#science #physics #ideas The Biggest Ideas in the Universe | 23. Criticality and Complexity

#science #physics #ideas The Biggest Ideas in the Universe | 23. Criticality and Complexity 72,711 viewsAug 25, 2020 Sean Carroll 154K subscribers The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is Idea #23, " Criticality and Complexity." Having spend a lot of time on the basic ingredients of our universe, it's time to contemplate how they come together to make complex systems. The idea of critical behavior -- things happening at all spatial scales -- is an important organizing principle. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/p... The Biggest Ideas playlist: https://www.youtube.com/playlist?list... Blog posts for the series: http://www.preposterousuniverse.com/b... Background image: https://en.wikipedia.org/wiki/Wikiped... #science #physics #ideas #universe #learning #cosmology #philosophy #complexity #criticality 173 Comments rongmaw lin Add a comment... Paul C. Paul C. 1 year ago Hi Professor Sean, really sorry to hear that we are coming to the end of this amazing series. But THANKS a million anyway, for the most informative, educational & interesting videos on the whole of YouTube. Please don’t forget about the possibility of releasing the entire series on DVD. That would be great, and I’m sure you’d have plenty of takers. Best wishes as always from West Wales. And my sincerest thanks once again. 7 Tanay Mehta Tanay Mehta 1 year ago Professor you made my quarantine SPECTACULAR, just OUTSTANDING. Its a dream to learn such high-level topics in such a comprehensive manner from a professor of your stature. Feynman would’ve been proud!👍🏼👍🏼👍🏼🙏🏻🙏🏻🙏🏻 49 : Antypas : Antypas 1 year ago Professor Carroll: I wish you'd make a "bonus video" on the way you organized or designed this whole project. You clearly allowed for enough spontaneity in the presentations, and Q&A, underpinned by a a conceptual plan. If you could share with us your cognitive experience, how you imagined it, and how it came out. I think this project was a big idea too, and I thank you for it...and look forward to its published book form. 29 Om3ga Om3ga 1 year ago As always, AMAZING, ENTHRALLING, INFORMATIVE AND MIND BLOWING. You make it easier for us to understand complex subjects. Thanks Professor 13 MyLameAnimations MyLameAnimations 1 year ago Your "Biggest Ideas" videos are way over my head, but I still sit here and watch them all. You're so good at explaining that I actually feel like I understand what you're talking about. Just don't ask my to explain what I learned to anyone else. 10 Petru Galanton Petru Galanton 1 year ago For me, this series is right up there with Feynman's Messenger Lectures. Thank you for this amazing series! 4 Rhonda Goodloe Rhonda Goodloe 1 year ago Sean, Sorry there are only 2 more topics left in the series, but a Big thank you for all of them! Looking forward to seeing the elephant! 54 Paps Aebus Paps Aebus 1 year ago I wish someone combined this series in one ginormous book. It would be Penrose’s “The Road To Reality”, but much more accessible. 18 D Monroe D Monroe 1 year ago My Gawd, Sean! You’re prolific! Fun watching the method to your madness come together in this great series! Thanks! Wondering about criticality/phase transitions in systems characterized by Tracy-Widom distribution. 2 x2Shae x2Shae 1 year ago I'm not ready for this to end... Thank you for the series , Sean! This has been one of my favorite series I have ever watched on youtube. I'm glad I can support on different sites hym279 hym279 1 year ago You make it too difficult, Prof. Carrol. Instead of elephants we would've understood a lot easier with spherical cows! Thanks a lot for this series!!! so informative, fun, enjoyable, etc. it's a honor to be part of your community :) Best possible use of our quarantine time, both yours and ours. 3 pizzacrusher pizzacrusher 1 year ago So good! I keep watching them all over and over again, hoping that some day I'll understand it all, or at least be able to articulate it all as well as you do. 1 Rattus Norvegicus Rattus Norvegicus 1 year ago Thank you so much for making this lecture series and for making it free for all on YouTube. 2 sudip patra sudip patra 1 year ago Dear Professor thanks a ton for this wonderful series! it is sad that this is going to end ...will really miss..but hope we can still continue discussing and exploring rafael muñoz martinez rafael muñoz martinez 1 year ago You explained it so well, that you made extremely difficult concepts, understandable, I think yours is the best Relaitivity theory explanation I have had. 1 Grol Midri Grol Midri 1 year ago Thank you so much for this series of videos and all the other ones you have made. They are fantastic. Marc Merlin Marc Merlin 1 year ago (edited) Sean, in case you're looking for a "bonus" for the Q&A for this video, you might want to consider a brief discussion of Benford's Law. I've always been fascinated by this surprising observation about the distribution of the leading digits of real-life data sets. I imagine others would find it interesting, as well. Qman545 Qman545 1 year ago I love your videos! Reminds me of college haha. But that's a great thing. You explain and break things down on a spectacular level! Crass Flam Crass Flam 1 year ago (edited) Could we define "systemic complexity" as the length of the shortest algorithm that can predict the next state of the system? (given some current or starting state) NoWhereMan NoWhereMan 1 year ago Dr. Carroll, may you succeed in your own breakthroughs. You have made the world a better place by making this series. 