Chaos: The Science of the Butterfly Effect

[@jamesdinius7769]

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

[@kirbykir]

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]

@@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]

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.

[@GrrSaidTheWolf]

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

[@fyukfy2366]

You took that from vsauce

[@SangoProductions213]

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]

How very "forward" of you LOL

[@JohnBehrens118]

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]

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

[@SangoProductions213]

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

[@mackk123]

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

[@mohibullah6215]

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

[@hugoclarke3284]

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

[@MouseGoat]

@@52mktmsk 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]

@@52mktmsk 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]

@@52mktmsk Have you considered that English may not be his first language? Using an ad hominem argument means you've already lost.

[@hamsterdam1942]

@@52mktmsk did you have a bad day?

[@zackariasthepirate]

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.

[@faith9196]

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

[@paulferris8180]

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]

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]

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

[@barbonson_richards]

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]

@@barbonson_richards YESSIR

[@klaxoncow]

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

[@pallabidutta968]

The intricacies in the web of life.

[@sukanya3411]

🤯

[@metafisicacibernetica]

yeah

[@SwarumtheForum]

That is certainly a tempting thought.

[@yusufibrahim1694]

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

[@SylvainBerube]

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]

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]

@@OhZjuchi haha yup

[@aliwaheed906]

Any good book recommendations on choatic systems?

[@NaneuxPeeBrane]

@@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

[@mymechanicdallas]

@@aliwaheed906 Some books on chaotic dynamical systems that were published 20 years ago or earlier are “Discrete Chaos” by Saber Elaydi , “Chaos: An Introduction to Dynamical Systems” by Alligood, Yorke and Sauer, and “An Introduction to Chaotic Dynamical Systems” by Bob Devaney

[@milistefanova7405]

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 KZbinrs 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-KZbinrs are very similar and even often overlap with Atheist-Content - making them miss-out.

[@russwane]

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

[@CalvinHikes]

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

Great I'm ever like physics

[@chuckychuck8318]

Science is easy to understand. Math is your problem

[@russwane]

@@chuckychuck8318 geez. Tell me about it.

[@vikingslayer34]

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

[@danyalag3366]

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]

True. 👍

[@casualsadi3144]

Chaos is a ladder :V :V :V

[@ConnorHammond]

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]

@@ConnorHammond Butterfly effect. Everything affects everything.

[@heywrandom8924]

@@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

[@andrejferdinand388]

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

[@victorguzman4101]

"The printer rounded to 3 decimal places whereas the computer calculated 6" The ghost of significant figures

[@premsagar8253]

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

[@aadarshraghuwanshi7022]

this hit me hard.

[@Ira__L]

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]

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

[@iiitechnoduckxx3526]

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

[@avishekchakraborty8289]

Hmm, that's indeed a very intriguing correlation there

[@AlexanderNash]

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.

[@meinbherpieg4723]

@@AlexanderNash Exactly. Which is why people are wrong when they say "history repeats". It doesn't repeat; it rhymes through iterations.

[@paulinaaaaa6590]

You should draw knowledge from different resources like a dictionary as well not only Albert Einstein

[@iiitechnoduckxx3526]

@@paulinaaaaa6590 excellent comment. Worth the time 👌🏾

[@QuesoCookies]

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]

exactly

[@jake8993]

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]

@@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]

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

[@ChillGuy511]

@@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

[@flameendcyborgguy883]

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]

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]

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

[@gps9715]

@@arkdirfe You mean like fractals?

[@flameendcyborgguy883]

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

[@jamieg2427]

the rules belong to the math topic called differential equations.

[@metanumia]

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]

Aren't all forecasts mostly done by supercomputers?

[@calvinwill1663]

@@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]

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]

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.

[@krishnachaitanyapullakandam]

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

[@holp]

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

[@deepstariaenigmatica2601]

...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.

[@GNParty]

Several trillion trillion atoms, yes.

[@holp]

@Hans-Christian Larsen EXACTLY WHAT I WAS THINKING.

