Chaos: The Science of the Butterfly Effect
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- เผยแพร่เมื่อ 10 พ.ค. 2024
- Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: ve42.co/VeLP
Animations by Prof. Robert Ghrist: ve42.co/Ghrist
Want to know more about chaos theory and non-linear dynamical systems? Check out: ve42.co/chaos-math
Butterfly footage courtesy of Phil Torres and The Jungle Diaries: ve42.co/monarch
Solar system, 3-body and printout animations by Jonny Hyman
Some animations made with Universe Sandbox: universesandbox.com/
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.
I have long wanted to make a video about chaos, ever since reading James Gleick's fantastic book, Chaos. I hope this video gives an idea of phase space - a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable - two different initial conditions that are very close together can end up arbitrarily far apart.
Music from epidemicsound.com "The Longest Rest" "A Sound Foundation" "Seaweed"
Having a bad math teacher at very young age, has the butterfly effect on the rest of your life; for example
"The printer rounded to 3 decimal places whereas the computer calculated 6"
The ghost of significant figures
Having a bad math teacher at very young age, has the butterfly effect on the rest of your life; for example
this hit me hard.
At school I was really good at math until there was a very irritable algebra teacher with anger management issues. Her explanations were super short, if you zone out for several seconds - congrats, you understand nothing. I did ok, but I learnt to lay low. In high school and university I studied foreign literature and languages. When I was 20 - 21, during university practice, I went to my school to work with an English teacher, and I was assigned to this one class of pupils. Once I sat through their algebra lesson with that wonderful teacher. I think she didn't remember me but she felt OK to start shouting at these poor kids and shaking a dirty blackboard sponge right in their faces to make them think faster, I guess. She had also retained another beautiful habit of hers - gesticulating with both hands, but with one hand she would hold a piece of chalk, with another one - her glasses. She would use all her fingers except the middle ones, and she would raise both of her middle fingers and shake her hands to emphasize her point. She would basically give the double middle finger
to the whole class😂
Honestly that’s just an excuse and I’m sorry. My friends had the same poor math teacher at a young age for a good amount of years. One went on to be brilliant at math while the other was mediocre at best
Sensitive dependency on initial conditions: The exact present exactly predicts the future, but the approximate present doesn't approximately predict the future.
Seems like you believe in Laplace's demon.
When you get information to the quantum level, predicting the exact future is going to be nigh impossible. Or maybe quantum stuff can be predicted. ¯\_(ツ)_/¯
@@kirbykir "When you get information to the quantum level, predicting the exact future is going to be nigh impossible. Or maybe quantum stuff can be predicted. ¯\_(ツ)_/¯"
There are people who believe in deterministic quantum mechanics and those who don't. As of right now, there is no way to tell which is right; hence they are consider "interpretations of quantum mechanics" where each are near equally valid until evidence comes out otherwise.
so now the question becomes whether or not you can observe an exact state of a system. the easy answer would be no, but i wonder if the future has any solutions that we are not yet aware of.
@Juan Cortez Muro For the second time, are you proud of yourself fam?
You took that from vsauce
It's amazing how such a complex topic can be so entertaining and presented so understandable. It sparked my interest in the butterfly effect. I really loved the animations and examples of the points he made.
Keep yourself updated with the amazing Problem-tackling TH-camrs Illumainugthii, knowing Better, and Some More News.
These 3.
Whetever its Crops, Water, Hate, LGBT, Bias, Ukraine, they cover so much and more.
And before you ask: Haha, no, there was no deeper Reason for this comment, i just like to share Science,
Knowlegde and Atheism
in a world where many Science-Fans havent even NOTICED that Atheist-TH-camrs are very similar
and even often overlap with Atheist-Content - making them miss-out.
"Can I have chaos? "
"Best I can do is a figure 8"
When they talk about time travel, people almost always state that they'd make enormous changes for present day with small actions in the past.
But rarely do people think that they can take small actions today to cause great change tomorrow.
How very "forward" of you LOL
That's because they have a point of reference by virtue of knowing how the past played out. They'd hypothetically know that any differences over the course of history would be due to whatever changes they made. They don't know how the future would be changed by whatever actions they take today because as the video so succinctly explains, we can't predict the future very accurately beyond a very limited point.
Yeah, but when you cannot predict what will happen, does it even matter to think about that?
@@Lambda_Ovine Yes. Get out there and make one small step towards a better future. You have the power.
If you put a bag on your head you can time travel at a rate of 1 second per second
"Sometimes when I consider what tremendous consequences come from little things, I am tempted to think... there are no little things."
- Bruce Barton
The intricacies in the web of life.
🤯
yeah
That is certainly a tempting thought.
i have been trying to put that feeling into words for years. thanks person
The graphics, the explanation, the presentation, everything about this video is top class. I am just speechless.
I'm pretty sure the "butterfly effect" is from Ray Bradbury's short story 'A Sound of Thunder', where a man changes the future by stepping on a butterfly on a hunting trip 60 million years in the past. The story was first published in 1952 so it's more than 50 years old. Great video!
That's a fun story about it.
That was a good story! Bradbury was an incredible author
it was probably called the butterfly effect long before that.
