Feynman: Mathematicians versus Physicists

now I would like to make a number of remarks on the relation of mathematics and physics it's a little more general the first is that the mathematicians only are dealing with the structure of the reasoning and they do not really care about what they're talking they don't even need to know what they're talking about or as they themselves say or whether what they say is true now I explained that if you state the axioms you say such as such a saw in such and such a so instruction such a saw what then then the logic can be carried out without knowing what the such and such words mean that is if there if the statements about the axioms are true I mean I'll carefully formulate an incomplete or not it is not necessary for the man is doing the reasoning to have any knowledge of the meaning of these words and will be able to deduce in the same language new construct new conclusions if I use the word triangle in one of the axiom there be some statement about triangles in the conclusion whereas the man who's doing the reason you might not know what the triangle is but then I can read his thing back and say oh a triangle that's just a three side or what have you this is so and so and so I know this new fact in other words mathematicians prepare abstract reasoning that's ready to be used if you will only have a set of axioms about the real world but the physicist has meaning to all the phrases and there's a very important thing that the people who a lot of people who study physics should come from mathematics don't appreciate the physics is not mathematics and mathematics is not physics one helps the other but you have to have some understanding of the connection of the words with the real world if necessary to at the end to translate what you figured out into English into the world into the blocks of copper and glass that you're going to do the experiments with to find out of whether the consequences are true and this is a problem which is not a problem of mathematics at all I've already mentioned the only other relationship that the cause it's obvious how the mathematical reasonings which have been developed our great power and use in for physicists that be on the other hand sometimes the physicists reasoning is useful for mathematicians mathematicians also like to make their reasoning as general as possible if you say I have a three-dimensional space the ordinary space I want to talk about ordinary space you know you're in it that you measure distances and there are three what numbers you need to tell where something is you're going Brett width and height three dimensional space and you're beginning to ask them about theorems then they say now look if you had a space of n dimensions that here are the theorems well yeah but I only want the case 3 well substitute N equals 3 and then it turns out then it turns out that very many of the complicated theorems they have are much simpler because it happens to be a special case now the physicist is always interested in a special case he's never interested in the general case he does he's talking about something he's not talking abstractly about anything he knows what he's talking about he wants to discuss then gravity law he doesn't want the arbitrary force case he wants the garbage and so there's a certain amount of reducing because the mathematicians have prepared these things for a wide range of problem which is very useful and later on it always turns out that the poor physicist has the compactors excuse me when you wanted to tell me about this four dimensions now another item that's interesting in this relationship is the question of how to do new physics is it important to have a feeling of kind of into oh I must mention one other item when you know what it is you're talking about that these things are forces and these are masses and this is inertia and this is so on then you can use an awful lot of common-sense seat-of-the-pants feeling about the world you've seen various things you know more or less how the phenomenon is going to behave well the poor mathematician he translates it into equations and the symbols don't mean anything to him and he has no guide but precise mathematical rigor and care in the argument whereas the physicist who knows more or less how the answer can go is going to come out can sort of guess partway and go right along rather rapidly they met the mathematical rigor of great precision is not very useful in the physics nor is the modern attitude and mathematics to look at axioms now mathematicians can do what they want to do one should not criticize them because they are not slaves to physics it is not necessary that this because this we'd be useful to you they have to do it that way they can do what they will it's their own job and if you want something else then you work it out yourself the next point is the question of whether we should guess when we try to get a new law whether we should use the seat-of-the-pants feeling and philosophical principle I don't like a minimum principle I do like a minimum control or I don't like action at a distance or I do like action the question is to what extent models help and it's a very interesting thing very often models help and most physics teachers try to teach how to use these models and get a good physical feel for how things are going to work out but the greatest discoveries it always turns out abstract away from the model it never did any good Maxwell's discovery of electrodynamics was first made with a lot of imaginary wheels on idlers and everything else in space if you got rid of all the idlers and everything else in space the thing was okay Dirac discovered the correct laws of elective quantum mechanics for relativity quantum mechanics simply by guessing the equation and the method of guessing the equation seems to be a pretty effective way of guessing new laws this shows again that mathematics is a deep way of expressing nature and attempts to express nature in philosophical principles or in seat-of-the-pants mechanical feelings is not an efficient way I must say that there is possible in a note I've often made a hypothesis that physics ultimately will not require a mathematical statement that the machinery ultimately will be revealed just to prejudice like one of these other prejudices it always bothers me that in spite of all this local business what goes on in a tiny is naive no matter how tiny a region of space and no matter how tiny a region of time according to the laws as we understand them today takes a computing machine an infinite number of logical operations to figure out now how can all I'd be going on in that tiny space that why should have taken infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do and so I made a hypothesis often that the laws are going to turn out to be in the end simple like the checkerboard and that all the complexity is from size but that is of the same nature as the other speculations that other people make it says I like it you don't like it it's not good to be too prejudiced about the things to summarize I would use the words of jeans which says that we said that the great architect seems to be a mathematician and for you don't know mathematics it's really quite difficult to get a real feeling across up to the beauty of the deepest beauty of nature see peace node talked about to culture I really think that those two cultures are people who do and people who will do not have had the six people who have had and people who have not had this experience of understanding mathematics well enough to appreciate nature 1 it's too bad that it has to be mathematics and mathematics for some people is hard when one of the kids reputed I don't know if it's true that when one of the Kings was trying to learn geometry from Euclid he complained that it was difficult and Euclid said that there's no Royal Road to geometry and there's no Royal Road it's not the JA if we cannot as people who look at this things a physicist cannot convert this thing to any other language you have if you want to discuss nature to learn about nature to appreciate nature it's necessary to find out the language that she speaks it she offers her information only in one form we are not so on humble as that's a demand that you change before we pay any attention it seems to me that that it's like them all the intellectual arguments that you can make would not in what in any way or very very little will communicate to deaf ears what music the experience of music really is and all the intellectual arguments in the world will not convince those of the other culture the philosophers who tried to teach you by telling you qualitatively about this thing me who's trying to describe it to you which is not getting across because it's impossible I'm thought we talked to debbie is and it's when they it's perhaps that the horizons are limited which permit such people to imagine that the center of the universe of interest is man