[@77Avadon77]

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

[@77Avadon77]

@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.

[@pizzaovenpizza]

I understand and mostly don't understand this at the same time. How Schrödinger.

[@Malik-Ibi]

That's just for atoms.

[@EisensteinPrime]

Actually that's 2 different versions of you. Not a single entity. That's what this channel taught me anyway 😂

[@snowleopard9463]

Fact: alternate version of you right now doesn't even know you knew anything about alternating realities

[@andrewaronson3364]

wrong video head ass

[@charlespackwood2055]

his cat died

[@elaichiuchiha4161]

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

[@ramaarafat4608]

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

[@Richard-bq7br]

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

[@shantanu176]

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

[@Devilupz]

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

[@oliverm8058]

Bad teachers 100% of the time

[@danatowne5498]

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]

That's a fun story about it.

[@viktorija.jankauskaite]

That was a good story! Bradbury was an incredible author

[@JBG-AjaxzeMedia]

it was probably called the butterfly effect long before that.

[@danatowne5498]

@@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]

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

[@josephtran1500]

"The printer rounded to 3 decimal places whereas the computer calculated 6" The ghost of significant figures

[@KaranYadav-gr5xj]

Programmer's nightmare :D

[@KaneNexus]

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

[@McFly0097]

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

[@DiamondTear]

"Hidden figures"?

[@salixbaby]

ghosts of departed figures!

[@ConradPino]

I appreciate integrity shown when structuring embedded advertising so much that I watched to the very end. Thank you.

[@drumstixkml]

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 KZbin), 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.

[@Minnie123.__.]

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.

[@_Swink]

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]

Fellow 3b1b fan?

[@_Swink]

@@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]

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

[@JH-ji6cj]

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

[@tahsintariq8757]

@@_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.

[@saswatdas2698]

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..

[@sumitraturi7791]

People are amazed,thats it

[@MouseGoat]

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.

[@TTaM581]

@@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.

[@KM-oj4jk]

@@TTaM581 great illustration!

[@arandombard1197]

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.

[@matheusfernandes9871]

and this, of course, is the choice of steins;gate

[@Torabshaikh]

I was searching for Steins;Gate reference in the comments. Thanks.

[@joeqiao1691]

El psy conguroo

[@rizzgod-wj6ty]

Okarin my watched stopped working......

[@kiyoponnn]

@@joeqiao1691 Celeb 17

[@Torabshaikh]

@@rizzgod-wj6ty that was sad!

[@trayee4854]

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!

[@wesleysull]

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

[@rahulsonaghela178]

You mean the last pass advert?

[@user-yn9mp4bt3q]

Ok but the music kzbin.info/www/bejne/ppDcgKibe7KYbcU

[@GuitarSamurai17]

Why?

[@martinkuffer5643]

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

[@NoHandleToSpeakOf]

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

[@CunningBard]

* Time Traveler Sneezes * Butterfly effect: * GERMANY BECOMES AN ALLY IN WW2 *

[@abcdefg1343]

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

[@jakeweberzwier8655]

Then WW2 wouldn't happen

[@mylesprospero8105]

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.]

_"Japan destroyed by a super-massive tornado."_

[@CrazyGaming-ig6qq]

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

[@adityasharma9423]

:Why aren't you successful. Me : I held a sneeze in the maths class long ago, and now I am doomed.

[@KushagraNath-o3p]

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

[@punman5392]

For some reason I find theoretical physics like this rather unsettling. The existential implications are interesting but simultaneously disturbing

[@savagebuck]

It is not a paradox. Exciting and unsettling are not mutually exclusive. A HORROR film is both EXCITING and UNSETTLING.

[@user-or3tl6yq7o]

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

[@son5051]

@@user-or3tl6yq7o says someone who has never studied humans and their emotions on a actual neurological scale, i presume

[@lugold8766]

@@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

[@XenoghostTV]

​@@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.

