From: Seth Lloyd <MINI > To: "jeffrey E." <jeevacation®gmail.com> Subject: Re: Date: Wed, 10 Aug 2016 00:08:02 +0000 Dear Jeffrey, It was very fun talking with you the weekend before last. I have downloaded The Improvement of the Mind and am reading. I feel my mind improving already ;-) The conversation and your ideas fit in closely with work I've been doing and am proposing to do. Maybe this is not surprising because we've been talking about these topics for years. I've been traveling around (Santa Fe, now in San Francisco, soon to be in Banff) and so have had time to think more about what we discussed. Here is a succinct summary of my own take. I know yours is somewhat different. Information is a fundamental quantity, measured in bits. Information can be random, like the typical string of bits one gets by flipping a coin 0101110110101000011 (I just flipped a coin and let heads = 1 and tails = 0), or it can be ordered, like the bit string 0000000000000000. There is a technical definition of order and randomness: a bit string is ordered if there is a succinctly describable method, e.g., a short computer program, for producing it. By contrast, a string is random if the shortest program for producing it is the same length as the string itself. For example, the string consisting of a billion 0's can be produced by a short program: Print '0' 10^9 times. By contrast, the shortest program to produce the string 0101110110101000011 is something like: Print 0101110110101000011. This way of defining order/randomness is called algorithmic information. The interesting thing about algorithmic information is that the short program can be hard to find. A string can look very random and still have a short program. For example, the first billion bits of pi, written in binary, have a short program, but if I just give you those bits, they would look statistically random. This means that so far as we or any other information processing system is conc