Mitchell Feigenbaum (1944–2019), 4.66920160910299067185320382…
blog.stephenwolfram.com
blog.stephenwolfram.com
Godspeed, Dr. Feigenbaum. Thank you.
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.
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.
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.
Now, like oxygen, pi and e are certainly more prevalent ...
They only give Nobels to living people, and typically only young people.
Maybe there is some other award recognition?
Edit: 72 years in average across all prizes, although first half of 20th century was lower.
Update: user "ISL" says "that was Nobel's original intent, but the reality of the prize has changed with time."
Yes, Nobel Prize is only given by living people to encourage innovation rather than remembering the death, yes. However, it's very common for the Nobel Prize to aware scientists after a discovery has been made. Nobel Prize of Literature is the same, I believe.
For example, Albert Einstein won the Nobel Prize in 1921 for "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", but Einstein's relevant papers were published in 1905 on Annalen der Physik, it's 16 years later after the discovery. Another recent example is the Nobel Prize of Physics of 2014, given to Isamu Akasaki, Hiroshi Amano, and Shuji Nakamura for blue LEDs, it's also 20 years later.
Due to this very reason, The Breakthrough Prize was established in 2012 by multiple entrepreneurs, including Mark Zuckerberg, as a prize, which its proponents claim to be that they try to give it to people just starting out in their field, to encourage them to continue, rather than as a prize for finishing. Although it has received some criticisms of being a rockstar award as well.
Is it, by any chance, the prize you were thinking about?
https://en.wikipedia.org/wiki/Breakthrough_Prize
https://en.wikipedia.org/wiki/Breakthrough_Prize_in_Fundamen...
The Fields Medal and the MacArthur Genius awards are very much in that spirit.
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.
Usually, after a certain level math problems become very narrow, and a small subfield develops around them. They are "easy" to get into, to catch up, read the important papers, sketch out the proofs for yourself, get a feel for the concepts and for the conjectures that lurk among them.
And usually that's it. Usually a few folks of that very particular topic/field have some ideas that they are working on, usually for at least a year, they try to formalize them, conceptualize them, communicate them, and naturally to prove them.
And sometimes draft/working papers are all we get. Sometimes someone becomes a "household" name after many persistent years like Wiles.
[0] https://onlinelibrary.wiley.com/doi/full/10.1046/j.1461-0248...
That's a neat connection!
As a nice bonus that video will also help you understand the Mandelbrot and Julia sets.
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(""));
}
} w=. 120
row=. [: (' *' {~ ] > 10 %~ >./) [: (1 #. i.@w =/ ]) [: <. w * (* ] * -.@])^:(<200)&0.5
echo (row"0) 2.4 + 1.6r100 * i.101
https://tio.run/##HYzBCoJAFEX3fsWhKGcmer4n1UJU/I@YNhFkG8GNi8...
But as I scrolled, I did see quite a bit of really interesting content in the article, and thought such a comment may turn people away from the article, which would be a shame, so I decided not to.
(Well, until I saw your comment).
However this post was great.
My own belief, based on work I did in the 1980s, is that it’s actually an intrinsic youthful genius phenomenon—analogous to the insufferability one sees in my rule 34 cellular automaton.
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.
This is a guy who have filed a patent on pure mathematics https://patents.google.com/patent/US4809202 and it was nowhere near original, compare to https://www.sciencedirect.com/science/article/pii/0167278984... and the folks 'round here are not hot on software patents and this is much worse.
There are a couple transcribed lectures of his on amazon, one of them "Computation and the Future of the Human Condition", they are short and deep and I find them very interesting, I read them maybe a couple years ago... somehow within that little context I was so entranced by the underlying concepts and material which just clicked with me, that this aspect of Wolfram's personality completely escaped me... My partner tried to read them and immediately picked up on it, now identified - I find everything I read from him slightly tainted. I've yet to pluck up the courage to read NKS, i'm worried I will not be able to get through it.
It's a shame because I believe some of the work he has produced and ideas he has explored to be a truly fundamental and under-explored part of nature, hopefully enough of us will appreciate that without letting his personality get in the way.
It would have been a much nicer book if he had connected his ideas in universality, fundamental computing, math, physics and biology, to the rest of those fields. He mentions many of these connections/theories, but does not cite them or even attribute them to their respective fields of science.
Otherwise if you can read past all that, it's super interesting. It just leaves me with the inclination that, if I want to find out more about these new subjects, I'd be best of starting out looking for information not by Wolfram, if only just to get a good view/idea of the field right now, since Wolfram isn't citing anyone, but others probably are.
The entire book is available online for free. Here's the first section of the notes:
- [Note (a) for An Outline of Basic Ideas: A New Kind of Science | Online by Stephen Wolfram [Page 859]](https://www.wolframscience.com/nks/notes-1-1--mathematics-in...)
... but, after looking at some more sections of the notes, I think now I remembered very much incorrectly – there are in fact very few citations or specific references. There are, in my opinion, very many connections noted tho.
Also from the notes:
- [Clarity and modesty – Note (e) for General Notes: A New Kind of Science | Online by Stephen Wolfram [Page 849]](https://www.wolframscience.com/nks/notes-0-1--clarity-and-mo...)