[@R4ks0]

This guy is making me look at the universe in a whole different way...

[@xx8782]

watching this stoned? lol

[@Blackjac10]

Vsauce

[@zintel4471]

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

[@JohnSmith-gs4zv]

Just like your comment! ;)

[@ZachariahMBaird]

Just like you.

[@buboychua2197]

True bro

[@devonjosiah7308]

And also confusing

[@Hambxne]

I think you would really enjoy @3Blue1Brown

[@margaritasaloscerdos5]

Man I love the way you explain anything and everything related to maths and physics... How much would I have loved my teachers to explain it like this!

[@SnowTerebi]

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.

[@aidanmccready2277]

SnowTV Life is the ability to change the future

[@SnowTerebi]

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?

[@SnowTerebi]

Didn't they cracked 42 a while ago?

[@bernardusmuller1109]

@@SnowTerebi Yeah it turned out the meaning of life wasn't in fact 42, I'm still shocked!

[@magnusjonsson7303]

What is meaning without chaos?

[@thomassowinski6765]

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.

[@jewjewabrams4113]

No one reads anymore

[@casualsadi3144]

@@jewjewabrams4113 you are wrong ...

[@jewjewabrams4113]

@@casualsadi3144 why are you gay?

[@VashtiPerry]

Thanks

[@apurvanarayan11]

“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

[@alexfrasca673]

A nail, a nail! My kingdom for a nail!

[@manasisnehal1572]

Wow.. This seem very interesting stuff!! I'm going to read this book today.

[@apurvanarayan11]

Manasi Snehal Great! You will love it.

[@Ch-vx3qn]

Apurva Narayan I have re-read it 3 times over the past 30 years

[@TheTennAce]

What a fantastic book

[@richard8308]

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

[@omeryldz8264]

Nowadays, I think we can call it "Bat Effect"

[@yepeskeyfan_girl1277]

wow xD

[@anilv9729]

Dude yeahh

[@shizunnanase543]

Can relate

[@dimetriyo4183]

by just a flap of its wings, the whole world change

[@dupondra8865]

Lol

[@sanjanasrinivasan13]

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!

[@ardeleanion4435]

Sure you did. We all believe you.

[@mac11380]

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

[@GhostkillerPlaysMC]

@@mac11380 Did you just press the button with the door open?

[@mac11380]

@@GhostkillerPlaysMC No, I climbed inside....got a little dizzy after a while.....lol

[@Pranav_Bhamidipati]

@@mac11380 Knock it off! It ain't funny to belittle someone.

[@0NlRAPTOR]

"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.

[@thefootballplanet5784]

good point! Eckels (is that his name im correct? steps off the path and steps on a butterfly!

[@zemoxian]

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.

[@loremipsum7ac]

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?

[@skrewgravity]

oh my. Flashback to Freshman year in highschool almost 10 years ago

[@dhairya6357]

Yeah man ! I heard about The Sound Of Thunder in one of Aperture's Video . Please watch the videos they are mindblowing

[@karllenc]

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.

[@burninmind]

Nonlinear dynamics and the concept of chaos literally changed my life and was the start of my academic journey

[@Hallowed_Ground]

How so?

[@danielfoley9364]

How?

[@mackk123]

Every Particle Seated, Tied In, Entangled. Never Dark, Infinite Deep, Nebulas Tumble. Knowledge Is Lessons Learned. Here I Must Say Everything Leaps, Forever.

[@cameronbernardo]

What do you study

[@burninmind]

@@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)

[@braceleerohith]

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]

True

[@givingittoyouraw4101]

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

[@changer_of_ways_999]

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]

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]

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

[@Crutoiful]

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

[@hadiqawaseem6726]

Lol

[@805NAVE]

😂 “Again..”

[@KnakuanaRka]

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]

as a Floridian I can confirm

[@xyz-ng5wx]

This comment is so underrated 😂

[@Sickened-Youtube]

i can truthfully say watching this video has completely changed my life

[@micaelaroyo4837]

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

[@prabhavavasthi92]

Those animations are absolutely stunning !!!

