I have no diplomas, --> bad student and lack of maturity when I was a teen. Yet I found a thirst for knowledge in my 20s, decided to start from scratch all the science and math. Two years ago I finally reached the confidence to start learning about quantum physics. I bought the book, did the math on paper It's been my only book for two years I never skipped a page until I was fully able to play and understand the mechanics involved. I watched the lectures many Times. And I come here just to say thank you. Unfortunately I'll never work in physics, I am too old and still without a diploma, I have managed to make a great career in IA and machine learning. To each his own path eh? Living in this era of knowledge, where you can learn from home, find communities to help you improve, is the greatest gift we have. Stanford and Leonard Susskind I thank you again for making this class available and henceforth contributing to what is the best about the world we live in. I felt, even though this video is old, that a heartfelt comment here was needed. Thank you again. (a friendly Swiss fellow)

@feuzzionarts8129

8 ай бұрын

That’s…fascinating..!!}

@vincenzopanella2705

8 ай бұрын

Complete an high school diploma at least

@fra2025

5 ай бұрын

Wow!

@lucasmcguire1554

4 ай бұрын

Hey that's really interesting! Do you have some sort of contact details? I'd love to see how you are progressing

@user-tw2du9yz2c

4 ай бұрын

I've wanna praise your efforts to get more richer knowledges despite any obstacles You've have been through. Good Job! man!

Lecture 1 0:00:00 to 0:11:35 - Transition from classical to quantum mechanics 0:11:35 to 0:20:00 - The state of a system in classical mechanics 0:20:00 to 1:01:21 - The results of measurements on a qubit 1:01:22 to 1:15:10 - Vector space 1:15:11 to 1:24:12 - Dual of the vector space 1:24:13 to 1:46:31 - Inner products

@Haheat

3 жыл бұрын

50:00 cookie break

@pushanpore8365

3 жыл бұрын

great

@ricardo_boutique

2 жыл бұрын

@@Haheat thank you for that pearl

@NazriB

2 жыл бұрын

Lies again? Take Meds

@adammac.1342

Жыл бұрын

Thank you 😊

I'm surprised and pleased that this is online. I bought the Kindle book a few months ago, without knowing there is a set of free online lectures by the author. Thank you to Stanford and Leonard Susskind for making these lectures available.

@christopherplessinger4664

5 жыл бұрын

Yeah, but this is quantum mechanics minimum. The book covered classical mechanics.

@OlliWilkman

5 жыл бұрын

My path with the Theoretical Minimum is a bit random: I bought the quantum mechanics book at a whim in a bookstore, but then I first watched the classical mechanics video series, ordered the two other books online, then read the classical mechanics book, then started reading the special relativity book, but after a few chapters switched quantum mechanics book and having read the first third I now started watching this video series… On the other hand, I studied all this stuff at university, so it's familiar, but it was over ten years ago and I've forgotten a lot.

@speedcuber103

3 жыл бұрын

Christopher Plessinger there is a book for quantum mechanics too

@paddymcdoogle6753

2 жыл бұрын

Santa is that you?

@RalphDratman

2 жыл бұрын

@@paddymcdoogle6753 Of course, my child, it is me.

I have no clue what any of this means but for some reason I’m fascinated by hearing him talk so I’ve nearly finished the whole thing

@razza9647

2 жыл бұрын

Same here

@cryptic6969

2 жыл бұрын

Keep trying to hear and you shall hear. For your effort i say, “ Good Job.”

@victorvaca7429

2 жыл бұрын

At least you stayed

@majensen2007

2 жыл бұрын

Why no share button?

@jimc.goodfellas226

2 жыл бұрын

Dom great channel my friend, keep listening that's where I started and now I am learning more science/physics than I ever did in school

Special thanks goes to camera operator, who predicts all the movements not even causing a real headache.

@akash_goel

5 жыл бұрын

yeah, i would love to see the setup that was done to record this!

@yomamafatoshi

5 жыл бұрын

and to the sound person too!

@hishamhittini5069

4 жыл бұрын

I think it is a system guided camera called lecture tracker camera, equipped with sound systems that activate or deactivate mics across the room

@jlowe8059

3 жыл бұрын

I agree, this was really well filmed.

@itchyandscratchy7350

2 жыл бұрын

Pretty sure it’s an AI.

Tks Stanford, what a privilege to listen to this. And Susskind is an amazing teacher. I'm blown away by getting a glimpse into the theoretical minimum which I knew little or nothing about.

