Why do Power Laws Work so Widely? | Episode 2207 | Closer To Truth
ฝัง
- เผยแพร่เมื่อ 13 มิ.ย. 2024
- “Power laws” are mathematical relationships expressed by exponents or logarithms-why are they so powerful in describing the world? Why are power laws found in diverse complex systems in biology and society? How could simple arithmetic have explanatory potency?
Featuring interviews with Geoffrey West, Stuart Kauffman, and Aaron Clauset.
▶ Early-release episodes of Season 22 are available now on our website: bit.ly/3QwMzIA
▶ For subscriber-only exclusives, register for free today: closertotruth.com/register/
Closer To Truth host Robert Lawrence Kuhn takes viewers on an intriguing global journey into cutting-edge labs, magnificent libraries, hidden gardens, and revered sanctuaries in order to discover state-of-the-art ideas and make them real and relevant.
▶ Free access to Closer To Truth's library of 5,000+ videos: bit.ly/376lkKN
Closer To Truth, hosted by Robert Lawrence Kuhn and directed by Peter Getzels, presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.
really cool finding of a physicist showing that btc is a network driven by power laws
One of the main reason that powerlaws are not so ubiquitous is that so many scientists are still obsessed with measurement with Gaussian distribution blinding them to the real data.
For example it is only recently been noted in the last few years that sea waves mostly follow power laws after decades (and indeed centuries) of measuring them through guassian statistics.
If something so obvious as sea waves has been miscalculated then there are many other things we are simply using the wrong stats for.
The irony is that if you ask any seasoned sailor and they will tell you about rogue extra large waves that they have seen.
Power law relationships are the solutions to basically the simplest self-referential differential equations: y'=ky/x for some constant k. Basically if a dependent variable changes based on its value, a power law relationship is your first guess. We could just as easily ask why linear relationships work for so many problems. The answer seems to be that they don't really. They are just a simple first approximation for the relationship. In fact, the relationship could be much more complicated. We just use a simple mathematical relationship and accept the deviations from the expected values as unexplained or "random" variation. The actual relationship may be very complicated and never be known perfectly, but often a simple approximation is sufficient to understand the general trends. [EDIT: changed the differential equation from y'=ky=>y=Ae^x to y'=ky/x=>y=Ax^k. This is perhaps the simplest non-trivial homogeneous differential equation, with a trivial example being y'=k => y=kx.]
The solution to y' = ky is an exponential law a^x, not a power law a x^b.
@@entropica haha thank you for the correction! I got the definition of a power law mixed up in my head and should have looked it up to check!
If you plot the log10 of the price of BTC vs the log10 of the days from its creation it is a beautiful power law with power 5.82.
The first guy in first segment explained things so simply and eloquently. I plan to buy his book.
Scale is a fantastic book. Well worth the read. I reference and think about it all the time.
Oh wow. Thank you for doing an episode on complex systems. I feel this topic is underrated,... you often see stuff about mathematics, quantum physics, etcetera in "reality-investigating" videos and podcasts. But the complex systems approach is fascinating and gets overlooked for some reason.
Bitcoin brought me here.
Social effects and 100% math. Perfect for a power law. BTC.
Same!
This man, in this name or in another, physicist or biologist, or mathematician, or what? I love to hear him all the time, endlessly. I wish I had access to his publications, from A to Z, that he is leaving behind.
Would love a whole series on related universal laws
But all Laws of physics is not able to stand the test of time. Quantum entanglement already contradict Special relativity in terms of speed of light being the fastest possible speed.
Rghtly so, Laws are meant to be changed. Either that or the scientists who coined the "laws of physics" lacked understanding of the word Law and should have understood the problem with language which is art used to describe science
@@1stPrinciples455 oh I mean universal in the sense of across disciplines. Maybe a better word would be unreasonably effective functions/math concepts
Thank you Robert
One thing to note here is the difference between power law (more general) and power law distribution. Power law is any relationship x and y, where when plotting log(x) by log(y) gives you straight line approximation. Power law distributions are the special case where x is some outcome variable (e.g organism size) and y is a frequency or density (frequency summing up to 1) in some population of outcome variables and importantly* where you get a straight line approx. as well. Just to share because people saying "80/20 rule for wealth" are talking about power law distribution whereas West describing organisms is talking about power law more generally.
