“…our main hypothesis is that the brain makes decisions through a procedure that is similar to quantum measurements. This does not require the brain to be a quantum object, but merely takes into account the dual nature of the decision process, involving both conscious logical evaluations as well as subconscious intuitive feelings” From the paper… [Read More]

# Maths

Game theory, bayesian probability, logic, foundations, type theory, category theory... you know, all the sexy stuff!

## “What Mathematicians Can Teach Physicists”, by Peter Woit, AND, Is String Theory Science?

I just finished Peter Woit‘s book Not Even Wrong, about why he’s convinced String Theory is not really science. His book is more than that, it’s a wonderful romp through the history of 20th Century physics and the deep importance of mathematics to the development of quantum mechanics — not to mention his championing of… [Read More]

## John Von Neumann [Quote of the Day]

“The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.” — John… [Read More]

## John Maynard Smith [video]: 7 Wonders Of The World

“Mathematics is so much easier than words… mathematics makes things clear that words merely muddle and confuse and mess up.” — John Maynard Smith The father of Evolutionary Game Theory, John Maynard Smith, has always been one of my favourite biologists and thinkers. I’ve suspected this might have to do with how much he reminds… [Read More]

## The Crisis of Unreplicable Research: Bayes, Evolution, & Game Theory

There is a crisis in the not-so-hard sciences: “For the past few years, there has been a growing crisis in social science, and in biology, medicine, and other statistics-dependent fields, that many claimed research findings are fragile, are unreliable, cannot be replicated, and do not generalize outside of the lab to real-world settings (Ioannidis, 2005)…. [Read More]

## NOTES: Boolean Algebra Basics

DEF: Boolean Algebra A Boolean Algebra is a kind of bounded distributive lattice where every element $x$ has a compliment $~x$. DEF: Lattice A Lattice is a partially ordered set $(L,\leq)$, such that for any $x,y \in L$, there exists a greatest lower bound $x \wedge y \in L$, and least upper bound $x \vee… [Read More]

## How To Install Sage Mathematics On Arch Linux Distro’s

When I was in grad school — many moons ago — I was introduced to a fantastic platform for mathematics computation called Sage being developed at the University of Washington. You can think of Sage as a combination of Mathematica, Matlab, and a bit of R — only open source, free, and backed by the… [Read More]

## Sage Math Presentation: It’s Not About Finding X

“It’s not about finding X, but understanding Why.” — Arvind S Raj Back when I was still in grad school, the open-source mathematics software system Sage was very much in its development period. But, it’s since grown into an amazing set of tools for a mathematician — or anyone who needs to get math done…. [Read More]

## Myth Busted: The Golden Ratio Fact & Fiction

Is the Golden Ration REALLY that pretty? A wonderful follow-up video to the history of numbers, by Keith Devlin at Stanford, says NO… Maybe… sometimes! OK, we’ll just say “It’s complicated.”

## A Sweet-Ass, Dirty, & Quick History Of Numbers

by Keith Devlin, lecturing at Stanford: Right at the outset, he describes mathematics as: The Science of Patterns. Given that the human mind can be seen as a giant pattern recognizer, this makes the study of mathematics deeply important to the study of our essential nature. “It could be that the patterns of mathematics are… [Read More]