Chaos and Butterfly Effect - Sixty Symbols
HTML-код
- Опубликовано: 24 июл 2011
- The butterfly effect is associated with the unpredictable world of chaos... Two of our physicists have a chat about it.
They are Laurence Eaves and Mark Fromhold.
Visit our website at www.sixtysymbols.com/
We're on Facebook at / sixtysymbols
And Twitter at #!/periodicvideos 
Наука
I like Bradey, he's a nice guy. I respect that he does so much work with the sciences!
Of all the videos I've watched with him questioning and participating, he truly will be a top scientist/physic/math etc..some day. Young but brilliant, and a great attitude.
you guys continue to blow me away consistently - this is one of the best videos i've seen in a long, long while
Thank you so much for taking the time to make these! Keep it up!
Fascinating material, with engaging speakers and nice visual aids.
Thank you all for the time and energy you put into these.
Sixty Symbols along with any other of Brady's productions really know how to make things interesting. They make me excited to be going back to school.
8:36 omg i remember that toy when i was little and i've never realized how chaotic the toy was until now.
As an electrical engineer I love these videos and they have almost made me wish I had been a physicist . . . almost. Now I'm going to go back to designing flying cars.
So say we have a boy and a girl who are both very simple, would their relationship be uber complicated?
You understood chaos. Congratulations :)
I absolutely love these videos. Thanks ever so much for doing them sixtysymbols.
By typing this comment I am changing my entire life and everyone else's life who will ever live on this planet
Trippppyyyy bruuuh
Thanks for nothing.
This past year has been pretty lousy. I now blame you... 😋
48 people liked your comment by clicking left-button of their mouse. They moved the mice to click on your comment. By moving and clicking they wasted some electrical energy. This energy came from generators in dam or in hydroelectrical systems. The cables all the way from generators to home power outlet and to computer and to mouse increased the temperature a little bit. This temperature increase will cause a wind next year.
@ I burned five calories reading your reply, causing me to be slightly hungrier. When I sliced off a piece of banana bread that my daughter just made, it was slightly bigger than it otherwise would have been. I fumbled it, and as it fell to the floor by my foot my voracious canine lurched forward and accidently took a bite out of my big toe.
I blame... Chase Walker.
You killed stan lee how could you
Thanks for producing these. I always learn.
Very good introduction to the study of chaos.
@tapelegs thanks for taking the time to watch them!
Great Video! Have you ever thought about making a video about strange attractors in chaos theory? I'd love to see that one and I was a bit surprised not to see it in a video about the butterfly effect.
i love how, unlike many other videos on youtube, the cameran is not stupid. props for another very informative video!
@TheBentastic great to hear and thanks for watching
So the butterfly effect is nothing more than just ultra high sensitivity. But it's still much different from randomness.
kim gysen without having the initial conditions, the secondary initial condition might be random I suppose
I think you might need to alter your idea of randomness. The same applies to rolling dice or flipping a coin. We say these are “random” but really they are perfectly predictable given initial conditions. Few things are truest random, like collapse of the wave function assuming no underlying hidden variables
Good stuff, as always. Thank you.
Never seen a double pendulum built that way.
Great video Brady.
Can I ask a question? Are the tiny variations that affect something like weather predictions computable in principle, or are they so small that the uncertaincy principle would prevent us from ever having a complete and 100 reliable model?
Thanks for your efforts across all the Nottingham science channels.
my goodness i love this channel
Very interesting, and some very good explaining:) Thank you.
Upon watching this video the first thing I thought about was your "Magic Number" video that you posted a while ago Brady. You should link the two videos to each other because they pertain to the same general concept :D
G'day,
Thanks for yet another fantastic video.
Really interesting video! And we got to see Brady doing an experiment!
And also the semi-circles he drew are realy good!
I'm not sure why but I found this one of the Sixty Symbols videos particularly great! Well done explaining, nice examples, and gee the professor can scetch :o
Indeed keep on making work of this, the result is great. fascinating!
~Nout
I love your videos, thank you
This was my favorite video yet
Can you make one on quantum physics
these videos are amazing.
the double pendulum looks like two stars doing a gravity dance
I say the study of chaos is just an in between for mechanics and statistical mechanics/thermodynamics. For thermo, you give up using mechanics (Newton's Laws), because it's impractical to keep track of the motions of so many particles (on the order of Avogadro's Number), so you use statistics instead. For the study of chaos, the system is not so complicated that you have to completely give up, so you can do some mechanics to predict its evolution, but the result is not going to be simple.
Brady, your hair looks so amazing in this video!
awesome channel. keep it up!
