Nice! As someone who knows a thing or two, though, I'd like to point out that the undecidability of one thing from another thing depends on the choice of logic. For example, everything else being equal, if we state the basic rules of the system in both first-order logic and in ZF set theory, far more will be undecidable from the first-order characterization. So while it is convenient to make blanked statements of the form "global property X is undecidable from the local interactions", it isn't quite accurate.
This means that "in principle" all we need is a stronger logic-- we don't necessarily need to determine the results experimentally just because they appear undecidable. But, doing an experiment may be (immensely) more convenient. This has at least some relevance to symbolic-style AGI, because one of the primary examples of undecidable facts is the consistency of a particular logic-- it is only decidable in a stronger logic. I don't know if I can transfer this result to say "the eventual optimality of an optimization process is only decidable by a stronger optimization process"... which would be more directly relevant... --Abram On Mon, Oct 6, 2008 at 12:16 PM, Richard Loosemore <[EMAIL PROTECTED]> wrote: > > > > Perhaps now that there are other physicists (besides myself) making these > claims, people in the AGI community will start to take more seriously the > implications for their own field .... > > http://www.newscientist.com/article/mg20026764.100 > > For those who do not have a New Scientist subscription, the full article > refers to a paper at http://www.arxiv.org/abs/0809.0151. > > Mile Gu et al looked at the possibility of explaining emergent properties of > Ising glasses and managed to prove that those properties are not reducible. > > Myself, I do not need the full force of Gu's proof, since I only claim that > emergent properties can be *practically* impossible to work with. > > It is worth noting that his chosen target systems (Ising glasses) are very > closely linked to some approaches to AGI, since these have been proposed by > some neural net people as the fundamental core of their approach. > > I am sure that I can quote a short extract from the full NS article without > treading on the New Scientist copyright. It is illuminating because what Gu > et al refer to is the problem of calculating the lowest energy state of the > system, which approximately corresponds to the state of maximum > "understanding" in the class of systems that I am most interested in: > > BEGIN QUOTE: > > Using the model, the team focused on whether the pattern that the atoms > adopt under various scenarios, such as a state of lowest energy, could be > calculated from knowledge of those forces. They found that in some > scenarios, the pattern of atoms could not be calculated from knowledge of > the forces - even given unlimited computing power. In mathematical terms, > the system is considered "formally undecidable". > > "We were able to find a number of properties that were simply decoupled from > the fundamental interactions," says Gu. Even some really simple properties > of the model, such as the fraction of atoms oriented in one direction, > cannot be computed. > > This result, says Gu, shows that some of the models scientists use to > simulate physical systems may actually have properties that cannot be linked > to the behaviour of their parts (www.arxiv.org/abs/0809.0151). This, in > turn, may help explain why our description of nature operates at many > levels, rather than working from just one. "A 'theory of everything' might > not explain all natural phenomena," says Gu. "Real understanding may require > further experiments and intuition at every level." > > Some physicists think the work offers a promising scientific boost for the > delicate issue of emergence, which tends to get swamped with philosophical > arguments. John Barrow at the University of Cambridge calls the results > "really interesting", but thinks one element of the proof needs further > study. He points out that Gu and colleagues derived their result by studying > an infinite system, rather than one of large but finite size, like most > natural systems. "So it's not entirely clear what their results mean for > actual finite systems," says Barrow. > > Gu agrees, but points out that this was not the team's goal. He also argues > that the idealised mathematical laws that scientists routinely use to > describe the world often refer to infinite systems. "Our results suggest > that some of these laws probably cannot be derived from first principles," > he says. > > END QUOTE. > > > I particularly liked his choice of words when he said: "We were able to find > a number of properties that were simply decoupled from the fundamental > interactions..." > > Now where have I heard that before, I wonder? > > > > 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 > ------------------------------------------- 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=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
