
Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382… - techgipper
https://blog.stephenwolfram.com/2019/07/mitchell-feigenbaum-1944-2019-4-66920160910299067185320382/
======
chime
I 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.

~~~
quakeguy
I agree absolutely.

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ISL
Mitchell 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.

~~~
JackFr
> 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.

~~~
WhitneyLand
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.

~~~
ISL
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.

~~~
jordigh
Do we know the constant is irrational? I'd be surprised if we did.

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anbop
I 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.

~~~
miobrien
Can someone elaborate as to why Wolfram’s insufferable? I’ve only looked at
his blog once or twice.

However this post was great.

~~~
carapace
I have a lot of respect for the man despite his personality problems. He knew
what he wanted at a young age and pursued it with determination and
persistence and achieved it. Mathematica and the business he built to support
it are both great accomplishments. I'm sometimes surprised he's not more
popular on HN than he is.

I mention all that so it won't seem too mean-spirited when I repeat this:

I've heard a joke, "Which will achieve self-awareness first, Wolfram or
Wolfram Alpha?"

He's a great man, but flawed by too-great appreciation of his own greatness.

~~~
chx
> I'm sometimes surprised he's not more popular on HN than he is.

This is a guy who have filed a patent on pure mathematics
[https://patents.google.com/patent/US4809202](https://patents.google.com/patent/US4809202)
and it was nowhere near original, compare to
[https://www.sciencedirect.com/science/article/pii/0167278984...](https://www.sciencedirect.com/science/article/pii/0167278984902550?via%3Dihub)
and the folks 'round here are not hot on software patents and this is much
worse.

~~~
techgipper
Looks like the company he worked for filed that, not him?

~~~
chx
Well, the inventor is listed as Stephen Wolfram ... I mean legally it wasn't
him but in practice...

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peapicker
I 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.

~~~
gwf
I was there as well, also as an intern. Around the same time, Mandelbrot also
stopped by CNLS to give a talk. CNLS in the late 80s was truly a magical
place.

~~~
peapicker
It was pretty amazing. I recall Doyne Farmer was there too - he had this crazy
custom coprocessor card for his cellular automata explorations. I got to write
some stuff to run on a CRAY Y-MP. Got to to play with NeXT black box serial
no. 36. (LANL had the first 50 I think). Lots of crazy cool people and tech!

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madhadron
Feigenbaum barely ever showed up in the physics building at Rockefeller while
I was there. He had an office. I saw his retreating back once, but he chose
not to engage with the community there, despite it being full of people who
wandered as widely as he did.

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onychomys
One interesting place that period doubling shows up that the article doesn't
mention is in population ecology. I'm most familiar with the Tribolium work of
Constantino, Dennis, Cushing, and some other folks, which you can read an
example of here[0]. Basically, the beetles have three life stages (four,
actually - egg, larva, pupa, adult - but adding eggs in the model doesn't
increase accuracy any so they leave it out for simplicity), and if you model
the respective numbers of adults for a starting number of larvae, you can see
truly chaotic behavior, including period doubling. It's fascinating work.

[0]
[https://onlinelibrary.wiley.com/doi/full/10.1046/j.1461-0248...](https://onlinelibrary.wiley.com/doi/full/10.1046/j.1461-0248.2001.00223.x)

~~~
aeorgnoieang
There were several references to fish populations and and even "population
biology". I wouldn't have thought 'population ecology' was that different but
a cursory Google search leads me to believe I was wrong.

That's a neat connection!

------
ars
Here's a Numberphile on it if you want to understand the constant:
[https://www.youtube.com/watch?v=ETrYE4MdoLQ](https://www.youtube.com/watch?v=ETrYE4MdoLQ)

As a nice bonus that video will also help you understand the Mandelbrot and
Julia sets.

------
scarejunba
Chaos : Making a New Science by James Gleick
[https://www.amazon.com/dp/B003YL4KOO/](https://www.amazon.com/dp/B003YL4KOO/)
contextualizes the period-doubling thing and talks about some of the other
related stuff. Good book.

------
munificent
I 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 < max; r += (max - min) / height ) {
            var x = 0.5;
            var counts = [for (var i = 0; i < width; i++) 0];
            var greatest = 0;
            for (var i = 0; i < 200; i++) {
              x = r * x * (1 - x);
              var i = (x * width).toInt();
              counts[i]++;
              greatest = math.max(greatest, counts[i]);
            }
    
            print(counts.map((n) => n > greatest / 10 ? "*" : " ").join(""));
          }
        }

~~~
jonahx
Translated into J:

    
    
        w=. 120
        row=. [: (' *' {~ ] > 10 %~ >./) [: (1 #. i.@w =/ ]) [: <. w * (* ] * -.@])^:(<200)&0.5
        echo (row"0) 2.4 + 1.6r100 * i.101
    

Live:

[https://tio.run/##HYzBCoJAFEX3fsWhKGcmer4n1UJU/I@YNhFkG8GNi8...](https://tio.run/##HYzBCoJAFEX3fsWhKGcmer4n1UJU/I@YNhFkG8GNi8BfnyZ3l3MO95PS0glWazFP/3VvcCWh5LsS6THlsNJL5Tdl7IVRhoWuIm6sFRYCLuQ@cJYh@kfj2lrVH1Wuxev5nnD5faeeWi6cMLnNpprzUUwtpR8)

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lonelappde
"Chaos and Fractals", a huge tome of a book , from the 1990s, is an incredible
book to learn about Feigenbaum's work and others. The programming language it
uses is rather obsolete, but it's such a wonderful book for a motivated high
school or college student.

~~~
kenver
Any chance you know the author? There's a few with similar titles.

~~~
tobinfricke
Heinz-Otto Peitgen

------
j7ake
I really love these Wolfram biographies of famous people.

~~~
vtail
You might enjoy his "Idea Makers: Personal Perspectives on the Lives & Ideas
of Some Notable People", which consists of short essays on a few interesting
people, some of which he knew personally.

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simonebrunozzi
I am very ignorant, but here's a question: are Feigenbaum's discoveries
related at all to Langton's ant [0]?

[0]:
[https://en.wikipedia.org/wiki/Langton%27s_ant](https://en.wikipedia.org/wiki/Langton%27s_ant)

------
pseudolus
Incredible and insightful overview about the life of a man whose contributions
to science were unknown to me until today. Thank you for posting.

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ngvrnd
The HP-65 _was_ pretty swank.

~~~
aeorgnoieang
I'd hope so! It's $795 MSRP in 1974 'is' roughly $4,100 in 2019.

------
milemi
A completely frivolous and useless note: the photo at the bottom of the
article was taken at a table in the restaurant called Mediterraneo on the
corner of 2nd and 66th, and behind him is the block on which one of the scenes
in Annie Hall was shot.

------
jl6
Does Wolfram record and index all his voicemails?

~~~
dchest
He records everything he can record :)
[https://blog.stephenwolfram.com/2012/03/the-personal-
analyti...](https://blog.stephenwolfram.com/2012/03/the-personal-analytics-of-
my-life/)

