computerchemist is the ongoing solo project of Dave Pearson, who lives in S… Read Full Bio ↴computerchemist is the ongoing solo project of Dave Pearson, who lives in Székesfehérvár, Hungary, after moving from the UK in 2008.
Over the last 25 years Dave's music has been strongly influenced by "classic" Berlin School performers such as Tangerine Dream (mostly from the '72-'86 period) and Klaus Schulze, as well as taking inspiration from newer, more contemporary musicians with a diversity ranging from The Mars Volta to Csaba Vedres.

chaos theory
computerchemist Lyrics

We have lyrics for 'chaos theory' by these artists:

Aviators When I called you from the darkness When I whispered in…
Badly Drawn Boy You fly like an arrow I lie in the shadow Only to…
Break DARK SMOKE BLIND MY EYES WON´T LET ME SEE IF ITS…
Die Form Open your eyes, on a sign, Cage you, soldier, Overhelmed t…
Jumpsteady It's the chaos theory It's, it's the chaos theory It's,…
Ketos No, no I can't see Can't see this hell This hell,…
Knox Hill There′s a lot of words that I left in my…
New Million Analog nightmare This cannot compare Can now see that its al…
Paleface Chaos Theory Seeing red I'm so fucking short fused As these…

Rhythmic Thoughts A public display of human decay Justice delivered by gruesom…
ShockOne It was anarchy in a clockwork universe. The other side of…
Synthetic Breed Paralysed in fear From what stands before me Science canno…
The Dead Milkmen I am the king of the new white underclass I am…
The Honeymoon I am an accessory to a lifetime of memories Of borderline…
The Korea Тайна творца Точка отсчета Земля Точка отсчета Земля собират…
War Of Ages Hold the bottle to your throat before you breakdown Light pi…

Woody's a Girl Vox 1: "Okay, okay," I tell my subconscious "I k…

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Most interesting comment from YouTube:

@rybec

2y↑6

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.

All comments from YouTube:

@andrejferdinand388

4y↑13.5K

Having a bad math teacher at very young age, has the butterfly effect on the rest of your life; for example

@victorguzman4101

3y↑540

"The printer rounded to 3 decimal places whereas the computer calculated 6"

The ghost of significant figures

@premsagar8253

3y↑146

Having a bad math teacher at very young age, has the butterfly effect on the rest of your life; for example

@aadarshraghuwanshi7022

3y↑191

this hit me hard.

@Ira__L

3y↑200

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😂

@Ckdude100

3y↑40

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

121 More Replies...

@mohibullah6215

3y↑5.7K

He explained such a complex topic with so much simplicity that i am just speechless.

@hugoclarke3284

3y↑82

It IS simple. People can't help but complicate things.

@MouseGoat

3y↑49

@@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.

@hugoclarke3284

3y↑29

@@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.

@TTaM581

3y↑32

@@Arrowaceofspades Have you considered that English may not be his first language? Using an ad hominem argument means you've already lost.

@hamsterdam1942

3y↑7

@@Arrowaceofspades did you have a bad day?

32 More Replies...

@SylvainBerube

3y↑1.3K

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!

@OhZjuchi

2y↑30

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

@MrDrew-qh2es

2y↑3

@@OhZjuchi haha yup

@aliwaheed906

2y↑4

Any good book recommendations on choatic systems?

@samk7400

2y↑3

@@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.

@NaneuxPeeBrane

2y↑4

@@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

1 More Replies...

@QuesoCookies

3y↑718

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.

@robosergTV

3y↑9

exactly

@jake8993

3y↑27

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?

@QuesoCookies

3y↑20

@@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.

@ChillGuy511

3y↑31

@@jake8993 But exact conditions to infinite decimals can never be known...

@ChillGuy511

3y↑14

@@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

23 More Replies...

@milistefanova7405

2y↑240

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.

@loturzelrestaurant

Keep yourself updated with the amazing Problem-tackling Youtubers 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-Youtubers are very similar
and even often overlap with Atheist-Content - making them miss-out.

@krishnachaitanyapullakandam

2y↑79

The graphics, the explanation, the presentation, everything about this video is top class. I am just speechless.

@SangoProductions213

4y↑7.1K

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.

@MikinessAnalog

4y↑246

How very "forward" of you LOL

@JohnBehrens118

4y↑454

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.

