Sorry for the long delay between posts; I was temporarily sucked in to the infinite. While doing some reading about set theory (foundational stuff for probability and, in fact, all of mathematics), I veered off into the infinite and had a hard time climbing back out. I’m guessing you already know most of the basics about sets: compliments and unions and intersections. You may even know some of the stranger parts, like G. Cantor’s cascading crescendo of cardinalities. But knowing those in a cursory way (and really, that’s all a work-a-day statistician or even probabilist needs) isn’t the same as really exploring them.
Looking up again now after several weeks, I feel like I’ve traveled three levels deep in a dream, lost in a purgatory I could only escape by answering questions like “Is a line made up of points, or does it have points?”, “Is it possible to count what you cannot fully name”, and “In an unbounded universe, is the compliment of the compliment of an object the same as the original object?”. I know, I know. I should have taken that left back at Albuquerque, I shouldn’t have swallowed the red pill. Still, it’s been an interesting trip to say the least, and I feel like I may now be coming back up the the surface, a little bit wiser and a lot more confused than when I began.
Meanwhile, I’ve added a couple items to the “Manifesto” and, The Architect permitting, will be posting a theory on Types of Randomness soon. Post should take between 1 and 10 days to complete, with 95% confidence. Hum… better make that an 80% confidence interval, I still haven’t wrapped my head around the whole idea of forcing.
Tags: cantor, inception, infinite, set theory