This guy clearly states: "I'm a senior math major at MIT".. he's 22 .. he's an undergrad .. he's visibly a young whippersnapper .. yet, comments take him to task for his flaws and shortcomings .. can any of you math geniuses step back and see the obvious .. he's presenting a fully complete set of lectures on a profoundly important and influential and pulitzer prize winning work - and he's doing a pretty damn good job of it .. what's the matter with y'all .. shame ..
it's similar to people that call out grammar and spelling errors.... they miss the point / focus on the wrong thing ... basically it is beyond their ability to comprehend lbs
Hahahaha I started reading GEB my sophomore year of high school and finally bought my own copy my senior year. I’ve been taking notes and stuff. Ins honestly a monster of a book.
Lecture Notes 1/2: ***Tool for thinking (from non-self to self) 1) Isomorphism - means equal in this course but means something more specific in abstract algebra - [[8:40]] - [[11:02]] e.g. skateboard vs. car, each structure can be mapped onto the other (inverse). But this example is homomorphism since skateboard is missing parts. 2) Recursion - repetitive process that includes self. - [[11:10]] - [[17:14]] - e.g. mixing egg or Fibonacci sequence or fractal [[13:42]] - [[17:14]] - which is the number of dimensions in a doubling process 2^d = N. 3) Paradox a) Veridical (eventually true) b) falsidical c) antinomy - [[17:20]] - [[26:30]] e.g. Birthday paradox a) Veridical (eventually true) e.g. Zeno's paradox & atom movement; b) falsidical e.g. 1+1-1+1-1=0 or 1? illegal moves c) antinomy e.g. the liar in Russell's paradox "This sentence is not true." & barber's paradox cannot shaves his own beard [Omega = {all set that doesn't contain themselves as a member}, so is Omega contains itself?] 4) Infinity integers vs. real numbers[][](ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qGYDQWm49wU.html) - [[26:34]] 5) Formal systems - how do things gain meaning and exit the system [[38:35]] which is metathinking - [[27:37]] - [[37:58]] e.g. MIU puzzle from MI to MU -> algebra system with axiom, string, rules, and theorem. ***About the system - [[39:20]] The lecturer's favourite quote on metathinking by Hofstadter (p24 in lecture notes, p37 in book): "Of course, there are cases where only a rare individual will have the vision to perceive a system which governs many people’ lives, a system which had never before even been recognized as a system; then such people often devote their lives to convincing other people that the system really is there, and that it ought to be exited from!" e.g. Karl Marx and communism exiting bourgeois' system; the media / the government / the church / the school (contrary by Montessori Education). 3 modes of interacting with the system - [[42:33]] 1) mechanical - follow 2) intellegent 3) unmode / zen
Classic...right as he begins to describe what the class is about a student immediately raises his hand and asks "what is the class about." And all the poor guy can do is say "okay, so that's what I'm going to go through right now" as if it wasn't obvious he is trying to begin to describe what the class is about. lol...even at MIT undergrads are undergrads.
+The Devil (Satan) If you examine his behaviour in early minutes of the class, you can see that he was out of breath and had a weird tone to his voice. He was probably too excited and nervous at the time. Happens to anyone.
Just to clarify on the Birthday Problem mentioned at 17:30 : The lecture refers to the high probability of another person, from a group of 40, sharing your birthday. It should be the high probability of at least two people from the group sharing a birthday. If you constrain beforehand who one of the people will be (ie. yourself) then it becomes a lot less likely. The chance of a unique pair is extremely high, the chance of you being part of that pair is relatively low.
@@l.w.paradis2108 "Misspoke"? He said, and then published, something utterly wrong and quite stupid. He had the chance to correct it, and didn't Don't you think this suggests both laziness and lack of pride in his own work?
After I knew him Kurt Gödel by the book written by Rebecca Goldstein, I met this book by chance in the local bookstore year ago. And now, I even hesitate to open it because i cannot imagine from what he says while reading. I just know it is profound work but, It makes me terrible if i can't reach his thought so that i think i should stop reading and need to read something else that help my depth of thought be deep+my English speaking. I didn't imagine these kind of lecture talking about such a book and get impression of people and you professor. Thank you for offering these video. Now these are my guider to understand it with deep depth.
By the time I got to college, my copy of GEB was dogeared. It was my bible. How I would have dreamed to have a class such as this on offer at my university. Finally, in the 90's I had a chance to attend a lecture by Hofstadter himself. The lecture was about computer music and alluding to the Turing test.
