As a joke with my mathematician and engineering friends (I'm a physicist) I've been saying for years: "Whereas physics is math with the constraint of reality, engineering is physics with the constraint of money."
LEE NEO SALEN-GA, A PILIPINO DISCOVERED AND PROVED THE POINCARE CONJECTURE PROVES THAT HIS SALEN-GA QUANTUM TANGENT THEOREM IS VALID, USING THE FIRST QUANTUM GEOMETRY SALEN-GA AXIOM: REAL WORLD POINTS IN QUANTUM GEOMETRY HAVE PHYSICAL DIAMETERS. HE THEN RENORMALIZED THE MEANING OF A LOCALLY QUANTIZED PHYSICAL CIRCLE AS " [ CIRCLE ]: A SERIES OF LOCALLY EUCLIDIAN FLAT LINES AS PART OF A GLOBALLY RIEMANIAN POINCARE LOOP WITH A COMMON EQUIDISTANT POINT CALLED THE CENTER.". LEE TO SALEN-GA, A PILIPINO AMATEUR SCIENTIST PROVED THE EMBARRASSING OBVIOUS TRUTH THAT ELUDED MANKIND FOR CENTURIES: THAT THE GLOBALLY ROUND EARTH IS QUANTUM LOCALLY FLAT!!!!!!! THE CHINESE ADAGE RUNG: FOOLS ARE AWED BY WANDERS, WISEMEN BY COMMON PLACE THINGS. LEE-TO SALEN-GA IS PROPHET YSRAEL {{{ ISAIAH 44:5 HOLY BIBLE}}} SENT BY GOD TO FULFILL ISAIAH 29:14, 15; " THE WISDOM OF THE LEARNED WILL DROP DEAD AND INVERTED". LUALHATI' Y SUMMA ABBA= TO THE FATHER EL ELYON BE ALL THE GLORY!!!!!!!!!!!!!!!!!!!!!!!
He's talking in the context of "real world stuff." Math makes sense of abstract, general structures within itself, which, really, is all you'd really need. The physicist needs a truncated view of very specific cases of said general structures to solve actual "real world stuff."
Feynman used to practice sometimes up to 5 hours in an empty room before the lectures. That's why all his lectures are gold! He gave whole of his heart in teaching!
I'm a small-time stage actor, and that 5:1 ratio is about the same ratio of time we rehearse plays in (five hours rehearsal for one hour of stage time).
It’s really not about the individual lectures. Feynman spent an enormous amount of time thinking about problems in great detail. Every statement he makes here, he has thought about it in so many ways and in a sense, very lecture took a lifetime of prep.
Mathematicians, Physicists, Engineers, are all important fields. The world needs all three to work together to advance humanity. And, if anyone of them catch a fever or the flu, we have Doctors.
@@smkxodnwbwkdns8369 "The mathematicians are only dealing with the structure of their reasoning and they do not need to care what they are talking about." You misquoted him. Of course, pretty much every American speaks English poorly, as though it's a second language, but Feynman was extremely good at articulating his thoughts.
@@adrrda6091 I am not misquoting him, its been nearly half a month since I’ve watched this video, but it is a verbatim quote at some point in the video exemplifying his poor english. I’ve heard him talk at length in interviews and other contexts and have never been impressed by his language skills.
@@smkxodnwbwkdns8369 As a text corrector, I've come to believe that diverting a conversation from the value of the things a person says to criticize them for their less-than-optimal language skills is the height of arrogance.
I recall a course in Fluid Dynamics that was thought in the Math department. As an engineering student I was a bit bothered by an equation that was being discussed since the units did not make any sense to me. I asked the professor what is the end resulting unit of this equation and his reply was in the math department we are not concerned with this as it is irrelevant. This was a 7000 level course and I don't think I have recovered yet after 20 years. That was an eye opening experience.
Many people don't realize (or are extremely uncomfortable with) the level of abstraction that math utilizes. It is it's greatest strength, but if you don't acknowledge it, then the subject is nothing more than building blocks.
Leonard Susskind does the same willy-nilly thing with units in his RUclips lectures on Cosmology and other areas of physics. The important thing is that the dimensional analysis be correct, of course, but the actual physical units (and the constants of proportionality among them) are unimportant when discussing the physical relationships (say, between pressure, volume, and temperature of an ideal gas) in the abstract. It's a relief to know that I don't have to memorize the numerical value of 1/(4 * pi * e0) to understand Coulomb's Law: I only need it if I have to furnish a prediction for a particular experiment.
At 5:29, we see a fundamental theorem demonstrated: the limit of the number of glass lenses divided by the number of students approaches 2 as the number of students goes to infinity.
I feel that Feynman was largely talking about pre-information era mathematics here, at least as far as the qualitative aspects of the work are concerned. With today's powerful and ubiquitous computers, mathematics research is now often "seat of the pants" reasoning. Basically, since this talk was given, the practice of mathematics has become more like physics, since we can cheaply set up mathematical worlds to explore. Though Feynman did a lot of work with computers and information theory, this was at a time where the resources were insanely expensive and slow compared to today.
The physicist, like the engineer, has the burden of physical reality to content with, of which the mathematician is completely free. However, that is not necessarily always an easy thing for the mathematician. For the pure mathematician must mentally contend with pure abstraction, far removed from any direct experience, whereas the physicist & engineer have physical reality to serve as a guide, while the mathematician has no guide but their own mind. This has been my experience as a chemical engineering undergraduate major and ex-engineer, having worked 2 years in calorimetry & corrosion research, who went on to mathematics in graduate school.
He's on point. As a person who likes math, people assumed I'd be good at physics, but I was no good at it. I couldn't connect my understanding of math to the real world.
Great video. Feynman's passion for physics and its profound epistemological potential always manages to make me question my preference for mathematics. I would argue, however, that since physics is hinged so heavily on the empirical, and ergo on the phenomenological, it doesn't describe the mechanisms of a pure, inner "reality" any more than mathematics does. To the contrary, by being so heavily conditional and having such a precise logical structure, mathematics achieves a cleaner, more absolute form of truth. Mathematical "understanding" is not as intuitive or palpable as physical understanding, but (perhaps ironically) its abstraction and pluralism make it in many ways more real.
***** except when people make mistakes in their accepted proofs in which case we wouldn't be able to distinguish it, unlike something applied like physics where you can observe at least some forms of truth to your mathematical statements
lavendermenace Mathematics is based upon axioms. Things we take as obvious truths. Moden mathematics is based on the Zermello-Fraenkel axioms which are essentially relationships between sets that we take as obvious truths. (Although there other proposed axiomatizations in addition to the ZMF axioms. The reason mathematics has "absolute proofs" is that we can construct logical arguments that can be ultimately reduced to these fundamental axioms. This is not to say that all mathematics is absolute and certain, there is also uncertainty in maths as well as various conjectures that have yet to be proved. Science doesn't have this luxury of an axiomatized universe via which we can derive absolute proofs of things. Yet maths is a critical part of science and in many ways serves as the language by which science expresses laws and theories. There is also an interdisciplinary dependency. Philosophers were instrumental in construction some of the logical framework of mathematical logic. Scientists have contributed to the development of maths, mathematicians have contributed to the development of sciences and oure mathematicians have played a major role in maths in and of itself.
HimJimRimDim To the contrary, I would argue that mathematics' foundation in the axiomatic is an instrumental part of its unique veritas! Mathematics achieves absolute truth insomuch as it invents and defines its own metric for truth: logical extrapolation from and consistency with axioms. Since 'truth' is ineluctably a vacuous term, tenuous and ambiguous (much like meaning, purpose etc) in our universe, a structure must first define what it is to be true before it can claim to satisfy any monolith of truth. Logic and axiomatic proof, though ultimately arbitrary and not tethered to any sort of vestigial 'inherent truth,' accomplish this. Ergo, they achieve a certain type of truth-absolutism, of objectivity. Constructed objectivity, yes, but (I would argue) the only form of objectivity humans can know. However, while mathematics accomplishes absolute truth, it also spurns singular truth. This has to do, of course, with the axiomatic system you expounded on. Mathematical truth is reliant on ultimately arbitrary axioms. But mathematics also acknowledges the arbitrariness of its own axioms! Herein lies the profundity of mathematical thought. Implicit in any mathematical argument is a conditional statement- "If this axiom holds true, then X, then Y, then Z," or some analogue. Really, we are not "assuming the axiom to be absolutely true," we are simply exploring what the implications of its theoretical truth would be. It is through this intrinsic conditional condition that mathematics becomes both absolute, in its logical consistency and autonomous self-definition, and plural, in its rejection of singularity and its study of all shades of the potential. In no way does this make it "uncertain." It is true that there rest conjectures to be proved, and Gödel illustrated that mathematics will inevitably fail to provide proper logical excavation for some of these. This does not attenuate the fundamental truth of mathematical method or structure. If anything, it exposes the limitations of human truth itself, and imbues mathematics with transcendental meta-cognition: an awareness (and a result meta-mathematical annexation) of its own bounds, a latent epistemology.
+lavendermenace They are both fascinating subject, each beautiful in its own way. and in many of the same ways as well. There are some elements of math that seem to be rather contrary to our intuition, the works of cantor bear this out. . But such is true in physics.. In fact one of the thins that makes quantum mechanics difficult is that it is often not intuitive at all.
Feynman is amazing. If youre reading about him youre missing out in his carisma and some of his humor. You should check out a documentary or two and an interview if you can. Its great to hear other peoples stories about him too :)
+nicosmind3 Thanks! I can see just from this there is so much to be missed in simply learning about him. I absolutely will take your advice and look up more things of him rather than about him!
Sadie Kitten Not a problem. I really enjoyed the documentary. TV is completely lacking for me but thankfully we have youtube and just about everything you could want to stimulate the mind :)
The problem with (pure) mathematicians, is that they believe that abstraction is all about the analytic, and neglect, any pre-analytic process which leads to it. Physics has often been, the top-down, path to mathematical abstraction.
fergoesdayton The "problem" with pure mathematicians is that they want to find a finite set of primitives (axioms and their schema) that can generate all theorems without having to rely on one's (fallible) senses. That sounds to me a much more attractive way to solve problems.
Dennis Oliver But don't axioms remain assumptions, as they depend on 'fallible' senses? What seems important, is that within any system of thought, there is a high level of consistent support for an idea. Instead of having faith in the validity of axioms; saying all of this is true, because x, y, and z seem undeniably true, one can have faith in the amount of consistency there is in an idea.
Caring about physical reality has many times opened insights that mathematicians would probably never have guessed or reasoned to on their own. Just look at Riemann hypothesis for example, new insights suggest that it's closely related to quantum physics. Physics is repeatedly showing that learning about reality is almost essential to advance a lot of mathematics, since it's so very related.
I must say that at 4:20 he says the mathematician does not have an intuitive feeling for manipulation of expressions, but skills like this are developed over time. In reality it seems to be no different from physics you start with an intuitive feeling and develop the expressions for special cases then you attempt to generalise it (in both math and physics this is done just in slightly different ways) and once you've generalised it you realise that a lot of your intuition comes from extra properties that are only there in the special case, so you have to redefine/restructure your intuition so that it only uses the properties that apply to all cases and not just the special ones. Note: you may use special cases to give an intuition about more general ones but you still have to be aware of the properties that do not apply in the general case, thus there is still some form of restructuring of intuition. I'm a math physics student nearly finished my bachelors degree so I can't say what I have said is true for actually researching in these fields as I only really have experience with studying, but it seems like it would apply. I'm curious to hear what other people think?
Great observation. I think physics differs from math in its focus and on penetrating the counter intuitive. In math, there are unlimited intellectual dimensions to explore; choose the one that fits best. But in physics, it's often experiments and simple questions that isolate the frontier. It's up to the thinker to meet the demand.
I am a good mathematics student - I study every day - I struggle with the abstractions of vector calculus and differential equations, discrete math, and real analysis. But, when I started taking physics classes to enrich my ideas concerning natural philosophy - man, did my head get a painful upgrade, and a realization of what RF is talking about here - I don't necessarily like it, but I understand and agree.
Mathematics develop the tools that other scientist get to take for granted. Without Gauss and differential geometry, there would be no Einstein or relativity. Any physical theory must be communicated in the language of mathematics in order to asses its relevancy.
Newton was a mathematician. Also, Leibniz more or less independently invented calculus around the same time. However, we now know that Archimedes was doing integration over two thousand years ago.