@@JBG-AjaxzeMedia , nope. I made the same observation on a literary expert's channel and he answered and said it was true. Someone else used the exact phrase a couple of years later in a different book - but not before.
@@danatowne5498 according to google, lorenz called it the butterfly effect
He explained such a complex topic with so much simplicity that i am just speechless.
It IS simple. People can't help but complicate things.
@@Arrowaceofspades but hes right.
In fact everyting is simpil when looked at from the right angle.
Just look at flatwaters overcomplicating the world because they cant grasp the fundmetals of gravity. Stupid is when you over complicated things you dont undstand because you applying the wrong models to the data.
@@Arrowaceofspades Reading into my comment like that is only making a case for my point. Humans need to translate things into a language they can understand. My comment would sound pretentious to anyone, myself included, but it is entirely objective.
@@Arrowaceofspades Have you considered that English may not be his first language? Using an ad hominem argument means you've already lost.
@@Arrowaceofspades did you have a bad day?
And this is why I will always smile and compliment strangers. Idk what kind words or gestures could majorly effect someone’s life.
Absolutely. I was told that life is like a game of "Snakes and Ladders" and to respect, but also remember to help those you meet along it. Because you never know where you or they will be should you meet them again before the game ends.
Ok but that's not how butterfly effect work. Those action might also even cause someone to suicide. Like i said, this is "Chao".
But that is not predictable, what predictavle is that compliment stranger make someone day better. It is not butterfly effect but it is a good thing to do and would make this world a better place.
@@paulferris8180 This is why the movie Groundhog Day is one of my favorites
According to the butterfly effect you could also fart on them because it could have a major positive effect on their lives. But that's probably not as predictable as giving them a compliment.
@@a7G-82r YESSIR
The relationship between this chaos theory, and the definition of insanity (doing the same thing over and expecting different results) is VERY intriguing.
Hmm, that's indeed a very intriguing correlation there
I've always felt that you can never do EXACTLY the same thing over and over. No matter how you try there will always be some difference.
You will never be the same person again. The more steps you take the more different you are. Even if you go back to the start you are different, and the place is different. I love how his explanations make me visualize concepts of my own existence.
If only someone had explained science this way when I was younger.
I'm just happy someone explaining it this way now. TH-cam has really been a blessing that way. I'm finally enjoying science and physics and math and things I hated when I was a kid.
Great I'm ever like physics
Science is easy to understand. Math is your problem
@@chuckychuck8318 geez. Tell me about it.
They did. You were just too high to stay awake.
"The printer rounded to 3 decimal places whereas the computer calculated 6"
The ghost of significant figures
Programmer's nightmare :D
That's how 1+1=3 for large values of 1.
at least he didn't have to program in an era of timezones
"Hidden figures"?
ghosts of departed figures!
Thank you so much! I've been so confused about the chaos theory in general and my textbooks weren't helping at all. You explained it all so well. Sincerely thank you.
Thank you Derek, after watching a series of motivational videos with no effects, this one actually made me shut down the screen and open my physics textbook!
"That's on the scale of atoms, pretty insignificant on the scale of people," said the pile of atoms.
...said the pile of atoms in command of one of the most mysterious conglomeration of atoms called the brain. We may be insignificant in the grand scheme of things but definitely in a unique kind of way.
Several trillion trillion atoms, yes.
@Hans-Christian Larsen EXACTLY WHAT I WAS THINKING.
So if the moon was conscious would it to be impossible to predict? Of course not
@Michael Enquist Consciousness doesn't change the fact that you behave according to Newtonian physics (just like the moon). Every operation in your brain is macroscopic and predictable. You can't beat physics. You're not a subatomic particle. Sorry.
That's pure gold. 20 years ago I had the chance to study chaotic dynamical system during my undergraduate study in mathematics. There were a few good books on the subject, I remember an interesting video too, but nothing of that quality. To the younger generation: savor and take advantage of your luck!
Exactly what I was thinking during this video, we're so fortunate to have this education at our fingertips, whereas you'd have to either have to travel, pay alot of money or first apply and get accepted to receive such information
@@OhZjuchi haha yup
Any good book recommendations on choatic systems?
@@aliwaheed906 A professor I had recently recommended An introduction to chaotic dynamical systems by Robert Devaney. Haven’t had time to look at it, but as it’s his field of study, I take his word that it’s good.
@@aliwaheed906 The Quark and the Jaguar deals with complex systems... Chaos by James Gleick nice intro - check out the Stanford lectures on Chaos and Reductionism too
Amazing video! I did my masters project on a parametric pendulum, and I wish I had something like this around then, shows the concepts so clearly
Cool!
This video reminded me of my professor of physics in the university who was obsessed with fractals and chaotic systems. Thanks for this explanation.
I would like a 60 min documentary on the content just presented in the last 2 mins of this video.
You mean the last pass advert?
Ok but the music th-cam.com/video/p_yOueFMe7c/w-d-xo.html
Why?
