7 ms·

Mitchell Feigenbaum, physicist who pioneered chaos theory, has died

185 points by yeellow 7y ago

hazeii 7y ago
As a kid I remember playing with the logistic map (possibly pointed at it by Dawkins?) following Robert May and Verhulst explanations of population dynamics. Feigenbaum's constant(s) seemed to point a way through the chaos (this at a time when plotting the mandelbrot set - slowly - was all the rage). [0]https://en.wikipedia.org/wiki/Logistic_map https://en.wikipedia.org/wiki/Logistic_map [1] https://en.wikipedia.org/wiki/Feigenbaum_constants https://en.wikipedia.org/wiki/Feigenbaum_constants With modern computers and software this stuff should be so much easier.
- phkahler 7y ago
  Has anyone found insight into where those two constants come from after all this time? That always seemed like an important question to me.
  - kkylin 7y ago
    One of Feigenbaum's best known contributions to the subject is a heuristic theory, based on renormalization group ideas borrowed from statistical mechanics, that explains the period doubling cascade and lets one calculate these constants. The first mathematically rigorous computer-assisted proof was due to Oscar Lanford. I think now there are proofs that are not computer assisted, though I'm not as familiar with these developments. The Wikipedia article linked above links to some of this information. The following article has a slightly more technical summary together with references to many of the original papers (including Feigenbaum's): http://www.scholarpedia.org/article/Period_doubling http://www.scholarpedia.org/article/Period_doubling For those of you with a bit more matheamtical background and access to technical books, I like the summary of Feigenbaum's renormalization picture in Guckenheimer & Holmes.
dreamcompiler 7y ago
I was peripherally involved in chaos theory in the early 80s. I never met Mitch but I still think of him as a kid not much older than me. I had no idea he was 74. Age creeps up on one.
hanoz 7y ago
I dwell on chaos theory. I don't think its significance has been properly absorbed by the public consciousness yet. There's something simultaneously liberating and unsettling about it. For instance I'm often conscious that it's a mathematical near certainty that if I'd done anything different in my earlier years, absolutely anything at all, then my children would not exist, and therefore I cannot bring myself to regret anything I ever did. Conversely it's unnerving to consider how unlikely my own existence is in the first place. Also, since appreciating chaos theory, I can no longer enjoy any movie involving time travel.
- jes 7y ago
  This is my experience as well. I don’t believe we have libertarian free will, either. I guess I’m aligned with the Harris / Sapolsky / Caruso / Cashmore crowd.
- donaq 7y ago
  Correct me if I'm wrong, but chaotic systems are unpredictable because they are complex and infinitesimally small variations in starting conditions result in hugely different outcomes. They are not, however, non-deterministic. If the universe is merely chaotic and not actually stochastic, then the existence of you and your children are not only not unlikely, it was inevitable.
  - dreamcompiler 7y ago
    Exactly right. Unless you believe quantum mechanics throws a monkey wrench into determinism. Which it certainly does in the realm of the very small. Chaos theory and QM are completely orthogonal (by which I mean they say different things about the universe, not that they are in conflict with one another). And they both screw up the idea of a predictable universe.
    - colordrops 7y ago
      Quantum mechanics demonstrating non-determinism in the realm of the very small necessarily means that the macroscopic realm is also non-deterministic. A non-zero percentage of events occur in which that one particle appearing in one place rather than an is just enough to cause the macroscopic object to take a materially different path. In fact a simple thought experiment shows that a system could be engineered to demonstrate this. Add a sensor that reads which way a particle goes in a double slit experiment and based on the direction, flip a switch that makes a train go east or west based on the sensor read out.
RappingBoomer 7y ago
death...uh.. finds a way
chicob 7y ago
I spent some good times exploring deterministic chaos. Mathematica had sound outputs for the logistic map. I remember one could distinctly hear the octaves progression, then noise, then a fifth. I remember making a video overlapping the sound and the cobweb plot to "see" what I was hearing. Instead of studying calculus, I fell for the trap of trying neverending, eardrum busting, iteratibly non-converging functions. My study method was pretty chaotic.
whyenot 7y ago
I remember reading about him in Chaos: Making a New Science where James Gleick portrayed him as a young man. That was in the late 1980s when I was a high school student. Time flies :(
- Gibbon1 7y ago
  I read the same book. I felt it was very useful. I remember a homework assignment to calculate bearing under various conditions. One of them wouldn't solve and I realized it was because the conditions produced chaotic behavior. So of course you couldn't produce a closed form solution. I was pleased with that book indeed.
- taneq 7y ago
  Great book, I read it a bunch of times. It made chaos theory really accessible even to a highschooler.
- signal_space 7y ago
  I highly recommend Nonlinear Dynamics and Chaos by Steven Strogatz.
- chaoticmass 7y ago
  I first read that book when I was 13 and I still go back for another read every few years. Not only did it make the subject accessible, it didn't over simplify. The stories of the people making the discoveries kept it personal and engaging throughout, and Feigenbaum's chapter(s) were my favorite. After finishing the book, you never see the world the same way again.
mycall 7y ago
Chaos Monkey is sad.
misil 7y ago
If you're interested in Feigenbaum's constant, check out Numberphile's video about it: https://www.youtube.com/watch?v=ETrYE4MdoLQ https://www.youtube.com/watch?v=ETrYE4MdoLQ.
- eridius 7y ago
  I learned about that function and the resulting output back in high school, but haven't looked at it since then. I wish he'd have given at least the beginnings of an explanation as to why you can't go over 4 for lambda though. What happens?
matthewfelgate 7y ago
He would still be alive today if wasn't for that damn butterfly....
- ChrisArchitect 7y ago
  too soooon haha
tomahunt 7y ago
The story of Feigenbaum presented in Gleik's Chaos is the reason I chose to do physics.

