what makes comprehension "intuitive" or not?

[swansont]

Again, Feynman has this covered, in a quote StringJunky recently posted

http://www.scienceforums.net/topic/56130-speed-of-electrons/page__st__20__p__599603#entry599603

 

Finally, there is this possibility: after I tell you something, you just can`t believe it. You can’t accept it. You don’t like it. A little screen comes down and you don’t listen anymore. I’m going to describe to you how Nature is—and if you don’t like it, that’s going to get in the way of your understanding it. It’s a problem that physicists have learned to deal with: They’ve learned to realize that whether they like a theory or they don't like a theory is not the essential question. Rather, it is whether or not the theory gives predictions that agree with experiment. It is not a question of whether a theory is philosophically delightful, or easy to understand, or perfectly reasonable from the point of view of commonsense. The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is—absurd.” QED: The Strange Theory of Light and Matter

 

i.e. if you find physics to be counterintuitive, blame mother nature, not the physicists.

[mississippichem]

 

Generally that's true but in light of the context you posted for the Feynman quote, I can see how it refers to avoiding misinterpretation. Maybe I misinterpret it just because I can't stand the defeatism of giving up linguistic description and reasoning altogether to avoid the risk of misinterpretation. That would be as bad, imo, as giving up progress in science and technology altogether because some people use them to make deadly weapons and destructive and oppressive technologies of control. Oh wait, did I just tie it back into the nuclear weaponry issue?

 

I just can't see what advantage a linguistic/descriptive approach can offer. It has already been established, over the course of this thread and a plethora of others, that a linguistic approach to understanding counter-intuitive science concepts is inferior in terms of accuracy, reproducibility, verifiability, as well as internal consistency.

 

The only advantage I see to a descriptive approach is that it opens up a certain degree of flawed understanding to the lay person. Sure, it may provoke the interest of some guy on an internet forum; but it really offers no additional scientific insight. I think you may have the goal of science backwards. The goal of science is not for Lemur and Mississippichem to understand with our imperfect human minds the workings of the universe. We are not trying to achieve a god-like cognitive state. The goal of science is to produce a working model of nature that brings with it a large degree of predictive power. Mathematics is the only avenue that has thus far been able to deliver on that tall order.

 

Even if you were to descriptively understand the most complex workings of QM, what good would it do? How do I know that your mental picture is the same as mine? What happens when we need to convey these ideas to someone in China who doesn't speak English? Upon quick examination you should find that there would be no objective standard by which to judge the consistency and integrity of ideas.

 

Mathematics is not some cryptic language that requires logical leaps and memorization of facts. The fact that 1+1=2, and 1+0=1 is all that is required to derive even the most complex of maths, at least in theory.

[lemur]

i.e. if you find physics to be counterintuitive, blame mother nature, not the physicists.

But what basis do you have to say this except your current knowledge of mother nature based on how physicists have described experiments they have conducted?

 

I just can't see what advantage a linguistic/descriptive approach can offer. It has already been established, over the course of this thread and a plethora of others, that a linguistic approach to understanding counter-intuitive science concepts is inferior in terms of accuracy, reproducibility, verifiability, as well as internal consistency.

Because depth of insight can stimulate innovative insights. How would Planck have been able to compare electrons in a conductor with gas purely based on comparisons of quantitative models of current with quantitative models of sound waves? How would heat have been revealed to be rooted in molecular motion instead of a substance in and of itself? How would heat and pressure and energy have been related in a general way? How can any really meaningful scientific discovery be conceived of or expressed without qualitative mechanism of some kind?

 

We are not trying to achieve a god-like cognitive state. The goal of science is to produce a working model of nature that brings with it a large degree of predictive power. Mathematics is the only avenue that has thus far been able to deliver on that tall order.

Knowledge of truth always brings with it a relative "god-like cognitive state" so that's not an issue. The goal of science has always been to describe, explain, and conceptualize, as much as to predict, no?

 

Even if you were to descriptively understand the most complex workings of QM, what good would it do? How do I know that your mental picture is the same as mine? What happens when we need to convey these ideas to someone in China who doesn't speak English? Upon quick examination you should find that there would be no objective standard by which to judge the consistency and integrity of ideas.

Well, different languages and even different understandings among different individuals using the same language can result in nuances that raise critical conflicts of meaning that can result in enlightenment from resolving the conflict/confusion. As for what good it would do to have a intuitive descriptive understanding of QM, it would allow you to model various empirical situations at a more complex level by sacrificing a certain amount of accuracy. It would allow you to understand in a deep concrete way the connection between observed phenomena and what's going on at the (sub)atomic level. It would allow you to explore numerous potential further implications, extensions, and developments of known concepts and issues.