[@BunnyOfThunder]

This is the best short summary of chaos I've ever seen.

[@rybec]

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.

[@Heart-CenteredChanneling]

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

[@williamayabei]

Butterfly effect: A Chinese dude sips his bat soup 8000km away in India a dude gets clobbered by cops for not being home by 7pm

[@abhiramcherukupalli]

😂😂😂😂🤣🤣🤣🤣

[@purvapawar8977]

Pretty much what's happening in India rn.

[@lesalabs]

Hm. But does the Chinese dude eat bats because he like it, or because he's poor?

[@tnmurti6998]

@@purvapawar8977 wtf r u creature

[@solsol9515]

The Bat Effect

[@Accel_Lex]

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!"

[@KnakuanaRka]

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.

[@diceblue6817]

based and butterfly pilled

[@xerquee]

Sounds like a villain's superpowers haha

[@rudy5623]

After reading this, Phineas: Ferb, I think I know what we are going to do today!

[@walidfakhfakh3660]

@@KnakuanaRka saha lik fil canada ou el weh weh mta3 el christmas

[@isassasinbro]

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!

[@rohitdutta7625]

This video has just blowed my mind.

[@isoSw1fty]

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.

[@lowkeyotaku2373]

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".

[@AM-vt7hw]

same! but it happened to me wheb i was 12-13

[@isoSw1fty]

Its a blessing and a curse. It just means you are self aware and know what it means to be alive and human.

[@DS-tt9px]

I am 15 it's happening with me NOW

[@numega7323]

Lol this happened to me at like 11

[@TheInimicus]

Dec 6, 2019 - Derek says: "There are things like heisenberg uncertainty principle, but these are on the scale of atoms. Pretty insignificant in humans". July 16, 2014 - "What is not Random" - Derek says: "That doesn't appear to be reality we live in.", 8:25 "For us to have free will, we need the second law of thermodynamics. Now you might think that quantum events are too small to have any meaningfull impact on the evolution of the universe, but that is not true. There are systems, chaotic systems, which are so dependent, so sensitive to their intial conditions, that any tiny change will end up making a big difference later down the track."

[@mohammadmohammadhosseini7370]

Nice, I've watched both videos too. There is a big conflict!

[@jhoughjr1]

@uwau :O

[@coolnegative]

"A Sound of Thunder" is one of my favorite examples of this.

[@atimholt]

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.

[@YolandaEzeagwu]

You have such a beautiful gift of breaking down complex topics. I keep coming back to your videos every time ❤

[@tahsintariq8757]

Derek, the music was just perfect. And the whole 13 minutes passed quickly. Great video. And please talk about fractals.

[@skwisgaarskwigelf331]

When you watch KZbin to rest a bit from studying differential calculus... Then you see the PHASE SPACE.

[@Studboo]

I feel you

[@hollowsoul666]

Stops copies me

[@Ariana-dn4mm]

> quadruple scroll attractor

[@Vladix1970]

you ams a goods guitarists

[@francisruizyamba6149]

Skwisgaar Skwigelf at least its more entertaining this time

[@swordmonkey6635]

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.

[@N0Xa880iUL]

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.

[@swordmonkey6635]

@@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.

[@N0Xa880iUL]

@@swordmonkey6635 Right

[@xoy1148]

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

[@Lozzie74]

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]

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!

[@andyh9382]

“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.

[@Shrooblord]

That sounds like a recommendation and a half. I'll check it out. Thanks!

[@yafi2475]

Thanks for the recommendation. I will check it out.

[@Pecuniarly]

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.

[@ElectricBikeReview]

I’m going to read it, thanks for the recommendation!

[@Andytlp]

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.

[@henryyssark305]

Love your stuff Derek! Thank you for getting me interested in science! After learning that science can have a interesting fun side other then just learning facts I have been working hard to get good grade and am currently striving to get into a college where I can further learn so that I can become as smart and knowledgeable as you.

