On Mon, Jun 16, 2014 at 5:52 PM, Mike Archbold via AGI <[email protected]> wrote:
> It seems like compression is at the heart of any AI method, or even > any computer method. The best programs are small (physically). I'm > not sure you can disentangle compression from generalization. > A point that I once made was that computers are effective just because we can do arithmetic on numbers expressed in n-ary form without needing to decompress the numbers. If we had to use an unary computations, like combining two collections of objects together and then recount them to compute the total, computers would not be very useful. Because we can do transformational procedures like arithmetic on the n-ary representations that means that adding two numbers can be done in log-n time rather than n time. A logical formula is a precise compression of the expansion of the formula (into a truth table of true and false rows.) So this means that generalization can be disentangled from the compression - at least in that one way. There are other aspects of the compression-generalization that are not revealed by the expansion of a formula into a truth table. I have found those to be quite subtle and I wouldn't know how to explain how it works to other people. So this suggests that the methodology of the compression may not be fully revealed by the decompression methods and that the methodological relationships of the compression are also bound implicitly into the compression. So, strangely enough, the compression is actually adding additional information into the compressed form of the data! The fact that there are equivalences in logic where different logical formulas can be expanded into the same truth tables shows that the compression method is not perfectly packed. (I have to think about that a little. I think that is what it shows.) Furthermore, there are other meta-level 'equivalences' which also reveal some excess capacity for compression. For example you can apply the literals in a logical formula in an alternative way and get a formula with the 'same' characteristics just expressed with different literals. There are other meta-level equivalences as well. This means that (I think it means that) according to information theory (or the Omega-theory thing) that the compression implicit in logical formulas is quite loose. This is all evidence that there is a polynomial time theory waiting to be discovered. Generalization does seem to be a form of compression. But, generalization can also be used in component-combinations to make novel transformational conclusions. The preposition is the classic example. If you know that object 'a' is 'behind' object 'b' then without decompressing object 'a' and object 'b' you can make an inference about a relation between them. However, there are some issues in this process. Does object 'a' and 'b' have a front and back? They might not but might be moving in the same direction one behind the other. Or they may be ordered in some way where the preposition makes some sense. So the full details of the combined generalization may not be obvious from the compressed statement. But, if you find more information about the objects you can disentangle more information out as long as the information makes sense relative to the terms used in the statements made about the situation. I just thought of something. If someone wants to make an artificial computer language he doesn't have to use unambiguous terms, as long as the statements that the computer uses to disambiguate a preceding statement are consistent with a single meaning. This would be difficult for a complicated language but it would be very feasible for a simple (invented) language. Jim Bromer *If you can solve a problem by avoiding it then your attitude is part of the problem.* On Mon, Jun 16, 2014 at 5:52 PM, Mike Archbold via AGI <[email protected]> wrote: > It seems like compression is at the heart of any AI method, or even > any computer method. The best programs are small (physically). I'm > not sure you can disentangle compression from generalization. > > On 6/16/14, Ben Goertzel via AGI <[email protected]> wrote: > > Hmm...well, some folks believe one could create a future upload of a > > physically deceased human via analysis of their online texts... remember > > Giulio Prisco's idea of Mind Uploading via Gmail... > > > > http://giulioprisco.blogspot.hk/2010/09/mind-uploading-via-gmail.html > > > > Maybe, post-Singularity, Jim Bromer's upload will find a polynomial time > > solution