Wednesday, April 11, 2012

Leonid's Balls

One of the smaller bits of space-junk whirling mindlessly around the Randroid Belt calls itself "Leonid", whose name means "Son of a Lion."
This great leonine intellect recently roared the following on Sense Of Life Objectivists (SOLO):
"Stochastic process is not contingent. Each and every stochastic state in every given time is determined by interaction between all entities involved and couldn't be other. However the number of entities is so big that we unable to establish cause-effect connection. Mathematical procedures or telegraph process could be contingent but they are man-made, So is chess game, soccer game, a philosophy a symphony, a painting and many other products of man's mind."
In other words, according to this bright light, there is no such thing — no real causal force in the physical universe — as chance or randomness. According to this bright light, "chance," "randomness," and "stochastic state" (these terms can presumably be used interchangeably) are simply "placeholders", or "markers," for strict, mechanistic, physically determined causes that human minds simply happen not to know at the time they are thinking about the event or events in question. Thus, "chance," "randomness," and "stochastic states" are terms that mark our ignorance of the "real" causes involved, the word "real" being reserved by prior philosophical commitment to strictly mechanist, deterministic events.
So, for Leonid (as for everyone else floating in the Randroid Belt) words like "chance," "randomness," "stochastic state," etc., point to a state of consciousness (a deficient state, i.e., a state of ignorance); not to some aspect of material, objective reality, comprising matter and energy. A knee-jerk Randroid would probably phrase what I've just written thus: "The concepts of 'chance,' 'randomness,' 'stochastic state,' etc., are epistemological concepts, not metaphysical ones. They relate to some condition or state of man's mind, and not some aspect of physical, material Existence."
Now, if "chance", "randomness", and "stochastic state" are placeholders for our lack of knowledge concerning real mechanistic deterministic causes, what, precisely, are "mechanistic determinist causes"?
Son-of-a-lion doesn't say. But there is a commonly accepted idea in the philosophy of science as to the criteria for strict determinism:
An effect is said to have been "strictly determined" by a cause if we can predict with precision and accuracy the state of the system at time t=n by knowing nothing except (1) the initial state of the system at t=0, and (2) the overarching principle or law that governs the relevant aspect of the system.
I mention the "relevant aspect" of the system because there may be many irrelevant ones, too; e.g., if we are interested in how a billiard ball of mass X will vector away from a cue-stick after having been struck by it with force Y, we needn't take into consideration the color of the billiard ball, since the property of color is taken to be irrelevant to the properties we are interested in — changes in motion and position.
Indeed, in the case of the motion of the billiard ball at some arbitrarily chosen time t=n, we can predict with great precision and accuracy many things — the ball's acceleration, its direction, its deceleration, the angle it will strike the side of the billiard table, etc. — simply by knowing the initial conditions of the ball-stick-table system, and Newton's laws of motion.
So when Son-of-a-lion avers that the concepts of "chance", "randomness", and "stochastic state" are useful only as placeholders, he means that in certain explanations of events — actually, in most explanations of events — human minds lack either the knowledge of the initial starting conditions of the system (including an accounting of which entities are relevant and ought to be included in the system), or they lack sufficient knowledge of the overarching general law or principle that governs the entities in the system, or both.
All Randroids believe this. It's a requirement for membership around the Randroid Belt.
Additionally, they believe that, in cases of this kind, knowledge of the number and kinds of relevant components of the system, and knowledge of the general causal law governing the relevant components, are possible to achieve in principle. What prevents one from knowing these things is not any inherent "unknowability" about the system; rather, it is practical considerations, such as the state of technology and the precision of our measuring tools, as well as more obvious things, such as the amount of time and money available for directing into such investigations.  Son-of-a-lion complains that it is the problem of "the number of entities" being "so big" which requires that we substitute the "approximate" knowledge of probability for the "exact" knowledge of determinism; but that which is claimed to be "so big" in 2012 might not be "so big" in 2062. Therefore, in principle at least, according to Randroids, all statements about events that are expressed as probabilities today are inherently expressible as statements of strict determinism.
