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.
I'm gonna bring that up with my dietician. My mass^3/4 tells me I need more food! (jk) Thanks Prof. You make learning physics a gentle process in this format. I hope you're taking notes and talking with colleagues because this format is far more effective than any online course I've seen, and more effective than most of my in-person classes from undergrad through my PhD (in nutrition). I think your joy in your material is obvious, and a big part of your effectiveness.
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!👍🏼👍🏼👍🏼🙏🏻🙏🏻🙏🏻
Hey it's cool to see someone your age inspired to comment, and I'm sure Carroll would appreciate the Feynman allusion. And yeah, the internet can reveal so much about... almost everything! You've just got to skip over the bright & sparkling, steer around the dark & murky, and keep going for the SPECTACULAR and OUTSTANDING. Good luck, and stay safe.
What quarantine? The local grocery gave me a hard time because I didn't have a face covering, but I told them I had no way to get one if I couldn't shop, and they didn'thave any to sell! Other than that nonsense, I didn't do anything different or unusual for the past few decades.
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.
He should make a playlist of what to watch next. My suggestions: * Brian Greene daily equation * 3Blue1Brown lockdown math * old SETI Colloquium recordings * SLAC public lectures
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.
Thank you Dr. Carroll. I'll watch the series several times again hoping to understand, not just be inspired. BTW, multiplying numbers is using a slide rule's relative lengths to get a number. Heaven help us to figure where the decimal point goes. That's where I started. Thanks again.
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.
How true -- I am still stuck in the "The Road to Reality" -- without much hope I will understand most of it.... Here to one should give credit to Sean Carroll -- he gives credit to Roger Penrose where it is due and gives 50% probability estimate about "inflaton" field and cosmic inflation -- a courageous position. Roger Penrose is on record that he considers inflation a fantasy than can't explain key features of post-Big Bang.... - including in his famous book "Fashion, Faith and Fantasy"
Oh man, I've tried to read "Road to Reality" so many times over the years. I absolutely love the early chapters, but I always end up hitting a wall around chapter 9, at which point I become unfamiliar with much of the math. Penrose claims in the introduction that he intends the book to be readable and useful even for those with only high school level math (he basically says "just skip over the equations and focus on concepts!"), but as someone with undergrad minors in both math and physics, I've always been dubious of that claim. Maybe I should just keep pushing through the book and I'll actually get something out of the later chapters, but I can't help but feeling my time is better spent on either slightly less technical content (like this series) or by actually rigorously digging into the topics discussed. I tend to just get frustrated or lost in the in-between approach of "Road to Reality." I admire the intent of the book, and I'm glad it exists, but it's just... tough!
It is wrong to make fish of one and flesh of the other, but I'd rather have Professor Carroll's series any day : nobody explains it more lucidly than Sean.
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 RUclips. 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.
I haven't been this hooked on a course in a very very long time. You're an incredible teacher and science communicator. Thank you. I hope you keep doing these.
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.
You explained it so well, that you made extremely difficult concepts, understandable, I think yours is the best Relaitivity theory explanation I have had.
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.
How do these videos have tens of thousands of views, but only a couple thousand likes?... I love these videos, and the whole series... Thank you for your devotion to science education.
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
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.
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.
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
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. en.wikipedia.org/wiki/4_Vesta#Physical_characteristics
That's a real problem I have with the current definition of a planet - that it has to clear out its orbit. They made a post-hoc definition that excluded Pluto. Pluto is still working on it! It has not revolved around the sun nearly as often as the inner planets, so it hasn't had the chance to clear its orbit. Besides, what did Mercury have to clear out? How much material was in stable orbit in Mercury's path that didn't quickly fall into the sun early during accretion or get cleared away by Venus or Earth? There are other objects in Earth's orbit that have not been cleared out, so it has to be a matter of degree, but when I read that definition, I don't remember there being any minimum or maximum degree of allowed material still in the orbit, or any specification of how far from the orbit debris can be allowed. Yes, I am sentimental about Pluto, and I accept that it is obviously a Kuyper Belt object (orbital eccentricity and non-circularity, other KB objects being larger and of similar composition, etc.), but they need another definition of a planet that does not seem custom-designed to exclude Pluto. It's more planetary bigotry than objectivity. What is the justification for needing to clear out its orbital path as a definition for a planet? That just means it's massive, old, and close to the parent star. While our current 8 planets were busy clearing out their orbits, were they not planets then? Which asteroid impact signaled Earth's transition from non-planet to planet? When was its path clear enough?
