Lecture 1 | Topics in String Theory

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Stanford

Stanford

Күн бұрын

(January 10, 2011) Leonard Susskind gives a lecture on the string theory and particle physics. In this lecture, he begins by describing the theory of reductionism and then goes on to tell why string theory and other modern theories spell the end of reductionism.
In the last of course of this series, Leonard Susskind continues his exploration of string theory that attempts to reconcile quantum mechanics and general relativity. In particular, the course focuses on string theory with regard to important issues in contemporary physics.
This course was originally presented in Stanford's Continuing Studies program. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.
Stanford University:
www.stanford.edu/
Stanford Continuing Studies Program:
csp.stanford.edu/
Stanford University Channel on KZbin:
/ stanford

Пікірлер: 133
@WorldBurial
@WorldBurial 12 жыл бұрын
It's really great that Stanford puts lectures as these online. And as a bonus we're being taught by a great teacher and physicist as Susskind.
@MnM4516
@MnM4516 12 жыл бұрын
Susskind and Feynman are the best lecturers I've ever listened to, IMO.
@joabrosenberg2961
@joabrosenberg2961 3 жыл бұрын
Reductionism philosophy; Fermions and Bosons fields 6:30; Electric and Magnetic monopoles 14:15; D-Branes and F-Strings 27:00; S (Strength)-duality 32:00; String is not the right theory of the world but teaches us a lot 1:17:30;
@sfsoma
@sfsoma 12 жыл бұрын
What a great treat to have this entire course to watch. Professor Susskind is one of the best lecturers.
@Aiden057
@Aiden057 13 жыл бұрын
Leonard Susskind is such a brilliant lecturer. Thank you for posting this series.
@scorpionsdangle9
@scorpionsdangle9 12 жыл бұрын
Hello, I am 14 years old and im approching 9th grade and i dream of being a physicist. Currently i stay home and and studdy physics on the down low because my parents are too religious to understand science. I would just like to say how impressed and how outstanding your videos are, i could watch them all day. Thank you for making these lecture videos.
@channel-ug9gt
@channel-ug9gt 5 ай бұрын
physics is not bad... I have PhD in it... I like to watch videos like this before falling asleep... it gives me a "feel" for something...
@Zoro-fl2mn
@Zoro-fl2mn 27 күн бұрын
Where are you now?
@rv706
@rv706 3 жыл бұрын
"My guess is that SUSY will really be discovered at the LHC" - Hello from 2020 ;-)
@SeanMauer
@SeanMauer 10 жыл бұрын
Another Illuminating Lecture from One of Today's Top Thinkers.
@wafikiri_
@wafikiri_ 3 жыл бұрын
Among the few facts that we know for sure about reality, the following stands: things (objects, events, whatever) are not the same everywhere and everywhen. We call a (distinguishing) feature whatever thing that makes two things different. Then features of features must exist to distinguish the latter among themselves. This all leads to a lattice of things. Here Prof. Susskind tells us that sometimes we should consider some nodes in the lattice as more fundamental, others as more complex, and sometimes the other way around. The lattice becomes a network. The root of a lattice can be any node of the network: pull it up (conceptually), the rest will go underneath; the relationships between them will not vary but the view of reality we get will do.
@wafikiri_
@wafikiri_ 3 жыл бұрын
What is most fundamental, the feature that a table's cell belongs in a column or the feature that it belongs in a row? I would say both are.
@DanielFBest
@DanielFBest 6 жыл бұрын
I love you Professor Susskind
@OskourDuservo
@OskourDuservo 9 жыл бұрын
What a great lecture and what a brilliant lecturer!
@iOnline72
@iOnline72 8 жыл бұрын
Ok, I have to be honest here. Didn't get half of what was trying to explain, but couldn't stop listening.
@rav9993
@rav9993 10 жыл бұрын
Excellent Lecture....Thank you....
@PerpetualParakeet
@PerpetualParakeet 12 жыл бұрын
These are just models for description purposes. A 4th dimensional shape cannot be drawn. Imagine the end of a rod moving around on the world of a 2-dimensional flatlander. What they see is a particle moving in their 2 dimensions, and are oblivious to the rod stretching into the 3rd. If you live in 3 dimensions, a 4th dimensional rod would appear as a particle moving in 3 dimensions, but you would be oblivious to its 'rod' character because it stretches into a 4th spatial dimension.