@peterkay7458

7 жыл бұрын

He really is and it takes one to know one. I totally disagreed with the final outcome of the black hole wars so I had to eat a lot of crow when i finally understood it. Totally worth it to have an insight into string theory.

@sherlockholmeslives.1605

5 жыл бұрын

He is actually quite a knowledgeable man, Leonard Susskind. I can grasp Plato's 'Wax Tablet Hypothesis', Aristotle's 'Theory of Everything' and Goethe's 'Theory of Colours' but these lectures are beyond me. Cheers - Mike.

I really enjoy Susskind's lecture because even as a practitioner and expert, I like how he gets to the heart of the physical idea and it is wonderful that he is taking the time and effort to educate in this venue for continuing education.

NOTES: Systems have states A set of states can include subsets Inclusive (union) and exclusive (intersection) propositions can be made The space of the states of a system in QM doesn't follow the set logic It's a vector space An apparatus detects the status of Q-bit that like a coin (with H and T) could be in two states , 1 for pointing up or -1 for down, only one of them at any given time Both the apparatus and the Q-bit have a sense of direction of their own The directions of the apparatus and Q-bit in relation to one another, determines and changes the probability of the results Observing the system once prepares the result and will give you the same answer until the detector has been turned off and on again, If the internal vector of the apparatus lies in the same axis as the Q-bits we get the same answer over and over again, which is its component, meaning if we rotate the apparatus 180 deg, we get -1 in which the negative sign indicates the opposite direction Also even when we start with the apparatus on it's side (internal vector and Q-bit are in different axes) results are the same as long as the system is not disturbed. However 90 deg rotation of the apparatus around any axis makes the results random with probability of 50% for each, averaging at 0 Results of an angled apparatus are also random but they average in the component of the initial axis along the rotated internal vector (Cos of the angle apparatus makes with its initial axis) Mathematical vector space contains objects that aren't ordinary Vector space is a collection of mathematical objects In the vector space numbers are one dimensional and complex numbers are two dimensional Vector a is written as: |a> You can add vectors: |a>+|b>=|c> Vectors could be multiplied with complex numbers in the complex vector space: z|a> = |a'> Vector's components are represented in the form of columns in brackets Addition: n'th row of one column adds to the n'th of the other Multiplication: the number is multiplied with all of the rows in the column Complex conjugate vector that has a one to one correspondence with its elements Complex conjugate vectors lies in complex conjugate vector space Duel of a vector sum is the sum of their individual duels Duel of a vector |a> multiplied with a complex number z is ) = = α1. β1* + α2. β2* = = α1*. β1 + α2*. β2 Using postulate (1) must be true that: = * which means it's always real (its imaginary component is zero so the conjugate doesn't change it) and always positive (the real part is being multiplied by itself), resulting in the square of the vector's length (using Pythagorean theorem) T = * = α1.α1* + α2. α2* The orthogonality causes the inner product to be zero (because: cos 90 deg=0) Maximum number of mutually perpendicular non-zero vectors in a space determines the dimension of it

@BennettAustin7

4 жыл бұрын

good stuff, the ones I took are similar as well

@AniSepherd972

2 жыл бұрын

you are legend

@5:14 what an awesome sermon. I am loving these lectures. I am pissed that, in my far reaches of the world, this exposure and influence has been denied me via my class, cast, socio-econ, and generational & physical demographic. More knowledge. more brains. I am hungry to intuitively know more. I love Educaton X Generation :D Thank you Stanford and Prof+Team

I can't say Thank You enough. It's been a year since I started with this course and now I am learning to apply all of this in my Quantum Computing course. To whomever this concerns: the explanations and tricks (not really) that you're gonna learn here will stay with you your whole life. Its THAT clear. Thank You Professor Susskind and Stanford University for this. ALWAYS and FOREVER.

I love that Lenny is so old-school that no matter how white the white board is, he still calls it a "blackboard."

@wafikiri_

3 жыл бұрын

The 'black' in blackboard does not mean the black colour any longer. A blackboard, whatever its colour, always is a blackboard. Or do you think an atz has to be made of stone just because, since millenia ago, atz means stone?

@heath8358

3 жыл бұрын

@@wafikiri_ That may be true but a white board is still called a white board and not a black board

@abbyh5158

2 жыл бұрын

He doesn't see color 😉

@liberteen22

2 жыл бұрын

its not a blackboard, it is a quantum object that your evolutionary structure cannot conceive, so you label it a blackboard, it is both a blackboard and a white board at the same time, it depends on the observer to determine which. 50% of people believe it to be a white board and 50% a blackboard. Although if it is rotated too exactly 45 degrees, the number suddenly spikes to 85% of people bellowing it is one of these but then returns to 50/50 outside that angle.