@@beenaplumber8379 You won't come up with a proper definition that includes _only_ Pluto. The same story played out with Ceres and Vesta -- textbooks shows them as planets! But once astronomers realized they were members of a "belt" they dropped the designation with little fanfare. Clearing the orbit, different from Mercury: Pluto's actually under Neptune's thumb. It's locked into a 3:2 resonance, along with many other bodies.; It's not doing any clearing! Rather, it's shepherded into position by the planet that rules that region. I think the real definition needs to be "what's interesting/unique" to be learned by the general population. Like with bodies of water: you don't learn every pond in the world, and not only the "great lakes"/"inland seas" either, but some that are of novel character or special importance, regardless of size. Others are just groups like "the finger lakes", a feature made up of many individual bodies. Lake Vostok in Antarctica is _interesting_ and the first found and largest of its class, but not "large" like the Nile or the Med. But it's on the list of things people learn about.
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.
No, since you would need to specify where in the digits of pi your sequence starts, and that specification will most likely be more complex than the sequence itself.
Not because they are pseudo-random, but because they are patternless and infinite. Being found in the digits of pi does not make any finite string simple, (nor did he imply that) since you would also need to give the place in pi where that string takes place, and that is likely longer than the string itself, (proof left as an exercise). You would need to find a algorithm for every finite string which is shorter than the string itself.
I think the answer is: No, because the finite substring is defined by two parameters in addition to the function for pi itself: the length of the substring, and the number of digits of pi you have to discard from the function before you can start consuming them. But how do you determine where to stop discarding? Well, you have to search for it, and in particular to search for the thing, you have to know *what* it is you are searching for, which means the actual complexity is equal to the complexity of the number you are searching for in addition to the complexity of pi (and searching itself.)
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.
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.
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.
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!)
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.
It will depend somewhat on the training algorithm and also there will be cutoff and normalization effects, but yes, it seems that a power law is the best fit, and that\s not unexpected considering.
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.
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.
In this video I would have expected some reference to Leonard Susskind's work on Complexity and quantum theory, which i find extraordinarily intersting
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.
"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 😛
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?
@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?
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???
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 )
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.
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.
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?
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.
If the big bang could be loosely considered a phase transition, does it kinda track that we can't know the structure of space before it since the passing through criticality meant that scale-dependent relations were lost? EDIT: Additionally, could the reemergence of scale-dependent relations appear like a change in observable scales in the universe? Expansion, perhaps?
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.
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
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?
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.
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 :)
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.
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
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.
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)
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! :)
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...
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?
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).
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.
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
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?
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.
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.
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?
It would be too heavy to stand on legs of that size and shape. Probably could not stand on two legs either, because it would require too high blood pressure for supply its brain.
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.
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.
Could you give us your take on Constructor Theory?
I'm gonna bring that up with my dietician. My mass^3/4 tells me I need more food! (jk)
Thanks Prof. You make learning physics a gentle process in this format. I hope you're taking notes and talking with colleagues because this format is far more effective than any online course I've seen, and more effective than most of my in-person classes from undergrad through my PhD (in nutrition). I think your joy in your material is obvious, and a big part of your effectiveness.
@@kabirmunjal9149 Another new quantum mechanics book? Have you checked out Sean's book "Something Deeply Hidden"?
@@darektidwell1158 YES, just YES!
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!👍🏼👍🏼👍🏼🙏🏻🙏🏻🙏🏻
Hey it's cool to see someone your age inspired to comment, and I'm sure Carroll would appreciate the Feynman allusion.
And yeah, the internet can reveal so much about... almost everything! You've just got to skip over the bright & sparkling, steer around the dark & murky, and keep going for the SPECTACULAR and OUTSTANDING.
Good luck, and stay safe.
What quarantine? The local grocery gave me a hard time because I didn't have a face covering, but I told them I had no way to get one if I couldn't shop, and they didn'thave any to sell! Other than that nonsense, I didn't do anything different or unusual for the past few decades.
Dr. Carroll, may you succeed in your own breakthroughs. You have made the world a better place by making this series.
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.
The book is always better than the movie...
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!
Wait he’s stopping after 25 episodes? :(
Same, I'll be sad when these end. I was stupid when I started watching...I'm still stupid, but I feel like I've made a friend.
He should make a playlist of what to watch next. My suggestions:
* Brian Greene daily equation
* 3Blue1Brown lockdown math
* old SETI Colloquium recordings
* SLAC public lectures
@@JohnDlugosz Also Leonard Susskind's lectures.
@@ScienceMessiah im afraid that is true 😏
As always, AMAZING, ENTHRALLING, INFORMATIVE AND MIND BLOWING. You make it easier for us to understand complex subjects. Thanks Professor
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.
Thank you Dr. Carroll. I'll watch the series several times again hoping to understand, not just be inspired. BTW, multiplying numbers is using a slide rule's relative lengths to get a number. Heaven help us to figure where the decimal point goes. That's where I started. Thanks again.
