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Let's consider a very simple situation: you're an agent playing a game like this: A random point x∈X is generated, which is shown to you. Then you have to choose an action a∈A. This leads to a world-state w(a,θ)∈W, where θ∈Θ is some "hidden variable", which is randomly generated but...
Crossposted from my personal website Alternative title: Wolves hate him!! Shepherd compares the size of large sets with this one easy trick! Previously: Recognizing Numbers Let's do a thought experiment. I place an empty box in front of you. Then, while you're watching, I put these objects into the box:...
(Crossposted from my personal website) Thermodynamics is really weird. Most people have probably encountered a bad explanation of the basics at some point in school, but probably don't remember more than * Energy is conserved * Entropy increases * There's something called the ideal gas law/ideal gas equation. Energy conservation...
Context: Logical Induction is a framework that makes sense of intuitively plausible statements like "the probability that the 10101010th digit of π is odd is about 0.5". People often do this sort of informal reasoning about mathematical conjectures. Like "The Collatz conjecture has been checked up to 268, and held...
Suppose the US presidential election is tomorrow. You currently assign a probability of 50% to each outcome. (We are ignoring the small possibility that neither of the main party candidates will win). A man approaches you, and offers you a bet of $10, at 2-1 odds. In other words, if...
Inspired by: Joy in Discovery, Class Project Your task: Prove either of the following statements: * There exists a polynomial p(x) of degree five over the rational numbers, with a root x, so that x cannot be obtained from the rationals by field operations and iterated extraction of roots. *...