2 choblet choblet choblet choblet 1 year ago Hello! I'm a tutor and would love to know what software Sean has been using for this series. I finally have enough to get myself a nicer tablet and my students and I would love this type of setup, but I can't seem to find it with my searches. Teddy Brow Teddy Brow 1 year ago (edited) "idea number 23 **out of 24**" 😭😭😭 Just as so many others have expressed in the comments, I'm sad to see this series ending, but also thank you so so incredibly much for all the time and effort you've put into it! I feel confident these videos will be a go-to resource for physics-enthusiasts for decades to come. They came at a perfect time for me, as I've been contemplating shifting from my current field of software engineering back toward physics (my first love). Your videos have been very informative/helpful as well as inspirational. Side note: by coincidence it looks like I'll be caught up just in time for the release of the final topic + Q&A videos! I got a late start on the series at some point in early August and didn't set any sort of schedule for getting through them, so I was surprised to see the timing work out so nicely for me 😛 Sandip Chitale Sandip Chitale 1 year ago (edited) Thanks for the video. Given the chemical properties of hydrogen, carbon, oxygen, nitrogen and some metals, has any one done power law analysis and preferential attachment analysis for formation of complex organic molecules, amino acids, proteins, RNA, viruses, DNA and eventually life? is that even applicable to the stated problem. Nader Chmait Nader Chmait 1 year ago Great lecture. The computer scientist in me can't help but to note that the (Solomonoff-)Kolmogorov complexity is uncomputable (so I'd advocate that it should only be used as a bound on algorithmic complexity rather than an estimate). Shera Shera 1 year ago @Sean Carroll Can you please do provide a 24-episode series about criticality you mentioned in this video! That would be very interesting I think! (and thanks in advance 😇). I also have a question, can the Per Bak model also explain honey coiling? stick109 stick109 1 year ago (edited) Sean, you can represent first N digits of any irrational number as a ratio of two integer numbers of length sqrt(N). Whether it is pi or sqrt(2) does not make a slightest difference. It is absolutely not easier to represent pi or sqrt(2) in terms of Kolmogorov complexity than any other irrational number. Or any random sequence of digits of the same length, for that matter. Nathan Okun Nathan Okun 1 year ago The city walking speed increase with larger cities may simply be that the spacing between places that people want to go is bigger in a bigger city so they have to walk faster to get anywhere in a reasonable limited time -- lunch break time, for example. Not necessarily a mystery, is it? Sean Carroll Sean Carroll 1 year ago (edited) Erratum: In Kleiber's Law (1:28:00), metabolism goes as mass to the power 3/4, not 1/4. Thanks to Angry Satsuma in the comments. Also sigma should be squared in the formula for the normal distribution. 16 Denis Nichita Denis Nichita 1 year ago (edited) Hello Sean. Love you work. You talked about criticality and touched upon phase transitions. Could spacetime be thought of as a phase transition of the underlying quantum mechanical degrees of freedom? The metric could be the order parameter. We go from a phase with 0 metric (the qm dof not yet transformed into spacetime) to a state with a non-vanishing metric (the qm dof have now 'coagulated' into spacetime) similarly with a second order phase transition. This could be the mechanism of emergence of spacetime. Sidney Jacobs Audio Sidney Jacobs Audio 1 year ago Love your videos man such an inspiration for me to make my own videos and help people. 6 Michael Schnell Michael Schnell 1 year ago In this video I would have expected some reference to Leonard Susskind's work on Complexity and quantum theory, which i find extraordinarily intersting 1 Jacky Chan Jacky Chan 1 year ago (edited) Sean, thanks for your good work. Black Jack 21 Black Jack 21 1 year ago Professor i appreciate videos like this but i would also appreciate full fledged lectures by you. Will Pittenger Will Pittenger 1 year ago Actually, Pluto passes the spherical test. Even Charon, while considerably smaller than Pluto, also passes. Where they fail the 3 criteria set by astronomers is the "clearing of the orbit" test. Shytam Shytam 1 year ago It's called the "normal" distribution because it is normalized. That is the data undergoes a specific transformation that ensures certain parameters get predetermined values, just like you mentioned (Variance = 1, Mean = 0). The transformation in question is achieved by subtracting the mean and multiplying by the standard deviation. Statistics 101 to the rescue! :) William Whitt William Whitt 1 year ago NOOOO. Only one more? This series is amazing because it's like your solo mindscapes. Gonna be real sad when it's over. Nick B Nick B 1 year ago Weekly drop by Sean is great as usual. teflontelefon teflontelefon 1 year ago So much substance compressed into these. Thank you thank you thank you. Deep Bayes Deep Bayes 1 year ago Nice talk Sean. I think it is normal because samples cannot be extreme, so the mean is representative, as opposed to say power law or heavy tail distributions where there is no normal size. Bill Holland Bill Holland 1 year ago Professor Carroll, at the end of this series, could you mention where the concepts in it would be covered nowadays at Caltech? I’m curious where the concepts would be taught (at a problem solving level) in the undergraduate and graduate level courses in physics and math at Caltech. (I received a BS degree in Engineering and Applied Physics from Caltech in 1977. If I had you for Physics 1 or 2, I would have switched my major to Physics!) 1 Shytam Shytam 1 year ago And criticality got its name from the physics concerning critical points, as defined in calculus. For a single variable function it's any point where the derivative over the variable is 0. Criticality is the physics of such points as you've so admirably explained in this video. atomly atomly 1 year ago Sad it's nearly done, one of my favorite video series on youtube. parkokosasd1 parkokosasd1 1 year ago Honestly big big shoutout to Sean. He didn't have to make these videos, he certainly doesn't make much money from them, and he took a LOT of time to make them, even going to the trouble of finding some cool graphics to make the whole thing a little more dynamic to watch. Some of the topics are way over my head but he balances talking to laymen vs showing you how deep the subject is and alluding to things you might have a tiny grasp of, and you gain just that little bit more when someone leaves a bit of the complexity in the lecture. He was really born to teach and explain. Whether or not he makes some big monumental physics discovery one day, he will no doubt be responsible for fostering the love for this topic in many young people who will further the cause. If i wasnt a 30-something lawyer with crappy math skills, I'd definitely go become a physicist and a big part of it is inspiring figures like this man. Jainal Abdin Jainal Abdin 1 year ago Question for Q&A: How is entropy related to complexity? For example, black holes have very high entropy, but low complexity (No Hair Theorem), so the relation seems