Francisco Reyes Newton was interested in limits and reality, Leibniz was more interested in the abstract . Newton was driven to create calculus to answer physical phenomena, I would say he is more of a physicist than mathematician. So even if Leibniz had not existed, we would still have calculus, thanks to the greatest physicist of all time, Isaac Newton.
Francisco Reyes True, but the discovery of some of these mathematics was at least in part inspired by the desire to understand things like gravity, etc. Just as games of change (gambling) at least in part inspired the discovery of probability theory. Math can be pure (abstract) in its own right but, as Feynman pointed out the various disciplines help each other.
Joey Castro Actually it is a common misconception that newton was only concerned with applied math. He advanced virtually every branch of math that was studied in his day. I'm not going to argue about newton because I think we can all agree that he is the man and is in fact the father of modern physics. However in his day there was no such occupation as physicist and he was in fact a mathematician by trade. He was the lucasian professor of math at cambridge to be precise.
An important point on generalization in mathematics: sometimes the special case is the HARD case. For instance, many problems involving forces are very hard to solve in the case of gravitational forces because gravitation has a singularity at the origin. So what do you do? You generalize! You assume you have an arbitrary force and you assume it has some nice properties. So you solve this easier case and then try to say something "in the limit" of gravitational forces.
Euclid told the king who complained it was hard, "There's no royal road to geometry." Ha, a classic. Substitute for "geometry" - law, investing, economics, writing, chess, martial arts, piano, and so on. 8:24
Airdish Pal (Paul Erdős) described Applied Mathematics as the Art of "Dead Mathematicians". As a kid I had the good fortune to have him as one of my mentors. He drove me to tears setting more and more difficult problems, that had two or even more answers! ... "Pick the best one!".... At that time, aged 8 years old, Alec Harley Reeves was teaching me how to build computers. Later I had a Dead Applied Mathematics bone to pick with our dearest departed Richard Feynman. The "AXIOM" (Unproven) that something can never be created out of nothing. Specifically Energy. A Thought Experiment violates this 'axiom'. ..... "There is an evacuated tube a kilometer in diameter, Inside this tight vacuum is a permanent magnet linear bearing that supports a very heavy shuttle, let us say 200 metric tonnes. This is perfectly possible. and for arguments sake the shuttle travels around this tube at 1000 m/s. The Radius is 5 kilometres. There are of course quite strong forces of centripetal acceleration. we can calculate them at different vacuum tube diameters. and angular velocities from reliable and well trusted equations of Vector Forces. Sir Isaac Newton tells us that a body in motion has a tendency to continue in the direction of that motion. If a circular track free of friction prevents a linear path, "Vector Forces" arise. Centripetal, because the Force is always perpendicular to the Tangent and directed in line with the centre. ... Now for THE GIGANTIC PROBLEM WILL ALL OF SCIENCE AND ALL OF SO-CALLED PHYSICS BASED ON UNPROVEN AND MERELY SPECULATIVE "DOGMATIC AXIONS" THAT APPEAR TO BE REASONABLE. (There is no such thing as a free lunch, just before Sir Isaac Newton sitting under an apple tree, conceived of the lars of gravity.) ... This Vacuum Tube is mounted on Hydraulic Stainless Steel Concertina Elastic Pressure Pumps. With a little Leverage included. As this 100 metric tonne speeding shuttle travels round all the Vacuum Tube mounts are shifted by a couple of millimetres or perhaps a little more. A square meter 1.0 mm thick is one litre. Let us say the movement is 2.0 mm. and the pressure area is 0.5 square metres. Pi x 1000 is about 3,142 metres. (Pi * D) so it takes about 3.142 seconds to complete one revolution. So by logical mathematics, every second 1,000 litres of high pressure hydraulic fluid is pumped. with each complete revolution. This energetic speculation is always extracted perpendicular to the tangent. the 2.0 mm. excursion is so slight as to have negligible effect upon the angular velocity. Kinetic Energy is the product of half the mass in Kilos e.g. 200,000 * 0.5 = 100,000 and the velocity squared 1000^2 in total a Stored Kinetic Energy of 100,000,000,000 Joules. Frictionless motion is possible in deep space, but unlikely in a vacuum tube. We could measure the loss of velocity with all the hydraulic pumps locked. (Valve Closed) and then measure again "Valve Open". a pure guess is that the 200,000 kilo shuttle would lose a micro-second of velocity with each circuit compared to the closed valve time. In any case we are looking at the Shuttle losing 200 Joules of kinetic energy per second. 628.2 Joules per revolution of Pi seconds. A circle of radius 500 metres and velocity 1000 m/s gives a gigantic force of centripetal acceleration. A Jet fighter pilot, could black out from the G-Forces turning such a tight radius in a dog fight. A tonne of high pressure hydraulic fluid per second fed into many hydraulic motors, as used on Oil Tankers to avoid electric sparks, is a lot more than 200 watt total output. (Subtract a micro-second from 1000 m/s and square the result then multiply by half the mass 100`,000 kilos. SOMETHING IS TERRIBLY WRONG WITH UNPROVEN AXIOMATIC QUASI-RELIGIOUS DOGMAS.
He wasn't even a mathematician he was some loser who sent his work to cambridge on something that had already been done. Why not William Sidis or Ted Kaczynski.
Very interesting insight, still the final word is physists can't work without mathematics, while mathematicians can be completely independants, even from reality.
i do agree that physics is a form of art, but you can also say that for mathematics (for example : Noether's theorem, differential geometry of manifolds, geometrical analysis, group theory(= the most badass way to study symmetry), Galois theory, combinatorial analysis, topology ...etc..). I think that physics and mathematics have many differences as they have many similarities in their approaches. Both, to my eyes, are a work of art (and maybe the most timeless products of human thought)
What Feynman is talking about is the difference between rationalism and induction. Mathematics have *always* been particularly attractive to rationalists (all the way back to Plato) because they believe they can combine mathematics and deduction as a means of understanding reality without performing what the real work of a scientist *should* be: looking at reality and forming inductive generalizations by reference to empirical observation.
Yeah, except it's actually not like that in our world. Mathematicians still must do empirical observations of their own abstract models to discover new things. In reality most of useful math is discovered by induction. The proofs come only a posteriori once you have a reasonable belief that some result might be true. In this respect, the only difference between mathematicians and physicists is that physicists are satisfied once they believe something. That's why their theories are so advanced and don't have rigorous footing. Mathematicians on the other hand are more careful and ask for proof. That naturally takes much more work, but once that work is done you can be _really_ sure the result holds, in contrast with physical results which are often more like (very informed) guesses.
Simplest example is Riemann Hypothesis, i.e. the conjecture that all non-trivial zeros of the Riemann zeta function have real part 1/2. This has been tested empirically quite well, by finding millions of those zeros (I don't have a precise count, but it's a lot). If we didn't have these tests, nobody would believe the conjecture as much. Examples like this are common all over the mathematics: very often you first observe (for example by writing a program) some relationship between objects such as numbers, spaces, functions, or whatever it is you study and once you see a pattern, you can formulate a conjecture and prove it. I repeat, almost nobody in math proves anything purely syntactically from axioms. It's always guided by some intuition, experiments, insights from other sciences or whatever.
I don't think I totally agree. It's true that nobody would believe the Reiman conjecture without the empircal demonstrations, but that is only because there is no actual proof; if there was, giving examples would not be needed to convince anybody. I do agree that mathematicians use intuition in the sense that they actually think about what they are doing and what connections there may be to make, and this guides their thought process as opposed to randomly shuffling around symbols and words till something is discovered. However, thinking deeply about the subject matter doesn't nescessarily (or usually) translate to mathematicians testing things empircally, and that's using "empircally" generously (doing examples as opposed to actual real world observation). And yeah, things are rarely proved right from the axioms, but that's because it's not needed when a plethora of other results and theorems have already been proven and thus are availabe to use.
Perhaps one of the reasons we can't seem to reach an agreement here is that there's no such thing as a model mathematician. Some are really strictly logically/formally oriented, some are deep thinkers, some are experimentalist (in the sense I mentioned), some are close to science, some are theory builders while others are problem solvers or conjecture-makers, etc. I guess my bottom line is that mathematics is a spectrum and parts of it are really very close to sciences, in stark contrast with the black&white naive view presented by Feynman. Even though many things he (and you) mentions are actually true, of course.
He has the most impressive mind I've been able to listen to. He ran the group of human calculators for the building of the nuclear bomb. He was known as the best problem solver the humankind has seen. I love you Richard!!! He develop QED. And was the first to calculate electrons orbit accurately with math he developed.
+ Coach McGuirk: Yes, QED = Quod Erat Demonstandum, has been around since Latin hadn't yet killed the Romans. What Richard Feynman developed, was QED = Quantum ElectroDynamics = EM + SR + QM = the marriage of electromagnetism in its special-relativistic form, with quantum mechanics. For which he was awarded the 1965 Nobel Prize in physics.
What I like so much about Feynman is how intelligent he is, yet seems to have no trouble explaining in terms everyone can and most likely will understand.
I actually agree here. Mathematicians seem to be aware that an infinite amount of applications can exist through different dimensions, but might be too curious with the infinite possibilities, when the only relevant application would be for our universe. Physicists seem to be able to understand and master our current universe without getting distracted by other possibilities. Then, after understanding our universes physics, eventually a physicist will acknowledge that there may be a 4th higher dimension, and then come back to the mathematician and ask " what can you tell me about this dimension and its constraints?" As a mathematician. I dont understand why someone would put math versus physics. If you like math or physics. Your are eventually gonna love both of them.
I'm not a mathematician by far, but as someone who's on currently on Book 4 of Euclid's Elements I can definitely say that Mathematicians are a rigorous folk.
@@AlanCanon2222 That is true, often times though what we care about in computer science is software. The best way to develop software is by building implementations, then the abstractions for reusability. It may not feel like mathematics at first but it is.
Feynman has, on more than one occasion, been my sanctuary. A place where I go to escape the noise and bullshit in the world. A place where inspiration and heartfelt fondness can be gained, absorbed, and reveled in
what i would give just to have been to even one of this mans lessons. if teachers made learning even half as fun as feynman did then the world would be a much smarter place.
Isn't it wonderful that you can watch this video of Feynman from your computer? It's almost as good as having been in his classroom. It would not have been possible without physics and mathematics.
@@MarkChimes one video does not speak for 5 years of studies and a lifetime of constant learning. If only I could have 5 years of someone like Feynman teaching at my university. The absolute garbage level most of my professors are at is embarassing. No one cares any more, not like Feynman, he cared, and it's noticable for anyone..
Bret Brown I agree with you but there's a very slim chance that it's true and real, just that we don't have the technological capabilities to verify it experimentally yet
As a mathematician I must argue a bit with this video. Despite what many say, mathematics is a lot of times not isolated from the real world. Take information theory for instance. You really wanna tell me that information is not the real world? Even the idea of space is something we all experience, abstract or not. It's not a matter of one being more too abstract for real world or one not knowing the significance of axioms or whatever to understand real world; it's about how you want to view your world. You can view it either abstractly or intuitively and both are just as valuable. Historically though it is interesting to see that physicists thought (or maybe still do think) this way.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858-1932), David Hilbert (1862-1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day. Galileo Galilei (1564-1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss (1777-1855) referred to mathematics as "the Queen of the Sciences". Benjamin Peirce (1809-1880) called mathematics "the science that draws necessary conclusions". David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise." Albert Einstein (1879-1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." French mathematician Claire Voisin states "There is creative drive in mathematics, it's all about movement trying to express itself." Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.
Even as a mathematician I do agree with Feynman, on that at time our reasoning may not depend on understanding what we talk about. We use the very backbones of reason, namely Logic in its abstract form. however i disagree with excluding physicists to this "nature" of doing things. Even today no man ,even Physicist , UNDERSTANDS what Gravity is or what causes it. We may come up with models such as general relativity and say it is cause by the bending of space time, but then one can ask what causes the bend... What I am saying is that like Physicists, like mathematicians, also have axiom-like concepts that do not need to be understood in depth in order to come up with Remarkable theories like the big bang, string theory etc. we cannot always try understanding everything, otherwise we have to define everything, and that is why Mathematicians have axioms, and other concepts that do not need to be defined or understood in detail. Physics in not possible to have its elegance and rigor without Mathematics, mathematics needs physics and other related fields to have meaning.
Sabelo Letsoalo Physicists know we'll what gravity is. it's not caused by the curvature of space-time, it is the curvature of space-time. And that curvature is caused by the presence of mass.
Sabelo Letsoalo What you said makes sense, maybe gravity isn't the best example but the charge of particles or some other phenomena is. Having said that, I still believe mathematics use pure logic much more often than physics.