 

Mathematics is not some cryptic language that requires logical leaps and memorization of facts. The fact that 1+1=2, and 1+0=1 is all that is required to derive even the most complex of maths, at least in theory.

Try using a descriptive equation as a 1-to-1 correspondence with empirically observable phenomena. I can rarely even begin to see the connection between the parts of an equation and the thing purported to be described or explained. Something is always being squared or square-rooted to ensure non-negative results or something like that. They are designed to calculate, not explain or describe (really). Granted, it is handy and neat when you can plot a line and have the area under the line represent something related, etc. It's just not a direct dissection of empirical observabilities. Don't get me wrong, I am far from giving up on using equations to enhance my knowledge of something I'm interested in. I can just tell you that I am fairly often disappointed in the enlightenment-effects I get from studying them.

 

 

[Cap'n Refsmmat]

Try using a descriptive equation as a 1-to-1 correspondence with empirically observable phenomena. I can rarely even begin to see the connection between the parts of an equation and the thing purported to be described or explained. Something is always being squared or square-rooted to ensure non-negative results or something like that. They are designed to calculate, not explain or describe (really).

Perhaps your problem is that you don't deeply understand the mathematics. Mathematics can indeed explain and describe, but one must first understand how it works.

[lemur]

Perhaps your problem is that you don't deeply understand the mathematics. Mathematics can indeed explain and describe, but one must first understand how it works.

Let's assume I don't. Does that mean that I have to abandon the pursuit of intuitive/qualitative knowledge until I master reading math? If someone told you you couldn't philosophize until you learned to read Kant, would you stop and dedicate your life to Kant? Or would you maybe try to read what others have written about Kant's work in language that you could more easily grasp? Then, once you understood various aspects of Kant's philosophy in a way that moved your own philosophy along a bit, would you accept it if professional philosophers told you that you can't really philosophize until you read Kant in the original text and write in the same style?

 

Personally, I think people should explore knowledge, scientific or otherwise, to the best of their ability according to their talents, and express what they find to others for critical review and exchange. They might come up with some valid thoughts in their process and be a benefit to others around them. I'm getting a little frustrated with this topic because the more I defend intuitive/qualitative approaches, the more responses I get defending the institutionalized anti-intuitive approaches. Why can't people just see how qualitative aspects of science are an important part of it instead of always arguing for how essential math is? Yes, the math makes it more accurate, but even when you don't get the math it's still useful to know that, e.g., phase transitions consume energy without resulting in temperature increase. That can be intuitively/qualitatively explained in terms of energy-conservation and thus the fact that energy has to do SOMETHING, it can't just disappear.

 

 

 

[Cap'n Refsmmat]

Let's assume I don't. Does that mean that I have to abandon the pursuit of intuitive/qualitative knowledge until I master reading math? If someone told you you couldn't philosophize until you learned to read Kant, would you stop and dedicate your life to Kant? Or would you maybe try to read what others have written about Kant's work in language that you could more easily grasp? Then, once you understood various aspects of Kant's philosophy in a way that moved your own philosophy along a bit, would you accept it if professional philosophers told you that you can't really philosophize until you read Kant in the original text and write in the same style?

A more apt analogy would be, "If someone told you that you couldn't understand Kant until you learned to read Kant, would you stop and dedicate your life to Kant?", because it is exactly analogous to, "If someone told you that you couldn't understand physics until you learned to read physics," and physics is written mathematically. Anything else is merely interpretation. Reading a qualitative description is like reading another author writing about Kant, instead of reading Kant.

 

Why can't people just see how qualitative aspects of science are an important part of it instead of always arguing for how essential math is?

Possibly because you insist on intuitively understanding parts of physics which are nearly impossible to intuitively understand, and subsequently end up getting things very wrong.

 

Certainly there are parts of science which may be easily understood without the use of mathematics, and it is good that you try to understand them. But understand that some things are best expressed with mathematics.

[lemur]

A more apt analogy would be, "If someone told you that you couldn't understand Kant until you learned to read Kant, would you stop and dedicate your life to Kant?", because it is exactly analogous to, "If someone told you that you couldn't understand physics until you learned to read physics," and physics is written mathematically. Anything else is merely interpretation. Reading a qualitative description is like reading another author writing about Kant, instead of reading Kant.

For some people, that is the best way to understand concepts written about by Kant. Do you think it is any different when someone gets a concept by reading a second or third hand version of it then when they read the original author? I understood the logic of the double-slit experiment before watching Feynman's 1960s lecture this morning, yet I have the feeling that you would have said that I couldn't really get it until I understood Feynman himself.

