I don't quiet agree. It is well known that cellular automata evolve in a few somehow precise type of behaviors, one of which is precisely the type found by John Conway. I don't think he designed the Game of Life, or even if he did I wouldn't say so simply because there is a whole big class of CA of that type so that with an initial intuition one can easily find (using it as a kind of filter) a CA of an equivalent type. The experiment is very simple, if you constraint the space of all possible 2D CA to those clearly non-trivial (avoiding periodic and fractal evolutions) by applying a simple filter (based on compression, topology parameters or others published techniques), one ends up with 2 classes of CA identified by Stephen Wolfram as complex and random (a single class at the end by following what he calls the principle of computational equivalence or PCE). The probability of a complex 2D CA to behave as the Game of Life and to be universal is very likely according to these discoveries, even though we don't have the techniques to prove that large sets of these systems are so. But as it has been proven, many of these interesting but not uncommon 1D, 2D or ND CAs share some fundamental properties reaching a maximal degree of sophistication (namely complexity/universality).
It is of great merit of Conways' however to have brought the attention to this particular 2D CA and to have had analyzed it in such a detail. Another example of this, is Rule 110 elementary cellular automata, it is not that rule 110 has something special in particular other than have been proven to be universal. It is that rule 110 was so extensively studied by Wolfram and eventually proven universal by him and his assistant M. Cook that makes rule 110 so special, but what rule 110 is meant to prove is that universality can be reached by even so simple systems so that one can expect that all those interesting/complex CA turn out to be of the same kind. Each time that anyone has tried enough to prove that an arbitrary interesting CA is universal has been able to prove it. Cases start from Conway's Game of Life, Wolfram's rule 110, Ed Fredkin's salt model, and just to cite the most recent, Maurice Margenstern and Yu Song universal cellular automaton on the ternary heptagrid (accepted papers for http://www.csc.liv.ac.uk/~rp2008/accepted.php, 2nd Workshop on Reachability Problems). Rule 110 just as the Game of Life was discovered, not built. These discoveries are the product of an exhaustive ('random') search (over the whole or a part of all possible rules), which doesn't mean that they were random discoveries. One can of course misunderstood the discovery, because in low dimensional CA spaces it is very easy to explore the space of possible rules by changing the rules themselves before letting the system to evolve for some initial steps to see how it evolves, as if one would have designed the system other than have had explored a part of the space, but it is not the case. But even if it were, it is a misguide to think so, because of the reasons I just gave, which is that all those complex systems have the potential to behave just as complex and universal as the Game of Life. Furthermore, by what Stephen Wolfram's call irreducibility, one cannot infer in general (this applies particularly to complex CAs such as the Game of Life) how a CA rule will evolve without having to run the CA itself. That's why the study of CAs has been recently so succesful and people have started to look at them, because we have now the tools to let these systems to run and see how the develop (computers). But the idea of irreducible systems is very simple and powerful, it basically says that one cannot shortcut any of these interesting complex CAs, so there was no other way to Conway to test his CA other than running it! Which means that if it were not behaving in the right form he would then change the rule of the CA and again test it again. This doesn't mean that he wouldn't be able to figure out some basic properties of the rule he was trying to find, if that were the case, but it means that he wouldn't ever be certain but by running the CA itself. This has been the case of other rules such as rule 30, which never have been able to crack by coming up with a kind of function or formula to shortcut the evolution of rule 30 and provide the value of the rule at an arbitrary step without having to calculate the previous (i.e. running the CA up to the step in question). Even if rule 30 were crackable it is my strong believe based on computational complexity that most of these systems are irreducible in several terms, from undecidability of the properties of those CA to incapability of our systems (including ourselves) to compress the information of these systems. Applying Wolfram's PCE, a system with a maximal degree of computational degree of sophistication would have the same computational power of another system of maximal degree, so