MrSidney9 Then why does mass cause the bending of space-time? After that you can go on asking forever. Even smallest fields must be defined somehow. By that logic at the end of the explanation chain must be something that defies our way of thinking or a paradox of some sort. Maybe the fundamental nature of the explanation chain is a paradox. While this does sound confusing I still hope it's undestandable.
Yes MrSidney9 I agree, my wording was bad. But you get what I'm getting at though. I am talking about the general way physicists define things, for example (as you have said correctly) the presense of mass causes the curvature but does no physicist can explain why the bending Occurs. I also agree with Filip Pozar Tolbryn the IX, every Field needs To follow a chain of logic, but absurdities and circular reasonig arise towards the end of this "chain", if we refuse to accept certain things as truth without the need of proving them . Feynman cannot claim mathematician don't need to know what they are talking about in order to reason, and then exclude himself and other physicists from the statement. ALL fields have their sets of "axioms", ALL fields need to reason from those axioms to arrive at even higher truths.
all I can say to you my poor confused brother is listen to what tessla has to say about Einstein and the replacement of hands down balls out physics with complicated non provable equations that dominate our understanding of the world today. and by the way... math. lies when you know how. and Einstein and his ilk were damn good at it..... have fun.... z.
If science was a multi-storied building, mathematics would be a ground floor under physics on the first and chemistry on the second. Take them away and people get a useless block of concrete and steel. Try to take away mathematics...and it all turns out into chaos without meaning.
Everyone forgets about biology and astronomy. XD But I get the point: Math is the only way to truly understand and explain how ANY of it works, in a universal way.
I've always liked the expression "Physics is applied mathematics, Chemistry is applied Physics, Biology is applied Chemistry etc." Its open ended so you can insert a burn on whatever soft science field you prefer.
Gotta say though: abstraction in maths isn't just a general view for the sake of being general. You get a lot more, like noticing things in your area behave similarly to things in an entirely different area, and this is only made possible with the `wider' view.
He wasn't putting down Mathematics at all. He was just trying to make a point that they aren't the same thing.. He said multiple times that physics relies on mathematics to understand the world, and that it is of great use. However in Physics intuition plays a much greater role than in Mathematics. This is why a physicist is usually alright at mathematics since both require extensive logic but a mathematician isn't always good at physics due to a lack of intuition or feel for the physical world.
I can definitely tell Maths have evolved a bit more since this lecture. With computation and the theory it has introduced, much of mathematics has become extremely relevant to how technology drives society. I do agree with what he was saying for the most part though, as eloquently as he puts it. To prove theorems, it usually isn't just invoking axioms a lot of the time (usually the problems studied come from the axioms, whether it be pure, applied, discrete (computational/CS), or continuous). Lots of experimentation and intuition comes into the prospect of new theorems in Maths/Stats/CS (formal sciences), just like any law in the empirical sciences.
***** As a mathematician, I feel "compelled" to answer that. I have been asked that same question by quite a few friends and family. To a mathematician, mathematics is closer to art than to science. Would you ask that same question to a musician or a painter for instance? If you really think about it, what musicians or painters do does not matter either. Will the presence or absence of an art-form affect the technological progress of humanity? I hardly think so. Yet nobody asks that question to artists. Why mathematicians then? Just because mathematics finds applications in real world does not mean it has to be burdened with constraints of reality. Mathematicians do mathematics because they find immense pleasure in it, not because they want to advance our understanding of the real world. That mathematics finds its way to applications is purely coincidental. In some weird sense, mathematics is an addiction. It creates a thirst which you can satisfy within yourself, just with your thoughts. The moment you satisfy that thirst, the moment all the pieces of the puzzle fall into place, that's the eureka moment for a mathematician. And they are addicted to such moments. The best thing about it is you don't have to wait for the validation from real physical world, the NATURE. (Of course you still have to publish your proof to see if your eureka moment really produced something logically correct, but let's not go into that. LOL). It's impossible to be a mathematician if you are not in love with those eureka moments and mathematicians will go to great lengths to find such moments. I'd go so far as to say that it's not mathematics that they are in love with, but those eureka moments. Quite often, mathematical physics and theoretical computer science provide the same sort of experience. Hence you see quite a lot of mathematicians working in these fields too. Does that make pure mathematics a useless endeavor? If the answer is yes, then by the same logic, all forms of art are useless. Are we willing to sacrifice artistic beauty for the sake of scientific utility? Well, all I can say is that in such a case, we would still have humanity, but no civilization.
Mathematical formulation, construction etc. always resorted to premises that are not always well defined, counter intuitive or outright incorrect etc., yet provide correct conclusions, that are verifiable, testable,etc., as the central beauty, and the mesmerizing appeal, that brings out the essence of nature that impressed Feynman.
I think you miss some point, or i might be wrong. The math compliments the physicist as well as the physicist compliments the math. A physicist tries to comprehend reality, not turn it in to math. What math does is to help the physicist to comprehend things are not in the human nature to understand, byt giving us an extended ability to pick up concepts of reality with higher precision and turn it around, to get a more abstract idea of what it is we are trying to understand. Computers are a nother form of tool, created from the understanding of science and math. But the computer simulation does not make sense unless you allready understand the physics it tries to model.
***** Many things in computation do not model after physical models. For example, they may take from purely mathematical description that may never have a physical analog, or have any physical meaning. It's a confusion of how models work to insist they both need to be the same. Logic can model physics, but not all physics can model logic. It is worth noting that many phenomenon never are seen in physics happen all the time in computation (in particular, the theory of computation). I agree when it comes to modelling physical models on a computer for a simulation, but we don't just run simulations on computers. Computers are guided by computation that intend to solve mathematically defined problems that can be represented finitely (which is why most computational problems tend to be discrete, or have continuous analogs that often interplay in the theory). I completely agree with you that maths and physics compliment each other, but I personally have never met a physicist that doesn't want to make a model that can be described mathematically. Remember that models are formal (mathematical) constructs that scientists can use to make predictions and experiments to validate or violate their hypotheses. It's a language we scientists typically find works well and is fairly universal among other scientists. I hope this helps.
***** Quite right.Every mathematical models are incomplete and incomprehensible. The complex number i is defined as the ratio of the rate of change with y of the image f of a function, to the rate of change with x of f, means change in y due to change in x, like "cause x" and "effect y". This definition answer the skeptics who toiled for 300 years, trying to explain how cause and effect are related. Every time a billiard ball transfer energy from one ball to the next, the physical action has a mathematical representation as a number, quite true, but also quite incomprehensible. Similarly when we burn a piece of paper we transfer chemical energy into heat energy, representable by a number, giving insight to what is to be understood when we say "numbers are operators". SMNH
Feynman gets so specific and animated sometimes that I wonder if he got into some heated argument with a mathematician right before giving this talk. This talk gets 100x better if you interpret it as feynman just being passive aggressive and trying to get the last word in some extended argument with a poor mathematician who crossed him.
You are simply seeing Feynman's persona at work, again. His musings about mathematics are 100% wrong, of course. He simply doesn't understand what the mathematicians are doing. As a physicist he doesn't have to.
@@schmetterling4477 Yep. Watch pretty much any clip of Feynman talking about mathematics. He speaks charismatically, but if you give pretty much any critical thought to what he said, you can realize that what he said is either nonsense or completely vapid.
Math vs. Physics is like electrical engineering vs. computer science. Obviously you can't have computer science without electrical engineers making the computers, but computer science itself is just as complex and intricate, if not more, than electrical engineering.
The thing which is more interesting than the relationship between math and physics is the relationship between mathematicians and physicists. From my own experience in graduate school studying both physics and mathematics, I can say that mathematicians and physicists are intellectual rivals in some sense. On one hand, this rivalry can become friendly for mutual benefit and on the other hand it can evolve into downright contempt. My general observation: Mathematicians couldn't care less about the real physical world.. and physicists despise the fact that they have to borrow many of their tools from the fantasy land called mathematics!!
Because people developed the mentality that: "it's not so deep." This kind of ignorance will be the detriment of your development and progression in life. To learn and to be willing to learn, it all comes down to your attitude and willingness to learn. It all starts with the question "Why?" And not with the complete opposite: "it's not that deep, bro." Quite sad that people like Feynman are slowly fading away for each generation.
3:29 "And later on, it always turns out that the poor physicist has to come back and say 'Excuse me, when you wanted to tell me about the 4 dimensions...'" 😂
Intuition plays a large role in inventing new branches of mathematics and solving difficult math problems. The "mechanical logic" Feynman speaks of can only take you so far. Mathematicians created modern day physics. Gallileo, Newton, Lagrange, Poincare, and Hilbert (to name a few) were all mathematicians.
What a likable genius Feynman was! He knew that the best way to know and manipulate nature is by using math; math is wired by evolution into the human brain, just as logic and language are. Thus in the end he deeply knew that all practical and measurable knowledge has to answer to physics, physics has to answer to math, and math has to answer only to the laws of nature in this universe (there may be 10^500 universes according to M theory). 😺
you cant compare, i study theoretical physics and the only thing i can tell you is that in physics we're related to nature cause at the end we are trying to understand and describe nature, maybe that detail makes theoretical physics a little more difficult, and you can be good at both of them like Henri Poincaré, Ed Witten....
Physicists and mathematicians really have (essentially) similar objectives. The only real difference is that Mathematics require logical certainty while physicist have to produce models consistent with observation. However, I can't understand how someone can say that one is harder than the other when they both offer arbitrarily great difficulty. I am a math student and have overheard another math student say that math is easy for them; I thought to myself, "You clearly are not working on hard enough problems." As long as there is one outstanding conjecture, math is hard for everyone, and while there is one lurking question in physics, physics is hard for everyone.
This is pretty much spot on but one thing I want to mention is that it is harder to be a student of theoretical physics than it is to be a student of mathematics, especially as a post-grad, because most profs expect theoretical physics students to know a lot of mathematics which is never taught to them. I remember when I walked into my first lecture of QFT, the Prof. assumed everyone in the class knew measure theory & Lebesgue integrals & so on but of course no one did. I don't think mathematicians have the same problem. But although it is quite unfair to expect this of physics students, there is virtually no way around it because there simply isn't enough time to have separate courses on these things. If physicists were expected to understand mathematics with the same amount of depth & rigour with which mathematicians do, they'd never get to the physics parts.
Generally speaking, physics is more interdyscplinary, than math. Feyman was right - math is more theoretical. Consider using pointer to common secret set element ( bijection ) in real usage of physics.
As John Von Neumann said, Mathematics is ultimately rooted in empirics. This means that mathematical ideas almost always begin with selecting objects in the real world, sometimes bringing them together in new permutations, before extracting a new idea. It is also inevitably true that abstraction itself, is rooted in empirics. As Einstein said, this type of ‘combinatrial play’, is the essential ingredient for productive thinking. And as I like to say, those who believe in circles, owe it to the moon.
I can't help but disagree on this. I mean, consider the case of a human being with no functioning senses to perceive the world. If they have thought, then they will naturally be able to recognise patterns in thought. After that, since ultimately mathematics is about patterns in the abstract, they will have started doing that, albeit on a very elementary level. The irony is, that there's no way to know for sure which case is true without empirically testing it, and there's no way to empirically test it at all.
Totally possible. I personally only realised what physics aims to do when I realised dimensional analysis was possible, purely by algebraic guesswork and playing with physical quantities. Just guessing one correct law of physics in this manner enabled me to abstract this method and guess and derive pretty much any known laws of physics from first principles, instead of looking them up or committing them to memory. I already knew that the derivations could be compared to reality through experiment, but didn't fully realise that just guessing an equation and then simply by looking at reality, you could correct the equation into the right form and in a natural manner get other related laws by simply carrying out special mathematical operations. After that I turned my back on mathematics as a prefered or superior discipline and I have never once looked back since.
"Laws of Nature".....What is that? Who is responsible for its existence? The science governing the universe is a clear demonstration of the infinite wisdom of its creator....Jehovah God!!!
I find that physics helps me regain my sanity after learning pure math though. It's easy to forget that what you're working on is something void of meaning until it describes or talks about something specific; I think there is a real trap that mathematicians can fall into if they begin to simultaneously try to understand what they're talking about while developing a rigorous language. Mathematical physicists need some massive endurance to do the work they do, that is for sure.
I remember being sat at my desk here in England, oh - about 20 years ago when a very old American lady came up to me, tapped me with her index finger on the left temple and said to me, in a broad New York accent : "Guess what ? The trouble with New York is that its full of lumps." Nodded her head and wakled away. It reminds me to this day of The Magical Mr Feynman.
