Category: Science

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.

What is the purpose of dreaming? And more on Circadian Rhythms

Continuing with our recent exploration of sleep, I came across this passage by sleep researcher Rosalind Cartwright in The Twenty-four Hour Mind: The Role of Sleep and Dreaming in Our Emotional Lives, on the role of dreams:

Despite differences in terminology, all the contemporary theories of dreaming have a common thread—they all emphasize that dreams are not about prosaic themes, not about reading, writing, and arithmetic, but about emotion, or what psychologists refer to as affect. What is carried forward from waking hours into sleep are recent experiences that have an emotional component, often those that were negative in tone but not noticed at the time or not fully resolved. One proposed purpose of dreaming, of what dreaming accomplishes (known as the mood regulatory function of dreams theory) is that dreaming modulates disturbances in emotion, regulating those that are troublesome. My research, as well as that of other investigators in this country and abroad, supports this theory. Studies show that negative mood is down-regulated overnight. How this is accomplished has had less attention.

I propose that when some disturbing waking experience is reactivated in sleep and carried forward into REM, where it is matched by similarity in feeling to earlier memories, a network of older associations is stimulated and is displayed as a sequence of compound images that we experience as dreams. This melding of new and old memory fragments modifies the network of emotional self-defining memories, and thus updates the organizational picture we hold of ‘who I am and what is good for me and what is not.’ In this way, dreaming diffuses the emotional charge of the event and so prepares the sleeper to wake ready to see things in a more positive light, to make a fresh start. This does not always happen over a single night; sometimes a big reorganization of the emotional perspective of our self-concept must be made — from wife to widow or married to single, say, and this may take many nights. We must look for dream changes within the night and over time across nights to detect whether a productive change is under way. In very broad strokes, this is the definition of the mood-regulatory function of dreaming, one basic to the new model of the twenty-four hour mind I am proposing.

(*Update*) While not on dreams, this passage on circadian rhythms from Zoobiquity: What Animals Can Teach Us About Health and the Science of Healing, fits very much into our recent look at sleep:

Studies have shown that disrupting circadian rhythms by even one hour during the switch to daylight saving time may increase depression, traffic accidents, and heart attacks. These rhythms affect consumption and metabolism in animals—it is hard to imagine that they aren’t also playing a role in human appetites as well. Controlling environmental light with lamps, TVs, and computers gives us incredible flexibility and productivity. But it interrupts daily and yearly cycles that were billions of years in the making and are shared by countless creatures on our planet.

We are never certain

Gilbert Keith Chesterton

We are never certain; we are always ignorant to some degree.
Much of the information we have is either incorrect or incomplete.

— Peter Bernstein


Gilbert Keith Chesterton, the English literary critic and author of the Father Brown mysteries:

The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait

Michael Mauboussin: Three Things to Consider in Order To Make an Effective Prediction

Michael Mauboussin commenting on Daniel Kahneman:

When asked which was his favorite paper of all-time, Daniel Kahneman pointed to “On the Psychology of Prediction,” which he co-authored with Amos Tversky in 1973. Tversky and Kahneman basically said that there are three things to consider in order to make an effective prediction: the base rate, the individual case, and how to weight the two. In luck-skill language, if luck is dominant you should place most weight on the base rate, and if skill is dominant then you should place most weight on the individual case. And the activities in between get weightings that are a blend.

In fact, there is a concept called the “shrinkage factor” that tells you how much you should revert past outcomes to the mean in order to make a good prediction. A shrinkage factor of 1 means that the next outcome will be the same as the last outcome and indicates all skill, and a factor of 0 means the best guess for the next outcome is the average. Almost everything interesting in life is in between these extremes.

To make this more concrete, consider batting average and on-base percentage, two statistics from baseball. Luck plays a larger role in determining batting average than it does in determining on-base percentage. So if you want to predict a player’s performance (holding skill constant for a moment), you need a shrinkage factor closer to 0 for batting average than for on-base percentage.

I’d like to add one more point that is not analytical but rather psychological. There is a part of the left hemisphere of your brain that is dedicated to sorting out causality. It takes in information and creates a cohesive narrative. It is so good at this function that neuroscientists call it the “interpreter.”

Now no one has a problem with the suggestion that future outcomes combine skill and luck. But once something has occurred, our minds quickly and naturally create a narrative to explain the outcome. Since the interpreter is about finding causality, it doesn’t do a good job of recognizing luck. Once something has occurred, our minds start to believe it was inevitable. This leads to what psychologists call “creeping determinism” – the sense that we knew all along what was going to happen. So while the single most important concept is knowing where you are on the luck-skill continuum, a related point is that your mind will not do a good job of recognizing luck for what it is.

Mauboussin is the author of The Success Equation: Untangling Skill and Luck in Business, Sports, and Investing.

Erik Hollnagel: The Search For Causes

A great passage from Erik Hollnagel‘s Barriers And Accident Prevention on the search for causes:

Whenever an accident happens there is a natural concern to find out in detail exactly what happened and to determine the causes of it. Indeed, whenever the result of an action or event falls significantly short of what was expected, or whenever something unexpected happens, people try to find an explanation for it. This trait of human nature is so strong that we try to find causes even when they do not exist, such as in the case of misleading or spurious correlations. For a number of reasons humans seem to be extremely reluctant to accept that something can happen by chance. One very good reason is that we have created a way of living that depends heavily on the use of technology, and that technological systems are built to function in a deterministic, hence reliable manner. If therefore something fails, we are fully justified in trying to find the reason for it. A second reason is that our whole understanding of the world is based on the assumption of specific relations between causes and effects, as amply illustrated by the Laws of Physics. (Even in quantum physics there are assumptions of more fundamental relations that are deterministic.) A third reason is that most humans find it very uncomfortable when they do not know what to expect, i.e., when things happen in an unpredictable manner. This creates a sense of being out of control, something that is never desirable since – from an evolutionary perspective – it means that the chances of survival are reduced.

This was described by Friedrich Nietzsche when he wrote:

[T]o trace something unknown back to something known is alleviating, soothing, gratifying and gives moreover a feeling of power. Danger, disquiet, anxiety attend the unknown – the first instinct is to eliminate these distressing states. First principle: any explanation is better than none … The cause-creating drive is thus conditioned and excited by the feeling of fear.

Hollnagel, continues:

A well-known example of this is provided by the phenomenon called the gambler’s fallacy. The name refers to the fact that gamblers often seem to believe that a long row of events of one type increases the probability of the complementary event. Thus if a series of ‘red’ events occur on a roulette wheel, the gambler’s fallacy lead people to believe that the probability of ‘black’ increases. … Rather than accepting that the underlying mechanism may be random people invent all kinds of explanations to reduce the uncertainty of future events.