 

Possibly because you insist on intuitively understanding parts of physics which are nearly impossible to intuitively understand, and subsequently end up getting things very wrong.

Really I don't insist on anything. If I ask questions in qualitative terms that people find impossible to discuss without reference to math, they can either post their math if they want or decide not to bother because it might be wasted on me (though someone else might read their post and get it - and it's also not impossible that I will). What I don't get is the attitude that people decide once they're bona fide physicists that they have total insight over every possible descriptive possibility for physical phenomena. Surely there are as many ways to describe physicalities are there are physicalities themselves.

 

Certainly there are parts of science which may be easily understood without the use of mathematics, and it is good that you try to understand them. But understand that some things are best expressed with mathematics.

Mathematics expresses the things it expresses perfectly. How could mathematics do otherwise? It is designed to be perfect in its own right, no?

 

Thank you for acknowledging that there is goodness in the attempt to understand physicalities, regardless of method chosen.

 

 

[swansont]

Really I don't insist on anything. If I ask questions in qualitative terms that people find impossible to discuss without reference to math, they can either post their math if they want or decide not to bother because it might be wasted on me (though someone else might read their post and get it - and it's also not impossible that I will). What I don't get is the attitude that people decide once they're bona fide physicists that they have total insight over every possible descriptive possibility for physical phenomena. Surely there are as many ways to describe physicalities are there are physicalities themselves.

 

If you think this is the result of physicists' attitude then it just confirms you don't understand the problem. The problem is not with physicists' attitude. You're shooting the messenger, and your last sentence contradicts the first — you are insisting that there be other descriptions.

[imatfaal]

 

Really I don't insist on anything. If I ask questions in qualitative terms that people find impossible to discuss without reference to math, they can either post their math if they want or decide not to bother because it might be wasted on me (though someone else might read their post and get it - and it's also not impossible that I will). What I don't get is the attitude that people decide once they're bona fide physicists that they have total insight over every possible descriptive possibility for physical phenomena. Surely there are as many ways to describe physicalities are there are physicalities themselves.

 

 

 

You are imputing unfair motives when you state that physicists "decide ... that they have total insight over every possible descriptive possibility" - from my experience of watching and talking to professional and academic scientists they will use anything, that anyone has come up, created from any standpoint if it does one thing - give good predictions. There are indeed many ways to describe our physical reality; poets might use a certain way they feel to be beautiful or moving, a cartographer in order to help others find their way, a teacher so that others may learn - but science works on experimental results and any method that doesn't tally with those results is useless

[lemur]

If you think this is the result of physicists' attitude then it just confirms you don't understand the problem. The problem is not with physicists' attitude. You're shooting the messenger, and your last sentence contradicts the first — you are insisting that there be other descriptions.

I'm simply questioning whether the fact that one method of representing scientific truth is the only possible method. There's a big leap between saying that the method you came up works and saying that there's no other method possible. One involves rigorously testing the method you have. The other involves a belief that total oversight over all scientific logic is possible from the perspective of one scientific method.

 

You are imputing unfair motives when you state that physicists "decide ... that they have total insight over every possible descriptive possibility" - from my experience of watching and talking to professional and academic scientists they will use anything, that anyone has come up, created from any standpoint if it does one thing - give good predictions. There are indeed many ways to describe our physical reality; poets might use a certain way they feel to be beautiful or moving, a cartographer in order to help others find their way, a teacher so that others may learn - but science works on experimental results and any method that doesn't tally with those results is useless

I don't think physicists decide in the sense of actively choosing to favor the method that has built up inertia in their discourse. I think they just continue extending their paradigm into new applications and take each practical success as a confirmation of the validity of the paradigm generally. There is nothing wrong with that. The paradigm is working. But why does that somehow imply that there is no other paradigm possible or that only one paradigm may be allowed at any one moment and all others must be relinquished until the dominant paradigm falls? Why shouldn't the town be big enough for more than one sheriff (or other investigators), so to speak?

[Cap'n Refsmmat]

I'm simply questioning whether the fact that one method of representing scientific truth is the only possible method. There's a big leap between saying that the method you came up works and saying that there's no other method possible. One involves rigorously testing the method you have. The other involves a belief that total oversight over all scientific logic is possible from the perspective of one scientific method.

We were talking about intuitive understanding and how it is impossible in some parts of science. That is not to say there is only one possible method. There may be several, but intuition is not one of them.

[swansont]

I'm simply questioning whether the fact that one method of representing scientific truth is the only possible method. There's a big leap between saying that the method you came up works and saying that there's no other method possible. One involves rigorously testing the method you have. The other involves a belief that total oversight over all scientific logic is possible from the perspective of one scientific method.

