I love how he brings us all in to his decision making process. Very Feynman, how cool to see this in action from a personal friend of his. Top level Physicist & a guy you'd want to have a beer with, all in one.💯
I'm more intrigued by the question of why is there a book "exploiting online games" on the shelf? Next to Organic chemistry and Design Patterns. Elements of reusable object-oriented software. Who lives in this apartment? Computer geek, biochemist, WoW farmer?
It's usual for a physics department to have a common room for the students to hang out during lunch and to study in during afternoons. In those type of rooms it is common to have a bookshelf where its meant for you to leave your old textbooks for new students. Since it's a social room the books left on those shelves are usually off topic as well.
@@nicolascalandruccio He may be referring to the smoothness problem perhaps? It's not that there is an "error" or "paradox," just that we haven't been able to prove that a smooth solution (continuous/differentiable everywhere) to the N-S equations always exists for 3 dimensions (we have proven this to be true for 2D). However, this is mainly a theoretical problem in mathematics, not physics. Physicists and engineers can use the crap out of the N-S equations without ever knowing or caring whether this problem is solved :)
Navier Stokes. Only because as a M.E. I have wrestled with them and pretty much lost. They can be coupled with Maxwells equations to study magnetohydrodynamics. I've got a headache now....
Almost like being asked to pick your favorite constant. π? e? 0 or 1? The golden ratio, φ? Or maybe one of the less obvious constants with a deep meaning such as γ, or the Feigenbaum constant, or i?
Little steps, quanta or infinitesimals, are the modulated pulse of Calculus, and the Universe is connected in one mathematical format from which the conception of symmetry and equality of division within unity form all these equated formats as aspects of infinity by 1-0 axial-tangential, angled orthogonality of these .dt infinitesimal sum-of-al-histories QM time duration pulses in superposition, compound conception of calculus in infinities of infinities-> unity. Either it's all beautifully integrated or an incomprehensible mess, depending on how you see the Math.
Deterministic theory of quantum computing function will be the best theory and Schrodinger's equation of the wave function is the best differential equation for now.
Beautiful reply by beautiful mind.... The equations asked here are elegant and master equations depicting the fundamental reality of nature. All four equations hold their importance in their realm of knowledge.
Could it not be argued that differential equations may also be describing 'discretely' by summing the function into epsilon intervals approaching infitessimally small or finitely massive - in the 'limit', and that the 'continuous' function could be the smoothed out resultant of something that is made up of fundamentally discrete Planckian steps?
By itself, F = dp/dt is not a differential equation. You need a specific system. For example, "Hooke's Law" dp[t]/dt = -k x[t] is a differential equation.
The questioner did not mention Lagrangian which describes both classical and quantum level conservation. Maxwell's equations describes e/m fields, but Einstein's field equations does not describe gravitational fields, but only say its geometrical structure. If I were asked the question, I would side with Maxwell. I do not remember the famous man who said that after ten thousand years, physicists would look back, not to praise Einstein, but Maxwell. Perhaps it provides us with the direction of the theory we still do not know.
"Is the final theory going to be described with a differential equation?" All quantization arises from boundary conditions of a differential equation, Dr. Susskind. "All" is a big claim, but I stand by it. All we see, touch, taste and feel are waves. There are no particles. In the entire universe, there isn't a single particle, only waves. And when those waves are discretized, it is due to boundary conditions, not inherent in the underlying constituent phenomena. The answer is "Yes."
I'm surprised he didn't mention the Euler-Lagrange equations. Despite being a pure mathematical tool, they lead to the equations of virtually every physical theory that we know of.
Which differential equation changed physics most? Newton's law of gravitation. (It may not look like a differential equation at first glance, but force is the time derivative of momentum). This was the first instance of a universal quantitative law of physics.
As a vector, F=dP/dt. It is only that case that F=ma when the mass doesn't change. (An example of when mass changes, is in an aircraft applying thrust.)
