- Our natural intuition is not to be trusted: that all effects must have a cause.
- Chance disarms us, causing us to attach significance to events that have no significance.
- Two divided camps of scientists:
- Life started by chance, a cosmic coincidence
- Biological Determinists assume chance is secondary and that the right sort of molecule obligingly form as a result of the laws of nature.
- Algorithmic information theory seeks to quantify the complexity of information by treating it as an output of a computer program.
- If DNA is to store information efficiently, it should not contain too many patterns.
- Opponents of Biological Determinism point out that crystals form to mathematical symmetries but lack are almost devoid of information. Sequences of amino acids in proteins are too random.
- Perhaps life's hardware is determinant, but the informational components derive from the laws of information theory.
- Darwin's theory of Natural Selection does not adequately explain Speciation.
- Indication is that speciation is the result of random single accidental event.
- Random or chance can sometimes cause clumping whereby an unusual coincidence can happen.
- A study of lucky people found that they were skilled at creating and noticing opportunities by, for example, networking, adopting a relaxed attitude to life, and being open to new experiences.
- Rock, paper, scissors (RPS) is a function in maths known as intransitive relation, which means it creates a loop of preferences with no beginning or ending.
- According to Game Theory, the ultimate RPS player would have to know the throw of the player. RPS computer programs were devised to figure out opponent patterns to win.
- To win at RPS humans have to be unpredictable. This is not easy.
- A system is said to be random if what it does next does not depend upon what it has done in the past.
- A system is ordered if its past history affects its future.
- Chaos is not random. In a chaotic system, the past does have an effect on the on the future, but the sums to predict the outcome are extremely sensitive to tiny observational errors. Any initial error grows so rapidly that it ruins the prediction.
- A branch of mathematics called Ergodic theory grew from the idea (from Boltzmann) that random systems can sometimes be modelled statistically to give deterministic outcomes.
- John Bell's work seems to indicate that at the Quantum level, randomness rules.
- Probability theory describes the behaviour of infinite randomness in a finite world.
- Poisson distributions: Probability theory shows that e can be expected to pop up when lots of randomly triggered events are spread over a restricted interval of time.
- Bayesian reasoning???? the chance of something being true if it depends on something else being true.
- Frequentists probability: observe, sample, model. Can't know uncertainties resulting from real-world processes whose outcomes appear random. Uses big data.
- Bayesian statistics: don't know uncertainty. If you keep abreast of relevant info then you can be more certain. Sometimes priors can be subjective.
- Kurt Godel and Alan Turing showed that is impossible to obtain a consistent and complete axiomatic theory of mathematics and a mechanical procedure for deciding whether an arbitrary mathematical assertion is true or false, or is provable or not - see the Incompleteness Theorem.
- Turing showed that there is no set of instructions that you can give a computer, no algorithm, that will show in advance whether a given program will ever halt.
- Quantum mechanics seems to have dramatically changed the picture of deterministic physics, demonstrating randomness at the particle level.
- All science is founded on the assumption that the physical world is ordered.
- Though individual chance gives the impression of lawlessness, disorderly processes, on the whole, may still display statistical regularities.
- It was believed that apparently chance events were always the result of our ignoring vast numbers of deterministic actions.
- Two major developments put doubt in the idea of a clockwork reality: Quantum physics (Heisenberg's Uncertainty Principle; and Chaos Theory concerning the evolution of predictive errors.
- It was supposed that determinism went hand in hand with predictability, but this need not be the case. Determinism implies predictability only in the idealised limit of infinite precision.
- In non-chaotic systems, the errors grow slowly. In chaotic systems, the errors grow at an accelerating rate.
These notes were taken from the book "Chance - The science and secrets of luck, randomness and probability".
See Profile Books to find out more.