I realized that traditional logic is a system of compression which allows for some computations that can be run without fully decompressing the data. However, at certain steps at some (relatively low) levels of complexity the data has to be decompressed (to a great degree). So this example proves the system is feasible and it is not completely based on binary addition or multiplication methods (which are also examples of compression systems which can operate on compressed data without decompression.) I did not want to use binary arithmetic as an example because computers were designed around those principles.
So since an example is easy to find, this proves that the methodology can be studied as a separate branch of computer science. The question then is whether other, more powerful systems, can be developed. Jim Bromer On Sun, Jun 4, 2017 at 4:42 PM, Jim Bromer <[email protected]> wrote: > The Halting Problem shows that the results of programs (programmable > logic) cannot be completely computed - for every possible program - without > running the program. (The Gödel Incompleteness Theorem shows that there > are -some- comprehendible logical problems that could not even be > theoretically resolved programmatically.) > > But there are some programs that can be computationally processed so that > a system of results can be produced more quickly than actually running the > program. > > The significance of this came to me after I started criticizing the > proposition that an advanced representational compression could > be sufficient to produce AGI at this time. The problem is that > representational compressions have to go through stages of decompression > and recompression in order to do any computation on the data, and given the > degree of compression that would be needed for AGI that would make the > system way too slow. > > While logical computation is a simple process using binary representations > of simple logical states for each literal (logical variable), the problem > is that logical Satisfiability statements are (most familiarly) > compressions of multiple logical states. A logical statement is (typically) > a compression of a system of individual 'solutions'. So what would > be needed would be a computational method that can act efficiently on a > wide variety of logical solutions. In other words we need a compression > method which can do computations on the compressed representations without > (excessively) decompressing them for each computation. I started thinking > about this project from the view that my goal is not to make p=np but to > try to develop a methodology that might one day be more efficient than > methods that we currently use. > > I started thinking that it might be possible to create compression > representations that acted from different levels of abstraction. These > levels of abstraction might be thought of as programs. I started thinking > about Turing's Halting Problem and I realized that while you cannot find a > shortcut to the completion state of every possible computer program, > you can for some kinds of programs. The results of a system that I > am imagining could be decompressed (at the end of the analytical > computational stages) to produce solutions using the levels-of-abstraction > sub-program. but the system could run through the computational steps > without actually running that sub-program. The compressed representations > would not have to be excessively decompressed in order to run a computation > on them. > > I am all but certain that an example is feasible (although I do not have > one right now). > > And incidentally, an advancement that shows that a compression system > might be accompanied by an effective computational method that can act on > the compressed representations without fully decompressing them might be > interesting to some people. The system does not have to beat Turing at > run-around-the-house chess or to prove Gödel wrong from under a table at a > week-long Oktoberfest or be dependent on winning a million dollars, it only > has to be interesting, incrementally improvable and salient to the study of > logic. > Jim Bromer > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
