The Butterfly Effect is Much Worse Than We Thought
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- Опубликовано: 18 мар 2024
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A butterfly flaps its wings in China and causes a Tornado in Texas - that’s a popular example of the “Butterfly Effect.” However, scientists now say that the Butterfly Effect might be even more dramatic than previously thought, and that molecular noise can do it. Let’s have a look.
Paper: journals.aps.org/prl/abstract...
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I'm kind of unclear on why it wasn't obvious that Brownian Motion would be sufficient to trigger instability in chaotic systems. Anyone who's done any work on computer systems that exhibit cyclic behavior knows that unless you build in artificial correction, even the smallest floating point error can and will cause the system to deviate on meaningful scales within a very limited timespan. This problem was in fact the bane of many early attempts at networked gaming.
The natural world doesn't generally offer algorithms to correct floating point errors - indeed, the randomicity of quantum systems suggests that these minute deviations are very much a feature, not a bug of our reality - and should be expected to affect the behavior systems up to the scale of planets within a measurable time frame. The formation of the early universe was almost certainly similarly sensitive.
This was my thought as well. If you look at the paper, the novel result seems to be about the time in which small stochastic response propagates - they have a concrete result regarding when energy fluctuations smaller than your grid size can be expected to effect the statistics of a simulation of the NS equations in finite time. There is nothing novel about the idea that arbitrarily small deviations in initial conditions will affect trajectories - this is chaos by definition, and goes all the way back to Hadamard.
But the deviation doesn't proceed to infinite deviation, even in QM, does it? There must be natural limits. Though there is renormalization come to think of it. (not a physicist)
I suggest there must be some kind of dampening force to change that keeps everything from becoming truly chaotic, even maximum entropic.
The ability to renormalize and its utility in QM indicates there is a natural limit of some kind to chaos in QM that shows up in actual real world measurements. (not, etc.)
This paper doesnt really say anything new, and is exactly what the mathematics work out to if you studied chaotic systems in depth.
The intuition that a prediction model has arbitrary input sensitivity is exactly that, arbitrary there is no scale difference between a butterfly, a molecule or a plane. And the use of stochastic models has been motivated by this realization for about a hundred years now.
Hm, an "alive and well" type of comment section, how surprisingly nice!
You're not the only one who is wondering why this isn't obvious!
I always thought of the butterfly as simply a metaphor of a very insignificant event, because individual molecule movements are not a very relatable example.
It's a language trick, mostly. When you deal with hurricane massive levels of fluids, for instance, a small disturbance can be amplified to change its course. But the disturbance cannot be controlled, so it is just a random observation in the infinite parts of the hurricane dynamics.
it is a metaphor yes, taken seriously in the video in order to make the argument for things even more subtle than butterfly wings.
If i help someone today. It might seem small in the big picture. But that person goes out to helps another and so on. Yes this thing is real.
If a storm destroys someone's house and that person now will not meet a person they were supposed to do so it changed history for everyone.
That person that was never met, meets now someone else and all the people those 2 were to come into contact also also impacted. It's all connected.
If a butterfly flaps its wings and kills a mosquito that was supposed to sting someone and delay them for 5minutes. Bla bla etc.
It is real but a butterfly causing a tornado? Mhm. You gotta stretch that fact to a point where it becomes ilogical.
@@iAmNothingness"It's all connected, bro."
a hurricane is going to happen somewhere, and it has a cause. Did it start with a butterfly flapping its wings over the Sahara? Could be, but I never understood the sort of wierdness people associate with it. Like, duh, common sense tells you that a small change can alter history, and it has been played out as a trope in many stories, especially ones about time travellers. Hello! Hello, McFly! Duh! (Smacks people on the forehead for being so dense.)
As a meteorologist I was often struck (and confused) by the thought that energy was cascading down from large systems to smaller ones and eventually to gusts of wind. But also that butterfly gusts were working their way up the space/time scale to make cumulus clouds, then to thunderstorms and mesoscale features to large depressions. Thanks Sabine for an excellent video.
Remember that when the atmosphere is stable, small scale perturbations may get damped out, thus not working up to larger scales.
Wonder about the effect of those wind farms extracting energy from the atmosphere.
@@thadtheman3751 Good point to raise. But I think the maths will show that it's an incredibly small percentage of the atmosphere's energy.
@@richardfile4001 You mean like a flap of a butterfly?
Wasn't this already known? Even if we assume we need at least a butterfly sized disturbance, a smaller disturbance can cause the butterfly sized distyrbance in a chain of events.
Sounds logical. Can causality be atomar, if time isn't?
Exacty, and isn't that also how the the 'many worlds' multiverse of QM is explained? Due to random quantum fluctuations on the atomic scale larger and larger systems are affected until you get one universe where a cat is dead and another where it is alive.
@@Marcel-yu2fwI don't see it. the butterfly effect doesn't require at all more worlds. In the butterfly effect, the butterfly and the effect surely happens in the same world. And on the other side, the many worlds don't require a butterfly effect. The whole point of Shroedinger's experiment in the many worlds interpretation is that in one world the cat is alive, and in another, the cat is dead, but in no world, the cat gets to be unexpectedly a butterfly. Neither QM or QFT in any interpretation, don't require the butterfly effect. They predict something will happen, but not necessarily something unexpected. Sure, BE may very well emerge from a physical theory, like QM/QFT, and likely will since we'e observed both in the same.. one world, the one we're in. But that's only if QFT is worth it's salt and we're not missing anything that's relevant for the BE. Although we're surely missing something that may or may not be related to BE, but we are missing something, because otherwise QFT would work with GR.
yes, but the butterfly effect isn't about how something can happen, but about how in real world, that something, sometimes, has a very short chain of events for it to happen.
Yes, some molecules move can make a butterfly flap, which causes something else, but generally you wouldn't expect that to cause Jupiter to switch course and hit the Sun. At least not in our lifetime. What you normally expect, and what you describe is that maybe... after a very long chain of events, in some billions of years, the butterfly flap of today is causaly related to Jupiter hitting the Sun, but surely not tomorrow. The butterfly is pretty much saying "hold my nectar, cause you'll be surprised by my effect". Now I wouldn't be scared that Jupiter will hit the Sun tomorrow, but the whole point of the butterfly effect is that this possibility cannot be excluded. The butterfly effect is about how small disturbances may turn any stable system into an unstable system.
