The Wonderful World of Probability

June 15, 2008

I have to confess at school I was not very good at maths. I managed to fail my O-level when I was 16 though a year later I did a retake and was able to pass. I don’t really blame my teachers because I probably wasn’t ready for it. I didn’t really see the relevance and I didn’t really have a natural aptitude for it. Now in later life I have started to appreciate its importance. The problem is that I lack that foundation. Even so I think that maths is not entirely a hierarchical subject and anyone can appreciate its beauty and the insight it gives on our world. It is essential to have an understanding of mathematics. I don’t just mean to avoid financial mismanagement and running up consumer debt. It goes much deeper than that.

For me probability is the most illuminating area of mathematics. An example is the way people think about risk. We seem to have a poor assessment of risk. After a plane crash many people refuse to fly but have no problem taking the car, which is far more dangerous.

We are often fooled by randomness. If there are a lot of cases of cancer near a mobile phone mast, this does not necessarily mean that there is a problem with the mast. When we think of bad things occurring  randomly, we seem often to expect that they will be evenly distributed. But a cluster is perfectly ordinary; in fact what would really be bizarre would be a world where there were no clusters. It is like the gambler’s fallacy where people think if it has been heads four times in a row, it must be time for tails.

            The history of how probability theory came about is vital for understanding our contemporary world. In Against the Gods Peter Bernstein shows how a series of groundbreaking discoveries in mathematics helped to spark the affluence of the Western capitalist world. We can have investments and stock markets and the economic growth that they permit because we understand the concepts of probability and risk management. Many of those who worked on this in the 16th and 17th centuries were compulsive gamblers, but also mathematicians and fascinated by the mechanics of gambling. One of them was Pascal who thought about the existence of God and thought about how to manage the risk implicit in that bet. This is of course the famous Pascal’s Wager. The important point for Pascal is that risk is not just about probabilities but also consequences. It goes like this:

If you believe in God and you are wrong, you lose nothing (if death is the absolute end), whereas if you correctly believe in God, you gain everything (eternal salvation). But if you correctly disbelieve in God, you gain nothing (death ends all), whereas if you wrongly disbelieve in God, you lose everything (eternal damnation).

            A sceptical perspective is provided by Nassim Nicholas Taleb author of The Black Swan. He describes himself as a “sceptical empiricist” and a “philosopher of probability”. For Taleb too many experts overestimate the value of of rational explanations of past data and underestimate the prevalence of inexplicable randomness in that data. The title of the book refers to the fact that we tend to believe all swans are white because we’ve probably never seen a black swan. Taleb distinguishes between two domains of chance – Mediocristan and. Extremistan. For example people’s weights lie in Mediocristan. Some people are fat others are thin but even a very fat person is only a few times heavier than a very thin person and it will still only represent an insignificant percentage of the total weight of everyone. They will converge at a normal (Gaussian) distribution. This is what Taleb calls “mild randomness”. Now, for Extremistan, instead of weight, think about income Think of Bill Gates or Warren Buffett. Their wealth is a million times greater than that of the average person. This is “wild randomness” The exceptional in this case is not unimportant. In the summer of 1982, large American banks suddenly lost close to all their past earnings made cumulatively in the history of American banking. They were fooled by  a small sample; they’d had a number of consecutive good years and had forgotten about the small probability of something really bad  happening. This kind of thinking is rife in financial markets, although they do not have the monopoly. According to Taleb no statistician produced a model that predicted the subprime crisis. His conclusion is that we can trust experts and statistics with events that come in a normal distribution but we must be  prepared to admit our ignorance in these events which have an extremely low probability but  with exceptionally severe consequences.