inverse? Attila Beregi Attila Beregi 1 year ago Tom Scott made a video on the walking speed problem, and in there was an interesting idea, which is that it's simply younger people live in bigger cities. John Długosz John Długosz 1 year ago 1:08 Before you got to "sand pile", I was thinking about "Strange Attractors" in Chaos (and their visualization via fractal drawings that were so popular in the late 80's -- remember FRACTINT on DOS?) Re sandpile for real: I recall reading about an experiment where a mechanism was built to drop one grain of sand at a time and study the pile. This was decades ago now. Much was learned, including the observation that the pile would become steeper until a shallow landslide took it back down to the bottom of the range again. These large sheet movements took place on different scales... I don't remember the details. llydndrsn llydndrsn 1 year ago Professor Carroll: I am curious whether you have any thoughts on the work of Ilya Prigogine. Decades ago he explored how order arose from chaos, postulating that dissipative structures arose in out of equilibrium systems to minimize the growth of entropy. You had César Hidalgo, something of an intellectual descendant of Prigogine, on your podcast Mindscape. Do you think Prigogine's work sheds light on complexity, phase transitions, and criticality? Michael Shapiro Michael Shapiro 1 year ago Dear Prof.Carroll: What about Wigner experiment and its implementation by Proietti et al.? What do you think about it? I think this is a relevant question for your upcoming QnA 23. James Stewart James Stewart 1 year ago Here's a shot in the dark at a time of day when it is far too late/early to bother considering it myself - Is complexity an entropic system? Is there a relationship between or binding the two as they both inherently increase over time? Or is it that I'm just too tired at the moment to be bothering here this week? Allen Taylor Allen Taylor 1 year ago Great video in a great series. However, Pluto was not demoted to dwarf planet status because it was insufficiently spherical. In fact, it is much closer to sphericality than is Saturn. It was demoted for scurrilous political reasons. The argument was that it had not cleared out its orbit of other objects. If that were valid, then Earth would not be a planet. There are thousands of so-called "Near Earth Objects" )NEOs that have not be cleared out of the Earth's orbit. Furthermore, if Earth were at the same distance from the sun that Pluto is, it would not have cleared its orbit any more efficiently. The demotion of Pluto to dwarf planet status was a bogus political stunt that happened in a vote that occurred after many of the delegates to the conference had left for home. Those remaining were overwhelmingly not planetary astronomers. JK JK 1 year ago Totally random question... what's the relationship between power laws and entropy? Nathan Okun Nathan Okun 1 year ago Small fact: Using a fixed strength of steel for the barrel, a fixed projectile muzzle velocity, a given fixed powder type, and a fixed projectile shape and design, just scaled in proportion to the gun size, a gun's weight goes up roughly with the 4th-power of the bore diameter because the area on the projectile base that the powder blast pressure is pushing on is getting larger by the square of the diameter and the projectile weight is going up with the cube of the diameter, so more and more powder has to be added to push harder along that barrel and the gun has to be made stronger and stronger to handle the additional force as its size goes up, needing more steel. Modern guns look thinner than old guns only due to stronger, tougher steels being used to make them. Lionel Sacks Lionel Sacks 1 year ago (edited) Re heavy tails: you say "calculate the mean". You can always calculate a mean of actual data. But a mean is meaningful only for finite standard deviation... And the SD of a power law distribution is, almost infinite. IMHO it is an error data analysts make - stuffing a vector of numbers into the mean() function, without checking if there's really a normal distribution around LeapDaniel LeapDaniel 1 year ago I have heard it said that everything ever written can be found encoded in the digits of pi, since although the digits are not random they are pseudo-random. 10:58 Here you imply that "being found in the digits of pi" is sufficient to make any finite string of digits simple, at least in terms of the Kolmogorov complexity. Wouldn't that imply that every finite string of digits is simple? Since every finite string of digits will eventually be found in the digits of pi. 3 dk6024 dk6024 1 year ago For all programming languages the relative complexity of the strings may not be the same. Cognitive Gear Cognitive Gear 1 year ago (edited) I'd just like to say as a casual viewer, as someone who is moderately familiar with mathematics & physics: I really appreciate this series, and hope you can go into more depth at a later date. You're filling a niche that doesn't really exist on youtube yet, and the platform as a whole (never mind the internet) can benefit from having experts like you simply make their own content, the way they want it, and cut through the middlemen. 2 Henry J. Henry J. 1 year ago God, if she exists, knows how many YT physics/cosmology videos I've seen (Susskind, Feynman, et al, ad nauseum). The Biggest Ideas in the Universe series is by far the best. Much better and more complete explanation than anywhere else. Not a big fan of the Brian Green/Degrasse Tyson/PBS type of program that's heavy on CGI and lite on content and depth in any case. I especially like the Q&A follow up to clarify points many of us get wrong. I wish you'd explain why the progress of particle physics/cosmology has sort of stagnated since ~1973. We keep looking for some things and never find them (proton decay, dark matter particles, quantum gravity). Some of the explanations we do have seem contrived to fit the data but don't lead to any deeper understanding (no patterns, no overarching structure, no method to the madness). What's up with that? We need a breakthrough. 1 jursamaj jursamaj 1 year ago The problem for Pluto is not its shape, but the fact that it hasn't "cleared its neighborhood". 1 Gary Huntress Gary Huntress 1 year ago Untrained neural networks often contain millions of weights that are initialized from a normal distribution. They are iteratively trained and the weights evolve to a point where it can successfully perform the task ("is this a picture of a cat or dog? Y/N"). I'm going to analyze my nn model weights and look for power law and criticality behavior. 