to 3SAT? > > > > > > ;-) > > ben > > > > > > > > On Mon, Jun 16, 2014 at 8:55 PM, Anastasios Tsiolakidis < > > [email protected]> wrote: > > > >> Shame on you Ben, again! He Creative Commons licensed his mind, that's > >> why. > >> > >> AT > >> > >> On 16.06.2014, at 14:52, "Ben Goertzel via AGI" <[email protected]> > wrote: > >> > >> > >> I wonder why you enjoy talking to yourself on a public email list? ;-) > >> > >> > >> On Mon, Jun 16, 2014 at 8:48 PM, Jim Bromer via AGI <[email protected]> > >> wrote: > >> > >>> I am probably wrong. The solution to finding a solution to a logical > >>> satisfiability problem in polynomial time is probably going to be based > >>> on > >>> a natural solution that does an accounting of the number of solutions > to > >>> the logical problem. > >>> > >>> Jim Bromer > >>> > >>> > >>> On Sun, Jun 15, 2014 at 9:05 AM, Jim Bromer <[email protected]> > wrote: > >>> > >>>> Traditional logic is a compressed format. Since there are so many > >>>> possible equivalences we know that logic is not a perfectly packed > >>>> compression method. So there is no need for a list of alternative > >>>> compression conversion algorithms which were in a list of possible > >>>> algorithms that was in np. (I expressed that idea incorrectly. I > should > >>>> have talked about a list of possible algorithms which were in exp > space > >>>> or > >>>> something like that. If the list of possible compression-conversion > >>>> algorithms were in np then that implies that finding an algorithm > >>>> solution > >>>> might itself be in np.) > >>>> > >>>> > >>>> > >>>> Jim Bromer > >>>> > >>>> > >>>> On Sun, Jun 15, 2014 at 8:36 AM, Jim Bromer <[email protected]> > >>>> wrote: > >>>> > >>>>> >> Of course I have no idea if this is even possible. But my next > >>>>> question is whether the inclusion of the compression formatting with > >>>>> the > >>>>> compressed string is inherently too inefficient to be useful.. > >>>>> > >>>>> Presuming that different classes of logical formulas could be > >>>>> compressed in different ways, is it possible to use a single > >>>>> polynomial > >>>>> time algorithm to do this? It might be possible, for example, using a > >>>>> numerical method to choose an algorithm based on a numbering system > >>>>> (where > >>>>> an ordering of algorithms might, to continue with this conjectural > >>>>> example, > >>>>> be associated with a log-based number - an n-ary number - to choose > >>>>> the > >>>>> algorithm from a system of algorithms which are in their entirety in > >>>>> np). > >>>>> This is too complicated for me, but if the parts of the algorithms > >>>>> were > >>>>> ordered and enumerated then large numbers could be used to refer to a > >>>>> particular ordering scheme. I am just trying to establish that there > >>>>> could > >>>>> be a way to express variations in how a compression conversion method > >>>>> might > >>>>> be chosen even if the entire list of algorithms were themselves in > np. > >>>>> > >>>>> But, is a compression method which includes some way to describe or > >>>>> refer to the particular compression scheme used in the compression > >>>>> going to > >>>>> be so much less efficient than a system that leaves that kind of > >>>>> information out to make this whole idea theoretically impossible? I > >>>>> think > >>>>> that it is theoretically possible. > >>>>> > >>>>> > >>>>> Jim Bromer > >>>>> > >>>>> > >>>>> On Sun, Jun 15, 2014 at 8:20 AM, Jim Bromer <[email protected]> > >>>>> wrote: > >>>>> > >>>>>> > >>>>>> > >>>>>> Jim Bromer > >>>>>> > >>>>>> > >>>>>> On Sat, Jun 14, 2014 at 9:20 PM, Jim Bromer <[email protected]> > >>>>>> wrote: > >>>>>> > >>>>>>> I have spent some time looking at the problem of finding a > >>>>>>> polynomial > >>>>>>> time solution to logical satisfiability and I have come to a few > >>>>>>> conclusions about the problem. > >>>>>>> > >>>>>>> There may be a natural solution, but if there is, I certainly can't > >>>>>>> see it. > >>>>>>> > >>>>>>> So if this is at all feasible, a more contrived method needs to be > >>>>>>> concocted. I believe the solution would have to use an alternative > >>>>>>> way to > >>>>>>> compress a logical problem so that individual solutions could be > >>>>>>> turned out > >>>>>>> in polynomial time. I can imagine compressing-some- logical > formulas > >>>>>>> that > >>>>>>> way but I can't think of a general method. > >>>>>>> > >>>>>>> But, since it looks like there is no one compression formatting > that > >>>>>>> could be used for every