This would mean that instead of accepting the idea of 3 fundamental types of causes in the universe — strict determinism, goal directedness, chance — Randroids accept only  the first two. To repeat: "Chance" for a Randroid is simply a name for our lack of specific knowledge of the criteria pertaining to the first.
The great advantage to this belief is that it makes one feel good, safe, and "in control"; for even if a Randroid knows absolutely nothing about the state of a given system, he could always claim that the knowledge of deterministic causes and completely predictable effects is "there", "objective", and "in" the system; he just lacks the time, funding, and precision instruments with which to discover them.
The great disadvantage to this belief, alas, is that it happens not to be true. In other words, it is NOT true that all physical events can, in principle, be reduced to tight, neat, causal chains in which a clearly known specific cause produces one and only one specific effect under the guidance of a grand, overarching law or principle. That Randroids ardently hew to this belief marks them as not only naive, but as inherently anti-scientific. Their position is a reactionary throwback to a much older viewpoint, no different from "naive materialism" and "simple reductionism" of the 19th-century.
To understand why this is so, we can consider the following hypothetical experiment by the great quantum physicist, Alfred Landé, known as "Landé's Blade."
A heavy ivory billiard ball rolls down a hollow, inclined tube; immediately on exiting the tube, it encounters a thin metal blade. The straight-line motion of the ball is now interrupted by having to roll atop a very thin, sharp, piece of metal, causing it to wobble either to its left or to its right, and to fall into a waiting box positioned on either side of the blade. We see that the blade adds a "randomizing" cause to the billiard ball's otherwise strictly determined motion along a straight line (guaranteed by the constraint of the tube).
Now, assuming the blade has been positioned precisely in the middle of the tube's exit opening, and the ivory billiard ball is a "fair" one (i.e., not biased in its mass in any particular direction), then our understanding of probability would lead us to conclude that there is a 50% chance of the ball falling in the left box or the right box. For the sake of brevity, we'll call the first event an l-ball and the second an r-ball.
After rolling, let us say, 10,000 billiard balls down the tube, Landé's Blade would guarantee that about 5,000 of the balls would find their way into the right-most box, and 5,000 into the left-most one.
A Randroid studying this experiment would probably say the following:
"If we had the time, money, and precision measuring instruments (such as very powerful microscopes that see down to the level of individual atoms), we could observe the individual forces inside the tube that affect the way in which the billiard ball is rolling, the way in which encounters the "lip" of the end of the tube, etc., and the way in which the sharp edge of the metal blade affect it, as well, thus permitting us to predict — in principle, at least — with 100% confidence, into which box the ball will drop on any given trial. Therefore, the idea that something called 'chance' governs which box the ball will drop is ultimately mistaken; 'chance' is simply a name covering our lack of specific knowledge of these atomic-sized and more fundamental causes."
The problem with such an explanation is this: the final effect is the same; i.e., 50% of the time the ball drops to the right, 50% of the time it drops to the left. What we need to explain is not why one particular ball, on one particular roll, falls to the left or to the right; we need to explain why there is statistical stability: why ON THE AVERAGE, about half of the rolls result in l-balls and why half in r-balls, and why THIS IS ALWAYS THE CASE.
Perhaps the best insights into the significance of Landé's Blade comes from Karl Popper, writing in his collection of essays on science titled "The Open Universe: an Argument for Indeterminism." [Linked]  In a chapter dealing with the problem of trying to erase probabilistic statements by looking for hidden deterministic laws that will give us a sense of certainty and stability, Popper writes the following:
"No physicist that I know of has seen this problem more clearly, or done more to show what is involved here, than Alfred Landé [NB: see his "Probability in Classical and Quantum Theory" (1953)  and "Foundations of Quantum Theory" (1955)]  His argument is designed to show that we must accept probabilities of single events as fundamental, and as irreplaceable by any statement except by other probability statements. Moreover, his argument shows that even if we combine a prima facie deterministic theory with statistical assumptions concerning initial conditions, we only get an infinite regress; and an interpretation which sticks to this assumption is bound to become untestable, metaphysical (or 'purely academic' in Landé's terminology)."
[Emphasis added]

Or we might say that an interpretation which sticks to this assumption becomes a rigidly held dogma around the Randroid Belt, whose members habitually substitute untestable metaphysical statements for scientific ones.
