Benoit Mandelbrot, RIP(kottke.org)
kottke.org
Benoit Mandelbrot, RIP
http://kottke.org/10/10/benoit-mandelbrot-rip
28 comments
He died at 85. He had a long full life and accomplished far, far more than you or I ever will, combined, multiplied by 256. (I'd like to think that's an exaggeration; alas.)
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.
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.
> It should be a time for celebration, of the incredible way in which Mandelbrot has contributed to the sum of Humanity's Greatness.
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.
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.
Celebrating the life of the dead is a coping mechanism for the living, not as a feel-good benefit for the corpse.
There's no value in pointing out that most of the things we do when somebody dies make no sense. We all know that they make no sense, but we do them anyway, because we feel the need to do something, and aside from the bare mechanical fact of getting the corpse out of the way before it starts to smell there's really not much to do that does make sense.
There's no value in pointing out that most of the things we do when somebody dies make no sense. We all know that they make no sense, but we do them anyway, because we feel the need to do something, and aside from the bare mechanical fact of getting the corpse out of the way before it starts to smell there's really not much to do that does make sense.
Coping makes sense and celebration can be a wonderful way to cope.
My grandma’s brothers and sisters, kids and grandkids came spontaneously together in her living room shortly after she died at the age of 85. We told each other stories about her life, how she fought her illness late in life, about pranks her kids played on her, how she, as the oldest, had to take care of her brothers and sisters after her parents died early. It was absolutely wonderful and we laughed a lot. Not for her benefit but for us. Much better than the phony consolation and rigid structure of the funeral that followed.
My grandma should never have died. Nobody should ever have to die. But I have become convinced that if someone does celebration is the right way to say goodbye. The mourning will come anyway, be sure to celebrate a little.
My grandma’s brothers and sisters, kids and grandkids came spontaneously together in her living room shortly after she died at the age of 85. We told each other stories about her life, how she fought her illness late in life, about pranks her kids played on her, how she, as the oldest, had to take care of her brothers and sisters after her parents died early. It was absolutely wonderful and we laughed a lot. Not for her benefit but for us. Much better than the phony consolation and rigid structure of the funeral that followed.
My grandma should never have died. Nobody should ever have to die. But I have become convinced that if someone does celebration is the right way to say goodbye. The mourning will come anyway, be sure to celebrate a little.
Nobody should ever have to die.
I don't think that's a particularly useful or healthy attitude to have towards death, actually.
I don't think that's a particularly useful or healthy attitude to have towards death, actually.
Why? And what could be healthy about something as destructive as embracing death?
I like to be pragmatic. I know very well that I will most likely die in a few decades. That’s just how it looks to be at the moment. I do however strongly believe we and the generations that follow us should fight death and that we can win.
I like to be pragmatic. I know very well that I will most likely die in a few decades. That’s just how it looks to be at the moment. I do however strongly believe we and the generations that follow us should fight death and that we can win.
Well, since you are a pragmatic ...
If we could live forever, than we couldn't have any children (our reproduction rate is exponential, but there's only one planet that can hold us all and it doesn't grow any larger).
Stretching this, there would be no real notion of parents or grandparents. And it would get pretty boring too.
As most of us here, you're probably too young. Do you have children? Wait until you see your first toddler walking towards you while laughing.
It's a sentiment worth dying for ;)
If we could live forever, than we couldn't have any children (our reproduction rate is exponential, but there's only one planet that can hold us all and it doesn't grow any larger).
Stretching this, there would be no real notion of parents or grandparents. And it would get pretty boring too.
As most of us here, you're probably too young. Do you have children? Wait until you see your first toddler walking towards you while laughing.
It's a sentiment worth dying for ;)
So I'm not sure if I agree with this argument.. And I'm going to link to the ultra-layman's version here: http://www.fanfiction.net/s/5782108/39/Harry_Potter_and_the_... but why celebrate at someone dying at 85 when we can/should be able to make them live till 170. Or longer.
On a related note -- for anyone who hasn't read "Harry Potter and the Methods of Rationality" -- It's brilliant.
On a related note -- for anyone who hasn't read "Harry Potter and the Methods of Rationality" -- It's brilliant.
