4,515 karma · joined July 11, 2008
Please checkout my book: Practical Data Science with R http://practicaldatascience.com/
Games like backgammon (that have betting and the doubling cube to continue), Go (which is calculated in stones), and bridge (again having points) have more natural intermediate scoring systems than chess.
In my opinion the "winner takes all" aspect of chess is similar to what makes analyzing voting systems difficult. In a non game context: Aspnes, Beigel, Furst, and Rudich had some amazing work on how all or nothing calculation really changes things: https://www.cs.yale.edu/homes/aspnes/papers/stoc91voting.pdf .
The "singularity is going to be exponential" fantasy is based on assuming change simply becoming proportional to recent advances. Hence the exponential shape. Even conceding "chartism" one would need to at least propose some imaginary mechanism that goes reciprocal to pretend that sort of curve is coming.
I remember from a lot of combinatorial problems (like cutting up space with hyper-planes or calculating VC dimension) that one sees what looks like exponential growth until you have a number of items equal to the effective dimension of the system and then things start to look polynomial.
BTW: I was going through some of your lambda calculus write-ups a while ago. Really great stuff that I very much enjoyed.
Roughly it accepts inputs that have at least 2/3rds of witnesses accepting and rejects inputs that have no more than 1/3 of witnesses accepting. Witness means additional input (usually considered random input). The super nicety is the huge gap between 1/3 and 2/3.
One can simulate a BPP recognizer to a high degree of fidelity. Just try a bunch of random witnesses.
However, we don't yet know how to efficiently perfectly implement a perfect recognizer. Until we have sampled a lot of witnesses we really don't know what fraction the of overall population we are drawing from is accepting.
However (as the book points out) we know the strategy for perfect solution. We can decide BPP perfectly and efficiently if and only if certain very strong efficient pseudo random number generators exist. And the existence of such is very much tied to if certain problems are hard (require large circuits to solve) or not.
The arguments always feel to me too similar "it is good Carnegie called in the Pinkerton's to suppress labor, as it allowed him to build libraries." Yes it is good what Carnegie did later, but it doesn't completely paper over what he did earlier.