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.
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
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.
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.
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 :)
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!
At 17 I sat with the book for 4 days straight on a train ride across the country. Got it all. That said most people don't have that kind of time to focus on one thing.
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.
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?).
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.)
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+2
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.
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.
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!
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[][](ruclips.net/video/qGYDQWm49wU/видео.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
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!
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
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.
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
All intelligence, complex or simple, must be recursive in nature. The feedback loop is necessary for references and definitions to evolve into a human language. Human language is the byproduct of a logical system that is recursive. Biological evolution is a variable, naturally occurring, recursive process(albeit an incredibly slow one) that only stops when the conditions needed for specific DNA mutations are met.
“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.
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.
When I read the book in the early nineties it was about the god-feeling, that every piece of the puzzle falls into it's place, but you can't prove it's right, because you need to step out of the framework you just built. Now it's about the "I"... Times and interpretations change. Although this lecture is interesting I highly recommend to stop watching and read the book first.
I mean no disrespect but to those of you who are exploring GEB for the 1st time, please buy the book. This guy isn't great at communicating or connecting the ideas, though I appreciate his effort. The book is multi-faceted and there are parts that will leave you amazed, truly enlightening. This lecture proves why Douglas H. took his 'sweet time' laying out the fundamentals.
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.
🛹 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
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.
2 + 2 = 4 breaks down in the real world, because no 2 things are identical. Numbers are abstractions with tremendous usefulness but contrary to the dreams of mathematics experts, there is a dimension (in a manner of speaking) of reality which is beyond numbers. E.G. consciousness.
Ever notice how many major unsolved problems in physics and AI lie at infinity. I would argue that we still don't really understand what infinity even is....
I am 44 mins in, I'm gonna guess that it is impossible because in order to anihillate all the Is the number of them must be divisible by 3, but by doubling them the product will always be at 2 to the D power.
No, thats not what I did. I ventured a guess and im not afraid to be wrong. Looks like you are projecting your failed academician mentality on to me. Not only this but you pretend to be in some elite club by having "the slightest inkling" about what this lecture is about. Im pretty sure the lecture was meant to be EASILY understood. You are the epitome of the Dunning-Kruger effect. Im expecting you to make an anger filled response, but I can't expect it to be very impressive considering your go-to argument is "Your a fucking moron" I guess this college educated genius never learned what an argument is or how to use the correct form of your (you're).
Not to mention you are insulting someone on their merit on a FAKE ACCOUNT, accusing me of being morally bankrupt while not even accepting accountability for your own words.
My god they offered this to high school students?! Wonder how much in depth the students can appreciate this..I started reading during my final year at degree college and read the preface THRICE to understand what was going on lol
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: ruclips.net/video/5AScGzf5Of4/видео.html
somebody named Tyreen in the class thought he was very intelligent and asked so many mundane questions that it completed ruined the course. Half the time of the instructors was taken up kindly answering this guy while the other students twiddled their thumbs. This course should really be called the discussion of the topic with Tyreen.
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
When the book was new, I read it about 8/10 through, but I was not a math/logic major, so when the text was mathematical/logic symbols, I bailed. Gave my copy to a CompSci undergrad patent attorney from Harvard.
33:00 how do you go from meaningless to meaning. Think CODE pg. Think materialism. Think idealism. Also an isomorphism seems to just be a translatablism.
"Headlights" would have been a better example of a "homomorphism" than a steering wheel; because the functionality of steering is on both, but only a car has headlights.
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.
In the first three minuets one the most profound questions pops up: HOW CAN we think if we are a collection of primitives? Then five min later an equally profound question: HOW DO we think? look @7:00 in none of those things seem to have anything to do with thought on the face of it.... lol crazy
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".
The solution to liar's paradox seems rather obvious to me. The paradox arises due to the fact that the analysis is static. However, if your analysis is dynamic, the paradox immediately resolves itself. In other words, dynamically you can say as follows: "This sentence is false." is true. Then you check it again and decide that it is false. Then you check it again and decide that it is true. As long as you have memory of the previous state, you can judge the next state. Furthermore, it is possible for dynamic checkers to disagree with each other. This shows that they can have internality (or an internal frame of reference that makes sense only to themselves. Kinda like living things experiencing their own subjective world). As to Russel's paradox, the same applies. As soon as the man becomes a barber he shaves himself once after which he never shaves himself again. Paradox resolved.