@Lambda_Ovine

4y↑73

Yeah, but when you cannot predict what will happen, does it even matter to think about that?

@SangoProductions213

4y↑96

@@Lambda_Ovine Yes. Get out there and make one small step towards a better future. You have the power.

@mackk123

4y↑143

If you put a bag on your head you can time travel at a rate of 1 second per second

93 More Replies...

@iiitechnoduckxx3526

1y↑155

The relationship between this chaos theory, and the definition of insanity (doing the same thing over and expecting different results) is VERY intriguing.

@avishekchakraborty8289

46w↑2

Hmm, that's indeed a very intriguing correlation there

@AlexanderNash

41w↑5

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.

@zackariasthepirate

2y↑42

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.

@danatowne5498

2y↑108

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!

@TucsonDude

2y↑6

That's a fun story about it.

@viktorija.jankauskaite

2y↑6

That was a good story! Bradbury was an incredible author

@JBG-AjaxzeMedia

1y↑2

it was probably called the butterfly effect long before that.

@danatowne5498

1y↑3

@@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.

@JBG-AjaxzeMedia

1y↑5

@@danatowne5498 according to google, lorenz called it the butterfly effect

7 More Replies...

@braceleerohith

3y↑325

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.

@shubham25.36

3y↑8

True

@givingittoyouraw4101

3y↑30

Sounds like Laplace's demon was more about an imaginary god-like intellect analyzing as an external observer.

@changer_of_ways_beep_bop_boop

3y↑25

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!

@Rudxain

3y↑29

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

@moonmoonFoXhandle

2y↑2

You have just described why the scenario of DEVs wouldn't work.
Need to re-watch to see if they addressed this paradox there.

2 More Replies...

@yuki-zn4co

2y↑11

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.

@jamesdinius7769

4y↑4.3K

Sensitive dependency on initial conditions: The exact present exactly predicts the future, but the approximate present doesn't approximately predict the future.

@kirbykir

4y↑126

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)_/¯

@josephburchanowski4636

4y↑222

@@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.

@davidlewis6728

4y↑63

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.

@RandomWyvern

4y↑1

@Juan Cortez Muro For the second time, are you proud of yourself fam?

@fyukfy2366

4y↑9

You took that from vsauce

63 More Replies...

@micaelaroyo4837

3y↑74

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

@trayee4854

2y↑12

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!

@karllenc

2y↑7

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.

@shagerg2238

3y↑58

It’s crazy how chaos relate so much to harmony

@jasonpowell1445

3y↑2

relates no opposes, just like positive & negative, this is not crazy this is balance.

@alexchristakis4539

2y↑9

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.

@faith9196

4y↑2.2K

And this is why I will always smile and compliment strangers. Idk what kind words or gestures could majorly effect someone’s life.

@paulferris8180

3y↑47

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.

@prumchhangsreng979

3y↑72

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.

@YAHOOISNOTG

3y↑6

@@paulferris8180 This is why the movie Groundhog Day is one of my favorites

@a7G-82r

3y↑41

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.

@randomguy-hv1go

3y↑6

@@a7G-82r YESSIR

47 More Replies...

@Lozzie74

3y↑51

I look forward to the video on fractals. My kids asked about the lyric in the movie Frozen (Princess Elsa sings about the fractal shape of her ice palace in the song “Let it Go”) and I explained “the shape is the same no matter the scale” and cited that mountains are typically fractal. I’ve long been fascinated with the mathematics of fractals, first encountering the “blancmange” function in high school.

@demonreturns4336

2y↑1

Seeing as this video was couple years ago and your comment is o my like almost a year ago

I’m guessing that fractal video still haven’t been done huh

@4799balaji

Seeing your comment is 6 months ago. I wonder if it hasn't been released yet!

@editg121

3y↑5

Im always blown away by his video. Wow, simple explanation on such complex concept without single equation. Great video.

@richard8308

3y↑6

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

@therealestninja

I've seen several of your videos and even recommended some to others. This is by far my favorite of your videos.

@holp

4y↑7K

"That's on the scale of atoms, pretty insignificant on the scale of people," said the pile of atoms.

@deepstariaenigmatica2601

4y↑276

...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.

@hans-christianlarsen7538

4y↑169

and isn't THAT the butterfly effect?

@GNParty

4y↑36

Several trillion trillion atoms, yes.

