Hi Nick, Given the energy (and time!) apparently available to this thread, it is with some trepidation that I poke my head out of the weeds. (On the other hand, congratulations, Steve).
I like your last post about patterns, except for the strong emphasis on psychological/mental attribution, if causality is the example we wish to talk about. As in the case with data compression or phase transitions in condensed-matter physics, it is all fine that someone notices the data redundancy or order parameter in the material. But this should only be possible with any reliability if such a pattern is available in the system, to be recognized. My typical (and probably tiresome by now) example for the phase transitions is: give me water at +1 deg C and -1 deg C at 1 atm pressure, and then apply any learning algorithm you like to provide a short algorithm to ask whatever questions I put to it about the orientation and motion of the molecules, and how they differ in the two samples. Maybe some algorithms won't learn anything useful for short descriptions, but in a fair casino I would bet that most of those that do learn anything will learn to estimate the order parameter, and then to use it as the starting point for quick prediction of many observables. There simply isn't anything else that has particularly changed between the properties of the two samples, and everything that has changed is a deterministic function of the order parameter, even the moments of all the distributions for fluctuations. And however they name it or represent it, I expect that the predictive content of what they learn will be more or less the same as that in what we call the order parameter (the existence and direction of crystalline orientation). Something like that would seem appropriate to causality, at least for the simple forms that we largely understand, such as classical dynamics in physics, or Pearl's boolean nets in inference. To argue that psychological/mental attribution is anything beyond one-of-many possible learning processes, you would have to convince me that the concept of causation is at root a behavioral one -- perhaps some kind of agent-patient relation, or even something in the social domain -- and that as a result the attribution of causation by people contains particular aspects that other learning algorithms would not typically produce. For astrology and a large part of the metaphor we apply to nations and other institutions, and things of that sort, I would go along with this. Otherwise I counter that the pattern is "in the thing (the process in question)", and not particularly in one learner versus another, who try to learn about the thing. This small point of dispute, which maybe wouldn't even bother you, is quite in keeping with your overall assertion that repeated experience is needed to decide whether a pattern is appropriately characterized with the logical structure of causality (a properly contextualized if not-x, then not-y). Of course, having agreed with you so far, I suddenly realize that I will probably disagree with you now and start an argument, which had I known it, would have kept me from starting this note. If a relation (a compressed description of some regularity) is available in a process to be learned, and described with the logical structure of causality, then in what sense does the system itself care whether the learner needs repeated exposure to learn it. The repetition is a feature of the needs of learning algorithms, largely irrespective of what they are trying to learn about. How does it do anything but needlessly complicate my description of nature, to suppose that other instances than this one (of some process) have anything to do with the existence or non-existence of an aspect of the process that admits description as causal? If it exists, the simplest description of its existence is whichever one omits all un-needed elements of context; such a description would then put its existence in each instance without further qualifications. So causation (in ordinary material processes or appropriate branches of information theory) is admissible in our descriptions as a property of the thing, in each instance, and largely independent of the fact that we should be the ones characterizing the thing; the need for repeated exposure is a property of us, largely independent of whether causal relation or some other pattern is what we will notice in the thing. Anyway, don't know if those opinions will address what you are after, and they are probably less sophisticated than what has already been said here. All best, Eric ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