2 John Długosz John Długosz 1 year ago re the brain: The fact is that there are limits to the scales allowed, from the smallest unit of activity up to the entire brain being the largest. Add to this the fact that the population is actually discrete and finite, so if you were to measure all of them you would get an average! I wonder if it might be the case that some particular flavor of normal curve like the lognormal might be indistinguishable from a power distribution given the entire population. Just speculating here... it might be the case that the parameters of the lognormal curve vary widely between individuals, even though the power curve slope is nearly the same. In this case, the former would be a better model for predictive power and classification, even though it's actually a physical approximation to what should be a power distribution if you modeled it abstractly. Boris Petrov Boris Petrov 1 year ago (edited) Kolmogorov's complexity is an elegant concept -- also used to measure intelligence (in a sense of solving problems) of various animal species (not only humans ;-)) ) On scale -- your readers might be interested in book by Geoffrey West - "Scale". He is a physicist who spent decades working on Texas collider - a project that was cancelled by mandarins in Congress -- after that he studied physics in bio-systems -- highly recommended PS: I just heard that Sean extensively describes West's book "Scale" -- my apology Sebastian Dierks Sebastian Dierks 1 year ago At 18:50, I think you need a sigma squared in the denominator of the exponent. 2 Sandip Chitale Sandip Chitale 1 year ago (edited) Can you please make a clarifying comment on Stuart Bartlett’s statement that models of Darwinian evolution show a evolution from complexity to simplicity? I had never heard of this before. Are you aware of such experiments. It is my understanding that in biology Darwinian evolution i.e. random mutation modulated by the natural selection (at each generation consistent with the environment at that time – and the environment itself may change over the full time frame of the evolution) results in complexity from simplicity given that the environment remained within the tolerance band so that complexity could build up. It is true that Darwinian evolution does not have “simplicity to complexity” as the only possibility. It is a special case when the environment remains stable enough over the time frame in questions so that the complexity can build up. And fortunately for earth this has been the case since the last catastrophic event of an asteroid hitting earth 65 million years ago which has allowed shrew like animals to evolve into animals with brains capable of self awareness and reflection (complex). IN the immediate aftermath of that catastrophic event the complexity did go down. I think of this to be somewhat similar to the V shape of entropy (in a quantum fluctuation) you talk about whereby there can be a phase where entropy is going down or going up. Our current universe is a special case and happens to be on the right arm the V where the entropy is increasing. I thought Theory of Darwinian evolution was a settled science at least to the same level as General Theory of relativity. I think in your podcast you were a very polite host (at some level you should be and are expected to be and you always are) and did not push back more on him to the extent I would have liked. Sorry for the sociological comment, but I feel that the scientific statements without evidence that refute established science need to be pushed back harder. I would put Stuart’s comment closer to flat earth people. Barefoot Barefoot 1 year ago Is anyone else intensely reminded of the Ultraviolet Catastrophe when we talk about Gaussian vs. Power Law vs. lognormal? Lognormal looks like a real physical system to me. Power laws... don't. Actually, I was bothered right away by the discussion of the power law "not having a preferred scale". I realize that what you meant was that there is "no preferred zoom level"... but power laws very much have a preferred size/scale, which is that almost all samples will be infinitesimally small, because the number of samples, as the size approaches zero, is asymptotic to infinity. The truth of almost all physical systems is that there are boundary conditions. For example, with the distribution of wealth, there are boundary conditions imposed on the left by various circumstances and eventualities. It's impossible to have zero wealth and remain alive, so people who really do approach zero wealth either die off or use violence to change that fact. Then, of course, various social safety nets also provide a boundary condition. The result is that it can be neither Gaussian, nor a true power law, at wealth --> 0. Likewise, while there is a heavy tail, it is not an infinite tail. A single person cannot have more than a certain proportion of the total global wealth of our species. Certainly not 100%. Probably not even 10%. (As a formality, it's possible to go above that, such as considering that technically, Queen Elizabeth II owns all of Britain, all British subjects, all ships in British waters, all whales within so many miles of British beaches, and so on, but let's assume we're talking about real, tangible, de-facto wealth, which is how the world actually runs.) The real distribution of wealth is thus a very complex plot that has a number of boundary conditions, artificial bumps at certain values from social assistance programs, and so forth, but it certainly feels like lognormal distribution does a much better job of modeling that than either power law or Gaussian distributions can do. This also goes for something like the universe. The distribution of phenomena by scale cannot truly be a power law there either. It seems pretty likely that there's a boundary condition at extremely small scale, and of course (for the observable universe at least), no phenomenon can go above 180° on the sky. In a much firmer way, in the universe as a whole, the universe itself is scale=1. Nothing else can possibly be larger, so the number of phenomena at scale > 1 must go to zero, which power laws do not do. Anyway, it just very much reminded me of the Ultraviolet Catastrophe, where it was believed that the distribution of black body radiation was effectively a power law, when in fact, with the boundary condition at high energies