Oh, certainly. And people living until 85/100 has become common only recently (relatively speaking).
I'm merely mourning the emotional complex of otherwise-logical humans. I happened to have a frustrating week due to coworkers being unwilling to think about logical benefits of proposed solutions, letting their emotions overwhelm their judgement. "Schedule feature requests? Schedules cause pain, anguish, and suffering; also monsters will materialize and devour your soul. Your whole soul. Scheduling is out of the question. P.S. I assigned you a bug to get done before tomorrow evening (seriously). Drop your multi-week project and work on that, now. Don't worry, I cleared it with the lead programmer."
So when I read the top comment of the top article on HN, and realized it was negatively charged with emotion, I suppose I got a little cynical. :)
I'm merely mourning the emotional complex of otherwise-logical humans. I happened to have a frustrating week due to coworkers being unwilling to think about logical benefits of proposed solutions, letting their emotions overwhelm their judgement. "Schedule feature requests? Schedules cause pain, anguish, and suffering; also monsters will materialize and devour your soul. Your whole soul. Scheduling is out of the question. P.S. I assigned you a bug to get done before tomorrow evening (seriously). Drop your multi-week project and work on that, now. Don't worry, I cleared it with the lead programmer."
So when I read the top comment of the top article on HN, and realized it was negatively charged with emotion, I suppose I got a little cynical. :)
I'm catching up on my HN 100 feed, and want to thank you for recommending that work...it's amazing!
In case anyone else is as skeptical as I am ("another Harry Potter fan fic? Why is it special?), I want to point out that this work is by Eliezer Yudkowsky, a major contributor to Less Wrong (lesswrong.com).
He has a remarkable ability to define and express rational ideas. He takes concepts and terms that I've only encountered in a classroom, and puts them in the middle of a sentence like they're ordinary ideas, and it makes sense. I know I'm not doing a very good job of expressing why I like his writing so much, but I do.
In case anyone else is as skeptical as I am ("another Harry Potter fan fic? Why is it special?), I want to point out that this work is by Eliezer Yudkowsky, a major contributor to Less Wrong (lesswrong.com).
He has a remarkable ability to define and express rational ideas. He takes concepts and terms that I've only encountered in a classroom, and puts them in the middle of a sentence like they're ordinary ideas, and it makes sense. I know I'm not doing a very good job of expressing why I like his writing so much, but I do.
Any man's death diminishes me, because I am involved in Mankind;
-- John Donne
-- John Donne
I don't get why people think it is "OK" if somebody dies at age 80 or older. Yes, it is the course of life. But nobody likes to die - no matter how old (except maybe when suffering from terrible painful illnesses).
I saw a documentary on people over 100. Just about all of them felt their time had come some 20 years earlier, and some were very bitter about it.
Now, you could make the argument that they wouldn't want to die if they were in good health. But then you'd have to start thinking about how good your health needs to be - good enough not to need help? Good enough to be able to do anything you want? Good enough not to worry about doing stupid things? Good enough to keep up with the world as it races ahead, knowing you will eventually be required to understand all the new things?
Now, you could make the argument that they wouldn't want to die if they were in good health. But then you'd have to start thinking about how good your health needs to be - good enough not to need help? Good enough to be able to do anything you want? Good enough not to worry about doing stupid things? Good enough to keep up with the world as it races ahead, knowing you will eventually be required to understand all the new things?
I admit I don't know many people over 100. My grandma is 90, but I never asked her if she wants to die. From what I've read, I would have expected a positive outlook on life to be a character trait shared by many old people.
I guess nature has also made it so that it becomes easier to die. As I said, if your physical health is dwindling day by day, perhaps there is a point when it doesn't seem so much fun to be alive anymore. Also if all friends have already died, perhaps it becomes lonely.
All these are just more reasons to feel sad, though. What if we could become 80 and still feel fit?
I guess nature has also made it so that it becomes easier to die. As I said, if your physical health is dwindling day by day, perhaps there is a point when it doesn't seem so much fun to be alive anymore. Also if all friends have already died, perhaps it becomes lonely.
All these are just more reasons to feel sad, though. What if we could become 80 and still feel fit?
My grandparents are also close to 90, and they do feel very lonely, I can see it in them whenever I visit.