Yes, it is true that Maths is the essential tool of Physics but that doesn't mean that one is better than another. They should be treat as different subjects, for example You wouldn't compare English or any language to, lets say history etc as they are both completely different subjects. However you need to know the basic tool of using the language. This is the same with Maths, it's simply a tool that can be applied to many things, computing and statistics etc. It's ridiculous to compare and it all comes down to personal preference.
Is it really 'simply a tool'? (I'm asking cause I need to know) .. Is it really purely logic built around assumptions which are true until proven false? And does physics really deal with 'objective reality' or can it be applied in understanding a ''subjective'' experience?
Outsiderkaa Yes it is a tool that has many application. Everything in Maths needs proof for it to be valid. As for physics, I have limited knowledge or experience to give you an answer.
I'm taking a Mathematical Physics course for Theoretical Physicists, being taught by a Theoretical Physicist, and he literally stated, when covering complex calculus, and going over the formal definition of analytic functions, "just think of em as functions that are differentiable, f-ck this stuff about the region." Wondering if he's just trolling the math students.
analyticity is much more restrictive and powerful condition than differentiability in both math and physics. In physics, it allows to switching from complex calculation to real framework, because the regularity (differential structure and stuff..) on real space can be recovered by the restriction of complex plane to real line. The more correct intuition is to think at them as differentiable function of z but not z(bar)
Oh, yeah! As a student of both maths and physics, I usually cringe during those times when physicists think up some clever idea that doesn't even work! (Ok, ok, so in those cases it does, but not in general, okay!?)
If you have difficulty with complex analysis, I _highly_ recommend you check out Lars Ahlfors' book on the topic. It's simply _the_ premiere text on the subject of complex variables. You'll also want a firm grounding in real analysis _and_ complex analysis before you venture into functional analysis, which will detail the mathematics of _infinite dimensional_ vector spaces. As you can imagine, the class is basically Linear Algebra on steroids.
Blech. It goes both ways. You can both use your observational intuition to lay asymptotic approximations for your equations, or find the patterns in pure mathematical relationships as a hint of what to look expect and look for. For instance, anti-matter was discovered long before observational data was available, when Paul Dirac solved for a general equation reconciling relativistic properties with small particles. It's not a "which is better" type of question. You use both avenues of thought whenever there's the opportunity, or risk crippling your intellect.
His statement "mathematicians are not slaves to physics" irritates me... Rather mathematicians don't need physicists but physicists need mathematical reasult...
So mathematicians make the tools which physicists use to solve problems. A mathematician doesn't need to know all the possible uses of the tool, but that it can be used to make sense of particular patterns.
I'm tempted to call upon the Dravidian doctrine of manifold perspectives. It tells us that no single viewpoint can fully capture the truth, that each perspective provides only a partial understanding of reality, and one must consider multiple perspectives to approach the whole truth. By attempting to pit one perspective versus another, one might fall prey to the illusion of separateness. Just as the universe is a harmonious blend of seemingly separate elements, we must realise the larger picture that both physics and mathematics are essential synergistic components in our quest for knowledge.
While I love Feynman, i disagree with him on math, math sets the foreground of logic and reason. and in doing so creates a language, a language in which physicists can later use for construction. But not only physicists but every scientific discipline needs mathematics to some level. think of a field of science as a program on your desktop, the source code of it is the mathematics, and in developing mathematics the code becomes more accurate, more diverse and simple to write. Any great level of understanding of physics and how it works depends entirely on the mathematics used to explain it. #mathematics #physics
I actually think this is exactly what he was saying. He said mathematicians don't care about the meaning of the axioms because their language applies to many fields, universally. And he took several minutes to say that physics is understood in the language of math--he said it's unfortunate that physics is in the language of math because some people find math hard, but it just is.
***** That's not what he means. He's not comparing logic to math, he's comparing math to physics. Math IN RELATION TO PHYSICS sets the foreground of logic and reason. Math provides physics with the rules it has to live by. Physicists try to understand the world, but they have to do so in a way that does not violate mathematical laws.
***** Yes, physicists make their livings by making assumptions about reality (like "everything is zero at infinity"). But QM is all about the math. L_x, L_y, L_z are incompatible (they are not commutable) but L^2 is commutable with each one of them. Physically it's hard to even wrap your head around what that means, but mathematically it's right there in black and white. There is no denying it. You can hardly (correctly) say that QM _came_ from physical observations. In fact, exactly the opposite happened. Einstein started with some assumptions the quantum physicists were saying, and in order to ridicule them took those assumptions logically to their natural conclusion. Then it turns out, all those conclusions, which Einstein thought were absurd, turned out to be true. All this is what Feynman is saying. Physics rests on top of mathematics, surely not the other way around. A specific example from QM, one that I particularly love, is the orbits of electrons in atoms. When I was in high school I HATED chemistry when they started telling us about how the "orbitals" all have these bizarre different shapes. The HS chem teachers of course had no idea why. But the reason is a purely mathematical one: Spherical harmonics simply create the patterns seen in orbitals. It's just mathematically how it is, and so it's physically how it is too. It would be sort of meaningless to argue that the physics of the spherical harmonics of an electron leads to the math that describes it rather than vice versa. Obviously both are true. But again, I think you are missing the point that Feynman is making. He's saying that physicists are GUIDED by mathematics. Mathematicians could not care less whether there is a physical application for their math--in fact they explicitly say don't try to picture it!--physicists RELY on math to guide their research and conclusions. And of course this is not to denigrate either one! The point of this lecture is only to say how they are different. I hate physics because it relies on this intuition of what is physically possible. Physicists hate math because it is only logical without caring about the physical implications. QM drives me up the wall because half of the proofs rely on "of course this term goes to zero at infinity."
***** What? Do you think I said something remotely implying that QM violates logic of involves something non-physical? You somehow got away from the point of this conversation. The point is that physicists make assumptions all the time when they are proving things. They assume all the time, for instance, that things are zero at infinity. They just hand-wave it. I am certainly not criticizing it--the point all along has been that physicists and mathematicians think and see the world in a completely different way. Neither one is better or above or below the other, they are just vastly DIFFERENT.
You know the problems on IQ tests that ask what come next, (2, 8, 16, 32, X)? Someone had to bring the numbers together in a new permutation, in the first place. Feynman was an empiricist, someone who believes that truth can be seen from observation and experiments (for example, the experiment of bringing together and analyzing a new combination of numbers). Maintaining his character in a society who in his time and since has become relentlessly rationalist, must have been extremely difficult. I think rationalist, and especially IQ proponents, have a difficult time accepting that creativity and high level problem solving come from this type 'combinatorial play', as Einstein called it. But rationalist don't have a choice. In matters of higher complexity, the novelty of the set, comes before the novelty of the operator by induction.
Feynman was ignorant. No, that's not a bad thing in any sense at all. He just didn't realize the true power of rigorous generalization when it came to physics. Bear in mind this was back in the emerging days of Quantum Mechanics. I'd like to see him make this speech today.. R.I.P Feynman. Shine on, you brilliant diamond.
I think most physicists are tbh. Physicists quite frankly don't learn much math, and then they get along thinking that math has limited applications. But the converse is true, and you need a lot of mathematical sophistication to appreciate it.
While I greatly admire Feynman and find this talk very entertaining, his main arguments are quite off. I'm saying that as a theoretical physicist myself. 1/ The last 200 years of theoretical physics have been ultimately concerned with finding nature's underlying axioms. The principle of least action in classical mechanics is an axiom (or a consequence of equivalent axioms, like Newton's, if you will). Sure, it might be as intuitive as Euclid's parallel postulate (yet another word for "axiom"), but nevertheless, the foundations of theoretical physics are axioms. Some are more intuitive, some are less. Look at the principles of quantum mechanics. Speaking of which, Feynman is famously quoted in the context of QM with "if you think you understand QM, you don't understand it at all", and best to "shut up and calculate". 2/ Mathematicians think extremely intuitively. His depiction of the poor mathematician, slave to his mechanistic process of logical deduction is completely wrong. An excellent description of that is given by Terence Tao in a recent Numberphile video. 3/ His hope to find the "laws that turn out in the end" are philosophically unsatisfiable, see Münchhausen's Trilemma.
Feynman was one of my idols back in the early 1970s when I was a physics undergraduate but as the years have passed I have, increasingly, come to realize that I never really understood the "Feynman Lectures on Physics" trilogy of books that my lecturers (and many others across the world) were so keen on. As a university lecturer, following a PhD, I met a guy who had attended Feynman' lectures and he admitted to me that he had the same experience and that many of his fellow students were equally baffled. I have it on good authority that Feynman himself was disappointed with the effectiveness of his lecture course. This uploaded lecture is very interesting, as anything presented by this great scientist would be, but it demonstrates, yet again, that even great minds like Feynman are capable of talking rubbish.
+Leslie Nelson I dont think he was talking rubbish. Sure it seemed more of a motivational speech than a technical one on a specific topic but his primary profession was math/physics, not oration. The real meat of this short clip, though, was the first 2 minutes in which he says (possibly indirectly) to recognize the definitions of your problems (the axioms) and in the later part where he implies to use logic to shorten your trip to the final answer.
Stephen M OK points taken-I will give the clip another try. I guess "rubbish" was too strong a reaction. There is no denying that the the great man is still capable of getting people talking about physics even after all this time. A uniquely talented scientist.
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As a joke with my mathematician and engineering friends (I'm a physicist) I've been saying for years: "Whereas physics is math with the constraint of reality, engineering is physics with the constraint of money."
Can you be booked for dinner parties?
+Danny Smith You think I'm funny? You must have a twisted mind. LOL
+Christine Berven Did you made it? Nice one
Dolbo Dolb there is none... xD
Obsidian Rock excellent point
As a budding Mathematician it is so reassuring to know that I don`t need to know what I`m talking about.
😂😂😂
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No you missunderstood. You don't need to know about what you are talking. You do still need to know what you're talking about.
He's talking in the context of "real world stuff."
Math makes sense of abstract, general structures within itself, which, really, is all you'd really need. The physicist needs a truncated view of very specific cases of said general structures to solve actual "real world stuff."
Steve MetalHammer LOL
Feynman used to practice sometimes up to 5 hours in an empty room before the lectures.
That's why all his lectures are gold!
He gave whole of his heart in teaching!
Same with Walter Lewin
seriously?
I'm a small-time stage actor, and that 5:1 ratio is about the same ratio of time we rehearse plays in (five hours rehearsal for one hour of stage time).
@@AlanCanon2222 That's amazing to know.
It’s really not about the individual lectures. Feynman spent an enormous amount of time thinking about problems in great detail. Every statement he makes here, he has thought about it in so many ways and in a sense, very lecture took a lifetime of prep.
the original TED talk
first name full form of TED pls
Wow
Home Sweet Technology Education Design
Tuantum Electrodynamics :D
best TED talk
Unbelievable scientist he was, and such an inspiring teacher. I hope those people were realizing how lucky they are to listen to his lectures.
MrCorvusC I hope you realize how lucky you are that you can listen to his lecture, too ;). This is possible partly due to physics btw.
Nik G And mathematics too! :D
Taylor Borodavka anything is physics uses math...
+Ivan Ereiz that is not the point feynman is trying to demostrate
MrCorvusC we are just as lucky, we can listen to this anytime
Mathematicians, Physicists, Engineers, are all important fields. The world needs all three to work together to advance humanity.
And, if anyone of them catch a fever or the flu, we have Doctors.
What if any of them is hungry
And if anyone of them gets into a fight with one another, we have lawyers to come to the rescue.
And what if one of them needs to travel internationally? Pilots do that for them?
Sheldon beg to differ
And now we have the coronavirus
Feynman really had it all. He was witty, eloquent, and intelligent.
“You do not need to know what you are talking”. He had awful grammar and spoke like English was his second language.
@@smkxodnwbwkdns8369 "The mathematicians are only dealing with the structure of their reasoning and they do not need to care what they are talking about."
You misquoted him.
Of course, pretty much every American speaks English poorly, as though it's a second language, but Feynman was extremely good at articulating his thoughts.
@@adrrda6091 I am not misquoting him, its been nearly half a month since I’ve watched this video, but it is a verbatim quote at some point in the video exemplifying his poor english. I’ve heard him talk at length in interviews and other contexts and have never been impressed by his language skills.
@@smkxodnwbwkdns8369 As a text corrector, I've come to believe that diverting a conversation from the value of the things a person says to criticize them for their less-than-optimal language skills is the height of arrogance.