possible logical formula I believe that a > >>>>>>> solution > >>>>>>> - if one is feasible - would have to use different compression > >>>>>>> encryptions > >>>>>>> for different formulas. The formulas, encoded in one of > >>>>>>> these yet-to-be-invented compression formats would probably need to > >>>>>>> contain > >>>>>>> the encoding methods used to explain how they were encoded, since > >>>>>>> different > >>>>>>> formulas (or different classes of formulas) would have to be > >>>>>>> compressed > >>>>>>> differently. > >>>>>>> > >>>>>>> But, then since a part of logical formula that had been partially > >>>>>>> expressed in one of these formats would, using this theoretical > >>>>>>> framework, > >>>>>>> need to be converted into another compression format for the next > >>>>>>> part of > >>>>>>> the formula, that suggests that the compressions would have to be > >>>>>>> converted > >>>>>>> into other compressions without fully decompressing them and this > >>>>>>> compression transformation would have to take place in polynomial > >>>>>>> time. So > >>>>>>> one compressed format would have to be transformable into another > >>>>>>> format as > >>>>>>> the formula was converted in a step by step fashion. > >>>>>>> > >>>>>>> So in conclusion: > >>>>>>> 1. Different classes of logical formulas would have to be converted > >>>>>>> into different compression formats and this compression would have > to > >>>>>>> be > >>>>>>> done efficiently. > >>>>>>> 2. The new compressed formulas would have to be efficiently > readable > >>>>>>> so, in the worse case, individual solutions could be read out > >>>>>>> efficiently. > >>>>>>> 3. The individuated compression formats would have to > >>>>>>> include something about the encoding used for the formatting. > >>>>>>> 4. These formats would have to be convertible into another format > >>>>>>> efficiently in order to process the logical formula in a stepwise > >>>>>>> fashion. > >>>>>>> > >>>>>>> This shows that there are at least 3 different conversion or > >>>>>>> transformation methods necessary for the new individuated > >>>>>>> compression > >>>>>>> methods. > >>>>>>> > >>>>>>> An initial analysis of the structure of a logical formula might be > >>>>>>> used to immediately convert the formula into a different format > >>>>>>> without > >>>>>>> going through a step by step conversion- reconversion process. But > >>>>>>> even if > >>>>>>> that was possible we would still want to be able to treat logical > >>>>>>> formulas > >>>>>>> in a step by step manner. > >>>>>>> > >>>>>>> Of course I have no idea if this is even possible. But my next > >>>>>>> question is whether the inclusion of the compression formatting > with > >>>>>>> the > >>>>>>> compressed string is inherently too inefficient to be useful.. > >>>>>>> > >>>>>>> Jim Bromer > >>>>>>> > >>>>>> > >>>>>> > >>>>> > >>>> > >>> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > >>> <https://www.listbox.com/member/archive/rss/303/212726-deec6279> | > >>> Modify > >>> <https://www.listbox.com/member/?&;> Your Subscription > >>> <http://www.listbox.com> > >>> > >> > >> > >> > >> -- > >> Ben Goertzel, PhD > >> http://goertzel.org > >> > >> "In an insane world, the sane man must appear to be insane". -- Capt. > >> James T. Kirk > >> > >> "Emancipate yourself from mental slavery / None but ourselves can free > >> our > >> minds" -- Robert Nesta Marley > >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > >> <https://www.listbox.com/member/archive/rss/303/14050631-7d925eb1> | > >> Modify > >> <https://www.listbox.com/member/?&;> > >> Your Subscription <http://www.listbox.com> > >> > >> > > > > > > -- > > Ben Goertzel, PhD > > http://goertzel.org > > > > "In an insane world, the sane man must appear to be insane". -- Capt. > James > > T. Kirk > > > > "Emancipate yourself from mental slavery / None but ourselves can free > our > > minds" -- Robert Nesta Marley > > > > > > > > ------------------------------------------- > > AGI > > Archives: https://www.listbox.com/member/archive/303/=now > > RSS Feed: > https://www.listbox.com/member/archive/rss/303/11943661-d9279dae > > Modify Your Subscription: > > https://www.listbox.com/member/?&; > > Powered by Listbox: http://www.listbox.com > > > > > ------------------------------------------- > AGI > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/24379807-f5817f28 > Modify Your Subscription: > https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- 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
