On 10/6/07, Richard Loosemore <[EMAIL PROTECTED]> wrote: > In my use of GoL in the paper I did emphasize the prediction part at > first, but I then went on (immediately) to talk about the problem of > finding hypotheses to test. Crucially, I ask if it is reasonable to > suppose that Conway could have written down the patterns he *wanted* to > see emerge, then found the rules that would generate his desired patterns. > > It is *that* question that is at the heart of the matter. That is what > the paper was all about, and that issue is the only one I want to > defend. It is so important that we do not lose sight of that context, > because if we do ignore that (as many people have done), we just go > around in circles.
Is it reasonable: I doubt precisely stating your goal is enough to reach it. (that is, unless you're Oprah and believe very strongly in The Secret) I just realized your question is if Conway could have written two frames of cells, then reverse-engineered the transformations that move from A to B. That transformation would be absolutely correct in getting from A to B, however as a candidate for the Universal ruleset, it would have to apply to every transformation from B to C or X to Y. Probably this candidate would prove unusable outside the fragile case for which is was written. I can write a very simple loop to output the records of a table with known fields, it takes much more consideration to generalize the solution to any number of unknown fields. Consider states T1 and T5. Use the same transformation hypothesis generator employed in the paragraph above. Given four steps from T1 to T5, there may have been one complete transform and three static states or four 'normal' transformations. How can a T1 to T5 transformation rule be written? Consider a cyclic behavior with a period of 4 - the transformation rule would have to observe a static state because it's observation moments are not granular enough to detect the changes. A glider with a period below the observation interval would give rise to a transformation rule describing, "Given this collection of cells, the next observation in open space it will appear to have moved one unit left" Of course that rule requires open space, the number of configurations of impact with other cells during the observation interval give rise to an explosion of possibility. The hypothesis generation algorithm will have a computational complexity that is orders of magnitude larger than the classical GoL rules making observations/computes at each 1 unit of time. To pull back from the simplistic GoL example, consider the planetary motion example. I think I better understand the rules prediction you were talking about - the true planetary motion rules are as unavailable to Kepler as an observer in the GoL world. So by observation, he detects a regularity to the moon's path around the earth and works out a theory for why that happens. Then he uses the theory to predict the future state of the moon - and he's right. Has he found the absolutely Truth in planetary motion? No. He has found a good enough approximation for the purpose of predicting local observed phenomenon. Is there an extra term in the True formula, for which our local observation conveniently sets a value of 1 in a multiplication process? Then this predictive function has limitations on use. it is still sufficiently useful when the hidden variable maintains the value of 1 (for our locally observable universe) Think of a multidimensional motion function that has been curried down from higher dimensions, leaving only those dimensions Kepler could observe. I initially thought we were discussing the patterns than can arise from examining the actual rules, rather than trying to discover the rules from observation of states. In the context of AGI research, I think the discovery of explanations is a much more interesting problem. I think resource limitations make brute force "compute every possible permutation" approaches to hypothesis generation absolutely unfeasible. Even with only a few known parameters, the combinatorial explosion will cripple the largest machine we have - but with an unknown number of parameters, the task of finding every permutation is impossible. So the ability to reason about classes and test hypothesis by proof (without requiring exhaustive search) is important to working intelligence. I feel there is a great deal of value in reasoning about AGI as a class of computation rather than a single solution or program. ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=50795592-49b3a8