@holp

4y↑61

@@hans-christianlarsen7538 EXACTLY WHAT I WAS THINKING.

@77Avadon77

4y↑6

So if the moon was conscious would it to be impossible to predict? Of course not

103 More Replies...

@gmgadho

2y↑10

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

@briandennehy6380

3y↑3

The explanation of the topics and visualisation of the ideas on this channel are phenomenal. Well done to all involved

@xoy1148

22w↑1

This video is so good I keep Coming back to re-watch it time to time

@jonsaboe2019

3y↑7

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.

@calmcalm6203

2y↑1

U mean love ?

@periodictable118

1y↑4

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

@josephtran1500

4y↑2.8K

"The printer rounded to 3 decimal places whereas the computer calculated 6"

The ghost of significant figures

@KaranYadav-gr5xj

4y↑90

Programmer's nightmare :D

@KaneNexus

4y↑114

That's how 1+1=3 for large values of 1.

@McFly0097

4y↑27

at least he didn't have to program in an era of timezones

@DiamondTear

4y↑7

"Hidden figures"?

@salixbaby

4y↑2

ghosts of departed figures!

19 More Replies...

@rybec

2y↑6

@Heart-CenteredChanneling

interesting that just that tiny lag in CPU processor time had an observable effect. Cool story dude!

@Lyre-Archon

2y↑2

questions like this keep me up all night

@EpicNova

3y↑3

My brain hurts watching these videos even with the simplistic style you explain them in, and I want more!

@sakhanna1

3y↑2

Thanks for the informative video. What is the background music being used at the end of your video? The seaweed music files plays different.

@DO1Metalformings

25w

the way you explain things is incredible.

@klaxoncow

3y↑4.5K

"Sometimes when I consider what tremendous consequences come from little things, I am tempted to think... there are no little things."
- Bruce Barton

@pallabidutta968

3y↑34

The intricacies in the web of life.

@sukanya3411

3y↑13

🤯

@metafisicacibernetica

3y↑3

yeah

@SwarumtheForum

3y↑9

That is certainly a tempting thought.

@yusufibrahim1694

2y↑16

i have been trying to put that feeling into words for years. thanks person

4 More Replies...

@suhel19690

3y↑1

it was my M. Tech. thesis topic...I am so amazed to see how he explained it in most simplistic way... just awesome...👍👍

@there_can_only_be_one__unicorn

Thanks for the time and effort you invest in your productions they are very much appreciated

@billk6585

3y↑1

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!

@nmarbletoe8210

indeed, the field of quantum biology is generating some real results.

@siddhumyl

Your videos are very good in explaining the complex topics in simple terms. Thanks a lot.

@ethangroat8333

3y↑4

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

@russwane

4y↑3.7K

If only someone had explained science this way when I was younger.

@CalvinHikes

4y↑207

I'm just happy someone explaining it this way now. YouTube 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.

@AKABILASETOFICIAL

4y↑5

Great I'm ever like physics

@chuckychuck8318

4y↑35

Science is easy to understand. Math is your problem

@russwane

4y↑5

@@chuckychuck8318 geez. Tell me about it.

@vikingslayer34

4y↑21

They did. You were just too high to stay awake.

49 More Replies...

@dr.ramkishorsah495

3y↑1

you know when that music hit at the end I always get chills

@amylimschwander9042

3y↑5

Thanks for the videos - another beautiful example of rheostatic order which includes states of variability in relation to higher order predictable potential action. :)

@MrGarysjwallace

3y↑3

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

@60pluscrazy

3y↑2

This explanation explains so much about the mystery of our mysterious world. Deterministic chaos🙏

@royfablooo2810

3y↑8

Just finishing Life is Strange Game and I've become really interested on Chaos Theory and Butterfly Effect.

@wesleysull

4y↑831

I would like a 60 min documentary on the content just presented in the last 2 mins of this video.

@rahulsonaghela178

4y↑104

You mean the last pass advert?

@user-yn9mp4bt3q

4y↑3

Ok but the music https://youtu.be/p_yOueFMe7c

@GuitarSamurai17

Why?

@martinkuffer5643

4y↑13

If you have a little background on calculus, you can read Strogatz's book "Non Linear Dynamics and Chaos". It's absolutely amazing

@NoHandleToSpeakOf

4y↑5

there is "secret life of chaos" https://www.imdb.com/title/tt1674741/

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@pratishdewangan132

3y↑5

Everything in universe is understandable, we need only a good teacher and perspective

@rohitdutta7625

2y↑1

This video has just blowed my mind.