@frankfrancia2053
@frankfrancia2053 5 жыл бұрын
So Great Professor. Thanks Stanford
@imegatrone
@imegatrone 12 жыл бұрын
I Really Like The Video Leonard Susskind gives a lecture on the string theory and particle physics From Your
@soulskies
@soulskies 12 жыл бұрын
@scout6686 the parameters are the constants which cannot be derived inside the theory but must be put from outside by experimental measurements.
@williamotule
@williamotule 8 жыл бұрын
So much the teacher I wish I had had!
@mathemystician
@mathemystician 3 жыл бұрын
Dude absolutely loves cookies.
@williamvanleuven2645
@williamvanleuven2645 3 жыл бұрын
When you go to the top of the sandwich, you come out in the bottom. IMHO, this is because the extra dimensions are curled up like the famous calabi-yau manifold, some kind of knot. You keep moving in circles.
@Dilaton100
@Dilaton100 13 жыл бұрын
A ha, cool :-))) Thanks @ Lenny Susskind and Stanford for this new Lecture Series. I`ll come back here to see all of the videos later. (still busy with the SUSY-Lectures at the moment ...) Cheers :-)))
@GreaterDeity
@GreaterDeity 11 жыл бұрын
Yes, they are ridiculous. You are the only one that has made a comment worth reading. Susskind knows this; but his job is not to give an opinion, only present the information in these type of lectures.
@abhishekchowdhuri9129
@abhishekchowdhuri9129 7 жыл бұрын
great lectures.......
@yuriobilo5400
@yuriobilo5400 Жыл бұрын
Listening to Susskind from Kenya.
@soulskies
@soulskies 12 жыл бұрын
In general relativity you have a set of differential equations which gives the local geometry=physics at every point. But there is no restriction on the global geometry. We put the global topology by hand (ex: we make the phi coordinate periodic in Schwarzschild solution to get a reasonable interpretation). Reductionism may also end in this case. Which is our priority? global or differential topology of our universe? according to reductionism local laws must completely determine the global laws.
@samsamhuns928
@samsamhuns928 9 жыл бұрын
Prof Leonard Susskind looks like Mike Erhmanntruat from Breaking Bad
@justingreen1887
@justingreen1887 9 жыл бұрын
Who?
@lazarivkov879
@lazarivkov879 8 жыл бұрын
+Sam Samhuns Agreed
@owenpeter3
@owenpeter3 8 жыл бұрын
+Sam Samhuns Actually, he looks like me!
@WhatIsGod
@WhatIsGod 11 жыл бұрын
10:43 "rotate this end around by 2 pie"..... love it. not 360 degrees but 2 pie.
@GreaterDeity
@GreaterDeity 11 жыл бұрын
That's because it is made up. But not 'made up' in the way you are thinking. Verified data can support but not really give credence to this material. This lecture is about ideas. No one said you had to adhere to it. But... you are right to a point.
@chrishawk93
@chrishawk93 10 жыл бұрын
I'm so happy I stumbled upon this, while watching something very unrelated.. :P
@jpacemen01
@jpacemen01 13 жыл бұрын
@Dilaton100 Excuse me for being curious, but which lectures are you talking about? :-)
@BrotherWoody1
@BrotherWoody1 13 жыл бұрын
Superb! Thank you.
@PerpetualParakeet
@PerpetualParakeet 12 жыл бұрын
The sandwich example is to describe a 2-dimensional reality encountering a third. One way to imagine that they only see this at small sizes is to imagine a field of cylinders, each with some small spacing between them. They form a 2d plane, and flatlanders could only see the 3rd dimension if they could examine their reality at a distance small enough to "see" between the cylinders. You just have to kind of abstractly extrapolate this to a 3d world and imagine what its consequences would be.
@lidan9805
@lidan9805 3 жыл бұрын
And the example of fermions and bosons refers, i agree fermions and bosons are the same thing. The reason of only Fermions obey Pauli Exclusion Principle (for electron case) is the numbers of available extra plane for wave functions. Since electrons (fermions) "circulate" around a massive nuclear, they are trapped in the 3d world with limited planes for motion, (i.e. 2,8,16....). For photons (bosons), they don't "circulate" around a massive nuclear, so they are not trapped in 3d world, and therefore can travel in the same energy state in higher dimensions. My point is the universe itself is (not yet proved) already a multi-dimension spacetime.... Thanks for reading =)
@flixerstudios1862
@flixerstudios1862 2 жыл бұрын
What is the difference between this lecture series and the other one on String Theory?
