Re: chaos and the LGP-30
Carlos E Murillo-Sanchez wrote: Will Cooke via cctalk wrote: Theoriginal paper is Edward N. Lorenz, "Deterministic Nonperiodic Flow", Journal of TheAtmospheric Sciences,Vol. 20, March 1963, pp. 130-141. It is at multiple locations in the web. One source is: http://www.astro.puc.cl/~rparra/tools/PAPERS/lorenz1962.pdf At Cornell I took John Guckenheimer's and Steve Strogatz's courses, inaddition to the more EE-focused nonlinear systems course taught byHsiao-Dong Chiang. Really beautiful stuff. carlos. Thanks! Looks like a really interesting read. Will What I think is most awesome, in terms of the role that computing held in this discovery, is that mathematicians since the early 20th century took as granted the idea that the "limit sets" of the trajectories of solutions of time-differential equations were either periodic (also called limit cycles) or singletons (stable or unstable equilibria at a single point in space). Lorenz, through digital integration of a simple third-order differential equation, proved that there were other kinds of limit sets. These limit sets are distributed in space and occupy geometries that we now call "fractal". When they are the result of a chaotic solution to a differential equation, we call them "strange attractors". The first one that was studied was Lorenz's strange attractor, which, in 3D space, looks like a butterfly. I don't know if there is any connection between its shape and the popular "butterfly altering an initial airflow in the dynosaur's era" interpretation (by the way, utterly dumb for anyone who knows about real-life nonlinear dynamical systems). But what I do know, is that mathematicians had to suddenly backtrack 50 years and try to understand how they could be so wrong. And that's how chaos theory emerged. Thanks to numerical computation. carlos. "dinosaur", argh.
Re: chaos and the LGP-30
Will Cooke via cctalk wrote: Theoriginal paper is Edward N. Lorenz, "Deterministic Nonperiodic Flow", Journal of TheAtmospheric Sciences,Vol. 20, March 1963, pp. 130-141. It is at multiple locations in the web. One source is: http://www.astro.puc.cl/~rparra/tools/PAPERS/lorenz1962.pdf At Cornell I took John Guckenheimer's and Steve Strogatz's courses, inaddition to the more EE-focused nonlinear systems course taught byHsiao-Dong Chiang. Really beautiful stuff. carlos. Thanks! Looks like a really interesting read. Will What I think is most awesome, in terms of the role that computing held in this discovery, is that mathematicians since the early 20th century took as granted the idea that the "limit sets" of the trajectories of solutions of time-differential equations were either periodic (also called limit cycles) or singletons (stable or unstable equilibria at a single point in space). Lorenz, through digital integration of a simple third-order differential equation, proved that there were other kinds of limit sets. These limit sets are distributed in space and occupy geometries that we now call "fractal". When they are the result of a chaotic solution to a differential equation, we call them "strange attractors". The first one that was studied was Lorenz's strange attractor, which, in 3D space, looks like a butterfly. I don't know if there is any connection between its shape and the popular "butterfly altering an initial airflow in the dynosaur's era" interpretation (by the way, utterly dumb for anyone who knows about real-life nonlinear dynamical systems). But what I do know, is that mathematicians had to suddenly backtrack 50 years and try to understand how they could be so wrong. And that's how chaos theory emerged. Thanks to numerical computation. carlos.
Re: chaos and the LGP-30
Theoriginal paper is > Edward N. Lorenz, "Deterministic Nonperiodic Flow", Journal of > TheAtmospheric Sciences,Vol. 20, March 1963, pp. 130-141. > It is at multiple locations in the web. One source is: > http://www.astro.puc.cl/~rparra/tools/PAPERS/lorenz1962.pdf > At Cornell I took John Guckenheimer's and Steve Strogatz's courses, > inaddition to the more EE-focused nonlinear systems course taught > byHsiao-Dong Chiang. Really beautiful stuff. > carlos. Thanks! Looks like a really interesting read. Will
Re: chaos and the LGP-30
Will Cooke via cctalk wrote: On July 27, 2020 at 7:33 AM Will Cooke via cctalk wrote: On July 27, 2020 at 6:44 AM Bill Degnan via cctalk wrote:> Does the code listing exist on the web?Bill>I'm not aware of the code being available anywhere, but I haven't really looked. I did find one paper by Lorenz where he describes his weather forecasting simulations. I can find it again and send a link if anyone wants. Here is the link to the paper. "the Nature and Theory of the General Circulation of the Atmosphere" It's 10 MB and 180+ pages. http://users.uoa.gr/~pjioannou/historical/Lorenz-1967.pdf This is more like a research monograph that was published later. The original paper is Edward N. Lorenz, "Deterministic Nonperiodic Flow", Journal of The Atmospheric Sciences, Vol. 20, March 1963, pp. 130-141. It is at multiple locations in the web. One source is: http://www.astro.puc.cl/~rparra/tools/PAPERS/lorenz1962.pdf At Cornell I took John Guckenheimer's and Steve Strogatz's courses, in addition to the more EE-focused nonlinear systems course taught by Hsiao-Dong Chiang. Really beautiful stuff. carlos.