@naturalistamoderno9051

One of the best science chanel on YouTube.

@ian2

3y↑2

Really good explanation of the concept and I'm glad you used both meteorology and astrophysics as examples. People often ask "Why can we predict where a planet will be millions of years down the line but not the weather in a week?" They're both chaotic but depend on the temporal scale much differently among other factors. A week is a long time for the weather, but for space it's nothing.

And along with that, weather models are never "correct". Their predictions may match what ends up occurring in some areas, but they can never be perfect. Even though meteorologists have moved away from doing hardcore math to make predictions because computers have allowed for more predictions to be made much more quickly, they still need humans to interpret them and to determine whether or not the outcome is realistic. This is why weather apps on your phone (The Weather Channel, etc.) are often wrong, because they're pretty much purely model output with no human interpretation. Also, ensemble runs (multiple runs often at a lower resolution to save time computing) are very useful with portraying uncertainty in a forecast and deterministic runs (single runs at a higher resolution) will likely be more accurate than any single run in the ensemble members. Both have their uses, along with taking the average of ensembles (including when your ensemble members are multiple different models rather than the same model being run multiple times).

@fritzzz1372

weather apps and tv weather forecasts are mostly created the same way (which means they are both inaccurate and stop working at more than a week into the future.

@ian2

@@fritzzz1372 Yep, they often have virtually no human input. Apps can be good for a quick glance at what to expect but specifics are often wrong. This misconception gives meteorologists a bad reputation unfortunately.

@fritzzz1372

@@ian2 but there are also weather apps which make weather forecasts the same ways as TV weather forecasts (pr are just the app version of the same forecast)
and the "bad reputation" comes from the misconception that it is easy to predict the weather accurately when you can predict non-chaotic systems accurately

@navsenjoy

2y↑3

Quite interesting. Never gave a serious thought to 'butterfly effect' untill this.... Thanks. If possible talk about concept of 'dark matter' 🙂

@_Swink

4y↑463

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.

@tahsintariq8757

4y↑7

Fellow 3b1b fan?

@_Swink

4y↑25

@@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

@_Swink

4y↑16

@@tahsintariq8757 OH 3blue1brown yeah I love his videos too

@JH-ji6cj

4y↑1

The Information by James Gleik is an amazing read as well!

@tahsintariq8757

4y↑4

@@_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.

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@SpruceOaks

3y↑3

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.

@shivasamadhi

3y↑11

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

@smeyer6960

2y↑5

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.

@wren_.

2y↑1

@@smeyer6960 Imagine this turns into a butterfly effect of discovering something new about physics

@smeyer6960

2y↑2

@@wren_. Our little comment thread has already altered the pathway by which our universe has evolved since 2021...

@JohnSmith-gu6hf

probably one of the best youtube channels ever. Nice job

@timothydoyle3380

Was explained so well. Excellent job!

@areyoukind5645

23w↑2

A very helpful video on the buttercream effect

@CunningBard

3y↑652

* Time Traveler Sneezes *

Butterfly effect: * GERMANY BECOMES AN ALLY IN WW2 *

@abcdefg1343

3y↑113

I would say rejecting a kid form an art school was a perfect example of the butterfly effect already

@jakeweberzwier8655

3y↑5

Then WW2 wouldn't happen

@mylesprospero8105

3y↑11

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

@VonKey.

3y↑6

"Japan destroyed by a super-massive tornado."

@CrazyGaming-ig6qq

3y↑7

And a man named Abradolf Lincler wins nobel prize for his life work on his theories of parallel dimensions.

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@pointman1921

3y↑2

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.

@jamesrosar3823

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?

@nmarbletoe8210

@@jamesrosar3823 I imagine an earthquake goes by the math of 'self organized criticality.'

@joshuagharis9017

You are so great. I am thankful for the work you do.

@alvisepersegato8681

41w

you're my new favorite youtuber and generally guy on the internet

@mbogomahad3125

Amazing explanation..great video.

@_el_yeyo

is there a good introductory book onto the study of dynamical/nonlinear/chaotic systems? For background, I have knowledge up to calculus 2 so far. Any advice will do!