EL equation has almost the same content as Hamilton’s Equation, and Newton’s equation is only a small subset of EL equations and Schrödinger’s Equation. You are not correct, Newton’s equation is a special case of Hamilton’s Equation(it’s a reformulation of Classical Mechanics), but it encompasses all of Physics, QM, QFT, SR, GR.... and Hamilton’s Equations are vector-less, Everything is written in terms of energy
They are parallel but equivalent formulations. Newton's formulation is very hard to apply in complex systems. Hamilton's equation and E-L equation are much easier to apply. The energy and action principle underlies all of Physics. But in action principle, 'kinetic energy minus potential energy' is the Lagrangian so it's abstract. Hamiltonian is just total energy. So picking up Hamilton's equation is quite justified. But I repeat, these all are equivalent.
Alex, What do you mean? There is no reason not to suppose that F=ma instantaneously at all points, even as the fuel is going out the back -- modulo only the notion that the mass of the aircraft is increasing as it acquires momentum.
by his own words he didnt defeat him. he rather found an answer to a question that hawking asked. an answer that differed from the implications of of hawking's question. now, i am far from qualified to answer this in details but i think i got it right
If you want to blow your fucking mind, read Aristotle's Physics and then listen to what Leonard Susskind says at the end of this video. Modern physics has answered a lot of questions, yet, in a way, it hasn't answered anything at all.
Yes, indeed space and time are discrete and are consisting of metrons. This is exactly how Burkhard Heim proposed long long time ago. The world is made up of a highly complex quantizied geometrodynamics and its mathematics is discrete.
@@sixsoxsex1 In a manner of speaking, yes, but it is a mutual dependency. Recall that energy is a property of matter, and most fundamentally, matter is made of fermions and bosons. Specifically, it is the exchange of bosons between fermions that form the basis of any energetic interaction or phenomenon, regardless of whether it is in kinetic or potential form. This material energy can be thought of as being "positive", as opposed to the "negative" energy property of spacetime. As Prof. S. W. Hawking pointed out, "In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero." What this implies is quite profound! There is a deep relationship between matter and spacetime that we are still trying to figure out. It could be the ultimate yin-yang principle of physical reality itself, the ultimate "conservation" or "symmetry" if you will.
I think he was taking a differential equations course. He said something about modelling something in differential equations near the end, so I think it's just on his and his classmate's minds.
It's kind of like this comment section... Some of these people are saying some really weird things LOL! Like, just spouting off random equations and some of them make no sense why someone would say that. It's just because that's a big deal to them at the time. Someone even put the equation for velocity as the most important one XD
By contrast, and assuming the arbitrary Philosophers view point at the analytical (cause-effect) origin-vanishing point of all information, ..in my totally unqualified opinion, (neither qualified or quantified), ..Schrodinger's Equation. Because, by implication, it says that "discrete" is the delusion of separateness, unless it's qualified and quantized like the elements of sets. The ultimate reality.., of Calculus, is the infinitesimal instant, .dt in the wave of eternal history Phi, the identity of position in infinite connection. ***** Over the passing of relative-timing experiences, ..all in THE discrete eternal event Interval, one automatically starts asking awkward questions about how past-future distribution of such revealed memory associations should be reintegrated and represented. The ultimate sum-of-all-histories is Zero-infinity nothing, integrated by Singularity positioning into Absolute Zero Kelvin i-reflection containment, vanishing-into-no-thing-> Perspective, or WYSIWYG @.dt e-Pi-i infinitesimal Fluxion-Integral Temporal Calculus-Principle.., depending on POV fixed definitions of Convention or sequences of pure-math actions. In other words, is continuing to show intermittent progress in concept development useful, or adding to the difficulties of thinking for yourself? Professor Susskind's lectures at least have a particular study objective and is the preferred resource of research materials.
I love how he brings us all in to his decision making process. Very Feynman, how cool to see this in action from a personal friend of his. Top level Physicist & a guy you'd want to have a beer with, all in one.💯
I'm more intrigued by the question of why is there a book "exploiting online games" on the shelf? Next to Organic chemistry and Design Patterns. Elements of reusable object-oriented software. Who lives in this apartment? Computer geek, biochemist, WoW farmer?
Mr. Susskind is bronze elo
It's usual for a physics department to have a common room for the students to hang out during lunch and to study in during afternoons. In those type of rooms it is common to have a bookshelf where its meant for you to leave your old textbooks for new students. Since it's a social room the books left on those shelves are usually off topic as well.
the best "differential equation": d/dt \int^t ds f(s) = f(t). Your solution can "never" be wrong.