Is there a link between the mathematics of Power Laws and the mathematics of Entropy
It's all fractal it it's just like Rodger Penrose says
💯
i didn't hear you mention one of these laws??
Bitcoin price and utilisation follows the same Cube logarithmic (log-log) rules - facinating !!! Growth of self-organising networks..
as above, so below
What is the predictive power implication of this finding? It appears that there must be predictive power.
It would have been really good to have a round table discussion on the similarities of ideas about complex systems with Geoffrey West, Stuart Kauffman, and Aaron Clauset. Such a discussion can provide important input for the theory of conscious agents by Donald Hoffman and Stephen Wolfram's theory.
It would be good to apply the power law of heavy-tail distributions for the prediction of natural events (e.g., tsunami/earthquakes/volcanic eruptions) and specifically to assess the risks of existential events for human society, especially in the context of the 'Big History' singularity.
It would be good to apply scaling laws to find optimal variables of human settlements from various perspectives. Maybe there could be a path to a theory of the perfect city, suitable for a certain geographical location with potential solutions for solving extreme irregularities like crime, fire, or medical events.
Is the gist that rare & large events are actually more common than one would expect assuming distribution is normal?
More so, why that “normal distribution” is even able to maintain a near constant state of normalcy at all. Especially when you consider how seemingly dissimilar the things measured can be.
@@michaelmilson7538 maybe insight in the proof of the central limit theorem
Read Ervin Laszlo and his perspective on Systems Science and Philosophy.
Great video, but I think due to the mathematical focus more equations or graphs elucidating (or visualizing) the ideas talked about could have helped.
I have heard it so many times especially in the quest of explaining complex systems: fractals that coastlines are. In fact they are not. Only in some cases they are and that too not so much. See: How Fractal are Coastlines Really? Observation and Theory by Murray et al.
This begs the question: maybe power laws and all such fantastic generalizations are actually mere artifacts of our limited biased brain?
What I have never heard explained is why most of the equations of physics have at most second order derivatives in space and time. Why shouldn't they have higher order derivatives?
It kind of depends on what you want to know. There are higher order equations such as jerk = d3x/dt3, or the rate of change of acceleration. This is useful for discussing how smoothly something accelerates. In terms of fundamental forces and how they affect objects' motions, we don't really find third order ODEs or PDEs (to my knowledge), but larger systems such as those with multiple particles quickly scale up to having huge orders on a fundamental level. Much of this can be ignored at large scales due to the dampening caused by the electromagnetic or gravitational force (holding solid bodies together), but on the microscopic scale the particles are interacting with each other in a cascade. Consider pushing a long rod from one end. The particles you interact with electromagnetically then interact with their neighbours, and so on until the energy you impart reaches the other end and it moves away from your hand. However, the motion of the whole rod can be approximated using F=ma with very little error because the rod is rigid and essentially elastic under the compressing deformation you applied.
www.tcm.phy.cam.ac.uk/~gz218/2010/01/higher-derivative-theories.html
This is explained by the Holographic Theory described by David Bohm and also Michael Talbot in his book of the same name.
It’s just because the complex system arises from simple systems. And so the simple presents itself in the more complex picture
Why isn't everything static? Or at least linear?
This whole episode has the feel of a bunch of academics who are wowed by something just slightly more involved than numerology. [The guy stressing “the number 4” is a neon sign indicating magical thinking.] As another commenter noted, finding simple logarithms and simple exponents results from solving some of the simplest differential equations which scale with constants. Sure they are interesting , and even fun, even very fun, but there is no need to get mystical or pseudo-religious about it. [And the terrorism power law thing was just a naive overreach. I’m sure it’s good for grants and talks, but they need to dig a LOT deeper for valid explanations.] Cheers.
One of rare simple weighted comments in this discussions
"Why do power laws describe complex systems?"
Describe or deter? Not determine, deter? Is it not psychology rather than math that rules these relationships? Size is a type of quantity, true, but is it a more powerful type than say color, shape, loudness?
Without the linguistic Urge and its cognition of "meaningfulness" the meaning of size, as differentiated from color, shape, sound would have no "deterrence" to being mistaken for color, shape, sound.
Network effects, power laws. This is a principle the tech companies understand well. That's why they try to grow big, grow fast, lock one into a whole ecosystem of offerings, be robust and resilient, and try to dominate the market.
