"Almost everything in social life is produced by rare but consequential shocks and jumps; all the while almost everything studied about social life focuses on the "normal," particularly with "bell curve" methods of inference that tell you close to nothing. Why? Because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty. Its nickname in this book is GIF, Great Intellectual Fraud."

The Bell curve is a fact of life. The blacks on average score 85 per cent on IQ and it is accurate, nothing to do with culture. The whites score on average 100. Asians score more … the Bell curve authors put it at least 10 points higher. These are realities that, if you do not accept, will lead to frustration because you will be spending money on wrong assumptions and the results cannot follow.

I quickly felt that I belonged at the American Enterprise Institute. The week I arrived in Washington I was introduced to a man I had long hoped to meet, Charles Murray, who in 1994 cowrote The Bell Curve. When his book was published I was still a student at the University of Leiden, where it seemed everyone was talking about this horribly racist book that argued that black people were genetically of lower intelligence than white people. I read it, of course, and I found it to be the opposite of racist, a compassionately written book about the urban challenges that confront black people more than white. All black people should read it.
When I as introduced to Murray, I couldn’t help thinking that even his head was shaped like a precise bell curve. While we exchanged greetings, I mentioned that I recognized his name from reading his book, at which point he gritted his teeth, no doubt bracing himself for another attack from an offended black person. When I said how great I thought his book was, his smile was so broad and so surprised. We became instant friends.

"A key point in my work: Randomness has more than one "state," or form, and each, if allowed to play out on a financial market, would have a radically different effect on the way prices behave. One is the most familiar and manageable form of chance, which I call "mild." It is the randomness of a coin toss, the static of a badly tuned radio. Its classic mathematical expression is the bell curve, or "normal" probability distribution-so-called because it was long viewed as the norm in nature. Temperature, pressure, or other features of nature under study are assumed to vary only so much, and not an iota more, from the average value. At the opposite extreme is what I call "wild" randomness. This is far more irregular, more unpredictable. It is the variation of the Cornish coastline-savage promontories, craggy rocks, and unexpectedly calm bays. The fluctuation from one value to the next is limitless and frightening. In between the two extremes is a third state, which I call "slow" randomness."

If you are going to use probability to model a financial market, then you had better use the right kind of probability. Real markets are wild. Their price fluctuations can be hair-raising-far greater and more damaging than the mild variations of orthodox finance. That means that individual stocks and currencies are riskier than normally assumed. It means that stock portfolios are being put together incorrectly; far from managing risk, they may be magnifying it. It means that some trading strategies are misguided, and options mis-priced. Anywhere the bell-curve assumption enters the financial calculations, an error can come out.

Why do [people] confuse probability and expectation, that is, probability [vs.] probability times payoff? Mainly because much... schooling comes from examples in symmetric environments... the... bell curve... is entirely symmetric.

The whole edifice of modern financial theory is, as described earlier, founded on a few simplifying assumptions. It presumes that homo economicus is rational and self-interested. Wrong, suggests the experience of the irrational, mob-psychology bubble and burst of the 1990's. A further assumption: that price variations follow the bell curve. Wrong, suggests the by-now widely accepted research of me and many others since the 1960's. And now the next assumption wobble: that price variations are what statisticians call i.i.d., independently and identically distributed-like the coin game with each toss unaffected by the last. Evidence for short-term dependence has already been mounting. And now comes the increasingly accepted but still confusing evidence of long-term dependence.

The most remarkable feature of Bell's work was undoubtedly the possibility it offered to determine experimentally whether or not Einstein's ideas could be kept. The experimental tests of Bell inequalities gave an unambiguous answer: entanglement cannot be understood as usual correlations, whose interpretation relies on the existence of common properties, originating in a common preparation, and remaining attached to each individual object after separation, as components of their physical reality.

In the ensuing decades, experimentalists performed increasingly sophisticated tests of Bell’s inequalities. But these tests have always had at least one “loophole,”...

This is what I did in... Ages of Discord, I looked at more than 200 years of American history... an aggregated measure of well being... the blue curve has gone through two cycles, and the red curve is a measure of instability...

"Well," he said thoughtfully, "it is my considered opinion that most coincidences are simply quirks of chance—if you extrapolate the bell curve of probability you will find statistical abnormalities that seem unusual but are, in actual fact, quite likely, given the amount of people on the planet and the amount of different things we do in our lives."

In the end, the Impressionists made the right choice, which is one of the reasons that their paintings hang in every major art museum in the world. But this same dilemma comes up again and again in our own lives, and often we don’t choose so wisely. The inverted-U curve reminds us that there is a point at which money and resources stop making our lives better and start making them worse.

An Incoherent Strategy When a company’s value curve looks like a bowl of spaghetti — a zigzag with no rhyme or reason, where the offering can be described as “low-high-low-low-high-low-high” — it signals that the company doesn’t have a coherent strategy. Its strategy is likely based on independent substrategies. These may individually make sense and keep the business running and everyone busy, but collectively they do little to distinguish the company from the best competitor or to provide a clear strategic vision. This is often a reflection of an organization with divisional or functional silos.

Murray and Herrnstein’s assertion, however, was that the discrepancy was so great that environment likely couldn’t explain it all. Similarly, environmental factors alone may not account for why, globally, Asians have on average higher IQs than other racial groups. The idea of measurable variations in average intelligence among ethnic groups is not one, I admit, I want to live with. But though The Bell Curve’s claims remain questionable, we should not allow political anxieties to keep us from looking into them further.