That’s awesome. I’m unable to locate my copy, an 80s softcover. I’m just thrilled with these videos. His mention of Fibonacci sequence at 12 minute mark is telling😉
vos je do you have training in algebra? If so, the book can be supplemented with companion text that explains in depth exactly what Hofstadter means. The similarities between the drains in your sink, the shape of hurricanes, and the structure of some galaxies (like our own) are so intimately tied to mathematics that we will eventually be able to create something congruent with human consciousness out of math. Or something.
17:22: The birthday paradox is stated incorrectly. If you are in a room with 40 people, the probability that someone shares your birthday is actually low. However, the probability that there are two people in the room with the same birthday is very high. It is this that is called the birthday paradox.
Also, pi can be in included in a correspondence with the natural numbers (27:00). It seems what he meant to say is that given any list, you can always find an irrational number which is not included in the list.
He stated correctly. Leonard Blackburn you are completely wrong Before you write here it was enough to assert with Google. It is not so easy to be a lecturer on MIT. In a room of just 23 people there's a 50-50 chance of two people having the same birthday. In a room of 70 there's a 99.9% chance of two people matching.The birthday paradox is strange, counter-intuitive, and completely true. If you are in a room with 40 people, the probability that someone shares your birthday actually is not low but very high.The probability is % 89.1
I quickly read through the book after high school thinking it was a spiritual book on consciousness. 10 years later, I come to find it was a book on mathematics!
And people say its difficult to learn/educational opportunities are limited. We live in a time when one can get GEB pdf online and take the MIT companion course for free. Instead people decide to put their time into FB and twatting (or is it tweeting?).
Jason, thanks so much for posting this video! I am on the last chapter of GEB and thought it would be fun to watch these videos to help me digest the book a little better. It's the most creative book I have ever read, but I never would have tackled it had my software engineering son not encouraged me to (dared me?). These videos are a great summary. Thanks again!
He goes from logical elements without value and works it to selfawarness. Isolated the most pertinent parts of the text. Read the book for 7 years. I got to know the book from the outside, but never read it myself. It is a book you treat with reverence, it looks like a good book. Godel, Escher, Bach.
Thank You. This is going to be so much fun. You saved me at 27:51. Skipping the first 3 chapters. Ive been stuck in that part of the book.....also you are a very good teacher. I can tell already. This whole course is going to be so fun. ♒♒✨✨✨✨
37:51 Great lecture series... I really liked the idea suggested here about the importance of stepping out of a formal system to see the larger truth about it. Justin generalized this idea to breakthroughs happening in human society. He quoted the example of how Carl Marx. For good or for evil, these people stepped out of the cultural formal system and introduced new ones.
@Abhishek jha You should go to websites like math stack exchange if you have specific questions. The people there will guide you well. You should also try reaching out to seniors, teachers and professors of your school/college.
I have just read David Foster Wallace History of Infinity, finishing Rebecca Goldstine about Godel, and have read few chapters in GEB by Hofstadter. Thank you for this lecture. It is like a candy for the mind :)
Have you heard of sci-hub.io? It literally unlocks any research paper that would otherwise cost money. The founder is this Russian women that believes exactly as you do and says cost-barriers are prohibiting advancement of science and higher qualities of life, super cool, check it out
He pushed through the S-triangle example too fast, which is a great shame. A few more minutes would've made the argument clear. The issue is that the S-triangle upon doubling gives an empty triangle in the middle and three triangles that are exactly identical due to a property of fractiles called self-similarity. This is why you have three *identical* S-triangles left after the doubling process. If we had a normal solid triangle, it would have had four copies of the original triangle, yielding a dimension of 2 (log_2(4) = 2). Similarly, if we were looking at the triangle's two dimensional perimeter, it would have twice the number of each edge, for a dimension of log_2(2)=1.
Thanks, I was wondering why it was 3 and not 4... I was guessing (correctly) the whole in the center was the cause; but I didn't fully understand until I read your explanation.
Right, he is changing the function on the set (number of dimensions). He defines the line as 1 dimensional and then bisects it in one dimension to get 2. He defines the square as two dimensional and then bisects it in two dimensions to get 4 squares. He defines the cube as 3 dimensions and bisects it on each dimension to get 8 cubes. Then he changes the function; the triangle is set in two dimensions but he no longer bisects it, he trisects it. He is no longer operating on the same premise he originally defined. If you change the function, of course the results are different. This is not a partial dimension or "A really cool concept".
