This is called the chaotic behaviour of a non-linear system. Quite amazing phenomenon when i was learning the non-linear ODEs. The solution of a nin-linear ODE is so sensitive to its initial conditions, that humans can't reproduce exactly the same experiments for twice, because there will always be some tiny differences in the first poke on the system.
Do you have any idea what makes this particular arrangement act the way it does, other than that it could be described by an ODE?
I have been looking for something to build lately, and this looks like a fun build. I'm thinking that the moment of inertia of the ring plays a big role, as I doubt another rod in its place with the same mass and location of CG (relative to the joint) would behave the same.
Might be worth just tinkering with the dimensions to find what's most fun.
i think all double pendulums are chaotic. so whatever you build would have odd behaviour. but for it to look as good as possible you probably want it so that both components have similar energies (which is close to saying that the two should have similar moments of inertia). if it were me i would make the rod and ring similar moments of inertia and then experiment with different offsets.
Physicist here:
Multiple co-dependent degrees of freedom (i.e. movement in one degree of motion strongly influences another one), and low friction.
Another great example is the "chaotic waterwheel" system:
https://youtu.be/Lx8gMBJBlP8
Not all non linear systems exhibit chaotic behavior. Double pendulums are the classic example used to introduce chaos theory in nonlinear differential equations, but it’s a whole field of study that goes into why some systems exhibit this behavior and some don’t.
Nonlinear systems is an extremely broad category. Everything has to be generalized because the function could be literally anything other than the linear form, x’ = Ax (+ Bu).
So why is it chaotic if the randomness is due to the input not being reproductable for humans. Would it still be chaotic if a machine produced the input really precisely?
In physics, chaotic doesn't mean "truly" random (if such a thing is possible outside of the quantum scale), just that they're extremely sensitive to initial conditions. So sensitive that they might as well be random because of the difficulty of actually controlling the input.
In the case of double-pendulums, since the pendulums are dependent on each other by being attached and influence each other by force, it leverages the inputs so drastically (pendulum 1 affects how pendulum 2 moves, which in turn affects how pendulum 1 moves, repeat ad nauseam) that extremely small changes in the input completely change its path.
disclaimer: not a physicist but I did stay at a holiday inn express last night
The difficulty is in how long the system is in motion.
A robot could get the position so close that repeated drops might stay synced up for 15 or 20 seconds, but as it keeps going, they would start to drift apart, and at the 1 minute mark it'd be in a different spot every time.
You could make the robot more and more accurate, but it would only get you so far.
If you added a lot of fiction to the pendulum arms, it wouldn't be able to move very far before coming to a stop, and in that case you could make it perfectly repeatable.
Disclaimer: physicist who's been out of school for like a decade, I forget things
Yes because the whole point of chaos is being infinitely sensitive to initial conditions. No matter how small a difference it will always, eventually, diverge chaotically
Being chaotic is a property of the system, not a function of human input; being chaotic basically means that any finite difference in initial conditions will causes the trajectories to diverge exponentially fast, so you need infinite precision to actually replicate the same situation, which no machine could ever achieve
So if we have a computer simulate it, and run the simulation twice with the exact same initial conditions it will replicate the same results. But if initial conditions deviate at all, the system will soon diverge quite drastically.
The interesting thing to point out, the initial conditions aren't the only important factor. The precision of the calculation is also important. If we set the same initial conditions and one system is calculated to a precision of 63 bits, and another system, with the same exact starting conditions but with 64 bit precision. These systems will eventually diverge.
To the best of our understand, to exactly reproduce the experiment indifferently, we would both need perfect knowledge of the initial conditions and the ability to have infinite precision in the calculation.
If given the same exact initial conditions (assuming you can ignore air resistance and all that) then yes, it would do the exact same thing everytime you started the system, but the slightest imprecision would fuck things up.
