X-Message-Number: 8285
Date: Thu, 5 Jun 1997 16:29:30 -0400 (EDT)
Subject: probability and chance

1. Eli Brandt (#8277) was on the button with respect to certain aspects of
the foundations of probability theory. No event is excluded from probability
considerations, even though in many cases the probable error will be
substantial and hard to quantify.

Everyone uses subjective or intuitive probability estimates many times every
day, even though dogmatists of the von Mises school may say such questions
are not in the purview of probability. (Is it safe to cross the street now?
Etc........) We  vary in skill and accuracy, but we all find it not only
useful but indispensable; and it is always based, implicitly at least, on

As an extreme example of something not amenable to probabilistic analysis,
von Mises gave the statement that "the Odyssey and the Iliad have the same
author." Actually, I can think of at least two ways to asssign a probability
to this possibility:

a) Look at the consensus track records of students of literary history, in
cases as similar to this as possible (even though there may be none closely
similar) that have already been resolved. The percentage of success is your
(very approximate) number.

b) Use modern computerized style analysis, which I understand has pretty good
reliability in determining whether two pieces of work have the same

Mr. Brandt also mentions the Bayes a posteriori probability formula (e.g.
probability of an hypothesis in light of a given result), which requires an
estimate of the a priori probability of the hypothesis. When I studied this
question 45 years ago, almost all statisticians declined to use the Bayes
formula, on the grounds that the prior probability in most cases wasn't
"known." But in fact, in most cases, it IS known at least to some degree. As
an example of a practical application, I used the exponential life parameter
(used e.g. in connection with the mean life of vacuum tubes). Instead of
using the usual "maximum likelihood estimate," which essentially assumes that
all values of the parameter are equally likely a priori, I assumed a more
reasonable a priori distribution, and obtained a much more useful formula.
This is real world stuff, with money on the line.

2. Mike Perry (#8281) discusses some possible ways in which the universe may
or may not have elements of "chance." I just want to reiterate my very
general reason for tending to reject any hypothesis involving "chance" as a
fundamental element of reality.

"Chance" or "randomness" in the usual case is just a matter of the state of
knowledge (or ignorance) of the observer. In classical physics (leaving out
of account for now certain questions involving chaos theory etc) an event is
"random" simply if the observer cannot predict it exactly. But ordinarily he
CAN predict certain features of the frequency distribution. You can't predict
the height of the next stranger you meet, but you can confidently predict
that he will not be taller than 1 kilometer or shorter than 1 millimeter.
("Randomness" also has the feature of indifference to place selection, which
I won't pursue further.)

But a universally objective or fundamental randomness might be, for example,
of the kind implicit in the (now generally discarded) cosmology of Bondi,
Gold & Hoyle--the "steady state" hypothesis. This held that the universe is
constantly expanding, but nevertheless remaining at the same average density,
because hydrogen atoms are popping into existence everywhere at just the
necessary rate. These pops could only be interpreted (literally or
figuratively) as interventions by the hand of God.

Quantum randomness as usually interpreted has this same character. But if we
leave out some conscious extra-universal or mystic agent such as God, the
conceptual problem goes beyond the question of "uncaused" events. The quantum
"randomness" is a STRUCTURED randomness! The probability or frequency
distribution has a known form! Quantum jumps of various kinds are
allowed--but most of them must be near the mean!  

In statistical mechanics we have perhaps the best classical examples of
"objective" probability relatable to underlying physical laws. But we know
the cause and structure; no mysticism is involved. But in the usual view of
quantum randomness, we are in effect asked to believe that there is a one-way
curtain between the observable universe and some larger or "outside"
universe, and behind this curtain someone or something is calling the shots,
in a way that is capricious (unpredictable) but still orderly. 

Obviously, we don't yet know the answers, and may not for a long time. But I
prefer to think that in the future, as in the past, if we study and poke hard
enough we will find that understandable and manipulable cause/effect
relationships exist in all phenomena, and down to the finest details.

Robert Ettinger

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