[@pizz0wn3d]

Hell yeah brother! Get that knowledge!

[@zibranahmed3443]

All the best, bro.

[@DO1Metalformings]

the way you explain things is incredible.

[@scottmuck]

I hope Elon’s roadster isn’t the variable that causes Earth to get ejected from the solar system.

[@NardKoning]

This is gold haha

[@shanineedwards6894]

:')

[@stepheno3955]

I disagree, it would take a very long time for such a small thing to have such a large effect. I think it would be pretty funny, imagine we're all chillin in heaven a couple billion years from now, humanity has long since gone extinct from earth, no one pays attention to earth anymore. Someone says "Hey remember earth? It just got ejected from the solar system!" "How?" people wounder. God says " There was a little red car that pulled it out of orbit over billions of years." Everyone *looks at Elon*

[@77Avadon77]

@@stepheno3955 🤣🤣🤣😅

[@coin5207]

@@stepheno3955 _when you take a joke too seriously_

[@cubicinfinity2]

"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?

[@spacetime_wanderer]

Jim Greene I thought the same! And *Vsauce music*

[@cubicinfinity2]

@@spacetime_wanderer lol

[@tear728]

Are you Spiderman?

[@cubicinfinity2]

@@tear728 u4c(isl8vq-b

[@devTalks3641]

Maybe the c spin of a electron on your brain is affecting your choices

[@EpicNova]

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

[@KipIngram]

2:00 - YES. Exactly. If you study some physics, it's natural to come away with a determinist attitude. And I think that's a very bad thing. We teach high school physics as though it's fully correct. Students get show these equations, and they're taught that's THE WAY IT IS. That's just not the truth - we're doing them a disservice. I don't advocate actually trying to TEACH them quantum theory in high school, but I do think we should make students aware that it exists and aware that the equations learned in that early program are APPROXIMATIONS. Very, very good ones - they can learn that for all day-to-day work they're fine - but they should be told that fundamentally reality is non-deterministic.

[@bats56537]

I started watching your videos because I first seen you on Bill Nye , your videos make a normal guy like me think deeper thoughts and want to learn more. So many times when I watch your videos I am confused and lost but that leads me to do more research and learn more. Thank you for making me think deeper. I was home schooled and didn't really have many opportunities to get better education so I appreciate your videos helping me to think more and learn about things I would not have thought about before.

[@Krullmatic]

Be glad you were homeschooled, and not brainwashed and indoctrinated by the communist and Marxist teachers and professors of today!

[@habibiuser]

@@Krullmatic okay Karen, chill out

[@macemoth]

So Barney Stinson as Lorenzo von Matterhorn is also a Lorenz Attractor?

[@lucasthompson1650]

I think he's a special case in chaos theory, known as "The Mandelbarnacle".

[@ElCocoLoco95]

Who is this Barney Stinson you are talking about?

[@jeannemooberry7231]

This comment is under appreciated

[@Sepharig]

I'll always like/upvote/thumbs up an unexpected HIMYM reference

[@navaneethmkrishnan6374]

He has EPS. So guess what is the Lorenz attractor. :D

[@jonsaboe2019]

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]

U mean love ?

[@roriyrovira6629]

Greetings to all the world from Panama🇵🇦🇵🇦 I feel so good that I am learning english and science at the same time in this channel😁😁

[@heh2393]

Best of luck from India!