one cannot expect any of them to figure out what the other is doing without having to emulate it step by step (or almost step by step). This doesn't mean that the cleverness of the Game of Life is an unmerited achievement of Conway as the discoverer of this interesting evolution of a 2D CA. But the Game of Life became so popular an interesting not because it is rare, but because it was the better studied as a particular instance of an interesting complex 2D CA. Furthermore, it was given a meaning related to what one can interpret as some basic game theoretical principles of how life develops in real. Interesting enough, I met John John Conway 3 weeks ago, I should have asked him about it, but fortunately we still can. As far as I can remember, Stephen Wolfram himself asked John Conway how he came up with the Game of Life, unfortunately John Conway seemed to say that he was not certain anymore. Hector Zenil On Sat, Aug 2, 2008 at 10:21 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > Well, there may have been a lot of trial and error in figuring out which > local, binary 2D CA rule would give rise to complex patterns (though I feel > pretty confident it was clever-intuition-guided trial and error, not true > random search...), but > > 1) the idea to look at that particular class of local, binary 2D CA rules > in the first place > > 2) the idea that a 2D local binary CA rule giving rise to apparently > complex patterns would actually give rise to Turing-complete behaviors > > were guided by Conway's excellent intuition into this particular class of > complex systems. Basically, his intuition told him where to look, and then > finding the actual rule was a sort of "parameter tuning" in a fairly small > discrete space. > > So I think this is a pretty good example of someone designing an > interesting complex system via > > * coming up with the basic system design using an intuitive understanding > > * setting the parameters of the system via intelligently-guided trial and > error > > However, one thing that wasn't done here was to try to create a system that > depends relatively smoothly rather than extremely sensitively on the > parameter values (in this case the "parameter" being the local rule). > > -- Ben G > > > > > On Sat, Aug 2, 2008 at 6:31 PM, Richard Loosemore <[EMAIL PROTECTED]>wrote: > >> David Hart wrote: >> >>> On 8/2/08, *Richard Loosemore* <[EMAIL PROTECTED] <mailto: >>> [EMAIL PROTECTED]>> wrote: >>> >>> Thus: in my paper there is a quote from a book in which Conway's >>> efforts were described, and it is transparently clear from this >>> quote that the method Conway used was random search: >>> >>> >>> I believe this statement misinterprets the quote and severely >>> underestimates the amount of thought and design inherent in Conway's >>> invention. In my option, the stochastic search methodologies (practiced >>> mainly by his students) can be considred 'tuning/improvement/tweaking' and >>> NOT themselves part of the high-level conceptual design. But, this topic is >>> a subjective interpretation rabbithole that is probably not worth pursuing >>> further. >>> >> >> No, not at all. >> >> Conway is still alive, you know. Why doesn't somebody ask him? >> >> I defend what I say to the hilt. Conway and his helpers knew what target >> they were aiming for (they decided on one aspect of the global behavior >> before time), but I believe they did nothing at all besides try various >> possibilities until one of them worked. >> >> I can find no evidence, anywhere, of any theorems, or any mathematical >> analysis that allowed them to target a specific set of rules that would give >> them the birth-death ratio that they were looking for. >> >> If anyone does believe that they did some analysis to achieve this goal, >> the onus is on them to find it. Failing all else, ask Conway himself. >> >> It is not good enough for people to go around making wild allegations (as >> Linas did yesterday), without any supporting evidence, and then for me to >> produce apparently clear counter-evidence, only to have it dismissed by some >> vague suggestion that perhaps I may have misinterpreted the evidence. >> >> >> >> Richard Loosemore >> >> >> ------------------------------------------- >> agi >> Archives: https://www.listbox.com/member/archive/303/=now >> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >> Modify Your Subscription: https://www.listbox.com/member/?&; >> Powered by Listbox: http://www.listbox.com >> > > > > -- > Ben Goertzel, PhD > CEO, Novamente LLC and Biomind LLC > Director of Research, SIAI > [EMAIL PROTECTED] > > "Nothing will ever be attempted if all possible objections must be first > overcome " - Dr Samuel Johnson > > > ------------------------------ > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Hector Zenil http://zenil.mathrix.org ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=108809214-a0d121 Powered by Listbox: http://www.listbox.com