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.
He might have made it because of you!
THX!
I wish someone combined this series in one ginormous book. It would be Penrose’s “The Road To Reality”, but much more accessible.
How true -- I am still stuck in the "The Road to Reality" -- without much hope I will understand most of it....
Here to one should give credit to Sean Carroll -- he gives credit to Roger Penrose where it is due and gives 50% probability estimate about "inflaton" field and cosmic inflation -- a courageous position.
Roger Penrose is on record that he considers inflation a fantasy than can't explain key features of post-Big Bang.... - including in his famous book "Fashion, Faith and Fantasy"
Oh man, I've tried to read "Road to Reality" so many times over the years. I absolutely love the early chapters, but I always end up hitting a wall around chapter 9, at which point I become unfamiliar with much of the math. Penrose claims in the introduction that he intends the book to be readable and useful even for those with only high school level math (he basically says "just skip over the equations and focus on concepts!"), but as someone with undergrad minors in both math and physics, I've always been dubious of that claim. Maybe I should just keep pushing through the book and I'll actually get something out of the later chapters, but I can't help but feeling my time is better spent on either slightly less technical content (like this series) or by actually rigorously digging into the topics discussed. I tend to just get frustrated or lost in the in-between approach of "Road to Reality." I admire the intent of the book, and I'm glad it exists, but it's just... tough!
For me, this series is right up there with Feynman's Messenger Lectures. Thank you for this amazing series!
It is wrong to make fish of one and flesh of the other,
but I'd rather have Professor Carroll's series any day :
nobody explains it more lucidly than Sean.
I have Feynman's 6 hour vid & all of this series saved for a second viewing. Hope I live long enough to watch again.
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 RUclips.
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.
I haven't been this hooked on a course in a very very long time. You're an incredible teacher and science communicator. Thank you. I hope you keep doing these.
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.
Thank you so much for making this lecture series and for making it free for all on RUclips.
You explained it so well, that you made extremely difficult concepts, understandable, I think yours is the best Relaitivity theory explanation I have had.
Love your videos man such an inspiration for me to make my own videos and help people.
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.
At 18:50, I think you need a sigma squared in the denominator of the exponent.
How do these videos have tens of thousands of views, but only a couple thousand likes?... I love these videos, and the whole series... Thank you for your devotion to science education.
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
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.
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.
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
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.
en.wikipedia.org/wiki/4_Vesta#Physical_characteristics
That's a real problem I have with the current definition of a planet - that it has to clear out its orbit. They made a post-hoc definition that excluded Pluto. Pluto is still working on it! It has not revolved around the sun nearly as often as the inner planets, so it hasn't had the chance to clear its orbit. Besides, what did Mercury have to clear out? How much material was in stable orbit in Mercury's path that didn't quickly fall into the sun early during accretion or get cleared away by Venus or Earth? There are other objects in Earth's orbit that have not been cleared out, so it has to be a matter of degree, but when I read that definition, I don't remember there being any minimum or maximum degree of allowed material still in the orbit, or any specification of how far from the orbit debris can be allowed.
Yes, I am sentimental about Pluto, and I accept that it is obviously a Kuyper Belt object (orbital eccentricity and non-circularity, other KB objects being larger and of similar composition, etc.), but they need another definition of a planet that does not seem custom-designed to exclude Pluto. It's more planetary bigotry than objectivity. What is the justification for needing to clear out its orbital path as a definition for a planet? That just means it's massive, old, and close to the parent star. While our current 8 planets were busy clearing out their orbits, were they not planets then? Which asteroid impact signaled Earth's transition from non-planet to planet? When was its path clear enough?
@@beenaplumber8379 You won't come up with a proper definition that includes _only_ Pluto. The same story played out with Ceres and Vesta -- textbooks shows them as planets! But once astronomers realized they were members of a "belt" they dropped the designation with little fanfare.
Clearing the orbit, different from Mercury: Pluto's actually under Neptune's thumb. It's locked into a 3:2 resonance, along with many other bodies.; It's not doing any clearing! Rather, it's shepherded into position by the planet that rules that region.
I think the real definition needs to be "what's interesting/unique" to be learned by the general population. Like with bodies of water: you don't learn every pond in the world, and not only the "great lakes"/"inland seas" either, but some that are of novel character or special importance, regardless of size. Others are just groups like "the finger lakes", a feature made up of many individual bodies.
Lake Vostok in Antarctica is _interesting_ and the first found and largest of its class, but not "large" like the Nile or the Med. But it's on the list of things people learn about.
Thank you so much for this series of videos and all the other ones you have made. They are fantastic.
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.