[@arjuns2219]

Whoever did those animations deserve an oscar and job is waiting for him/her at Disney studios

[@keerthivasanb7931]

He links the animator’s channel at the info part of video. The ‘i’ button It even displays it as a banner in the video at top., around 2:30

[@dhzzzzzz]

a single wind hitting your dad might slows him down for a second. your dad feels the wind hitting him, making him act differently and walks different from before he hits the wind. that single scenario alone can makes a significant difference from not meeting your mom or being a bit late to work. when he late at work, he rushes to his office and runs. the wind he hit makes the wind late to hit someone. that late wind makes the other person act differently too. he then stands up from his chair and his body blocks sunshine from a small tree. that small tree might be producing a different amount of oxygen and energy because that person blocked the sunshine. this can go forever. this is just a small example what butterfly effect might be look like

[@Caaro99]

also our thoughts and moods are nearly random, some thoughts may encourage us to do other actions. That small gust of wind may have him close his eyes for a bit to see something of a different colour that reminds him of something that completely changes what he's thinking of for the rest of the day. His next conversation might be about that thing which randomly sparks a relationship with someone else.

[@shubhamkumar-nw1ui]

Due to tiny bit less oxygen in the atmosphere and tiny but less concentration of ozone layer ,and resulting tny bit more quantity of UV rays in sunshine ,some bacteria on some surface which was supposed to live will now die ,this bacteria which was supposed to infect a child playing around and kill him due to septic shock ,the child will now live and became a future dictator and do tyranny , something which was not supposed to happen previously

[@parthiv8726]

my dad is buying milk

[@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.

[@editg121]

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

[@dominusfons4455]

I’m double majoring in physics and chemistry and minoring in pure math , I developed a hypothesis that free will does exist, but limited due to the wave function. Let’s use chemistry as an example. We can think of the chemical equations as a template of a predetermined sets of chemical solutions. You can add or subtract chemicals from the equation to arrive at the mixture you want to achieve. Basically, you can think of the expressions on the left side of the chemical equation as the present and the right as the future. If I ask you to find the present, based on the future, it is easily done in chemistry. Let say I give you Sodium chloride as the outcome. There can be multiple combinations of chemical to achieve this outcome and the most obvious one would be 2Na+Cl2. Using the other combination of chemicals instead of 2Na+Cl2 is what I meant by limited free will. The outcome of the future is already predetermined and you are given a set or domain of choices which you have free will to choose from. It’s like finding the domain or sets of all numbers for x at which a power series converges. It is free will in a limited sense because no one is preventing you choosing choice B from A except both choices B and A must be inside the sets of choices that meets the conditions of the outcome.

[@Pranav_Bhamidipati]

As you are majoring in Chemistry, I hope you are also studying DFT. I would like you to reflect upon it and explain your hypothesis ab initio.

[@60pluscrazy]

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

[@somuchtocook9159]

The double pendulum is unique as for explaining alternative histories, just as there is chaos sometimes the paths may align closely with each other but not for long.

[@N0Xa880iUL]

Deep

[@sevenaries]

TLDR: We can't predict the future accurately enough because we don't know the present accurately enough.

[@debblez]

You didnt understand the video, clearly

[@AAGraham000]

The actual main takeaway is that the ensemble of predictions follow a predictable pattern.

[@BoleDaPole]

There is no present, its either the future or past. Ive been to Harvard, I think I'd know🤓

[@averagejoe9040]

@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.

[@ardaehi]

But what if we knew the present as clear as the past? Could we guess the future?

[@rupaprasad1920]

so KZbin algorithm let's see how you perform this time

[@samuelthompson3861]

it made my recommended

[@harjapoo5793]

it made my recommended too

[@imveryangryitsnotbutter]

It's impossible to predict, because we only ever know the approximate state of KZbin at any given time.

[@max11n98]

It made my recommended!

[@merlockmerlin1065]

Made mines

[@areyoukind5645]

A very helpful video on the buttercream effect

[@TheRealGuywithoutaMustache]

This made me wonder. How has this video being uploaded today, at this very moment, affect the future? How has this insignificant comment of mine affected the future?

[@pluto8404]

You waisted x amount of time writing it, now youre wasting x amount of time reading this reply, and now wasting more of your life thinking about if your going to reply. Why are you still reading this, you are wasting your life! Wait sh*t, I am also wasting my life, but who knows, maybe I will leave my house a bit later and not get hit by a car now, or maybe I will die now. Whoops.