If you have a little background on calculus, you can read Strogatz's book "Non Linear Dynamics and Chaos". It's absolutely amazing
there is "secret life of chaos" www.imdb.com/title/tt1674741/
A Mathematician once stated the chaos of nature using the example of a pool table:
" During the familiar game of pool, if a man is to calculate the collisions between the balls, the prediction of the first collision is simple enough that any college student can do it. The prediction of the fifth collision requires such things as the gravitational attraction of the two people standing nearest to the pool, while the prediction of the ninth collision is impossible, as it requires exact knowledge of all the positions and momenta of all the particles ( electrons, protons, and neutrons ) in the Observable Universe."
True.
👍
Chaos is a ladder :V :V :V
Please tell me this is merely a metaphor and that people near the pool table aren't effecting the gravitational attraction on the balls enough to have any significant impact on the 5th collision. Surely not..
@@ConnorHammond
Butterfly effect.
Everything affects everything.
@@ConnorHammond I have personally heard this claim as well by a phycisist researcher. He said you would have to take into account the gravitational force of the people around
I've seen several of your videos and even recommended some to others. This is by far my favorite of your videos.
Thanks for the time and effort you invest in your productions they are very much appreciated
Bottom line: we can't predict the future because we'd need to know the exact conditions of the beginning, but we can't know the exact conditions for the beginning because the margin for error in estimating the beginning conditions is infinitely small. However, every point in time was determined from the beginning based on that initial state. So the future is determined, but there's no way for us to know what it is.
exactly
Not necessarily, if we could see the exact conditions at any given moment in time (e.g. right now) hypothetically we could predict the future from that moment onwards. At least I think so?
@@jake8993 Lorenz' observation of chaos came about because he was getting different values for the same points in time when he changed the starting point of the calculations. So starting at any point other than the exact same starting point will produce different results. They could happen to produce similar results, but it'd still be impossible to know exactly how similar they might be beforehand.
@@jake8993 But exact conditions to infinite decimals can never be known...
@@QuesoCookies That's actually not true. See that part of the video again... The values were actually slightly different due to the rounding off of the printer. He mentions this. They are deterministic systems, ie., they produce the exact same results for the exact initial conditions. But not even approximate results for approximate conditions
* Time Traveler Sneezes *
Butterfly effect: * GERMANY BECOMES AN ALLY IN WW2 *
I would say rejecting a kid form an art school was a perfect example of the butterfly effect already
Then WW2 wouldn't happen
If WW2 didn't happen, there could be a worse global war than that. Also, our technology developed much faster because every country wants to improve militarily and/or economically
_"Japan destroyed by a super-massive tornado."_
And a man named Abradolf Lincler wins nobel prize for his life work on his theories of parallel dimensions.
I was lucky enough to find chaos by james Gliek in my school library and i think this video might have been inspired bby it....... It is a fantastic read and you even get to know about the interesting side of math rather than the blunt equations we think math is
Your videos are very good in explaining the complex topics in simple terms. Thanks a lot.
This is one of those science videos that aren't just interesting, but also beautiful.
Just like your comment! ;)
Just like you.
True bro
And also confusing
I think you would really enjoy @3Blue1Brown
My favorite thugh on the matter is: Chaos is not anti-order. It has its own rules, secred to common eye, but quantificated, mesurable and predictable. we may not know the sequence, but we can know the rules it must obey.
If we assume that the universe is deterministic then chaos really is just rules we haven't understood yet (and may never understand). The problem is that we, from within the system, can not figure out whether the system itself is deterministic or not because any "full" prediction of the future would involve predicting your prediction and whoops infinite recursion.
"... and predictable." I think you missed something somewhere.
@@arkdirfe You mean like fractals?
@@gps9715 I meant rules are predictable not system itself. Statistics and rules it obeys can be seen from the function itself.
the rules belong to the math topic called differential equations.
My brain hurts watching these videos even with the simplistic style you explain them in, and I want more!
I'd like to mention that even if one vector/data point/object in the system were to reach the exact same state by some weird chance (like discrete numbers rounding the results at each step), the other vectors in the system would be different and so the paths each would still not be periodic. Very interesting summary of chaos theory, thank you! I like the way Jeff Goldblum explained it best still lol
Why am I interested in this and not in my studies?!
Maybe you should change your studies then lol. But maybe its your destity...
This were written to make you interested. All the boring stuff were taken out.
@@Richard-bq7br yes, the devil lies in the details
@@shantanu176 yeah, it's real, I'm the devil.
Bad teachers 100% of the time
Read "Chaos" by James Gleick if this stuff interests you. Probably my favourite book of all time, totally changed my outlook on everything, no joke.
Fellow 3b1b fan?
@@tahsintariq8757 No but ill check it out. Big fan of Robert Sapolski's lectures on human behavioural biology, he assigned this book to his students. He is the best lecturer of all time, makes me question my computer engineering degree
@@tahsintariq8757 OH 3blue1brown yeah I love his videos too
*The Information* by James Gleik is an amazing read as well!
@@_Swink in a video on differential equations 3b1b talks about phase space...and I heard about the book "chaos" in another one of this videos though I forgot which video it was.