@boomclan5163
@boomclan5163 5 жыл бұрын
6:29 is when the lecture starts.
@soulskies
@soulskies 12 жыл бұрын
@soulskies But this is not the case in general relativity. Neither of differential laws and global topology completely determines the other. This may be the problem of gr or any field theory. Otherwise reductionism does not make sense. I wanted to point out that the reductionism may not break only for the fundamental constituents of the universe, they also could break in the way we formulate the physics: local laws.
@otonanoC
@otonanoC 12 жыл бұрын
Has anyone else noticed that this material is more fascinating than science fiction?
@Dilaton100
@Dilaton100 13 жыл бұрын
@jpacemen01 Hi all of Prof. Susskind s Lectures are available from the lower part of the Wiki page about him (search for Leonard Susskind) including the SUSY lectures I mentioned. For some reason I`me not able to post any link here :-/ ... All of the Theoretical Minimum courses are very good, I`ve checked them up to SUSY by now :-) Cheers
@scorpionsdangle9
@scorpionsdangle9 12 жыл бұрын
your great sir
@eereths
@eereths 11 жыл бұрын
you do understand that classifying philosophical terms is almost completely subjective with regards to many factors
@VishalSharmavish121989
@VishalSharmavish121989 4 жыл бұрын
I enjoyed the lecture. Can I get the mathematical equations explaining the reason why string theory need more dimensions ?? Thank you.
@lidan9805
@lidan9805 3 жыл бұрын
theoreticalminimum.com/courses/string-theory-and-m-theory/2010/fall/lecture-5
@JamesCarmichael
@JamesCarmichael 12 жыл бұрын
Well in most cases science fiction is built on real science, but its often exaggerated and theoretical material is used. A lot of science fiction (expecially these days) has to be explained to the viewer and that is when this /\ /\ /\ kind of material is very useful as it is just as or as you pointed out more fascinating than science fiction.
@MrDevin666
@MrDevin666 12 жыл бұрын
As a high school student, I really don't understand most of it because you really have to know your stuff.
@karabomothupi9759
@karabomothupi9759 Жыл бұрын
How about now?
@MatthiasBehrends
@MatthiasBehrends 8 жыл бұрын
IMHO the guy asking at 1h 11m:30s has a point that the cyclic nature of the extra dimension gives "a kind of infinity". Moving in a circle requires a (constant) change in direction, which in the first case is not necessary. Probably this is being resolved mathematically, but nonetheless a beautiful thought.
@jomen112
@jomen112 8 жыл бұрын
+Matthias Behrends It is not "probably" explained. It is a explained and was so by Susskind as well. Susskind said, but in other word, on a circle you can travel an infinite distance but the actual distance is bounded by the circle. Did you not pay notice to that?
@ThatsTooSmall
@ThatsTooSmall 11 жыл бұрын
i accidentally started playing this and Take Five by The Dave Brubeck Quartet. it's sounds cool and artsy.
@TheShenergy
@TheShenergy 11 жыл бұрын
Hi Brendon! I So wonderful to hear a youth discovering physics in an era where YOU very well could be another Newton! Keep dreaming! and doing you own homework! The library can teach you as fast as you want! Have fun! Does theory perhaps stems from dreaming?- there is no box... just keep thinking and dreaming... Have you discovered Prof Walter Lewin "For the love of physics" Have fun! I'll be watching for your theories sooner than 'they' think. Peace from Canada :)
@trajtemberg
@trajtemberg 11 жыл бұрын
What does the D stands for?
@glasswalker82
@glasswalker82 12 жыл бұрын
THANKS
@hackerisslv
@hackerisslv 11 жыл бұрын
Thinking that you understand something doesnt mean that you really understand it!
@nurlatifahmohdnor8939
@nurlatifahmohdnor8939 Жыл бұрын
What is a contour map?
@FeederForLife
@FeederForLife 11 жыл бұрын
I love the contrast between the two top comments at the moment: a critique of ignorance and retroactive reasoning among philosophers followed by "pehnut buttah sandwich".
