It was fractals that managed to re-ignite my interest in math after having it de-constructed by highschool teachers.
Amazing images embedded in suspiciously simple formulas. Irresistible.
I owe the man a lot, this is really not a good thing to go to sleep with.
I don't get why humans mourn the death of people who die at >80, and especially people who have lead such illustrious, incredible lives. It should be a time for celebration, of the incredible way in which Mandelbrot has contributed to the sum of Humanity's Greatness. We should literally throw a party in His honor.
Humans die around age 80, with a variance of about 55-105. It's just a fact. For all our claims of progress, we are still hopelessly emotional animals who are influenced by whatever-happens-to-influence-us rather than solely by logic and reason.
What's the point of celebrating now that he's dead?
My great grandmother used to tell all of us -- if you're planning to come to my funeral: don't. Use the money and time you'd spend then and come visit me now.
I think now is a reasonable time to mourn. A great mathematician is no longer around to give talks (I went to one a few years ago and thought it was very neat), and if you know him personally then you won't get to see him and converse with him anymore. That's very sad. Sure, he may have done abstractly great things, but there's no denying there are sad aspects to it.
But as for celebrations and parties, those should be done while the guy is still around to enjoy, I think.
On a related note -- for anyone who hasn't read "Harry Potter and the Methods of Rationality" -- It's brilliant.
-- John Donne
This is a common snowclone (X is <far superior in some dimension - often intelligence> than you or I) that really bothers me. It's a kind of hero worship that attributes too much to the hero in question and makes unfounded assertions about "you or I".
I can understand that people become enthuisiastic about their heroes and that exaggeration is even a form of showing respect. But too much is no good for anyone.
Because we wanted a little more time with him? Because we don't have enough geniuses?
-Benoit Mandelbrot
Interactive version: http://www.tagxedo.com/artful/87f79fa9bb6340be
I was fascinated by fractals when I was very young, and in retrospect, and I owe a lifetime interest in Mathematics and computer science to him.
Farewell, sir!
One of the first programs I wrote on the IBM PC was a Fractal explorer (on a PS/2 using Turbo Pascal)
Benoit Mandelbrot, 1924-2010 A Greek among Romans
* "To Benoit Mandelbrot A Greek among Romans" is the Incipit of The "Black Swan" Taleb's book.
* Taleb calls Mandelbrot the "poet of Randomness" in the chap.16 "Aesthetics of Randomness"
* "Intellectually sophisticated characters were exactly what I looked for in life" (and they are seldom). Taleb p.255 The Black Swan, 2007.
* He could also have said an "Athenian among Boeotian" but Romans are powerful (vs. Boeotians) and Benoit Mandelbrot had to fight the establishment with his visual research. "Pariah amongst French Mathematicians". With his Fractal images, his work was "remarkably easy to understand" for the general public.
* Unlike in Rome, the most popular shows in Athenes were not Circus WWE gladiator fights, it was going to Aeschylus or Sophocles tragedies.
Taleb's homepage http://www.fooledbyrandomness.com/
I admire the wit of Taleb to call Mandelbrot a Greek--in this modern world of very Roman panem et circenses.
Not even. Taleb values a combination of intellectual integrity, street smarts, empiricism, and humility in the face of uncertainty.
Far from considering ordinary people 'like you and me' to be philistines, he finds those traits he values in many different walks of life - from the Brooklyn born street-smart trader 'Fat Tony', to casino operators (their risk is not the actual games), to military planners (the risk managers with the most at stake).
He also finds the opposite - the Platonists (those who make the mistake of believing their highly complex yet nevertheless oversimplified models can reliably represent reality) and the philistines (people who value commerce above all else, and art, science, literature only for their capacity to make money or signal it, if at all) - everywhere as well. His particular targets are Wall Street, financial academia, and Economics Nobel, not 'you and me'.
He's quite clear on this in his books and writings.
http://en.wikipedia.org/wiki/Ludic_fallacy#Relation_to_Plato...
The expression "A Greek among Romans" is used maybe because Mandelbrot perspective to geometry was a bit different than the common scientific community in 1975-1985. There were many mentions about the "fractal set" just being "fancy" maths. He learned from the community while remaining unique in the community. But now there are many relationship with other model like "diffusion-limited aggregation" (DLA) and the fractal set is now one of the many models to describe our environment.