In the university of Alberta's science building there is a double pendulum in the main hallway in the basement where you can go and spin it yourself. Every time I spin that thing it never ceases to amaze me, making me think deeply about the nature of the universe
This video is so good I keep Coming back to re-watch it time to time
This was one of the best videos you've made! Meteorologists and atmospheric science researchers don't receive much respect or recognition from the public, who often mock them whenever a forecast is even slightly inaccurate. Most people have not yet comprehended _just_ _how_ _difficult_ a forecaster's job is. Nor do most people realize just how much progress these scientists have collectively accomplished in the past 30 years or so. The job of an atmospheric scientist is _literally_ *to* *predict* *the* *future* state of the extremely complex and multivariate set of dynamical systems that constitute the Earth's atmosphere. This was one of the best and most concise educational videos about chaos theory I've ever seen and should help viewers better understand the difficult challenges that forecasters in any physical domain are tasked with on a daily basis. Once again, thank you Veritasium, for another enlightening, entertaining, and educational video! :)
Aren't all forecasts mostly done by supercomputers?
@@Pranav_Bhamidipati I don't know but even if so, people must create the system first and fix the system when it is imperfect.
The problem is with their lack of honesty. If the job proves impossible, they shouldn't keep pretending to forecast.
Weather forecast regularly fails miserably in only one day. It's so bad that simply knowing the date and looking out of the window gives better results.
zwz • zdenek that was so rude and accurate at the same time
@@Pranav_Bhamidipati computers run models, but the models do not always agree. the weather experts can add a level of "AI" as well as explain the situation (including the uncertainties).
most weather folks on the news don't go into the detail, but a few will explain all the steps they use to make the prediction. Ronchetti for example.
:Why aren't you successful.
Me : I held a sneeze in the maths class long ago, and now I am doomed.
This explanation explains so much about the mystery of our mysterious world. Deterministic chaos🙏
Was explained so well. Excellent job!
I appreciate integrity shown when structuring embedded advertising so much that I watched to the very end. Thank you.
A person in Florida whose house has been destroyed by a tornado: ,,Those freakin’ butterflies flying in Madagascar again”
Lol
😂 “Again..”
But a person in China might thank those butterflies for extinguishing a tornado that would hit them. In chaos theory, things are short-term insensitive to initial conditions, but not long term.
as a Floridian I can confirm
This comment is so underrated 😂
Really enjoyed this. You should show the equations. I think by looking at the equations and the variables causing the feedback, people would have a better understanding. - just a thought
Beautiful. You final wrap-up with the Lorenz Attractor caused me to think of the ACTUAL "Great Attractor" -- that structure to which our local galactic group is rushing towards.
U mean love ?
I understand and mostly don't understand this at the same time. How Schrödinger.
That's just for atoms.
Actually that's 2 different versions of you. Not a single entity. That's what this channel taught me anyway 😂
Fact: alternate version of you right now doesn't even know you knew anything about alternating realities
wrong video head ass
his cat died
The reason I think people are fascinated by butterfly effect is that it gives a sense that our actions have greater cause that we are special something like that..
People are amazed,thats it
If you want to argue that you can take actions that truly have not affect, that simply goes against everything we know about the universe so far.
Even the flap of a butterfly wing has energy in it, energy that comes from somewhere and goes somewhere. Naturally one butterfly wing flap could never take credit for a hole tornado, yet to just because the tornado would be indifferent to you if I removed one butterfly, dosen mean its the same outcome.
Put it like this, i can take one atom from you, and you would not mind, you would surely be fine even if tok a thousand (well unless they were somehow specific ones in one of you cell causing it to become a cancer cell) but there come a point where the number of atoms taken from you becomes a problem.
Its not that a atom taken from you doesn't affect you, it's that it affects you to litel to make a noticeable difference by your standards, but there's still a difference.
@@MouseGoat A butterfly's wing flap, while its energy does dissipate into the surrounding atmosphere, could be the "straw that broke the camel's back." It could push conditions *just enough* for that tornado to either happen or not happen. A single atom, taken from your body, could cause you irreparable damage, if it's the right atom.
Here's a poem perfectly describing the effect of the butterfly effect:
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
Overall, the butterfly effect is about the chain reactions that happen from very small changes / influences to create very big changes in the future.
@@TTaM581 great illustration!
Also, it means that there is a certain amount of free will. With total determinism, our actions were decided before we were born and will be decided until we die. Effectively, we don't exist. We're just passengers to our body's existence.
your practical approach to this subject is just what i needed!
You are so great. I am thankful for the work you do.
and this, of course, is the choice of steins;gate
I was searching for Steins;Gate reference in the comments. Thanks.
El psy conguroo
Okarin my watched stopped working......
@@joeqiao1691 Celeb 17
@@rizzgod-wj6ty that was sad!
"A Sound of Thunder" is a science fiction story by Ray Bradbury, first published in 1952 was the first representation of the butterfly effect where the death of a butterfly in the past causes irreparable changes to the present.
good point! Eckels (is that his name im correct? steps off the path and steps on a butterfly!
I think it’s in the same vein but isn’t really the same. If I remember correctly, the butterfly was stepped on by a guy hunting a dinosaur. They got back and language was slightly off and a different political party was in power.
I think the butterfly effect would be a lot more intense. Just going back that far, just taking a single breath would change the outcome of natural history. The line that leads to the evolution of the genus Homo might not occur. Or even primates. I think our mammal ancestors were shrew like tiny little things back then.
The species you come back to might not be recognizable.