@johnnyboy4ever

2 жыл бұрын

Lenny? I thought his name was Mike... :)

I'm in college rightnow to learn about business, but I'm just doing this in order to become financially independent so that I may afford to learn about quantum physics, and get to solve our greatest mysteries and problems. Science is what I am truly fasinated about! I'm so exstatic to know that I live in an age where I can learn this information from the small technology in my hand. Thank you for posting this lecture!

I'm so happy this is online. He is a great teacher - simplifying as much as possible. Visuals help immensely.

Sir Leonard suskind wait for me for some years. I will definitely meet you in Stanford. I am currently at 7th. :)

@tymekbraciszewski447

3 жыл бұрын

Good luck!

So happy that person in the audience mentioned the collapsing of a wave function, because that was the moment all of this made sense to me

I agree ErnestYAlumni. I also enjoyProf. Susskind's dry humour like the bit where he says in answer to a question at about 54:50 "They might have got the Qbits from a Qbit store!" . . . humour helps the process of learning. ;-)

the thing I love about these lectures is that he starts with the fundamental concepts, then illustrates how the theories differ, at that fundamental level. IMO, Feynmann didn't really do that...

Thnks Stanford and Mr Susskind, his teaching is gold, i guess he learned a lot from mr Feynmann :P

I can visualize five dimensional space time.., but don't you Dare ask me what I was doing when I saw it.

@brendawilliams8062

3 жыл бұрын

✅

this guy is a legend.

Both upper and lower case are valid depending on the frame of reference of the observer.

One of the greatest men alive. Without a fringe of doubt!

Thank you Stanford for this guy's lectures ❤️❤️❤️

Leonard Susskind is A living Legend, you know as students we call "legends" the great or greatest teachers...

@schmetterling4477

2 жыл бұрын

Well, he is 81 years of age now... so don't expect too much teaching from him. I take that back! Surprise... he is still teaching "PHYSICS 361: Cosmology and Extragalactic Astrophysics". Cool!

Every second of this lecture reminds me how important Feynman's learning technique is.

Thanks so much prof. Susskind as a student and undegraduate in architecture I appreciate . Thanks.

What cookies does he use to eat? I want them.

@schokoladenjunge1

7 жыл бұрын

Somebody asking the right questions.

@MrGOTAMA420

7 жыл бұрын

chocholate chip

@nihadtp539

4 жыл бұрын

Its actually scone. He told that in one of his previous lectures of Classical Mechanics

Stanford's reputation is reproved by you!

This lecture is great. The professor is obviously starting from baby steps to demonstrate the foundation of quantum mechanical statistics, but some of his students are either bored or want to show off their "advanced" knowledge. Actually, this is very similar, if not identical, to Dirac's experiment and treatise on a 45 degree polarizer sandwiched between two polarizers oriented at 90 degrees to each other. Very beautifully prepared lecture.

Thank you, Stanford and Susskind

You know shit's getting serious when Paul Dirac comes back from beyond the grave to set things straight.

What a beautiful series of lectures!! Actually I bought the book before discovering the lectures were on line on KZread!! As a mathematician, my objective was to get in touch with the Quantum Mechanics and to have a higher level understanding of the underneath models. And I really loved Susskind's way to be so clear and consistent without turning into a 100% formal and axiomatic lecture. BTW, are you aware of any online discussion group or forum about those lectures?

@ganeshie8 No. Once you get a value for some orientation of the apparatus, you will consistently get the same value while measuring the same system with the same orientation. You have just collapsed its wave function. Until a measurement has collapsed the wave function, the actual orientation of the system doesn't make much sense in QM. You just have the probabilities for each result for the different orientation angles (that's the wave function or the state vector). That's all there is to it.

I was so spooked when the guy asked a question at 30:00

@jorgepeterbarton

4 ай бұрын

was slightly patronising response given he gave away what heads come tails could represent half a minute later haha... Quantum spin States, or any other state really, that could be bound by uncertainty principle but he was introducing the abstract logic with a familiar concept

Okay I'm halfway through the lecture and I want to raise my hand and asked a question, what a classical analogous system be as follows, imagine a coin flipping experiment in which any time the coin flipper was fasting in the East-West Direction he would get a random 50/50 coin toss. But if he was facing in the north Direction he might always get heads and if facing south always tails?