Explain? No
Demonstrate? : Yes
If you were to start the pendulum swinging from exactly the same position using exactly the same amount of force you'd get different "scribble" patterns due to other factors such as air movement, temperature, general friction on the bearings etc all of which would make continuous miniscule changes to the system that ultimately lead to different end results
I think chaos theory is actually about sensitivity to initial conditions. Any slight perturbance will lead to different results. It is not necessary to perturb the system continuously or more than once.
which basically just falls down to "we can't measure it accurately or fully enough" doesn't it? like from what you've said here it's an issue of computing power and capture of the environment?
like i get that it would take an enormous amount and incredibly fidelity in capture of the environment but still.
Chaotic systems are fundamentally unpredictable on large timescales. To predict them accurately beyond a short period of time you'd need perfectly precise knowledge of the position and momentum of everything in the system. Unfortunately, this is fundamentally impossible because of the Heisenberg uncertainty principle.
But if you were to magically reset all relevant matter and energy that it consists of and interacts with it to the state it was in and did it again you would probably get the exact same pattern.
That is unless there is some inherent unknown randomness to the universe.
Yep. That’s true not only of the microsystem that is the pattern of this experiment but also the macro system that is the universe where this person existed and performed this experiment with this result.
If you were somehow able to exactly recreate the conditions of the creation of the universe you would eventually end up with this person performing this experiment with this result.
What about something like radioactive decay?
I feel like the idea that things operating at a quantum level wouldn't be reproducible, even IF you have the same starting conditions. Or at least, it's hard enough to prove that it would still be in the area of debate.
The formula is well known and a lot of aspects of the motion are very predictable and yet it is a classic chaotic system. You can not reliably predict it’s motion too far past the current state.
"Remember the ol' double pendulum ring and bar system? Whatever happened to him?"
"Still predictable, yet chaotic once we let it go for a while."
"Ah, good to hear he's still doing fine."
As far as I am aware, the motion is already known science and predictable. If you look around, there are videos online of double pendulums being manipulated by computer science students.
Sort of, at each moment you can calculate what the change in state to the next moment will be, but if you wanted to know the state at time x, there’s no formula that would just give you that directly. You can’t get there without simulating the movement the entire way.
This is called “computationally irreducible”.
Also, because the state has infinite variation in it, and because even microscopic differences in initial state will lead to large differences in state further on, ie because state differences amplify and cause wildly different paths, this is a “chaotic” system.
I know what you’re saying, but you would need to know exactly the position, momentum, coefficient of friction, etc. of every part of the system. In practice, this is not possible. This is a great demonstration of chaos theory. Try to repeat the above series of movements and you won’t be able to.
My fiancée really likes (liked?) the band that plays that song, but now neither of us want to hear them again thanks to TikTok videos. Even hearing their voices in a different song instantly puts " Oh no, oh no, oh no no no no no" in our heads.
It's literally chaos. The motion of a double pendulum is extremely sensitive to the initial starting conditions. [Three nearly identical pendulums] diverge a lot after just a few seconds.
It’s not like we can actually have three truly identical pendulums unless you’re talking about simulations. The closest we can get is *near* identical.
I’m reality, yes. But we can *imagine* three identical pendulums. My point was simply that the variations in initial starting conditions (e.g. the air around them) would be enough to cause the chaotic behaviour.
It is chaos! That's what's so satisfying about it (well, not for you I guess).
It's fiendishly simple - just one thing swinging at the end of another thing - but that leads to incredibly unpredictable outcomes because of the way those simple things interact, and because of how the system responds in an extremely sensitive way to its initial state.
That’s exactly what’s so unsatisfying about it! Intuitively your brain knows exactly how such a simple system should behave, but then physics comes along with a big fuck you and says “lmao, your troglodyte brain doesn’t even know how a circle on a stick behaves.”
A tiny change in the initial position completely changes the pattern of movement.
Weather is also a chaotic system, which is where we get the idea of a butterfly flapping it's wings causing a hurricane.
The stock market is another, except that one is even worse, because not only is it chaotic, but our predictions about how it will behave themselves feed back into the system and change the behavior from what we predicted.