This relates to your video in one obvious way at least. You said when you combine two simple machines you completely randomize the result. Or in similar words. After thinking about it I realized you may have answered my question already.
Chaos is a matter of perspective. Small things can have enormous impact that we may not be able to always follow yet since we're not all knowing. We tend to focus more on what we can figure out with our minds than the subtler energies that we can feel naturally that would open our minds up to understand things on new levels allowing us to gain new perspectives. I believe when we enjoy the chaos we can see the order in it more easily and predict things more easily too. And at that point what does it matter, just sit back and enjoy the ride. :)
I have never ever been bored in any sixty symbols video. And I'm just a regular Joe.
Can you do an episode on the Lyapunov exponent? I'm still having trouble wrapping my head around that one.
I have a request for something sort of related to chaos theory. Fractals.
I've used fractals as wallpapers on my computers for a few years now, and i love their self-similar patterns. In particular i like mandelbrot and cantor. I also like just watching 3D representations of various fractal sets.
Do any of the professors have fractal wallpapers, or work with fractals?
I've always thought of this, and could never explain it to anyone. This video explains it.
@weberbeat to quote Richard Dawkins in The God Delusion:
"I must admit that even I am a little taken aback at the biblical ignorance commonly displayed by people educated in more recent decades than I was."
AND
"I have probably said enough to convince at least my older readers that an atheistic world view provides no justification for cutting the Bible, and other sacred books, out of our education."
I like making Bibledex videos. I learn stuff. But just don't subscribe if you don't like them!
I had Dynamical Systems two semesters ago. The chapters covering chaos were extremely interesting.
Very interesting, but also entertaining!
Working out in the gym watching this, hell yeah who needs music vids
Lovely stuff.
Re: ~9:50 and onwards: In the rectangular case you are not guaranteed to get a periodic orbit. In fact the probability of getting a periodic orbit for any randomly chosen angle is exactly zero. A periodic orbit will only happen if the inclination of the initial shot direction in units of one side of the rectangle is a rational number in units of the other side of the rectangle. Since there are infinitely many irrational numbers for every rational number that means the probability of choosing a rational number and thus a periodic orbit is exactly zero.
the butterfly would have the most effect at the beginning of a system, or as a tipping point to push a system into a new one, so in a way it could possibly be the most significant single thing, based on being in the right time at the right place.
I liked the trail effect with the long exposure shutter to show the chaotic motion of the double pendulum.
If you have AfterEffects you can make a very effective trails using the 'time echo' filter, which I have used to great satisfaction for tracing the path of my sister's crazy dog's tail...
Because people revel and comfort in the thought of being right and knowing, even when they might be wrong, especially when it comes to the unknown and unpredictable. it's just best to drop angry arguments and keep an open mind, like you said.
Brady, you're awesome.
Why are none of the comments about chaos theory? >.<
P.S. Great video! 10-ish minutes each day of physics from this channel really adds up!
@Etaukan you're welcome... comments like yours make it much more fun to do!!!
Perhaps deviating slightly from the theme of the video, but i've got to say, that's some of the best freehand straight line drawing ever...
@theshiz0 glad you think so
then there would be friction and it would end up in a motionless state somewhere on the table. the location on the table would depend on how fast it was spinning and how fast it slowed down. I don't know if that's considered chaotic since it comes to an end. good question though!
@Pioucopter In the long run it matters as well, perhaps not directly on that particular tornado a month later but the effect of the butterfly flapping its wings instead of sitting still will have numerous other consequences (for example a bird flaping its wings to catch it or not, etc.) that might produce small and large effects as time progresses. In that sense the universe is very deterministic as everything depends on that which went before it, or at least appears to be.
Thats quite amazing,the more you know!!
That sprinkler is the most hilarious thing i have seen in a serious physics lesson
When I think of chaos, I think of having no idea what will happen.
It seems of these guys, chaos means it becomes hard to predict what will happen.
@sixtysymbols I had a question though. Is a system "chaotic" simply because to us it is too difficult to assign a predictive framework to? To a hypothetical species with superhuman brains, would the motion of a two pendulum system be as simple and predictable as a one pendulum system is to us? Or, would even absurdly small measurement errors eventually propagate, causing the system to become unpredictable given arbitrarily large amounts of time, regardless of who/what is doing the measuring?
@madprocess hmmm, maybe Brady said that so the "popular definition" could be dealt with?
When you stir a cup of coffee, and are trying to mix in some sugar without sloshing and burning yourself, you have to alter the pattern of the stir to keep from setting up waves that amplify from recurring patterns, or spinning that eventually creates a whirlpool which would also slosh out. Similarly, if your don't vary your stride, or change your routine you end up with repetitive motion injuries, or decreased mental flexibility. Is there some concept that relates all of these together?
you just made me late for work...
worth it
Guys, how about you focus your discussion on butterfly effect instead?