1:35:12 inner product of the vector with itself is the square of its length. It is a Real number and positive

Thank You, it is helping me to understand logic principles and abstract thought

I don't know what he is saying sometimes, but I love his voice.

Finally, they started to treat vectors as functions. Functions are vectors because then can be added together and scaled. But, functions are also vectors of single variable. The argument is called "index" or "coordinate" in the vector space. Vector a=[a0,a1,a2] is a map a(0)=>a0, a(a)=>a1 and a(x)=>a_x in general. This is a function of single variable. Vectors are just discrete functions in the narrow view.

@sudharsank5780

4 жыл бұрын

That's a good explanation! Thanks!

Right, I purchased it. I think it's the best calculus intro I've ever read.

I read the book, Quantum Mechanics(The Theoretical Min). Your book was specular parts, matrix math.... Thank you... Republic of Korea

Thank you Leonard Susskind. You are a new hero if mine. I am reintroduced the awe that I felt studying physics in university. I absolutely love having these lectures available. Are there lecture notes available anywhere? I often listen while doing other things, and I'd like to be able to review the notation before moving in.

@sparkymist8650

Жыл бұрын

I think he has a book he wrote with all the lecture summaries written in it :)

Yes, the q-bit doesn't have to "reset" at a specific angle to come up with the same ratios... I feel like he keeps it that way because it will uphold the integrity of the experiments being "wiped clean" with every new q-bit.

Thank you Pr. Susskind, Stanford ! As crazy French say: "Chapeau bas, M. Susskind" !!

What a great professor. Literally feeling this rn. I detect that kid is a brat! I'll leave it at that. So grateful for these free lessons!

stanford,thank you very much for this free knowledge

Bought the book and felt it was a bit too rushed, I wanted to expand more on the maths behind it so I went online to search for further explanations and turns out his lectures are all available on youtube! Thanks for providing these videos to the internet.

@pradyumnak641

11 ай бұрын

Do you think the book adds any more value over these lecture? I'm contemplating buying the book but if it's just a transcript of these lectures, it may be a waste

My last math class was about 20 years ago. Understood all of lecture one, now I boldly go to lecture two :D

@ScreamingatWhispers

4 ай бұрын

To infinity and beyond 🎉

or in other words: the degree by which i rotated the aparatus after a measurement defines the likelyhood to get the same measurement at the second measurement of the same quark? so at the third measurement, the outcome of the first measurement has no impact on the result whatsoever anymore? but the outcome of the second measurement has a decisive impact on the probability? this is soo cool!

a flipped coin is a process that is in motion or not. It is on the edge when in motion and on either side when not. The universe is organized in sets of three gravity medium dimension sets with an observer in the middle. The set of three straddles a force set of four. Both form a process of 12 parts every three cycles. The minimum value of each, is a non event and can only exist within the other as an opposite value, in the opposite direction.

I can't get over how much this professor looks like Mike from Breaking Bad.

Hey, sorry for the late reply. The reason you don't hear much about fractals in a class about quantum mechanics is because the quantization of matter prevents true fractals from existing. Approximate fractals appear on cosmological scales through microscopic scales, but eventually there's a fundamental limit, so for example a coastline is not actually infinite. A better place to look for fractal theory would be a course on complex variables or chaos theory, graphics design or fracture mechanics.

look like the dentist of Mr bean

@Abdullah Naeem, The answer is no it doesn't take it out of the quantum world. Or rather, you are only out of the quantum world about that specific axis. If you know the spin around one axis you have maximal uncertainty (i.e. a 50-50 chance of either result) about its spin around an orthogonal axis. That's quantum mechanics. It should become more clear as the lectures go on and he covers more of the mathematics describing this weird situation.

What a great fucking gift to humanity. Thank you Stanford and Mr. Susskind.

When the apparatus is upside down, does the -1 mean that it's pointing opposite to the direction of the apparatus ? Which means it's pointing up.

Great teaching - thanks!

If a function is a vector of infinite dimension, can the components be thought of as the terms in a Fourier or Taylor series expansion of that function? If memory serves, the terms of a Fourier series are orthogonal in the sense that the product of any two of them, integrated over one period is zero.

I didn't know lord Tywin was a Physics professor.

@ameyajatinshah458

6 жыл бұрын

He is like a fusion of tywin and mike from breaking bad

@andrewcriscione

5 жыл бұрын

I was thinking John Malkovich.