The other more recent example is the role of scaling in LLM's unexpected capabilities. This is assuming a diverse enough training data set, cross relationships, and enough model parameters to capture this. Some have proposed "emergent properties" over and above what would be expected.
What you say about tech companies is true, but on the other hand ordinary consumers have also benefited massively. In the past only governments and corporations could afford to have and use the best technology. Google and ChatGPT, the most advanced technology in internet wide search and AI have been freely available to the public from the start precisely because a scale of up to billions of users means the cost per user is peanuts. But that only works if you have that scale, and to do that you have to dominate the market. It’s a Faustian bargain for sure, but the alternative is costly, more balkanised and less capable multiple alternatives.
There’s a similar effect in smart phones. We don’t even call them that anymore, they’re just phones. My daughter has literally the most advanced, capable pocket computer on the planet, complete with dedicated AI chip, an incredible sensor suite and stunning photography and special video technology. It’s not cheap for sure, but these things are affordable for ordinary people you walk past every day on the street. They’re not exotic super spy gadgets only the elite get to play with. The only way that is possible is through mind bendingly huge scale.
I’m not in any way arguing for complacency, the economy has to work for us, to our benefit both as customers and employees. We can’t just assume these companies have our benefit at heart, the don’t. But it’s also true the vast scale of some of these technologies does also work to our advantage too.
Monopolies like Alphabet and Meta?
Me and Cosmin Visan are gonna be famous!!!
Where is the cosmin?
'Brain is just an idea in consciousness'
@@S3RAVA3LM I think him and Leo Gura are hanging out.
For animals, we are an exception... see 'expensive tissue hypothesis' as to how we got big brains and small guts.
first!
@@No.One357 Yes, thank you. My greatest and only achievement. 😂
Seems telated to the pursuit of efficiency.
9th grade is junior high school? Where? In Leave It To Beaver decade?
No. Right now. 9th is a freshman. 9 10 junior high. 11 12. Senior high.
@@lucinity4351Where is that?
@@Maryland_Kulak USA. Northeast
They aren't separated buildings anymore but we still call it that.
Sports = junior varsity and varsity. Freshman can make varsity but unlikely due to their development
Most would come away from this more certain in their atheism. This galvanizes me further into creationism.
Not everything is mathematically ordered. Ordered things don't all follow the same maths.
For mathematics to be applicable to prevent evil, the DIGITS must first be identified as uniqie particles.
So long as DIGITS are not identified as unique types of particles and the structure of the system of NUMBERS linked to sizes of particles with the 4 basic rules of arithmetic operations (+ - × ÷) as the only laws of motion for interaction among them, for then deriving the mathematical model of the mechanism how particle interactions inside the core of the earth develop PLANTS on its own surface, to then deliver and sustain beings here through them, its application to prevent evil on this earth would remain a pipe dream.
But if such a model is derived, then the accuracy of that model can easily be verified by how well it serves to influence growth of (and on) plants to satisfy needs of beings and PREVENT disasters (earthquakes, volcanic eruptions, storms, floods, droughts, etc.).
At present mathematics works well only in social field (economics, politics) as its accuracy is verified only by how well it serves to fulfil the rules we ourselves (the humans) make, but to be applicable to describe natural phenomena it must first be integrated with physics of the earth as mentioned above , which so far nobody has even attempted. Then mathematics (and all social sciences, as a consequence) would be branches of GEOPHYSICS.
Lack of this realization is the reason why the human race as a whole in its entire history, from antiquity to present day , from Thales of Miletus to Stephen Hawking (and still continuing), has failed to derive the mathematical model of even a single natural phenomenon in such a way that it PREDICTS when that phenomenon could turn harmful to life function, let alone PREVENT such.
Preventing evil is not found even in the vocabulary of science.
Heisenberg's uncertainty principle, as well as Albert Einstein's conclution in STR (Special Theory of Relativity) that "no physical experiment could ever prove whether the earth goes around the sun or the other way around", clearly indicate that there are no laws of nature as such to DISCOVER, but nature is malleable and permits us to INVENT our own laws that would serve best to sustain evil free life function and implement them.
Current science serves, and is sustained mainly by, inventing ways to manufacture more and more destructive weapons. All conveniences we enjoy are byproducts (offshoots) of that endeavor.
