Yes, I agree that your Turing machine approach can model the same situations, but the different formalisms seem to lend themselves to different kinds of analysis more naturally...
I guess it all depends on what kinds of theorems you want to formulate... ben On Tue, Sep 2, 2008 at 3:00 PM, William Pearson <[EMAIL PROTECTED]>wrote: > 2008/9/2 Ben Goertzel <[EMAIL PROTECTED]>: > > > > Hmmm.. > > > > Rather, I would prefer to model a self-modifying AGI system as something > > like > > > > F(t+1) = (F(t))( F(t), E(t) ) > > > > where E(t) is the environment at time t and F(t) is the system at time t > > Are you assuming the system knows the environment totally? Or did you > mean the input the system gets from the environment? Would you have to > assume the environment was deterministic as well in order to construct > a hyperset? Unless you can construct a hyperset tree kind of thing, > with branches for each possible environmental state? > > > This is a hyperset equation, but it seems to nicely and directly capture > the > > fact that the system is actually acting on and modifying itself... > > > > I'll use _ to indicate subscript for now. > > I think s_n+1 = g_s_n(x) encompasses the same idea of > self-modification, as the function that g performs on x is determined > by the state if you consider g to be a UTM and s to be a program it > becomes a bit clearer. Consider g() and f() to be the hardware or > physics of the system. > > Will > > > ------------------------------------------- > 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 RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