And then Benoit Mandelbrot died yesterday. Very odd coincidence. Rest in peace, Mr. Mandelbrot.
I programmed my first mandelbrot in basic, then in pascal and C.
Fractint represent! http://spanky.triumf.ca/www/fractint/fractint.html
Atleast in network traffic analysis, there seemed to be a lot of buzz about "self-similar" nature of TCP/IP,Ethernet, till around 2005-2006- you can see heavily cited papers on Google scholar.
But,of late -atleast in the past three years- you wouldn't find heavily-cited research/publications on fractals in top conferences. ( I may be wrong, I only did a quick look up)
Has the interest in application of fractals fizzled out in the past few years?
I see kids in schools being lauded for correctly identifying triangles, squares and circles and for saying "the moon is a circle". I've wondered whether teachers ever found it strange that true triangles, squares and cubes were hard to find in nature. Wondered whether we're teaching kids to look through the peep hole of classical geometry.
Then I think of Mandelbrot and take comfort in that this man who probably schooled that way too managed to break free, drop the peep hole, and mathematically see what we all see day in and day out, but are blind to. That gives me hope that we as a society are a capable lot.
It also gives me hope that fractals have been around in societies for much longer than we commonly know of .. presented beautifully by Ron Eglash at TED - http://www.ted.com/talks/ron_eglash_on_african_fractals.html
If you have Java and a (recent) NVidia or ATI graphic card you can download the software here http://jogamp.org/jocl/www/ (it is one of the demos). It requires OpenCL.
Great man, great contribution to humanity.
function inValues= mndl(limits) %no inputs needed, used by the script to zoom in
%amount of detail to calculate; larger number = better resolution, slower calculation stepsR=300; stepsI=300;
%maximum iterations used in calculations maxIter=50;
if exist('limits')~=1; %intial range of real and imaginary numbers to compute lowerR=-2; lowerI=-1.25; higherR=1; higherI=1.25; else numel(limits)==4; %range to compute after zooming in, determined by axis lowerR=limits(1); lowerI=limits(3); higherR=limits(2); higherI=limits(4); end
%Constants: slR=(higherR-lowerR)/(stepsR-1); slI=(higherI-lowerI)/(stepsI-1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Create the Mandelbrot image.
[x,y]=meshgrid([0:stepsR-1]slR+lowerR,[0:stepsI-1]slI+lowerI); inValues=ones(size(x)); z=zeros(size(x)); c=(x+1iy);
h_z=1:(stepsRstepsI); for counter=1:maxIter z(h_z)=z(h_z).^2+c(h_z); h_z= h_z(abs(z(h_z))<2); inValues(h_z)=inValues(h_z)+1; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%format presentation of Mandelbrot image colormap jet; pcolor(x,y,log(double(inValues))); title('Mandelbrot Image: Zoom In and Sharpen for Details'); shading interp; axis off;
zoom %turn on zoom feature initially clear inValues
%Buttons:
%recalculate image to enhance after zooming in (just calls the function %again with new input argument based on current axis) h1= uicontrol('Parent',gcf,'Units','points', ... 'Callback',['mndl(axis);zoom;'], ... 'Position',[105 5 105 20],'Style','pushbutton','String','Sharpen (after zooming in)');
%turn the zoom button on or off h2= uicontrol('Parent',gcf,'Units','points', ... 'Callback',['zoom'], ... 'Position',[215 5 55 20],'Style','pushbutton','String','Zoom On/Off');
%reset the image h3= uicontrol('Parent',gcf,'Units','points', ... 'Callback',['mndl();zoom;'], ... 'Position',[275 5 40 20],'Style','pushbutton','String','Reset');
One site that was pointed out here in particular was the Mandelbub, which looks amazing:
dc -e '[lolssdsl0lqx]sx[1+lddd*lld*-ls+dsdrll2**lo+dsld*rd*+4<kd15>q]sq[q]9ksk[d77/3*2-ss47lxx-P1+d78>0]s00[d23/.5-3*so0l0xr10P1+d24>u]dsux'http://www.youtube.com/watch?v=zOPQ1l4sCjY
And here's Benoit Mandelbrot's giving a talk at TED: