How Chaos Theory Unravels the Mysteries of Nature


If someone showed you a swinging pendulum—like
this and asked you to calculate the pendulum’s position at some point in the future, you
might think it’d be relatively simple. We should be able to predict that with the
known laws of motion, right? But this calculation is actually so complicated
that it requires a relatively powerful computer. And even if you did do this calculation, and
then are offered slightly different initial conditions, you would think that the output
might also only be slightly different. But instead, you get….chaos. Specifically,
deterministic chaos. See, as humans, we’re always trying to know
more about how our world works, so we make models. For example, we have a bowling ball. We know the weight of the bowling ball, the
effect of gravity, the density of the air, and the height of the balcony from which the
bowling ball is to be dropped, and we can put all those things together into a system
of equations that we could use to tell us things like how fast the bowling ball would
fall, or the force with which it would impact the ground. That means we can also reasonably predict
what might happen if any of those variables were to change. This is a deterministic system—the behavior
of certain variables is determined by their known characteristics. But not a lot of the
world is like the bowling ball example. It’s a whole lot messier. Take the weather. Just think about all the things that go into
making weather—temperature, humidity, wind strength and direction, rotation of the earth,
I mean the list is exhaustive. We do have models for how all these many variables
behave, but a perfect weather prediction would require highly accurate measurements of all
of the contributing variables over every square inch of the piece of atmosphere we’re looking
at. In a system like this, little measurement errors can result in HUGE fluctuations of
our calculated result. Tiny changes of the input mean a LARGE variation
of the output. Now don’t get me wrong—the system is still deterministic. The variables behave the way we expect them
to based on their physical properties, so it’s quite different from something that
is ‘random’. But it’s highly unpredictable and subject
to vast variations. The system may look disorganized, but there
is a set of rules that apply to the chaos. Deterministic chaos—you may have also heard
of it as chaos theory or the butterfly effect. Weather is actually how chaos theory was first discovered. Edward Lorenz, a meteorologist at MIT, was
performing an early weather simulation in the 1960s, when he took a shortcut and used
input numbers rounded to the nearest thousandth. He expected to get slightly different results
from the version with the full numbers…but what he got instead was completely different. His
investigation into this unexpected outcome led to the birth of chaos theory, or the idea
that chaotic systems magnify even the tiniest changes in the component parts of that system. Chaos can make it impossible to accurately
predict the behavior of such a system at a faraway point in time. You know how you like to complain that the
weather report is always wrong? Blame chaos. We can never measure the initial conditions
precisely enough to accurately predict the weather past a certain point in time. That tiny bit off that we will always be is
enough to produce a wildly inaccurate prediction as the system progresses. If sensitivity to
initial conditions is one defining factor of a chaotic system, the other is something
called a strange attractor. Which is just as odd and exciting as it sounds. Lorenz and his team found that when they ran
the weather simulation over and over with slight variations in input resulting in vastly
different results, when you visualize these patterns, the paths never overlapped. But at the same time, the paths seemed to
circle these empty areas of space—this pattern is an example of what’s called a strange
attractor and one thing that differentiates a chaotic system from random behavior. With
Lorenz’s particular chaotic example, the visualization starts to look a bit like a
butterfly. The phrase ‘if a butterfly flaps its wings
in Brazil it could cause a hurricane in Texas’ is not what the theory is named after, it’s
just a memorable example. This first chaos work required some innovative
computing, and although Lorenz typically gets all the credit for being the ‘father’
of our modern chaos theory, he actually did this work with two young mathematicians, Margaret
Hamilton and Ellen Fetter. Hamilton later went on to develop the math
that got Apollo 11 to the moon, and is credited with coining the term ‘software engineering’. So many natural systems are chaotic, like
the climate as a whole, the dynamics of clouds, population dynamics, the patterns of the stock
market…the way your milk swirls into and combines with your coffee? That’s chaos theory in fluid dynamics. These
systems may be chaotic and have seemed impossibly daunting in the past. But the math of chaos theory is now small
potatoes to the huge supercomputers that we can use to calculate the progression of chaotic
systems like the climate with more accuracy than ever before. Even outside of modeling, chaos theory proves
exceptionally useful in other fields…like encryption. And as we move into brave new worlds
of exascale computing, quantum computing, machine learning and other kinds of artificial
intelligence, it’ll be exciting to see just how far we can push chaos theory to help us
predict the behavior of chaotic systems…essentially looking further into the future than we ever
have before. If you want more on unusual math, check out
our video on fractals over here, and subscribe to Seeker for more deep dives into tangled
topics like this. Let us know what math subject you want us
to tackle next in the comments below, and as always, thanks for watching.

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100 thoughts on “How Chaos Theory Unravels the Mysteries of Nature

  1. Hi, thanks for watching! Want to learn more about supercomputers? Check out this video: https://youtu.be/NU3Mz6R0idQ and let us know what you'd like us to cover next!

  2. Neat. I liked the video but one thing I'll point out is that list of weather variables is far from exhaustive. But it would be exausting to describe and model all of the factors to which I know nothing about. The wording in the video bugged me.