- [Citations and references – Note (d) for General Notes: A New Kind of Science | Online by Stephen Wolfram [Page 850]](https://www.wolframscience.com/nks/notes-0-1--citations-and-...)
https://www.wolframscience.com/nks/notes-0-1--citations-and-...
In developing the ideas described in this book I have looked at many thousands of books, papers and websites—and have interacted with hundreds of people (see page xiii). But rather than trying to give a huge list of specific references, I have instead included in these notes historical information tracing key contributions. From the names of concepts and people that I mention, it is straightforward to do web or database searches that give a vastly more complete picture of available references than could possibly fit in a book of manageable size—or than could be created correctly without immense scholarship. Note that while most current works of science tend to refer mainly just to very recent material, this book often refers to material that is centuries or even millennia old—in some ways more in the tradition of fields like philosophy.
> and on the very first day that I showed up as 17-year-old particle-physics-paper-writing undergraduate, I ran into him
Almost every blog post mentions that he was a child prodigy.
I liked this post though. Well written
>(Confusingly enough, with typical “machine precision” computer arithmetic, this doesn’t work correctly, because even though one “runs out of precision”, the IEEE Floating Point standard says to keep on delivering digits, even though they are completely wrong. Arbitrary precision in the Wolfram Language gets it right.)
The man can't help but promote himself. He worded this in a way that makes it look to a lay person like he invented arbitrary precision arithmetic, but in a way that is still technically correct. It's like he's actively trying to peddle something to people who don't know any better.
I think that's pretty uncharitable. If what you claimed were true, particularly of his intentions, I'd expect him to have written something like "Arbitrary precision in the Wolfram Language got it right.".
But then I can't imagine a layperson having any idea what almost any of the sentence you quoted means anyways so your point seems pretty moot.
For anyone that already understands or is at least familiar with 'machine precision', 'floating point numbers', or 'arbitrary precision' (computer arithmetic), I'd think his claim that "Wolfram Language gets it right" would seem to be a pretty innocuous plug. Yes, the man regularly promotes the products of the company that bears his name on his own blog. I think it's fine.
>But then I can't imagine a layperson having any idea what almost any of the sentence you quoted means anyways so your point seems pretty moot.
You're not being honest here. If you can't imagine it, it is because you're not trying. People walk away with impressions, even if they don't retain the facts. He always writes to give an impression, not to give facts. Facts are always the cover for the impression.
Here's another example from the article:
>But what is actually going on in a phase transition? I think the clearest way to see this is by looking at an analog in cellular automata.
Is he being honest here? Is this actually the best way to understand a phase transition? And is this cellular automata the one he should be using?
Of course! It's His Holy Cellular Automata. It must be introduced, even if only in passing.
Yeah, "it's fine." He knows what he knows, and you can't fault someone for speaking to what they know. But it is a grating and self-serving stylistic choice, and it does undermine his message. But if you're an investor or someone looking for a savior to worship or a bandwagon to jump on, he's certainly got all the answers for you.
I was being honest. Please don't tell me I'm lying; assume good faith. I still claim that his wording 'Wolfram Language gets it right' versus 'Wolfram Language got it right' would leave a layperson with the impression different than what you claim.
I could be wrong. I'd be willing to make a (nominal) bet about the outcome of a reasonable proxy if you're interested in testing our disagreement. I'm not claiming near-certainty tho. I don't think you're 'definitely' or 'obviously' wrong.
For the second example, I think his cellular automata is a pretty good way to see a phase transition. I'm also interpreting his claim pretty charitably, e.g. not that it's literally the clearest way for anyone to see, let alone understand generally, for whatever reference class of 'people' would possibly be the best definition to use in this case. I think you're splitting hairs pretty finely here.
I do agree that his writing style is "grating and self-serving". There's lots of evidence that that's the case, just in the comments on this post alone. I think part of that interpretation is warranted and valid. I think another, significant, tho lesser part is confirmation bias.
Stephen Wolfram definitely doesn't have all the answers for me, or likely anyone. I'm pretty confused why you wrote the last sentence in your reply to me. I think my comment was pretty anodyne. You seem to have pretty strong feelings about it.
I'm also unsure why you'd think an "investor" would be particularly interested in him or his companies. Wolram basically sells enterprise software and related services. It doesn't seem like a likely undervalued opportunity for significant growth.
I'm also unsure why you think anyone would "worship" him as a "savior". I don't regardless.
I'm happy enough to wish him and anyone that's jumped on his bandwagon well tho. I think he's got a very good point about the likely benefits of engaging in what I'd call 'exploratory computational discovery', as he describes in NKS. Yes, he uses much stronger and strident language to describe the same thing, and I think the magnitude of his claims are too large, but I do think his point is underrated, even significantly. I'm more skeptical of how much low hanging fruit there's likely to be from applying methods like what he advocates, but not radically so.
pro.
Used to refer to an indefinitely specified person; one.
In any case, this issue is not important enough for me to be spending any more time on it, so if you don't understand me, we'll just have to live with that.
Just one of many grating examples of how he communicates. He's a genius though, so he has that going for him...
Were he to include a WolframAlpha link to a working snippet, and mention that you need true decimals, because IEEE floats won't cut it would have probably conveyed the same without what the other commenters perceive as useless boasting.