My Jupiter example is extreme, but that's exactly what this study tried to do, to draw a line somewhere, because we don't really believe that a butterfly on Earth can really make a supernova go kaboom in Andromeda in a limited amount of timesteps, but we have observed that it can cause a surprisingly big effects in another city. There's obviously a relation between the size of the flap and the distance it can cause something and the number of timesteps. This study focused on the size of the flap at a fixed distance in a fixed amount of time, so that we have more data as to figure the relation between these variables. Their result is surprising in that they expected the size of the flap to be smaller for the other fixed variables than what they observed.
Yes we did: ever since "Period 3 implies chaos" (Li and Yorke, 1960s or so; but Soviet mathematicians had already discovered the same results before them) we know that even the simplest systems can have a strange attractor and display chaotic behaviour, and that there is no lower limit on the required disturbance.
Of course in those days we still used the meaningful term "sensitive dependence on initial conditions", which says it all, rather than a meaningless, misleading, and useless term like "butterfly effect".
My bad: Li and Yorke published in 1975. But their example was much simpler than Lorenz's.
A single butter and a single fly can cause major turbulence.
A single electron deciding which side of a atom it feels like hanging out on in a particular nanosecond can chande thr future of the whole world.
@@ishner true all, but in nature there are processes which introduce negative feedback loops, which, for some things, limit choice of possible, or at most, probable evolution paths of states of systems. So reality is a dance of variety of differential equations.
@@salec7592 I was thinking that but I never could have worded it so well. You just described in words how the upper and lower limits of stable chaos happen. Cheers. 🙂
A single butt er.. I mean, a fly, can do the same by itself. :)
Even a single butt. Let alone if it's even butter.
I don't know who Benedict Jacka is, but in Asimov's "the end of eternity" written in 1955, the time travelers calculate the minimal change (like moving a vase a few centimeters) necessary to make a huge needed change centuries later.
It was also Asimov who had a story about a man going to a fortune teller to change his life. He was convinced to change his name from Zebatinsky to Sebatinsky. Through other events, that changed his life for the better, but also prevented a nuclear war, or something like that. Back at the fortune teller's place, one alien observer says to another, see, I told you I could make a Class A effect from a Class F change, the bosses won't even notice a Class F change. Yes, said the co-worker, but they will notice a Class A effect. You will be in trouble when they find out.
The minimal change is.. any change. There is no change you could make that wouldn't make huge changes centuries later.
Realistically, if time travel ever existed, then you'd just have to accept that you're essentially "rerandomizing" the universe so to speak, and things will never go back to how they used to be. Don't expect anyone that's conceived after you time travelled to have the same DNA for instance.
A book I read a while back, it may have been David Lindley's "Where Does the Weirdness Go?", describes a computer program that was developed to simulate the collisions of air molecules, according the book, an.initial variant equivalent to the force of the gravity of one electron located 10 billion light years away (I know, right?) was introduced, and after around 30 simulated molecular collisions, the pattern was unrecognizable. Unfortunately, no sources were referenced.
😎👍
People forget how many competing "butterflies" there are which, because of the way that scales down towards similar effects working up from quantum mechanics strongly reinforces the idea that the smallest "computer" required to simulate a universe is universe sized. 🦋🦋🦋🌌
(Aha! And don't get me started on how do you quantise the changes in gravitational effects of dancing ants at each "side" of the universe... ;p~)
I'm pretty skeptical since adding small numbers to large numbers in computers drops the effect to zero. I suppose you could use infinite precision math packages but that would be hugely slow. In any event the effect would be like adding a constant to all the atoms.
Look up the theoretical physics conjecture "ER = EPR", there's a lot of really exciting ideas in high energy physics and Quantum gravity contrary to what this channel says....
If this is true I suspect round-off or some kind of numerical error.
For the very first time watching one of Sabine's videos I can honestly say that nothing in this video came as a surprise to me. Having read James Gleick's brilliant 'Chaos: Making a New Science' at least 5 times since 1988 I had understood it to suggest that the 'Butterfly Effect' operated at all scales, including the sub-atomic scale. With the development of wave field theory it seems natural to assume that certain sub-atomic wave interactions will produce 'rogue' waves, just as ocean waves occasionally do.
Yes!! What came as a surprise to me that I finally heard it mentioned. This comment section is fantastic, so many people get it, I'm glad to know you are all out there.
Such a great book, especially if people are interested in learning more about chaos, which is just a fascinating scientific field. Thanks for mentioning it. :)
TLDR: chaos is chaotic.
I don't think there's anything special about molecules. I assume subatomic particles and whatnot have the same effect on chaos.
Something something initial conditions
Chaos is a deterministic system, actually.
I think you're making a significant assumption, there. "Chaos is chaos" is not a correct summary of this finding, which was investigating the scale at which chaotic processes can contribute to larger chaotic systems. The brownian motion of molecular movement apparently being sufficiently large scale as to contribute to atmospheric evolution. But does that mean we can automatically assume that subatomic unpredictability gives rise to that chaotic motion in the first place, rather than exclusively interactions at the molecular scale? I don't think so
@@Jan-pk6inyep, by definition. I still remember programming a 10 line BBC BASIC routine which produced (overnight) my first fractal - the Sierpinski triangle - and blew my mind. The fact that such an apparently trivial and non random algorithm produced such boggling complexity still seems almost mystical.
😎👍
Most important quote to remember from this fellas: "It's not just about size, it's more importantly also about energy"
... even mor bad news...
it's not the size of the wave function, but the rotation of the phase.
It ain't what you do, it's the way that you do it
@DrDeuteron
😆😆😆
Why are the “toys” consistently a bigger size though. Measuring usually around 8-9 inches😅
I believe 747 flapping its wings would definitely influence a lot of people, journalists and engineers at first, but it has that chaos potential, yes
Sabine's science communication is just top notch. Humorous and to-the-point.
But does she spend too much time talking about quantum mechanics and not enough time on Chaos Theory?
THAT'S what we'll talk about today. 🙂
Look up privately.
Some people thing this is counterintuitive. But there are many working examples of small energies controlling the flow of much greater energy fluxes. A mains switch is a great example. But also a transistor. Or even the helmsman of a seagoing yacht who is able to use the strength of his muscles to direct a multi-tonne vessel in rough sea (been there, done that).
Trim tab!
Quantum effects seem to average out at macro levels. I have a hard time believing that a butterfly could cause a hurricane without understanding what is multiplying its impact. Why not say that gophers can cause earthquakes?
