Spent a bit of today trying to get through a backlog of podcasts from econtalk and it conversations. The econtalk with Paul Romer and itc with Nassim Nicholas Taleb and the Peter Thiel talk at the Singularity Summit all touched on non-normal probability distributions in the context of managing risk to make yourself or the place around you better.
Taleb has spent the last few years running around posting signs around situations that have non-normal distributions and massive negative payouts. The front of the sign says "Here be Dragons!" and the back of the sign says "You're probably not as smart as you think you are.". It seems to him that in finance, we see interesting chains of new events that periodically result in either a boom or a bust. Since he runs money, he wants to make bets that pay off when a boom or bust happen, so he buys options and presumably also goes long on volatility like the VIX. Regardless of direction up or down, when situations destabilize, he makes money.
Thiel follows on that with the nice observation that selling insurance (Taleb would call this foolish) has 4 result conditions: 1) nothing happens and you make some money; 2) something small happens and you lose money that you cover by selling enough insurance, 3) something big happens and the government bails you (looking at you, AIG), or 4) the world ends and you don't care. On the other hand, you also can make a bunch of small investments in biotech or some promising area, and if one pays off, you're set.
Romer points out that while it'd be nice to invest in the company that invents a cancer vaccine, we still get the benefits of having a cure for cancer. So, it's the institutions and culture that foster the combination of people, material, and ideas that matter over all else to our general welfare. While other cultures may show short-term investment potential, unless they have / develop "proper" institutions ("proper" = still improperly defined ;), they will not have long-term potential. Of course, while the US has apparently benefited from having the "proper" institutions, the US may have or now be in the process of disassembling those institutions and we wouldn't know.
Say you were back in high school or college, and 1) you were plotting a potential life course, and 2) you knew the above probability info, and 3), you believed that pretty much any high-paying job would have many interesting features. What could you do?
Taleb and Thiel would urge you to go into a field where the median pay outranks most other professions and had a power law distribution of pay, so that with some work and luck, you have a chance of making a slew of money. And worst case, you're probably making more than you would in any other job. So now you just need the data. And luckily, the US Bureau of Labor Statistics provides some of it (they don't publish data on incomes greater than $140K per year).
From the wage data breakdown by percentile, you can roughly characterize the distribution. And given the US employment projections by occupation for the next decade, you can choose your career accordingly.
Naturally, that leaves the following questions: 1) how will you invest your money so as to avoid a possible market meltdown at retirement age? and 2) how will you live your life?