@GreaterDeity
@GreaterDeity 11 жыл бұрын
Well, he's right. Do you disagree with him? Just a question.
@MangaFood
@MangaFood 12 жыл бұрын
"here's a 3-brane.. Ha! This isn't a 3-brane it's a 2-brane, too bad!"
@alphalunamare
@alphalunamare 6 жыл бұрын
Calculus and reductionism ... how on earth did he keep a straight face?
@CPLains
@CPLains 13 жыл бұрын
rofl. i paused to get a peanutbutter sandwich, and then as i unpause it he mentions peanutbutter sandwich within 5 seconds x)
@newtonrhodes7093
@newtonrhodes7093 2 жыл бұрын
Always a theory taught as fact. Here's a fact...water is LEVEL. No theory changes that.
@knightsofempathy6768
@knightsofempathy6768 4 жыл бұрын
Can we not agree that reductionism is also fractal in nature??
@isedairi
@isedairi Жыл бұрын
Lenny,at the LHC you will discover what!? Wrong
@FirstRisingSouI
@FirstRisingSouI 8 жыл бұрын
I can picture a 4-brane. It helps to understand that we naturally see in two dimensions, but think in 3. We naturally apply strategies to expand our 2D experience to 3D thought, and we can apply similar strategies to expand to 4D thought.
@deanrubine2955
@deanrubine2955 8 жыл бұрын
This is a great lecture series, perhaps the capstone of the Theoretical Minimum idea, bringing in ideas from statistical mechanics, quantum mechanics, special and general relativity and string theory to study black holes and the expanding universe. The focus is mostly on event horizons of black holes and expanding spacetime. They're very neatly illustrated by Penrose diagrams. We learn Dark Energy = Vacuum Energy = Constant Hubble Constant = Cosmological Constant = Exponentially Expanding Universe. Unfortunately, this series is misnamed. The only parts about string theory are in Lectures 1, 6 & 7. This one here, Lecture 1, should really be Lecture 11 String Theory and M-Theory, as it continues the ideas of Lecture 10 of that series. You could safely skip it as it doesn't have anything to do with Lectures 2 through 10 in this series. Lectures 6 & 7 derive the entropy of a black hole from string theory by considering a black hole a string and adiabatically increasing gravity, but that's about it for string theory in this series. Also be careful not to confuse these with some similarly named lecture series by Dr. Susskind.
@HigherPlanes
@HigherPlanes 10 жыл бұрын
Many highly intelligent people have little quirks like that in common.
@matharoofmaths
@matharoofmaths 12 жыл бұрын
I was the sixty-fourth person to like this. 64 is my lucky number.
@dodecapusrex
@dodecapusrex 12 жыл бұрын
Oh good, we still can't explain existence. I thought so!
@WhatIsGod
@WhatIsGod 11 жыл бұрын
you don't understand it. you think you do, but you don't. I started studying thins stuff at 12 when hyperspace came out. i am now 30 and after 3-5 hrs of this level of study a week, every week.... it is almost like i know less now then i did then. there is no understanding it there is only understanding what happens.
@tariqxl
@tariqxl 12 жыл бұрын
You did 2 paragraphs i something I know and now my brains numb lol. If you read my comment again maybe you'll pick up on the humour, maybe not. It was an attempt at mimicking the string theory in-joke, don't know if you've heard it Michio Kaku's told it plenty of times. Thanks for the reply though aim to educate and all that :)
@darrylwillard2419
@darrylwillard2419 6 жыл бұрын
According To Professor Lewin the magnetic monopole doesn't exist.
@mamjuzinnekonto
@mamjuzinnekonto 11 жыл бұрын
mike?:D
@JasonDeveau
@JasonDeveau 11 жыл бұрын
Or maybe they could zoom out a bit...
@williamcottrell72
@williamcottrell72 12 жыл бұрын
I love how wanna-be philosophers try to retroactively act as if everything that physicist discover is "obvious". Susskind is not the one confused here - his very point is that reductionism runs into difficulties and that this is a property of the particular models which physicist have been led to through research. It is not 'a priori' or obvious, since this kind of reductionism works in certain theories and not in others. Thinking that this is obvious just displays real ignorance.