Re: chaos and the LGP-30
> On July 27, 2020 at 7:33 AM Will Cooke via cctalk > wrote: > > > On July 27, 2020 at 6:44 AM Bill Degnan via cctalk > > wrote:> Does the code listing exist on the web?Bill>I'm not aware of the > > code being available anywhere, but I haven't really looked. I did find one > > paper by Lorenz where he describes his weather forecasting simulations. I > > can find it again and send a link if anyone wants. Here is the link to the paper. "the Nature and Theory of the General Circulation of the Atmosphere" It's 10 MB and 180+ pages. http://users.uoa.gr/~pjioannou/historical/Lorenz-1967.pdf
Re: chaos and the LGP-30
> On July 27, 2020 at 6:44 AM Bill Degnan via cctalk > wrote: > Does the code listing exist on the web?Bill > > I'm not aware of the code being available anywhere, but I haven't really looked. I did find one paper by Lorenz where he describes his weather forecasting simulations. I can find it again and send a link if anyone wants. But on the broader spectrum of chaos theory perhaps the most notable introduction is James Gleik's book "Chaos." Here is a link to it on archive.org https://archive.org/details/chaos-james-gleick Will
Re: chaos and the LGP-30
On Sun, Jul 26, 2020, 8:44 PM Jecel Assumpcao Jr via cctalk < cctalk@classiccmp.org> wrote: > Jay Jaeger wrote on Sun, 26 Jul 2020 19:24:24 -0500 > > So, either he mis-entered something, or possibly the result of a > > different state of a random number generator somewhere? > > He dumped the full state of the simulation to paper with six digits > after the decimal point even though the internal calculations used eight > digits (I don't remember the actual precisions involved). So when he > restarted the simulation from the middle he introduced errors of less > than 1 per million and fully expected the results to be the same for the > days he had already simulated so he could continue a little further. But > he was shocked that the simulation went in a different direction and the > results were totally different after only a few days. > > This is an absurd sensitivity to initial conditions that had never been > noticed in any system before. He compared it to whether a butterfly > flapped its wings or not in the middle of the Amazon making a difference > on there being a nice day or a huge storm on the other side of the world > a week later. This is the infamous "butterfly effect". > > All this came after eliminating all kinds of possible errors, of course. > The first thing we thought back then when something like this happened > was not "I found a new theory" but "the hardware is probably flaky or > there is a compiler bug". > > - Jecel > Does the code listing exist on the web? Bill >
Re: chaos and the LGP-30
Jay Jaeger wrote on Sun, 26 Jul 2020 19:24:24 -0500 > So, either he mis-entered something, or possibly the result of a > different state of a random number generator somewhere? He dumped the full state of the simulation to paper with six digits after the decimal point even though the internal calculations used eight digits (I don't remember the actual precisions involved). So when he restarted the simulation from the middle he introduced errors of less than 1 per million and fully expected the results to be the same for the days he had already simulated so he could continue a little further. But he was shocked that the simulation went in a different direction and the results were totally different after only a few days. This is an absurd sensitivity to initial conditions that had never been noticed in any system before. He compared it to whether a butterfly flapped its wings or not in the middle of the Amazon making a difference on there being a nice day or a huge storm on the other side of the world a week later. This is the infamous "butterfly effect". All this came after eliminating all kinds of possible errors, of course. The first thing we thought back then when something like this happened was not "I found a new theory" but "the hardware is probably flaky or there is a compiler bug". - Jecel
Re: chaos and the LGP-30
On 7/25/2020 8:26 AM, Will Cooke via cctalk wrote: > The LGP-30 has been discussed here (often fondly) a few times so I thought > this might be of interest. Adds a bit of fame to the little guy that I > wasn't aware of. > > I was reading the wikipedia web page on chaos theory and found this passage: > > "Edward Lorenz was an early pioneer of the theory. His interest in chaos came > about accidentally through his work on weather prediction in 1961.[12] Lorenz > was using a simple digital computer, a Royal McBee LGP-30, to run his weather > simulation. He wanted to see a sequence of data again, and to save time he > started the simulation in the middle of its course. He did this by entering a > printout of the data that corresponded to conditions in the middle of the > original simulation. To his surprise, the weather the machine began to > predict was completely different from the previous calculation. " > > https://en.wikipedia.org/wiki/Chaos_theory#History > > Will > So, either he mis-entered something, or possibly the result of a different state of a random number generator somewhere?
chaos and the LGP-30
The LGP-30 has been discussed here (often fondly) a few times so I thought this might be of interest. Adds a bit of fame to the little guy that I wasn't aware of. I was reading the wikipedia web page on chaos theory and found this passage: "Edward Lorenz was an early pioneer of the theory. His interest in chaos came about accidentally through his work on weather prediction in 1961.[12] Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation. He wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather the machine began to predict was completely different from the previous calculation. " https://en.wikipedia.org/wiki/Chaos_theory#History Will