  3. Maren you are in an incredibly creative face but the important thing is that you are happy I do not like so much to put my intellect to accept a chaos theory I think that there science loses the soul and that does not make you happy microbiology for medicine and renewable energy is much more human there science approaches life by being happy

  4. Maren I think there are limits to creativity and those limits have to be put one so as not to lose your heart the human this video you made makes me fall in love do not let them manipulate you in this video I see the most beautiful woman I saw in my life no let them jealously abuse you this is another item that with your inner beauty you can inspire for the good many humans

  5. Maren you are very young there are limits where I think it is better not to expose the intellect with time you will realize that the human behavior of greed may want to submit your beauty just for envy look at this movie you have to be free but with certain moral limits

  6. Maren is such a catch! So smart/inquisitive/funny and least we forget she's B-E-A-UTIFUL! #SEEKER #NerdCrush
    Much love from #Bradenton #FL !

  7. Fibonacci sequence can be found in all of nature and the universe….. So not chaos per say but intelligent design….. Or say God's sequence by his hands that holds it all together!

  8. Hmmm, I just realized that the reason I never noticed any deviation in the weather forecast has been because instead actually looking outside to know the weather, I would just look at the forcast.
    kinda a self reference on that one.

  9. Chaos THEORY is just that….. for now…. Like gravity and dark matter. Once completely figured out it can all be used and predicted. It'll just take a few more years of tech innovation and discovery of more complex math.

  10. I feel like Seeker tells their workers to explain things with the most physical movements possible. Great vid tho

  11. If supercomputers can already carry out such tasks then imagine quantum computers when coupled with AI can pave toward breakthrough through the roof.

  12. I love everything about you. Your voice, your looks, your dressing Sense. Please please talk to me. I don't follow any celebrity but you

  13. Apart from the strange attractor aspect, chaos theory seems to be describing the obvious.If you change a small condition, cause and effect are bound to result in larger and larger differences over time.

  14. This reminds me a lot of tensors in calculus. The amount of information (and it precision) will give us a more correct answer.

  15. Patterns of strange attractor seem to circle empty patches of space? So they're kind of similar, since their path is similarly shaped, yet not the same since they never coincide or interfere? Not sure I fully comprehend…

  16. #seeker
    "STRANGE ATTRACTOR" = GLOBAL ELECTRIC CIRCUIT (high energy charging / low energy discharging)
    VIA BIRKLAND CURRENTS (electromagnetic filaments from the sun)
    The earth and all it's concentric atmospheres act as a multi layered capacitor regulating solar driven electical potential.

    Hopefully your future videos will acknowledge this primary electrical force of nature instead calling it a "strange attractor"
    It's really not that strange when you understand the work of Hannes Alfvén, Christian Birkland, Anthony peratt and their work in Plasma physics / Plasma cosmology.

  17. Can anyone explain the milk example..like how chaos theory effects fluid dynamics and does solubility has an effect on it?

  18. Margaret Hamilton is A FUCKIN BOSS!

    Between YT and Reddit, I've heard about her weekly for the last 2 months, she's a stud, female version of most interesting man in the world! Clone her!

  19. Impossible to predict weather however we know what the climate is going to do in the future and exactly what the cause is , really ?

  20. It seems to me that another system that exhibits deterministic chaos is the brain. Trillions of neurons which, when observed, can be shown to have patterns on a macro level but can act in an extremely unpredictable way. And with a high enough level of resolution in measurement, we could start to decode the randomness just like if we measured the properties of every cubic meter of the atmosphere to predict weather more accurately.

  21. Have you read “A Sound of Thunder” by Bradbury? I’m pretty sure that’s where the butterfly name comes from

  22. I remember when I had my first beer… I was in high school and didn’t care about math, nine years later here I am… CHAOS (theme music plays)

  23. Why must it be the case now that I see no Seeker videos for over a week, and then several appear at once… And I'm burdened by a backlog to watch. Old YouTube has my heart.

  24. Like how a stone that blocks a small water springs change how the river will flow and where the water will end, same stuffs. Sort of

  25. In fact, it’s deterministic not chaotic. A misnomer. We are not controlling the weather or anything else for that matter on the sub atomic scale.

  26. Chaos Theory is based on 2 dimensional highfalutin theories and the Discovery of the Duo phi Vector System of order has been rejected and suppressed. How come intellectuals reject perfect order in 3 dimensional reality ? You keep hyping up chaos with lots of highfalutin talk but why not prove the Duo phi Vector System in 3D reality that can give us 3 phase sine waves , sound waves and DNA infrastructure is not correct ?
    Maybe your computer can tell us why 3d Geometry in practical reality is not important and why intellectuals should only focus on Chaos in 2 dimensions as they have done for about 6 decades.

  27. So you put in a computer and it doesn’t look right well that’s cause it’s not in real life it’s a computer ohh surprised

  28. In Kinesiology (specifically in Motor Development) we actually use Chaos Theory and Dynamical Systems Theory to try to explain how a Human being develops motor skills…

  29. If you would travel back in time to the dinosaur age and just kill one diinosaur, the whole earth as we now it today would be completely different

  30. You are so in balance, the chaos of the reality is a mess, but watching you is like things suddenly get together in a pleasent way.

  31. I was something like 15 years old when I realized, out of my own, Chaos Theory and how sensitivity in initial conditions can make big changes in future results

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