@@StanislavMudrets My point is that the liar paradox turn into a loop when you use dynamic analysis and that's why is a paradox. One thing is to understand the paradox and another to solve the paradox. Maybe I'm not have been clear. Thanks for take your time to answer my first comment.
@@alioshenko The looping is a problem in a static analysis. It isn't a problem in the dynamic analysis. Why? Because in a static analysis you want the loop to eventually stop so that you get a particular answer. The loop is considered nothing but a trace with a finite set of operations. In the dynamic version you don't necessarily want the loop to stop. I'll give you an example of this. In a living cell, the various proteins and bigger structures are constantly falling apart and are recreated anew. However, it isn't that some external entity is recreating them. These different chemicals contribute to recreation of other chemicals etc. etc. which eventually recreate the original ones in a cycle. In other words, the dynamic process of life is cyclic. You don't want the loop to stop. For it to stop implies certain death with each chemical eventually falling apart and the increase in disorder. In static analysis, we do not take this kind of one hand washes the other seriously. We want an answer of some kind to be recorded somewhere. We don't see the cyclic action itself as the answer (foreground/background distinction). These paradoxes are not exactly about living processes, but they have something in common with them - namely the cyclic nature. Imagine a car engine. It isn't alive, but a cycle is essential to its proper operation. If it stops, it will not be able to push the car. See what I mean?
Why did the instructor tell the students that he would give them 20 bucks to solve the MIU riddle and then get pissed when they weren't listening to him.
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?
31:40 the puzzle is considered to be impossible to solve, but he didn't want to risk more than 20 bucks that it is in fact impossible to solve. That's how much faith this guy has in the mathematicians before him.
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
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?
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.
Why he ignores the triangle in the middle? If we define 2 dimensions as function with 2 arguments and each point of an object can be defined by these arguments lets define the metacentric of the big triangle? If you double the size of the triangle by only 3 small triangles but ignore the forth one in the middle you get logical nonsense.
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'I got through it in seven years'; Good to know it's not just me.
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.
I'm trying hard too
@Reed Morris I speed read through War and Peace in 1 week too... It's about Russia.
I got through it in 18 years. And today slowly its analogical knowledge becomes absorbing to the universities.
😂
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
I don't think he's an undergraduate, he said he taught the course two years ago.
@@nickshelbourne4426 probably in his masters or PhD track.
@@nickshelbourne4426 He says very clearly in the first 30 seconds that he is a senior in mathematics at MIT.
''y'all''
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.
Beat me to it, naturally. It was a minor lapsus; he knows, he just misspoke.
So.. framed another way: "In a room of about 40 people, you should be able to find at least *one* you should be able to tolerate enough to date."
@@taylorj6177 That probability becomes > 1/2 when you reach 23 people in the room.
Good call out. The way he stated it is the way I always hear it discussed where "you" is stated. But those are indeed very different probabilities.
@@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.
sir. would you please tell me how I can approach to its understanding
?
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.
@@dalef9441 A copy can be bought on ebay for $5.00 Yes, I was shocked myself!
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.
@I unless they are stupid...
He said he would talk about zen. He challenged him to give a short reply. It looked like he thought about it
Hahaha so true
I also noticed this. He handled it well. That student is now immortalized as owner of Bill Engvall's "Here's your sign!"
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 :)
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!
Any books they are a close second? I’d love to know!
I've read GEB 3 times and I recommend it to people all the time. It was very influential on a book I wrote on Forensic Science.
At 17 I sat with the book for 4 days straight on a train ride across the country. Got it all. That said most people don't have that kind of time to focus on one thing.
This is brilliant!! thank you for posting this!!! i love lecture videos
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 god. I’ve been reading this book forever lol
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?).
Or people decide to talk gossip about others on you tube. Plus, not quite sure it is worth to download the pdf.
Arash Karimi
/r/iamverysmart
Yo, Arash Karimi , please do instruct me where I could get a degree online, would you?
Arash Karimi the knowledge is useless without a certificate
Metagross923 Funny, I was thinking the exact opposite.
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.)
HappyLobsterShow.
You should be into Wittgenstein .
Have you checked him out yet ?
c c
His PS skills are way better than Terrence Tao's.
I read the first hundred pages of Godel Escher Bach and struggled a bit. Watching your lecture after really helped.
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".
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.