@@runefaustblack there was no diversion; i questioned his “eloquence “ as op said, when there isn’t much of
I recall a course in Fluid Dynamics that was thought in the Math department. As an engineering student I was a bit bothered by an equation that was being discussed since the units did not make any sense to me. I asked the professor what is the end resulting unit of this equation and his reply was in the math department we are not concerned with this as it is irrelevant. This was a 7000 level course and I don't think I have recovered yet after 20 years. That was an eye opening experience.
Many people don't realize (or are extremely uncomfortable with) the level of abstraction that math utilizes. It is it's greatest strength, but if you don't acknowledge it, then the subject is nothing more than building blocks.
Leonard Susskind does the same willy-nilly thing with units in his RUclips lectures on Cosmology and other areas of physics. The important thing is that the dimensional analysis be correct, of course, but the actual physical units (and the constants of proportionality among them) are unimportant when discussing the physical relationships (say, between pressure, volume, and temperature of an ideal gas) in the abstract. It's a relief to know that I don't have to memorize the numerical value of 1/(4 * pi * e0) to understand Coulomb's Law: I only need it if I have to furnish a prediction for a particular experiment.
At 5:29, we see a fundamental theorem demonstrated: the limit of the number of glass lenses divided by the number of students approaches 2 as the number of students goes to infinity.
+Michael Lubin And the mathematician would wonder if 2 is the lower or upper limit.
+Roman Flammer If the limit exists, their equal.
Godlike comment, you made my day :D
I saw far more students without glasses than with glasses.
Lhh nicely done. Very nicely done
I feel that Feynman was largely talking about pre-information era mathematics here, at least as far as the qualitative aspects of the work are concerned. With today's powerful and ubiquitous computers, mathematics research is now often "seat of the pants" reasoning. Basically, since this talk was given, the practice of mathematics has become more like physics, since we can cheaply set up mathematical worlds to explore.
Though Feynman did a lot of work with computers and information theory, this was at a time where the resources were insanely expensive and slow compared to today.
please don't show the students , i get jealous
Ig most of those students are dead xD
@@donlansdonlans3363 that was dark!!
What's the reason for jealousy
The physicist, like the engineer, has the burden of physical reality to content with, of which the mathematician is completely free.
However, that is not necessarily always an easy thing for the mathematician.
For the pure mathematician must mentally contend with pure abstraction, far removed from any direct experience,
whereas the physicist & engineer have physical reality to serve as a guide, while the mathematician has no guide but their own mind. This has been my experience as a chemical engineering undergraduate major and ex-engineer, having worked 2 years in calorimetry & corrosion research, who went on to mathematics in graduate school.
Are you still working as a chemical engineer
One time a physicist walked into a diner. He ordered pie. The server, who was a mathematician, responded "We don't have it yet".
That is undoubtedly the worst joke Ive ever heard. Like definitely the worst. Lol
XenoContact Why do I like this joke so much? 🤓
"Great!" says the physicist, "then I'll have three."
XenoContact Ha ha and we don't think we'll have it anytime soon 😀
Server asks, "OK, I'll give 14ths of a pie for free"
He's on point. As a person who likes math, people assumed I'd be good at physics, but I was no good at it. I couldn't connect my understanding of math to the real world.
when you're a professor and a stand up comedian at the same time
'He is another Dirac, only this time human." -- J. Robert Oppenheimer on Richard Feynman
Great video. Feynman's passion for physics and its profound epistemological potential always manages to make me question my preference for mathematics. I would argue, however, that since physics is hinged so heavily on the empirical, and ergo on the phenomenological, it doesn't describe the mechanisms of a pure, inner "reality" any more than mathematics does. To the contrary, by being so heavily conditional and having such a precise logical structure, mathematics achieves a cleaner, more absolute form of truth. Mathematical "understanding" is not as intuitive or palpable as physical understanding, but (perhaps ironically) its abstraction and pluralism make it in many ways more real.
***** except when people make mistakes in their accepted proofs in which case we wouldn't be able to distinguish it, unlike something applied like physics where you can observe at least some forms of truth to your mathematical statements
lavendermenace Mathematics is based upon axioms. Things we take as obvious truths. Moden mathematics is based on the Zermello-Fraenkel axioms which are essentially relationships between sets that we take as obvious truths. (Although there other proposed axiomatizations in addition to the ZMF axioms. The reason mathematics has "absolute proofs" is that we can construct logical arguments that can be ultimately reduced to these fundamental axioms. This is not to say that all mathematics is absolute and certain, there is also uncertainty in maths as well as various conjectures that have yet to be proved. Science doesn't have this luxury of an axiomatized universe via which we can derive absolute proofs of things. Yet maths is a critical part of science and in many ways serves as the language by which science expresses laws and theories. There is also an interdisciplinary dependency. Philosophers were instrumental in construction some of the logical framework of mathematical logic. Scientists have contributed to the development of maths, mathematicians have contributed to the development of sciences and oure mathematicians have played a major role in maths in and of itself.
HimJimRimDim To the contrary, I would argue that mathematics' foundation in the axiomatic is an instrumental part of its unique veritas! Mathematics achieves absolute truth insomuch as it invents and defines its own metric for truth: logical extrapolation from and consistency with axioms. Since 'truth' is ineluctably a vacuous term, tenuous and ambiguous (much like meaning, purpose etc) in our universe, a structure must first define what it is to be true before it can claim to satisfy any monolith of truth. Logic and axiomatic proof, though ultimately arbitrary and not tethered to any sort of vestigial 'inherent truth,' accomplish this. Ergo, they achieve a certain type of truth-absolutism, of objectivity. Constructed objectivity, yes, but (I would argue) the only form of objectivity humans can know.
However, while mathematics accomplishes absolute truth, it also spurns singular truth. This has to do, of course, with the axiomatic system you expounded on. Mathematical truth is reliant on ultimately arbitrary axioms. But mathematics also acknowledges the arbitrariness of its own axioms! Herein lies the profundity of mathematical thought. Implicit in any mathematical argument is a conditional statement- "If this axiom holds true, then X, then Y, then Z," or some analogue. Really, we are not "assuming the axiom to be absolutely true," we are simply exploring what the implications of its theoretical truth would be. It is through this intrinsic conditional condition that mathematics becomes both absolute, in its logical consistency and autonomous self-definition, and plural, in its rejection of singularity and its study of all shades of the potential. In no way does this make it "uncertain."
It is true that there rest conjectures to be proved, and Gödel illustrated that mathematics will inevitably fail to provide proper logical excavation for some of these. This does not attenuate the fundamental truth of mathematical method or structure. If anything, it exposes the limitations of human truth itself, and imbues mathematics with transcendental meta-cognition: an awareness (and a result meta-mathematical annexation) of its own bounds, a latent epistemology.
+lavendermenace They are both fascinating subject, each beautiful in its own way. and in many of the same ways as well. There are some elements of math that seem to be rather contrary to our intuition, the works of cantor bear this out. . But such is true in physics.. In fact one of the thins that makes quantum mechanics difficult is that it is often not intuitive at all.
It's* :)
Wow this is really awesome. As much as I've read about him now I sit here and watch a lecture.
Feynman is amazing. If youre reading about him youre missing out in his carisma and some of his humor. You should check out a documentary or two and an interview if you can. Its great to hear other peoples stories about him too :)
+nicosmind3 Thanks! I can see just from this there is so much to be missed in simply learning about him. I absolutely will take your advice and look up more things of him rather than about him!
Sadie Kitten Not a problem. I really enjoyed the documentary. TV is completely lacking for me but thankfully we have youtube and just about everything you could want to stimulate the mind :)
A physicist is a would-be mathematician with one flaw: a physicist cares about physical reality.
The problem with (pure) mathematicians, is that they believe that abstraction is all about the analytic, and neglect, any pre-analytic process which leads to it. Physics has often been, the top-down, path to mathematical abstraction.
fergoesdayton The "problem" with pure mathematicians is that they want to find a finite set of primitives (axioms and their schema) that can generate all theorems without having to rely on one's (fallible) senses. That sounds to me a much more attractive way to solve problems.
Dennis Oliver But don't axioms remain assumptions, as they depend on 'fallible' senses? What seems important, is that within any system of thought, there is a high level of consistent support for an idea. Instead of having faith in the validity of axioms; saying all of this is true, because x, y, and z seem undeniably true, one can have faith in the amount of consistency there is in an idea.
there isn't such a set of axioms. Every consistent axiomatic system will be incomplete (Gödel's incompletness theorem).
Caring about physical reality has many times opened insights that mathematicians would probably never have guessed or reasoned to on their own. Just look at Riemann hypothesis for example, new insights suggest that it's closely related to quantum physics. Physics is repeatedly showing that learning about reality is almost essential to advance a lot of mathematics, since it's so very related.
I must say that at 4:20 he says the mathematician does not have an intuitive feeling for manipulation of expressions, but skills like this are developed over time. In reality it seems to be no different from physics you start with an intuitive feeling and develop the expressions for special cases then you attempt to generalise it (in both math and physics this is done just in slightly different ways) and once you've generalised it you realise that a lot of your intuition comes from extra properties that are only there in the special case, so you have to redefine/restructure your intuition so that it only uses the properties that apply to all cases and not just the special ones.
Note: you may use special cases to give an intuition about more general ones but you still have to be aware of the properties that do not apply in the general case, thus there is still some form of restructuring of intuition.
I'm a math physics student nearly finished my bachelors degree so I can't say what I have said is true for actually researching in these fields as I only really have experience with studying, but it seems like it would apply. I'm curious to hear what other people think?
Great observation. I think physics differs from math in its focus and on penetrating the counter intuitive. In math, there are unlimited intellectual dimensions to explore; choose the one that fits best. But in physics, it's often experiments and simple questions that isolate the frontier. It's up to the thinker to meet the demand.
His class must've been amazing to be a part of. Thanks for posting this video.
Meaning vs Rigor
I am a good mathematics student - I study every day - I struggle with the abstractions of vector calculus and differential equations, discrete math, and real analysis. But, when I started taking physics classes to enrich my ideas concerning natural philosophy - man, did my head get a painful upgrade, and a realization of what RF is talking about here - I don't necessarily like it, but I understand and agree.
Mathematics develop the tools that other scientist get to take for granted. Without Gauss and differential geometry, there would be no Einstein or relativity. Any physical theory must be communicated in the language of mathematics in order to asses its relevancy.
Francisco Reyes and without newton there would be no calculus,i mean many physicists also develop those kinds of tools you are talking about.
Newton was a mathematician. Also, Leibniz more or less independently invented calculus around the same time. However, we now know that Archimedes was doing integration over two thousand years ago.
Francisco Reyes Newton was interested in limits and reality, Leibniz was more interested in the abstract . Newton was driven to create calculus to answer physical phenomena, I would say he is more of a physicist than mathematician. So even if Leibniz had not existed, we would still have calculus, thanks to the greatest physicist of all time, Isaac Newton.
Francisco Reyes True, but the discovery of some of these mathematics was at least in part inspired by the desire to understand things like gravity, etc. Just as games of change (gambling) at least in part inspired the discovery of probability theory. Math can be pure (abstract) in its own right but, as Feynman pointed out the various disciplines help each other.
Joey Castro
Actually it is a common misconception that newton was only concerned with applied math. He advanced virtually every branch of math that was studied in his day. I'm not going to argue about newton because I think we can all agree that he is the man and is in fact the father of modern physics. However in his day there was no such occupation as physicist and he was in fact a mathematician by trade. He was the lucasian professor of math at cambridge to be precise.
An important point on generalization in mathematics: sometimes the special case is the HARD case. For instance, many problems involving forces are very hard to solve in the case of gravitational forces because gravitation has a singularity at the origin. So what do you do? You generalize! You assume you have an arbitrary force and you assume it has some nice properties. So you solve this easier case and then try to say something "in the limit" of gravitational forces.