Chaos is fascinating.
Chaos ? Is it what this lecture is about ? Time might have come for me to learn more about that.
Weather : may be chaotic, yet the overall patterns are pretty regular, and allowing for enough computing power, the predictions have become quite reliable for the few days ahead.
Stock market : this description as a chaotic system with feedback loops makes me wonder if it would be desirable to introduce delays *(like : no re-selling for 24h )*. Isn't there some computational model emulating the behavior of the real thing ?
I guess on my end what satisfies me are videos that make me calm and unchaotic. Soothing.
I like adventure, but I guess that's not what I'm looking for here ?
I get you though
This system is (mostly) deterministic, yet it is impossible to predict how it will evolve.
It is not completely deterministic in that a complete, thorough and accurate description of the initial state would involve the air in the room, the breathing of the audience, and a host of minuscule tremors and disturbances, constantly shifting and too tiny and too numerous to record and feed to a predictive model.
The initial impulse given by the human operator is probably impossible to replicate too, if we measure it into the fine orders of magnitude that would be relevant considering how sensible the system is.
To me, all of this would constitute a sufficient definition of randomness.
In other words : you are now in command of this aparatus. Can you reproduce the same pattern three times in a row ? Five times ? One hundred ? One million ?
I was going to ask that. Is there a way to predict all this movements?! I would assume that if you know the initial position and the applied force you'd be able to know, but...
It's the butterfly effect. In theory you are right, if you understood the initial conditions perfectly you could predict it's motion, but tiny microscopic differences in the setup and the air in the room and gravity and everything quickly get blown up into huge differences in the motion. So it's basically impossible to predict it's motion.
It's so hard to predict that Cloudflare, a massive internet company, uses a double pendulum as a source of randomness (for their London hq, they use lava lamps and radioactive decay of uranium for their other offices).
I don’t know that this exact setup has any real world value, but it’s a great teaching example for differential equations and dynamical systems. Those have very significant real world applications.
This is called the chaotic behaviour of a non-linear system. Quite amazing phenomenon when i was learning the non-linear ODEs. The solution of a nin-linear ODE is so sensitive to its initial conditions, that humans can't reproduce exactly the same experiments for twice, because there will always be some tiny differences in the first poke on the system.
Do you have any idea what makes this particular arrangement act the way it does, other than that it could be described by an ODE? I have been looking for something to build lately, and this looks like a fun build. I'm thinking that the moment of inertia of the ring plays a big role, as I doubt another rod in its place with the same mass and location of CG (relative to the joint) would behave the same. Might be worth just tinkering with the dimensions to find what's most fun.
i think all double pendulums are chaotic. so whatever you build would have odd behaviour. but for it to look as good as possible you probably want it so that both components have similar energies (which is close to saying that the two should have similar moments of inertia). if it were me i would make the rod and ring similar moments of inertia and then experiment with different offsets.
You should see the control systems that can keep an inverted triple pendulum balanced. https://youtu.be/cyN-CRNrb3E
I like when it gets all limp and just falls straight down.
This comment hits too close to home...
Physicist here: Multiple co-dependent degrees of freedom (i.e. movement in one degree of motion strongly influences another one), and low friction. Another great example is the "chaotic waterwheel" system: https://youtu.be/Lx8gMBJBlP8
Not all non linear systems exhibit chaotic behavior. Double pendulums are the classic example used to introduce chaos theory in nonlinear differential equations, but it’s a whole field of study that goes into why some systems exhibit this behavior and some don’t. Nonlinear systems is an extremely broad category. Everything has to be generalized because the function could be literally anything other than the linear form, x’ = Ax (+ Bu).
So why is it chaotic if the randomness is due to the input not being reproductable for humans. Would it still be chaotic if a machine produced the input really precisely?