Yes, I know that. Just wish he'd done a better job of it from his video.
Thanks.
Gravitation can be used to model a physical system that exhibits Godel incompleteness. This gravitational system is the three body problem.
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?
I think I read about this in an amazon review of the book... and I hate spoilers :)
@@viezlimo Sorry, I now updated my comment with "Spoiler Alert". However, I have never met anyone who realized the mentioned twist.
fascist emotok
@@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.
this valuable lesson refreshes my sight on how to observe the mathematical world. Great thanks!
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!
Whats the book called thanks ?
@@coolkidcrypto386 I'm not sure whether you're asking me the obvious, in which case the clue is in the title and my initials (Godel Escher Bach)
@@b00i00d yes ! Im asking the obvious question, what's the book name.
@@b00i00d thanks for the smart ass reply
@@coolkidcrypto386 Anytime... Ever heard of Google search?
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[][](ruclips.net/video/qGYDQWm49wU/видео.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
c is a key,phonetics discus has no abstract sanity too write of too to?!..feefiefoeSpyWiserQueen
🏆✊🏿👏🏿👍🏿
Thank you!!
Thank you!
Many thanks!!!
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. ♥️🧠🤯
I’m stuck between starting that book or GEB... which one should be started first? Are they essentially about the same subject?
@@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!
"Finally, there is the concept of infinity. I can't really talk too much about it..." XD (and note "finally" ;)
XD you caught me off guard there but I did get it at the end after reading your comment twice
This is why we say .. copyrights sucks ! Lets all hope for a free world.
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
Deus Ex Machina! Finally I can read a very critical piece i needed
@@clintgolub1751 it is locked in this point. can you tell me another one?
I think the extract would have been allowed under "fair use", but the law isn't entirely clear, which makes people err on the side of caution.
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.
Acabo de comprar el libro, estoy emocionado por empezarlo 😌
I bought GEB when it came out. Best non-fiction book I have ever read & I treasure it, even if it is only a paperback!
flamencoprof I recommend The Fabric of Reality by David Deutsch. Its equally as mind blowing!
You were too patient: I ordered the hardcover as soon as I heard about it. :-)
my paperback copy has really fallen apart
Very instructive, Jason, Thank you for posting. I'll follow on with your four other posts.
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?
Not "very likely", but better odds than a toss of a fair coin.
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
What a fascinating and fun lecture!
In Zen and the art of Motorcycle maintenance, Persig talks about dynamic quality ans stratified levels of static order. it is a vision of complexity.
desCeasERdoltSPApar0tER
All intelligence, complex or simple, must be recursive in nature. The feedback loop is necessary for references and definitions to evolve into a human language. Human language is the byproduct of a logical system that is recursive. Biological evolution is a variable, naturally occurring, recursive process(albeit an incredibly slow one) that only stops when the conditions needed for specific DNA mutations are met.
no natUREz,No logiCAl..
@@stephclements6226 ???
“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.
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.
any info has 0moored explain,2unes allieds!?..
When I read the book in the early nineties it was about the god-feeling, that every piece of the puzzle falls into it's place, but you can't prove it's right, because you need to step out of the framework you just built. Now it's about the "I"... Times and interpretations change. Although this lecture is interesting I highly recommend to stop watching and read the book first.
suduku/timesLitSupp'crossWord'[Win10/95!]!CSgas
This was posted ten years ago. It’s 2023 and ai brought me here to gain more insight self. We are in the future
please turn on community-contributions for a subtitle to let people add subtitles...
I started reading this about 6 years ago, got about 1/3 in and stopped for no particular reason. I have been thinking about it again recently...
If that guy that asked the question @1:48; "What's this class about?" wasn't wearing a tanktop I'd be really surprised.
He's in a tanktop and at MIT, you're not in a tanktop and not at MIT
Gray Wagner dude relax
@@Sam-um9nu k
@@goosew3266 thanks
I mean no disrespect but to those of you who are exploring GEB for the 1st time, please buy the book. This guy isn't great at communicating or connecting the ideas, though I appreciate his effort. The book is multi-faceted and there are parts that will leave you amazed, truly enlightening. This lecture proves why Douglas H. took his 'sweet time' laying out the fundamentals.
maze spy key sink mass ,waste2x'plains?.. parallels networking synch!..
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.
I think you may be correct, I also think that everything may exist and may not exist
@@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.