My grandfather in particular was an agricultural scientist, he loves plants and outdoors and working with tools, and used to be very energetic.
Now he has to sit on a wheelchair, and grows bored of watching TV and reading (it doesn't help that his eyesight is very bad).
Their current enjoyment are their grandchildren, and we've grown old. I just hope they can get to see their grand-grandchildren (my girlfriend and I expect to have children in 2 to 3 years' time), that might get them some enjoyment again.
My grandfather in particular was an agricultural scientist, he loves plants and outdoors and working with tools, and used to be very energetic.
Now he has to sit on a wheelchair, and grows bored of watching TV and reading (it doesn't help that his eyesight is very bad).
Their current enjoyment are their grandchildren, and we've grown old. I just hope they can get to see their grand-grandchildren (my girlfriend and I expect to have children in 2 to 3 years' time), that might get them some enjoyment again.
I keep wondering if I should introduce my grandma (90 years old) to World Of Warcraft. A couple of years I gave her her first computer (against the advice of the rest of the family), and she does a lot of stuff with it (for example email, online banking, what I know).
Hm, maybe I'll just give her a WoW account + better graphics card for christmass. Who knows :-)
In theory the internet should be great for lonely people stuck at home. My problem is that apart from Hacker News, I don't really know where to turn on the internet when I feel lonely, either.
Any pointers? Most chat rooms seem really tacky, but I didn't do that much research.
Is there a MMORPG for the iPad yet?
Hm, maybe I'll just give her a WoW account + better graphics card for christmass. Who knows :-)
In theory the internet should be great for lonely people stuck at home. My problem is that apart from Hacker News, I don't really know where to turn on the internet when I feel lonely, either.
Any pointers? Most chat rooms seem really tacky, but I didn't do that much research.
Is there a MMORPG for the iPad yet?
"accomplished far, far more than you or I ever will"
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.
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.
Can't we all just accept that the whole "I am so sad that X is gone" combined with the "Oh well, he was 85 and lived a good life" thing is just a natural part of the human dealing-with-death process? Do we have to take it all so literally and deconstruct every part of it?
I'll be the first to admit that the reason I'm sad about the not-particularly-untimely death of some dude I've never met has nothing to do with him, and everything to do with the reminder that I, and everybody I care about, will also die at some point. Mouthing the meaningless platitudes which we associate with death helps to take the sting away.
I'll be the first to admit that the reason I'm sad about the not-particularly-untimely death of some dude I've never met has nothing to do with him, and everything to do with the reminder that I, and everybody I care about, will also die at some point. Mouthing the meaningless platitudes which we associate with death helps to take the sting away.
> I don't get why humans mourn the death of people who die at >80
Because we wanted a little more time with him? Because we don't have enough geniuses?
Because we wanted a little more time with him? Because we don't have enough geniuses?
And because getting frail, sick, and dying is no fun at all for all parties involved.
Fine. Because we would like him to have a couple more decades of a healthy and productive life.
Better now? ;-)
Better now? ;-)
It's not sad that he died, he was 85 years old. He gave a lot to the world and had a long (and judging by the last talk of his I attended, happy) life. Pretty good deal if you ask me.
At whatever age someone dies, it is sad. It's always sad. Let's not deny that.
People morn the death of babies, who have accomplished nothing. Ought we not then morn to an even greater extend those who have accomplished something?
We mourn babies and children more because they did not get a chance to live a full life - a loss of potential in more formal terms.
People who reach old age have fulfilled all the potential they can realistically expect to, and death is less unexpected (i.e. "everybody dies, you're lucky to have made it this far"). While we still mourn them, we can also celebrate their life and achievements.
People who reach old age have fulfilled all the potential they can realistically expect to, and death is less unexpected (i.e. "everybody dies, you're lucky to have made it this far"). While we still mourn them, we can also celebrate their life and achievements.
They mourn the loss of the potential of what their lives might have been, not their accomplishments.
He's not dead, he's just transformed into a similar form at a different level of zoom.
"RIP Beniot Mandelbrot, fractal man. Assume he's survived by a number of smaller versions of himself." Eliot Reuben / @ereuben
Random thought: Every human is a fractal, and our age is our level of zoom.
