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RANDOM & PSEUDORANDOM

http://www.bbc.co.uk/programmes/b00x9xjb

★★★★

  • Randomness: can’t determine what will happen next in the series
  • Humans aren’t great at picking randomness.  We tend to assume that coincidental patterns (eg, 90 heads in a row) won’t happen in a random system
    • Can there be true randomness?
    • Quantum theory says that quantum behaviour is objectively random
      • Since computers can’t generate truly random numbers, pseudorandomness is used
      • Statisticians’ tests for randomness – looking for patterns
      • Pseudorandom sequences (eg, pi) pass these tests and mimic  the behaviour of random numbers (eg, each digit takes up approx. 10% of the sequence) – but not truly random because they CAN be determined; eg, could work out all the digits of pi
      • Measures of randomness – Kolmogorov complexity (descriptive complexity – how you can describe a sequence, eg to a computer, in order to generate it) suggests that randomness is where a string of numbers is “incompressible” in the sense that “it is impossible to give a representation of the string using a program whose length is shorter than the length of the string itself”

http://en.wikipedia.org/wiki/Kolmogorov_complexity

 

STOCHASTICITY

http://www.radiolab.org/2009/jun/15/

★★★

  • Coincidence? – Story of the two girls and the red balloon
  • Making sense of patterns in the brain
    • Story of woman with Parkinson’s who became addicted to gambling – hit of dopamine every time she played the pokies http://www.boston.com/news/globe/ideas/articles/2007/08/19/your_brain_on_gambling/
    • Schultz’s experiments with monkeys – ‘prediction neurons’ fire in anticipation of rewards, but a reward that comes unexpectedly feels 3-4 times more exciting. Hence, “random rewards of gambling are much more seductive than a more predictable reward cycle” – we become hooked on trying to work out the ‘pattern’, and predict the rewards

Meanwhile: Cutting a jungle out of coloured paper.

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