9 лет назад
Matthew Du Puy Evan Siegel i think the explanation is not really clear in this video, but the concept of fractal dimension is about how the area is increased when the figure is scaled using a 2x factor. In the case of the S-triangle is the area is increased 3 times when triangle is scaled using 2x factor instead been increased 4 times as you expect for any 2d figure. I think it would be clearer if the area was shaded and you can see the inverted triangle in the middle is not part of the area.
The Birthday Paradox concerns the probability of find two people in a room with the same birthday. The probability of a particular person finding another with the same birthday is a different thing and much smaller.
“When I taught this course two Springs ago…” as a Sophomore. I didn’t get up in front of a class and formally teach a subject until my Senior year, and that was about once every 2-3 class days, since all of us MathEd-majors had to take turns.
Thank you!! Love this lecture. And the work of Hofstadter. Currently reading 'I am a strange loop'. I always enjoyed thinking about that kind of issues. ♥️🧠🤯
@@bendavis2234 GEB I have never read strange loop but I have heard some people are turned off by it because it is too preachy compared to the example filled GEB
@@dylanesguerra3492 I've actually started Strange Loop since my last comment and I didn't like it that much. I'm about half way through but have given up unfortunately. I was listening to the audio book and the reader was driving me nuts! I'll have to order the printed GEB and see if it's any better.
@@bendavis2234 I think you will like it more. I’m halfway done with it and started about a month ago. No matter what you will find certain parts very interesting whether or not you believe in the grand message of the book.
@@dylanesguerra3492 yup I think you’ll be right. The subject matter is extremely interesting so you can’t go wrong. I think it was just his writing style that turned me off in Strange Loop for some reason. From what I’ve heard GEB is unanimously liked more so it’s worth giving a shot despite my opinion of his other book. Also it would be nice to finish this lecture series while I’m at it. Completely forgot about this until you commented!
Does this lecture go into any analysis and further development of the book and subject or does it simply explain it and expand on the concepts that go into it to make it understandable for people who otherwise wouldn't get it?
at 8:09, someone walked out. This brings me back to my university days. Whilst the lecture is talking, some students gobble up his dictation verbatim. Some listen to his spew, and actually have original thoughts of themselves for themselves . This is a brilliant lecture 😊👌
The term "fractal" refers to the fact that the set presents many details at many scales (fractionated in the sense of broken set) not to the fact the dimension is not integral. In fact fractals can have integral dimension and when the dimension is not integral it is usually irrational and hence not a fraction.
Beautiful - thanks for posting this! I partially read GEB two decades ago as a young undergrad, and it was a profound influence. I've taken it up again now that I find myself with lots of spare time (hope I'll read it all this time!...) and it's interesting to see other people's takes on it. Thanks again!
This gets SO much more interesting as it goes on. Even though this guy needs to work on his public speaking skills, he is clearly well-versed on some seriously deep sh*t. More power to ya, boooyyy. I'm watching all these vids. Quantum physics is getting boring. I'm interested in the limits of logic, and how it applies to philosophy and the mind of [the creator of the universe]. Logic, symbols, and how they fit together and break down might define human reality. (Although I think there is much more, somehow.)
With the way he describes zeno's paradox.... Would a base 0-9 real number axiom be necessary for "infinitely infinite"recursion and imaginary numbers of half steps?
🛹 and 🚗 - no steering wheel, but you can abstract the function of steering and still map since both systems do have steering - lots of ways to cut and sort
2m32s -- "You may remember Dick Clark's famous statement, 'I think therefore I am.' " I don't think Dick Clark said that. I think he said, "I rock therefore I am." Fred
Ever since I read Godel Escher Bach, I have maintained that "isomorphism" is the most important word of our age for properly understanding the universe. Also, I suspect the answer to whether the universe is deterministic or not may be "both".
I read 90% of the book at age 18 in the eighties and followed up with "The Mind's I" by Hofstädter and Dennett which was similar but different in its form of presentation. Both books deeply influenced me (I called them my personal bible) and when internet came out in the late nineties one on my first e-mails went to Hofstädter asking him about how he could cope with his overwhelming knowledge? He kindly responded that it was no problem for him. I was clearly struggling to find meaning in life and not become a nihilist back then. I'm still around and I'm still fascinated by GEB that uses a twist that AFAIK no one ever mentioned anywhere: SPOILER ALERT!!! The book itself is self-reflecting and it ends where it starts - like an eternal golden braid. Am I the only one who noticed that genius move by Hofstädter?