@@kurtiserikson7334 Computer systems prove that this isn't true unfortunately. If some errant neuron in Putin's brain decides to press the button and start WWIII, that sequence of events will literally unfold into a massive energetic holocaust that would reshape the surface of our planet in under an hour.
You can say that this isn't like the weather - but the truth is that it really is. A tornado or hurricane is just the result of a system that's sitting in a high-energy state right next to some tipping point, the real question is exactly *when* and *where* it tips over that line. Same with our nuclear arsenals. Both cases can be tripped by energy events vastly smaller than the system they are tripping into motion.
It's wrong to think of the gopher causing an earthquake - the earthquake was ready to happen and would have happened sooner or later, the gopher just generated the minute tremor that finally pushed it over the brink. But that still makes the difference whether the earthquake happened today, or next week, and all the further ramifications of that difference.
A good example I saw recently was how wind waves form, and how they can be quenched... It starts of with just tiny, mm high waves that the wind catches more and more until they swell into large waves.. If you stop the micro wave build-up ability you can calm stormy water. This old sailors trick involves pouring fish / whale oil (or vegetable oil) into the sea. It has worked enough to save lives using a few barrels in stormy waters, to make a crossable path a lifeboat for a fragile lifeboat. A few cap-fulls into a flat lake you perturb will stop the waves really quickly.
@@kurtiserikson7334 do we know that tectonics are governed by chaotic processes, the way we do know for atmospheric motion? It's not apples to apples
Loved "Sound of Thunder" episode of "Ray Bradbury Theater" when a rich guy goes on a TIME SAFARI to shoot a T-REX seconds before a tree falls on it and falls off the floating walkway and upon returning finds the world is run by some kind of Nazi like regime (very German!) and the tour guide IS NOT HAPPY ! He pushes the guy down onto a bench and lifts up his boot and picks up a dead Butterfly... and .... save it to say things dont end well for the rich hunter.
Been trying to remember this story for years ty!
haha yeah was thinking of the same thing
I have a feeling it might have been a moth, but I read this story decades ago, so I'm not 100% certain.
Also made into a full-length movie, with Ben Kingsley as the owner of the time travel business.
When I read that story as a teenager, I thought it was odd that they only worried about macroscopic living things. The floating walkway was sure to interact with some bacteria.
This paper makes it clear that a tiny change a few weeks back would be enough to change where a hurricane makes landfall. Seems like a hurricane would kill quite a few butterflies.
I bet even the slight gravitational fluctuations caused by the energy of your actual brainwaves moving around is enough to influence turbulence. I think everything affects everything else, and given enough time, it results in everything being completely different.
😎👍
Yeah but what are brainwaves?
Spot on, in reverse
Turbulence is created corruptly to destroy our psyche; our brain receives corrupted consciousness
@@squidwardfromua brainwaves are just the electromagnetic "leakage" of the electrical signals being transmitted in your neurons. It's all made of molecules, but I'm saying that in addition to just the molecular movement, even the movement of the energy like that in a brain or in an electrical system or anything else but has its own effect.
Brainwaves are the effects of your brain activity/maintained stactics than intertwined with other ppl's brainwaves, some may call it AURA
Brain, or machine/cpu, both consums lots of energy in similar ways, the computer in fact is a close simulation of brain function, although pcs mostly are costomised/fixed structures, brains although differ according to different regions/households, however, ppl's brains are growing more and more alick with unified functioned objects by eliminating nature with factorized machines
we HAVE to stop these butterflies
This is why i don’t tend to put too much faith in “long term” simulations beyond, perhaps, qualitative conclusions.
Time-stepping through of nonlinear system with feedback is just BEGGING for exponential positive/negative error accumulation.
What kind of "simulations"? How often are "simulations" being really significantly affected by "butterfly-effect" noise either "randomly biased" to one side or actually tipping a causal scale to one side? Don't people making "simulations" in general put things in terms of error margins that more often end up usually being wide enough to capture the eventual observation, while also being meaningful? I mean, excluding "bad" models or those fed with bad data.
I couldn't agree more with your opinion of never being able to produce models that take in to consideration the tiny energy inputs of molecules . Why you'd need to design a computer program that simulates the entire universe including all living beings , have it run for billions of simulated years and you'd have to make sure the life forms were totally unaware of it's existance ... oh , wait ...
Stop ruining the experiment man
The Navier-Stokes equations may be chaotic, with each scale of resolution being eventually coupled to every other scale, but this is kind of a moot point considering we cannot either measure, much less control the local dynamics of the atmosphere at any scale of resolution.
"seagulls crapping - I mean flapping" - your stochastic sense of humor at its best! Thanks for yet another great episode!
Made me laugh too.👍
ctrl f crapping. yep
The flapping reminds me of a Heisenberg statement ( and in place of memory I broadly paraphrase ) : "When I die I shall ask the lord ' Why the quantum? ' and 'What's with turbulence anyway ?' . 'I do expect an answer regarding the quantum .'
I guess the old guy just likes to play dice.
Adds a whole new depth of meaning to "knowledge is power". Someone who knows what molecule to move to do X doesn't need a lot of force to have a lot of power.
But how much energy does one need to consistently obtain such knowledge?
Beware the probability engineer, for they always cheat at cards.
I knew there was a catch. OK, the AGENT of the one who knows all that does not need to use much force to have great power....@@mauriciosmit1232
Actually you don't have a lot of power if you cannot predict the results of your action. And while chaos means that small changes can have huge consequences, it also means that you have no chance to predict those consequences. So yes, you might cause a Hurricane by waving your hand. But just as likely, you are preventing one. Or redirecting one. Or just make the wind blow slightly stronger or slightly less strong. Or from a different direction There's absolutely no way to tell which one it is.
Didn't we already know this? My understanding of "chaos" has always been that _any_ perturbation of the initial conditions, _no_ _matter_ _how_ _small,_ would eventually randomize the system, and that this held even for disturbances much smaller than butterflies, the only question being the time scale. The solar system itself is chaotic (Google "Solar System's Future Could Be Bumpy"), but the time scale there is billions of years.