Remember, Nobel prizes, including for peace, are given from the profits of weapons sales by the company started by the inventor of dynamite, Alfred Nobel.
The crisis human race faces is solely due to this separation of mathematics from particle physics. Only if we recognize which unique particles correspond to digits can we discover the connection between life function and particle interactions, hence which combination of arithmetic operations when and where are most suitable for sustenance of life function eternally.
Terror is a poor man's war. War is a rich man's terror. He should include war in his terror calculation and scaling.
Cut across diverse fields of knowledge
12:48 power laws also give many new technologies that make the species extinction issue moot
Law is a misnomer. What you have is a statistical fit, or a family of fits to a variety of phenomena that express regularities. We don't call linear regression (the fitting of a line to a set of points) a law simply because there are a lot of cases where a line of some sort fits (more or less significantly) to a lot of data. The capacity of equations to more or less approximate a pattern found in data is a fundamental aspect of math. The derived equations are not laws, and they are definitely not to be treated like magic.
Power laws are a function of the metric properties of space no?
Ok. So what's the true reason for "power laws" to exist?
What's the true real natural process behind it,...all meaning 'WHY'? 🙄🤔
My God is a beautiful woman.
Additional budget requiredcti find out out budget is required to study phenomenkn you mentioned
*AC: **_"It gives us the idea that we can tie together phenomena that seem completely different from each other using a single kind of physics or rule."_* ... I have always been a proponent of "Existence" evolving into greater complexity by using prior templates that have been proven successful. Existence will use the same template until a better template emerges that can supplant it. ... This type of thinking obviously does not support top-down causality.
One such template is Existence evolving from *simplicity to complexity,* which I posit as a rule (or law). *Example:* You can regress the complexity of life down to a single-celled prokaryote. You can regress the complexity of matter from Oganesson down to the simplest element; Hyderogen. You can reduce the entire complexity of the universe down to a miniscule point of singularity. So, the question that remains is if you can enact this same type of regression beyond that singularity. ... I argue that you can!
If a nondimensional "information-only" state existed just prior to Big Bang's singularity that had reached peak complexity (a point of redundancy), ... then where do you end up if you regress that information down to the simplest form that's conceivably possible?
As far as we know, mathematical starting point for the physical is the quantum wave.
Einstein wasn't sure that the Universe was infinite, because it is finite in a spatially closed geometry. He was right about human ignorance - - that can be Limitless.
More on the unlimited.
My guess is that the quantum probability wave function is our closest mathematical descriptions of the manifestation of God, and our physical universe, the panoramic brushstrokes of "being" and its evolving conscious preferences (with our internet interactions and global wars providing optional pastel colorings to the overall artistic landscape).
th-cam.com/users/shortsDSKKJVF060Y?si=Upx4QdHOAma3UzgS
I agree with Einstein and I also love his bagels. Give me an Everything bagel with a huge schmear of chive cream cheese.
“The important thing is not to stop questioning. Curiosity has its own reason for existence. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvelous structure of reality. It is enough if one tries merely to comprehend a little of this mystery each day. Never lose a holy curiosity.”
Every letter/number has power
Your name either gives you power or not
People give their baby a name, placing their future in their head boundaried
What if one was to remain nameless from birth?
Bitcoin follows a power law.
Do insect societies obey these “laws “?
Two children walking near a house hear a dog barking.
One of them says:
"let us get back."
The other says: "Come on! Don't you know barking dogs seldom bite?"
The former answers:
"How can dogs know about it? They never go to school."
🗯🔋💫🔥💭
It all looks like a put up job to me
bitcoin
So what? Power laws describe a lot of stuff. It is just a description. It does not explain anything or provide an accurate predictions. It is just a description. It is interesting but too much is made of this.
17:30
@@xdouble00 Am I missing something important when I find that to be unimpressive?
@@jjharvathhwe can use power laws to help predict terrorist events and decrease human suffering..
@@xdouble00 You can not predict terrorist events.
@@jjharvathh if terror events underlie on scaling variant mechanisms and power laws.. yes we can..maybe not exactly when and where lol but general predictions .. why don’t you think so?
Anyone else catch the mild undertone of this video?
