Chaos theory and geometry: can they predict our world? - with Tim Palmer
ฝัง
- เผยแพร่เมื่อ 6 พ.ค. 2024
- The geometry of chaos can explain our uncertain world, from weather and pandemics to quantum physics and free will.
This talk was recorded at the Ri on 21 April 2023.
Join Tim Palmer as he explores how it provides the means to predict the world around us, and provides new insights into some of the most astonishing aspects of our universe and ourselves.
Watch the Q&A here: • Q&A: Chaos theory and ...
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00:00 Introduction
00:55 Illustrating Chaos Theory with pendulums (demo)
02:44 Fractal geometry: A bridge from Newton to 20th Century mathematics
08:43 The three great theorems of 20th Century mathematics
11:24 The concept of State Space
14:43 Lorenz State Space
19:24 Cantor's Set and the prototype fractal
22:52 Hilbert's Decision Problem
24:04 The link between 20th Century mathematics and fractal geometry
27:21 The predictability of chaotic systems
32:26 Predicting hurricanes with Chaos Theory
43:44 The Bell experiment: proving the universe is not real?
51:45 Counterfactuals in Bell's theorem
56:29 Applying fractals to Bell's theorem
01:03:57 The end of spatial reductionism
Buy Tim's book 'The Primacy of Doubt' here: geni.us/5bgfg
Tim Palmer is a Royal Society Research Professor in the Department of Physics at the University of Oxford. Following a PhD in general relativity theory, he spent much of his career working on the predictability and dynamics of weather and climate, developing probabilistic ensemble prediction systems across a range of weather and climate timescales. He also researches the foundations of quantum physics, in addition to applications of quantum and imprecise computing. He is a Fellow of the Royal Society and an International Member of the US National Academy of Sciences. Amongst other awards, he has won the Institute of Physics Dirac Gold Medal, and the top medals of the American and European Meteorological Societies.
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Fascinated from start to finish. Thank you Dr. Palmer xx
This was difficult at first but once I got accustomed to Mr. Palmer's speaking mannerisms it was really quite fascinating. By the end I wanted to hear more.
🤔👊🔥✌💫
But I am still confuse
He's using simple English language.
I believe that this idea (particularly), of Chaos Theory being able to link General Relativity, and Quantum Physics is truly fascinating!
It's also completely wrong. ;-)
The math doesn't pencil
@@schmetterling4477Elaborate please?
How can you say that with absolute certainty ?
@@hanzohasashi3788 He pulled it out of his own rear.
The audio gets better about 2:30 for those first listening
Thanks, I was wondering if I could take that for the full length 🤣
The tilted table flabbergasted me in the sense that I could not imagine a better example of how things work within the range of probability and keeping them in a frame of reference. Very well done!
This was fascinating!
Anyone noticed that one of his coauthors is Sabine Hossenfelder (1:03:15)?
Great lecture
Great talk! So much to think about here. The connection with P-adic numbers was fascinating. Have you considered where something like the reiman-zeta function or the central limit theorem, which are both intimately related to primes and large scales of reference, might be connected to something like chaos theory?
Thank you for the lecture and the sharing. At 62, I still learn things and as you are "pedagogue" (in french) you make it easyer to understand and keep me interesting. Thank you so much ! Look forward to watch another one.
This lecture was very chaotic
This is fascinating because I was thinking about time travel or teleportation would function as a concept and how quantum entanglement is the cosmos way of helping with the math
The universe as a chaotic system evolving into a fractal attractor is indeed a great idea!
Two words: "computational irreducibility".
Dr. Wolfram could not have said it better! I could hear him whispering in my ear...
Always great content on here glad I found this page!!!❤
Pants with hue, saturation, value(brightness), reflectivity, porousness, cotton-ness, vinyl-ness, width, length, elastic band tightness, total volume of pockets 0 to 100...and how much sound they make.
Correct. I work in 3D animation, and at a certain point you realize anything can be parameterized, in essence each parameter is a dimension.
Points of an object can be defined in XYZ space, which is the 3D we're familiar with, but a point can also contain color data, velocity, spin, etc.
Color itself can be separated into many different dimensions depending on how you want to define it. It can be RGB, CMYK, LAB, etc.
There are many dimensions within dimensions.
I really loved the talk. Thanks!
This is so damn interesting and fascinating. Presented in a pretty nice way. ❤
You're kidding, he does not seem to know himself what he's trying to explain.
AMEN @@En_theo
Enjoyed the lecture - however I didn't get the Bell experiment results part (at about the 46 minute mark) I thought that entanglement would mean (like he mentioned with the Red and Blue balls earlier in the talk) that if 0 (or one type of spin) was at the first experimenter - the other could be predicted to be the other ie. 1 (a opposite spin) ?
