I keep emphasizing the idea that evidence slides probability because of research that shows people tend to use spatial intutions to grasp numbers. In particular, there's interesting evidence that we have an innate sense of quantity that's localized to left inferior parietal cortex - patients with damage to this area can selectively lose their sense of whether 5 is less than 8, while retaining their ability to read, write, and so on. (Yes, really!) The parietal cortex processes our sense of where things are in space (roughly speaking), so an innate "number line", or rather "quantity line", may be responsible for the human sense of numbers. This is why I suggest visualizing Bayesian evidence as sliding the probability along the number line; my hope is that this will translate Bayesian reasoning into something that makes sense to innate human brainware. (That, really, is what an "intuitive explanation" is.) For more information, see Stanislas Dehaene's The Number Sense.

"The first author must state that his coauthor and close friend, Tom Trobaugh, quite intelligent, singularly original, and inordinately generous, killed himself consequent to endogenous depression. Ninety-four days later, in my dream, Tom's simulacrum remarked, 'The direct limit characterization of perfect complexes shows that they extend, just as one extends a coherent sheaf.' Awaking with a start, I knew this idea had to be wrong, since some perfect complexes have a non-vanishing K_0 obstruction to extension. I had worked on this problem for 3 years, and saw this approach to be hopeless. But Tom's simulacrum had been so insistent, I knew he wouldn't let me sleep undisturbed until I had worked out the argument and could point to the gap. This work quickly led to the key results of this paper. To Tom, I could have explained why he must be listed as a coauthor."

"If Math were an animal, I think it would be a gorilla. If you mess with Math, it's like messing with a gorilla; it'll destroy you, and eat your brains."

much or in fundamentally new ways (and some of his

"Hefferon’s emphasis on real-world examples is admirably balanced by an abundance of proofs"

"On the spectrum from "Mathematical Techniques" through "Analysis of Algorithms" and ending up with "Catalog of Algorithms", I would start with Graham, Knuth and Patashnik "Concrete Mathematics", travel through this book, on to Knuth "The Art of Computer

One of these days someone will link this to mathomat and make a wonderful freehand algebraic calculator.