"Landé's argument may also be used to criticize the doctrine that probability considerations enter into science only if our knowledge is insufficient to enable us to make predictions with certainty.In order to see the weakness and even the irrelevance of this doctrine, let us assume again that we are faced with an arrangement as described by Landé, with balls dropping onto a steel blade, and a 50:50 ratio of r [right] and l [left] balls."
For the sake of clarification, note well what the steel blade in the experiment is really doing: it is segregating r-balls from l-balls, determining or deciding (and feel free to interpret those words either literally or metaphorically, as it makes no difference to the outcome) the path, or "fate", of each ball as it emerges from the end of the tube. So Popper uses the word "blade" in his argument to mean "anything in the arrangement that performs the action of segregating an l-ball from an r-ball," and which determines or decides the path, or "fate," of each ball as it rolls down the tube. The only difference is that each successive "blade" we might discover acts on the ball at an earlier stage of its trajectory down the tube, and can thus be seen as a more fundamental or determinative "blade" than the metal one which only segregates the balls "at the last moment," as it were. Keep this usage in mind, for Popper will soon speak of an "optical blade" that a hypothetical determinist — such as a Randroid — might assume to be acting on a ball at an earlier stage than the metal one, and thus being more of an ultimate "cause" for the ball becoming segregated to the left or to the right.  Popper continues:
"Let us further assume that we have an optical blade with the help of which we can know with certainty of every oncoming ball whether it will be a right ball or a left ball. This undoubtedly makes it unnecessary to invoke probabilities so far as the prediction of each single ball is concerned. But it does not in any way affect our problem. The balls, we may assume, fall to the right or to the left of the steel blade exactly as before, with the same 50:50 ratio, and with the same statistical fluctuations; and the problem of explaining statistical results, and that of explaining our ability to predict that future sequences will lead to similar results (provided the conditions are unchanged), remain precisely the same as before, in spite of the fact that we now know every single result in advance.
But does not our advance knowledge of the r and l balls enable us to change their ratios? We may assume that the balls come through Landé's tube sufficiently slowly, and sufficiently space from one another, to observe them with the optical blade and to remove each r-ball by hand (putting it in a box, say). As a result, we shall obtain only l-balls instead of a 50:50 ratio. Thus, on the basis of our precise knowledge, we can control our statistical results as we like.This argument is certainly correct. But we shall still find that the ratio of the l-balls to the balls now put away in the box [NB which were the early-detected r-balls that we removed before they had a chance to encounter the metal blade and fall into the r-box, and which Popper now calls box-balls] is 50:50, as before; and the problem of explaining this ratio, and the statistical fluctuations, remains unchanged: it has again been merely shifted.
The 50:50 ratio, it will be clear by now, depends upon the objective experimental conditions [NB: the physical arrangement we established when we decided to perform the experiment], and has nothing whatever to do with our knowledge, or lack of it. In so far as we changed the experimental conditions — replacing the r-balls by box-balls — there was a change in the results [NB: that is, we were able to get ONLY l-balls]; and in so far as we did not change the conditions, leaving the tube and the blade untouched, there was no change."
In the same chapter, Popper goes on to say that probabilities — which he renames "propensities" — should be viewed not as placeholders for our lack of exact knowledge of assumed deterministic causes, but rather as real, physical, objective causal traits or causal properties, not of any one individual element within an arrangement of elements, but of the entire arrangement itself. The 50:50 ratio of l-balls to r-balls is not some atomic or chemical property of ivory, but a property of the entire experimental set-up comprising: ball+inclined tube+metal blade, acting in concert.
I agree with Popper, and believe his approach to this problem is original and an important contribution to our whole way of conceiving of probability: i.e., probability, chance, randomness, stochastic state, or propensity, as an emergent property among aggregates of entities, and not some physical property inherent in the chemistry or atomic composition of any single one of them.
We conclude, therefore, that the universe contains at least three distinguishable kinds of causes, each cause being unique and non-reducible to the other two:
1. Strict determinism; 
2. Goal-directedness; and 
3. Chance.

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