Great video, Brady! I wonder where do you get the ideas for those videos. Are these topics suggested by the viewers?
Also glad the professors have spent their time talking about science. I like academic environments, these people are usually fun to hang out with.
The long exposure double pendulum part was epic.
4:40 mad top spin on that cue ball Brady! I'd hate to be £1m against you in a billiards game!
Brady is a billiard master! You should really do a video that has a geologic premise to it!
Can you guys do a video on chaos and fractals/ Mandelbrot sets?? Please please please?? lol
@SonOfNye thank you
the different positions of the red balls after breaking with the cue ball not an example of chaotic motion. II caused by the small variations in the placement of the red balls in the rack, the angle which the cue ball hits, the force of the cue stick hitting the ball and many many other variables.
What is the relationship between sensitivity to initial conditions, thermodynamic (or information) entropy and Gödel's Incompleteness Theorem?
I had one of those flower sprinklers, it was marketed as a summertime children sprinkler. One kids would run through to cool off.
I used it once, then it sat in the yard until it grew old and worthless. Neat concept though.
Thank you!
0:34 it is said that because a butterfly is so insignificant it doesn't really have an effect.
Correct me if I'm wrong but my understanding of the mathematics of chaos means that even though it may be a tiny tiny variation - that doesn't really matter. A completely different result is still obtained?
Thumb this guy up. This is a really interesting question.
Does the drawing take into account the spin of the ball? A billiard ball could be rolling forwards whilst having a slight spin, so when it hits the cushions it could simply spin until it stops. Alternatively, it could cause the ball to roll up the cushion and onto the floor, where it will generally roll under the fridge or other hard to access location.
The ball could also be rolling forwards, and upon losing velocity, rolls to the left or right and backwards for the perfect snooker.
It's about monthes now that I watch your videos and realise I didn't even subscribe because I was so sure to have done it by reflex... Let's do it now... XD
Anyhow, nice video, very clear explanations, as ever.
The editing in this video is demonstration of chaos. ;)
As far as I have understood this video, in order to achieve a chaotic system, you need to couple two or more systems, for example the coupled pendulum. But what about the Bunimovich stadium? There is only one billiard ball, one system, and it isn't coupled with anything, is it? Is this another case of chaotic motion?
is it ok to say that if you get a measurable effect from a measurable cause, then you change the cause from 1 unit, you measure the change on the effect, you get a number which could represent the complexity of a system? if it's the case, does that mean its possible to compare complexity of totally different systems. Thank you for answering, Y. B.
Dammit I have a thermodynamics exam tomorrow....reaaaaaalllly need to stop watching these videos..
I can't stop!
@Aviatorsmith Well not necessarily, because in certain instances the variation could be the result of such incredibly small changes that the uncertainty principle would prevent you from accurately measuring the initial conditions from which you would make a prediction. Even a small degree of uncertainty would increase exponentially with a meager increase in the number of interactions taking place after the initial conditions, so that's not at all unreasonable.
@oORoBeOo check out our sixty symbols website... we started making videos about sixty different physics and astronomy symbols... we've now done more than 130 I think!!!
i love this video! The Butterfly thing is very relevant to biology as well = )
What if you had the original pendulum you started with; with the short arm and the long arm and then you ADD a third pendulum that oscillates forward and back while the other two oscillate left and right? Would have any kind of affect on the other two?
"It's another double pendulum system because we've got one pivot here for this tube and another one here for the head. The motion's really the same as this double pendulum". Sure, but there's also a very interesting difference between that yellow double pendulum with its rigid arms and the garden sprinkler. In the latter the head is linked to the water feed tube by a length of flexible hose, which in the video you can see writhing and bending this way and that like something possessed when water is pushing through it. What we have here is perhaps describable as not a double but infinity-tuple pendulum, since there are a huge number of indeterminately located pivots along the flexible section.
The point is that by changing the initial conditions slightly, maybe the angle by 1/100 degrees (I'm just making an assumption) then you will end up with a drastically different configuration. This is unlike a simple pendulum, where if you vary the initial conditions, such as the mass or height of the pendulum, the resulting motion is still similar, thus stable.
I like the flower sprinkle!!
Can you do a video on superconductors? Thanks!
Nice top-spin Brody
@natemcgraw How different was the rest of your day based on that small change in initial conditions?
That's a good question, it's like what would happen if i woke up a minute later than I did today. How would the rest of my day change from what I am experiencing right now?
