While surfing Google I came across this website which may help me later on, when I am writing my section about quantum mechanics:
http://www.faqs.org/docs/qp/chap01.html
Here is an extract of a Reckoning with Risk review, written by Helen Joyce:
"Gerd Gigerenzer is not a mathematician or statistician per se, but primarily a psychologist, working across disciplines to understand how human beings make decisions in the face of uncertainty. What he offers here is nothing less than a prescription for how to think, how to choose, and how to live, when the information on which we base our decisions is necessarily incomplete and flawed. For example - how worried should you be if you have a positive mammogram as part of a screening programme for breast cancer, or a positive HIV test despite the fact that you are in a low-risk group? You may be surprised to learn that the answer may well be "not too worried" - what should really worry you is that not many medical personnel know this!
The book also looks at the way courts deal with uncertainty, and offers some suggestions for improving the handling of statistical evidence such as DNA testimony"
The fact that Gerd Gigerenzer is not a mathematician or statistician may make the book less reliable. The book in general does not seem to talk about randomness, but more about uncertainty. There is a clear difference between the two because something that is uncertain may not be random. However, I did find a lot of information that will help me with my probability section of my dissertation. For example, at the end of the book, there is a chapter called "Fun Problems". The Monty Hall Problem is included in the chapter, along with many problems that I have never come across:
"The First Night in Paradise.
It is the night after Adam and Eve's first day in paradise. Together,they watched the sun rise and illuminate the marvelous trees, flowers, and birds. At some point the air got cooler, and the sun sank below the horizon. Will it stay dark forever? Adam and Eve wonder, What is the probability that the sun will rise again tomorrow?
[...] If Adam and Eve had never seen the sun rising, they would assign equal probabilities to both possible outcomes. Adam and Eve represent this initial belief y placing one white marble (a sun that rises) and one black marble (a sun that does not rise) into a bag. Because they have seen the sun rise once, they put another white marble in the bag. [...] Their degree of belief that the sun will rise tomorrow has increased from 1/2 to 2/3. [...] According to the rule of succession, introduces by the French mathematician Pierre-Simon Laplace in 1812, your degree of belief that the sun will rise again after you have seen the sun rise n times should be (n+1)/(n+2)."
This quote shows a different, unusual way to use probability which may be very useful to my dissertation.
Reckoning with Risk was a very interesting book but I don't think that it really gave me a lot of information that helped me progress in my project. I guess it showed me a more psychological side to mathematics but I do not know how relevant this actually is to randomness. In general, there was barely any information about the concept of randomness but it has shown me that randomness and uncertainty are two very different things.
Monday, 6 September 2010
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