 

Again, you are creating a straw man. Nobody is claiming that no other solution is possible. But that's different from saying that another solution is demonstrably wrong.

[lemur]

We were talking about intuitive understanding and how it is impossible in some parts of science. That is not to say there is only one possible method. There may be several, but intuition is not one of them.

Intuition isn't its own method. It's just that certain methods are more intuitive than others. E.g. when you think about molecules in a gas getting excited, it is intuitive that they move faster and collide with more momentum. It's not that you're relying purely on intuition. It's just that you are able to move back and forth between intuitive modeling and testing your intuition and its implications against empirical data.

 

Again, you are creating a straw man. Nobody is claiming that no other solution is possible. But that's different from saying that another solution is demonstrably wrong.

I never said that QM was demonstrably wrong. I just said that there's no way to know whether some more intuitive alternative method could also have explanatory and/or predictive value without that model being on hand. So if every time someone comes forth with a seed of an intuitive model and you bash it for not being as strong as QM, that may have some stifling effect on the development of new modeling/methods. I'm not suggesting you should encourage intuitive modeling by avoiding criticizing it. I'm just saying that they should should be critically responded to in a way that stimulates them to prove themselves and develop greater rigor instead of undermining them by any means possible.

I don't think there's any danger of advancing false knowledge by doing this. Ideas collapse under their own weight when they build on weak foundations.

 

I think this is what happens in practice most of the time when marginal thinkers post their ideas on this forum anyway, actually. I find it usually only gets really harsh when someone claims to put forth a radically new theory of everything or claim that they have some new model/method to replace existing ones because they claim those are terribly inferior. I just think there should be some room between using proven science to constructively critique ideas and the insistence that proven science is superior and must be accepted by everyone as the only possible approach to studying nature and if they have any thought that doesn't already conform to proven science, they should jettison it and first indenture themselves to becoming experts in academic science and not post a creative thought until they have.

[Cap'n Refsmmat]

Intuition isn't its own method. It's just that certain methods are more intuitive than others. E.g. when you think about molecules in a gas getting excited, it is intuitive that they move faster and collide with more momentum. It's not that you're relying purely on intuition. It's just that you are able to move back and forth between intuitive modeling and testing your intuition and its implications against empirical data.

And intuitive modeling is unreliable or impossible in some parts of science, and the only functional methods are non-intuitive.

 

I never said that QM was demonstrably wrong. I just said that there's no way to know whether some more intuitive alternative method could also have explanatory and/or predictive value without that model being on hand. So if every time someone comes forth with a seed of an intuitive model and you bash it for not being as strong as QM, that may have some stifling effect on the development of new modeling/methods. I'm not suggesting you should encourage intuitive modeling by avoiding criticizing it. I'm just saying that they should should be critically responded to in a way that stimulates them to prove themselves and develop greater rigor instead of undermining them by any means possible.

I don't think there's any danger of advancing false knowledge by doing this. Ideas collapse under their own weight when they build on weak foundations.

How can one test an intuitive model if it does not provide mathematics to compare results with experiments?

[swansont]

I never said that QM was demonstrably wrong. I just said that there's no way to know whether some more intuitive alternative method could also have explanatory and/or predictive value without that model being on hand. So if every time someone comes forth with a seed of an intuitive model and you bash it for not being as strong as QM, that may have some stifling effect on the development of new modeling/methods. I'm not suggesting you should encourage intuitive modeling by avoiding criticizing it. I'm just saying that they should should be critically responded to in a way that stimulates them to prove themselves and develop greater rigor instead of undermining them by any means possible.

I don't think there's any danger of advancing false knowledge by doing this. Ideas collapse under their own weight when they build on weak foundations.

 

I didn't say that you did. What I'm saying is that classical physics is demonstrably wrong at the quantum level. Saying that a classical/intuitive model is wrong is not the same as saying that QM is the only correct model. It is, however, the best one we've come up. It works.

 

Undermining people has nothing to do with it — this isn't personal. But testing a model to see if it works? Yes, falsify by any means possible. If a model is wrong, there is no scientific point to entertain further discussion about it. The proponent has to go and fix it or abandon it, at least in the realm where it fails.

 

I think this is what happens in practice most of the time when marginal thinkers post their ideas on this forum anyway, actually. I find it usually only gets really harsh when someone claims to put forth a radically new theory of everything or claim that they have some new model/method to replace existing ones because they claim those are terribly inferior. I just think there should be some room between using proven science to constructively critique ideas and the insistence that proven science is superior and must be accepted by everyone as the only possible approach to studying nature and if they have any thought that doesn't already conform to proven science, they should jettison it and first indenture themselves to becoming experts in academic science and not post a creative thought until they have.

