# Aha! Gotcha, reviewed by Victor Niederhoffer

February 27, 2008 |

The book Aha! Gotcha by Martin Gardner contains much food for thought and enjoyment in the field of self-referential paradoxes and coincidences that arise in many fields. He starts with variations of the Liar's Problem. Epimenides said "all Cretans are liars." But considering that he was a Cretan, did he speak the truth. In exploring such paradoxes, Gardner explores some of the profound questions and unusual insights that such paradoxes lead to. I believe that such explorations will give similar insights into markets.

Gardner cover probability paradoxes in the ares of average, small world, patterns, and clumps. An example from averages is that most great mathematicians were first born sons. The fallacy is that first born sons are more common than second born sons because of one son families so that any group is likely to have more first borns. The fallacy arises in the work of those who predict stock market disasters. They point out that an inordinate number of disasters come when the market has not gone up or some such, leaving out the fact that most great booms come from the same preconditions. The Good to Great boys make a similar error in pointing out that most great companies pay attention to a core. They leave out the same from bad.

The small world paradoxes are based on the experiments of Stanley Milgrom that show that people are connected to vastly more people with a few steps than might be expected. He found that it took five steps to mail a document on average to a given person in another state. Watts has subsequently shown the lack of reliability of the study and in the age of Internet, it might take two minutes for such a chain to happen if the people were wired. However, one thinks of the recent \$7 billion loss and the three weeks of study that it took the bank to verify it and the many people that were involved in the trade, and no wonder the US stock market went down 60 points in the five minutes before or just during the unwinding of the trader's positions.

The third set of probability paradoxes introduced by Gardner are based on variations of the Birthday Problem. If there are more than 23 people in a room, the chances that at least two have the same birthday is 50%. Similarly if four people in a room, the chances that at least four have the same sign of the twelve is 40%. This should give one pause when noting coincidences. With the 20 markets that one looks at, the chances are well over half that two of them will have exactly the same sequence of rises and falls. Similarly,the chances that you'll find a day that will show the same direction of big or small change as one of the days last week is quite high.
A related set of coincidences is based on the digits of pi. You can find a run of seven threes in the workout and you'll be able to find 15 up or down days in a row if you examine enough markets , changes, or chart patterns. The fourth set of paradoxes is related to clumping. You're going to find if you mix up red and black balls in an urn, that they look like they form a meaningful mosaic of large clumps of the same colors. You'll suspect adhesion, but really you're seeing random numbers. Gardner applies this theory to the spins of roulette wheels, and the applications to what looks like valid charting ideas is clear. It's a good caution.

One of the more interesting things about Gardner's book is that he is not a mathematician. He uses common sense and consults with experts to explain all the unusual phenomena. This common sense approach leads to many AHA's by him, and when you translate it into your own bailiwick, it's like a child looking at things that are second nature to you but are not so obvious.

The book is highly recommended for those who like childlike areas of discovery in their field.

Vic's review of 'Aha, Gotcha' also got me thinking about trading and life in general from the existential perspective. It is both uplifting and depressing.

Whilst I am not mathematically inclined, I have always had an appreciation of probabilistic events in life. I feel this gives me an inner strength because I appreciate and am comfortable with the likelihood of the downside events, especially when they are outside of my control. For example, when I was mugged a few years ago, I was scared but the event didn't scar me mentally, because I figured that the mugger was out to mug someone, and it just happened to be I. In fact, staying rational gave me an upper hand and I actually managed to get the mugger to give me my mobile phone and wallet back to me (minus the cash). Another time, my car (parked) was involved involved in a hit and run. I reasoned that these things happen, and I wasn't being personally targeted. The bit that upset me was the potential cost and inconvenience. Also, I try to live a healthy life, but I appreciate the high odds of dying of cancer or heart disease. It's the probability distribution of life. And as life goes on, we gain more knowledge of the bigger picture, of the likelihood of various events, and of the uncertain.

We come to appreciate the fact that there is a 50% chance of two people having the same birthday in a room of 23 people, of the fact that we will probably be involved in a car accident in our lives, of the fact that we will all one day die, of something. I feel this is a powerful awareness because it keeps us in the driving seat of life. It is harder to be knocked off kilter.

However, whilst being armed with the knowledge of probability helps us to see through many of the common fallacies, it brings with it a problem that relates to the emotional response to upside events, specifically the sense of surprise. For example, should I feign surprise when two people in a room share a birthday? What about if I have a run of ten successful trades in a row? The trading example is less likely than the birthday example - its just over 1/1000 if we assume 50/50 odds. However, if I trade frequently enough, the real surprise would be if this never happened. My question is if I have a rough idea of the probability distribution, should my degree of surprise vary depending on whether I experience a low probability event or a high probability event? I suggest my emotional response should be the same, unless something out of the ordinary happens (ie beyond one's mental model of what is likely).

It's important to qualify that I only talking about the surprise element here. As this gets stripped out of my life, I feel I am more balanced but also that I am less human because I am no longer easily surprised. I am still amazed at the beauty of life and all that jazz, but its just this sense of surprise is increasingly missing from my life. Is my thinking faulty? I feel a bit like the Albert Camus's 'The Outsider', who, in the words of Camus himself: 'is condemned because he doesn't play the game … He refuses to lie. Lying is not only saying what isn't true. It is also, in fact especially, saying more than is true and, in the case of the human heart, saying more than one feels.'

This is such an honest and thought-provoking post — I love it, and thank you for it!

It speaks to so many issues, not the least of which is that no one gets out of life alive. That is a given and we shall all live and die with it.

Going further, as we age, we forget how to play. We lose the childlike wonder, the ability to be surprised and the sheer joy of being alive.

Traders take themselves altogether too seriously. I have found this to be true through many years of trading and teaching. It is good to have emotions under control when trading, but even better to learn to let the emotions run free when we are not trading. I have been accused of laughing too much and smiling too much. So be it, because that is who I am. I don't want to be free of emotions and the ability to laugh at myself and experience new things. I don't want to become Dr. Spock. I want to cry, dance, sing, laugh and realize that everything exists only because of the existence of its opposite. Without sadness, we would not know joy. Without boredom, we would not know excitement and surprise.

In the greater scheme of things, life is to be lived on one's own terms and the choices one makes are highly personal. If someone feels that there is no surprise, and likes it that way — wonderful.

If someone wants surprise, then it is within that person's power to see the world from that perspective. Everything is a choice, both in trading and in life. Life is never about what happens to us. Rather, it is about who we are and what we do with what happens.

The late Peter Drucker once asked: For what do you want to be remembered? This question may induce us to renew ourselves as the person we want to be or become. It may not, but it is worth asking just to find out. If you ask yourself that question a few times, the answers may be surprising.

There are some 50 trillion single cells in our body. We have the ability to use our brain to enrich, nourish and nurture these cells. We are able to put these cells into balance and harmony with our environment and to be gentle with ourselves, whilst continuing to push ourselves forward into the true freedom of authentic self.