In Manolo Martinez's recent talk at CUNY on the Rationalizing Role of Pains, he presented a model describing the decision-making process of a mind faced with multiple conflicting sensory messages of varying reliability. This model was by no means the focus of his talk, but it is what I'd like to focus on here.
I just learned about the Knuth up-arrow notation yesterday. Basically, Knuth's up-arrow is the answer to the question "What comes next in the sequence \((+, \times, \wedge)\)?" You could call it iterated exponentiation. Later operators in the sequence are called "higher-order", and may be defined in terms of the previous order function.
While taking notes for ai-class, I found myself in a conundrum that any amateur mathematician can relate to: I ran out of appropriate letters in the Roman and Greek alphabets.
I've been playing around with the iPhone 4 since I took the plunge about two weeks ago. Amazing device. I really love the iTunes U feature. Access to countless hours of educational material. I've been falling asleep to The Tolkien Professor and the 99% Invisible podcast. The other day I took a long walk while listening to a lecture on the history of probability theory and found myself playing basketball (more vigorously than I'd expect). Why sit in a class, half-asleep, when you can listen to the same lecture while getting some cardio? As Steve Jobs would say, This is HUGE.
I've been reading Dawkins' The Selfish Gene. What I love most about the book is how my mind is just overflowing with genetic systems, simulatable quantitative machines; I'm just dying to code up some simulations of the systems he exposes so eloquently in the book. Every few pages, a new system comes into view. I have to pause, just stare into the void as my mind runs fast, imagining the mathematics needed to construct from the theory a working computer model.