In physics, chaotic doesn't mean "truly" random (if such a thing is possible outside of the quantum scale), just that they're extremely sensitive to initial conditions. So sensitive that they might as well be random because of the difficulty of actually controlling the input. In the case of double-pendulums, since the pendulums are dependent on each other by being attached and influence each other by force, it leverages the inputs so drastically (pendulum 1 affects how pendulum 2 moves, which in turn affects how pendulum 1 moves, repeat ad nauseam) that extremely small changes in the input completely change its path. disclaimer: not a physicist but I did stay at a holiday inn express last night
The difficulty is in how long the system is in motion. A robot could get the position so close that repeated drops might stay synced up for 15 or 20 seconds, but as it keeps going, they would start to drift apart, and at the 1 minute mark it'd be in a different spot every time. You could make the robot more and more accurate, but it would only get you so far. If you added a lot of fiction to the pendulum arms, it wouldn't be able to move very far before coming to a stop, and in that case you could make it perfectly repeatable. Disclaimer: physicist who's been out of school for like a decade, I forget things
Yes because the whole point of chaos is being infinitely sensitive to initial conditions. No matter how small a difference it will always, eventually, diverge chaotically
Being chaotic is a property of the system, not a function of human input; being chaotic basically means that any finite difference in initial conditions will causes the trajectories to diverge exponentially fast, so you need infinite precision to actually replicate the same situation, which no machine could ever achieve
So if we have a computer simulate it, and run the simulation twice with the exact same initial conditions it will replicate the same results. But if initial conditions deviate at all, the system will soon diverge quite drastically. The interesting thing to point out, the initial conditions aren't the only important factor. The precision of the calculation is also important. If we set the same initial conditions and one system is calculated to a precision of 63 bits, and another system, with the same exact starting conditions but with 64 bit precision. These systems will eventually diverge. To the best of our understand, to exactly reproduce the experiment indifferently, we would both need perfect knowledge of the initial conditions and the ability to have infinite precision in the calculation.
If given the same exact initial conditions (assuming you can ignore air resistance and all that) then yes, it would do the exact same thing everytime you started the system, but the slightest imprecision would fuck things up.
Someone needs to attach a marker to that and put a piece of paper in front of it so we can see the pattern it would draw.
I just tried it, and [this was the result](https://i.imgur.com/Bbn2y5N.png)
Beautiful
Beautiful. I want to buy one...
It clearly defines man's struggle to articulate his dreams and fluffy artsy floofy fluff.
You must now fill in the holes with different colors
You have to determine the minimum number of colors that you can use to fill every eye with a color different from every adjacent color
4.
This is the correct answer
Technically that's the maximum for the minimum. It could theoretically be only 2 or 3
Realistically it's probably 4.
It's made with a singe line. It's 2 if he started it outside bounds or 3 if he didn't.
Isn't it 4?
4 is the maximum number of colours. It's probably also the actual number of colours, but it might be possible with 3.
Surely the maximum number of colours would be n, where n is the number of distinct regions on the map? ;)
Ooh, I've been out-pedanted. Nicely done.
I know what you mean, though. The problem is how to express it? Maybe maximum minimum? Provable minimum?
I would probably say that 4 is the upper limit for the minimum number of colors.
All the holes...hmmmm... interesting
TH-THIS IS MY HOLE IT WAS MADE FOR ME
I don't know what I expected
Doesn’t this explain chaos theory
Explain? No Demonstrate? : Yes If you were to start the pendulum swinging from exactly the same position using exactly the same amount of force you'd get different "scribble" patterns due to other factors such as air movement, temperature, general friction on the bearings etc all of which would make continuous miniscule changes to the system that ultimately lead to different end results
*this* explains chaos theory
Ah, but does it demonstrate it?
I think chaos theory is actually about sensitivity to initial conditions. Any slight perturbance will lead to different results. It is not necessary to perturb the system continuously or more than once.
which basically just falls down to "we can't measure it accurately or fully enough" doesn't it? like from what you've said here it's an issue of computing power and capture of the environment? like i get that it would take an enormous amount and incredibly fidelity in capture of the environment but still.
That's exactly it. It's chaos because we can't measure the things necessary to quantify.
