Rereading my original message I realized that what I said may not have been very easy to read. It is, however, interesting and serious programmers should be aware of it.
An algorithm can be (and usually is) like a procedural compression method. (I have sometimes called it a transformational compression method.) That is not to say that algorithms typically compress data, but that they are extremely efficient. For instance, multiplication is defined as the repeated addition of a particular number. However, the standard multiplier algorithm is much more efficient than doing the repeated additions because it is, what I am calling, a procedural compression method. Furthermore, both addition and multiplication can use binary numbers which, as I explained, are extremely efficient compressions of the representations of values. It is difficult to compare the complexity (that is the efficiency) of these compressed procedural methods, so one way to do so is to expand the algorithm into a true formula of Boolean Logic where only AND, OR, Negation and parentheses are used with atomic Boolean variables. If you can find the shortest Boolean Formula then we can say (if we agree to do so) that this is a measure of the complexity of the algorithm. Most programmers (including myself) do not know how you go about it and the problem of efficiently finding the most efficient Boolean Formula may be a problem that has probably not yet been solved. However, we can expand some algorithms into Boolean formulas and at least get an intuitive sense of just how efficient these algorithms are. What I said in this thread is that I was surprised to find that the real engine of efficiency in arithmetic procedures is found in additions of multiple addends. Multiplication is more efficient than repeated addition for one class of multiple addends, but even there it is my opinion that the real power of multiplication comes from the addition of the multiple partial products. Most examples of compressed data cannot be used without decompressing the data. The benefits of addition and multiplication is that it is not necessary to 'decompress' the binary representations of values in order to use them in arithmetic operations. So addition and multiplication (and of the computational-numerical methods which are derived from addition) are not only procedural compressions but they also use data in it's compressed form without first decompressing it! This is an amazing power, and I believe that it is exactly where the power of computation comes from. What does this have to do with you? It is my opinion, based on this analysis, that if you can -effectively- use multiple addend addition in your programs you would be well advised to consider doing so. The problem with many supposed numerical 'solutions' to AGI is that no one has been able to find an effective method to use numbers to represent or model the problem space of AGI. 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