@kurosenchou
@kurosenchou 11 жыл бұрын
i was wrong, watching TBBT does not make me understand this
@sterbenthanatos8549
@sterbenthanatos8549 7 жыл бұрын
Bosons are more fundamental....how is that even a question?
@XCyclonusX
@XCyclonusX 11 жыл бұрын
Could we just be going down a mathematical rabbit hole? That the simple math leads us to more complex math to more complex until we're trying to shape reality simply to please a mathematical equation. What if the is a particle we can go down to say a quark, and that 3 dimensional quark is made up of nothing smaller. Its simply a pure quark, and when we break it apart we're not freeing smaller particles just shards of quarks. BTW, I love string theory, and totally believe it.
@kn123able
@kn123able 11 жыл бұрын
he defines reductionism wrong. A theorem is reductionist if for example its supposes that the genetic determinism is to be explained only by quantum mechanics and the biology has to be excluded.as an explanatory tool --> such a theorem would reduce the biological level to the quantum physical level.
@MarcoAurelio-vb9hl
@MarcoAurelio-vb9hl 10 жыл бұрын
If my math is right then you should already be 15 years old or become 15 soon enough. How are your physic studies going? Did you stick with it? :)
@1isaacmusic
@1isaacmusic 12 жыл бұрын
That's a pretty thin sammich. I want my money back.
@ddavyCn
@ddavyCn 11 жыл бұрын
Peanut Butter with Jelly Sandwich
@gogoteca
@gogoteca 9 жыл бұрын
Funny how most of the comments for this video have nothing to do with physics.
@sterbenthanatos8549
@sterbenthanatos8549 7 жыл бұрын
I'm confused as to why the question of "usefulness" is being discussed in the context of developing fundamental physical models - this attitude strikes me as being a significant stumbling block to theoretical physics in the modern era. The founders of quantum mechanics were able to make such genius breakthroughs because they cared about developing elegant and simple models of Nature. There is a very practical reason why the primary goal of theoretical physicists should be elegance - a simple and elegant model at the core of a theory acts as a guidepost in developing more useful models, so physicists can branch out and be creative without losing their bearings. Without a well-defined foundation physical model that one can point to and say "that's what Nature _really_ is," (again, by definition) the physics community is doomed to wander around in the dark always just groping for a slightly more useful model. In this process, a lot of _really good ideas_ will go unnoticed because the community lacks a coherent framework of terminology with which to evaluate exactly how newly proposed models fit into the overall theory. The theoretical physics community has turned into a stampeding mob of half-baked mathematicians who are more interested in playing with big shiny "super" toys (SO(10), E8xE8, etc.) than they are in understanding Nature's secrets.
@tariqxl
@tariqxl 12 жыл бұрын
And this is why I've never quite got string theorists... The mathematics tell them the universe has to have 11 dimensions the observers say well I only see 3 so one scientist tries to cheat and says well if i have this 3d piece of bread and put some 3d filler then another 3d pieces of bread on the top we have a multidimensional universe... No u have a 3d sandwich
@homekatsushi
@homekatsushi 6 жыл бұрын
I want to study the “M theory”! But, Wait, I like a little different idea because I don’t like the basic idea of the “STRING”. Everything from physical universe, galaxy, our solar system, earth and moon, to molecules, atoms, subatomic particles, elementary particles, and quantum world have(there is a notion of spin) notion of rotating or spinning in common. Why we can’t express in the term of spinning or rotation, not sting. Considering the idea of spinning (rotating) leads naturally to a concept of spins (classical mechanics). I feel like more natural direction than going with the string. Can anyone develop a new little different theory from the string( or M-theory)?
@Dyslexic-Artist-Theory-on-Time
@Dyslexic-Artist-Theory-on-Time 13 жыл бұрын
Could quantum mechanics represent the passage or Arrow of Time? This theory is based on just two postulates, 1.The first is that the quantum wave particle function explained by Schrödinger’s wave equation represents the forward passage of time or Arrow of Time itself photon by photon, quanta by quanta or moment by moment. 2. The second is that Heisenberg’s Uncertainty Principle that is formed by the wave function is the same uncertainty we have with any future event.
