematics, nor the equations of physic in whatever area. Knowing a seesaw balances when two equal weights put from the same distance from a central point isn't physics. Thats just acklnowledgement of visual fact. 
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The irony in all of this is that during my short stint as a college instructor (I was teaching first year intro physics), I was a stickler in emphasizing INTUITIVE APPROACH at every step of the way. This is because a lot of the stuff that is being covered really is a part of the students daily observations. I often ask them "if Newton said that a body that is being applied a force will accelerate, how come you have to push on a cart just to keep it moving at a constant velocity?", and things like that. I tried to appeal to their intuition and common sense all the time, or else they will tend to memorize the physics rather than understand them. But notice what's the difference here. First year physics (at least the classical part) can EASILY be built upon their already established understanding of how the world around them work. We just need to tweak it a little bit. So the learning process here is a LOT simpler since we can appeal to what they have already seen and understand. We build on top of that understanding. However, as I've said, this can't be done all the time, and certainly can't be done with QM. So you'll notice that this is consistent with my view that the best way to learn is to build the new knowledge on top of what we already know. And just so there's no misunderstanding and before you demand an apology from me for twisting your words, I know you didn't make these claims about intuition being enough, etc.... etc. I was just continuing the the main point of the thread. :) Zz. 
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As the Opening Poster, I'm referring to the "useful kind," the spontaneous subconscious falling into place of previously, apparently random or disconnected inforation you have worked hard to gather.* 
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