Abstract: "Benoit Mandelbrot's scientific legacy spans an extraordinary range of disciplines, from linguistics and fluid turbulence to cosmology and finance, suggesting the intellectual temperament of a 'fox' in Isaiah Berlin's famous dichotomy of thinkers. This essay argues, however, that Mandelbrot was, at heart, a 'hedgehog': a thinker unified by a single guiding principle. Across his diverse pursuits, the concept of scaling -- manifested in self-similarity, power laws, fractals, and multifractals -- served as the central idea that structured his work. By tracing the continuity of this scaling paradigm through his contributions to mathematics, physics, and economics, the paper reveals a coherent intellectual trajectory masked by apparent eclecticism. Mandelbrot's enduring insight in the modeling of natural and social phenomena can be understood through the lens of the geometry and statistics of scale invariance."
max_ 72 days ago [-]
“The fox knows many things, but the hedgehog knows one big thing.”
Berlin interprets this aphorism as articulating a profound distinction among thinkers, writers, and, more generally, human beings.
libraryofbabel 72 days ago [-]
It’s a cute aphorism, and useful sometimes, but when you look closely or from different angles hedgehogs often have foxy attributes, or vice versa. Some moments in a person’s life they look more like a fox, other times like a hedgehog. Perhaps the distinction applies better to specific ideas or to pieces of work than as a fixed essence of a person.
Einstein might seem like a quintessential hedgehog (surely the principle of relativity is a Big Hedgehog Idea if ever there was one). Then you learn he once invented a refrigerator. Tolstoy looks like an obvious fox earlier in his writing career, but increasingly a hedgehog towards the end of his life. And slightly less exaltedly, I feel like a fox in some contexts and a hedgehog in others. It might change day to day, or depend on who I’m talking too.
(People are complicated. All aphorisms are wrong, but some are useful I guess. I still quote this one sometimes.)
zkmon 72 days ago [-]
For thinkers of that time, there was a vast unexplored green field infront of them, to plough and harvest. It's not hard to imagine ploughing skill of one field could help ploughing others too. My friend used to say, if you have quick enough reflexes to play table tennis, you can be good at other sports too.
nairboon 72 days ago [-]
I wonder if the people in 100 years will refer to the current time period (now) the same way as we sometimes do to about ~100 years ago.
As in did the scientist and curious minds in the last century really have this golden period to just wander around in all these greenfields, whereas nowadays the fields are not so green anymore. Or is this just a normal phenomena of any time period?
PaulHoule 72 days ago [-]
It certainly was easier to get an academic job circa 1960. Things have gotten more difficult in physics because the experimental frontier has moved further away, I mean, you can make whatever theory you want and it is meaningless because we don’t have a machine that can measure the neutrino mass, observe neutrino decay, confirm physics at the GUT or string scale, detect the darkon, etc.
Even something like Mandelbrot’s work was disappointing if you were in grad school in the 1990s because it was not like enough progress was made in fractals post-Mandelbrot that you could get a job working on fractals or chaos.
ontouchstart 72 days ago [-]
There is a third type: rabbit. This is a golden age of rabbit holes. A quick rabbit jumps through complicated holes and tunnels to escape from something or chase something.
We can also call someone chasing a rabbit a fox. Like all the ones chasing LLM agents now.
direwolf20 72 days ago [-]
Sounds like the money's in being a rabbit
ontouchstart 72 days ago [-]
To some extent. Many mathematical breakthroughs are not from mathematicians thinking in the office but mathematical minded people doing engineering work and bumped into big ideas. Mandelbrot was one of them, so was Alan Turing, Claude Shannon, Tony Hoare, …
They are engineers by trade, that is chasing the money as food. But money is not enough for them. So I would call them rabbits instead of foxes.
bpavuk 72 days ago [-]
the world is in a loop, and that loop repeats itself approximately every 33 years!
Xmd5a 72 days ago [-]
elaborate please
d-lisp 72 days ago [-]
Unfortunately that is the end of the loop sentence. You have to wait 33 years now to learn about the elaboration.
bpavuk 71 days ago [-]
that's a Netflix series reference and observation of cyclic nature of history in one package :)
Berlin interprets this aphorism as articulating a profound distinction among thinkers, writers, and, more generally, human beings.
Einstein might seem like a quintessential hedgehog (surely the principle of relativity is a Big Hedgehog Idea if ever there was one). Then you learn he once invented a refrigerator. Tolstoy looks like an obvious fox earlier in his writing career, but increasingly a hedgehog towards the end of his life. And slightly less exaltedly, I feel like a fox in some contexts and a hedgehog in others. It might change day to day, or depend on who I’m talking too.
(People are complicated. All aphorisms are wrong, but some are useful I guess. I still quote this one sometimes.)
Even something like Mandelbrot’s work was disappointing if you were in grad school in the 1990s because it was not like enough progress was made in fractals post-Mandelbrot that you could get a job working on fractals or chaos.
We can also call someone chasing a rabbit a fox. Like all the ones chasing LLM agents now.
They are engineers by trade, that is chasing the money as food. But money is not enough for them. So I would call them rabbits instead of foxes.
https://youtu.be/q3SMxgofZgA
Is it AI? Doesn't seem so