It feels so wonderfully weird reading about some else seeing a manatee today. I too saw a manatee while walking with my kids today. The interesting part was our navigational strategies complementing each other (me – misremembering the details of a road closure, and them - getting curious about what a bunch of people at a marina are looking at) to find a group of manatees in a place we didn’t know they can be found.
It may be immaterial whether we call Culture a utopia or a dystopia. I haven't studied Banks' works in exhaustive detail, but the impression I got is that people in the Culture can do almost anything, because none of it matters. And if it did matter, they may have no agency to do that. So the Special Circumstances could have been created to accommodate people who want at least an impression of some agency (while - from a vague memory of one of the Culture books - chasing successfully a list with what turned out to be coordinates of all stars in a region of space).
I got thinking about this aspect of Culture starting with a broader premise - are there works where humans arrive at higher levels of human-embedded intelligence as a species or in a more limited scope as individuals? While describing higher levels of intelligence may be impossible, I find it curious science fiction doesn't appear to have too many attempts at that. Some of Vernor Vinge's works come to mind, but even there humans appear to be about the same as at present.
> while - from a vague memory of one of the Culture books - chasing successfully a list with what turned out to be coordinates of all stars in a region of space
That wasn't a Culture novel; it was in The Algebraist, and that society was almost an anti-Culture (highly hierarchical, quasi-capitalist, religious, racist/speciesist).
Thank you for the correction. I wasn’t completely sure that "a list" was really all there was to it, but turns out I was mistaken maybe in a more important part of that sentence.
I think the second paragraph in the parent comment fits really well with mimetic theory and this René Girard quote: "Man is the creature who does not know what to desire, and he turns to others in order to make up his mind. We desire what others desire because we imitate their desires." This, however, doesn't mean that the current Netflix solution is the only one possible.
Vastly parallel reinforcement-learning-like self-play with no obvious in-game real-time feedback loop. No breaks to explicitly integrate experience into strategy ("... there’s no point to doing that <remembering> between each life.”). How the protagonist learns ("matures") in this game?
Weierstrass function is used prominently in Abbot's (2015) "Understanding Analysis" book. Abbott also relies heavily on three other mind-bending functions - Dirichlet (nowhere continuous), Thomae (discontinuous at every rational and continuous at every irrational point), and Cantor (increasing and continuous on [0, 1], yet constant at [0, 1]\C. where C is the Cantor set that is of measure zero).
Dirichlet, Thomae, and Cantor functions are central in Abbott to introduction and exercises on continuity, differentiation, and integration. I thought that was an interesting pedagogical choice for an undergraduate book, especially when it is used for the very first course in mathematical analysis as in Princeton’s MATH215 (I do think it is a really nice book).
I think the author uses minimal set because it allows constructing any sigma-algebra from it. This (minimal set-based construction) is only possible for finite spaces. It allows, for example, an intuitive explanation of how sigma algebra F2 is coarser than F1. It serves a similar purpose as Borel sigma algebras in the general case, although a minimal set does not need to be a sigma algebra.
Using different sigma algebras allows describing easily all events on which the probability is defined, and how those events may change with time (filtration). I am not sure how use of sigma algebras (or algebras for finite case) can be avoided in general.
There is an example in Mathematica [1] that illustrates a similar point using Rock-Paper-Scissors game. It uses a very simple strategy to predict human opponent [2], but it appears to work well. (Although, at the moment the demonstration does not seem to be working at all (I tried it in Firefox and Chrome)).