I speculate that the butterfly effect would be particularly hard on time travelers. I think it’s funny in time travel stories where people go back and change things, yet, just about every sperm hit the exact same egg on a global scale. Each one of those chaotic situations has like a 1 in 200,000,000 chance assuming the parents happened to get frisky at the exact same time in both timelines. I would find that odd if it happened once, yet usually that happens billions of times all over the world. Maybe once, like on the CW Arrowverse, one person might be replaced.
And don’t get me started on how the entire crew of the Enterprise could turn up for the same jobs on the same star ship in an alternate history where violence and despotism won over peaceful democracy. And, of course, minor style changes to facial grooming and wardrobe.
The same insect but a couple of decades before Lorenzs's paper. I wonder if just a coincidence or if Lorenzs was familiar with that book?
oh my. Flashback to Freshman year in highschool almost 10 years ago
Yeah man ! I heard about The Sound Of Thunder in one of Aperture's Video . Please watch the videos they are mindblowing
the way you explain things is incredible.
I'd love to see a video on the Hummingbird Effect! It's a very interesting one that I ended up reading about in the book "How We Got to Now" and I'd love to see a more visual take on it from you!
“The three body problem” the most interesting sci-fi book you’ll ever read. Don’t read spoilers or anything about the book. Just start listening to it or reading it. Your mind will never be the same.
That sounds like a recommendation and a half. I'll check it out. Thanks!
Thanks for the recommendation. I will check it out.
I'm at the start of part 3 of Cixin Liu's trilogy now. I can say parts 1 and 2 are definitely worth reading.
I’m going to read it, thanks for the recommendation!
x doubt. People should be mindful to what they put into their heads. Things that dont exist. Sci fi often serves as inspiration for new inventions so theyre not all bad.
For some reason I find theoretical physics like this rather unsettling. The existential implications are interesting but simultaneously disturbing
It is not a paradox. Exciting and unsettling are not mutually exclusive. A HORROR film is both EXCITING and UNSETTLING.
Matt that though shows how simple humans and there emotions are, I’m sure you can’t understand that because you are just a 3D life form with neurological signals that go to a main muscle blob
@@user-or3tl6yq7o says someone who has never studied humans and their emotions on a actual neurological scale, i presume
@@son5051 he probably has not but you dont have to study that hard to realize that Humans are 3D life forms with a very simple mindset that turns basically everything into good and bad
@@user-or3tl6yq7o How can you even conceive degrading humanity like that? Our bodies alone are much more than just "a 3D life form" or whatever meaningless nihilist oversimplification you're trying to push as opposed to thousands of years spent trying to understand how we work. And we are more than just our physical presences, love is indeed a thing, and it's huge. You don't know a thing. Me neither. We all know nothing.
Ok, so chaos theory is fascinating, and this video does a great job of explaining it.
If you want to go one better though, and simulate how quantum randomness can affect macroscopic effects over time, read on!
Back when I was a CS undergrad, some students in the CIT department suggested I talk to one of their professors about simulation, because I had a habit of writing particle simulations for fun. After around two years of this, I finally did it. At the time, I was planning to write a swam simulation in Haskell. He gave me some interesting advice. He suggested I not worry about state. Normally, in simulations like this, one would use a buffering technique, so that the state currently being generated is based purely on the previous state. If you don't do this, early changes can affect later changes, blurring state between frames. I took this advice to mean that I shouldn't concern myself with this, so I wrote a simulation that advances each particle based on wherever the others happen to be _at this moment_, instead of buffering state. The result was that behavior of the simulation was far more organic, lacking artificial looking patterns that tended to show up in the state buffered simulations I had previously written.
This isn't the _really_ interesting part though. Another thing I did to achieve this indeterminate state was to based advancement on time passed, rather than progressing a set amount per "frame". Frames really only made sense when trying to preserve state integrity, and since I wasn't doing that, I fell back to an older method I used to use when writing video games.
So, here is how the simulation worked: I started with a list of particles. During each loop, I would advance the first particle in the list, based on the amount of time passed since I had last advanced that particle (and based on the positions of the other particles in the list). Then I would move that particle to the end of the list. (Using functional programming techniques in Haskell make this extremely easy.) This completely abandoned state integrity, which did manage to achieve very interesting results.
The _most_ interesting result, however, was what happened with, on a whim, I ran two identical instances of the simulation side-by-side. Starting them at exactly the same time randomly placed the particles in the same places. To be clear, this is the _only_ place in the simulation where randomness was used, and because the RNG was seeded based on system time, starting them simultaneously seeded them identically. So, they started with particles in exactly the same positions, and the particles then started moving in exactly the same patterns. Except, imagine my surprise when I noticed the simulations begin to deviate. They started in identical states. There was no additional randomness going into the simulations. So they should have matched perfectly.
