On Tue, 08 May 2001, you wrote:
> Re Paul C's [5510]:
>
> You didn't really answer, though, the first group
> of questions that I asked (see above). These
> questions are related to another one that I asked
> in [5500]: "How simple is *too* simple?".
I thought that I had tried to answer it by
the point I made later in my letter to the
effect that Value form theory was simpler,
but that it was as you put it too simple, in that
it made no predictions about prices at all.
>
> Occam's razor (also called Ockam's razor) and
> the MDL principle suggest that the simplest
> theory that is capable of explaining a phenomenon
> is the best. Yet, if the phenomenon under
> investigation is inherently complex then one can
> *over-simplify* the subject to such an extent that
> essential aspects of that subject are not included
> within the explanation. It seems to me that there
> are many instances of the latter in the history
> of political economy. I think that this was a
> major part of Marx's critique of authors such as
> Torrens, McCulloch, and James Mill. I.e.
> part of Marx's critique of the 'vulgar economists'
> associated with the 'disintegration of the Ricardian
> school' (see _TSV_, Part 3, Ch. XX) was
> that these economists represented a step
> backwards from Ricardo to the extent that their
> theories were *too* simple.
I agree with this.
The problem given the MDL principle is that
one counts the information content of the input to
the theory and compares it to the information you
have to add to the predictions of the theory in
order to get to the actual observations.
The process that determines prices is complex, so
that if one wants to have a theory of prices, whether
it be the classical labour theory of value or the Sraffian
theory of prices, the set of inputs to your theory is
going to be at least as big as the input output matrix.
Since these contain more information than is present
in the final price vector, any theory that attempts to
predict prices will be longer than one which says
'hey presto' look at what the prices actually are.
The point you make about complexity is I think correct.
In information theoretic terms one can measure two
properties about a number or set of numbers, be these
prices, the digits of pi or whatever.
1. Is the information content. This is given by the shortest
formula capable of reproducing the numbers.
2. Is the complexity of the number, this is given according
to Bennet by the logical depth of the process required
to reconstruct the number.
Let us consider three numbers in turn.
The first is formed by concattenating the digits of the
pricevector supplied in the US input output tables, taking
each number as a log to the base 10 and taking 4 digits
of the log. This will give us a number that is about 400 digits
long.
The second number is the first 400 digits of pi.
The third number is the sequence 0101... for 400 digits.
Clearly the last number is both the least complex and contains
the least information, in that we can provide a concise
description of it, and given that description can quickly
and simply determine the entire sequence.
The second number, pi, can be defined in a short formula,
which is almost certainly less than 400 characters long, so
its information content is strictly less than 400 digits. On the
other hand it is costly to compute pi to 400 digits, so its
logical depth or logical complexity is very high.
The first number is probably computationally irreducible,
in other words, there is no shorter formula that can reproduce
it. Only the observational practices of the bureau of statistics
in conjunction with the real processes of the US economy
can produce it.
Now if a number is computationally irreducible, then it is its
own minimum description - so the pure application of occams
razor would favour just taking it as given, not attempting to
predict it. However it may be the result of a complex process,
technically, a lot of information has to be discarded to arrive
at the answer. In computing pi one discards a huge number
of intermediate results to get to the final one.
Anlogously, the price vector we see in the IO tables is
the result of discarding a huge amount of information, both
when the prices of the individual firms that go into
the sector are taken into account, and within each firm.
The practice of cost accounting is an information destroying
process. From a final costing of a production process you
can not work backwards to the costs of all the inputs.
Thus in modelling an information destroying process like
capitalist cost accounting, one has to accept that the
theorems that predict the price may require more input
data than they output.
>
> But, figuring out what is "too simple" is by no
> means an easy task (although I don't think
> that it requires that we throw up our hands and
> "choose not to choose" a la Feyerabend. See
> Nicky's [5513]).
>
> Consider again the first question I asked above
> (I'll expand on it here). VFT (e.g. our own R/W)
> have suggested that a systematic dialectical
> reconstruction in thought of capitalism should
> identify money with value and should not consider
> either labour-power or money to be commodities.
> They (especially Mike W) has offered many
> reasons for this shift. One of the reasons offered,
> it appears to me, is that these concepts in
> Marx are not only outdated and erroneous but
> are *also* unnecessary and redundant. That last
> argument seems to me to be an appeal to Occam's
> razor and the MDL principle. Yet, if we are
> going to appeal to the MDL principle, wouldn't
> Sraffa and surplus approach theory be a 'winner'
> in relation to *both* Marx and VFT? Indeed,
> didn't Steedman's critique of Marx in its claim
> that value theory is 'redundant' and 'unnecessary'
> implicitly appeal to Occam's razor and the MDL
> principle? So if both theories implicitly appeal
> to the MDL principle, how do we then choose
> between VFT and surplus approach theory?
> I think that the answer has to concern trying
> to draw a line a proverbial line in the sand where
> on one side of the line there are unnecessary
> assumptions and on the other side there is over-
> simplification to such an extent that essential
> aspects of the subject under investigation are
> abstracted from. To address this question more
> concretely would thus, for example, require that
> we consider to what extent money and value are
> essential to comprehending the subject matter of
> capitalism. This, though, can not be resolved
> through an appeal to Occam's razor and the
> MDL principle -- or so I am inclined to believe.
>
> In solidarity, Jerry
--
Paul Cockshott, University of Glasgow, Glasgow, Scotland
0141 330 3125 mobile:07946 476966
paul@cockshott.com
http://www.dcs.gla.ac.uk/people/personal/wpc/
http://www.dcs.gla.ac.uk/~wpc/reports/index.html
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