Also, it would be helpful to distinguish "weather", which is chaotic, from "climate", which is emphatically *not* chaotic. Next winter is going to be colder than next summer; no butterfly is going to randomize _that!_
This also affects our understanding of the brain. How nanoscale perturbations arising from quantum mechanical interactions grow to macroscopic scale, inherently random, and forming the basis of free will --- the brain can shape those fluctuations as they grow, and the ones we like grow larger until we become consciously aware of them
I assumed all this was obvious. A butterfly itself is also a system vulnerable to chaos theory. It only takes 1 molecule in a buterflys brain to alter when/if it flaps its wings. The same would be true for an elephant. Every scale is subject to a complex system potentially becoming divergent.
This is still true, but less so, for systems of decreased complexity. The complexity determines how exponentialy quick starting conditions (at any time) can diverge. So a galaxy, with significantly less complexity, less forces making significant changes, less interractions of things, will take exponentially longer for a single molecules uncertainty to make significant changes. But, it will eventually, in some cases.
I can see The Onion headline now: "Area Molecule Causes Super Hurricane"
Florida molecule, for starters.
@@haraldmilz8533Of course there's also, "Area molecule prevents super hurricane". That would not be a Florida molecule.
Seriously? I thought about this as a logical consequence as a kid, as described here. And then I thought String Theory was the explanation for that (we know how that turned out). Glad it's becoming scientific consens finally.
“a seagull crapping!!!” Gotta pause Hossenfelder’s presentations sometimes until I can stop laughing. OTOH, she really DID mean “flapping.” (She DID!)
You earned a subscriber from Kenya. Kudos Prof.
And each time a windmill steals a bit of energy from the wind.....
... it might prevent a Hurricane elsewhere in the world.
I'm confused. I thought the most important point in the butterfly effect paper was not knowing which butterfly or butterflies it would be because in the actual measurement it was a rounding error. Looking more at the actual theory, I thought the entire point of chaos theory was about how precise of a measurement is needed for predicting a certain length of time into the future.
Isn't simply the fact that smaller things can cause slightly bigger things enough to almost prove that deliberately small things can influence deliberately big thing using n+1 proof?
The part that has always mystified me is that it seems other effects going on at the same time should be able to easily cancel the initial butterfly effect. It is not like the world is static and only one event is happening at any one time.
I agree. It's like the butterfly is placed in the perfect location in time to shake the whole universe. Whil we know the universe left room in our atmopshere which makes butterflies be able to flap wings and overcome the density of the atmosphere with their energy.
I think they forget the energy the butterfly needs to just do that. I don't see a surplus of energy that can chain reactions. it's energy surplus given is canceled out the moment it flaps wings and gains lift. Guess that why they fly chaotic. lot of turbulence for such a tiny weight with wide span.
Anyways if anything could create a butterfly effect i give the hum of the bee more credit.
to exactly predict a tornado in the distant future it would be necessary to know how every butterfly is flapping its wings (plus all the other factors involved)
The reason it doesn't cancel out is because some systems are macroscopically sensitive to incredibly small deviations. Think of a pencil perfectly balanced on its tip - it's going to fall, but what determines which direction it is going to fall? Even sealed in a container with perfectly still air it will still fall due to Brownian motion in the air or a minute tremor. Just a few more molecules hitting it from one side or the other as the air randomly bounces around it will do the trick.
The real world actually involves quite a few systems that represent pencils balanced on their tips - Earthquakes are a great example. You can see that you are looking at a pencil balanced on its tip and that there is likely to be an Earthquake sooner rather than later, but you still can't tell what tiny shove is going to push it over or in which direction.
@@Vastin I appreciate your thoughtful answer. But the situation you described was in balance with its environment, so any change in that environment of a great enough magnitude would upset that balance. Even the earthquake example is a situation in balance until an event upsets that balance. Especially considering the fact that gravity is a universal constant present in all systems. One more thing is every single earthquake on record had tremors going on before the major event occurred even if the tremors were on the micro side.
it doesn't cancel out perfectly therefore the big changes in end results still happen.
I always try to apply this to me yelling at my TV when my sports team is blowing it.
For every butterfly flapping it's wings and causing a storm. There's a butterfly flapping it's wings preventing a storm
A butterfly flaps its wings, and an apostrophe is misplaced.
Thank you so very much for sharing your experiences and thoughts. This is an excellent video. I appreciate your content
It never ceases to amaze me how people who do understand sensitive dependence on initial conditions and the fact that we can't forecast weather 5 days in advance, go into such a frenzy over and with such confidence over what the weather will be like 100 years from now (and invariably over things like "climate sensitivity" which implies a linear, or at least a locally linear, model).
Yes, how can they have such conflicting and seemingly mutually exclusive ideas in the single personality without their brains exploding?
THAT'S what we'll talk about today. 🙂
you're conflating what people are predicting. the weather is a gigantic fluid simulation whereas when people talk about the climate all they're really saying is that we're increasing carbon in the atmosphere which necessarily will trap more sunlight and thus increase temperature.
Climate change is similar to filling up a glass with water, if you put more water in the glass, more water will be in the glass. co2 concentration does trap more energy in our atmosphere, we are increasing co2 concentration, simple as that.
Now we can argue about whether or not the climate will be better or worse but peoples main concerns are the extremely unnatural pace of the shifting climate and the very obvious consequences for things like food sources. If we have a unnatural seasons that calls into question crop yields. If you have unstable weather patterns, growing food becomes hard. It seems pretty obvious that for some areas it will become better and some worse.
Also there are some pretty obvious effects, if you increase temperature, more ice on the poles will melt, if more ice melts, sea levels will rise. Put more water in the ocean, more water will be in the ocean.
Climate is not weather. Climatologists are not saying whether or not will rain on May 1, 2124. Yes, small weather variables can sometimes cascade into larger "random" effects, but even then it's reasonably safe to say hat this summer will be warmer than this spring and so forth. While for the seasonal cycle the broadest astronomical aspect of things pretty much suffices, long-term climate change itself adds some factors learned from climatology, still in a rather broad scale of things, not at the scale of a weather forecast.
Global average temperature is known to depend also on the atmosphere's composition, and that is known to be changing gradually in a way that's physically theorized and empirically observed to increase temperatures. Observed currently and in paleoclimatology.
This trend remaining the same, the only thing that can be reasonably expected is for the consequence to remain the same as well. Anything else requires some large factor, yet unknown. There are no candidates analog to comparably much more minute/short-term variables cascading in different weather patterns, frustrating the prediction of a non-rainy day.
The "butterfly effect" can't really substantiate any random arbitrary disbelief in scientific predictions. To the extent it could be said to be relevant, it would be in both directions, not only reducing the predicted observation, but just as likely possibly amplifying it.