I liked Leonard Susskind. I hated it when Heisenberg shot him in his car :'(
holy shit lol this took me way too long
I don't get it
You're sure you're not thinking of Werner Erhardt?
Huh?
He's referring to Mike Ehrmantraut.
Leonard Susskind was one of the best things about Community's later seasons.
Ends with him holding his coffee, tea, or whatever he's drinking like a pimp. Any Theoretical Physics students has got to love this guy.
He's definitely an O.G.💯
i love Leonard Susskind. Him and Lee Smolin are my favourites
Nice interview of a legend. I'm so sad that Navier-Stokes and Boltzmann have been forgoten btw
aren't Navier Stokes incomplete? They have some errors/paradaoxes right?
@@Alen1000Pro What do you mean exactly by incomplete, errors and paradoxes?
@@nicolascalandruccio He may be referring to the smoothness problem perhaps? It's not that there is an "error" or "paradox," just that we haven't been able to prove that a smooth solution (continuous/differentiable everywhere) to the N-S equations always exists for 3 dimensions (we have proven this to be true for 2D). However, this is mainly a theoretical problem in mathematics, not physics. Physicists and engineers can use the crap out of the N-S equations without ever knowing or caring whether this problem is solved :)
Navier Stokes. Only because as a M.E. I have wrestled with them and pretty much lost. They can be coupled with Maxwells equations to study magnetohydrodynamics. I've got a headache now....
I was asking myself what the worst differential equation is and immediately Navier-Stokes came to mind.
Navier Stokes is only Newton's Second Law in Halloween costume.
When I look at the generalized Navier-Stokes equation: I say ''this doesn't look like anything to me''
And then you have relativistic magnetohydronamics.
*head explodes*
Almost like being asked to pick your favorite constant. π? e? 0 or 1? The golden ratio, φ? Or maybe one of the less obvious constants with a deep meaning such as γ, or the Feigenbaum constant, or i?
PenguinF pi. Easy choice
the way he delivers the line "if I knew the answer to that, I would publish it", unreal
Little steps, quanta or infinitesimals, are the modulated pulse of Calculus, and the Universe is connected in one mathematical format from which the conception of symmetry and equality of division within unity form all these equated formats as aspects of infinity by 1-0 axial-tangential, angled orthogonality of these .dt infinitesimal sum-of-al-histories QM time duration pulses in superposition, compound conception of calculus in infinities of infinities-> unity. Either it's all beautifully integrated or an incomprehensible mess, depending on how you see the Math.
You definitely wrote all of that. There it is. The thing you wrote.
Deterministic theory of quantum computing function will be the best theory and Schrodinger's equation of the wave function is the best differential equation for now.
Beautiful reply by beautiful mind....
The equations asked here are elegant and master equations depicting the fundamental reality of nature. All four equations hold their importance in their realm of knowledge.
I love Susskind even when I disagree with him.
somehow I would also add Bolzman's formula to those four.
Statistics one?
i love his answers
The Best Differential Equations is yet to be discovered.
every system figured out and explained is important.
Could it not be argued that differential equations may also be describing 'discretely' by summing the function into epsilon intervals approaching infitessimally small or finitely massive - in the 'limit', and that the 'continuous' function could be the smoothed out resultant of something that is made up of fundamentally discrete Planckian steps?
The best differential equation is F = dp/dt. without that, we would have lagrangians or hamiltonians.
The Lagrangian or Hamiltonian approach is actually easier and much more useful.
Not the best, but IMO the one that really changed physics, also considering Newton had to invent calculus first.
Newton had to invent Calculus for describing the Solar system. Did he discover Calculus even before this formula? I don't know.
Don't leave out Leibniz!!
By itself, F = dp/dt is not a differential equation. You need a specific system. For example, "Hooke's Law" dp[t]/dt = -k x[t] is a differential equation.
The questioner did not mention Lagrangian which describes both classical and quantum level conservation. Maxwell's equations describes e/m fields, but Einstein's field equations does not describe gravitational fields, but only say its geometrical structure.
