Subject: BHA: RE: In which kind of world is probability theory useful? Date: Mon, 30 Aug 1999 11:15:46 -0400Hans, I found this very interesting. Here are two other cases, and my crack at dealing with them in CR terms: * Quantum Mechanics: Physicists treat the location of sub-nuclear matter as a probability distribution in space. -- This may be a combination of epistemic and ontological uncertainty. On the epistemic side, humans are thus far incapable of comprehending the behavior of sub-nuclear matter. Hence, physicists find it useful to treat matter as if it were a located at a point and, alternatively, as if it were a probability distribution in space. Heisenberg's uncertainty principle comes into play, but this may still be human transitive understanding of reality rather than intransitive reality itself. Ontologically, it may in fact be the case that sub-nuclear matter occupies space according to a probability distribution an intrinsic indeterminacy in the sense that sub-nuclear matter doesn't exist as anything else. * Stochastic processes: Many things in nature, and in society, may be inherently random, not because of overdetermination or lack of closure, but because they are just random by nature. Perhaps we might try to attribute this to a multiplicity of micro-causes, but this sort of reductionism rarely helps. For example, mean rainfall in a geographic region is a random event, and we won't get too far if we try to reduce it to the determinants of Brownian motion in the atmosphere. In many spheres, modern science associates phenomena with randomness (e.g., heat is associated with increasingly random molecular motion). This is a case of an ontological property of the world. Also note that the Central Limit Theorem is a great example of your point about the micro-macro relation. Marsh Feldman -----Original Message----- From: owner-bhaskar-AT-lists.village.virginia.edu [mailto:owner-bhaskar-AT-lists.village.virginia.edu] On Behalf Of Hans Ehrbar Sent: Sunday, August 29, 1999 11:09 AM To: bhaskar-AT-lists.village.virginia.edu Subject: BHA: In which kind of world is probability theory useful? This year I am teaching econometrics again, and I am trying to look at it more and more through critical realist lenses. Here is a passage from my class notes which is similar to something you might find in any introductory textbook on probability theory: Probability theory and statistics have been proven useful in dealing with the following types of situations: * Games of chance * Quality control in production: you take a sample from a shipment, count how many defectives. * Actuarial Problems: the length of life anticipated for a person who has just applied for life insurance. * Scientific Eperiments: you count the number of mice which contract cancer when a group of mice is exposed to cigarette smoke. * Markets: the total personal income in New York State in a given month. * Meteorology: the rainfall in a given month. * Uncertainty: the exact date of Noah's birth. * Indeterminacy: The closing of the Dow Jones industrial average or the temperature in New York City at 4 pm. on February 28, 2014. * Chaotic determinacy: the relative frequency of the digit 3 in the decimal representation of $\pi$. In the probability theoretical literature the situations in which probability theory applies are called ``experiments,'' but I avoided this terminology here, since we are talking here of several different types of situations, not one single type. Likewise I avoided attributing one unitary ontological reason why probability applies here, called ``chance.'' Instead of asking the question: why is probability theory applicable in the above situations, I want to ask here: What does the fact that probability theory is appropriate in these situations tell us about the world? (This is no longer in my class notes.) Let us go through the above list one by one. Any input on your part would be very appreciated: * Games of chance: Games of chance are based on the sensitivity on initial conditions: you tell a human to roll a pair of dice or shuffle a deck of cards, and despite the fact that the human is doing exactly what you ask him or her to do and produces an outcome which lies within a well-defined universe (a number between 1 and 6, or a permutation of the deck of cards), the question which number or which permutation is completely beyond their control. The precise location and speed of the die, or the precise order of the cards that are being shuffled, varies, and these small variations in initial conditions give rise, by the ``butterfly effect'' of chaos theory, to completely different final outcomes. A critical realist recognizes here the openness and stratification of the world: If many different influences come together, each of which is governed by laws, then their sum total is not determinate, as a naive hyper-determinist would think, but indeterminate. This is not only a condition for the possibility of science (in a hyper-deterministic world, one could not know anything before one knew everything), but also for practical human activity: the macro outcomes of human practice are largely independent of micro detail (the postcard arrives whether the address is written in cursive or in printed letters, etc.). Games of chance are situations which deliberately project this micro indeterminacy into the macro world: the micro influences cancel each other out without one enduring influence taking over (as would be the case if the die were not perfectly symmetric and balanced) or man's deliberate corrective activity stepping into the void (as would be possible if the cards being shuffled were not indistinguishable from the backside). The result is indeterminacy. * Quality control in production: you take a sample from a shipment, count how many defectives. Why is statistics and probability useful in production? Because production is work, it is not spontaneous, nature does not give us things voluntarily. Like a scientific experiment, production is the attempt to create local closure. Such closure can never be complete, there are always leaks in it, through which irregularity can enter. * Actuarial Problems: the length of life anticipated for a person who has just applied for life insurance. Not only production, but also life itself is a struggle with physical nature, it is emergence. And sometimes it fails: sometimes it is overwhelmed by the forces which it tries to keep at bay. * Scientific Eperiments: you count the number of mice which contract cancer when a group of mice is exposed to cigarette smoke: There is local closure regarding the conditions under which the mice live, but even if this closure were complete, individual mice would still react differently, because of genetic differences. No two mice are exactly the same, and despite these differences they are still mice. This is again the stratification of reality. But the reaction of the mice to the smoke is not completely capricious but can be predicted probabilistically. This is the transfactual efficacy of the smoke. * Meteorology: the rainfall in a given month. It is very fortunate for the development of life on our planet that we have the chaotic alternation between cloud cover and clear sky, instead of a continuous cloud cover as in Venus or a continuous clear sky. Butterfly effect all over again, but it is possible to make probabilistic predictions since the fundamentals remain stable: the transfactual efficacy of the energy received from the sun and radiated out into space. * Markets: the total personal income in New York State in a given month. Market economies are a very much like the weather; planned economies would be more like production or life. * Uncertainty: the exact date of Noah's birth. This is epistemic uncertainty: assuming that Noah was a real person, the date exists and we know a time range in which it must have been, but we do not know the details. But I doubt that probabilistic methods are a good way to represent this knowledge. * Indeterminacy: The closing of the Dow Jones industrial average or the temperature in New York City at 4 pm.\ on February 28, 2014: This is ontological uncertainty, not only epistemological uncertainty. Not only do we not know it, but it is not yet decided objectively what these data will be. Probability theory has limited applicability for the DJIA since it cannot be expected that the mechanisms determining the DJIA will be unchanged at that time, therefore we cannot base ourselves on the transfactual efficacy of some stable mechanisms. Regarding the temperature, it is more defensible to assign a probability, since the weather mechanisms have probably stayed the same, except for small changes in global warming (unless mankind has learned by that time to manipulate the weather locally by cloud seeding etc.) * Chaotic determinacy: the relative frequency of the digit 3 in the decimal representation of $\pi$: The laws by which the number $\pi$ is defined have very little to do with the procedure by which numbers are expanded as decimals, therefore the former has no systematic influence on the latter. (It has an influence, but not a systematic one; it is the error of actualism to think that every influence must be systematic.) But sometimes laws do have remote effects: there is one very simple and beautiful power series expansion of $\pi$, it goes something like $\pi/4=1-{1\over2}+{1\over3}-{1\over4}+\cdots$, and I have read in a math book that this is one of the most amazing theorems of mathematics. Any comments would be appreciated. Hans Ehrbar. --- from list bhaskar-AT-lists.village.virginia.edu --- --- from list bhaskar-AT-lists.village.virginia.edu ---