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...

 Keeping Students Motivated Using Future Rewards

Periodically remind students that their mental effort is relevant to pleasure in the near future. The younger the children, the less tolerant their brains are to activities that are not pleasurable now or expected to be so in the very near future. Fortunately, the dopamine-reward network releases motivating dopamine in expectation of pleasure. Let students know which of their enjoyable math activities will be coming up during the lesson and how what they are practicing now connects to the des...

 We are Living in an Ancestor Simulation

Now we get to the core of the simulation argument. This does not purport to demonstrate that you are in a simulation. Instead, it shows that we should accept as true at least one of the following three propositions: (1) The chances that a species at our current level of development can avoid going extinct before becoming technologically mature is negligibly small (2) Almost no technologically mature civilisations are interested in running computer simulations of minds like ours (3) You are...