Kathy and my final discussion on determinism follows (her response to me shows first). I want to thank those who participated in answering my query. This discussion made me think again about `just happens', and I am not all that uncomfortable with the notion any more. After all, causation and determinism are just concepts emerging from our macro experiences, which can be described by such concepts. Just as Bayesians must purge themselves of frequentist dogma in order to realize probability is about belief, perhaps we need purge ourselves of this need to believe things are unfolding in some causal manner.
At 05:52 PM 8/27/2006, Kathryn Blackmond Laskey wrote: >Rich, > >You have done a good job of articulating the puzzle of the meaning >of "random." Actually, it's even worse than things "just >happening." Let's say X has a 12.3% chance of being equal to x1. If >there is "real randomness" in the world, it would mean not only that >there is nothing forcing X to be one value or another, and not only >that sometimes in these kinds of situations x1 happens and sometimes >it doesn't, but also that somehow, over repetitions of this kind of >situation, we get a proportion of x1 values near 12.3%. > >How does this happen? Why does it happen? > >One possibility is that it just does, for no reason science can ever >discover -- it's just one of those mysteries of the universe. That >is the kind of non-explanation Einstein and Jaynes couldn't stomach. >Scientists seek explanations. Scientists are never satisfied with >"It's just a mystery we'll never understand." > >But no matter how much we might rebel against it, the possibility >can't be ruled out. Maybe there just are random things -- things >that can happen either one way or another, and which way it happens >in any given instance is something that "just happens," but somehow, >we don't know how, all these "just happens" events manage to >converge to stable frequencies. > >Another possibility is that there is some kind of deterministic >pseudo-random process going on. We know how to build deterministic >pseudo-random processes. We do it all the time when we implement >stochastic algorithms. So maybe something like that is behind the >probabilistic phenomena we observe. > >Another possibility comes from game theory. Game theory deals with >systems of agents, each of which can choose a strategy, where a >strategy is a rule for picking actions on the basis of the agent's >information. Each agent has a utility function that represents how >highly that agent values each of the outcomes. An equilibrium is a >set of strategies, one for each agent, such that each agent's >utility-maximizing strategy conditional on the other agents playing >their equilibrium strategy is to play its equilibrium strategy. Some >kinds of games have "mixed strategy equilibria." That means that >each agent's best response to the other agents' equilibrium >strategies is to chose actions randomly according to an equilibrium >probability distribution. When there is a stable mixed strategy >equilibrium, you expect behavior to emerge that "looks like" >randomness whether or not the agents are explicitly >randomizing. The reason is that if some agent starts to make moves >with frequencies that differ noticeably from the equilibrium >distribution, the equilibrium strategy is no longer optimal for the >other players, and so they will tend to change their behavior to >something more optimal for them. This will (if the equilibrium is >stable) make the player who deviated worse off. So it is to >everyone's advantage to stick to the equilibrium frequencies. > >Game theory can be applied even if the agents in question are not >explicitly "trying" to maximize their utility. All you need is some >form of selective pressure that drives the system to >equilibrium. In biology, it is survival -- organisms that follow >near-equilibrium strategies have higher chance of survival than >organisms that deviate too far from their equilibrium strategies. So >organisms that (approximately, given prevailing environmental >conditions) behave like they are "trying" to survive will tend to >evolve. In economics it is market pressure -- firms and consumers >that deviate too far from their equilibrium strategies will be >driven out of the market. The agents don't need to conceive of >themselves as utility maximizers -- I doubt that bacteria have any >concept of themselves. But game theory is applied extensively in >biology, and biological systems can usefully be thought of as >optimizing survival probability. > >Perhaps many phenomena that seem "random" arise when a system has >the structure of a game with a stable mixed-stragegy >equilibrium. Agents in such a system have actions they can choose, >and something "makes" them choose particular actions. If the agents >are biological, it is biological drives and instincts that cause the >choices they make. If they are human agents, in addition to the >biological drives and instincts, they also have values and >beliefs. They choose on the basis of drives and insincts (and >perhaps values and beliefs), but the details of what makes them do >what they do are inherently unobservable to external systems such as >scientists studying them. Survival pressure and market pressure >creates conditions under which stable probabilities emerge. > >I don't think any of this answers your question. I don't think >science yet has an answer to your question. But I hope scientists >don't stop asking the question. I don't rule out the possibility >that "it just happens" is all we'll ever get to no matter how hard >we try to do better, but if we don't even try, then even if there is >an explanation, we won't get there. > >You wrote just to me and not to the list, but if you want to forward >this to the list, please feel free. > >Kathy > > > >>Kathy, >>Thanks much for discussion. For reasons I won't go into I currently >>can sometimes send emails from this address and sometimes from the >>other. It is always easier for me to receive at this one (The whole >>matter is not probabilistic). >> >>I guess this statement summarizes it all: Let E(t) be all of >>existence up until time t. If the random number generated at time t >>is based on E(t), we have determinism. If it is based on something >>other than E(t), then it is based on something that does not exist, >>which contradicts the notion of existence. Therefore, if we have >>indeterminism, we must conclude that the random number is not base >>on anything. That is, it just happens. Would you agree? Do you have >>a reference for a decent paper on `just happens?' >>Rich _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