@@petitio_principii Yes we all know climate is not weather. Weather modelling is a serious science. Although with an impossible task. You have to integrate thermodynamics with fluid dynamics with quantum phenomena (e.g. forming of crystals in the atmosphere) with gravity (e.g. gravitational effect on rain drops). If your model is even slightly wrong (e.g. you don't know how to integrate quantum and gravitational phenomena 100% accurately), the butterfly effect will kill you - even if you can measure the initial conditions perfectly. But weather modellers at least are doing serious science. "Climate" "scientists" on the other hand not so much. They reduce the temperature field to a single scalar variable called the "global average temperature". And then they build models which do not exceed a high school physics level of complexity and have no basis in any real physics. "Global average temperature" is a quantity which is neither properly defined, nor measurable, nor does it have predictive power (initial conditions of all the field averages - if you could properly define and measure them - have no predictive power about the evolution of their values. You need the detailed information about the underlying fields to predict the evolution of the entire underlying fields, and different values of the underlying fields with the same averages will give you different future evolution trajectories of the averages). However, the problem starts with the fact that terms such as "global average temperature" cannot even be defined. Average over what? A sphere with radius 7000km centred at the centre of the Earth? Average over the boundary between the solid/liquid and gaseous phase of matter? What is even the Hausdorff dimension of that boundary? 2/3 of the Earth's surface is constantly and chaotically oscillating up and down (ocean waves). Do you take your sample at the water surface? Just above the surface? Just below the surface? 10 metres above the surface? Temperature in my room right now is 23 degrees C. Temperature in the room next door which is 3 metres away is 13 degrees C. The temperature field is varying non-linearly and violently both in space and time. What set you average over makes all the difference. How do you make predictions about a variable with a precision of 0.1 degree C over a timescale of a century if you cannot define how to measure it, and where how you choose to measure it can affect the value by 10 degrees C? If you could even define what the term "global average temperature" means, how do you measure it? Unless you take simultaneous samples with an enormously fine spatial resolution instantaneously, you cannot get a meaningful measure of it.
I'm sorry to say that unlike meteorologists who deal in real science, "climate" "science" deals in language which has no meaning. Variables which cannot be correlated with anything in the real world, and which cannot be measured. It then makes statements about those meaningful values which have no basis in science or in reality. I.e. "climate" "science" is just like religion. That's because it is religion, not science. There is therefore no "climate science" which could be "arbitrarily disbelieved". Only religious dogma which can quite legitimately be rejected.
Even a farmer with no formal education can tell you that it is the Sun which drives temperatures on the Earth, not human beings. Solar output is 1kW per m^2 of Earth's surface area. Assuming a population of 7 billion, that's 73MW per person. Solar output varies by much more than +/-1%, which is 730kW per person. The average power consumption by human beings in a typical developed country is 200W per person (e.g. 500W (4000kWh p.a.) per 2.4-person household in the UK). Even if we all stopped all energy consumption immediately, the effect of that would be a rounding error compared to random fluctuations in solar activity.
While it is true that atmospheric CO2 concentrations are higher during warmer periods, the effect is straightforward. Warmer seas can dissolve a lower amount of CO2, so when the oceans warm up, they release some of the dissolved CO2 into the atmosphere. Higher temperatures drive higher atmospheric CO2 concentrations, not the other way round.
CO2 is a trace gas while H2O is present in the atmosphere in macroscopic concentrations. It is H2O which drives any greenhouse effect. CO2's contribution is irrelevant.
All CO2 released into the atmosphere by burning fossil fuels got there by phytoplankton (oil) and trees (coal) binding atmospheric CO2 via photosynthesis before being turned into fossil fuels. We can only recover a small percentage of fossil fuels underground. Also, we cannot recover the atmospheric CO2 that was bound into carbonate shells by marine animals etc. So by burning fossil fuels, we are only recovering and returning to the atmosphere a small fraction of CO2 which was bound from the atmosphere by macroscopic living organisms at times when atmospheric CO2 concentrations were 2000-4000ppm. And there was plenty of macroscopic plant and animal life roaming the planet. It was not a burning Venutian inferno which climate alarmism doom and gloom saying priests say the Earth will turn into next decade unless we all stop breathing and all the cows stop farting immediately. CO2 is plant food; the optimal level for plant growth is 1500ppm, and below 150ppm all plant life as it currently exists will go extinct. If we dug up all the fossil fuels we will ever be able to recover, and burned them all on a large bonfire tomorrow, this would not bring atmospheric CO2 concentrations to anything like they were when plants first started photosynthesising.
The only concern over CO2 is that over the long term, atmospheric concentrations will drop to a level below which there can be no plants, and life on Earth will go extinct. However, that is a long way into the future. There is no way human activity, or any known natural phenomenon, can drive atmospheric CO2 concentrations to a level which would be in any way harmful.
Real scientists, like the late Freeman Dyson, Ivar Giaever, Richard Lindzen, John Francis Clauser (you will note that those names include several Nobel Prize winners) know all that. Uneducated farmers have a pretty good idea of that. Holier-than-thou doom mongering "climate science" cult priests and corrupt politicians, on the other hand, either don't know that, or pretend not to know that. But then real scientists and uneducated farmers don't have a God complex and they realize that nature, and the Sun, are bigger than us.
@@slivnik All right man, you are my hero! That is the second best if not best description of climate as it relates to CO2 that I have ever heard. Can I quote this? Cheers. 🙂
Sabine's courses on Brillinat are, euh, brilliant. She has one about quantum mechanics, and one about relativity. Don't underestimate them. They're no walk in the park.
Is there a translation tool for non-native-English speakers?
no@@Thomas-gk42
I'm brushing up on the mathematics first, but yeah Brilliant courses are... well.. brilliant.
@@SammiCPC79I've also noticed that lots of my math is gone. I didn't know anymore that ( c²-b² ) / c² = 1 - b²/c² . When I saw that used I thought surprised: can you do that?
People say that one person isn't enough to change the course of history ... but now it turns out that even a single molecule might do it.