This is what the internet is meant for

When you take the second deterctor, you have perturbed the system...so you will get the randomness again....

10 months into my own comment below: This guy is the king of physics.

Have you seen the Susskind's lecture? Why you cannot visualize dimensions other than 3? Which tools have you developed to be not able to do that?

Say you have the experiment at 51:29, so you have a tilted detector at about 30 degree, then you have cos(30) probability of getting a 1, then you take another detector at about 60 degree and measure the same thing, you have the probability of cos(30)*cos(30) for the final result to be 1, this is different from take a detector with tilted degree of 60 degree, it is higher than that, is it true that you can tilt any vectors to any degree with probability 1?

I strongly agree with his assertion that the abstract intuitions and math are extremely powerful and important to develop. I disagree that that higher dimensional visualization (or lower) are impossible or useless. He is right that most people don't correctly visualize what two or 1 dimension are like though they think they are. The story of flat land is a good place to start.

I wish this lecture had existed when I was studying physics.

@AniSepherd972

2 жыл бұрын

same man,

Hello friends- My daughter, in 2nd year of university, gave me The Theoretical Minimum for Christmas, as she knows I appreciate the thought experiments around physics, and can hang in there during a discussion. However, when reading this text, and watching these inspiring videos, I am lost. I can kinda follow, but feel there are some foundations I am missing (I am 62, and I believe I was stoned during an essential class in high school, double entendre). What do you suggest I study/watch/practice to get up to some semblance of understanding to continue this text and lecture? I am willing to put in some time.

Thanks for great lecture 🙏

Downloading it all.

"What does heads and tails have to do with it? What's the purpose of using heads or tails?" Interruptions of this nature make my blood boil.

@archyology

8 жыл бұрын

+Jo Do It's a continuation on the previous lecture series where they talked about it as an example for laws of Physics.

@capitanmission

8 жыл бұрын

+Jo Do hahaha people are actually answering your question.

@ThePurestOnes

7 жыл бұрын

Jo Do dude I don't get how someone that would ask such a question got into Stanford university

@mistadopeyy

7 жыл бұрын

Jo Do mr. perfection

@abhishekcherath2323

6 жыл бұрын

They aren't students of Stanford. Well, for the most part.

these students....he spent so much time trying to get 2 simple ideas across to them...holy hell. this lecture couldve been 1/3 as long and i wouldve got just as much! sheesh! i cant get enough of these! (the lectures, not the students)

@dangiscongrataway2365

8 жыл бұрын

It's much easier to understand stuff behind a screen than irl at least for me

@abhishekcherath2323

6 жыл бұрын

way easier to get stuff when you can pause mate.

is this correct: ? when i measure the spin to be 1 at 0° and then measure the spin at 90° to be whatever and then measure again at 0° the probability to get a 1 at the third measurement is 50% ? this is using the same quark in all three measurements. BUT when i measure the spin to be 1 at 0° and then measure the spin at 1° to be whatever and then measure again at 0° the probability to get a 1 at the third measurement is very high ? this is using the same quark in all three measurements. thx!

1:03:51 quantum system space is vector space: a collection of vectors

You are just a legend!

If you have a set of "up" qubits prepared... and then turn the messauring device an angle for a random distribution based on the degree. It means you can DECIDE the outcome depending on the angle, if you turn it up you get more +1 and turn it down get more -1, right? And your choice determines the outcome. Makes you wonder if you can "alter" the reality outcome by how you meassure things. "positive thinking gives positive results" sort of speaking... ?

there seems to me to be a rotational direction bias in this first explanation. the orientation of the :Detector : is making an inference that is the case.

5:00 when to update? how do you mesure how long its been?

this course on quantum mechanics is good but I found the previous series entitled "Modern Physics- Quantum Mechanics" more helpful, these are not bad though..

Would be nice to have captions enabled

This explanation finally Made me understand what and how a sin/cos really is😂 It's been years since I graduated and always have been using them but I always used to get into arguments about what it really was with my teachers as they only kept saying its an division which never satisfied me into abstractly grasping the concept. This is way easier and better than math Well at least the part that never clicked in my head. Been using it for years but I never had an analogy for goniometrie like how I have a basic understanding of how to simplify and use other stuff. Everything made sense except for this til just now. Awesome Also always got into fights about dividing by zero and never truly understood math til I studied complex numbers in my final year. Schools should really start with this and complex numbers and build from there, at least these things make sense when you look at the world around you and when trying things and applying things to calculate, design and make things or theories and analogies. Anyway, would've saved me a lot of fights with teachers who would just state things instead of teach you what it is and how it works and give you concepts so you can apply it to everything in life.