 

Again, there is no restriction on using some other approach, as long as it works. For most people, nature is not intuitive at the quantum level (or relativistic level) so a simple ball-and-stick model based on the macroscopic world simply fails. Thus, intuitive reasoning doesn't work.

[lemur]

And intuitive modeling is unreliable or impossible in some parts of science, and the only functional methods are non-intuitive.

I know this is true of known science. Swanson also explains this quite well.

 

 

How can one test an intuitive model if it does not provide mathematics to compare results with experiments?

Because there are qualitative applications of logic. Conservation of energy, momentum, etc. for example can be applied qualitatively to a number of issues without doing any math. The fact that a black body radiates energy as well as it absorbs it is logical according to conservation logic. If it would radiate less efficiently than it absorbs, energy would have to build up in the material like water flowing into a reservoir faster than it can escape. It also explains why electron levels have to be quantized, since if photons are emitted from electrons in whole packets, that would make it logical that electrons increase and decrease energy levels in corresponding whole amounts.

 

I'm not trying to put qualitative knowledge in competition with quantitative calculation, because they support each other generally. I'm just trying to show that even quantum physicists apply qualitative thinking in some ways and that there's no reason why qualitative concepts can't be applied rigorously without the use of math. It's a question of deducing reasonable applications of logic from known parameters and laws. This doesn't exclude the use of empirical testing and quantitative measurment. The two can be and usually must be in dialogue with each other to work.

 

 

[Cap'n Refsmmat]

Because there are qualitative applications of logic. Conservation of energy, momentum, etc. for example can be applied qualitatively to a number of issues without doing any math.

How do you suppose I

 

• Define energy
• Define momentum
• Determine energy before collision
• Determine momentum before collision
• Determine energy after collision
• Determine momentum after collision
• Compare before and after to see if energy and momentum were conserved

...without any math?

The fact that a black body radiates energy as well as it absorbs it is logical according to conservation logic. If it would radiate less efficiently than it absorbs, energy would have to build up in the material like water flowing into a reservoir faster than it can escape. It also explains why electron levels have to be quantized, since if photons are emitted from electrons in whole packets, that would make it logical that electrons increase and decrease energy levels in corresponding whole amounts.

This doesn't explain why electron energy levels change in discrete amounts in collisions along with in photon emission and absorption. (Incidentally, I experimentally and mathematically tested this just a couple months ago.)

 

I'm not trying to put qualitative knowledge in competition with quantitative calculation, because they support each other generally. I'm just trying to show that even quantum physicists apply qualitative thinking in some ways and that there's no reason why qualitative concepts can't be applied rigorously without the use of math. It's a question of deducing reasonable applications of logic from known parameters and laws. This doesn't exclude the use of empirical testing and quantitative measurment. The two can be and usually must be in dialogue with each other to work.

You should watch how a mathematical physicist like ajb works. Oftentimes physical predictions will be made on the basis of new mathematics alone -- and turn out to be correct, before anyone can figure out an intuitive explanation. It's fascinating.

[lemur]

How do you suppose I

 

• Define energy

As potential or kinetic and how?

 

 

• Define momentum

I use p=mv as a short hand for remembering the qualitative notion I have of it. I still think of it in terms of a thing carrying energy in the form of motion though.

 

 

• Determine energy before collision
• Determine momentum before collision
• Determine energy after collision
• Determine momentum after collision
• Compare before and after to see if energy and momentum were conserved

I'm not saying calculation and measurement aren't handy. I'm saying that some things can be reasoned without calculation, not that everything can.

 

This doesn't explain why electron energy levels change in discrete amounts in collisions along with in photon emission and absorption. (Incidentally, I experimentally and mathematically tested this just a couple months ago.)

Nothing explains that, does it? But they are logically related as quantized behaviors, aren't they? By the same logic, I would expect redshift/blueshift to be quantized. Has this been empirically tested?

 

 

You should watch how a mathematical physicist like ajb works. Oftentimes physical predictions will be made on the basis of new mathematics alone -- and turn out to be correct, before anyone can figure out an intuitive explanation. It's fascinating.

Can you give an example? I really do find that interesting. Although I have a hard time understanding and conceptualizing things in terms of math, I have deep respect for it and sometimes I understand the logic of something mathematical and am amazed at how counterintuitive yet useful it is. AJB strikes me as a very learned scholar, though a lot of what he says sounds esoterically inaccessible to me.

Edited April 7, 2011 by lemur