The Positional Notation System of numbers, like Binary and Decimal numbers, is a representational system which is a compression of the most natural way to represent a count, the unary system where a single mark is used to denote each individual item that is being counted. This Positional Notation system has a complexity value of a lossless exponential increase in efficiency for each digit of the binary representation. The method of addition, when converted into a true Boolean Form almost certainly has an exponential increase in complexity for both the number of bits of the addends and the number of addends. Multiplication represents an exponential increase in efficiency over the method of addition for that special class of addends which represents one multiplicand being added over and over again by the number of times represented by the value of the other multiplicand. These standard algorithms of addition and multiplication are both lossless. Algebra, which might represent one of the earliest programmable systems imagined, is so effective just because you can use addition, subtraction, multiplication and division of the coefficients of the literal variables of an algebraic statement.
So the binary system, addition and multiplication are really the engines of computation. I believe that the reason these methods are so powerful is because they can use extremely efficient compressed representations of numbers without needing to decompress them everytime they are used. I have tried to come up with some kind of terminology to represent this and I have suggested that addition and multiplication are procedural compression methods and transformational compression methods because they are able to use compressed data in its compressed form. Perhaps I should say that they are procedural methods that can act on a kind of compressed data. The reason why I mention this is because it may help to better define what is needed to make AGI feasible. I believe that many schemes which have used efficient numerical methods on objects of AGI have failed because they really did not adequately model the kinds of things that need to be modeled in an AGI program. So my thesis is that if we cannot just throw numerical methods at AGI programs and make them work, then maybe we should take a look at the reason why these methods are so powerful. And they are powerful. Jim Bromer ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
