Inspired by quasi426's thread :shy: https://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?
Oh, you can reach the highest levels of hand-waving 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.
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 ......" :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.
However, the problem here is that we are not born with an innate set of fixed intuition and common sense. They evolve and expand as our knowledge increases. And that's where we run into trouble with QM, because almost every aspect of QM is counter-intuitive. There is an obvious discontinuity between "what we already know" and "what QM is saying". It is the mathematical formalism that saves us from dangling in mid-air 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.
Just to make a point for arguments sake: 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 x-factor ask me how I come up with my responses to these threads!
There's a difference between being FED the information and accepting it, and UNDERSTANDING the information that you are given. You can do homework assignments, grind through the math, etc. etc, but yet, not understand what you are doing. I see this in many students. This is especially true if the students memorize the set of info they were given. 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 "spin-charge 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 time-dependent 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.
Your intuition lead you to misunderstand my previous post... read it again, I never claimed that you could progress on pure intuition. You chose to intuitively judge my position. You were wrong. I would not have pointed that out had you read and understood before you responded. I stick to my original post. an x factor or a multiplier relies on the value first... i think you should know this better than I... as i'm not a physicist. I prefer to twist my own words, I don't appreciate having my words twisted for me, thank you. an apology for your oversight would be accepted in the name of progression of this thread, which I think is a valid question on your part.
Now it is your turn to actually reread at what I posted. Notice that in the first two paragraphs, I was addressing what you said here: And then, noticed what I did. I said: I posed a question in trying to go BACK to the original question of this thread. I did not attribute that to you, nor to your posting. Now maybe I should have said something to the effect that we are now going back to the original question, but I believe nowhere in there did I make a claim that you said this. It was STILL addressing the original point made in this thread. Zz.
QM is only the most recent BIG roadblock. Most of physics is counter-intuitive. Look at how long Aristotle reigned supreme with his essentially intuitive descriptions before he was questioned. That a body in motion or at rest tends to stay in motion or at rest unless acted on by an outside force is a counter-intuitive revelation that took milenia of thought to arrive at. If you traveled the remote corners of the world asking physics-naive peoples to figure out the laws behind how things move you would never find any who could arrive at Newton's first. The very fact that physics, or any discipline, has to be formally taught is just about a guarrantee that it's counter-intuitive. 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.
Hum... you are probably correct. 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.
Consider a very simple example: Does trigonometry spring from intuition? As Descarte pointed out, we can imagine a triangle but still have to discover its properties. So I'd say that one can't even get past tenth grade math with intuition. There is nothing intuitive, even when it comes to something as simple as Pythagoras' Theorem.
This is why I asked the Opening Poster to explain what was meant by "intuition" in his/her question, because there are at least two separate things one might call by that name; one of them very useful in physics, the other not at all. The one you've described in this, and previous posts, is the useful kind, and is a sort of spontaneous subconscious falling into place of previously, apparently random or disconnected inforation you have worked hard to gather. The useless kind is the shallow, off-the-top-of-the-head speculation, that is uninformed. Your case for QM being a whole different kind of counter-intuitive physics than ever previously encountered is completely persuasive to me. Hehehehehehe. :)
To clear up confusion, 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.*
The person who got the farthest with this kind of intuition has to be Michael Faraday. Through careful, deliberate thorough experimentation, and precious little math, he informed himself to the point where he once offered the intuition to a lecture audience that visible light was probably a form of electromagnetic radiation.
How far with intuition? new stuff in green When you are in school, you are riding on the intuitive ideas of the lineage of scientists before you. You did not come up with these ideas or theorem SO YOU NEED NOT INTUITION to be a student. Someone with intuition bridged the gaps for you to walk over. These are the scientists who dared to think outside the box and challenged themselves to devote their life to their work. As students, one needs not intuition to learn anything. FORCED FED OR NOT, THE GOAL IS TO LEARN. As you said, TRUEST FORM OF LEARNING IS UNDERSTANDING. WITH UNDERSTANDING, YOU MAY BECOME MORE INTUITIVE, AND FURTHER CONTRIBUTE TO SCIENCE BY SHARING A HIGHER UNDERSTANDING. Intuition is not necessary to learn. However, it will be helpful if you intend to be great.
So now it's my turn to ask, where exactly did I say that I didn't agree with this? I even said that *I* used my intuition almost every day in deciding what to and what not to do? So why are you telling me this? Zz.