Tag: Physics

Benoit Mandelbrot — The Fractalist: Memoir of a Scientific Maverick

“I have never done anything like others,” Benoit Mandelbrot (1924-2010) once said.

That statement is proven time and time again in his autobiography: The Fractalist.

Mandelbrot is independent almost to a fault, his book an interesting memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at physics, engineering, arts, medicine, finance, and biology.

The Fractalist: Memoir of a Scientific Maverick

Nearly all common patterns in nature are rough. They have aspects that are exquisitely irregular and fragmented—not merely more elaborate than the marvelous ancient geometry of Euclid but of massively greater complexity. For centuries, the very idea of measuring roughness was an idle dream. This is one of the dreams to which I have devoted my entire scientific life.

Let me introduce myself. A scientific warrior of sorts, and an old man now, I have written a great deal but never acquired a predictable audience. So, in this memoir, please allow me to tell you who I think I am and how I came to labor for so many years on the first-ever theory of roughness and was rewarded by watching it transform itself into an aspect of a theory of beauty.

Mandelbrot was full of insight.

What shape is a mountain, a coastline, a river or a dividing line between two river watersheds? … Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

While that sounds obvious it wasn’t at the time. In showing that triangles, squares, and circles are more prevalent in textbooks than reality, he brought to life the discipline now known as fractal geometry, a general theory of “roughness.”

Mandelbrot was fascinating, in part, because he never stayed in one place very long.

An acquaintance of mine was a forceful dean at a major university. One day, as our paths crossed in a busy corridor, he stopped to make a comment I never forgot: “You are doing very well, yet you are taking a lonely and hard path. You keep running from field to field, leading an unpredictable life, never settling down to enjoy what you have accomplished. A rolling stone gathers no moss, and—behind your back—people call you completely crazy. But I don’t think you are crazy at all, and you must continue what you are doing. For a thinking person, the most serious mental illness is not being sure of who you are. This is a problem you do not suffer from. You never need to reinvent yourself to fit changes in circumstances; you just move on. In that respect, you are the sanest person among us.”

Quietly, I responded that I was not running from field to field, but rather working on a theory of roughness. I was not a man with a big hammer to whom every problem looked like a nail. Were his words meant to compliment or merely to reassure? I soon found out: he was promoting me for a major award.

Is mental health compatible with being possessed by barely contained restlessness? In Dante’s Divine Comedy, the deceased sentenced to eternal searching are pushed to the deepest level of the Inferno. But for me, an eternal search across countless scientific fields beyond obvious connection managed to add up to a happy life. A rolling stone perhaps, but not an unresponsive one. Overactive and self-motivated, I loved to roll along, stopping to listen and preach in lay monasteries of all kinds—some splendid and proud, others forsaken and out of the way.

He had a different way of looking at things. For example, he saw math problems as geometry.

I would raise my hand and describe my findings: “Monsieur, I see an obvious geometric solution.” I quickly grasped the most abstract problem that the teacher could contrive. And then — with no effort, conscious search, or delay — I continued along a path that somehow avoided every difficulty…. I managed to be examined on the basis of speed and good taste in, first, translating algebra back into geometry, and then thinking in terms of geometric shapes. My analytic skills remained so-so, but that did not matter — the hard work was done by geometry, and it sufficed to fill in short calculations that even I could manage.

Ultimately, The Fractalist is proof that “force of character and independence” can take some to great heights.

Freeman Dyson on The Difference Between Science and Philsophy

Freeman Dyson, writing in The NY Review of Books:

On quantum physics

The essence of quantum physics is unpredictability. At every instant, the objects in our physical environment—the atoms in our lungs and the light in our eyes—are making unpredictable choices, deciding what to do next. According to Everett and Deutsch, the multiverse contains a universe for every combination of choices. There are so many universes that every possible sequence of choices occurs in at least one of them. Each universe is constantly splitting into many alternative universes, and the alternatives are recombining when they arrive at the same final state by different routes. The multiverse is a huge network of possible histories diverging and reconverging as time goes on. The “quantum weirdness” that we observe in the behavior of atoms, the “spooky action at a distance” that Einstein famously disliked, is the result of universes recombining in unexpected ways.

On the difference between science and philosophy

Science is about facts that can be tested and mysteries that can be explored, and I see no way of testing hypotheses of the multiverse. Philosophy is about ideas that can be imagined and stories that can be told.

