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Hand: Synchronicity is an attempt to come up with an explanation for the occurrence of highly improbable coincidences between events where there is no causal link. It’s based on the premise that existing physics and mathematics cannot explain such things. This is wrong, however - standard science can explain them. That’s really the point of the improbability principle. What I have tried to do is pull out and make explicit how physics and mathematics, in the form of probability calculus does explain why such striking and apparently highly improbable events happen.  There’s no need to conjure up other forces or ideas, and there’s no need to attribute mystical meaning or significance to their occurrence. In fact, we should expect them to happen, as they do, purely in the natural course of events.

Navin: What advice would you give investment managers about handling the risk of improbable events, especially considering how commonplace they can be?

Hand: The eminent statistician Dennis Lindley coined something he called Cromwell’s Rule. It was based on Oliver Cromwell’s letter to the Church of Scotland, in which Cromwell said “I beseech you, in the bowels of Christ, think it possible that you may be mistaken.” Cromwell’s rule says one should never assert something to be either completely impossible or completely certain, unless it is logically so. And that’s the point with scientific models: your model is not the reality, and it’s always possible that your model is wrong. So, while, under the conditions of your model, some event may be so improbable that you can safely ignore it, it’s also possible that your model is wrong and the event is far more probable than you think.

So my advice is, be prepared for those highly improbable events: they may not be as improbable as you think.

Navin: Without giving specific details, what types of investments have you made?

Hand: At present I’m constrained in the types of investment I can make because I’m partly employed by a hedge fund. I do have shares. I think the key thing is to be sanguine about the fluctuations, and take a long term view.

For the record, I do occasionally buy lottery tickets. In my book I talk about how to increase the amount you win if you win, and also how to increase your chances of winning. Some kinds of lotteries have structures that you can take advantage of. While I don’t expect to win on any particular draw, my long term expected winnings are greater than 1: that is, on average I will win more than I pay. However, as a general principle one should only play lotteries for fun, not in the expectation of winning - a bit like the casino example you started with. After all, even though my strategies mean I will make money in the long term, “long term” could mean many thousands of years, so I’m not holding my breath. In any case, the point about lotteries is the nature of the utility function: for the price of a coffee, which you probably won’t notice, you buy yourself a chance of winning a fortune.

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For special assistance in preparing this article, my thanks to Allan Combs, the Doshi Professor of Consciousness Studies and Director of The Center for Consciousness Studies at the California Institute of Integral Studies and Professor Emeritus at the University of North Carolina-Asheville.