http://arxiv.org/pdf/1401.3734v1.pdf
On Wed, Nov 26, 2014 at 12:34 PM, Ben Goertzel <[email protected]> wrote: > (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 -- Ben Goertzel, PhD http://goertzel.org "The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man." -- George Bernard Shaw ------------------------------------------- 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