Thank you very much for an inspiring lecture, Dr. Palmer!
Wow, The beautiful desk is back!
ITA kinda been guessing that just learning abt Fractal math and how it could be used to represent physics chemistry. Spooky action at a distance is that all our perceived reality matter is underlying connected in subspace effecting each other through emergent forces energy
Thank you for the video.
Brilliant!👍👏
1.5 X Speed sounds best for this lecture
Brilliant lecture. Faraday "like" in discourse.Upto date and cutting edge Physics concepts presented in a typically Oxford educated manner. Well done doesn't seem to accolade. Thankyou.
A tedious comment which you struggled to write.
@@0.618-0 Always fun reading the strawman arguments people resort to when they feel belittled. Do better.
thank you for the video
This was absolutely wonderful. It was a fantastic walk through some lovely ideas. Thank you for posting this.
We're very glad you enjoyed it!
I enjoyed this lecture!
Great video, very informative. Thanks
Is memory a projection of 4 dimension space for t
Cantor's set is a shuffle.? (taking triplets (three notes divided over the duration of one beat) and not playing the second triplet. 1(rest) 3, 1(rest) 3..)
Nice talk, but why has the Bells formula a negative sign "on thursday"? ie c1+ c2+c3-c4?
I think my stumbling block is, what do the three variables represent in the Lorentz state space? Why did Lorentz' state space have three dimensions, and where did the relationships between them (described/defined by the three equations at 15:49 ) come from? (The decision to gloss over this part to move onto the broader point was probably a wise one, but now I'd like to learn more.)
Lorenz was a mathematician and meteorologist so X,Y, Z are Thermodynamical states. X is proportional to the rate of convection, Y to the horizontal temperature variation, and Z to the vertical temperature variation. The equation are (if i remember correct ) a simplified weather system.
@@rogerforsman5064, Thank you, that does make sense. So I guess my next question is, why would the same "butterfly" shape show up in state spaces relevant to the Bell experiment? Is Thermodynamics even in play at the quantum level?
@@frixyg2050 Look up Statistical Mechanics
@@frixyg2050 Chaos theory( aka butterfly effect) is seen in nature in lot of systems as described in slides e.g. weather, economics, even society as a whole is a Chaotic system. As to why Tim showed butterfly for bell experiment here that he is hypothesizing that universe itself is a chaotic system which can have it's own attractor(butterfly shape) and by putting points on the attractor he is trying to explain why we see those non local correlations between particles it's not because universe is non locally real aka non deterministic as it popularly believed by physicists but can because particles on Monday, tuesday so on are on different lines(contractual worlds) on the attractor meaning different initial conditions leading to non computable (NOT non deterministic) outcomes.
I think it may have been Johannes Kepler responsibr describing elipses of planetary motion.
It was. :-)
I prefer to explain the difference between weather and climate as the difference between predicting dice rolls vs the how likely a die combo roll is. ie Roll 1d6= >17% of 1-6. For 2d6 2s and 12s are unlikely and 7s are more likely but less than 50% likely.
58:14 I wonder if the simulation would have been different, perhaps less dramatic, if the floating point approximation was better - higher resolution ?
The more precisely you can locate the starting points of the masses, the longer you can make the "stable" orbits last. But you can't avoid the chaotic result - even a difference in the 30th decimal place will eventually manifest itself, although you might get bored waiting for it. Eventually, the Planck length puts a limit on your ability to make finer and finer tweaks to the starting configuration. (Does that "connect" chaos and quantum physics? 🤔)
ETA: Mathematically, there are stable solutions to the 3-body problem, but no solutions for 4 bodies. Google "3-body problem" + "figure 8" if you want to go down that particular rabbit hole.
Thank you, nya.
Yes, big picture thinking! My idea is that reality is all possible combinations, with each pattern being a single awareness (timeline), so each of us is an individual universe unto ourselves, while also branching and interconnecting with one another in an expanded Pascal's triangle (Galton board) type fabric. It's deterministic randomness (pure entropy), and definitely fractal. I shared this idea with Stephen Wolfram and he ran with it as his recent new physics model.