I feel a lot better now, knowing that the 4 years it took me to finish I'm A Strange Loop is not out of the ordinary
🛹 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
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.
I started thinking on such a high level that I can't see the ground any more.
This is a great video
I just found this book at the bookstore and couldn't figure what the fuck it was, bought it, brought it home, am now here
what would happen if pinocchio said my nose will grow now?
Whoa
It wouldn’t because he was wrong.
He explodes of course!
It wouldn't if he genuinely thought it will grow without lying
He becomes a real boy
The atoms, proteins and molecules are not "meaningless" they are just "uncorrelated" into the set we refer to as "I"
...
I could sit down and read this in a day, it wouldn't be hard to read it. Absorbing it will take a long time.
please turn on community-contributions for a subtitle to let people add subtitles...
2 + 2 = 4 breaks down in the real world, because no 2 things are identical. Numbers are abstractions with tremendous usefulness but contrary to the dreams of mathematics experts, there is a dimension (in a manner of speaking) of reality which is beyond numbers. E.G. consciousness.
Next level MIT OCW.
Excellent, excellent lecture, thank you.
this guy is good
Ever notice how many major unsolved problems in physics and AI lie at infinity. I would argue that we still don't really understand what infinity even is....
It basicly states that I was a bad maths student because I was always metathinking
A: « Why did the chicken cross the road? » A: « To disprove Zeno’s Paradox! »
I am 44 mins in, I'm gonna guess that it is impossible because in order to anihillate all the Is the number of them must be divisible by 3, but by doubling them the product will always be at 2 to the D power.
I never lied, I might be wrong about something, and you are right nobody knows who I am, I am a high school sophomore in Brooklyn ;)
No, thats not what I did. I ventured a guess and im not afraid to be wrong. Looks like you are projecting your failed academician mentality on to me. Not only this but you pretend to be in some elite club by having "the slightest inkling" about what this lecture is about. Im pretty sure the lecture was meant to be EASILY understood. You are the epitome of the Dunning-Kruger effect. Im expecting you to make an anger filled response, but I can't expect it to be very impressive considering your go-to argument is "Your a fucking moron" I guess this college educated genius never learned what an argument is or how to use the correct form of your (you're).
Not to mention you are insulting someone on their merit on a FAKE ACCOUNT, accusing me of being morally bankrupt while not even accepting accountability for your own words.
+Luke Amendolara touche
+Luke Amendolara and fatality (as in MK)
I'm sitting here today because I want to really understand if the p vs np problem is beyond goedel's incompleteness
+Biswas Sharma Is't the goedels therm its self not the proof to negate P=np ! My feeling ..
My god they offered this to high school students?! Wonder how much in depth the students can appreciate this..I started reading during my final year at degree college and read the preface THRICE to understand what was going on lol
TheSupertoniefy No. This is MIT!
Really?
No, this is at MIT!
I'd've definitely taken it in high school.
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: ruclips.net/video/5AScGzf5Of4/видео.html
somebody named Tyreen in the class thought he was very intelligent and asked so many mundane questions that it completed ruined the course. Half the time of the instructors was taken up kindly answering this guy while the other students twiddled their thumbs. This course should really be called the discussion of the topic with Tyreen.
dynDiceCAratENterMS...
I have been at it (on and off) for 30 years now and still have not got through it!
That's smart lecture notes numbered for the use of the refto book
No matter how hard I try, my Kurt Godel jokes always seem incomplete, or recursive - 'very much like my Kurt Godel jokes...
k-G jayWaltz ENiGmoo...
Started out embarrassed, soon grew comfortable with the weak crowd, and destroyed their minds with philosophical wonders. That is a real lecturer.
par0sums characterised teknikola rotorations?..paint box 'komikchumps'..
Now I know why the chicken crossed the road! She'd never heard of Zeno!
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
@@bautibunge737 diamond pentiV too quad 'coyENteX!'caChaRi..
@@stephclements6226 ??
Fantastic lecture!
EXCELLENT, IS WONDERFUL. THANKS
Max Planck Institute in Marburg and the Philipps University in Marburg has stumbled upon the first regular molecular fractal in nature. April 2024
"Dialogue C cannot be spoken in this lecture series"
sincs fia oft lornderngsz!!.. KOkeynays
When the book was new, I read it about 8/10 through, but I was not a math/logic major, so when the text was mathematical/logic symbols, I bailed. Gave my copy to a CompSci undergrad patent attorney from Harvard.