applied, it turns out to look very much like a lognormal distribution. Bohan Xu Bohan Xu 1 year ago 48:30 having the same form with possibly different parameter <=> scaling invariant in the context Am I missing something? it seems different from scale invariant for field theory. Do we also need to make sure the parameter is only a trivial change of numerical value? (in that case I think...n(s) has to be dimensionless right?... so {the unit of k and s^whatever} can gives a trivial numerical change of k ) Jon Wesick Jon Wesick 1 year ago Here's a naive question that has bothered me since I worked in meteor burst communications decades ago. The distribution of meteors follows a power law p(m)=k/m where m is the mass. If you wanted to calculate the mean mass, you'd naively multiply this distribution by m and integrate from m=0 to infinity. This integral does not converge, which is clearly nonsense. Does anybody know how you should calculate this? Ronnie Tynell Ronnie Tynell 1 year ago Great series! I love your work. Now for a not very relevant comment: In this episode at approx. 1:14 you twice pronounce the word organism in a very subtle way. You might want to revisit the audio :-) I’m not a native english speaking person, so it may just be my ears 1 Vikram Singh Vikram Singh 1 year ago Please let this not be the 2nd last topic! Enjoyed every lecture but as a poker player really loved the explanation of binomial distribution. The entire lecture was great. I gave my best friend a Galton Box on her Birthday last year. By the way, Professor Carroll, why does binomial distributions show up in 2-card poker? Smth like No Limit Texas Holdem. I was reading Chaos by James Gleick and also perhaps mentioned in The Information - one thing that struck me was that a function in that bell shape is part of the Mandelbrot set...where there are bifurcations and all sorts of things happening & the applications even extend to why redundancy is error correcting (example - using Victor and Bravo, Fifer and Niner in the aviation industry to make sure V and B or 5 and 9 are not mistaken for each other) & the representation of the Mandelbrot set on a number line was awesome. There was also a mention of how chaos and bifurcations within a function belonging to that set are error predicting? Is this something you can answer in the Q&A video. Also, one Q&A video at the very end covering all the lectures - surely that could be a thing? The Q&A to rule all other Q&A. We'll call it The Lord even if it's not carrying a Ring. Jon Wesick Jon Wesick 1 year ago I think you need to square sigma in your formula for the Gaussian distribution (at 19 minutes). Nightmare Court Pictures Nightmare Court Pictures 1 year ago (edited) I actually disagree with Carrol here, and think power laws and complexity are really the only thing that truly exists, and that everything else is merely an approximation of it. The square cube law sounds cool and all but there's a problem in thinking that the square cube law isn't just a consequence of being an approximate notion of complexity in the laws of physics themselves. It shouldn't be a surprise that people are looking for theories of emergent space-time and emergent models of the standard model. Funnily enough there was just an announcement that CERN might have stumbled on the the fact that there could very well be even more fundamental forces smaller then the scale of the standard model. This shouldn't be a surprise knowing that if the world operates in accordance strictly in terms of complexity theory, then technically EVERYTHING is scale invariant, and all natural systems obey power laws. binaryalgorithm binaryalgorithm 1 year ago (edited) Scale free networks... the brain is one. The complexity seems to surface in between the very small and the very big, where different paradigms overlap. The criticality in the middle of the plot, maybe just the state our universe happens to be in between big bang and dilution by dark energy into inactivity. John Długosz John Długosz 1 year ago Correction: Pluto is easily large enough to be in hydrostatic equilibrium. What it lacks is "clearing out its orbit". For an example, look at the second-largest body in the asteroid belt. It's not classified as a dwarf planet -- it's sort of round but has a chunk missing. It would be in hydrostatic equilibrium if it were hotter, as it was when it had formed. But once it cooled, it happened to still be round but when a piece was knocked off the rest did not slouch back together. https://en.wikipedia.org/wiki/4_Vesta#Physical_characteristics 1 Alon Nissan-Cohen Alon Nissan-Cohen 1 year ago Can anyone explain that odd point out in the plot at 1:37:16? I mean, why on earth would people in cities with some specific number of people walk significantly slower than the power law suggests??? Jack CF Jack CF 1 year ago Maybe I'm taking this too seriously but animals of the past such as the larger Sauropods like Seismosaurus were larger than King Kong. Even some living animals today such as the humpback whale are larger than King Kong. So, could you please clarify why King Kong couldn't exist? HappyActiveHealthy100YearsPlus HappyActiveHealthy100YearsPlus 1 year ago (edited) For the first time in was disappointed with the content of this video series. Complexity and criticality is in most systems that have several components, large scaling differences, dynamic behavior and some form of uncertainty. Even a very simple controls system will in general be so complex that it cannot be „solved“. However, the human brain has a fantastic feature. And that is its associative highly parallel „thinking“. Sometimes called fast thinking, as opposed to the step by step, serial, slow thinking. In this video we heard a lot about how to approach in a slow thinking manner the problem of complexity. Ok, fine, If you have attended maths or computer science or controls system classes at university, then this all sounds very familiar. HOWEVER, if we want to activate the only part of our brain that can handle complexity, we need to dig into a strategy to setup our brains to develop into such intuitive”monsters” like Mozart or Einstein. We need to make sure that we create such brilliant brains, one of which intuitively produced fantastic music (if that is your type of music) and the other being able to think inside the curved space time continuum. So, in order to address complexity, we need to find the right way to set up our intuition to come up with sufficiently correct ideas. I do not