Non-quantitative-number-numeral symbol hyphen, - , concatenated with quantiative-number-numeral one, 1, doesn't result in something from either category and therefore, is excluded from a vector : something with magnitude and direction, space by definition.

This is such much fun!!

@~35m15"s into the video strikes me that apparetus might be represented as a ruler,

Let's imagine the grid structure of Planck pixels (plixels) and how they interact with vectors representing the changing states of hawking radiation over Planck time. We can explore how these vectors, characterized by the cosine of the angle (θ), relate to the speed of light and describe acceleration, which in turn corresponds to gravity. In QIH, the grid structure of plixels represents the fundamental fabric of spacetime at the Planck scale. Each plixel acts as a discrete unit, contributing to the overall information processing and entanglement within the holographic framework. Now, let's consider the vectors that represent the changing states of hawking radiation over Planck time. These vectors describe the properties of the emitted radiation, such as its energy, momentum, and direction. The cosine of the angle (θ) associated with these vectors represents the percentage of the speed of light contained within the hawking radiation. As the angle (θ) changes over successive moments, new hawking radiation is emitted, reflecting the evolving quantum state of the system. This changing angle and the subsequent emission of radiation correspond to acceleration within the QIH framework. Acceleration can be seen as a manifestation of the altering quantum states and entanglement patterns between the plixels and the emitted hawking radiation. In the context of the equivalence between acceleration and gravity, this changing angle and the resulting emission of hawking radiation can be understood as gravitational effects within the QIH framework. The modulation of quantum states and the interaction between the plixels and the emitted radiation encode the gravitational behavior, thereby linking acceleration, hawking radiation, and gravity. Through the lens of QIH, this perspective allows us to explore how the grid structure of plixels, the changing angles of hawking radiation, and their associated acceleration can provide insights into the interplay between quantum information, spacetime, and the gravitational phenomena. It offers a framework for understanding how gravity emerges from the quantum information processing occurring within the holographic structure of spacetime.

in the experiment in the case where we flip the apparatus by theta and we take multiple readings do all of them come randomly different and then average out to be cos(theta)?(since in the case of the apparatus totally flipped by 180° the outcome is always -1) and incase of it being flipped by 90° its average is 0?

@selimhassairi

7 жыл бұрын

Yeah! That's what he said in his lecture!

How do we know that the outcome is random? Is it simply a way of saying that we couldn't find any pattern in it no matter how hard we tried or is there some way to prove that there can be no deterministic algorithm that could be generating the sequence of ups and downs?

@jorgepeterbarton

4 ай бұрын

I don't think we can but we pick such an interpretation as we are at a limit of being able to observe further. If not random then a pseudo random state that is very perfect in its distribution. We can't really find a way into slicing a particle up to see what its thinking then its for all intents and purposes random. The interpretation is the non empirical philosophy, some metaphysics that allows us to proceed. Like Copenhagen interpretation, and most of them. Although others like bohmian mechanics speculated otherwise, it was other elements that sent it out of favour. We can say its non local as experimental data shows it is illogical to infer local causes. But asking about randomness is ontology, its not really a question that can be answered empirically, no less than asking if free will exists or if god controlled the randomness, its just what would seem to look random and we know we can't look further in detail due to limits of observation. So its a unfalsifiable and beyond asking a physicist the answer to that. It just gives random distributions from many repeated experiments and that is considered elementary state of things.

Who explained dimensions " Expanse of left and right, above and below, ahead and behind, before and after, good and evil" ?

At 1:19:30 could the right side be written as Z*

Interesting. So if we turn the detector to 45 degrees, we would measure a sample of 1's and -1's such that the average of the sample was sqrt(2)/2. How can the average ever be an irrational number? It doesn't seem mathematically possible to get some mean values.

You've just made my day!! :)

How comforting that even the smartest people can't visualize more than 3 dimensions. I always felt stupid.

thanks!! you are the man!!

@garybort some people have conditions that require them to take in a little sugar occasionally?????? ..so maybe it's not a 'meal' !

Good stuff. Well played, KZread.

bill clinton at 57:33

May God bless you sir

Thank you!

Why our neural architecture is it hardwired for abstract mathematics if it is not hardwired for n dimensions?

Imagine just casually dropping the line, “these are described with highly theoretical mathematics” - as though that’s not one of the most terrifying sentences ever uttered in the academe.

33:00 Very good!