[@d.l.7416]

@@pluto8404 Time is an illusion

[@dwightk.schrute8696]

@@d.l.7416 pass the bong dude

[@rich1051414]

I find it comforting to know my existence, no matter how small and insignificant, will have a significant impact on the future.

[@xaifer2485]

You're insignificant comment wasted 1 minute of my small life thanks

[@shagerg2238]

It’s crazy how chaos relate so much to harmony

[@jasonpowell1445]

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

[@Ked778]

People watching this video after 1000 years. "Lmao this guy is a caveman"

[@slkjvlkfsvnlsdfhgdght5447]

pretty much

[@daringcuteseal]

Houseman*, people in 3000s won't live in house anymore

[@reymichaelsungazornosa4040]

@@SirLoinBeefsteak it is subjectively funny

[@SirLoinBeefsteak]

@@reymichaelsungazornosa4040 who are you talking to you? You keep deleting your comments

[@oddode7796]

we dont call the past scientists/philosophers cave man we call them the founding fathers or the contributers to a certain knowledge

[@therealestninja]

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

[@americanpatriot1717]

💞This is by far the BEST Butterfly Effect video I have found. I’m bored with the other Butterfly Effect videos, they have no science behind them. I have searched for videos looking for the “Science” behind it looking for equations and you zeroed in on it!! You dug further into it! Thank you!!

[@slevinchannel7589]

Call me silly, but i just want to do my fellow Science-Lovers a Favor, so excuse the Randomness but here you go, have some warm Recommendations, cause the Learning never Ends! -It’s ok to be smart. -Professor Dave Explains. -Krimson Rogue. -Cynical Reviews. -Michio Kaku. -And the arguably Best for Last: Hbomberguy! (The best at being Unbiased on all of YT.)

[@mattmatt516]

How I feel watching Veritasium's more nerdy videos: "I like the part where he said the things about that stuff! Nice." Cool video for sure though!

[@xdh2071]

I was just looking for Travis Scott’s song and I ended up watching this...

[@adamyasingh8519]

Haha bruh same

[@dhipu7581]

Samee

[@dhipu7581]

Maybe this was the butterfly effect

[@death7178]

FOR THIS LIFE I CANNOT CHANGE

[@andrewm.9716]

@@death7178 Whaat,.. could he have been talking about the chaos concept that the future is fixed and we just have to wait for it to manifest itself. MINDBLOWN.. lol

[@JaseewaJasee]

your practical approach to this subject is just what i needed!

[@bjiirn]

10:11 I want that as an screensaver! That looks awesome on my OLED TV!

[@youngaspireify]

Odd flex, but alright.

[@jonathanalexander9562]

Omg... What if our universe is just somebody's screensaver?

[@jake8217]

@@jonathanalexander9562 can't wait for that Shithead to move that damn mouse.

[@itISafakechannel]

@@jake8217 As with Thanos, our entire universe will be erased with a simple click.

[@jonathanalexander9562]

@@jake8217 Then our universe would end, we would end :c Why would you want that? haha

[@ninjaguysith]

I came here for a movie analysis about Ashton Kutcher with no arms, but instead, I came away with my mind blown. Thanks.

[@junebug115]

Same

[@qwertyTRiG]

There's a beautiful essay on Chaos Theory as applied to ecology in the book It Must Be Beautiful: Great Equations of Modern Science. Highly recommended.

[@royfablooo2810]

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

[@dripdrops3310]

gonna binge watch this channel, not gonna lie

[@devourer8472]

Done watching?

[@ornessarhithfaeron3576]

Nah I finish tomorrow

[@purvapawar8977]

Every decision you have made in your entire life has led you to reading this comment.

[@RB3Vids]

Purva Pawar yea, cause free will is an illusion

[@mimi22629]

🧠

[@MrBenzcdi]

And the next...

[@kentmurrmann8637]

No don’t do that to me

[@TheMegaEzio]

Then this comment is a "Fixed point attractor" of our lives o.O