@@PianoGesang It is very circular all throughout the book: GEB and EGB throughout: eternal golden braid. My memory, from a thousand years ago, is that it's constantly reiterated. Plus, all the circular figures in the book, the crab canon (and the crab canon dialogue), self-referentiality in general (and in LISP), the looping images from Escher. Eternal Golden Braid. Eternal Golden Braid.
Also, James Joyce's Finnegans Wake is usually considered the first literally circular book; it wraps around from its last sentence to the first. But Samuel Delany's Dhalgren might be much better known, and it too wraps around. Both books were published before GEB. Speaking of which, and circles, GEB is the father of the Egyptian gods (so to speak) and the god of snakes, which in Egyptian iconography have at times very famously swallowed their own tail, i.e.,, they form a circle.
I remember reading in the book of a inferior computer which wood claim defeat in a programmed chess game sooner than a computer of more circuitry so to speak. I myself found a gray area of interest in that determination.
Another ingenuous idea of Hofstadter related to Fibonacci numbers and recursion is to change a little bit the Fibonacci recurrence and to get another sequence with a really weird behaviour! ~This is explained here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5AScGzf5Of4.html
His assertion at ~17:30 about "finding someone else with your birthday in a room of 40 people" was misstated. He should have said "finding two people with the same birthday". The probability of the two statements are very different. The first one is not surprising, but the second one is.
Oh no! Adore this guy, but he misstated The Birthday Paradox! But that's really a good thing, and a lesson to us all. The very best minds have a lapsus; of course he knows, he's a tiny bit nervous.
QM-TIME singularity is the context of particular quantitative resonant phase-states of "self-referential" existence, persons, in a content that combined, has the quality of "I", and because all these resonant phase-states are tuned-timing images of the singularity, the individual combinations represent some degree of focus of the whole. (That's a short description in current terms of a very old repeat discovery of a personal self in the context of a Universal self. It is what it is, elaboration doesn't enhance the principle.)
Would someone explain the sierpinski gasket having ~1.5 dimensions? When you double it, it's true that it has 3 copies; however, it's 3 copies plus 1 original in the center (which equals 4, which equals 2^2...no surprises). Likewise, if you look at doubling the square, you have 3 copies plus 1 original. I can't help but feel there's either something I've missed or that there's a mathematical slight of hand that he just pulled.
I also had trouble understanding how fractals can live in fractional dimensions like 1.5 etc. What helped me most was this: Imagine the simplest fractal its a line that you divide in there slices and erase the one in the middle, you have now two smaller lines after the first iteration, in the second iteration of this process of dividing and erasimg you get 4 smaller lines but remember, a proper fractal doesn't have a finite number of iterations like 1 or 2, the process is done infinitelly many times. So the question now is what are you left with? You are left with infinitelly many lines that are infinitelly small, it is obvious that after every step you are ALWAYS going to be leaving some segments, no matter how small they are, you've done it infinite times so what you are left with is an object that's less than a line but more than a point, the line inhabits the first dimension and the point the 0 dimension your object lives in dimension 0.5, same with dimension 1.4789 it's an object that is less than a flat surface but more than a thin line, obviously it's physically impossible for us to create or observe such object since quantum mechanics tells is that space, energy and time is unsplitable (sorry I'm spanish) when we get small enough. I hope this was useful to you as much as it was to me :)
Yes, the fractal is built by starting with the original big triangle and drawing an inner triangle. But the way the fractal is built is not part of the proof. The proof for non-integral dimensionality is that the middle part is actually not self-similar to the rest of the triangles. If you look up the Sierpinski Triangle, you will see that the inner triangle is always completely empty, so it's not actually copy from that sense. But yes, I agree there is something weird about it. In the sense that the proof of it comes from outside the system. But I suppose that is the entire premise of this book.
Its been 6 years, I know. But for someone that reads it today, remember that when you add the trangles, you must leave the center empty, so when you double the length of the side of the triangles, you have three times the original triangle, not 4
I believe you misspoke when you were explaining the "Birthday Paradox". You said that most people assume that you would need a large group of people in order to ensure that someone in the room has the same birthday as you, and you said that you would really only need about 40 people in the room for this result. There is no way that that could be true. Did you mean to say that, in a group of about 40 people, there will very likely be two people with the same birthday as each other?