want to put the whole method in a comment, but here are some main prerequisites: - having the vision to increase wisdom and truth - having the certainty that this vision is achievable - having at least 20 years of time to get a good understanding of ALL sciences, including philosophy, psychology, artificial intelligence, logic, maths, physics, human behavior, brain structure and inner behavior, etc. The more the better, but never too deep in one topic, rather go deeper in another topic. Become a generalist. - learning how to use the most efficient way to learn. And that is to use the slow thinking part of your brain to feed your brain with knowledge and give your brain a task which you really deeply want (best is if it matches your vision), then leave your brain alone with all that knowledge plus the task. Some hour later, maybe after a good night sleep, challenge the result of your fast thinking part of your brain with your slow thinking brain, which is structured and logical and hence can spot the flaws your fast associative brain has put in. When you do this for many hundred iterations you will reach great results and if you do this for 20 years you might have developed a brain like Mozart or Einstein. It needs such brains to solve complex problems. Trying to solve complex problems with the slow and serial part of your brain is maybe 100 to 1000 times slower. There are many impediments to humans developing such powerful brains. But I am a strong supporter of this approach. Important is to develop a set of thinking tools and paradigms which you need to use deliberately for specific situations. One is: always look at your reasoning from the above. And when you have done that, look at it from one level above and so on until you find the meta explanation. Which you then draw on a blank paper while explaining it to n imaginary person. The next day you do it again and again. There are hundreds of such tools and paradigms. Use them wisely. Develop a feeling when to use which one. We should teach our kids how our brain work and they will be prepared to solve complex problems... Amlan mihir Amlan mihir 1 year ago Hey Sean, can you tell me what's that progam you're using for explaining the diagrams and stuff Michael Schnell Michael Schnell 1 year ago There is a trivial fact that would lead to the preference of big cities (proba(x(n)) proportional to n, in that you are more likely to choose a location where some of your acquaintances live :) John Długosz John Długosz 1 year ago If website links is a classic problem, it really dates your field! Shytam Shytam 1 year ago How do complex systems relate to entropy? finalman242 finalman242 1 year ago Imagine living in a city so small that you have to walk backwards Privat Privat 1 year ago A neutron star is by no means the size of the earth. You probably meant a white dwarf. Great series though!!! Rick Harold Rick Harold 1 year ago Rock on, awesome! : Antypas : Antypas 1 year ago The Q&A video for this lecture appears as ‘private’ ... I wonder if Professor Carroll is aware of this. William Tang William Tang 11 months ago (edited) real nice presentation. the weight of african bush elephants do not follow normal distribution because there will be no case of a weight bigger than 99999Kg and negative. But we can use it as an approx. thnx a lot. I learn a lot from U... Rusty Spotted Cat Rusty Spotted Cat 1 year ago "It doesnt mean the model is right .. it just means the model is not wrong" Iñigo Javier Puente Henales Iñigo Javier Puente Henales 1 year ago At circa 19:30 there is an error in the gaussian exponent denominator : should be 2*sigma squared ;-) David Hand David Hand 1 year ago I love you for making these buddy and I've learned a lot, but that introduction to criticality was a terrible detour Jakeem Ortiz Jakeem Ortiz 1 year ago I think the last one might be about Life and Evolution 1 Boris Petrov Boris Petrov 1 year ago PS: A Question: In your estimate how many there are googols (10 on 100) multiverses in your "mad-dog" Everett-ian hypothesis... ;-)) Angry Satsuma Angry Satsuma 1 year ago Kleiber's Law: power is 3/4, not 1/4 :)) 4 DanielWorcester DanielWorcester 1 year ago I don't think there are actually random numbers. Your pattern 7-6-0-6-3-1-0-9-8 ... Would "probably" be next a 7,6 or 0. There's is a pattern. Alex Tritt Alex Tritt 1 year ago Just as im going to bed again. I think this time I'll actually try for a good sleep schedule. See you all tomorrow! 2 Gilbert ENGLER Gilbert ENGLER 1 year ago 👍👍👍👍Many thanks! Hans Nuttin Hans Nuttin 1 year ago "That's why scientists are payed the big bucks" - these hidden gems inside an otherwise serious endeavour are priceless :lol: dePlant dePlant 1 year ago (edited) Oh i so wish he used “the airspeed velocity of an unladen swallow”.... rather than the mass of an elephant. #science #physics #ideas The Biggest Ideas in the Universe | Q&A 23 - Criticality and Complexity 21,071 viewsAug 30, 2020 539 DISLIKE SHARE DOWNLOAD CLIP SAVE Sean Carroll 154K subscribers The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is the Q&A video for Idea #23, " Criticality and Complexity." Two big themes here: the relationship between complexity and entropy, and the real-world technicalities of dealing with power-law distributions. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/p... The Biggest Ideas playlist: https://www.youtube.com/playlist?list... Blog posts for the series: http://www.preposterousuniverse.com/b... Background image: https://en.wikipedia.org/wiki/Wikiped... #science #physics #ideas #universe #learning #cosmology #philosophy #complexity #criticality 86 Comments rongmaw lin Add a comment... Rhonda Goodloe Rhonda Goodloe 1 year ago Sean, Wow! What a ride over the past several months. Thanks so much for making this information available to the average Joe (or Josie) on the street. I'll be listening to it all again! 22 RedSquirrelEater RedSquirrelEater 1 year ago (edited) What a great series! I've been through more in-depth videos with more math, but they tend to get very dry and tiring to follow. Your series should be a per-requisite for other in-depth lectures, because they make everything make so much more sense! 1 David Hand David Hand 1 year ago Has anyone tried analyzing the Fourier transform in relation to complexity and entropy? It seems like that would capture scale dependent behaviors better than linear comparison. 1 Professr Frank Professr Frank 1 year ago 51:13 Finally a good calculus lesson. Thanks! 