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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

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