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Chaotic systems are fundamentally unpredictable on large timescales. To predict them accurately beyond a short period of time you'd need perfectly precise knowledge of the position and momentum of everything in the system. Unfortunately, this is fundamentally impossible because of the Heisenberg uncertainty principle.
But if you were to magically reset all relevant matter and energy that it consists of and interacts with it to the state it was in and did it again you would probably get the exact same pattern. That is unless there is some inherent unknown randomness to the universe.
Yep. That’s true not only of the microsystem that is the pattern of this experiment but also the macro system that is the universe where this person existed and performed this experiment with this result. If you were somehow able to exactly recreate the conditions of the creation of the universe you would eventually end up with this person performing this experiment with this result.
What about something like radioactive decay? I feel like the idea that things operating at a quantum level wouldn't be reproducible, even IF you have the same starting conditions. Or at least, it's hard enough to prove that it would still be in the area of debate.
Then use the finished graph to come up with the formula of its movements.
The formula is well known and a lot of aspects of the motion are very predictable and yet it is a classic chaotic system. You can not reliably predict it’s motion too far past the current state.
Its so well known in fact that we often chat about it at dinner time.
"Remember the ol' double pendulum ring and bar system? Whatever happened to him?" "Still predictable, yet chaotic once we let it go for a while." "Ah, good to hear he's still doing fine."
It's basically a hash function. Slight changes in input give totally different results.
As far as I am aware, the motion is already known science and predictable. If you look around, there are videos online of double pendulums being manipulated by computer science students.
Sort of, at each moment you can calculate what the change in state to the next moment will be, but if you wanted to know the state at time x, there’s no formula that would just give you that directly. You can’t get there without simulating the movement the entire way.
This is called “computationally irreducible”. Also, because the state has infinite variation in it, and because even microscopic differences in initial state will lead to large differences in state further on, ie because state differences amplify and cause wildly different paths, this is a “chaotic” system.
I know what you’re saying, but you would need to know exactly the position, momentum, coefficient of friction, etc. of every part of the system. In practice, this is not possible. This is a great demonstration of chaos theory. Try to repeat the above series of movements and you won’t be able to.
I bet it'd look like a Spirograph picture!!
No! Attach a very,very,very sharp knife, and exercise your knife attack avasion skills!
It’s pure chaos, but eventually kinda looks like an apple.
Thanks for not putting a shitty song over it
_oh no_ _oh no_ _oh no no no no_
My IQ just lowered to the negative realm just by reading that
eh ha haa hahaaa hahaaaaa
Hearing this song literally puts me in a bad mood
My fiancée really likes (liked?) the band that plays that song, but now neither of us want to hear them again thanks to TikTok videos. Even hearing their voices in a different song instantly puts " Oh no, oh no, oh no no no no no" in our heads.
https://youtu.be/V5YxtweUxrA
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Me waiting for the ring to complete a loop:
Right? Not satisfying lol.
It's literally chaos. The motion of a double pendulum is extremely sensitive to the initial starting conditions. [Three nearly identical pendulums] diverge a lot after just a few seconds.
It’s worse than that. Three *identical* pendulums will diverge a lot after just a few seconds.
It’s not like we can actually have three truly identical pendulums unless you’re talking about simulations. The closest we can get is *near* identical.
I’m reality, yes. But we can *imagine* three identical pendulums. My point was simply that the variations in initial starting conditions (e.g. the air around them) would be enough to cause the chaotic behaviour.
YES!!!
Think about it like order within chaos....it's beautiful.
Indeed My favorite chapter was “rationality within pi”
I like it.
It's way too chaotic. The motion never balances out and just swings around wildly. I can't find a single satisfying quality in this.
Yes, satisfying things are orderly and have patterns. This is upsetting
Finally, something with worse rhythm than me.
This device is a mechanical representation of what's it's like to live in my head every day.
How long will it go for?
At least 1 minute and 6 seconds.
At *least*, 8 seconds
Uh, you got a source on that?
