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Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
21–30 of 81 posts
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#22Mitchell Feigenbaum has, for the last ~17 years, been my vote for the next Nobel Laureate in Physics. It is a rare thing to derive an irrational fundamental mathematical constant that appears in nature. The Feigenbaum constants are as fundamental as e and \pi, and they are readily observed experimentally (though, necessarily, not to full precision :) ). Godspeed, Dr. Feigenbaum. Thank you.
> The Feigenbaum constants are as fundamental as e and \pi I suppose its debatable how fundamental a constant is , but there is no way the Feigenbaum constant is even in the same neighborhood as \pi and e.
Yes, it's kind of hard to get more fundamental than waves and circles.
Although, as I was just about to say what math could you do without them on second thought, the answer seems to be quite a lot.
For example I couldn't say without researching it but how much did Gödel or Turing rely on them, at least for their most influential work?
That question will probably come back to bite hard given their footprints.
Another conjecture, most software developers will never have to use them extensively. Yes gaming, computer graphics, and I guess all signal processing would become suddenly more challenging but corporate IT and devops ought to be pretty safe.
Maybe it depends on a personal definition of fundamental. I think you could make an argument that Newton's results were more fundamental than Einstein's, however staggeringly less complete they might seem hundreds of years in the future.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#23The HP-65 was pretty swank.
Especially if you have it with you.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#24I know this isn’t written as a typical obituary but I can’t imagine a better way to say goodbye and thank you a true scientist. The entire blog post is beautiful- not just the presentation but also the content and sentiment.
I agree absolutely.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#25I am very ignorant, but here's a question: are Feigenbaum's discoveries related at all to Langton's ant [0]?
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#26I know this isn’t written as a typical obituary but I can’t imagine a better way to say goodbye and thank you a true scientist. The entire blog post is beautiful- not just the presentation but also the content and sentiment.
Save for the bits where it focuses on Wolfram's jilted ego.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#27I was an undergrad CS intern (and Chaos enthusiast) assisting the physicists at Los Alamos Natl. Labs Center for Nonlinear Studies when he visited to give the monthly “Tea Talk” on some subject in nonlinear mathematics/ chaos theory back in ‘88. I didn’t understand most of what he said. I asked the Deputy Director, a long-time PhD Theoretical Physicist, about the gist of the talk afterwards. He said “I didn’t understand most of what he said. Maybe if I had been collaborating with him for a few months...”
Feigenbaum was a fascinating man and some of his writing is what made me want to get an internship at the Center. I never dreamed I meet the man over tea.
A great man.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#28Earlier quoted context omitted.
> The Feigenbaum constants are as fundamental as e and \pi I suppose its debatable how fundamental a constant is , but there is no way the Feigenbaum constant is even in the same neighborhood as \pi and e.
Yes, it's kind of hard to get more fundamental than waves and circles. Although, as I was just about to say what math could you do without them on second thought, the answer seems to be quite a lot. For example I couldn't say without researching it but how much did Gödel or Turing rely on them, at least for their most influential work? That question will probably come back to bite hard given their footprints. Another…
Agreed -- I used the word "fundamental" to suggest that it emerges from pure mathematics. In that sense, Feigenbaum's constants are in the same class as \pi and e, which is distinct from the traditional "fundamental constants" of physics like c, \hbar, fundamental charge, etcetera.
The fundamental constants of physics have, as yet, no known mathematical origin. Feigenbaum's constants, on the other hand, emerge from pure mathematics and also appear in nature. That they are expected to be irrational, like \pi and e, only adds to the charm.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#29I normally find Stephen Wolfram insufferable (and he still is, in this article) but boy what a privilege it is to have a friend who will eulogize us like this. If I was an intellectual associate of Wolfram’s I’d ask him to write this article for me to read before I died.
Re: Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
#30I first saw that beautiful bifurcation diagram as a teenager in this book called "Fractals" that showed a bunch of fractals as well as programs to draw them. I was amazed that such simple arithmetic could lead to such weird, organic results. The code to draw it is astonishingly simple. Here's an implementation in Dart that prints it to your console:
import 'dart:math' as math;
const min = 2.4;
const max = 4.0;
const width = 120;
const height = 100;
main() {
for (var r = min; r n > greatest / 10 ? "*" : " ").join(""));
}
}