Chasing patterns

Some mathematicians and chess players obsessively chase patterns. When the skill is used properly it provides a huge competitive advantage. If the skill misfires, a person may be committed in the mental institute, usually with paranoia. Watching “The Queen’s Gambit” and recollecting “A Beautiful Mind”  I decided to learn a bit more about the subject. Also, read here.


There is a fancy word for seeing meaningful patterns in meaningless information. Apophenia has come to imply a human propensity to seek patterns in random information, such as gambling. It is not uncommon to see apophenia with schizophrenia, typically paranoid schizophrenia. And it is not uncommon to see brilliant people with this condition.

Some Nobel Prize-winning mathematicians like Nash definitely had some sort of paranoia dealing with conspiracies. The first world chess champion Steinitz also suffered a mental breakdown. We do not know if it was caused by his personality or by syphilis. We do know many additional authors, mathematicians, and chess players who had severe mental issues.

We cannot quite diagnose historical personalities, but we know when something is wrong. Newton suffered from huge ups and downs in his moods, indicating bipolar disorder, combined with psychotic tendencies. His inability to connect with people could place him on the autism spectrum. He also had a tendency to write letters filled with mad delusions, which some medical historians feel strongly indicates schizophrenia.

To be honest, ADD, autism, severe depression, and bipolar disorder are more common for great thinkers – but not for mathematicians! Gödel was a brilliant logician and mathematician, as well as a contemporary and great friend of Albert Einstein.  He thought that someone was out to poison him. He was so sure of this delusion, especially later in life.

Evolutionary advantage

I do feel that the great mathematicians became great not despite their paranoia, but thanks to their ability to see patterns hidden from everybody else. If only you can see meaning in seemingly meaningless patterns, some of the patterns you observe will be meaningful.

Day traders are always looking for patterns to trade. It does not matter if the trader is a human or an algorithm. Eventually, some patterns will appear and provide advantages on historical data. Will these patterns work on future data? We do not really know.

Historically, the best sailors, farmers, and hunters could see patterns nobody else noticed. You can claim that Christofor Columbus was a madman, yet he discovered America due to firm belief in patterns and shreds of evidence others disregarded.

Apophenia used to be very common with religious medieval and ancient people. The emperor Constantine was said to have seen a sign in the clouds from a Christian god.  Now apophenia is discouraged so it is less common. People with apophenia and gamblers, in general, tend to be bad team players, and costly for society. So we really try to reduce their number via education. Very smart and very stupid people kind of bypass this indoctrination.

The sources of apophenia

We kind of get apophenia when training neural networks. In fact, it is a large set of serious issues. If a neural network is larger than necessary, it will start to see patterns that were not there. The main purpose of procedures like data augmentation, synthetic data placement, and GANs (generative adversarial networks) is reducing the sensitivity of the neural networks to small changes.  In AI apophenia is a huge issue. Trying to understand why a network made a certain decision is hard.

Psychologists try to generate their own models. Some talk about large template matching, that generates detection when applied to random inputs. Others talk about prototypes – not something seen before, but some generic representation or visual representation of a definition. Yet others try to deal with the analysis of the specific features and how they can get wrong: in detection, pattern dissection, feature comparison in memory, and recognition.

Either way, as our detection system gets more sensitive and capable of detecting weak signals, it usually gets more prone to false detection: assigning meaning to random stimuli.

Skinner’s box

One of the founding fathers of conditioning, Skinner, made a very simple experiment:

This experiment involved taking a hungry pigeon, placing it in a box and releasing a food pellet at a random time. The pigeon received a food pellet while performing some action; and so, rather than attributing the arrival of the pellet to randomness, it repeated its action, and continued to do so until another pellet fell. As the pigeon increased the number of times it performed the action, it gained the impression that it also increased the times it was “rewarded” with a pellet, although the release in fact remained entirely random.

An animal might have no tools to analyze the causation of complex phenomena. However, it does not want to die of hunger. Thus rituals are born. Some would say it is the way religions were born.

Mathematicians and patterns

Usually, we recognize patterns with the area of the brain responsible for face recognition. Traders often recognize familiar asset patterns like their old friends. Chess players recognize familiar positions on the chessboard.

Normal people look at clouds and think of faces and animals. This is normal and positive behavior, a sign of creativity and humanity. Mathematicians see MORE.

Some mathematicians are not very great at recognizing the faces of other people. This quality might be on the autistic spectrum. This does not mean that pattern recognition in their brain is faulty. It is reused to recognize other things.

Mathematicians are great at guessing the next number or image in a sequence – one of the harders psychometric questions for the rest of us. They reportedly get the next number intuitively. A lot of mathematical fields deal with sequences of almost random numbers, like sequences of prime numbers.  A person with an exceptional perception of sequences has a natural advantage in these fields and is more likely to succeed.

Not an issue of hard work

There were thoughts 100 years ago that too much intellectual effort may lead to paranoia, depression, and so on. We understand burnout much better today. It is not a result of intellectual effort, as it is an outcome of stress. There is also reverse causation:  a person with deep psychological issues is more likely to invest heavily in his work and not face his demons.

Certain patterns of whole-brain waves experienced during a productive flow may increase the chances of epilepsy, but not of schizophrenia. Extreme stress may cause a nervous breakdown, like Steinitz experienced in 1897 after losing the world championship to Lasker. Lasker was a “psychological” player who often deliberately confused his opponents, mystifying his contemporaries. So stress might be a factor in mental health deterioration.

Nash experience his schizophrenia in 1959, when he was afraid of a communist conspiracy. This was soon after the death of McCarthy (1957) and before the Cuban missile crisis (1962). I kind of think most Americans were stressed at that ti,e. About the same time, in 1957, Howard Hughes believed that Dietrich wished to have Hughes committed as mentally incompetent, causing another famous mental breakdown.

Social responsibility

We might care less about eccentric billionaires, but we care about kids of gamblers. We definitely care about gamblers getting into strange military campaigns or ruining banks on day trading scandals (Barings Bank failure or Madoff investment scandal).

So as a society we would love to have fewer gamblers, even if it means having fewer genius mathematicians. Two thousand years ago, a mad gambler lost his family fortune and died from hunger. Now we have social responsibility. A lot of pension funds are invested in excentric entrepreneurs and have to support families of compulsive gamblers.

We are taught about chances, statistics, scientific methods, and everything else needed to reduce the risks for society. Stupid people may not understand what they are told. Very smart people may choose to ignore the statistics. Why?

Eurica moment

There is something very intoxicating in an epiphany, true or wrong. The “Aha!” moments, the misunderstood insights of geniuses generate a very romantic atmosphere. We may choose to take the chances simply to escape the boredom of ordinary existence. If the initial gambles are successful we might believe in the so-called “beginners luck” and increase the stakes.

I am addressed with Eurica moments of various people every day. Probably because I can actually evaluate strange and farfetched connections. Maybe because I have a track record of implementing some of them. Usually, my initial response is fear. I desperately try to understand why the next “eurica” will fail. Occasionally I can find no theoretical weaknesses I cannot overcome. Then I join, fully aware of the high risks I take. Maybe my caution contributes to some success track.

I would say that 99.9% of the Eurica moments I witnessed were totally bogus. But for the 0.1% of pure genius, we must suffer the rest…

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