That's so interesting. We are definitely self-similar, over and over in the course of our lives. If you could view a person 4-dimensionally (with time as the 4th), then the furthest level of zoom would be the person's entire life, replicating patterns at every instance. Zoom to any shorter time span and you would likely see something different but still similar. Could the narrowest level of zoom be a single thought in a single instance? That it itself probably has fractal-levels of complexity.
That reads like "Slaughterhouse five" by Vonnegut.
The NOVA episode on fractals (and Mandelbrot) was one the of best NOVA's that I've watched:
http://video.pbs.org/video/1050932219/
As recommended viewing I'd add Nigel Lesmoir-Gordon's "Fractals: The Colors of Infinity", presented by Arthur C. Clarke.
Benoit speaking on 'Roughness' at MIT (140min):
http://mitworld.mit.edu/video/52
We're sorry, but this video is not available in your region due to rights restriction
Here's my tribute to Benoit Mandelbrot (text from Wikipedia):
http://i.imgur.com/RoZ1j.jpg
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.
http://i.imgur.com/RoZ1j.jpg
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.
There are some things that literally change how you perceive the world. Learning about fractal geometry is one of those things.
Farewell, sir!
Farewell, sir!
NYT has confirmed it - http://www.nytimes.com/2010/10/17/us/17mandelbrot.html
One of the first programs I wrote on the IBM PC was a Fractal explorer (on a PS/2 using Turbo Pascal)
One of the first programs I wrote on the IBM PC was a Fractal explorer (on a PS/2 using Turbo Pascal)
Can someone explain "A Greek among Romans" from Taleb's homepage?
Benoit Mandelbrot, 1924-2010 A Greek among Romans
Benoit Mandelbrot, 1924-2010 A Greek among Romans
It seems that Taleb wants to separate Mandelbrot, a sophisticated, educated, refined, and übersmart person, from the rest of the crowd.
* "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/
* "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/
A few weeks ago I visited the Acropolis in Athens for the first time. To know that, about 25 centuries ago, Euripides and Sophocles presented their premiers in there, at the theater of Dionysos, suddenly gave a pile of rubble an extraordinary sense of purpose and meaning.
I admire the wit of Taleb to call Mandelbrot a Greek--in this modern world of very Roman panem et circenses.
I admire the wit of Taleb to call Mandelbrot a Greek--in this modern world of very Roman panem et circenses.
The Greeks were truly great. Not only did they know that the earth is a sphere, they also calculated what size it was, and considered the possibility that it revolves around its axis and around the sun. They conjectured that matter is made of indivisible atoms. They calculated the value of pi. Unfortunately their discoveries based on logic and observation would later be dictated to be false by the bible (including the value of pi)...
Taleb evidently respects (ancient) Greeks and doesn't respect Romans, presumably because one group had enormous contributions to philosophy whereas the other was merely an economic and imperial superpower. He's calling regular philistines like you and me "Romans" as an insult, one he sees as particularly vulgar. Such pomp is standard behavior from him, and it shouldn't be validated.
He's calling regular philistines like you and me "Romans" as an insult, one he sees as particularly vulgar.
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.
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.
Ironic that he opposes "Platonists" and yet uses Greek as a term of praise. Who are the Romans that Taleb is referring to, then? The comment suggests they are the norm, and that a Greek is rare.
FWIW, opposing "Platonists" doesnt mean opposing Greeks. Aristotlean and Socratic were two different ways of thought but both greek.
It has to do with platonicity.
http://en.wikipedia.org/wiki/Ludic_fallacy#Relation_to_Plato...
http://en.wikipedia.org/wiki/Ludic_fallacy#Relation_to_Plato...
Sorry nothing to do with "Platonicity" which Taleb strongly criticized. A "greek among Romans", is imo to describe somebody educated, vs a farmer like Cato the old, well versed in refined art vs. propaganda "pompier" political art (to show Power more than beauty or harmony; Romans could only copy Praxiteles), interested in Philosophy more than law. The Circus for the People of Athenes was tragedy by Aeschylus and Sophocles.
I think this is related to Mandelbrot's different perspective to the world and seeing the fractal set as a kind of "chaos" geometry (kind of contradicting).
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.