If I were asked the question, I would side with Maxwell.
I do not remember the famous man who said that after ten thousand years, physicists would look back, not to praise Einstein, but Maxwell. Perhaps it provides us with the direction of the theory we still do not know.
I agree about the Lagrangian. But I don't think great physicists will try to pick one set of equations over another. They want them all. ;-)
Lagrange's formulation can be derived from Hamiltonian mechanics.
Maybe, but I am not aware of it. Leonardo mentions how Lagrange's formulation applies to quantum mechanics, making it special.
4m30s "the world is really discrete" BOO! BOO! I'm a CONTINUOUS believer!
3:20 They don't "govern" but merely describe a special class of phenomena...
"Is the final theory going to be described with a differential equation?" All quantization arises from boundary conditions of a differential equation, Dr. Susskind. "All" is a big claim, but I stand by it. All we see, touch, taste and feel are waves. There are no particles. In the entire universe, there isn't a single particle, only waves. And when those waves are discretized, it is due to boundary conditions, not inherent in the underlying constituent phenomena. The answer is "Yes."
I'm surprised he didn't mention the Euler-Lagrange equations. Despite being a pure mathematical tool, they lead to the equations of virtually every physical theory that we know of.
dN/dt=kN easy to solve easy to use ;)
Yeah, I fuck with that!
It's a "how to do physics with a hammer" type of equation
N = Ce^(kt)
My best professor
Thatvwas a hreat moment for some great questions, thank you.
Which differential equation changed physics most? Newton's law of gravitation. (It may not look like a differential equation at first glance, but force is the time derivative of momentum). This was the first instance of a universal quantitative law of physics.
What about the Euler Lagrange equations? Or Newton's second law? Without F=ma, we wouldn't have hamiltons equations, or the rest of physics
As a vector, F=dP/dt. It is only that case that F=ma when the mass doesn't change. (An example of when mass changes, is in an aircraft applying thrust.)
EL equation has almost the same content as Hamilton’s Equation, and Newton’s equation is only a small subset of EL equations and Schrödinger’s Equation. You are not correct, Newton’s equation is a special case of Hamilton’s Equation(it’s a reformulation of Classical Mechanics), but it encompasses all of Physics, QM, QFT, SR, GR.... and Hamilton’s Equations are vector-less, Everything is written in terms of energy
Newton's second law is the father of analytical dynamics and therefore I'd say it is at the top.
They are parallel but equivalent formulations. Newton's formulation is very hard to apply in complex systems. Hamilton's equation and E-L equation are much easier to apply. The energy and action principle underlies all of Physics. But in action principle, 'kinetic energy minus potential energy' is the Lagrangian so it's abstract. Hamiltonian is just total energy. So picking up Hamilton's equation is quite justified. But I repeat, these all are equivalent.
Alex, What do you mean? There is no reason not to suppose that F=ma instantaneously at all points, even as the fuel is going out the back -- modulo only the notion that the mass of the aircraft is increasing as it acquires momentum.
Schrödinger's equation is the key of today's electronics and communication technology!
Feynman still holds record at Princeton? Not sure. Very nice Shalom
Great talk
Thanks
love the conclusion >
I discovered something AMAZING...pretty impressive
where is full pdcast please?
Hope I get to meet this guy someday in the near future. :)
radwizard i dont
I don't care dude.
Just want to say that I am one of those people. :)
3:34
Spam
a^2 + b^2 = c^2 im smart 😎😎😎
The boss who defeated Hawking
AlphaOmega I just found out about this awesome dude. Tell me the story
Tell me more, or at least a link to read about this please
by his own words he didnt defeat him. he rather found an answer to a question that hawking asked. an answer that differed from the implications of of hawking's question. now, i am far from qualified to answer this in details but i think i got it right
@AlphaOmega in which topic did he "defeated" him?
They are talking about the blackhole war ie the paradox of information loss in a blackhole.
It has to be the wave equation. Just because everything in the universe vibrates.
V=dx/dt
shook one That’s a definition
My man Leonard with the book on Exploiting Online Games.. lmao
watching his lectures for years now, but for the first time i see that he has blue eyes ... O.o
Bit of a John Malkovich thing going on?
