AI in Our Finite Universe

(14th-January-2021)

Universal AI would be computable if it used TMs with finite tapes and the next section will describe a way to do something much like that.

I argue that such difficulties are unnecessary if agent definitions are limited to finite sets (Hibbard 2014). Max Tegmark (2014, page 333) suggests that these difficulties are eliminated in a computable universe. Seth Lloyd (2002) has calculated that the observable universe has a finite information capacity of no more than 10120 bits. This number is based on a hard quantum mechanical limit on the number of possible physical states of the universe and is proportional to the age of the universe squared. That age is estimated currently to be 13.7 billion years, meaning that an assumption that our environment has an information capacity of no more than 10124 bits will remain valid for a trillion years. Alternately we could pick a much larger limit than 10124