Godel : Einstein = Leibniz : Spinoza
33:00 how do you go from meaningless to meaning. Think CODE pg. Think materialism. Think idealism.
Also an isomorphism seems to just be a translatablism.
jurno starbuks
Anyone starting this book now or planning to start anytime sooner ?
I am
Logic as allegory...Thomas Mann ...Venice adventures....
"Headlights" would have been a better example of a "homomorphism" than a steering wheel; because the functionality of steering is on both, but only a car has headlights.
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.
In the first three minuets one the most profound questions pops up: HOW CAN we think if we are a collection of primitives? Then five min later an equally profound question: HOW DO we think? look @7:00 in none of those things seem to have anything to do with thought on the face of it.... lol crazy
excellent that is he doing in 2020 .
While loop is not recursive..btw
I love provocative topics
Yes. I figured that if I forgot your reward, I should at least conjure up an expression similar to regret.
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".
synchro blots
The solution to liar's paradox seems rather obvious to me. The paradox arises due to the fact that the analysis is static. However, if your analysis is dynamic, the paradox immediately resolves itself. In other words, dynamically you can say as follows: "This sentence is false." is true. Then you check it again and decide that it is false. Then you check it again and decide that it is true. As long as you have memory of the previous state, you can judge the next state. Furthermore, it is possible for dynamic checkers to disagree with each other. This shows that they can have internality (or an internal frame of reference that makes sense only to themselves. Kinda like living things experiencing their own subjective world). As to Russel's paradox, the same applies. As soon as the man becomes a barber he shaves himself once after which he never shaves himself again. Paradox resolved.
I think that it's possible to understand the liar's paradox from a dynamic analysis. don´t you think?
@@alioshenko I thought that this is what I said in the first place.
@@StanislavMudrets My point is that the liar paradox turn into a loop when you use dynamic analysis and that's why is a paradox. One thing is to understand the paradox and another to solve the paradox. Maybe I'm not have been clear. Thanks for take your time to answer my first comment.
@@alioshenko The looping is a problem in a static analysis. It isn't a problem in the dynamic analysis. Why? Because in a static analysis you want the loop to eventually stop so that you get a particular answer. The loop is considered nothing but a trace with a finite set of operations. In the dynamic version you don't necessarily want the loop to stop. I'll give you an example of this. In a living cell, the various proteins and bigger structures are constantly falling apart and are recreated anew. However, it isn't that some external entity is recreating them. These different chemicals contribute to recreation of other chemicals etc. etc. which eventually recreate the original ones in a cycle. In other words, the dynamic process of life is cyclic. You don't want the loop to stop. For it to stop implies certain death with each chemical eventually falling apart and the increase in disorder. In static analysis, we do not take this kind of one hand washes the other seriously. We want an answer of some kind to be recorded somewhere. We don't see the cyclic action itself as the answer (foreground/background distinction). These paradoxes are not exactly about living processes, but they have something in common with them - namely the cyclic nature. Imagine a car engine. It isn't alive, but a cycle is essential to its proper operation. If it stops, it will not be able to push the car. See what I mean?
punchcardsss...
Why did the instructor tell the students that he would give them 20 bucks to solve the MIU riddle and then get pissed when they weren't listening to him.
Enjoying this. Are the class notes lecturer refers to somewhere online? ( I have the book )
k-means colostaaz!?..
Vidéo ended just when it got interesting
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?
fell in it in 94 and still in
The book is very interesting, if you can get through it…
So did the lecture end or did they cut out some of the end?Why did it fade out while the teacher was still talking?
31:40 the puzzle is considered to be impossible to solve, but he didn't want to risk more than 20 bucks that it is in fact impossible to solve. That's how much faith this guy has in the mathematicians before him.
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
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?
!!2&6?..[8/16/23|64!]..rot
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.
It's not possible to get MI to MU. There is no possible way to successfully eliminate I from the "equation".
windowsBuei/unix/9?..
Why he ignores the triangle in the middle? If we define 2 dimensions as function with 2 arguments and each point of an object can be defined by these arguments lets define the metacentric of the big triangle? If you double the size of the triangle by only 3 small triangles but ignore the forth one in the middle you get logical nonsense.
26 in it reminds me of that inverse calculus in field theory kinda, and cantor