185 points by yeellow 7y ago

As a kid I remember playing with the logistic map (possibly pointed at it by Dawkins?) following Robert May and Verhulst explanations of population dynamics. Feigenbaum's constant(s) seemed to point a way through the chaos (this at a time when plotting the mandelbrot set - slowly - was all the rage). [0]https://en.wikipedia.org/wiki/Logistic_map https://en.wikipedia.org/wiki/Logistic_map [1] https://en.wikipedia.org/wiki/Feigenbaum_constants https://en.wikipedia.org/wiki/Feigenbaum_constants With modern computers and software this stuff should be so much easier.

phkahler 7y ago
Has anyone found insight into where those two constants come from after all this time? That always seemed like an important question to me.
- kkylin 7y ago
  One of Feigenbaum's best known contributions to the subject is a heuristic theory, based on renormalization group ideas borrowed from statistical mechanics, that explains the period doubling cascade and lets one calculate these constants. The first mathematically rigorous computer-assisted proof was due to Oscar Lanford. I think now there are proofs that are not computer assisted, though I'm not as familiar with these developments. The Wikipedia article linked above links to some of this information. The following article has a slightly more technical summary together with references to many of the original papers (including Feigenbaum's): http://www.scholarpedia.org/article/Period_doubling http://www.scholarpedia.org/article/Period_doubling For those of you with a bit more matheamtical background and access to technical books, I like the summary of Feigenbaum's renormalization picture in Guckenheimer & Holmes.

dreamcompiler 7y ago

I was peripherally involved in chaos theory in the early 80s. I never met Mitch but I still think of him as a kid not much older than me. I had no idea he was 74. Age creeps up on one.

hanoz 7y ago

I dwell on chaos theory. I don't think its significance has been properly absorbed by the public consciousness yet. There's something simultaneously liberating and unsettling about it. For instance I'm often conscious that it's a mathematical near certainty that if I'd done anything different in my earlier years, absolutely anything at all, then my children would not exist, and therefore I cannot bring myself to regret anything I ever did. Conversely it's unnerving to consider how unlikely my own existence is in the first place. Also, since appreciating chaos theory, I can no longer enjoy any movie involving time travel.

jes 7y ago
This is my experience as well. I don’t believe we have libertarian free will, either. I guess I’m aligned with the Harris / Sapolsky / Caruso / Cashmore crowd.
donaq 7y ago
Correct me if I'm wrong, but chaotic systems are unpredictable because they are complex and infinitesimally small variations in starting conditions result in hugely different outcomes. They are not, however, non-deterministic. If the universe is merely chaotic and not actually stochastic, then the existence of you and your children are not only not unlikely, it was inevitable.
- dreamcompiler 7y ago
  Exactly right. Unless you believe quantum mechanics throws a monkey wrench into determinism. Which it certainly does in the realm of the very small. Chaos theory and QM are completely orthogonal (by which I mean they say different things about the universe, not that they are in conflict with one another). And they both screw up the idea of a predictable universe.
  - colordrops 7y ago
    Quantum mechanics demonstrating non-determinism in the realm of the very small necessarily means that the macroscopic realm is also non-deterministic. A non-zero percentage of events occur in which that one particle appearing in one place rather than an is just enough to cause the macroscopic object to take a materially different path. In fact a simple thought experiment shows that a system could be engineered to demonstrate this. Add a sensor that reads which way a particle goes in a double slit experiment and based on the direction, flip a switch that makes a train go east or west based on the sensor read out.

RappingBoomer 7y ago

death...uh.. finds a way

chicob 7y ago

I spent some good times exploring deterministic chaos. Mathematica had sound outputs for the logistic map. I remember one could distinctly hear the octaves progression, then noise, then a fifth. I remember making a video overlapping the sound and the cobweb plot to "see" what I was hearing. Instead of studying calculus, I fell for the trap of trying neverending, eardrum busting, iteratibly non-converging functions. My study method was pretty chaotic.

whyenot 7y ago

I remember reading about him in Chaos: Making a New Science where James Gleick portrayed him as a young man. That was in the late 1980s when I was a high school student. Time flies :(

Gibbon1 7y ago
I read the same book. I felt it was very useful. I remember a homework assignment to calculate bearing under various conditions. One of them wouldn't solve and I realized it was because the conditions produced chaotic behavior. So of course you couldn't produce a closed form solution. I was pleased with that book indeed.
taneq 7y ago
Great book, I read it a bunch of times. It made chaos theory really accessible even to a highschooler.
signal_space 7y ago
I highly recommend Nonlinear Dynamics and Chaos by Steven Strogatz.
chaoticmass 7y ago
I first read that book when I was 13 and I still go back for another read every few years. Not only did it make the subject accessible, it didn't over simplify. The stories of the people making the discoveries kept it personal and engaging throughout, and Feigenbaum's chapter(s) were my favorite. After finishing the book, you never see the world the same way again.

mycall 7y ago

Chaos Monkey is sad.

misil 7y ago

If you're interested in Feigenbaum's constant, check out Numberphile's video about it: https://www.youtube.com/watch?v=ETrYE4MdoLQ https://www.youtube.com/watch?v=ETrYE4MdoLQ.

eridius 7y ago
I learned about that function and the resulting output back in high school, but haven't looked at it since then. I wish he'd have given at least the beginnings of an explanation as to why you can't go over 4 for lambda though. What happens?

matthewfelgate 7y ago

He would still be alive today if wasn't for that damn butterfly....

ChrisArchitect 7y ago
too soooon haha

tomahunt 7y ago

The story of Feigenbaum presented in Gleik's Chaos is the reason I chose to do physics.