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...

 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...

 Uniformity, Non-Uniformity, and Irreversibility

We must make the following remark: a proof, that after a certain time t1, the spheres must necessarily be mixed uniformly, whatever may be the initial distribution of states, cannot be given. This is in fact a consequence of probability theory, for any non-uniform distribution of states, no matter how improbable it may be, is still not absolutely impossible. Indeed it is clear that any individual uniform distribution, which might arise after a certain time from some particular initial state, ...