To: Yogi - Paul who wrote (1866 ) 7/3/1999 1:27:00 PM From: appro Read Replies (1) | Respond to
Fascinating review by Mark Greenberg, Deputy Assistant Attorney General in the US Department of Justice. The method is more interesting than this particular conclusion as it has such universal application. Again, Yogi, you make us think. Thanks for the link!In fact, the most interesting questions....concern our susceptibility, when thinking about risk, uncertainty and probability, to a kind of cognitive illusion. The Doomsday Argument is a case-study in 'probabilistic illusion', for it rests on a web of insidious intuitions, hidden assumptions and seductive but imprecise analogies. <<The widespread sense that something is wrong with it is, however, correct, and its failings illuminate a main source of our trouble with understanding probability: its close connection to randomness or unpredictability. Randomness seems to confound us. For example, we have a tendency to infer non-randomness from apparent patterns in random events (witness the incorrigible optimists who spot trends in the spins of a roulette wheel or the ups and downs of the FT Share Index); at the same time, the history of statistics suggests that, when random samples are required, we often mistake the merely haphazard - or whatever happens to be near at hand - for the truly random. As I will show, the Doomsday Argument's fundamental mistake is to rely on the intuitive but misguided notion that we can in general take ourselves to be typical humans, and thus, in effect, random samples of the species. <<The effect of a new observation on pre-existing probabilities is specified by a mathematical formula known as Bayes's theorem, after the 18th-century English clergyman who discovered it. Roughly speaking, the idea is that the probability of a hypothesis is increased to the extent that the observation would be more likely if the hypothesis were true than if it were false. <<Leslie is cavalier about Bayesian reasoning, encouraging us to think that there is no need to 'dress up' non-mathematical 'common sense'. Human beings tend to be poor Bayesians, however. <<
