The most perfect pairing of author and subject since Nicholson Baker and John Updike. Here’s Wolfram on the great researcher of fractals:

In his way, Mandelbrot paid me some great compliments. When I was in my 20s, and he in his 60s, he would ask about my scientific work: “How can so many people take someone so young so seriously?” In 2002, my book “A New Kind of Science”—in which I argued that many phenomena across science are the complex results of relatively simple, program-like rules—appeared. Mandelbrot seemed to see it as a direct threat, once declaring that “Wolfram’s ‘science’ is not new except when it is clearly wrong; it deserves to be completely disregarded.” In private, though, several mutual friends told me, he fretted that in the long view of history it would overwhelm his work.

In retrospect, I don’t think Mandelbrot had much to worry about on this account.

The link from the above review came from Peter Woit, who also points to a review by Brian Hayes with this highly Wolfram-relevant bit:

What’s not so endearing is to see some of the supporting actors denied even a listing in the credits. . . . Adrien Douady and John H. Hubbard made crucial contributions to the understanding of the Mandelbrot set, but they too go unnamed here; this omission is particularly ungracious in that it was Douady and Hubbard who gave the set its name.

If only we could get that albedo guy into the picture, we’d be all set.

Shalizi’s review of the book is pretty awesome: http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfram/

In his review (from 2002), Shalizi writes that Wolfram’s book “is going to set the field back by years.”

Did this happen? I’d guess no, that the book was pretty much dead on arrival.

As far as Wolfram goes, Shalizi’s review seems spot on to me:

http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfram/

Mandelbrot, from my reading, seems to have craved the role of the iconoclast revolutionary mathematician and oriented his life around achieving that goal. Although he attained something like that kind of fame in his lifetime, fractals just aren’t anything like as useful as Madelbrot thought, and he’ll probably be just a footnote in a 100 years. He’s probably just a footnote now. After reading some of his papers from the 50’s and 60’s, I’m convinced this ugly striving for fame diverted him away from some bigger achievements that he was well positioned to have worked on. His tombstone should read “narcissism and math don’t mix”.

If only we could get that albedo guy into the picture, we’d be all set“Mandelbrot, Wolfram, Myhrvold: An Eternal Golden Ticket”

Sifu:

Oooh, that’s perfect, as it also fits with my view that Godel Escher, Bach is incredibly overrated.

In view of Andrew’s theory about tall people, I wonder if there is a theory about receding hairlines….

It boggled my mind that Wolfram had the nerve to write a book where he claimed to have invented complexity theory, when there’d been many people working in this field for almost twenty years by that time. It still boggles me.

I think you should warn readers more clearly that those pictures are not those of Mandelbrot and Wolfram, but of Douady and John (Hubbard)… I wondered for a while why they were posted on top of this (great) post. And yes I completely agree on Wolfram’s unbelievably conceited review (why would the Wall Street Journal ask Wolfram for a review?!) and yes I completely agree on Gödel, Eischer and Bach being way overrated.

It’s a pretty good likeness though, if you shave these guys, they might look like Mandelbrot and Wolfram.

X

I was originally going to post a picture of

GlennHubbard, but I thought that would be too much of an inside joke.> Gödel, Eischer and Bach being way overrated

Without a doubt

It’s really Wolfram on Wolfram, with Mandelbrot as the excuse.

Re GEB, many people agree that there is a marked drop in quality somewhere in the last third or so of the book. But has it occurred to you that that may just be the padding he added, having already finished the “real” book?

I may be overstepping it but isn’t Mandelbrot way overrated?

I mean fractals were a fad and fad means bubble. They made pretty pictures and that’s about it. Ok, so he did more than fractals, but he certainly monopolized on the notoriety in a way that many seemingly far more accomplished mathematicians would be reluctant to mimic.

And it’s not like he invented fractional dimensions. He just made the posters.

And, yes, Wolfram is a bit much too. If you could hear his former UIUC colleagues’ disdain for him (and his managing to use the ‘core’ in mathematica which others significantly contributed to and not have to pay any royalties, just by a stroke of corporate and legal structuring), it all makes sense.

Nick:

I don’t know much about the history of mathematics, so it well could be that Mandelbrot is getting way too much credit for other people’s work. That aside, I think fractals and self-similarity are a major contribution. Sure, at the level of technical difficulty the proof of Fermat’s Last Theorem is much more impressive, but, to me, fractals are much more important, the idea of a mathematical model for natural processes that makes much more sense than the simple geometric models and smooth curves that were the basis of previous mathematical models. My earlier Mandelbrot reactions are here.

Andrew,

I haven’t delved deeply into the subject, but it seems to me that the concept of fractals is important, but no meaningful methods or deeper insights have arisen within that overall field. At least that’s my impression: lots of promise, fascinating idea, not much actual work done with it.

[...] Wolfram on Mandelbrot (via Gelman) [...]

I think both Godel, Escher, Bach and Personal Days are terrific. If you want to know what I think of ANKOS, I wrote about it for Slate here:

http://www.slate.com/articles/life/do_the_math/2002/07/blinded_by_science.html

Jordan:

In 2002, you wrote: “with a few exceptions, journalists like the story nearly as much as Wolfram does.”

But I don’t think this has lasted. Now I think Wolfram’s just one more tech entrepreneur. My impression is that he staked his scientific reputation on that book—and lost. But his reputation as a publisher of software remains strong.

Scientifically, he’s not exceptional but nor worse than any one of thousands of prosaic academics. His early papers aren’t bad just incremental advances. It’s just that he over-hyped them as revolutionary.

He’s definitely not as great as he sells himself to be scientifically. But he’s no worse than a random professor at at Big10 Univ.