😊 1 James Stewart James Stewart 1 year ago Sean, thanks for the integration - that was a fun combination of both yelling at my phone and memories of high school! 1 Shytam Shytam 1 year ago Thanks, Professor! I feel like I could listen to you talk about Entropy forever, but that's obviously me not taking into account a possible change in my attitude at long enough periods. 1 Sully Sullivan Sully Sullivan 1 year ago Sean have you ever heard of the "grim reaper paradox"? interested in your take. I think it's pretty silly but tomahzo tomahzo 1 year ago (edited) 41:28: What troubles me here is that compression algorithms operate on entropy (as defined by Shannon), not complexity. High-entropy sources are difficult to compress, low-entropy sources are easy to compress. If you have a completely random source you typically do not manage to compress it very well. (have you ever tried to compress white noise using JPEG - it's not pretty) At least that is true when it comes to lossless entropy encoding. JPEG is not lossless so you would be discarding parts of the source data and partially reconstructing it during decompression. To me it would seem like it would be easiest to compress the low-entropy source (the left-most coffee cup), somewhat harder do compress the medium entropy source (the partially mixed coffee cup) and very difficult to compress the highest entropy source where you have a completely random distribution of coffee vs. cream. However, what you are saying is that you apply some kind of coarse graining to the distribution in that case to get rid of all the randomness, which seems like cheating to me simply because it amounts to lowpass filtering / blur kernel processing or whatever you want to call it. You can just pick a coarse graining filter kernel that very efficiently removes the randomness in the high-entropy source and produces a very smooth, uniformly distributed source. (all pixels have the same gray color) Once you have found a way to reduce the entropy post-filtering to a point where it has less entropy than the middle coffee cup then that will have proven your point and the JPEG compression will be able to more efficiently compress that source. Had it not been for the coarse graining then you would not be able to prove anything here. Unlike your previous discussion about coarse graining in a previous episode when you argued that coarse graining is not arbitrary (that is, you are not allowed to pick a coarse graining strategy that lets you prove that e.g. the universe started in a high-entropy state and started evolving towards a low-entropy state because that is inconsistent with observational data - perfectly fair point) in this case it is utterly arbitrary. You are tossing out details to make your mixed coffee easier to compress - that is all you are doing. The reason you need to do this is because you depend on entropy being lower in the fully mixed coffee cup and that will never be the case without some kind of filtering. The problem is that you really need a quantitative definition of complexity and it seems like you don't want complexity to be the same as entropy but data compression does not care about complexity - only entropy - so it doesn't work in that context. 44:37: Or, are you saying that you pick a coarse graining filter kernel that you apply consistently in all steps of the experiment / simulation that is bound to always minimize the post-coarse graining entropy of the fully mixed coffee cup in such a way that regardless of what model for how the coffee and cream mix in the intermediate steps (in the middle coffee cup) you can show that the tectonic model for mixing give rise to higher complexity in the intermediate steps and then fall back to zero complexity at the end? Ok, that I can buy as long as you are consistent with how you coarse grain in all steps and do not tune your filter kernel simply to reach your desired conclusions. James Stewart James Stewart 1 year ago I vote for Carroll's Law: Everything interesting happens in the middle. 23 Deep Bayes Deep Bayes 1 year ago To measure complexity, you should not measure the description of the image, but the description of the probability distribution from which the image is sampled. That would be simple on both extremes of entropy, but large in the middle. John Długosz John Długosz 1 year ago Consider average meteorite size with a sample spanning a few years... with a time including Tunguska... with a time including Chicxulub. I think the "meaningfulness" of the answer is that of the same time scale as was used in the original data: include next year's data, and the average won't change. But even with a complete characterization of the data over theoretical "all time" (via knowledge of NEO objects), how useful is that average? For planning purposes, you want a value that matches the time interval of applicability. Building all rooftops to withstand the "average" meteorite size is a waste of expense since the average is inflated by rare events that the entire building would not survive anyway. Paul C. Paul C. 1 year ago I didn't see this one until Monday morning, but as always, it was well worth the wait. Thanks again Professor Sean, for this amazing series. I am only sorry that we are near the end. Though there is still one more, yes ? This whole series has made this tiresome Lock-down bearable. I will be watching all the episodes again anyway. And I am really grateful that I could actually understand so much, without being able to do calculus. 1 David Hand David Hand 1 year ago I'll go ahead and recommend against JPEG size because it can vary considerably; you need to specify parameters Pavlos Papageorgiou Pavlos Papageorgiou 1 year ago (edited) It may be fruitful to ask how does the macrostate evolve vs. the information that you need to distinguish that macrostate from all others. The separated cream state needs just a few bits of information. The state with swirls needs a ton of information if you're trying to reproduce the specific swirls. But having generic swirls evolves from the separated state without adding any information. Thus distinguish the absolute rarity of the branch (initial information) from how the branch itself evolves. If you accept all branching as real, like in many worlds, the 2nd law should be stated as conservation of the information that selects a branch while all the sub-branches are expanded out. Alternatively you could say that branching, or to be precise decoherence and self-locating, adds information to define a sub-branch. The 