One thing to note is that because there is BOTH branching and reconnecting (see: a family tree where babies are produced and then grow up to mate with one another from nearby lineages) there is BOTH expansion of the number of individuals/universes in the whole multiverse, and there is contraction of those things into the larger volume. This is the fractal ability to fully contain a fixed amount of matter~energy that never gets destroyed nor added to while also adding more and more stuff infinitely into the future. This explains why we keep finding smaller and smaller "smallest parts" of the universe. It's not because we're just "better" at looking closely, but because reality is fractal, so the closer we look, the smaller the "smallest part" we can observe literally is. But ultimately there is no smallest part. Reality is expanding into the details or fractions of space~time, just like how we can zoom into the mandlebrot set and continue seeing infinitely new patterns.
So, rather than increasing entropy leading to some sort of boring (low entropy) "heat death", at least on a multiversal level, it leads to infinite life, expanding in complexity, creativity, and effectiveness at finding better and better collaborators to procreate with, genetically and memetically and whatever -etically there might be. The "heat death" is just local death of individuals physically dividing up. But those parts go on to continue to make ever more interesting sets of new individuals Entropy and a fractal reality of deterministic randomness means that there's no real death for any of the matter and energy of reality, only infinite natural selection and random mutation of patterns of all types.
At 49:50, would the second terms be wrt B in the equation at the bottom? I guess, it's a typo
thank you
15:00 could you give an example how these equations apply to a real world system?
Yes. X, Y, Z usually stand for things like humidity, temperature, etc. They evolve according to the equations.
RI talks usually have clear, crisp audio, even when the recording is quite old. Unfortunately, they seem to have been having trouble this time around. I found that the background crackle and muddiness made it very difficult to figure out what the speaker was saying. (That said, I have known audio processing issues.)
Not a math dude, but it should be possible to influence a system in state space to control the direction of the system, so we could perhaps learn to control even extremely complicated chaotic systems by detecting, observing and nudging the system in state space.
100% right man. If you're interested in any medical applications of this cool idea check out Michael Levin's work on bioelectric signals and directed cell growth. He's at Tufts and was one of the guys that created the self replicating xenobots in the news a while ago
Amazing good luck whit your theory.
I’m amazed at how accurate the weather forecasting has become here in the NW of the US. All the weather comes in off the Pacific Ocean. Very changeable. Used to be 50/50. Now much better. Better understanding of chaos?
Ensembles
What is the reason for the difference in statistics between classical and quantum cases? (2 vs > 2) 48:33 I mean, why are experimenters somehow limited in their measurement choices in the quantum case, but not in the classical? A measurement outcome clearly depends on the past light cone in both cases.
Classical vs quantum light cone ... quantum optics is higher up.
This is the guy Sabine collaborated with on the Covid song! 🎉
Right, and he is with her about superdeterminism.😊
Wow mind blowing didnt mention Bell's entanglement coming to 2.41
Totally 💯 agree
starting from the quantum scale it is impossible to predict the future due to all prior interactions lead to the next set of possibilities and its never repeating. To make it repeat you'd have to set up every single quanta as it was to make the "same" thing happen again.
What matters is past light cone.
Relativity and unitarity (Everett interpretation) doesn't forbid it, they are deterministic. Sweet. Wonder about his view on quantum mechanics now though to see if he's consistent...
6:15
It was Kepler, not Newton, who discovered the elliptical orbit of a planet (Mars).
In 1609 he published Astronomia Nova, delineating his discoveries, which are now called Kepler's first two laws of planetary motion.
Tycho Brahe Danish Astronomer 1542 1601 who recorded the planetary orbits and gave this data to Kepler. Kepler then used it to work out Kepler's laws. Which after analysis of Kepler's laws then Newton discovered the Calculus..also I suspect this focused Newton's intellect on Gsluleo and Gravity.....Newton.1642 1727
@@0.618-0 True. Tycho Brahe was meticulous in how he collated his astronomical measurements and data. He didn't see or was concerned with the elliptical patterns in the planetary orbits.
You can also go back to the ancient Greek Astronomers - although they didn't use ellipses to describe the orbits of the 5 planets they knew about, they were aware that these orbits were not precise circular orbits. The AntiKythera Mechanism which is the worlds first known analog computer used epi-circles and other techniques to compensate for these non-circular orbits.
In reality the orbits of most planets in our Solar System are very close to circular, with eccentricities of near zero. The eccentricity of the Earth's orbit is about 0.0167 for example. Mercury has the most eccentric orbit of any planet in our solar system (~0.2)
Newton was co-inventor of Calculus.
We must never forget the great Gottfried Wilhelm Leibniz.
yes indeed.
YAY!!!!!!!!!
I loved it. I study chaos all the time
this was a very interesting lecture ! I think fractals are also the key to solve the Riemann hypotesis
Why do you think that ?
There is no connection between fractals and Riemann hypothesis. Don’t get carried way by name dropping done during this talk a lot of it is totally random no pun intended.