Actually, he's right; you only need 23 people for a 50% chance that two people share the same birthday. You can read about it here: en.wikipedia.org/wiki/Birthday_problem
Gödel, Escher, Bach: A Mental Space Odyssey - OCW-MIT, presented by Justin Curry and Curran Kelleher (2007). Very interesting view of Douglas Hofstadter's excellent book...
49:52 Couldn't 'q' just mean "there are as many '-' on either side of 'q', and 'p' is/are ignored". Then the axiom wouldn't be broken, correct? In other words, isn't it just a matter of framing the symbols to fit the axiom in different contexts?
Wow, why the hell did MIT take this course down?!? I really wanted to know which readings were covered in each lecture. Does anyone know if there's a syllabus that says what the readings are?
I remember some of the book from when I read the book at age 15. There are these three contradictory ideas about what I thought it had in it: First, I don't remember clearly thinking that it was about trying to define a self. But, I found a paper I wrote for some philosophy class I took about the Mind-Body Problem - and the grader wrote on it "A book report on Godel, Escher, Bach is not a solution to the mind-body problem". And I guess it's funny now that when I think of the book, I don't think it had anything to do with the mind-body problem, because I don't remember that aspect of it. So here in lecture 1, I also don't understand how looking at math is going to answer anything about what it's like to have a mind. We're fundamentally physical bodies. The solution to the mind-body problem is that our brains are parts of our bodies and our bodies are part of the universe - so I think it's that everything is connected - I have read that the only consistent explanation for consciousness is that everything is conscious. And that is what actually makes sense to me.
@@jroc2201 it's good to be open-minded. And some day philosophers with their careful definitions and carefully built structures of thoughts might really succeed in making the world comprehensible, if philosophers actually exist
Unless you realize that without a mind you don't have a brain, you will remain stuck in naïve realism forever. The turn to "embodied consciousness" relatively lately is the beginning of a genuine paradigm shift. The Nobel Prize in physics last year that the universe is not locally real is the first major acknowledgment of this. GEB is too "in the 70s" to be addressing the problem you describe; I think that is correct. It was still very mired in the very false idea that the brain analogizes to a computer (never mind that a mind doesn't). Recursion is the magic bullet in the book, and self-referentiality is indeed essential. But the real kick in the balls is Gödel. The idea that no "system" can fully self-describe itself from within the system is exactly what connects GEB to the recently Nobel Prize. Uncomfortable as it makes people, the color "red" is not a property of things but arises only in the Mind, and attempts to reify "something out there" that is not already subject to the paradigm of Consciousness is an article of bad faith. Read some of the cyberneticians if you want to get a flavor how it works, especially Maturana & Varela's "Tree of Knowledge." It was (first-order) cybernetics fault that first analogized brain and computer, but cybernetics also realized the error (in second-order cybernetics), but the world hasn't taken up that baton in a big way yet. The paradigm is approaching for doing so, however. It is not only possible, but desirable, to do physics with space and time (that, again, is the gist of the Novel Prize); just let that sink in, physics without space and time as an assumption. Donald Hoffman is going to try to mathematize "Consciousness" (and that will still be a mistake), but it's a less critical mistake than imagining "space" and "time" (and all properties ascribed to "reality" including "reality") are literal. Of course, dharmic epistemology has known this for 5000 years. In 1957, Ross Ashby already said: living systems are open to energy but closed to information and control. Although he was writing when first-order cybernetics was the main framework, it is already the axiom of second-order cynbernetics. As Maturana & Varela put it, "Everything said is said by someone" (every perception arises from a perceiving living system). So, what we perceive is not "reality" (no serious philosopher thinks this anymore), but a description of an observation of an experience. When we say, "The sun set," we are already two removes from anything like "reality." Again, the illusion of maya has been known for 5000 years elsewhere. We're still playing catch-up, and looming extinction due to climate change is one of the most clear demonstrations that "we" have it incorrect. Meanwhile, again, until you realize that Mind is logically prior to Brain, you'll be hopelessly stuck in a self-created impasse.
At 5:00 "refers to itself" and "has meaning" are used as if they are the same thing or at least truth-equivalent. Is there a proof for this later in the lecture or in the book? It would be a waste of time for me to read a book or watch a lecture based on assumptions that I don't hold.
Does someone know how to get the course's notes the teacher gave to the students of these lectures? I really want to go into this fantastic book but I cannot find many information
Just google "download youtube videos" and you will find an abundant of websites that will allow you to download videos from youtube, in any format and available quality you want.