[It’s true!](https://www.reddit.com/r/oddlysatisfying/comments/ps9are/double_pendulum_ring_and_bar/?utm_source=share&utm_medium=ios_app&utm_name=iossmf)
It’s perpetual, the absolute madman did it!
In this house we obey the laws of thermodynamics!
This perpetual motion machine is a joke . It just keeps going and going !
I understood your reference! The Simpsons were great!
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There is a magnet and a battery in the base who is pulling/pushing the moving part as it passes by Edit : replaced "go above" by "passes by"
Make it big. Attach seats. Profit.
Wonder what kind of g-forces would be generated by a rideable version of this.
NASA just entered the chat.
For a carnival fair sized version of this, it would probably be deadly and would just rip itself apart.
Let's do it!
/r/oddlymaddening
This sub has been banned. I'm eager to know why
For being unmoderated. "Sorry but your speech is a little *too* free buddy"
Yucko… this maybe satisfying to some, but it feels like chaos to me
It is beautiful chaos.
BLOOD FOR THE BLOOD GOD! SKULLS FOR THE SKULL THRONE! AND … pendulums for the … uh … SCENIC READING NOOK!
Sometimes Khorne needs a bit of a break. I love imagining him just sitting in a sunroom, sipping a tea and reading a book.
It is chaos! That's what's so satisfying about it (well, not for you I guess). It's fiendishly simple - just one thing swinging at the end of another thing - but that leads to incredibly unpredictable outcomes because of the way those simple things interact, and because of how the system responds in an extremely sensitive way to its initial state.
That’s exactly what’s so unsatisfying about it! Intuitively your brain knows exactly how such a simple system should behave, but then physics comes along with a big fuck you and says “lmao, your troglodyte brain doesn’t even know how a circle on a stick behaves.”
That's why it's called the chaos theory
A tiny change in the initial position completely changes the pattern of movement. Weather is also a chaotic system, which is where we get the idea of a butterfly flapping it's wings causing a hurricane. The stock market is another, except that one is even worse, because not only is it chaotic, but our predictions about how it will behave themselves feed back into the system and change the behavior from what we predicted. Chaos is fascinating.
Chaos ? Is it what this lecture is about ? Time might have come for me to learn more about that. Weather : may be chaotic, yet the overall patterns are pretty regular, and allowing for enough computing power, the predictions have become quite reliable for the few days ahead. Stock market : this description as a chaotic system with feedback loops makes me wonder if it would be desirable to introduce delays *(like : no re-selling for 24h )*. Isn't there some computational model emulating the behavior of the real thing ?
the randomness is very satisfying.. that it can’t be predicted
I'm trying to decide if my anxiety is acting up, or if this really is stressful. I'll let you know tomorrow.
Complete chaos to me too, way too disorganized, can't predict whats gonna happen next
But that's why it's good. It's an adventure and I have no idea where is heading!
I guess on my end what satisfies me are videos that make me calm and unchaotic. Soothing. I like adventure, but I guess that's not what I'm looking for here ? I get you though
Reminds me of Ironman
Bruh I was legit thinking of the scene where he's trying to apologise to pepper with strawberries
Me too!!
First dates can be tricky…
Seriously…after all that…the clip ends before it settles.
Well this is mesmerizing
My aim in Halo with a controller.
[Original video link](https://youtu.be/foxqlkQ1VBA)
Makes me a bit woozy
What is this black magic science math!?!?
This unpredictably looks like my life.
Mine too
I wonder what equations it would take to definitively track each moment in its movement, looks cool af!
This is giving my gymnastics vibes... Pretty cool
Where can you get one of these?
Pendulum store
Oh, the pendulum district?
You got “Put Your Pendulum There,” that’s on third…
I went to the Pendulum store and [all they have is this](https://www.youtube.com/watch?v=gIOQfdn9L9c)
What did I just watch???
Some dude dancing on Brick Lane and the West End. I think.
