Subject: BHA: RE: In which kind of world is probability theory useful?
Date: Mon, 30 Aug 1999 11:15:46 -0400


Hans,

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.




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