In 1988, I was working at a major telcom in forecasting. I was asked to represent my company as our representative to the National Telecommunications Forecasting Conference. We had to read abstracts of papers to select speakers and slot them into tracks for different interests in forecasting methods. We were overwhelmed by very smart engineers writting papers on chaos theory it's role in forecasting. One day after reading a very detailed abstract, I told my boss I knew what every word in the paper meant individually, but was totally clueless as to what they meant when strung together in this paper. And I had a degree in Economics from a major university and an MBA. I was totally lost in the weeds of chaos theory.
doesn't it all come down to random quantum fluctuations? I'm confused on what's new in this paper or why they stop at molecules
the new, as Sabine explained is that you cannot carelessly discard the noise from your model, if your model operates on much larger scale. Which implies - no matter how large scale you take (galactic etc).. you will always have non-determinism due to butterfly effect.
@@igorstasenko9183 that has always been the case though. that's why big models are only predicting likeliness of a thing happening. like 80% chance of rain
Rincewind is also a very good candidate for your hero.
I’m kinda surprised there was a paper about this I always assumed the size was irrelevant and any change regardless of size given enough time would propagate through the entire system.
You need to study error propagation to see how certain trigger points set the divergence going. You also see harmonic concentration, the opposite effect.
And in passing, the earth isn't spherical, it's oblate.
Okay, but if a butterfly farts in a forest and there is no one there to hear it does it make a sound?
🤔
As farts generally generate a sound to accompany the release, I would say the answer is yes, though given the size of the insect, I doubt it would be heard by anything, or anyone in the vicinity.
Yes, however it will be heard on the other side of the world drowning out a rock concert.
The fart propagates into a typhoon a few counties over, they all heard it.
Depends on how you look at it. Generally the answer is no. Sound is subjective. Sound requires a brain, so if there is no brain to interpret disturbances in the air molecules then all you get is disturbances in the air molecules. However, the butterfly made the fart and I'm going to assume the butterfly has a brain that can interpret disturbances in the air. So yes?
The limited grid size and the rounding errors in computing perhaps make the forecast fuzzy enough? Somehow the butterfly effect feels a bit counterintuitive.
Which does not mean it's wrong. The argument from incredulity ("I can't get it so it must be wrong") is a very weak one. But flat earthers use it a lot.
And creationists.
@@arctic_hazewhy people share their “opinions” on topics they haven’t a clue about is beyond me
Think of the universe as being like a pool table with a nigh infinite number of balls bouncing off each other. If all you care about is the overall density of the balls, that's trivial to calculate - but if you want to actually calculate which balls end up going into which pockets, that's essentially impossible. In between we have local fluctuations in density, and that falls in-between, we can statistically guess at it, but our guess will be prone to error. That's where we're talking about things like the weather.
The issue is that those local variations in density are the cumulative result of the individual positions of the balls, which we simply cannot track - and couldn't track even with an *infinitely* powerful computer, as our efforts to gather the information about the position of every molecule would disturb the system, invalidating our results. The universe has been structured in such a way that perfect predictions of chaotic systems are not just extremely difficult - it's completely impossible.
@DEBO5 Your grasp of the obvious astounds me 😯 .. 😁 jk
The butterfly affect is best stated as a grain of dust lifted by a butterfly that ends up making a storm by nucleating a water drop.
I've often pondered how it would take the tiniest action to sufficiently change the course of history such that Earth is populated by an entirely different set of people 120 years hence...
Well... I have a solution for the equation, Sabine. But it's only going to work for spherical butterflies in the vacuum. 😬
Anyway, stay safe there with your family! 🖖😊
A Big Bang bangs resulting in a RUclips video being recommended to me 13.8 billion years later.👁️
Isn't that just beautiful 🤩
This is similar to what we learnt in control systems, linear, non linear and discreet. but I suppose the atmosphere is all one big control system. One of the ways to determine whether a system was stable or not, was to test whether the energy was increasing or decreasing.
The weather report for Farmington, NM is so uncertain that it will show 0% chance of rain while it is actually raining. It is so unpredictable because the town is located in the San Juan Basin, completely surrounded by mountains at least 2,000 ft higher in every direction. Exactly how the regional weather conditions will affect a particular local area is impossible to accurately predict, even a few hours in advance,
The "Butterfly effect" was first(?) elucidated in a 1950s time travel short story by Ray Bradbury "A Sound of Thunder"
Ppl were trying to make use of that effect for ages at Stock Exchange.
How far off I sat and wondered. Started humming a song from 1962...
It looks like Bradbury was the first. A Gun for Dinosaur was later and didn't really follow up on Bradbury's idea. This was why I read "escapist" fiction: It prepared me for the future unlike "literature".
I for one are so glad that you are here Sabine! Your humor and beauty are so fun and your intelligence is undeniable!
Exactly
Im hear for the content and qualify production values first, but ive grown to enjoy your accent and terms like 'motorway entry'. We say onramp and offramp in Iowa. Thanks for the cool content.
While a butterfly flapping in China will be far from the principal cause of a tornado in Texas, traveling back to the Tertiary and stepping on a butterfly could start a knock-on effect that drastically changes history, as depicted by Ray Bradbury in “A Sound of Thunder” (1952). I avoided Bradbury’s Cretaceous, considering that the Chixculub impact he knew nothing about might have erased the chain reaction begun by the butterfly fatality.
How does this intersect with your thoughts on superdeterminism?
chaos theory is completely compatible with determinism, chaos simply means that WE homo sapiens are unable to predict the future yet what occurs was already determined prior.
Actual physical determinism and chaos theory don't have much to do with each other except for one problem: Quantum uncertainty and chaos theory combine to ensure that from OUR POINT OF VIEW, the universe can never be treated as a deterministic system.
It's thermodynamically impossible for us to build a computer that could predict the future deterministically because we have no means of determining the current state of the universe without disturbing it.
Everything is determined.@@Vastin
@@Vastin I have solved this problem with my new computer which calculates everything at the Planck scale. Unfortunately, it requires eons to run even a small climate model.
@@Danuxsy The question isn't whether everything is determined (I mean, that is a question, but it isn't relevant), the question is whether it functionally matters. Even the behavior of a perfectly deterministic system can't be predicted if you don't know the state of the system - and we quite literally cannot know the state of the system.
Here's a serious question say if the laws of nsturr are ergodic and we are not picking from some pseudoacientuc post Neo spiritual pool of consciousness. Can a boltzman brain then form our exact configuration of identity memory consciousness? As we are of this "now" that we could possibly face some kinda of crazy resurrection. By the way you yslk about th universe lasting forever after the big freeze but don't we have false vacuum decay that is another way of permsntly destroying information? You only stated two in your book . And if the highs bison can lose its stability then can't penroses ccc happen somehow . Please answer my brain is melting
If the laws of nature are ergodic then yes, the exact configuration should recur. Of course if you cannot now remember an earlier configuration this means you won't be able to remember it then either... As to false vacuum decay. Well if that destroys the universe for good, then the laws aren't ergodic are they?