That final assessment, however, was actually wrong. There _was_ still some _tiny_ amount of randomness going in. This randomness was processor scheduling. The difference between the two simulations was the _time_ passing between iterations. Desktop operating systems assign processor cycles to programs using some algorithm. How cycles are assigned depends on a lot of factors, including how many processes are waiting for CPU time, the priority level of those processors, how much input and output is being generated, and so on. This means that even running the same program twice, at the same time, won't give them identical schedules. Anyhow, in the context of the simulation, this means that while each particle started in exactly the same state as its parallel in the other instance, it _didn't_ always take exactly the same amount of time between iterations, and this allowed tiny differences due to floating point error to work their way in. But, modern processors are extremely fast, so the actual differences in time were infinitesimal, barely big enough to make any difference in the floating point time values being generated, and further, the floating point error created by these slight difference were also infinitesimal. So how, after only a few seconds, could deviation be seen?
The answer is chaos theory. One might be tempted to suggest that the tiny differences would add up to big ones, but the truth is, the tiny difference _should be expected_ to just average out. If we are basing progression on time, the differences _do_ average out. The cumulative time that has been applied to any particle will always be within a few milliseconds of the total time passed since starting the program. And floating point error doesn't tend more toward one direction than another, so over many iterations that will also average out.
So what was actually happening was that tiny differences (perhaps on a scale closer to quantum than macroscopic) produced from effectively random influences were having the impact of chaos. Maybe an easier way to think of this is considering each iteration as a "starting condition" for all future iterations. So, the first iteration has some infinitesimal difference between the two simulations. That difference, while initially imperceptible, results in growing deviation between the simulations. And this happens _on every iteration_.
Now, this might seem like some merely interesting theoretical stuff, but it's far more than that. What degree of impact does quantum randomness have on the macroscopic world? It's easy to write it off as having literally no impact, except when we are deliberately measuring quantum effects and acting based on them. Chaos theory suggests otherwise though, and my simulation demonstrates exactly how even infinitesimal differences being added into the system on a constant basis can have a significant impact in even a fairly short period of time.
So the truth is, not only would the future be unpredictable even if it was 100% deterministic, due to chaos, our universe _isn't_ 100% deterministic, because the various sources of quantum randomness are constantly injecting random new information into the universe, and this means that even if we could know the initial conditions with infinite accuracy and precision, we _still_ couldn't predict the future, because tiny state changes are constantly filtering in, and those are injecting new tiny differences that chaos will eventually amplify into enormous differences.
interesting that just that tiny lag in CPU processor time had an observable effect. Cool story dude!
Quite interesting. Never gave a serious thought to 'butterfly effect' untill this.... Thanks. If possible talk about concept of 'dark matter' 🙂
When you watch TH-cam to rest a bit from studying differential calculus...
Then you see the PHASE SPACE.
I feel you
Stops copies me
> quadruple scroll attractor
you ams a goods guitarists
Skwisgaar Skwigelf at least its more entertaining this time
Math professor who actually studies dynamical systems here - EXCELLENT video! This is a great, non-technical introduction to chaotic systems and what makes them hard to study. The intuitive concepts behind dynamical systems can be easily obscured by intimidating technical details and computations, but you've done a fantastic job of making this topic accessible to a general audience. I'm teaching a special topics class on this in the spring and am now DEFINITELY going to show this video as part of our introduction to chaos theory.
I've followed this channel for years now (and saw your video on staying relevant on TH-cam), and I'm glad to see that you are maintaining your high standards for the quality of your videos. Thank you for your commitment to high standards in education.
Your early dismissal of quantum affects on people took me by surprise, it took me a few ticks to figure out why.
I read an article a few years ago saying that One of the inputs into the decision behind a neuron firing or not is actually based on a quantum state change.
To me this makes living beings huge amplifiers of quantum state change and the apparent randomness that introduces. Makes sense to me because it seems like evolution would embrace the ability for us to differ by a little randomness in our thoughts the same way we benefit from randomness in our dna.
You just reminded me that this is not a commonly held concept, so I thought I’d ask your opinion on the idea.
Your videos are amazing, I just watched the multiverse one and you explained that so clearly that it’s jaw dropping.
Thank you for your videos!
indeed, the field of quantum biology is generating some real results.
probably one of the best youtube channels ever. Nice job
"A Sound of Thunder" is one of my favorite examples of this.
It’s a fun way to fictionalize the idea, but it’s important to understand that literally any interaction with the past whatsoever, will prevent mankind as we know it from ever evolving, if you go as far back as they do in that story.
This guy is making me look at the universe in a whole different way...
watching this stoned? lol
Vsauce
I love your series on chaos!
Awesome video. I keep going back to our ability to process information. In a simple environment, say a pool ball striking another pool ball, we have the ability to isolate many points of information in that "relatively small" experiment. We can essentially tell the direct future for a few seconds. We don't really call this chaos. But when we work with a larger set of data and more points of information, we suddenly label it as chaos as we are unable to predict the outcome accurately. It's not that we are unable to predict, it's that we don't have the tools/understanding to quickly identify, map out, and "do the math". The math now resides within magnitudes of complexity. If given enough time and a massive amount of data points, (plus some wicked processing) we should be able to predict the outcome just the same. It just requires more on our part. More than we currently have.
And then what of the earthquake? What was predictable before vs. what was will be predictable after, and the need to know the exact when of that quake to plot the sequence of events? The precise when of that event has huge influences upon all the lives touched by it. Why is any other moment so different?
@@jamesrosar3823 I imagine an earthquake goes by the math of 'self organized criticality.'