2nd law is keeping track of the information that defines the branch, in either perspective. Alex Doll Alex Doll 1 year ago I tell my students "all models are wrong, but some are useful" to get them in the right frame of mind. John Długosz John Długosz 1 year ago So if you had a gas (or any substance really) in a very good isolating container, like a thermos, would it tend to approach a uniform distribution rather than a M-B distribution? Does it look more M-B the better the thermal coupling and more uniform the more isolated? What about the universe as a whole: with no "outside" will M-B not apply? Michael Wrenn Michael Wrenn 1 year ago When I attempted to give you a wholehearted "thumbs up," the number of "likes" was 137. So I made it 138. This was the very least I could do to quiet our minds about complexity. PrimatoFortunato PrimatoFortunato 1 year ago (edited) It would be simply too awesome that Dr.Carroll gave a course about statistical mechanics in this way. Somehow the XIXth century does not get the spotlight it deserves, be it in science or history. In science it’s maybe because the XXth was awesome, historically it’s probably because western civilizations were all about conquering and subjugating. Stil, many social questions we still struggle with today were posed there and then. Where was I? Yes! Statistical mechanics. Gotta love it. Traruh Synred Traruh Synred 1 year ago Isn't the change in energy change under expansion somewhat analogous to what happens when you boost relative to a source. If you look at photons arriving from the source they will be doppler shifted. If you look at arriving non-relativistic particles ("matter") they won't. least way there energy won't in the same approx of neglecting Kinetic energy. While energy and ratio of matter to radiation energy will be different, nobody would call that non-conservation of energy. What expansion has done is boost relative to the source. Gareth Williams Gareth Williams 1 year ago Its interesting that your complexity vs entropy plot is reminiscent of the entropy expression p.log(p) Jainal Abdin Jainal Abdin 1 year ago A great series coming to its conclusion - guess the final topic? Are we alone!? Don Wortzman Don Wortzman 1 year ago Because the middle mixing of cream and coffee was not special, I would not call it complex. Any other interim mix would be just as good. Sandip Chitale Sandip Chitale 1 year ago (edited) If the universe was simple and as such did not have any parts to have diifferent microscopic configurations, then it can be thought of as a system with one particle. If we agree so far, then like single particle system, its micro and macroscopic state are identical, then it almost trivially follows as to why the entropy was low at the big bang. Why do we need a further explanation for that? What is the fallacy in this argument. This argument is basically following what Sean said - at the beginning universe was very small, dense and smooth ie simple. Of course then the real question is why was universe small, dense and smooth. Sure. I sometimes think of big bang this way - when we watch a big bomb explode from close distance we are blinded by the light of the explosion and cannot see things near it. It is just the light of the explosion. Is that the case with observable universe. Does the blinding light of the big bang and the wall of CMB prevents us from seeing ambient surrounding, extended universe? Nic holas Nic holas 1 year ago These videos have reached a new level of criticality and complexity! 1 Jon Wesick Jon Wesick 1 year ago Thanks for answering my question. 2 Traruh Synred Traruh Synred 1 year ago I think your box analogy also is flawed. If I fill a box with light and expand it energy will still be conserved. The photons will not be reduced decreased in wave-length but only take longer to get across. I did notice you seemed to hesitate to use it. 4.669 4.669 1 year ago Hello Mr. Carroll. Is it possible to reverse entropy? Or is there insufficient data for a meaningful answer? J3GJ J3GJ 1 year ago Carroll, are these videos found any other websites? Such as not youtube. Thank you David Jordan David Jordan 1 year ago 40:59 When you chuckle and say "Well it's funny...."I started laughing so hard that I couldn't hear what you were saying. Because I knew with out a doubt, that what ever you were saying, COULDN'T be possibly be funny. I ran it back four times before I was able to hear it without laughing hysterically. Of course I was right. But what WAS funny is that I laughed knowing I was right. I am sure that you don't have a staff of comedy writers but never the less you are on to something. I wish Hollywood would make a movie about a theoretical physicist who was popular and did have a staff of comedy writers to appear less nerdy but only succeeded in popularizing the serious study of science by comics and strippers I wouldn't watch it but I would love to see people of below average intelligence coming up with thought experiments. Well gotta practice my Barry Harris "borrowing diminished" movements. 1 my Off Grid Forest Garden Adventure my Off Grid Forest Garden Adventure 1 year ago Results of this lesson, it's now late, I should have gone to bed, and I really want a coffee. Good talk tho 2 Максим Ширяев Максим Ширяев 1 year ago Isn't the Conway's Game of Life (https://en.m.wikipedia.org/wiki/Conway's_Game_of_Life) a counterexample of a statement that local interactions cannot produce complexity? Joel Nathan Henry Joel Nathan Henry 1 year ago e=mc2 m=e/c2 (3D printers creat through a single point) different way of explaining the same thing, entropy and thermodynamics, all laws of motion and particles right, wrong?.. Randy Hanna Randy Hanna 1 year ago Is this the last one or is number 24 gonna be the last of this series? 1 Rick Harold Rick Harold 1 year ago Cool. Thx for the video James Stewart James Stewart 1 year ago Publication is my currency and citation our reward 1 Nancy Mencke Nancy Mencke 1 year ago Don’t understand “empty “ space in relationship to gravity Chas R Chas R 1 year ago Yeay! You're reminding me of Ilya Prigogne me Sean Narf Whals Narf Whals 1 year ago The real world is important? Preposterous! Rattus Norvegicus Rattus Norvegicus 1 year ago What does a person do, who doesn't want to live, but doesn't want to die? Rebecca Wrongdaily Rebecca Wrongdaily 1 year ago So 42 then. Thank you. 1 David Jordan David Jordan 1 year ago I bet Dr Alan Feldman (U. of Maryland, Los Alamos.Pasadena, Danny's basement) will see this!!!