Only this one? Is a Church in the background coincidence? Kuhn's "Truth" he is so desperately seeking seems to involve an "Invisible Man" perched on a cloud, and quivering his lower lip "in his image", etc. so "He" must have one to quiver.... if you say something bad to damage his Ego, or don't put money in the Collection Plate. Kuhn has been doing this all along...
@@festeradams3972 No. You missed it.
I would guess your anger has taken over your reasoning. Understandable though.
I did? What did I miss? Spell it out in detail...@@jellojiggle1
No.
Doesn't it depend on what you label as a terrorist attack? Was the dropping of 2 atomic bombs on Japan a terror attack? Was Pearl Harbor a terror attack? Wasn't the recent attack by Hamas on Israel a terror attack that resulted in 1,200 deaths?
Terrorist is so louded. I really dislike the term. Perhaps we can define terrorist attack as a David type actor. A significantly disadvantaged antagonist.
@@HUSTLE_MONEY A freedom fighter is a terrorist depending on perspective.
@@Resmith18SR exactly.
I believe in the first and second laws of thermodynamics. I believe that the laws of physics will hold true from the initial Singularity to the End of Time Omega point. Dyson postulated an open Universe, not closed.
en.m.wikipedia.org/wiki/Dyson%27s_eternal_intelligence
My own guess is that the most fundamental laws of our local universe must arise so as to allow consciousness and free will to exist.
Free will in life might exhibit negative entropy at immeasurable slight mesoscopic scales.
simple.m.wikipedia.org/wiki/Negentropy#:~:text=Negentropy%20is%20reverse%20entropy.,Another%20example%20is%20life.
The secret of life lies in women's cycle to protect men, children and the entire subconsciousness in creation amd form.
Roughly speaking, life nudges the universe so as to allow light to circumnavigate the universe first in one direction, and then another. This is done repeatedly, an infinite number of times. There are thus an INFINITE number of circumnavigations of light before the Omega Point is reached.
Maybe the mind-body, wave-particle, dualities are the same stuff going through phase transitions, like "solids transitioning to liquids" or "particles transitioning to waves of probability", from being "spacial and time locked" to being "eternal, omnipresent and everywhere", like matter in its transition to energy (Matter = Energy /"Einstein's bombshell").
It's all just wordplay over meaning.
m.th-cam.com/video/BoUc4-q4Ibc/w-d-xo.html
Light can’t circumnavigate the universe, even if the universe is topographically closed. The space between us and the furthest objects we can observe is expanding so fast the distances between us are increasing at several times the speed of light. We can only observe them because far in the past,when the light we are seeing now was emitted from them, they were a lot closer to us. The light they are emitting now can never reach us.
@@simonhibbs887 given enough time, tunneling?
@@stephengee4182 Nothing is physically travelling faster than light. It’s space that’s expanding, not objects that are moving. It’s all consistent with relativity.
@@simonhibbs887 hawking radiation?
This was a bit shallow. Turning science and math into religion which is always sad.
Maybe in the final analysis, it's all religion?
Who gives a shyt what math represents--we make math fit our expectations.
“Closer to truth” 😂😂😂 There is no such thing as truth…how much does it weigh? What’s its atomic number? Sho7ld change the channel to “Closer to the bottom of the rabbit hole”
I don't think there's anything profound here. Seems like cherry picking to make the math work out.
I agree. The guy who said that the beach stays roughly the same at any scale? Firstly, it doesn't. It looks radically different when you go from the tiny to the large, just like everything else in the world. Secondly, a "shoreline" is an arbitrary set of sand or dirt or whatever other objects, so like most randomly defined sets, it's somewhat fractal to a few orders of magnitude, when you choose the correct resolution.
I found the whole argument to be meaningless. I don't think I'm missing anything, it's just so obvious I'm not understanding what they are trying to appeal to.
They are confusing the consequences of making a certain type of observation with something that has explanatory power.
It's like thinking that since we can understand calculus, the nth derivative of some function is driving my car
Einstein wasn't sure that the Universe was infinite, because it is finite in a spatially closed geometry. He was right about human ignorance - - that can be Limitless.
I not only agree with Einstein I also love his bagels.😂😂😂
@@Resmith18SR 😂
@@blijebij And I'd love right now a toasted everything bagel with a huge schmear of chive cream cheese. Maybe the Universe is actually shaped like a bagel.
@@Resmith18SR haha yup who knows :D at least with combining treats you maximize your lifes joy!