@Crutoiful

4y↑703

A person in Florida whose house has been destroyed by a tornado: ,,Those freakin’ butterflies flying in Madagascar again”

@hadiqawaseem6726

4y↑3

Lol

@805NAVE

4y↑1

😂 “Again..”

@KnakuanaRka

4y↑1

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.

@emilianocatano2700

4y↑3

as a Floridian I can confirm

@xyz-ng5wx

This comment is so underrated 😂

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@dakotarodman433

44w

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!

@haneulkim4902

2y↑2

Thanks for a great video! One question, to be considered a chaotic system it needs to have an attractor?

@ayushir33

How u r able to explain such complex theory so beautifully.👍
Hatsoff

@mommyandme6109

2y↑1

Excellent! There is a mention of planets colliding in a few million years and some planets completely going out of the solar system. To me, that was the most fascinating moment in the entire video. Everything feels so insignificant in light of that idea! Clearly for now we can do nothing about it. Living in space stations by then if something collides with earth :) Thank you!

@user-pk9qo1gd6r

That was misrepresented. In actuality, the orbits of the planets are completely stable, and what varies chaotically is the exact position of a planet along its orbit at a given year (in the far enough future). Planets are not at all at risk of colliding in the coming million years.

@followtheleadercluj

I love your series on chaos!

@danyalag3366

4y↑750

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."

@jareknowak8712

4y↑2

True.
👍

@casualsadi3144

4y↑7

Chaos is a ladder :V :V :V

@ConnorHammond

4y↑38

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..

@jareknowak8712

4y↑25

@@ConnorHammond
Butterfly effect.
Everything affects everything.

@heywrandom8924

4y↑22

@@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

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@kushaldevkashyap

@Derek - Infinite loop in a finite space seems similar to the uncertainity principle where in if you try to super enlarge the position graph you will see chaos/uncertainity in other factors like velocity and momentum.
Let me know if this makes sense.

@orbithom

i really really need the fractal video you talked about, my man

@cpinindia

3y↑3

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

@c4os79

such a beautiful video, very inspiring!

@Akwariah

43w↑1

Great explanation 👏

@elaichiuchiha4161

4y↑1.6K

Why am I interested in this and not in my studies?!

@ramaarafat4608

3y↑46

Maybe you should change your studies then lol. But maybe its your destity...

@Richard-bq7br

3y↑158

This were written to make you interested. All the boring stuff were taken out.

@shantanu176

3y↑75

@@Richard-bq7br yes, the devil lies in the details

@Devilupz

3y↑22

@@shantanu176 yeah, it's real, I'm the devil.

@oliverm8058

3y↑7

Bad teachers 100% of the time

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@charzy11

3y↑17

Q1. So could you theoretically perform a ‘Quantum Coin Toss’ to make a significant world scale decision, thus creating two deviated universes, that had 100% identical history prior to that moment?

@anuradhanunna

Yep

@jamesrosar3823

3y↑2

At least for arguments sake, as an axiomatic aid to discussion. As if time granted the opportunity for a new universe to start at any instant. We are possessed of a deep need to believe this is, has been, and always will be possible, or our agency would be lost. Either that, or the premise is in error.

@charzy11

@@jamesrosar3823 you’re skipping ahead, but indeed that’s where the determinism question takes us. Q. Are we therefore drivers of our own fate, or just conscious passengers?

@charzy11

3y↑1

To follow… Every instance of a being exercising True Free Will would be a deviation point, with each potential requiring its own unique base universe. Therefore, the number of unique base universes that eventually lead to Free Will is infinitely higher than unique deterministic universes. In other words, if Free Will is possible at all to exist, through evolution or creation , then … a. we almost certainly live in one of the universes that it does b. It is fundamental to the measure of existence .

@jamesrosar3823

3y↑2

We surf the expanding edge of possibility, What has happened is now fixed, and from Newton, objects in motion tend to stay in motion, until acted upon by an external force. We can be that external force, using periodicity to our advantage, for when preparation meets opportunity, luck has a way of sustaining the flows of energy we depend upon to perpetuate ourselves with.

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@Aengus42

I can remember my deterministic phase.
As a kid I got yo play on a home snooker table. When shown how to play I surmised that there must be s single solution. One place to strike the cue ball at a certain velocity & angle that if followed then all the balls could be cleared.
I did add that it would have to be a robot for repeatable accuracy.
But even now I blush thinking about it. My total deterministic view of physics as s young kid.
Reading Chaos by James Gleick years later took me back to that erroneous utterance many, many times!
Starting conditions is but one of a myriad of ways the butterflies would laugh at me!