On philosophy

When and why did philosophy lose its bite? How did it become a toothless relic of past glories? These are the ugly questions that Jim Holt’s book compels us to ask. Philosophers became insignificant when philosophy became a separate academic discipline, distinct from science and history and literature and religion. The great philosophers of the past covered all these disciplines. Until the nineteenth century, science was called natural philosophy and officially recognized as a branch of philosophy. The word “scientist” was invented by William Whewell, a nineteenth-century Cambridge philosopher who became master of Trinity College and put his name on the building where Wittgenstein and I were living in 1946. Whewell introduced the word in the year 1833. He was waging a deliberate campaign to establish science as a professional discipline distinct from philosophy.

Whewell’s campaign succeeded. As a result, science grew to a dominant position in public life, and philosophy shrank. Philosophy shrank even further when it became detached from religion and from literature. The great philosophers of the past wrote literary masterpieces such as the Book of Job and the Confessions of Saint Augustine. The latest masterpieces written by a philosopher were probably Friedrich Nietzsche’s Thus Spoke Zarathustra in 1885 and Beyond Good and Evil in 1886. Modern departments of philosophy have no place for the mystical.

Richard Feynman — Take the World From Another Point of View

In this clip from a documentary film shot in Yorkshire in 1973, physicist and philosopher Richard Feynman (1918-1988) talks with Fred Hoyle, an accomplished astronomer from the United Kingdom.

Feynman poses the question: “What, today, do we not consider part of physics, which may ultimately be part of physics?”

His answer (which should be cued up here at the 7:10 mark) is the initial conditions of the universe, as well as the possibility that the physical laws themselves, evolve with time.

As he explains, there was a time when we considered the properties of substances to be chemistry, but as the quantum mechanical understanding of the atom evolved, we came to discover that this was actually all a part of physics.

In physics, our acceptance of the way things are (i.e. given conditions) without wondering why they’re like that is akin to playing chess without asking where the pieces should be placed before the game even starts.

It’s as though we’re doing a chess game and we’re working on the rules but we’re not worrying about how the pieces are supposed to be set up on the board in the first place. We tell ourselves, that’s not our business, that’s the business of cosmology and how the universe came to be. It’s interesting that in many other sciences, there’s a historical question. Like geology, we ask “How did the earth evolve into its present condition?” In biology, it’s “How did the various species evolve to get to be the way they are?” But the one field that has not admitted any evolutionary question is physics. “Here are the laws!” we say. We don’t even think about how they got that way. We think, well it’s been that way forever, it’s always been that way. It’s always been the same laws. And we try to explain the universe that way. So it might turn out that they’re not the same all the time, and that there is a historical, evolutionary question.

 

This fascinating conversation between two great minds continues in the follow-up video. Listen on to hear Feynman explain why he’s afraid to speculate about things.

Richard Feynman on Why Questions

“But the problem, you see, when you ask why something happens, how does a person answer why something happens?”

— Richard Feynman

In this beautiful video Richard Feynman on the nature of why questions and how they help us understand the world.

Interviewer: If you get hold of two magnets, and you push them, you can feel this pushing between them. Turn them around the other way, and they slam together. Now, what is it, the feeling between those two magnets?

Feynman: What do you mean, “What’s the feeling between the two magnets?”

Interviewer: There’s something there, isn’t there? The sensation is that there’s something there when you push these two magnets together.

Feynman: Listen to my question. What is the meaning when you say that there’s a feeling? Of course, you feel it. Now, what do you want to know?

Interviewer: What I want to know is what’s going on between these two bits of metal?

Feynman: They repel each other.

Interviewer: What does that mean, or why are they doing that, or how are they doing that? I think that’s a perfectly reasonable question.

Feynman: Of course, it’s an excellent question. But the problem, you see, when you ask why something happens, how does a person answer why something happens? For example, Aunt Minnie is in the hospital. Why? Because she went out, slipped on the ice, and broke her hip. That satisfies people. It satisfies, but it wouldn’t satisfy someone who came from another planet and knew nothing about why when you break your hip do you go to the hospital. How do you get to the hospital when the hip is broken? Well, because her husband, seeing that her hip was broken, called the hospital up and sent somebody to get her. All that is understood by people. And when you explain a why, you have to be in some framework that you allow something to be true. Otherwise, you’re perpetually asking why. Why did the husband call up the hospital? Because the husband is interested in his wife’s welfare. Not always, some husbands aren’t interested in their wives’ welfare when they’re drunk, and they’re angry.