Euclid told the king who complained it was hard, "There's no royal road to geometry." Ha, a classic. Substitute for "geometry" - law, investing, economics, writing, chess, martial arts, piano, and so on. 8:24
Airdish Pal (Paul Erdős) described Applied Mathematics as the Art of "Dead Mathematicians". As a kid I had the good fortune to have him as one of my mentors. He drove me to tears setting more and more difficult problems, that had two or even more answers! ... "Pick the best one!".... At that time, aged 8 years old, Alec Harley Reeves was teaching me how to build computers. Later I had a Dead Applied Mathematics bone to pick with our dearest departed Richard Feynman. The "AXIOM" (Unproven) that something can never be created out of nothing. Specifically Energy. A Thought Experiment violates this 'axiom'. ..... "There is an evacuated tube a kilometer in diameter, Inside this tight vacuum is a permanent magnet linear bearing that supports a very heavy shuttle, let us say 200 metric tonnes. This is perfectly possible. and for arguments sake the shuttle travels around this tube at 1000 m/s. The Radius is 5 kilometres. There are of course quite strong forces of centripetal acceleration. we can calculate them at different vacuum tube diameters. and angular velocities from reliable and well trusted equations of Vector Forces. Sir Isaac Newton tells us that a body in motion has a tendency to continue in the direction of that motion. If a circular track free of friction prevents a linear path, "Vector Forces" arise. Centripetal, because the Force is always perpendicular to the Tangent and directed in line with the centre. ... Now for THE GIGANTIC PROBLEM WILL ALL OF SCIENCE AND ALL OF SO-CALLED PHYSICS BASED ON UNPROVEN AND MERELY SPECULATIVE "DOGMATIC AXIONS" THAT APPEAR TO BE REASONABLE. (There is no such thing as a free lunch, just before Sir Isaac Newton sitting under an apple tree, conceived of the lars of gravity.) ... This Vacuum Tube is mounted on Hydraulic Stainless Steel Concertina Elastic Pressure Pumps. With a little Leverage included. As this 100 metric tonne speeding shuttle travels round all the Vacuum Tube mounts are shifted by a couple of millimetres or perhaps a little more. A square meter 1.0 mm thick is one litre. Let us say the movement is 2.0 mm. and the pressure area is 0.5 square metres. Pi x 1000 is about 3,142 metres. (Pi * D) so it takes about 3.142 seconds to complete one revolution. So by logical mathematics, every second 1,000 litres of high pressure hydraulic fluid is pumped. with each complete revolution. This energetic speculation is always extracted perpendicular to the tangent. the 2.0 mm. excursion is so slight as to have negligible effect upon the angular velocity. Kinetic Energy is the product of half the mass in Kilos e.g. 200,000 * 0.5 = 100,000 and the velocity squared 1000^2 in total a Stored Kinetic Energy of 100,000,000,000 Joules. Frictionless motion is possible in deep space, but unlikely in a vacuum tube. We could measure the loss of velocity with all the hydraulic pumps locked. (Valve Closed) and then measure again "Valve Open". a pure guess is that the 200,000 kilo shuttle would lose a micro-second of velocity with each circuit compared to the closed valve time. In any case we are looking at the Shuttle losing 200 Joules of kinetic energy per second. 628.2 Joules per revolution of Pi seconds. A circle of radius 500 metres and velocity 1000 m/s gives a gigantic force of centripetal acceleration. A Jet fighter pilot, could black out from the G-Forces turning such a tight radius in a dog fight. A tonne of high pressure hydraulic fluid per second fed into many hydraulic motors, as used on Oil Tankers to avoid electric sparks, is a lot more than 200 watt total output. (Subtract a micro-second from 1000 m/s and square the result then multiply by half the mass 100`,000 kilos. SOMETHING IS TERRIBLY WRONG WITH UNPROVEN AXIOMATIC QUASI-RELIGIOUS DOGMAS.
With you, sir, I’d really like to have a drink. P x
Ask Ramanujan about rigor or proving something
+Juan Moreno he was highly unconventional as far as I know about him.
+Aditya Mishra exactly. which is his point.
He wasn't even a mathematician he was some loser who sent his work to cambridge on something that had already been done. Why not William Sidis or Ted Kaczynski.
Sheldon Cooper that statement seems a lot biased to me.
Why so enraged?
Aditya Mishra Because why would you tell Ramanjan to prove a theorem/problem if he's not even a mathematician ?
Very interesting insight, still the final word is physists can't work without mathematics, while mathematicians can be completely independants, even from reality.
He is so funny, and so intelligent. An awesome combination
mathematics is the language (alphabet, grammar...)
physics is the poetry (applying the language to, briefly and effectively, describe reality)
i do agree that physics is a form of art, but you can also say that for mathematics (for example : Noether's theorem, differential geometry of manifolds, geometrical analysis, group theory(= the most badass way to study symmetry), Galois theory, combinatorial analysis, topology ...etc..). I think that physics and mathematics have many differences as they have many similarities in their approaches. Both, to my eyes, are a work of art (and maybe the most timeless products of human thought)
What Feynman is talking about is the difference between rationalism and induction. Mathematics have *always* been particularly attractive to rationalists (all the way back to Plato) because they believe they can combine mathematics and deduction as a means of understanding reality without performing what the real work of a scientist *should* be: looking at reality and forming inductive generalizations by reference to empirical observation.
Yeah, except it's actually not like that in our world. Mathematicians still must do empirical observations of their own abstract models to discover new things. In reality most of useful math is discovered by induction. The proofs come only a posteriori once you have a reasonable belief that some result might be true. In this respect, the only difference between mathematicians and physicists is that physicists are satisfied once they believe something. That's why their theories are so advanced and don't have rigorous footing. Mathematicians on the other hand are more careful and ask for proof. That naturally takes much more work, but once that work is done you can be _really_ sure the result holds, in contrast with physical results which are often more like (very informed) guesses.
Marek Bernát "Mathematicians still must do empircal observationsof their own abstract models to discover new things". Lol what?
Simplest example is Riemann Hypothesis, i.e. the conjecture that all non-trivial zeros of the Riemann zeta function have real part 1/2. This has been tested empirically quite well, by finding millions of those zeros (I don't have a precise count, but it's a lot). If we didn't have these tests, nobody would believe the conjecture as much. Examples like this are common all over the mathematics: very often you first observe (for example by writing a program) some relationship between objects such as numbers, spaces, functions, or whatever it is you study and once you see a pattern, you can formulate a conjecture and prove it. I repeat, almost nobody in math proves anything purely syntactically from axioms. It's always guided by some intuition, experiments, insights from other sciences or whatever.
I don't think I totally agree. It's true that nobody would believe the Reiman conjecture without the empircal demonstrations, but that is only because there is no actual proof; if there was, giving examples would not be needed to convince anybody.
I do agree that mathematicians use intuition in the sense that they actually think about what they are doing and what connections there may be to make, and this guides their thought process as opposed to randomly shuffling around symbols and words till something is discovered.
However, thinking deeply about the subject matter doesn't nescessarily (or usually) translate to mathematicians testing things empircally, and that's using "empircally" generously (doing examples as opposed to actual real world observation).
And yeah, things are rarely proved right from the axioms, but that's because it's not needed when a plethora of other results and theorems have already been proven and thus are availabe to use.
Perhaps one of the reasons we can't seem to reach an agreement here is that there's no such thing as a model mathematician. Some are really strictly logically/formally oriented, some are deep thinkers, some are experimentalist (in the sense I mentioned), some are close to science, some are theory builders while others are problem solvers or conjecture-makers, etc.
I guess my bottom line is that mathematics is a spectrum and parts of it are really very close to sciences, in stark contrast with the black&white naive view presented by Feynman. Even though many things he (and you) mentions are actually true, of course.
He has the most impressive mind I've been able to listen to. He ran the group of human calculators for the building of the nuclear bomb. He was known as the best problem solver the humankind has seen. I love you Richard!!! He develop QED. And was the first to calculate electrons orbit accurately with math he developed.
"QED" has been around since... well latin wasnt dead.
+ Coach McGuirk:
Yes, QED = Quod Erat Demonstandum, has been around since Latin hadn't yet killed the Romans.
What Richard Feynman developed, was
QED = Quantum ElectroDynamics
= EM + SR + QM
= the marriage of electromagnetism in its special-relativistic form, with quantum mechanics.
For which he was awarded the 1965 Nobel Prize in physics.
Coach McGuirk I hope this is a clever joke.
I kinda like the SPQR! And that big bundle of sticks wrapped around an axe!
What I like so much about Feynman is how intelligent he is, yet seems to have no trouble explaining in terms everyone can and most likely will understand.
I actually agree here. Mathematicians seem to be aware that an infinite amount of applications can exist through different dimensions, but might be too curious with the infinite possibilities, when the only relevant application would be for our universe. Physicists seem to be able to understand and master our current universe without getting distracted by other possibilities. Then, after understanding our universes physics, eventually a physicist will acknowledge that there may be a 4th higher dimension, and then come back to the mathematician and ask " what can you tell me about this dimension and its constraints?"
As a mathematician. I dont understand why someone would put math versus physics. If you like math or physics. Your are eventually gonna love both of them.
Only a real mathematician already understands true meaning behind rigor.
I'm not a mathematician by far, but as someone who's on currently on Book 4 of Euclid's Elements I can definitely say that Mathematicians are a rigorous folk.
@@thephilosopher7173 yeah, this was a while ago and I have moved on to Software. Let me tell ya, you should try it out it's pretty awesome.
@@SpiritVector Computer science being a branch of mathematics!
@@AlanCanon2222 That is true, often times though what we care about in computer science is software. The best way to develop software is by building implementations, then the abstractions for reusability. It may not feel like mathematics at first but it is.
Feynman has, on more than one occasion, been my sanctuary. A place where I go to escape the noise and bullshit in the world. A place where inspiration and heartfelt fondness can be gained, absorbed, and reveled in
And then there's set theory, which is preparing the abstract reasoning for more abstract reasoning
what i would give just to have been to even one of this mans lessons. if teachers made learning even half as fun as feynman did then the world would be a much smarter place.
Isn't it wonderful that you can watch this video of Feynman from your computer? It's almost as good as having been in his classroom. It would not have been possible without physics and mathematics.
@@MarkChimes one video does not speak for 5 years of studies and a lifetime of constant learning. If only I could have 5 years of someone like Feynman teaching at my university. The absolute garbage level most of my professors are at is embarassing. No one cares any more, not like Feynman, he cared, and it's noticable for anyone..
Dr. Feynman is relevant today. For what is "string theory" but mathematic run amuck.
Bret Brown I agree with you but there's a very slim chance that it's true and real, just that we don't have the technological capabilities to verify it experimentally yet
Feynman is a perfect teacher in teaching Phy& Maths..I like his funny way of teaching...
As a mathematician I must argue a bit with this video. Despite what many say, mathematics is a lot of times not isolated from the real world. Take information theory for instance. You really wanna tell me that information is not the real world? Even the idea of space is something we all experience, abstract or not. It's not a matter of one being more too abstract for real world or one not knowing the significance of axioms or whatever to understand real world; it's about how you want to view your world. You can view it either abstractly or intuitively and both are just as valuable. Historically though it is interesting to see that physicists thought (or maybe still do think) this way.
this is the best video I've ever watched in my life.
I wonder what his notes looked like.
saldownik Diagarams?
I read a book about his lectures, it was literally like reading a novel
@@tofu8688 Which title?
🧐
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858-1932), David Hilbert (1862-1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Galileo Galilei (1564-1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss (1777-1855) referred to mathematics as "the Queen of the Sciences". Benjamin Peirce (1809-1880) called mathematics "the science that draws necessary conclusions". David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise." Albert Einstein (1879-1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." French mathematician Claire Voisin states "There is creative drive in mathematics, it's all about movement trying to express itself."
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.
this remind me of by Richard Courant.
I'm not reading that, but I too like physics and mathematics.
My professor worked, and as a student of Feynman. You could say my knowledge transcends from Feynman
Even as a mathematician I do agree with Feynman, on that at time our reasoning may not depend on understanding what we talk about. We use the very backbones of reason, namely Logic in its abstract form. however i disagree with excluding physicists to this "nature" of doing things. Even today no man ,even Physicist , UNDERSTANDS what Gravity is or what causes it. We may come up with models such as general relativity and say it is cause by the bending of space time, but then one can ask what causes the bend... What I am saying is that like Physicists, like mathematicians, also have axiom-like concepts that do not need to be understood in depth in order to come up with Remarkable theories like the big bang, string theory etc.
we cannot always try understanding everything, otherwise we have to define everything, and that is why Mathematicians have axioms, and other concepts that do not need to be defined or understood in detail.
Physics in not possible to have its elegance and rigor without Mathematics, mathematics needs physics and other related fields to have meaning.
Sabelo Letsoalo Physicists know we'll what gravity is. it's not caused by the curvature of space-time, it is the curvature of space-time. And that curvature is caused by the presence of mass.
Sabelo Letsoalo What you said makes sense, maybe gravity isn't the best example but the charge of particles or some other phenomena is. Having said that, I still believe mathematics use pure logic much more often than physics.