Got em lol
No, since you would need to specify where in the digits of pi your sequence starts, and that specification will most likely be more complex than the sequence itself.
@@juanmanuellosada2818 Ah makes sense, thanks!
Not because they are pseudo-random, but because they are patternless and infinite.
Being found in the digits of pi does not make any finite string simple, (nor did he imply that) since you would also need to give the place in pi where that string takes place, and that is likely longer than the string itself, (proof left as an exercise). You would need to find a algorithm for every finite string which is shorter than the string itself.
I think the answer is: No, because the finite substring is defined by two parameters in addition to the function for pi itself: the length of the substring, and the number of digits of pi you have to discard from the function before you can start consuming them. But how do you determine where to stop discarding? Well, you have to search for it, and in particular to search for the thing, you have to know *what* it is you are searching for, which means the actual complexity is equal to the complexity of the number you are searching for in addition to the complexity of pi (and searching itself.)
Weekly drop by Sean is great as usual.
NOOOO. Only one more? This series is amazing because it's like your solo mindscapes. Gonna be real sad when it's over.
Sean, thanks for your good work.
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.
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.
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.
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!)
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.
It will depend somewhat on the training algorithm and also there will be cutoff and normalization effects, but yes, it seems that a power law is the best fit, and that\s not unexpected considering.
THE UNIVERSE IS SIMPLY COMPLEX !!!
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.
ngl this is perfect with asmr in the background. The emergent form of Bob Ross
Professor i appreciate videos like this but i would also appreciate full fledged lectures by you.
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.
Sad it's nearly done, one of my favorite video series on youtube.
In this video I would have expected some reference to Leonard Susskind's work on Complexity and quantum theory, which i find extraordinarily intersting
Thanks
i loved the spherical elephant !
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.
"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 😛
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?
At circa 19:30 there is an error in the gaussian exponent denominator : should be 2*sigma squared ;-)
@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?
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???
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 )
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.
우리는 본능적으로 모두가 같은 생각을 하고 같이 움직여주길 바라고 있음.그래서 같은 언어문화에서 살려고 하겠죠.같은 것을 보면 같은 생각을 한다는 착각 하지만 여전히 다양한 생각을 하고 있고 표면만 볼뿐임.
👍👍👍👍Many thanks!
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.
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?
The problem for Pluto is not its shape, but the fact that it hasn't "cleared its neighborhood".
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.
If the big bang could be loosely considered a phase transition, does it kinda track that we can't know the structure of space before it since the passing through criticality meant that scale-dependent relations were lost?
EDIT: Additionally, could the reemergence of scale-dependent relations appear like a change in observable scales in the universe? Expansion, perhaps?
Kleiber's Law: power is 3/4, not 1/4 :))
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.
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
1:14:02 yep, me too. I definitely had to rewind five times to convince myself it wasn't "size of an orgasm". Which tbh would be a riveting topic.
Ok, on hearing the second Freudian slip I'm now pretty sure that Sean isn't really interested in organisms.
New podcast: Sexy Time with Prof. Sean Carroll
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?
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.
If website links is a classic problem, it really dates your field!
Hey Sean, can you tell me what's that progam you're using for explaining the diagrams and stuff
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 :)
Great video。
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.
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
❤ Very good 👍🏼
Thanks, Sean.
I predict idea #24 will be Life
24 + 42 + life = mindscape episode 100
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.
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)
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! :)
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...
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?
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).
1:02 min, spontaneous self organization...
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.
Why power law and not some other relation with a many small and few large events?
Totally random question... what's the relationship between power laws and entropy?
Please make a video on wormhole.
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
I think you need to square sigma in your formula for the Gaussian distribution (at 19 minutes).
I think the last one might be about Life and Evolution
And brain and mind.
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?
4:00 😆
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1:20:45 "scientists are paid the big bucks"?? What universe are you from, Sean? :-P
PS: A Question: In your estimate how many there are googols (10 on 100) multiverses in your "mad-dog" Everett-ian hypothesis... ;-))
Ok. Microscopic to macro etc. We haven’t Learnt the rapid expansion phase yet!
IIRC it's 'normal' because the area under the graph is one.
The Q&A video for this lecture appears as ‘private’ ... I wonder if Professor Carroll is aware of this.
RUclips is consistently recommending only the Q&A videos. Weird. I like the Q&A but, I'd like to watch the primary video first.
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.
Wow I will miss your videos ... You are my favorite.
PS I will miss Ariel as well.
Rock on, awesome!
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.
If Earth is inside the region where this "phenomenon" occurs, it would effectively span all 360° on the sky...
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?
It would be too heavy to stand on legs of that size and shape. Probably could not stand on two legs either, because it would require too high blood pressure for supply its brain.
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.