@pbezunartea It's not much of confusion between the mathematical term and the daily use.
In the pendulum explanation it was the mathematic, but the snooker example was the chaos I was talking about, and the challenge to repeat perfectly of the shot, had nothing to do with the mathematics, only with the disability of use to control all the parameters.
The butterfly affect came to show the order in the causal system, which nothing is random. Not even the quantum world.
wow, interesting stuff, I liked it
(1)I recall watching smoke tendrils from a campfire wen I was 6 years old, pondering this precise subject matter (minus all the vocabulary; I couldn't talk then) Imagining the shape, position and speed of all the eddie currents, both what I see & can't see, the effects of my hand motions has on the shape, position speed of the tendrils, concluding that even the movements of Mom's finger, tapping on the table several meters away will have the same effects many minutes later, but indiscernable-
Regarding the weather: What about Navier Stokes equations as an unsolved math problem? Does that not pose problems too? I mean, we have compressible turbullent flows, with different compositions, evaporation, CO2 emitions, radiation been absorbed at different rates depending on compsition... Predicting local weather would mean Navier Stokes would not bee locally solvable?
You would have to take some very complex calculations that will show where it is likely to go, then factor in your uncertaintity principal. The uncertainty principal states that no measurement is perfect. That means you have to add up all the uncertainty factors of energy put in, energy lost per bounce, uncertainty in the mass of both objects and distance traveled. You may be able to predict for a short distance where it will go, but as the uncertainties add up, your predictions begin to fail
Great job being the strange attractor, Brady. Computers do shave a huge chunk off the chaos pie.
More simply explained: Something with infinite possible outcomes can be influenced at an atomic scale. Something with minimal possible outcomes can be much easier to predict.
+Pablo Gringo Infinite outcomes are not real, because the world is divided into bits ( quanta ) but the possible outcomes can quickly become so large, as to be irreducible ( unable to be compressed ) by anything inside of the system, which means that it will become a chaos, for anything that isn't a clone of the "experiment".
These events can not be explained simply. They are unique, and full of q-m probability. You can write libraries of Babel, larger than Graham numbers about this "complex emergence", which would result in alternative ( real ) Worlds, and that would only scratch the surface.
Also. To prove the "minimal possibility", is extremely hard.
It's impossible for any system containing more than a handful of particles, and I think that's tied to Feynman diagrams, and the limitation of what is currently calculable.
Include a Universe with more than "a couple" of particles and it's uncharted territory, if any certainty is required, with the added uncertainty that any knowledge has a "physical cost" that feeds back into the "physical reality", which is ignored in standard q-m, but can not be ignored when constructing Worlds.
I.e. In q-m, measurements finalize and effect uncertainties,
but in World creation the calculation ( in itself ) is a form of measurement and creation, at the same time.
There is currently no proper framework for irreducible mathematics.
If you look closely ( and read between the lines ) you can see how this is tormenting every Scientist that touches the subject, and how most people "brush it off" with arguments like, - Why worry about something, that can't be calculated, but in reality the entire Universe is a congregation of "butterfly effects" that also goes through transitions where "matter creation" is required, leaving thermodynamics, energy conservation ( and every equilibrium model ) in the garbage bin.
I was just simplifying the theory. I knew all that.
@@server1ok hol' up, what you mean quantized qorld?
@@DheerajAeshdj Search Google for "Achilles and the Tortoise". Achilles can never catch up to the slower runner in a strict "geometrical way" but since reality is digital i.e. quantified into some kind of segments ( that are still mostly unknown ) at the QM level there are processes that allow for distances to be overcome and for objects ( or particles ) to overtake a peer and not always by aggregate speed but also by jumping or bypassing "particle spaces". And yet, the standard view of Gravity is the only modern framework ( that's still in use ) that doesn't allow for a "fundamental movement" since it's forbidden to cut up Gravity or perform any complexities higher than the standard expansion or contraction of the Universe. Standard Gravity leads to a massive simplification at the macro scale but also immense difficulty at the smaller scale since everything is floating without any set values i.e. "infinite resolution" and particles that can cluster together infinitely and not only inside of black holes. The black hole dilemma of standard Gravity is an issue everywhere and at all times. Bose and Einstein set up a mathematical framework that could successfully ignore this issue but it hasn't been solved. It hasn't been postulated in the right way. I.e. We don't even know what to ask.
one great example of chaos theory is the amusement ride TILTA-WORAL. when I was a kid me and my friends loved this amusement ride because it was unpredictably. the other rides got boring because you new what was coming in the next second but not with TILTA-WORAL. I Later saw an article in Scientific American on chaos theory with TILTA-WORAL as an example. a lot more fun then pendulums