With Educational Games, Even if the Kids Don't Get It, Yo...

...where does probability theory come from? What is its source? Clearly, like many other sciences, like arithmetic itself, probability theory emerged from observations of certain real-world phenomena, namely, random, unpredictable phenomena. And it is exactly these kinds of observations—fundamental to the formation of science—which are worth making together with kids. Well, not all of them, of course, just the simplest ones. Besides, kids are making them on their own; e.g., when they play...

 Natural Selection Resembles Bayesian Inference

The analogy is mathematically precise, and fascinating. In rough terms, it says that the process of natural selection resembles the process of Bayesian inference. A population of organisms can be thought of as having various 'hypotheses' about how to survive—each hypothesis corresponding to a different allele. (Roughly, an allele is one of several alternative versions of a gene.) In each successive generation, the process of natural selection modifies the proportion of organisms having each...

 The Proactionary Principle

People’s freedom to innovate technologically is valuable to humanity. The burden of proof therefore belongs to those who propose restrictive measures. All proposed measures should be closely scrutinized. Evaluate risk according to available science, not popular perception, and allow for common reasoning biases. Give precedence to ameliorating known and proven threats to human health and environmental quality over acting against hypothetical risks. Treat technological risks on the sa...

 Predictability and the Base Rate

Whenever a statistician wants to predict the likelihood of some event based on the available evidence, there are two main sources of information that have to be taken into account: (1) the evidence itself, for which a reliability figure has to be calculated; and (2) the likelihood of the event calculated purely in terms of relative incidence. The second figure here is the base rate. Since it is just a number, obtained by the seemingly dull process of counting, it frequently gets overlooked wh...

 Nature is Intrinsically Probabilistic

Here are the circumstances: source, strong light source; tell me, behind which hole will I see the electron? You say, 'Well, the reason you can't tell through which hole you're going to see the electron is, it's determined by some very complicated things back here: if I knew enough about that electron - it has internal wheels, internal gears, and so forth - and that this is what determines through which hole it goes. It's 50/50 probability because, like a die, it's set sort of at random - and...

 Bayes and Richard Price on Predictions

Bayes’s much more famous work, “An Essay toward Solving a Problem in the Doctrine of Chances,”24 was not published until after his death, when it was brought to the Royal Society’s attention in 1763 by a friend of his named Richard Price. It concerned how we formulate probabilistic beliefs about the world when we encounter new data. Price, in framing Bayes’s essay, gives the example of a person who emerges into the world (perhaps he is Adam, or perhaps he came from Plato’s cave) ...