@@paulhofmann3798 Maybe OP was just name-dropping fractals and the Riemann hypothesis because they're popular math topics, but your comment reads as silly and condescending to anyone with even a passing passion for math. Since when are functions (and hypotheses about functions) unrelated to fractals and dynamic systems? Claiming that two things in math are unconnected is just a strange thing to do.
It took me LESS than a minute to find a paper expressing the relations between the zeta function and fractals. Google "Fractal Geography of the Riemann Zeta and Related Functions Chris King"
Chaos hosts patterns too broad to perceive, but may be found with my collection of novel primes in an Excel file called The Box, containing the first 150 elements.
A measurement involves a phase transition where the macroscopic pointer variable of the apparatus goes from the initial metastable state to one of the stable states. Not doing an experiment means that nothing happens. Counterfactuals do not make sense. Getting the whole universe in the argumenting, means that they don't have any clue.
As attractive as order has been for human development, including our current understanding, thus far, of the universe, it appears that the greater our reliance on systems of order the more vulnerable we become to random interference.
That's because we've mistaken systems of dis-order for system of order.
Watching the 4-body system blow up makes me wonder how stable the solar system is! Obviously the planets get more than five trips around the sun, but if we waited ten or twenty billion years (longer than the sun will actually last), would one of the smaller planets eventually be ejected?
Perturbation is very difficult to predict but it is practically certain, especially as the sun changes density over time.
I mean, that's basically what comets are.
@@Duiker36 This is how comets get yanked out of the Oort cloud in the first place.
14:23 I feel like you could actually have X=TrouserLength, Y=ColourSpectrum, Z=Width and one could denote and visualise even, the particular ratio of, say Cotton:Polyester by creating a second X and Y Axis (call them X1, X2 and Y1, Y2). - By plotting the first 3 parameters using the X1, Y1 and Z Axis; this would result in the graph he displayed. However you could then use X2 and Y2 to plot the Cotton:Polyester ratio. One could then take the first plot point (P1) and then use the second plot point (P2); for simplicity let’s say the graph starts at X=0, Y=0 and Z=0. You then graph a curved line from 0 on all Axis’s to P2 and from P2 to P1. The Z Axis would remain as Z=0 for P2. I Posit that the graph which I have (hopefully clearly) outlined would allow one to successfully create the graph which he said you can’t do, would in fact allow us to graph 4 parameters and graph them. I personally think that he is conflating the idea of Axis’s with Dimensions. Can somebody who is a Mathematician, Physicist or I suppose anyone who knows these things better than myself (I have studied these topics out of curiosity, but I don’t have a degree or care for one quite honestly; I simply love to understand) please give me your thoughts on my suggestion. I would love to know if you agree and if not; why do you disagree or why am I mistaken? I’d really appreciate it. Thank you 🙏🏻
P.S - He has rather masterfully demonstrated Chaos by the very nature of this presentation itself.
I mean, he's wrong in the sense that we technically do have visualizations of hypercubes (4d surfaces). The problem isn't that it's impossible, but that you lose an immense amount of information. Even plotting 3 dimensions on a flat, 2d screen, you lose a lot of information. Imagine how much you're not seeing because it's going from 4d to 2d.
How crazy Simant Dubey must be to relate the fractal geometry with computably unprovable conjectures!
Geometry of Chaos at first sight appear a repeated module or a pattern. Lorenz attacter make the predictive pattern. Bell's theorem and a pattern in correlation naturally bring the subject towards future of physics. Uniform field near earth or heavenly body always sense a charge of G .
G is geometry of chaos or stochastic or a pattern in randomness. A riddle that flipped between Einstein and Newton now need a third leap like third reference or party of Bell's.
A quality lecturer makes me satisfied with few new results into gravity .
Sir Penrose namaste from me to all of you
& 2020.
Energy as plasma has five fundamental nodes, it can be stored compressed in a fractal space when space is deformed...there are sets of geometries for classes of archaic black holes, they could be dark matter. once an event occurs, they might exlode... or explode and persist...
Hear his words & see his Illustrations, butthis theory & ideas dramatically Divide the "Knowledgeable" & everyday mind populations......Old school here & just can't comprehend dependability & usefulness of a "Chaos" state....
From the beginning wrong - bell experiment was about locality, not hidden variables
Bell experiment was about proving ER VS EPR. locality and hidden variables. Hidden variables may exist but the notion he was on about is that fractal sets somehow interfere with locality and Bells experiment only proove what Penrose states, that quantum mechanics is lacking an insight just like the one GR brought to Newtonian gravity....
ok, what´s your qualificaton, to prove a professor of math and Nobel-winner wrong? Bell-like tests prove locality vs. nonlocality, hidden varialbles are nessecary in a local model. They do all that under the assumption of statistical independence.