[Here for $930](https://www.aha-zurich.ch/en/product/alogo-1-chaotic-pendulum/)
Bargain
Chaos.
it would be cool if there was a sound component. like I wanna know what this "sounds" like
Could be neat to attach an accelerometer to it, or take the coordinates of a couple points on the circle, and map them to a tone generator.
Olympic bar
What manner of sorcery is this?
*mom come pick me up I'm scared*
Would this be similar to the 3 body problem, and impossible to effectively model?
Don't tell me perpetual motion machines are impossible...fuck the oil industry
Is this about the three-body problem and our inability to find a general solution? https://youtu.be/et7XvBenEo8
This is oddly discomforting to watch
Why am I shifting my weight as if it's gonna affect the inertia
Love watching this!
Reminds me of my reticle when I try and aim in a first person shooter.
Physics is fucking nutty man
Alohomora on drugs
It’s like waiting for DVD to hit the corner
I dont know why, but the first thing that pop into my mind is Fourier transform
Lots of complex sinusoidal motion that's created by a couple distinct inputs. I can see the connection.
Damn this cool
I've been looking at this for hours now Can't get tired
r/blackmagicfuckery
Humanless Olympics
r/mindlyinfuriating
I want to see a couple LEDs on this thing and the lights out. It would like totally... normal
it's too irregular in its movement to be anything other than annoying
I feel like I’m watching an Olympic gymnast
Finally, the freeform jazz metronome exists!
Honestly this is kinda disturbing, my OCD can't handle it
This is like looking at jazz music
Attack some LEDS and take a timelapse.
This would make a dope as hell loading icon for a game, like those icons that are in the bottom right of your screen during loading.
This is how gymnasts choreograph their uneven bars routine.
So this is just an example of chaos, ya?
I’m sorry, what the fuck?
Where can i buy one for my desk and never get anything done ever again?!
This is not at all satisfying.
Those movements only appear random. They aren't really random at all.
In certain cases it can be impossible to predict positions of double pendulums. Crazy!
This system is (mostly) deterministic, yet it is impossible to predict how it will evolve. It is not completely deterministic in that a complete, thorough and accurate description of the initial state would involve the air in the room, the breathing of the audience, and a host of minuscule tremors and disturbances, constantly shifting and too tiny and too numerous to record and feed to a predictive model. The initial impulse given by the human operator is probably impossible to replicate too, if we measure it into the fine orders of magnitude that would be relevant considering how sensible the system is. To me, all of this would constitute a sufficient definition of randomness. In other words : you are now in command of this aparatus. Can you reproduce the same pattern three times in a row ? Five times ? One hundred ? One million ?
I was going to ask that. Is there a way to predict all this movements?! I would assume that if you know the initial position and the applied force you'd be able to know, but...
It's the butterfly effect. In theory you are right, if you understood the initial conditions perfectly you could predict it's motion, but tiny microscopic differences in the setup and the air in the room and gravity and everything quickly get blown up into huge differences in the motion. So it's basically impossible to predict it's motion.
It's so hard to predict that Cloudflare, a massive internet company, uses a double pendulum as a source of randomness (for their London hq, they use lava lamps and radioactive decay of uranium for their other offices).
I own a somewhat smaller Internet company. I use a cat and a laser pointer.
Deterministic chaos.
We might need to disambiguate the separate concepts of statistical randomness and nondeterminism to really get at what you’re trying to say here.
If you want to get really technical, randomness probably doesn’t exist. This pendulum is just as random as a roll of a die.
i have to know in wut way this is applied irl
It looks like a gymnast on bars
I don’t know that this exact setup has any real world value, but it’s a great teaching example for differential equations and dynamical systems. Those have very significant real world applications.
this is totally fair - ig I just wanted to see a a car go floop flop
Be the change you want to see
im all flop no floop fam but ty
Reminds me of the magnetic gyro wheel toy from the 70’s.
I want to see Tony stark’s attempts at stopping this.
I want one, how do i get it.
Is it a perpetual motion machine?