@davidwilkie9551
@davidwilkie9551 2 жыл бұрын
Suffixes ist and ism, "when I attended School" meant "a tendency towards", so very much like "prone to Opinionated, unsubstantiated Assumptions and Pronouncements" in the vernacular. Eg "Quantum Mechanics is weird and mysterious", is just plainly ill-informed. Speculation reduced to the minimum observation of what, how and why the Universe is as it is, was the theme of Henri Bergson in regard to Time Duration Timing phenomena. So Reducing observables, a pure-math activity in Thought Experimentalist's Intuitions is a recognition of Euler's Intuitions and Conjectures that were left open for Physicists to Research in conjunction with Mathematical Disproof Methodology.., recognising Logarithmic Time, in Evidenced Communication universally by AM-FModules of temporal mechanics wave-packaging formation, as Dr Disney has stated, (Theoretically) The self-defining sum-of-all-histories here-now-forever observational statements in Theoretical observational research corresponds to discovery of the Holographic Principle Imagery projection-drawing Actuality.., Logarithmic quantization coordination-positioning in Quantum-fields of Temporal continuity Fluxion-Integral, Superposition-point Superspin, "Mathemagical" Calculus.
@Roccdrummer
@Roccdrummer 10 жыл бұрын
What if none of it exists?
@apburner1
@apburner1 10 жыл бұрын
Nice troll you did there.
@eereths
@eereths 11 жыл бұрын
Ok Einstein... When you disprove one of Stephen Hawking's theories and become a physics professor fluent in string theory come back to me...
@computergenius365
@computergenius365 5 жыл бұрын
when did mike from breaking bad get a physics degree?
@amany247
@amany247 Ай бұрын
No god but Allah Islam way for peace and real monotheist Search about the truth with honest heart And first ask Allah to help you to find the way
@TJae1
@TJae1 13 жыл бұрын
I can't b-lieve this appeard on pier-ro's channel ~ soberity suxs & can b boring ~ thus ~ pyrrho314 is attempting to bridge the invigorating world of intoxication w/ boring yet enlightening wrld of science all w/ camtwist effects w/ sound effects 2 match ~ chck it out
@kn123able
@kn123able 11 жыл бұрын
you dont have to be einstein in order to classify philosophical terms properly. ironically you are the one declaring her/himself as the authority of physics.
@functiontopacket339
@functiontopacket339 4 жыл бұрын
God doesn't play spillikins ... ;-)
@1isaacmusic
@1isaacmusic 12 жыл бұрын
What does a Zombie String Theorist say ? " Braaaaaaaaaaannneesssssssssss "
@rmerkle1
@rmerkle1 11 жыл бұрын
Type "True Theory of Everything Quadrant Model of Reality 1" into KZbin for the Truth.
@111tato
@111tato 12 жыл бұрын
I have the same jacket, he has. Imma scientist
@Dyslexic-Artist-Theory-on-Time
@Dyslexic-Artist-Theory-on-Time 11 жыл бұрын
Not spam! In the mathematics of Hugh Everett Many Worlds interpretation the different universes or dimensions are all at right-angels to each other! In this theory they are just future possibilities in our one three dimensional Universe of continuous creation or energy exchange. The mathematics remains the same! They are at right-angels to each other because EM field are always at right-angles to each other as a process of continuous change as time unfolds.
@wolfpack9425
@wolfpack9425 11 жыл бұрын
im 15 years old and understand this but when i showed this to my science teacher at school he was totally lost lol
@CHeCKEyE5
@CHeCKEyE5 11 жыл бұрын
Camera has to stop following him every where on every move. Almost nauseating.
@Roccdrummer
@Roccdrummer 10 жыл бұрын
They've gone insane.
@zielon3r
@zielon3r 10 жыл бұрын
He's mad.
@Dyslexic-Artist-Theory-on-Time
@Dyslexic-Artist-Theory-on-Time 11 жыл бұрын
This is an invitation to see an alternative view! Where the different dimensions of String Theory are just future possibilities in our one 3D Universe Based on: 1 Is that the quantum wave particle function Ψ or probability function represents the forward passage of time itself photon by photon 2 Is that HUP ∆×∆p×≥h/4π that is formed by the w-function is the same uncertainty we have with any future event within our own ref-frame that we can interact with turning the possible into the actual!
@Roccdrummer
@Roccdrummer 10 жыл бұрын
When did science become faith based and "magical" and "this is where it gets crazy" in his own words?
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Lecture 1: Introduction to Superposition
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MIT OpenCourseWare
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