“For want of a nail, the shoe was lost;
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost,
For want of a battle, the kingdom was lost!”
- Chaos by James Gleick
A nail, a nail! My kingdom for a nail!
Wow.. This seem very interesting stuff!! I'm going to read this book today.
Manasi Snehal Great! You will love it.
Apurva Narayan
I have re-read it 3 times over the past 30 years
What a fantastic book
Me: *Releases hundreds of captive butterflies into the wild*
Stranger 1: "That's so nice. It's a beautiful sight to release gentle creatures like that."
Stranger 2: "He's obviously feeding the local birds. He'd release them in captivity if he cared about their safety."
Stranger 3: "He must just be doing something like blowing bubbles to feel good."
Me: *Thinking* "Go my pets! Use your butterfly effect to cause tornadoes across the world! Fly my pets! I will destroy it all with butterflies!"
Alexis Carrillo Part of chaos theory is that the future is short-term sensitive to initial conditions, but not long-term. Basically, the flap of a butterfly in Texas may cause a tornado in India, but it can also extinguish one in Chile, so the overall number of tornados stays the same.
based and butterfly pilled
Sounds like a villain's superpowers haha
After reading this, Phineas: Ferb, I think I know what we are going to do today!
@@KnakuanaRka saha lik fil canada ou el weh weh mta3 el christmas
questions like this keep me up all night
such a beautiful video, very inspiring!
Those animations are absolutely stunning !!!
Nonlinear dynamics and the concept of chaos literally changed my life and was the start of my academic journey
How so?
How?
Every Particle Seated, Tied In, Entangled. Never Dark, Infinite Deep, Nebulas Tumble. Knowledge Is Lessons Learned. Here I Must Say Everything Leaps, Forever.
What do you study
@@Hallowed_Ground By studying nonlinear dynamics in physical and chemical systems you realize that simple rules can create very complex patterns and behaviors. Consequently, you can have a pattern in nature (like a human being) and it doesn't need a designer to meticulously design everything about that pattern. For me it is a pretty compelling evidence against a creator. If you are interested in knowing more you can watch " The secret life of chaos" documentary or read "Nonlinear dynamics and chaos" by Steven Strogatz (it requires a bit of knowledge in differential equations though)
The animations are always awesome
An interesting take on the laws of physics as we know.
Amazed at the inquisitive minds that study into so much detail!
Do watch, especially if you are interested in Scientific knowledge that goes behind prediction of phenomenon like weather forecasts
For anyone interested, "Chaos" by James Gleick is a fantastic introduction (and look into the origins of) of chaos theory. Not too technical, and very engaging.
No one reads anymore
@@jewjewabrams4113 you are wrong ...
@@casualsadi3144 why are you gay?
Thanks
I had built a model of double pendulum with the help of my dad for my 12th grade project
I explained the butterfly effect, chaos theory relating it to the evolution of universe.
Physics is really awesome !!
I love the subject and I'm going to take up bsc in physics next year!
Sure you did. We all believe you.
I did a project proving the light turns off in a fridge when you shut the door, the line to my booth was huge......lol
@@mac11380 Did you just press the button with the door open?
@@GhostkillerPlaysMC No, I climbed inside....got a little dizzy after a while.....lol
@@mac11380 Knock it off! It ain't funny to belittle someone.
Thanks a lot for this extraordinary explanation on chaotic systems.
Thank you for this video extremly well explained ! ❤
Anything goes wrong
Me: It must be someone else's fault because The Butterfly Effect
Gets arrested
I blame the butterfly effect.
Judge: Sounds legit.
Nowadays, I think we can call it "Bat Effect"
wow xD
Dude yeahh
Can relate
by just a flap of its wings, the whole world change
Lol
Even though I am very young to understand the terms he uses but am very fascinated by how he explains. 😮
Till today i had a very different perspective about the nature. With all my knowledge in math, physics, and engineering, i thought that almost everything is deterministic and predicable.
And today, one of my friends sent this video link to me, when we were having a small discussion. This video was really thought provoking, and this changed my entire perspective.
This incident itself is a chaos!
A system trying to predict the future requires every tiny details of present which includes details of system itself. It creates a self referential paradox.
True
Sounds like Laplace's demon was more about an imaginary god-like intellect analyzing as an external observer.
Stored knowledge does require matter and energy to exist and the knowledge required to comprehend the infinite expanse would require its own infinite expanse... yeah!
This is simlar to the observer paradox. Using a computer to simulate an environment far from the computer would require simulating the computer itself, because just running the simulation makes tiny changes to that external environment, because total isolation of a quantum system is impossible in this universe
You have just described why the scenario of DEVs wouldn't work.
Need to re-watch to see if they addressed this paradox there.
This used to drive me insane when I was younger. Everything I did i would ask myself how will this effect my future me and at one point I had to submit myself to nature itself and let my future be wherever it must be.
I went through this crisis at age 15 and it wasn't until I was 16 that I finally let go of my controlled fall through life and finally let myself freefall through life like a leaf in the wind.
When I was around 13-14 years old, I would always be aware of every step I took and if it impacted my future, used to drive me nuts. Now at 32, I don't believe there is a "future".
same! but it happened to me wheb i was 12-13
Its a blessing and a curse. It just means you are self aware and know what it means to be alive and human.