Channel: TehPhysicalist

Views: 761,968

Rating: 4.9506993 out of 5

Keywords: Richard, Feynman, understanding, physics, math, mathematics, knowledge, science, experiment, philosophy, Messenger, Lectures, The, Character, Of, Physical, Law, Relation, Mathematics, Physics

Id: obCjODeoLVw

Length: 9min 46sec (586 seconds)

Published: Thu May 17 2012

Reddit Comments

[u/Xfacter]

His argument for why the laws of nature should ultimately be simple is great.

It always bothers me that in spite of all this local business, what goes on in a tiny region of space and time, according to the laws as we understand them today, takes a computing machine an infinite number of logical operations to figure out. Now how can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one stinking tiny bit of spacetime is going to do?

[u/Yogurt_Huevos]

As a math and physics double major, much of this seems to hold true, especially when taking 'pure' mathematics courses like abstract algebra and number theory.

[u/choc_is_back]

Aaaaah from his great The Character Of Physical Law series, right? I've watched these soo many times and am in awe of (and pride to be educated in) physics every single time.

The part that comes just before this bit - and he briefly refers to it while talking here when talking about 'taste' in laws - is amazingly interesting as well for example, it's how he is in awe how you can describe the very same phenomenon in so many 'qualitatively' different ways (forces acting at a distance versus a local field for gravity in this case).

Fuck it, I'm gonna go have another go at them now, thanks for the reminder!

[u/jstock23]

Finally! Some Dirac Equation love! And by Feynman of course!

[u/[deleted]]

Wish he was still alive.

[u/dont_tread_on_me_]

He was a great man, one of the best modern physicists

[u/cwm9]

Listening to him makes me think of the Honeymooners.

[u/cratylus]

Interesting what he mentioned in passing about Maxwell - imaginary wheels and "idlers"??? What did he mean?

[u/boonamobile]

For how fun his quotes are to read, he seems surprisingly long winded to me when listening to him talk.