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.
This is so odd. I just gave a quick presentation on him yesterday in theology class. The prompt was to "Use you creative genius to show God in a visual manner." I argued that we couldn't describe God in finite terms, so I used fractals because of their infinite detail. Much better response from the class than collages of waterfalls and sunsets. And now that I think about it, fractals came up in my Physics class too. My teacher was describing a talk he gave at Wolfram Research on the subject.
And then Benoit Mandelbrot died yesterday. Very odd coincidence. Rest in peace, Mr. Mandelbrot.
And then Benoit Mandelbrot died yesterday. Very odd coincidence. Rest in peace, Mr. Mandelbrot.
The first program written in C that I saw that did anything interesting was a Mandelbrot set generator. It's what hooked me on programming, I think.
I owe a lot to him. It was a picture of a Mandelbrot on a computer lab wall that inspired me to pursue programming and computer science in the 90s. It was the combination of math and art that was so beautiful to me.
I programmed my first mandelbrot in basic, then in pascal and C.
Fractint represent! http://spanky.triumf.ca/www/fractint/fractint.html
I programmed my first mandelbrot in basic, then in pascal and C.
Fractint represent! http://spanky.triumf.ca/www/fractint/fractint.html
Does anyone have pointers/links to application or research of fractals in the recent past ?
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?
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?
What profound ideas this man brought to the world. Just finished a project for a guy who mentioned he was deeply inspired by Mandelbrot. With the help of a few friends, he built the world's largest VW bus. Can you spot the hidden Mandelbrot set in this header image? http://www.walterthebus.org/the-scoop/tribe-walter/
Mandelbrot changed much of my world view and how mathematics relates to it.
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
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
even in his old age his thinking was still fresh. he had an unusual clarity of thought and was able to convey his theories even to the layman. the man may be dead but his ideas live on.
Learning about the fractional dimension of the coast of Britain was one of the most interesting discoveries I've had.
:(
I never really liked coastlines as an explanation of fractals. Sure, they have some of the same features as you zoom in from the world map level to the callipers-along-the-beach level. But it doesn't keep going forever -- you hit the atomic level where the coastline isn't so much fractal as poorly-defined.
I found some screenshot of a program which can render Mandelbrot fractals extended to the 4th dimension.
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.
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.
:(
I was fascinated by fractals when I was young, I even attended a Mandelbrot conference when I was 14. I could not understand any of the mathematical fundamentals, but there was something intuitively beautiful and irresistible about fractals.
Great man, great contribution to humanity.
Great man, great contribution to humanity.
1+i minutes of silence for him.
In his honor, here is Matlab code to generate a Mandlebrot set (from an old homework assignment):
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');
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');
There are some amazing images of fractals on the web.
One site that was pointed out here in particular was the Mandelbub, which looks amazing:
http://www.skytopia.com/project/fractal/mandelbulb.html
One site that was pointed out here in particular was the Mandelbub, which looks amazing:
http://www.skytopia.com/project/fractal/mandelbulb.html
I think I copied this from HN once. Paste to terminal:
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'Sorry about the weird formatting, it looks fine when I paste in the comment box. You'll need to add line breaks after the comments to get it working.
You might want to put that code in a site such as http://pastebin.com/ and link to it instead.
His 'Fractals and Scaling In Finance' helped me wrap my brain around power laws. Perhaps if certain folks had read it when it was first published (1997), we would have had less financial turmoil these past few years.
Goodbye professor. You were, and will remain, one of my greatest inspirations.
[deleted]
This is the full Mandelbrot Set song by Jonathan Coulton:
http://www.youtube.com/watch?v=zOPQ1l4sCjY
And here's Benoit Mandelbrot's giving a talk at TED:
http://www.ted.com/talks/view/id/909
http://www.youtube.com/watch?v=zOPQ1l4sCjY
And here's Benoit Mandelbrot's giving a talk at TED:
http://www.ted.com/talks/view/id/909
The song is free on Coulton's website:
http://www.jonathancoulton.com/songdetails/Mandelbrot%20Set
http://www.jonathancoulton.com/songdetails/Mandelbrot%20Set
Ahh if only we could discuss things in never ending complexity. Here's to the father of fractals.
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.