I am 15 it's happening with me NOW
Lol this happened to me at like 11
Another very well done video. I am surprised Dr. Muller did not mention Isaac Asimov's Foundation Series (which I am sure he has read), which is based on someone (Hari Seldon) figuring out the mathematics of predicting the future (called psychohistory), and how things can go wrong. I highly recommend the series, if you have not read it.
That metaphore of the bridge arching through the dense fog is phenomenal, and it made me think about past, present and future.
We always think that the future is blurry, somewhat predictable, but you can never be certain; however, the past is fixed: the ink is dry.
Or is it? How better are we at telling the stories of the past, than forecasting the future?
Stories are biased, memories are distorted, archeological findings are fragmented, the narrative of history is written by the winners. Information is lost. Everything on the grand scheme of things seems to be unpredictable, yet determined.
We're just passengers in a tiny self-driving car, hurtling through the blurry smokes of the unknown, and through just a small window seeing our immediate surroundings of spacetime.
Wow.
This is the best short summary of chaos I've ever seen.
TLDR: We can't predict the future accurately enough because we don't know the present accurately enough.
You didnt understand the video, clearly
The actual main takeaway is that the ensemble of predictions follow a predictable pattern.
There is no present, its either the future or past.
Ive been to Harvard, I think I'd know🤓
@Abhinav turbulent flow only looks chaotic because we dont have the capacity to know all the factors. If we could know the exact location and velocity of every atom in the system and a bunch of other factors we probably arent even aware of, we could predict where each atom would end up and how it would get there.
But what if we knew the present as clear as the past? Could we guess the future?
One of the best science chanel on TH-cam.
Thanks for a great video! One question, to be considered a chaotic system it needs to have an attractor?
So basically the meaning of my life is a rounding error.
Annnnnd my most upvoted comment is about the meaning of my life is a rounding error.
SnowTV Life is the ability to change the future
Aidan McCready Yea, but without the rounding error, won't all the decisions we made be predictable?
I remember reading about brain activity is at quantum level though, so maybe that will introduce some uncertainty in the decision making progress?
Didn't they cracked 42 a while ago?
@@SnowTerebi Yeah it turned out the meaning of life wasn't in fact 42, I'm still shocked!
What is meaning without chaos?
so TH-cam algorithm let's see how you perform this time
it made my recommended
it made my recommended too
It's impossible to predict, because we only ever know the approximate state of TH-cam at any given time.
It made my recommended!
Made mines
A very helpful video on the buttercream effect
It amazes me that videos like this get 4 million views and 6,000 comments. I mean, this is great stuff and really fascinating to total geeks like me, I'm just surprised there are that many more of us out there who have discovered this content.
"I mean sure, there's Heisenberg's uncertainty principle from quantum mechanics, but that's on the scale of atoms. -Pretty insignificant on the scale of people." Or is it?
Jim Greene I thought the same!
And *Vsauce music*
@@spacetime_wanderer lol
Are you Spiderman?
@@tear728 u4c(isl8vq-b
Maybe the c spin of a electron on your brain is affecting your choices
I’m so glad I’m in college... YAY MATH!!! This has opened my eyes further.
REMEMBER
there is no such thing as hard math and easy... only math you have yet to learn and math you know!
If only I had a physics and/or math teacher that was half as knowledgeable, descriptive and well versed as you are in those famous short "lectures" of Veritasium, I would certainly have been an immeasurably more educated person. I cannot thank you enough for your uploads.
i really really need the fractal video you talked about, my man
I think the butterfly effect also captured so many minds because we as humans are constantly asking "Do the choices I make matter?" and "In the grander scheme of things, am I important?" and the butterfly effect gives an answer which is in most cases, yes to both questions
What I loved about Lorenz was that his initial computer simulations were an early effort to prove long range weather forecasting was possible. What he got instead was the opposite. He said that if you were to place weather sensors in a grid around the earth every cubic mile in the sky, the space in between would still not be accurately measured and therefore, impossible to map long term. If you were to put sensors every 1/2 mile, the space between would be a mystery and so forth down and down the scale. That proved that no matter how much you tried to "map" a chaotic system, the space in between the measurements will throw you off over time. Therefore, a small change: like the slight turbulence of butterfly's wing could, over time, effect the system in an unpredictable way if it's "in between the sensors" and not measured initially.
But the silver lining is that the predictions do in fact get a little more accurate. And maybe that's a practical enough time-frame.
@@N0Xa880iUL yeah. It requires some of the most powerful super computers in the world to run modern weather models to try to "see" the empty spaces.
@@swordmonkey6635 Right
As I’m studying this more I feel like the chaotic attractor is some sort of substructure that is being indirectly mapped by the phase space. Could be the shadow of some higher dimensional geometry that plays a role in the evolution of natural systems
Five years deep into a PhD focused on complex dynamical systems and chaos, here. In short: yes, your theory has legs. I will probably spend the better part of my life working on a proof.
@@smeyer6960 Imagine this turns into a butterfly effect of discovering something new about physics
@@wren_. Our little comment thread has already altered the pathway by which our universe has evolved since 2021...
Everything in universe is understandable, we need only a good teacher and perspective