(half-baked brainstorming below, beware.... What I'm musing about is how to guess the causal direction of a correlation based on non-temporal data...)
> I've been re-reading this nice old paper on the foundations of the Second > Law.. > > http://necsi.edu/projects/baranger/cce.pdf It's a physics-y paper but I think one can apply it to AGI with some appropriate set-up The key thing that Baranger's arguments show there is that -- Within the view of a coarse-graining observer (one whose precision of observation is much less than the precision of the universe he's observing), it's more likely for -- two states that seemed the same at time T, to seem different at time T+1 than for -- two states that seemed different at time T, to seem the same at time T+1 (this is for an arbitrary trajectory in a conservative dynamical system, blabla...) Now, suppose we apply this reasoning (hands waving kinda wildly) to a space of **situations** in some universe. Each point in the state space is a certain situation. A trajectory in the state space is a series of situations, e.g. the series of situations encountered by some agent. Suppose that the trajectories of situations encountered by agents, when plotted in situation-space, are complex and fractal-looking like the ones in Baranger's paper. Each agent may be associated with a probability distribution over trajectories (the possible histories it experiences). A possible commonsensical cause or effect like "rain" or "dark", in this framework, corresponds to a set of situations (e.g. the situations involving rain). Thus it corresponds to a certain region in the situation space. Let's call these "event-sets". Each point on a trajectory through situation-space is going to pass through various event-sets. To say what it means for one event-set to cause another, relative to a certain set of trajectories (or probability distribution over trajectories), we can use the definitions from Luke Glynn's paper http://philsci-archive.pitt.edu/9729/1/Website_Version_2.pdf What Baranger's line of argument (via which he derives the Second Law) suggests is that overall -- same cause, different effects is more likely than -- different cause, same effects This is because "same cause, different effects" means "two different situations, which are put into the same event-set by the observer, lead to two different situations, which are put into different event-sets by the observer", etc. Since event-sets are regions of situation-space, and generally (because of the coarse-graining observer) an earlier time-point on a trajectory is going to be less spread-out through situation-space than a later time-point on the same trajectory --- therefore the cause is likely to be less spread-out than the effect. Thus overall we might conclude: given a pair of event-sets (X,Y) that are correlated (meaning e.g. that there is mutual information between the distribution of particular events within category X, and the distribution of particular events within category Y), -- the one with greater spread (i.e. the greatest differentiation, i.e. the greatest entropy, among the different particular situations in the event-set) is more likely to be in the future... The basic idea is: if event-categories X and event-categories Y are sufficiently correlated that it seems likely one of A) The states of the universe corresponding to observation of X tend to causally affect the states of the universe corresponding to observation of Y [within the assumed set of trajectories along which causation is being estimated] or B) The states of the universe corresponding to observation of Y tend to causally affect the states of the universe corresponding to observation of X [within the assumed set of trajectories along which causation is being estimated] then, to choose between X and Y, on the average we will guess right more often if we assume the lower-entropy one of X and Y is the cause and the higher-entropy one is the effect ... So according to this way of thinking, the asymmetry required in Glynn's analysis of causality could potentially be taken as entropy rather than time... maybe ;) -- Ben ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