@nicatina

3y↑4

I was done playing the Life is Strange (the first game) and I stumbled upon this video to learn more about the butterfly effect and chaos theory.

The ending I choose is Sacrifice Chloe, as sad and hard that this may sound, it goes to show that you can't keep changing fate and destiny for the people around you and for yourself, because in the end, you have to let go of the past. I like it how the blue butterfly in the end of the game represents on the right path.

@curtpanser9327

3y↑2

Same same hahaha

@abhir4872

39w↑1

i am selfish let the storm happen

@nicatina

39w↑1

@@abhir4872 dang, I forgot I commented, a year later I'm bae over bay 💀so YEAH

@danknfrshtv

"...each point uniquely identifies the complete state of the system." 3:50 Dude, thank you. I'd seen the models online and skimmed a few articles and Wikipedia of course, but the concept has never sunk in so clearly as it has via this explanation.

@mourning3301

Fantastic Presentation

@zintel4471

4y↑389

This is one of those science videos that aren't just interesting, but also beautiful.

@JohnSmith-gs4zv

4y↑7

Just like your comment! ;)

@ZachariahMBaird

4y↑7

Just like you.

@buboychua2197

4y↑5

True bro

@devonjosiah7308

4y↑4

And also confusing

@Hambxne

4y↑1

I think you would really enjoy @3Blue1Brown

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@dennisdahl3

35w

"you can't predict how any individual state will evolve, but you can say how a collection of states evolves".
Is inspiring to see there may be some reality to Hari Seldon's theories.
Something new for me to meditate upon.
Perhaps already used in targeted marketing.

@Tom-qg7jx

42w↑2

Good video, even thought i get headaches thinking about them. I understand how you can be certain a system has periodic behavior but how do you "know" a system is chaotic? It could be that the repeatition only starts after the furthest point we observed. Thx already for the help!

@CheezCharmer

3y↑1

what happens if you connect a double pendulum to a non rigid support. like in your syncing clock pendulum videos. what happens then? or maybe support the double pendulum on a platform on top of cans. what will happen then?

@balazsadorjani1263

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.

@nissrineouabbou273

Thank you for this video extremly well explained ! ❤

@flameendcyborgguy883

3y↑1.6K

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.

@arkdirfe

3y↑134

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.

@gps9715

3y↑3

"... and predictable." I think you missed something somewhere.

@gps9715

3y↑4

@@arkdirfe You mean like fractals?

@flameendcyborgguy883

3y↑16

@@gps9715 I meant rules are predictable not system itself. Statistics and rules it obeys can be seen from the function itself.

@jamieg2427

3y↑3

the rules belong to the math topic called differential equations.

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@andrewhone3346

28w

One subtle point about the curves not crossing in phase space: it is true that the actual trajectories (viewed as parametrized curves, with time as parameter) do not cross. However, even in the phase space of the pendulum (without friction, but with force proportional to minus the sine of the angle) there are heteroclinic orbits which meet at a hyperbolic fixed point (the unstable state in which the pendulum is balanced upside down). Similarly in the damped pendulum there is the attracting fixed point in the centre, and all the trajectories spiral in to meet at this stable state in the limit that time goes to infinity.

@rajatdash9198

The animations are always awesome

@thevineyardplanter6558

35w

I loved this video and how you explained it so well. You reminded me of Sheldon Cooper. 🙈

@Tom-sp3gy

Beautiful explanation

@user-gh5yg3qw9b

18w

Gorgeous video thank youuu

@metanumia

4y↑293

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! :)

@Pranav_Bhamidipati

4y↑1

Aren't all forecasts mostly done by supercomputers?

@calvinwill1663

4y↑5

@@Pranav_Bhamidipati I don't know but even if so, people must create the system first and fix the system when it is imperfect.

@zwz.zdenek

4y↑1

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.

@santiagodiez7022

4y↑1

zwz • zdenek that was so rude and accurate at the same time

@nmarbletoe8210

@@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.

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@siggyretburns7523

But what about self synchronizing rythms? Like if you put several metronomes on a table and start them, they all start unsynchronized. But after a while they all synchronize.
What effect does that have on caotic effects?