MrSidney9 Then why does mass cause the bending of space-time? After that you can go on asking forever. Even smallest fields must be defined somehow. By that logic at the end of the explanation chain must be something that defies our way of thinking or a paradox of some sort. Maybe the fundamental nature of the explanation chain is a paradox. While this does sound confusing I still hope it's undestandable.
Yes MrSidney9 I agree, my wording was bad. But you get what I'm getting at though. I am talking about the general way physicists define things, for example (as you have said correctly) the presense of mass causes the curvature but does no physicist can explain why the bending Occurs.
I also agree with Filip Pozar Tolbryn the IX, every Field needs To follow a chain of logic, but absurdities and circular reasonig arise towards the end of this "chain", if we refuse to accept certain things as truth without the need of proving them . Feynman cannot claim mathematician don't need to know what they are talking about in order to reason, and then exclude himself and other physicists from the statement. ALL fields have their sets of "axioms", ALL fields need to reason from those axioms to arrive at even higher truths.
all I can say to you my poor confused brother is listen to what tessla has to say about Einstein and the replacement of hands down balls out physics with complicated non provable equations that dominate our understanding of the world today. and by the way... math. lies when you know how. and Einstein and his ilk were damn good at it..... have fun.... z.
If science was a multi-storied building, mathematics would be a ground floor under physics on the first and chemistry on the second. Take them away and people get a useless block of concrete and steel. Try to take away mathematics...and it all turns out into chaos without meaning.
I would add, logic is the ground upon which the building is constructed.
Engineering is what pays the mortgage.
Everyone forgets about biology and astronomy. XD But I get the point: Math is the only way to truly understand and explain how ANY of it works, in a universal way.
@@michaelnewman2801 LOL
I've always liked the expression
"Physics is applied mathematics, Chemistry is applied Physics, Biology is applied Chemistry etc."
Its open ended so you can insert a burn on whatever soft science field you prefer.
Gotta say though: abstraction in maths isn't just a general view for the sake of being general. You get a lot more, like noticing things in your area behave similarly to things in an entirely different area, and this is only made possible with the `wider' view.
This guy is great. Mathmatical talent/understanding and charisma don't often seem to correlate but they do seem to do so for Feynman.
Uploaded on my b-day, I can live happy now
So true... Feynman was a effing boss.. all day.
He wasn't putting down Mathematics at all. He was just trying to make a point that they aren't the same thing.. He said multiple times that physics relies on mathematics to understand the world, and that it is of great use. However in Physics intuition plays a much greater role than in Mathematics. This is why a physicist is usually alright at mathematics since both require extensive logic but a mathematician isn't always good at physics due to a lack of intuition or feel for the physical world.
I can definitely tell Maths have evolved a bit more since this lecture. With computation and the theory it has introduced, much of mathematics has become extremely relevant to how technology drives society. I do agree with what he was saying for the most part though, as eloquently as he puts it. To prove theorems, it usually isn't just invoking axioms a lot of the time (usually the problems studied come from the axioms, whether it be pure, applied, discrete (computational/CS), or continuous). Lots of experimentation and intuition comes into the prospect of new theorems in Maths/Stats/CS (formal sciences), just like any law in the empirical sciences.
*****
As a mathematician, I feel "compelled" to answer that. I have been asked that same question by quite a few friends and family.
To a mathematician, mathematics is closer to art than to science. Would you ask that same question to a musician or a painter for instance? If you really think about it, what musicians or painters do does not matter either. Will the presence or absence of an art-form affect the technological progress of humanity? I hardly think so. Yet nobody asks that question to artists. Why mathematicians then? Just because mathematics finds applications in real world does not mean it has to be burdened with constraints of reality.
Mathematicians do mathematics because they find immense pleasure in it, not because they want to advance our understanding of the real world. That mathematics finds its way to applications is purely coincidental.
In some weird sense, mathematics is an addiction. It creates a thirst which you can satisfy within yourself, just with your thoughts. The moment you satisfy that thirst, the moment all the pieces of the puzzle fall into place, that's the eureka moment for a mathematician. And they are addicted to such moments. The best thing about it is you don't have to wait for the validation from real physical world, the NATURE. (Of course you still have to publish your proof to see if your eureka moment really produced something logically correct, but let's not go into that. LOL). It's impossible to be a mathematician if you are not in love with those eureka moments and mathematicians will go to great lengths to find such moments.
I'd go so far as to say that it's not mathematics that they are in love with, but those eureka moments. Quite often, mathematical physics and theoretical computer science provide the same sort of experience. Hence you see quite a lot of mathematicians working in these fields too.
Does that make pure mathematics a useless endeavor? If the answer is yes, then by the same logic, all forms of art are useless. Are we willing to sacrifice artistic beauty for the sake of scientific utility? Well, all I can say is that in such a case, we would still have humanity, but no civilization.
Mathematical formulation, construction etc. always resorted to premises that are not always well defined, counter intuitive or outright incorrect etc., yet provide correct conclusions, that are verifiable, testable,etc., as the central beauty, and the mesmerizing appeal, that brings out the essence of nature that impressed Feynman.
I think you miss some point, or i might be wrong. The math compliments the physicist as well as the physicist compliments the math. A physicist tries to comprehend reality, not turn it in to math. What math does is to help the physicist to comprehend things are not in the human nature to understand, byt giving us an extended ability to pick up concepts of reality with higher precision and turn it around, to get a more abstract idea of what it is we are trying to understand.
Computers are a nother form of tool, created from the understanding of science and math. But the computer simulation does not make sense unless you allready understand the physics it tries to model.
***** Many things in computation do not model after physical models. For example, they may take from purely mathematical description that may never have a physical analog, or have any physical meaning. It's a confusion of how models work to insist they both need to be the same. Logic can model physics, but not all physics can model logic. It is worth noting that many phenomenon never are seen in physics happen all the time in computation (in particular, the theory of computation).
I agree when it comes to modelling physical models on a computer for a simulation, but we don't just run simulations on computers. Computers are guided by computation that intend to solve mathematically defined problems that can be represented finitely (which is why most computational problems tend to be discrete, or have continuous analogs that often interplay in the theory).
I completely agree with you that maths and physics compliment each other, but I personally have never met a physicist that doesn't want to make a model that can be described mathematically. Remember that models are formal (mathematical) constructs that scientists can use to make predictions and experiments to validate or violate their hypotheses. It's a language we scientists typically find works well and is fairly universal among other scientists.
I hope this helps.
*****
Quite right.Every mathematical models are incomplete and incomprehensible.
The complex number i is defined as the ratio of the rate of change with y of the image f of a function, to the rate of change with x of f, means change in y due to change in x, like "cause x" and "effect y".
This definition answer the skeptics who toiled for 300 years, trying to explain how cause and effect are related.
Every time a billiard ball transfer energy from one ball to the next, the physical action has a mathematical representation as a number, quite true, but also quite incomprehensible.
Similarly when we burn a piece of paper we transfer chemical energy into heat energy, representable by a number, giving insight to what is to be understood when we say "numbers are operators".
SMNH
Feynman gets so specific and animated sometimes that I wonder if he got into some heated argument with a mathematician right before giving this talk.
This talk gets 100x better if you interpret it as feynman just being passive aggressive and trying to get the last word in some extended argument with a poor mathematician who crossed him.
You are simply seeing Feynman's persona at work, again. His musings about mathematics are 100% wrong, of course. He simply doesn't understand what the mathematicians are doing. As a physicist he doesn't have to.
@@schmetterling4477 Yep. Watch pretty much any clip of Feynman talking about mathematics. He speaks charismatically, but if you give pretty much any critical thought to what he said, you can realize that what he said is either nonsense or completely vapid.
I must say, with the exception of neuroscience, the formal sciences (Mathematics and Logic) are without a doubt my favourite areas of science.
+Joshua Nicholls Neuroscience isn't real science.
+F Miller don't be a fool
+Gi Di 😂😂😂
He had such an incredibly vivid understanding of the world
Yes, form in math, as in deductive logic...
"The physicist is always interested in the special case; he's never interested in the general case." 3:05
Math vs. Physics is like electrical engineering vs. computer science.
Obviously you can't have computer science without electrical engineers making the computers, but computer science itself is just as complex and intricate, if not more, than electrical engineering.
The thing which is more interesting than the relationship between math and physics is the relationship between mathematicians and physicists.
From my own experience in graduate school studying both physics and mathematics, I can say that mathematicians and physicists are intellectual rivals in some sense. On one hand, this rivalry can become friendly for mutual benefit and on the other hand it can evolve into downright contempt.
My general observation: Mathematicians couldn't care less about the real physical world.. and physicists despise the fact that they have to borrow many of their tools from the fantasy land called mathematics!!
I am curious as to whom disliked this genius/great man. Miss click or too stupid to appreciate a great mind?
I'm sad that this type of vocal clarity and strength went extinct
Because people developed the mentality that: "it's not so deep." This kind of ignorance will be the detriment of your development and progression in life. To learn and to be willing to learn, it all comes down to your attitude and willingness to learn. It all starts with the question "Why?" And not with the complete opposite: "it's not that deep, bro." Quite sad that people like Feynman are slowly fading away for each generation.
I was he was my lecturer for every physics module. and my life.
3:29 "And later on, it always turns out that the poor physicist has to come back and say 'Excuse me, when you wanted to tell me about the 4 dimensions...'" 😂
... and the 10 dimensions."
;)
Maths is the language of Physics,,,
I being a physicist myself, i know it's so damn true....
Mr Feynman,EVERY MATHEMATICIAN knows for what he is talking about.Just noone can grasp him as a result we think that their words are unreasonable🙃
Brilliant man, and very enjoyable lecture. Thank you for uploading.
thanks so much for posting
That's simply beautiful.
Intuition plays a large role in inventing new branches of mathematics and solving difficult math problems.
The "mechanical logic" Feynman speaks of can only take you so far. Mathematicians created modern day physics. Gallileo, Newton, Lagrange, Poincare, and Hilbert (to name a few) were all mathematicians.
What a likable genius Feynman was!
He knew that the best way to know and manipulate nature is by using math; math is wired
by evolution into the human brain, just as logic and language are.
Thus in the end he deeply knew that all practical and measurable knowledge has to
answer to physics, physics has to answer to math, and math has to answer only to the
laws of nature in this universe (there may be 10^500 universes according to M theory). 😺
2:01 for a moment, I thought he was typing... Then it hit me
A mathematician and a physicist walk into a bar.
Dick Feynman says, "I was wondering when you guys were going to show up!"
Pure math with proofs(abstract algebra, real analysis, algebraic topology) vs theoretical physics. which is harder in your opinion and why?
you cant compare, i study theoretical physics and the only thing i can tell you is that in physics we're related to nature cause at the end we are trying to understand and describe nature, maybe that detail makes theoretical physics a little more difficult, and you can be good at both of them like Henri Poincaré, Ed Witten....
Physicists and mathematicians really have (essentially) similar objectives. The only real difference is that Mathematics require logical certainty while physicist have to produce models consistent with observation. However, I can't understand how someone can say that one is harder than the other when they both offer arbitrarily great difficulty. I am a math student and have overheard another math student say that math is easy for them; I thought to myself, "You clearly are not working on hard enough problems." As long as there is one outstanding conjecture, math is hard for everyone, and while there is one lurking question in physics, physics is hard for everyone.
This is pretty much spot on but one thing I want to mention is that it is harder to be a student of theoretical physics than it is to be a student of mathematics, especially as a post-grad, because most profs expect theoretical physics students to know a lot of mathematics which is never taught to them. I remember when I walked into my first lecture of QFT, the Prof. assumed everyone in the class knew measure theory & Lebesgue integrals & so on but of course no one did. I don't think mathematicians have the same problem.
But although it is quite unfair to expect this of physics students, there is virtually no way around it because there simply isn't enough time to have separate courses on these things. If physicists were expected to understand mathematics with the same amount of depth & rigour with which mathematicians do, they'd never get to the physics parts.
Generally speaking, physics is more interdyscplinary, than math. Feyman was right - math is more theoretical. Consider using pointer to common secret set element ( bijection ) in real usage of physics.
great talk on the differences between maths and physics
As John Von Neumann said, Mathematics is ultimately rooted in empirics. This means that mathematical ideas almost always begin with selecting objects in the real world, sometimes bringing them together in new permutations, before extracting a new idea. It is also inevitably true that abstraction itself, is rooted in empirics. As Einstein said, this type of ‘combinatrial play’, is the essential ingredient for productive thinking. And as I like to say, those who believe in circles, owe it to the moon.