@SabineHossenfelder by the way your book was mind blowing! I absolutry loved it it should sell better than the bible. Maybe 1000 years from now humanity will know more about exustende and reality. It could all just be one big accident
Maybe for your next video you can do a review on kurzegesagts" paradox of an infinite univrse!" I would love to hear your opinion
@SabineHossenfelder doesn't that mean if the laws of nature are ergodic that false vacuum decay will happen and then unhappen itself?? Isn't that absurdly paradoxical
@@user-bc9fe7pd9rHer books are brilliant and a pleasure to read, I hope on a new one, before the vacuum decays.
I remember reading some years ago about chaos theory, and that weather models were limited to about 10 days out and that no amount of computing power and modeling can get much further than that. They did not discuss climate models which were not a "thing" when the book was written. The second thing I took away from the book(s) was that although our equations are deterministic, the physical world is not.
Consider if backwards time travel existed, even with simple molecules or energy, that small change not only would change the future, but our perception of the past.
Very informative video. As a lapsed mathematician who had a serious deficiency in PDEs, I'd like to ask: Does the behavior of solutions to Lorenz's simplified equations necessarily carry over to the full Navier Stokes?
Neither am I, but if I recall correctly, I think the Lorenz system even neglects a second nonlinear term of the Navier Stokes equation. The question becomes whether the additional term dampens or energizes a disturbance. In the Lorenz model you can see from the differential equations that depending on the values, you may have growth or dampening. So I reckon the gist of sensitivity to initial conditions will certainly apply, unless there is an overwhelming dampening effect of the additional terms.
@@maxtheflyingdutchman23 thanks
This is basically part of my philosophical ideas for a kind of clustering complexity gradient with emergent steps. That everything starts with a Planck-scaled fundamental randomness of "existence" and "non-existence" as an absolute energy state; basically a binary "on" and "off". Then it forms a gradient of complexity from its simplest on/off state through increasing clustered events up to a certain point of emergence in which things like particles and energy states emerge out of that clustered complexity. Those in turn produce a new clusters of complexity until a new emergence forms and so on. Each large emergent step in this gradient of complexity is affected by the lower large emergent step and so on down to even the smallest Planck scale fluctuation that can influence everything up the ladder. The only reason we're not having full blown reality chaos is due to each emergent system being increasingly rigid in determinism through the emergent effects of larger scale physical forces intersecting and acting on each other more and more intensely, and so up the ladder of this reality everything reaches a point of an almost "solid state" frozen existence. Basically like seeing the ocean up close; chaotic and random in shape, but at enough distance it looks like a flat blue marble. Moving up in scale just makes all things in reality look like frozen, unmoving and still.
Yeah, sounds like horseshit, but I don't claim any of it being empirically sound as it's more philosophy than based on scientific rigor for now. But sometime ideas can inspire real scientists to look in a certain direction so maybe I could help inspire something.
Love this.
I’d like to see if the Wolfram Physics model shows how this emerges at the molecular or lower level.
Kind of feels like computational irreducibility again.
I kinda struggle with these statements from a statistics point of view. Let's say the possible outcome is rain or not in southern France. If there are billions of states that can influence significantly this outcome, this is equivalent to say that each of the state has 1/a billion chances to be the decisive state hence, statistically, or has a weight of 1/a billion on the final outcome. Isn't this equivalent to say that a certain combination of several states is actually the "main driver" of the final outcome? Does this make sense even?
We could not solve Navier Stroke of course but measured the fastest chaos in a lab at half a terahertz using a Josephson junction as driven by infrared maser. Results could be seen even at charte plotters with around 1 Hz time résolution imbedded with intermittency. Quing Hu O.Liengme and M. Tinkham and others. Phys. Rev Letters and Phys Rev B.
We model the behaviour of our atmosphere with the famous Navier-Stokes equation. The atmosphere itself is not governed by the equations; it pays very little attention to them.
This reminds me of one of Murphy's lawa which states that in a most carefully controlled environment, micro-organisms will do just as they please.
Thanks. I wrote the same thing a few minutes ago before reading yours.
The Kelvin-Helmholtz instability can be modelled as a computer simulation in two dimensions using a repeating row of pointlike vortices, using a conformal transformation to obtain the coupling between any two vortices. Give one vortex a small displacement, say a Planck distance, and watch it go. The vortices can be set in Brownian motion to represent viscosity, as proposed by Alexandre Chorin, and we have a notional solution of the Navier-Stokes equation as a computer simulation.
Can we apply this sort of model to quantum mechanics? I think that there needs to be two modes of usage of a random number generator. One is as tachyonic Brownian motion like a type of viscosity. The other is as classical Brownian motion like an eddy viscosity.
I don't see how this is surprising. All the butterfly effect says is that the evolution of a chaotic system diverges for close but different starting conditions. Why should there be a threshold on how small that difference can be?
well, first of all, I am a bit surprised that this wasn't evident so far. chaos stems from nonlinearity (nonlinearity is a necessary, but not sufficient condition for chaos). just like the infinite complexity of certain fractals (e.g. Mandelbrot's set) stems from nonlinearity (recursion, or more generally, self-referentiality). why? because only this mathematical structure can generate infinite complexity. so it makes perfect sense that nonlinearity is a necessary, but not sufficient condition for chaos (another necessary, but not sufficient condition for a system to be chaotic is to have at least two degrees of freedom), and it is also trivial that this extreme sensitivity to initial conditions (input data) is unbounded. I mean, why would there be any bound? is there any size limit for this sensitivity in the case of fractals? no. why would there be any size limit for dynamical systems? I don't even understand this assumption.
but it is really interesting to connect this topic with the post quantum gravity theory. they can indeed be related...
Dont know whats more horrifying- Super determinisme or this...
Nobody is in control, thats for sure...
I had a thought experiment long ago similar to this, how we have shaped humanity & somewhat domesticated ourselves by discovering fire or agriculture. How our values and who we decide who wins or loses in our societies continues to shape our genetics. Would love for you to talk about this. Have good day.