And you begin to get a very interesting understanding of the world and all its complications. If you try to follow anything up, you go deeper and deeper in various directions. For example, if you go, “Why did she slip on the ice?” Well, ice is slippery. Everybody knows that, no problem. But you ask why is ice slippery? That’s kinda curious. Ice is extremely slippery. It’s very interesting. You say, how does it work? You could either say, “I’m satisfied that you’ve answered me. Ice is slippery; that explains it,” or you could go on and say, “Why is ice slippery?” and then you’re involved with something, because there aren’t many things as slippery as ice. It’s not very hard to get greasy stuff, but that’s sort of wet and slimy. But a solid that’s so slippery? Because it is, in the case of ice, when you stand on it (they say) momentarily the pressure melts the ice a little bit so you get a sort of instantaneous water surface on which you’re slipping. Why on ice and not on other things? Because water expands when it freezes, so the pressure tries to undo the expansion and melts it. It’s capable of melting, but other substances get cracked when they’re freezing, and when you push them they’re satisfied to be solid.

Why does water expand when it freezes and other substances don’t? I’m not answering your question, but I’m telling you how difficult the why question is. You have to know what it is that you’re permitted to understand and allow to be understood and known, and what it is you’re not. You’ll notice, in this example, that the more I ask why, the deeper a thing is, the more interesting it gets. We could even go further and say, “Why did she fall down when she slipped?” It has to do with gravity, involves all the planets and everything else. Nevermind! It goes on and on. And when you’re asked, for example, why two magnets repel, there are many different levels. It depends on whether you’re a student of physics, or an ordinary person who doesn’t know anything. If you’re somebody who doesn’t know anything at all about it, all I can say is the magnetic force makes them repel, and that you’re feeling that force.

You say, “That’s very strange, because I don’t feel a kind of force like that in other circumstances.” When you turn them the other way, they attract. There’s a very analogous force, electrical force, which is the same kind of a question, that’s also very weird. But you’re not at all disturbed by the fact that when you put your hand on a chair, it pushes you back. But we found out by looking at it that that’s the same force, as a matter of fact (an electrical force, not magnetic exactly, in that case). But it’s the same electric repulsions that are involved in keeping your finger away from the chair because it’s electrical forces in minor and microscopic details. There’s other forces involved, connected to electrical forces. It turns out that the magnetic and electrical force with which I wish to explain this repulsion in the first place is what ultimately is the deeper thing that we have to start with to explain many other things that everybody would just accept. You know you can’t put your hand through the chair; that’s taken for granted. But that you can’t put your hand through the chair, when looked at more closely, why, involves the same repulsive forces that appear in magnets. The situation you then have to explain is why, in magnets, it goes over a bigger distance than ordinarily. There it has to do with the fact that in iron all the electrons are spinning in the same direction, they all get lined up, and they magnify the effect of the force ’til it’s large enough, at a distance, that you can feel it. But it’s a force which is present all the time and very common and is a basic force of almost – I mean, I could go a little further back if I went more technical – but on an early level I’ve just got to tell you that’s going to be one of the things you’ll just have to take as an element of the world: the existence of magnetic repulsion, or electrical attraction, magnetic attraction.

I can’t explain that attraction in terms of anything else that’s familiar to you. For example, if we said the magnets attract like rubber bands, I would be cheating you. Because they’re not connected by rubber bands. I’d soon be in trouble. And secondly, if you were curious enough, you’d ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I’m trying to use the rubber bands to explain. So I have cheated very badly, you see. So I am not going to be able to give you an answer to why magnets attract each other except to tell you that they do. And to tell you that that’s one of the elements in the world – there are electrical forces, magnetic forces, gravitational forces, and others, and those are some of the parts. If you were a student, I could go further. I could tell you that the magnetic forces are related to the electrical forces very intimately, that the relationship between the gravity forces and electrical forces remains unknown, and so on. But I really can’t do a good job, any job, of explaining magnetic force in terms of something else you’re more familiar with, because I don’t understand it in terms of anything else that you’re more familiar with.

Related:
No Ordinary Genius
Cargo Cult Science
Feynman on Beauty
What does Bill Gates Read for Fun?