 

Further listening and reading

More or Less This BBC programme is presented by Tim Harford, author of the best selling book The Undercover Economist and it deals with the world of  numbers. You can listen to all the past programmes They have included stories about the numbers behind the immigration debate, measuring poverty, how much alcohol is too much, whether the financial mathematicians known as “quants” are to blame for the current credit crisis and Eurovision voting.

http://news.bbc.co.uk/1/hi/programmes/more_or_less/7115510.stm

 

Who’s Counting? In this website a prestigious mathematician analyses the news from a mathematical perspective.

http://abcnews.go.com/Technology/WhosCounting/

 

Nassim Taleb talks about the challenges of coping with uncertainty, predicting events, and understanding history.

http://www.econtalk.org/archives/2007/04/taleb_on_black.html

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My Media Week 15/06/08

June 15, 2008

Here is a piece about how some groups want to keep indigenous peoples trapped in poverty with an overly romanticised idea of life in a tribe. (ARTICLE)

http://www.spiked-online.com/index.php?/site/article/5305/

 

John Kay gives us his perspective on the current agricultural crisis. (ARTICLE)

http://www.johnkay.com/in_action/552

 

On the Philosopher’s Zone this week, a conversation with Simon Critchley, author of The Book of Dead Philosophers. We all know about Socrates and his hemlock but the case of Roland Barthes is less famous. The  man whose work influenced many fields including structuralism, semiotics, existentialism, Marxism and post-structuralism,  was hit by a laundry van while walking home through the streets of Paris. (PODCAST)

http://www.abc.net.au/rn/philosopherszone/stories/2008/2270057.htm

 

Lingua Franca is about the case heard last week, in a court in Athens, about the word ‘lesbian’, in which the plaintiffs are claiming that the prerogative to the term belongs to the inhabitants of the island of Lesbos. They are seeking for a ban to be placed on its use by the gay organisation, the Homosexual and Lesbian Community of Greece. (PODCAST)

http://www.abc.net.au/rn/linguafranca/stories/2008/2273968.htm


My Favourite Links #10

June 15, 2008

This week’s site is Political Compass. It is an extremely complete test, which helps to you to define your ideology. They place you on a compass depending on the answers you provide. With all the confusion there is about political labels this site is an excellent tool for understanding core concepts.

 

politicalcompass.org


A bit of trivia#1

June 15, 2008

I have trawled the internet to bring you these fascinating bits of trivia:

Most elephants weigh less than the tongue of the blue whale.

Mel Brooks’ Silent Movie mime Marcel Marceau is the only person who has a speaking role.

Underground” is the only word in the English language that begins and ends with the letters “und.”

Susan Sarandon’s last name is from her first husband,  actor Chris Sarandon. He played Prince Humperdinck The Princess Bride.

Al Capone’s business card said he was a used furniture dealer.

Gerald Ford was once a male model.

The term “devil’s advocate” comes from the Roman Catholic church. When deciding if someone should become a saint, a devil’s advocate is always appointed to give an alternative view.

The very first bomb dropped by the Allies on Berlin during World War II killed the only elephant in the Berlin Zoo.

Dentists have recommended that a toothbrush be kept at least 6 feet away from a toilet to avoid airborne particles resulting from the flush.

The longest one-syllable word in the English language is “screeched.”

Dr. Joseph Guillotin did not invent the guillotine; he just persuaded officials to use it as a means of executions because of it’s speed and efficiency. It is a myth that he died by the device.

Director Wes Craven claims to have named Freddy Krueger after a kid who bullied him in school.

In Some Like it Hot Marilyn Monroe required 47 takes to get “It’s me, Sugar” correct, instead saying either “Sugar, it’s me” or “It’s Sugar, me”. After take 30, director Wilder had the line written on a blackboard. Another scene required Monroe to rummage through some drawers and say “Where’s the bourbon?” After 40 takes of Monroe saying “Where’s the whiskey?”, `Where’s the bottle”, or “Where’s the bonbon?”, Wilder pasted the correct line in one of the drawers. After Monroe became confused about which drawer contained the line, Wilder had it pasted in every drawer. 59 takes were required for this scene.

In 1898 the German firm of Bayer devised a wonderful new cough suppressor called diacetylmorphine as a treatment for asthma, catarrh, bronchitis, emphysema and tuberculosis. They gave it the trademark name of Heroin and described it as “non-habit forming.”