To me it appears to be the difference between digital and analog and the Mandelbrot equations prove this. I have had a wonderful career repairing burners where fuel air mixtures are not absolute, close but absolutely not. It doesn't take much to destabilize a turbulent burn and the harmonic distortion can get to catastrophic levels.
Butterfly effect can be very dramatic: Sabine wears a new blouse and Russia wins the war...
If in China some butterflies or molecules are flapping, in Texas some others would be flapping, too. Wouldn´t that global flapping noise destroy the explosiveness of the effect?
Nothing there says that they would "cancel each other out" necessarily.
We can cull butterflies to prevent dangerous storms, but if molecules are guilty as well, things get more difficult.
Not if some of the flapping at key nodes is randomly exacerbating/multiplying rather than cancelling the flap. A flap meets another flap going the same way…
Nice shoutout to the Alex Verus series! Love those books.
Sabine, going from reflection in diamonds raw to a microchip and laser disc reading should be enough for the ever thirst of this coarse of why wouldn't it get answered ? It wasn't the point of just not solving a betrayal, it's being answered slowly. Thanks sharing.
2:39 You just uttered the biggest street-fear in my life. I've took a hit to the neck from their droppings twice in my life. Would've been well over 10 times if I didn't learn to dodge and stare them down.
They literally pick targets while gliding or wait on top of lamp posts to drop a bomb of poop and they'll stop their obvious stalking the moment you look at them. Acting like nothing was on their mind while literally laughing. Seagulls are vile disgusting creatures.
**PTSD achieved**
“seagulls crapping… I mean flapping, FLAPPING”! 😂😂😂
I thought she said "seagulls fapping..." 🤣
It seems we have a comedian ( maybe: commedienne?)in our midst!
The traffic here in the Philippines must have some sort of effect. It's certainly a chaotic system.
The differences we are talking about here are convergent systems vs. divergent systems… in Mech E classes we would call this the damping effect (coefficient infront of velocity or the first derivative). In physics this is the asymptotic graph of sin (e-wt)
I love these humorous interjections!
My Claude model gave me a .001% chance or less that I had solved the reimann hypothesis AND could expect my $1 million in the mail.
He gave me a 3-7% chance of proving Euler's identity is actually a dichotomy or trichotomy.
The clay institute might black list me if I also solve the Navier-stokes equations, so that is why I have not done so. 👍
0:41 thanks to your graphic design team for nice color coordination.
As I understood it, chaos theory always said this. There were just some simple non-linear systems which had regions where even the tiniest change would produce different outputs. Thus it didn't matter what the size of the change was. A butterfly flapping it's wings was just a metaphor for that.
"A Seagull flapping"
Yes, this hard to say...
Next woke agenda! "Nobody moves!"
What do you mean by woke?
What do you mean by agenda?
Woke simply means aware of racism. Are you a racist?
If I need to explain something so simple as this punch line you should not be listining about butterfly effect...🤣🤣🤣🤣
How is this any more enlightening than noticing the fact that you can topple an arbitrarily big domino from a sequence of smaller dominos?
The discovery of warm water...
The "Dynamical Systems Collective" already said, some fourty years ago, that 'strange attractors + quantum uncertainty = chaos and unpredictability'.
"What brings up quantum uncertainty to the macroscopical scale is the strange attractor".
This "New Paper" sounds almost as useful as toilet tissue.
The paper tells us that some methods for making certain predictions may not be appropriate. A lot of wasted research effort and money could be saved by having this knowledge, and not just esoteric "just for the sake of science" type of research, but instead research that feeds applications like where your local weather person gets their data, or how to simulate designs of future power plants so that you can continue to reliably expect your lights to turn on when you ask them to, etc (not just fusion, chaotic movement of liquid and gas is present in most power generation systems and presents complex design challenges).
I'm not sure why you see it as useless, perhaps you don't quite understand it.
So u gon use it twice a day?
your argument is worse than toilet because you have no evidence to support it. go to sleep
Very useful while being very simple? Is that what you meant?
Same as your comment
I see incorporating full heterogeneity into turbulence modeling as the next great frontier. Even after a century of intense work of the flow of biological fluids such as blood through living capillaries solutions require a number of simplifications. But as Gilbert Ling and Gerald Pollock as shown even water exhibits many different physical states - from quasi homogenous bulk water to organized layered gels (or ice-like) were solute exclusion occurs, changing key properties like the dielectric constant, kinematic viscosity and heat capacity.
Think of Richardson’s ditty about vorticity and viscosity onto the molecules themselves.
Hi Sabina , could you make a video about three body problem . I would love to hear your ideas and explanation on it
Science only relatively recently acknowledged "rogue waves" in the ocean that are gigantic, even though sailor folk lore has talked about them for centuries.
I find the butterfly effect fascinating. I have not heard af an analysis fo the following, so perhaps you will do one. There re innumerble butterfly effects going on simultaneously at any one moment, not just one buterfly but innumerable butterflys, aphid, earwig etc, plus all the other events which are occuring.
About the resolution problem, maybe you need a computer the size of the universe to fully accurately run a model of, well, the universe.
DOPE D.O.D Has a great track called The Butterfly Effect
I am still thinking about the butterfly effect, I remember the poem "For want of nail" and there might be something logical about locational events, like a battlefield, but flaping the wing in China to make a tornado in Kansas seems very far-fetched.
You can't copyright an idea, Sabine. So, write that novel! Your vision will be different than anyone else's.
Set up one million dominos in such an order that the first one can knock all of them over at a single touch, but if they are arranged randomly and the first domino might knock over the first 20 or 50 or 1,000 or none at all. My guess is that for a butterfly to effect weather patterns globally, the atmosphere would have to be perfectly pre-arranged just prior to the butterfly flapping its wings. The odds aren't impossible, but they are most likely nearly astronomical against it.
I can solve the Navier-Stokes for flow in a pipe! This picture is a bit deceptive. The exact flow velocity at a given time can vary a lot, but the maximum speed for a time range doesn't vary that much. That's why we normally use an average or constitutive model for turbulence. Few really care about the exact flow fields as functions of time.
But i digress. One of the weaknesses of climate models is that they cannot resolve atmospheric fingering -- say around urban heat islands.
Turbulence is more interesting than it looks. In the bubbly water of a crashing wave there are many microscopic vortices all tangled up like in a plate of spaghetti, some of them swallowing up others, some dying off. The models are also sophisticated. The smaller vortices can only be modelled in a statistical sense. Some models are made of layers of different models. Others mix statistics with grid modeling of the large vortices.