# Chaos and the double dendulum

#1

#2

A dendulum is a pendulum you hang from a tree.

#3

Given the starting conditions, a chaotic system is entirely deterministic.

Nothing is entirely deterministic. The whole point of chaos theory is â€śsensitive dependence on initial conditions.â€ť But Heisenberg (Werner, not Walter) showed that initial conditions are not knowable. It turns out God actually does play dice with the universe, and on a macro level, too.

#4

Of course chaotic systems where the starting conditions arenâ€™t known to a sufficient level of accuracy CAN be modeled as random. eg. rolled dice. Which are certainly large enough that quantum effects can be ignored. I would argue that MOST things that are treated as â€śrandomâ€ť are really cases of limited knowledge rather than things that are truly random.

#5

NB: For optimum performance it should be an apple tree.

#6

Nothing physical. The mathematical double pendulum system is a coupled pair of 2nd order ODEs (So, equivalent to an order 4 ODE.) Those are entirely determined by their precise initial starting position.

#7

â€¦which cannot be measured precisely.

Also, I didnâ€™t take God into consideration, Who is in there busily moving the state variables around.

#8

In one of the first lectures of Physics 1 at Caltech the professor (David Goodstein) had a double pendulum just like this at the front of the room and let it go and said something to the effect of â€śNobody can tell you what the motion of that pendulum is going to be.â€ť For some reason that has stuck with me for a lot of years as a profoundly interesting fact of the universe.

#9

Stop it, let it just hang down there at energy minimum, and its behavior becomes pretty predictable.

#10

You have to decide if you are going to talk about a physical pendulum or its mathematical idealization. If want the mathematical one, measurement is not a part of the theory. If you want the physical one, it isnâ€™t chaotic: the second law of thermodynamics will eventually stop the pendulum via the heat death of the universe.

#11

comes running, slaps dendropendulum
Howâ€™d you predict that?

#12

Yea, my engineering background is showing. I find reality more interesting.

#13

Stop it again, glue it in position. Problem solved.

#14

â€śGod actually does play diceâ€ť - or continually creates through an infinite succession of miraculous interventions. Iâ€™ve never really heard a good explanation of why a truly random event shouldnâ€™t be regarded as supernatural.

#15

The laws of quantum mechanics are entirely deterministic, itâ€™s just that the thing that actually exists is the wavefunction, not the high-level approximations like â€śpositionâ€ť and â€śmomentumâ€ť that we find intuitive. And if you did successfully model the wavefunction of a macro-scale â€śmeasuringâ€ť device, then there is no need for assuming randomness.

#16

I thought it was a pendulum with an addendum.

#17

Or it bounces off the trampoline.

#18

errata: what does it matta?

closed #19

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