Bad Boy Of Physics
Susskind Bad Boy? No... That would be Feynman.
@Ken MacDonald The term was used in a humoristic way... We are talking about scientists here, not the Mexican mafia.
What????
thats the breaking bad old badass man?
you can tell when the interviewer asks just the right question
If you want to blow your fucking mind, read Aristotle's Physics and then listen to what Leonard Susskind says at the end of this video. Modern physics has answered a lot of questions, yet, in a way, it hasn't answered anything at all.
John Malkovich lookalike!
Why don’t they teach us about the match of protons and neutrons? Too dangerous?
What do you mean by the match?
Yes, indeed space and time are discrete and are consisting of metrons. This is exactly how Burkhard Heim proposed long long time ago. The world is made up of a highly complex quantizied geometrodynamics and its mathematics is discrete.
See ùbrian ùgreene
how mass curve spacetime?
abcd Imho, might by stretching in
fabric of spacetime into center of the mass.
Any form of energy including mass is reflected in the curvature of spacetime. IOW, without spacetime curvature there would be no energy!
@@kenlogsdon7095 Interesting! The inertial mass effect is also due by spacetime curvature?
@@sixsoxsex1 In a manner of speaking, yes, but it is a mutual dependency. Recall that energy is a property of matter, and most fundamentally, matter is made of fermions and bosons. Specifically, it is the exchange of bosons between fermions that form the basis of any energetic interaction or phenomenon, regardless of whether it is in kinetic or potential form. This material energy can be thought of as being "positive", as opposed to the "negative" energy property of spacetime. As Prof. S. W. Hawking pointed out, "In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero." What this implies is quite profound! There is a deep relationship between matter and spacetime that we are still trying to figure out. It could be the ultimate yin-yang principle of physical reality itself, the ultimate "conservation" or "symmetry" if you will.
this interviewer is obsessed with diff. equations
Paulo Constantino So am I.
Yet it appears he doesn't know anything about them.
I think he was taking a differential equations course. He said something about modelling something in differential equations near the end, so I think it's just on his and his classmate's minds.
It's kind of like this comment section... Some of these people are saying some really weird things LOL! Like, just spouting off random equations and some of them make no sense why someone would say that. It's just because that's a big deal to them at the time. Someone even put the equation for velocity as the most important one XD
@@markhernandez9746
Why would it appear as he knows nothing about them?
You wait for a how.
There is something wrong with this comment section, the amount of wackos and people who don't know what they're talking about is overwhelming.
@Ken MacDonald
Hm? Just read it, there are < 100 comments. Won't take even an hour. If you don't agree, I don't give a shit.
Kid named finger
"They're not my children". Oops
einstein field equations are not differential equations
Yes they are
Nitpick: Heinrich Hertz proved the nature of light, not James Maxwell ... no love for Navier-Stokes here, bunch of amateurs ...
he doesnt give a straight answer to anything just beating around the bush 😂
By contrast, and assuming the arbitrary Philosophers view point at the analytical (cause-effect) origin-vanishing point of all information, ..in my totally unqualified opinion, (neither qualified or quantified), ..Schrodinger's Equation. Because, by implication, it says that "discrete" is the delusion of separateness, unless it's qualified and quantized like the elements of sets.
The ultimate reality.., of Calculus, is the infinitesimal instant, .dt in the wave of eternal history Phi, the identity of position in infinite connection.
*****
Over the passing of relative-timing experiences, ..all in THE discrete eternal event Interval, one automatically starts asking awkward questions about how past-future distribution of such revealed memory associations should be reintegrated and represented. The ultimate sum-of-all-histories is Zero-infinity nothing, integrated by Singularity positioning into Absolute Zero Kelvin i-reflection containment, vanishing-into-no-thing-> Perspective, or WYSIWYG @.dt e-Pi-i infinitesimal Fluxion-Integral Temporal Calculus-Principle.., depending on POV fixed definitions of Convention or sequences of pure-math actions.
In other words, is continuing to show intermittent progress in concept development useful, or adding to the difficulties of thinking for yourself?
Professor Susskind's lectures at least have a particular study objective and is the preferred resource of research materials.