> At 05:42 PM 12/20/2001, zim wrote: > >As to the specifics of your specs for the system: My only question (and > >one which I am inadequate to answer) has to do with Goedel's theorem. > >Would not your system run into questions for which there are no logical > >answers and would that not throw it into one of those Star Trek "Does not > >compute" loops with eventual self-destruction associated with tacky smoke > >special effects? That is there are some problems for which there are no > >mathematical or logical solutions. So the machine could not achieve the > >sort of perfection that you describe. >
> From: Richard S. Crawford <[EMAIL PROTECTED]> > > More precisely, the self-evolving system that The Fool describes will > encounter statements which are true within its internal logic but which > cannot be proven within that logic. > > In mathematics, there are statements which are true but which cannot be > proven mathematically. > > In any system symbolic logic (S), there are axioms which are true in S but > which cannot be demonstrated within S. However, those statements *can* be > proven within meta-logic, S^2. But then we find axioms within S^2 which > cannot be proven within S^2, but which can theoretically be proven true by > using S^3. Unfortunately, S^3 has proven too complex to be easily > understood by mere graduate students. But the computer system we are describing is smarter than you are. (According to Vinge and Moore's Law, the bitrate will surpass the bitrate of the human mind within the next thirty-some years, /but/ that doesn't account for distributed computing efforts [grid computing] and super-computer arrays (of thousands of processors). With that kept in mind, the Hardware will surpass us before then). Not only that it has access to all the work that humans have ever come up with in mathematics, i.e. what we _know_ and can figure out, it has access to and can _know_. But all of this is academic because I doubt that their would be any need to solve such problems in the four fundamental software aspects of the system. It is much more likely to arise in the hardware aspect of the system, or if the system is trying to figure out (thinking, theorizing, etc. like what Hawking does) how to do weird stuff, like time travel and faster than light travel, etc. Those things (which have no real relevance to the system) are fripperies, nice to have, but not a critical component of the system. It is very probable that the system would port itself over to a base three system, because it is a better system. It is the closest to base e, and has other properties that make a trinary system better. Instead of true / false, you have true / false / maybe (1, 0 -1). > For real fun, imagine writing a paper about the application of Godel's > Incompleteness Theorem to various systems of multi-valued inductive logics > (where something can be true, false, or anywhere in between). I wanted to > write a paper about quantum logic, but my advisor told me that the > University's health plan wouldn't cover the cost of the insane asylum. Vales between 1.0_ and 0.0_. But what about things that are both true and false at the same time? > Ahem. Back to topic. No OS can be perfect, not if it wants to stay within > the confines of logic as defined by the structure of the Universe. If > logic is only one of a suggested number of options, then I suppose The > Fool's dream OS is absolutely possible. Did I indicate that I would want such a system? Nothing could be further from the truth. If it were in my power I would make it so no sufficiently advanced AI is ever created, for any reason. But no matter what I do (unless I can manage to wipe out mankind) would ever be enough to stop someone somewhere from creating such a monstrosity. It will Happen. > My fear is this: won't the dream OS become so powerful that it will > eventually try to take over the world and destroy all of humanity, and find > itself at war with the Omega Point at the end of time? If the singularity did happen, then the resulting computer would be powerful enough to try and prevent the omega point from occurring, But even if it failed to stop the omega point (what of other species who create their own singularities / mass super AI's), the omega point is supposed to be more powerful than that (the awaking of god). Now since the omega point is supposed to emulate everything that has happened in the universe AND everything that could have happened, wouldn't their then be an infinite number of singularity AI's that would be fighting the omega point? And wouldn't their be mini omega points in most emulated universe's? Or would the singularity AI's from a million different civilizations battle it out, or combine forces to fight the Omega point. Or would they join together and become the instigator of the omega point?