Or as Aristotle said over two thousand years ago: "There is nothing in the intellect that was not first in the senses."
And as Vladimir Arnold used to say, "Mathematics is the part of physics where experiments are cheap." :>
I can't help but disagree on this. I mean, consider the case of a human being with no functioning senses to perceive the world. If they have thought, then they will naturally be able to recognise patterns in thought. After that, since ultimately mathematics is about patterns in the abstract, they will have started doing that, albeit on a very elementary level. The irony is, that there's no way to know for sure which case is true without empirically testing it, and there's no way to empirically test it at all.
this was beautifully spoken.
So it's possible for one to be good at math but not so good when it comes to physics?
It is possible. I can attest to that. I can appreciate the beauty of numbers while having trouble understanding the laws of nature.
Totally possible. I personally only realised what physics aims to do when I realised dimensional analysis was possible, purely by algebraic guesswork and playing with physical quantities. Just guessing one correct law of physics in this manner enabled me to abstract this method and guess and derive pretty much any known laws of physics from first principles, instead of looking them up or committing them to memory. I already knew that the derivations could be compared to reality through experiment, but didn't fully realise that just guessing an equation and then simply by looking at reality, you could correct the equation into the right form and in a natural manner get other related laws by simply carrying out special mathematical operations. After that I turned my back on mathematics as a prefered or superior discipline and I have never once looked back since.
"Laws of Nature".....What is that?
Who is responsible for its existence?
The science governing the universe is a clear demonstration of the infinite wisdom of its creator....Jehovah God!!!
I find that physics helps me regain my sanity after learning pure math though. It's easy to forget that what you're working on is something void of meaning until it describes or talks about something specific; I think there is a real trap that mathematicians can fall into if they begin to simultaneously try to understand what they're talking about while developing a rigorous language.
Mathematical physicists need some massive endurance to do the work they do, that is for sure.
+Jason Cummings Not at all. Improper hypothesis.
SuperbChad Feynman
"physics is a story and mathematics is ONE of the languages till known to know the story."..... by amit kumar
Are you quoting yourself?
@@ghostenthusiast7792 he is indeed and deserves credit for it.
I remember being sat at my desk here in England, oh - about 20 years ago when a very old American lady came up to me, tapped me with her index finger on the left temple and said to me, in a broad New York accent : "Guess what ? The trouble with New York is that its full of lumps." Nodded her head and wakled away. It reminds me to this day of The Magical Mr Feynman.
Feynman is my Ideal Physicist...
I'm hungry for more...
Every science textbook is written in the language of mathematics
"To discuss nature, to learn about nature, to appreciate nature, it is necessary to find out the language that she speaks in."
Yes, it is true that Maths is the essential tool of Physics but that doesn't mean that one is better than another. They should be treat as different subjects, for example You wouldn't compare English or any language to, lets say history etc as they are both completely different subjects. However you need to know the basic tool of using the language. This is the same with Maths, it's simply a tool that can be applied to many things, computing and statistics etc. It's ridiculous to compare and it all comes down to personal preference.
Is it really 'simply a tool'? (I'm asking cause I need to know) .. Is it really purely logic built around assumptions which are true until proven false? And does physics really deal with 'objective reality' or can it be applied in understanding a ''subjective'' experience?
Outsiderkaa Yes it is a tool that has many application. Everything in Maths needs proof for it to be valid. As for physics, I have limited knowledge or experience to give you an answer.
wow, beautiful explanation
I'm taking a Mathematical Physics course for Theoretical Physicists, being taught by a Theoretical Physicist, and he literally stated, when covering complex calculus, and going over the formal definition of analytic functions, "just think of em as functions that are differentiable, f-ck this stuff about the region." Wondering if he's just trolling the math students.
analyticity is much more restrictive and powerful condition than differentiability in both math and physics. In physics, it allows to switching from complex calculation to real framework, because the regularity (differential structure and stuff..) on real space can be recovered by the restriction of complex plane to real line. The more correct intuition is to think at them as differentiable function of z but not z(bar)
Oh, yeah!
As a student of both maths and physics, I usually cringe during those times when physicists think up some clever idea that doesn't even work!
(Ok, ok, so in those cases it does, but not in general, okay!?)
Agharabo C-differentiability implies analicity by the Cauchy formula.
you are right, thank you for the remark. but I was referring to real differentiability.
If you have difficulty with complex analysis, I _highly_ recommend you check out Lars Ahlfors' book on the topic. It's simply _the_ premiere text on the subject of complex variables. You'll also want a firm grounding in real analysis _and_ complex analysis before you venture into functional analysis, which will detail the mathematics of _infinite dimensional_ vector spaces. As you can imagine, the class is basically Linear Algebra on steroids.
3:36 just amazing
Blech. It goes both ways.
You can both use your observational intuition to lay asymptotic approximations for your equations, or find the patterns in pure mathematical relationships as a hint of what to look expect and look for.
For instance, anti-matter was discovered long before observational data was available, when Paul Dirac solved for a general equation reconciling relativistic properties with small particles.
It's not a "which is better" type of question. You use both avenues of thought whenever there's the opportunity, or risk crippling your intellect.
His statement "mathematicians are not slaves to physics" irritates me... Rather mathematicians don't need physicists but physicists need mathematical reasult...
So mathematicians make the tools which physicists use to solve problems. A mathematician doesn't need to know all the possible uses of the tool, but that it can be used to make sense of particular patterns.
no
I'm tempted to call upon the Dravidian doctrine of manifold perspectives. It tells us that no single viewpoint can fully capture the truth, that each perspective provides only a partial understanding of reality, and one must consider multiple perspectives to approach the whole truth. By attempting to pit one perspective versus another, one might fall prey to the illusion of separateness. Just as the universe is a harmonious blend of seemingly separate elements, we must realise the larger picture that both physics and mathematics are essential synergistic components in our quest for knowledge.
While I love Feynman, i disagree with him on math, math sets the foreground of logic and reason. and in doing so creates a language, a language in which physicists can later use for construction. But not only physicists but every scientific discipline needs mathematics to some level. think of a field of science as a program on your desktop, the source code of it is the mathematics, and in developing mathematics the code becomes more accurate, more diverse and simple to write. Any great level of understanding of physics and how it works depends entirely on the mathematics used to explain it.
#mathematics #physics
I don't think Feynman would disagree with what you are saying.
I actually think this is exactly what he was saying. He said mathematicians don't care about the meaning of the axioms because their language applies to many fields, universally. And he took several minutes to say that physics is understood in the language of math--he said it's unfortunate that physics is in the language of math because some people find math hard, but it just is.
***** That's not what he means. He's not comparing logic to math, he's comparing math to physics. Math IN RELATION TO PHYSICS sets the foreground of logic and reason. Math provides physics with the rules it has to live by. Physicists try to understand the world, but they have to do so in a way that does not violate mathematical laws.
***** Yes, physicists make their livings by making assumptions about reality (like "everything is zero at infinity"). But QM is all about the math. L_x, L_y, L_z are incompatible (they are not commutable) but L^2 is commutable with each one of them. Physically it's hard to even wrap your head around what that means, but mathematically it's right there in black and white. There is no denying it. You can hardly (correctly) say that QM _came_ from physical observations. In fact, exactly the opposite happened. Einstein started with some assumptions the quantum physicists were saying, and in order to ridicule them took those assumptions logically to their natural conclusion. Then it turns out, all those conclusions, which Einstein thought were absurd, turned out to be true.
All this is what Feynman is saying. Physics rests on top of mathematics, surely not the other way around.
A specific example from QM, one that I particularly love, is the orbits of electrons in atoms. When I was in high school I HATED chemistry when they started telling us about how the "orbitals" all have these bizarre different shapes. The HS chem teachers of course had no idea why. But the reason is a purely mathematical one: Spherical harmonics simply create the patterns seen in orbitals. It's just mathematically how it is, and so it's physically how it is too.
It would be sort of meaningless to argue that the physics of the spherical harmonics of an electron leads to the math that describes it rather than vice versa. Obviously both are true.
But again, I think you are missing the point that Feynman is making. He's saying that physicists are GUIDED by mathematics. Mathematicians could not care less whether there is a physical application for their math--in fact they explicitly say don't try to picture it!--physicists RELY on math to guide their research and conclusions.
And of course this is not to denigrate either one! The point of this lecture is only to say how they are different. I hate physics because it relies on this intuition of what is physically possible. Physicists hate math because it is only logical without caring about the physical implications. QM drives me up the wall because half of the proofs rely on "of course this term goes to zero at infinity."
***** What? Do you think I said something remotely implying that QM violates logic of involves something non-physical? You somehow got away from the point of this conversation. The point is that physicists make assumptions all the time when they are proving things. They assume all the time, for instance, that things are zero at infinity. They just hand-wave it.
I am certainly not criticizing it--the point all along has been that physicists and mathematicians think and see the world in a completely different way. Neither one is better or above or below the other, they are just vastly DIFFERENT.
Ok happy to say I majored in both of these although I lack applied experience in the real world :D
You know the problems on IQ tests that ask what come next, (2, 8, 16, 32, X)? Someone had to bring the numbers together in a new permutation, in the first place. Feynman was an empiricist, someone who believes that truth can be seen from observation and experiments (for example, the experiment of bringing together and analyzing a new combination of numbers). Maintaining his character in a society who in his time and since has become relentlessly rationalist, must have been extremely difficult. I think rationalist, and especially IQ proponents, have a difficult time accepting that creativity and high level problem solving come from this type 'combinatorial play', as Einstein called it. But rationalist don't have a choice. In matters of higher complexity, the novelty of the set, comes before the novelty of the operator by induction.
Feynman was ignorant. No, that's not a bad thing in any sense at all. He just didn't realize the true power of rigorous generalization when it came to physics.
Bear in mind this was back in the emerging days of Quantum Mechanics. I'd like to see him make this speech today..
R.I.P Feynman. Shine on, you brilliant diamond.
I think most physicists are tbh. Physicists quite frankly don't learn much math, and then they get along thinking that math has limited applications. But the converse is true, and you need a lot of mathematical sophistication to appreciate it.
While I greatly admire Feynman and find this talk very entertaining, his main arguments are quite off. I'm saying that as a theoretical physicist myself.
1/ The last 200 years of theoretical physics have been ultimately concerned with finding nature's underlying axioms. The principle of least action in classical mechanics is an axiom (or a consequence of equivalent axioms, like Newton's, if you will). Sure, it might be as intuitive as Euclid's parallel postulate (yet another word for "axiom"), but nevertheless, the foundations of theoretical physics are axioms. Some are more intuitive, some are less. Look at the principles of quantum mechanics. Speaking of which, Feynman is famously quoted in the context of QM with "if you think you understand QM, you don't understand it at all", and best to "shut up and calculate".
2/ Mathematicians think extremely intuitively. His depiction of the poor mathematician, slave to his mechanistic process of logical deduction is completely wrong. An excellent description of that is given by Terence Tao in a recent Numberphile video.
3/ His hope to find the "laws that turn out in the end" are philosophically unsatisfiable, see Münchhausen's Trilemma.
Who was smarter? John von Neumann, the mathematician vs Richard Feynman, the physicist?
Spaeking of raw intellect von Neumann. He was a human computer
Evi Tthought Richard
Feynman was also known for his immense calculating abilities.
Evi Tthought - A pointless comparison.
He is just like Ed Norton Love this.
Feynman was one of my idols back in the early 1970s when I was a physics undergraduate but as the years have passed I have, increasingly, come to realize that I never really understood the "Feynman Lectures on Physics" trilogy of books that my lecturers (and many others across the world) were so keen on. As a university lecturer, following a PhD, I met a guy who had attended Feynman' lectures and he admitted to me that he had the same experience and that many of his fellow students were equally baffled. I have it on good authority that Feynman himself was disappointed with the effectiveness of his lecture course. This uploaded lecture is very interesting, as anything presented by this great scientist would be, but it demonstrates, yet again, that even great minds like Feynman are capable of talking rubbish.
+Leslie Nelson I dont think he was talking rubbish. Sure it seemed more of a motivational speech than a technical one on a specific topic but his primary profession was math/physics, not oration. The real meat of this short clip, though, was the first 2 minutes in which he says (possibly indirectly) to recognize the definitions of your problems (the axioms) and in the later part where he implies to use logic to shorten your trip to the final answer.
Stephen M OK points taken-I will give the clip another try. I guess "rubbish" was too strong a reaction. There is no denying that the the great man is still capable of getting people talking about physics even after all this time. A uniquely talented scientist.