Conjunctive normal form

Conjunctive normal form (CNF) is an AND of ORs. Any boolean statement can be converted to CNF, but the conversion may not be trivial. e.g. (Cats in LA) or (Dogs in California) becomes (Cats OR Dogs) …

Common knowledge

There is a distinction between mutual knowledge and common knowledge. Mutual knowledge: knowledge that everyone knows. Common knowledge: not only knowledge that everyone knows, but something that …

Inspection paradox

The inspection paradox happens when the probability of observing a quantity is related to the quantity being observed. e.g. Average class size experienced by students will be larger than average …

Shut Up and Calculate

links arxiv, alternate arxiv-vanity link The main thesis is that the universe is a mathematical universe, i.e. mathematics does not describe a universe, they are the universe (a possible answer to …

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

links paper, wiki The opening quote is by Bertrand Russell: Mathematics, rightly viewed, possesses not only truth, but supreme beauty cold and austere, like that of sculpture, without appeal to any …

Gödel, Escher, Bach: An Eternal Golden Braid

From Hofstadter’s preface to the book’s 20th-anniversary edition: GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and …