@@Thomas-gk42 read the experiment criteria
14:35 Finally got his first laugh out of the audience. I was honestly feeling bad for him because there had been no response before this
ever define 'attractor'?
Its fascinating how similar chaos theory appears to the language of the philosophical system of dialectical materialism. I always thought that dialectical materialism could be used to unify the modern sciences. I feel as though this smart man has gotten miles ahead of me on this idea
Gets to the VERY RARELY MENTIONED ASSUMPTION until 51:58. COULD have and SHOULD have stated it RIGHT AT THE BEGINNING.
Bohr was not Einstein's advocate. He was his adversary..
👍
spooky action makes a huge amount of sense in a universe this vast.
The question is, how large is the universe, how could you measure it? How would you know you had measured all of it?
At the end he suggests that measurements result from the “geometry as a whole”. This sure sounds like the “spooky action at a distance” (non-locality) that he rejects at the start.
I like both the ideas presented in the lecture.
Spooky action in distance and one of tbe strong view point to explaining orr rather refusal to explanation is to accept it as it is. For thise who are either not interested in physics or dont have means to understand it, it leads to mysticism and metaphysical (which ends in out of date concept of religion and all that comes with it).
The "big picture" idea can truly revolutionize lot of fiels, human immune system understanding for example where it is quitr very well understood why a particular cell "behaves" in one manner but not when they are more than few.
Really great talk.
Particle is a Turing machine
Reminded me of the butterfly effect. The effect, not the movie, books etc.
The butterfly effect is the illustration of chaos.
So either nature/the universe is ordered to what we can only define as chaos, or there is simply no necessary order to the universe and there is only chaos... OR, there's a supernatural state of existence which interacts with and within the natural world, space-time, causality, whatever you like.
This presentations was all over the place. As someone who has little to do with this field I found it really hard to follow. Maybe I just got way too used to how easy the usual RI presentation are to follow.
"behold I say unto you, that by small and simple things are great things brought to pass; and small means in many instances doth confound the wise." Alma 37:6
True, quantum fields evolve superdeterministically. Moreover, all fields are *effective*.
Very happy to see indian 2:42
There is no something chaos, it is consciousness that chaos and order
Infinity Squared I.S. 010 Geometric Chaos.
making maths boring is a sin, but interesting stuff here.
As Above
So Below
21:08
surely chaos theory and geometry can predict, but we are not interested in prediction any more. we need solutions.
Emmy Noether ❤❤❤
The Mother of Cosmology. ☮️ ❤️ ^.^
@@TheMemesofDestruction the mother of symmetry☺☺☺
Mother of my babies
What if it had been a guy named Edward Noether? Would you still care?
Modern Álgebra mam
Things are very much hidden in geometric
Love a man that can explain somethingncomplex using a pair of pants
Be 🎉🎉😊
Yes they can, I have proof.
Lol nobody thinks diffusion is a "spooky action at a distance", yet, according to how you define "information" in the good ol' diffusion, you get infinite speeds (since diffusion is linear, it looks like every point affects every other points at a distance, but the truth is the "would-be information that about to come in the future" is already constructed in the locality by the previous local interactions). Hence Einstein is right.
Hari Seldon came up with this 500 years from now.
Efectivamente
The movement of the double pendulum is unpredictable. Similarly, the problem of three or more gravitationally bound bodies is unpredictable. I don't understand what you are talking about... A higher power is playing with you like cat and mouse and you want to guess the future... haha 💜💜💜💙💙💙
Except the movement of the double pendulum is NOT unpredictable. If you have two double pendulums with the exact same starting conditions, they would both trace the same path.
And as far as your claim about a higher power: there is no such thing. You are God. I am God. Everything is God, at all time. Study Pantheism and catch up with humanity. You'll feel better if you do.
@michaelc3977 The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. In popular media the "butterfly effect" stems from the real-world implications of the Lorenz attractor.
@@0.618-0 When idiots paste from Wikipedia. So tedious. The motion of a double pendulum is NOT unpredictable.
Patric Moore “Dearth of CO2”
So if gravity is chaotic why don’t we see satellites and planets flying off in all directions?
For the same reason we do not see air blowing in all direction inside a closed space, despite Brownian motion is a fact.
So, essentially, what you're saying is Chaos Theory is a useful cop-out for when simple physics gets too complicated to do the math on.
just assume audience has a CLUE what a fractal is?