File spoon-archives/marxism.archive/marxism_1994/94-07-31.000, message 169


Subject: Re: More on Labor and Logic 
Date: Fri, 29 Jul 94 11:50:16 +0100
From: wpc-AT-cs.strath.ac.uk



In reply to Chris:
>     As for Paul's observation that "Prices do encode
>information, probably about 10 bits of information per raw
>price":  I assume that Paul is using a hypothetical figure
>here.  It is my belief that prices `encode' an almost
>limitless amount of information which is concretized when
>encountered by a knowing subject.  A knowing subject, the
>social actor in a market context, concretizes the information
>transmitted by a price, and makes decisions accordingly.  The
>decision to buy a new pair of shoes is sometimes dependent on
>factors that transcend "how much money" a person has.  There
>are all sorts of preferences, priorities, and tacit factors
>that enter into such decision-making, not merely the crude
>utilitarian calculus of `economic man.'  (Austrians are
>notoriously critical of this calculus-approach to human
>action.)

I was not being hypothetical. A bit is the amount of
information that enables you to give the correct answer to a
question with two equiprobable answers. More generally, if 
we have a system capable of occupying a certain state space
and we wish to know if it is within a certain sub volume of
that state space, then the information required ( assuming
equal probability densities accross the state space ) is
-log2 of the fraction of the state space represented by the sub
volume.

Since prices are always quoted in units of some currency they specify
a volume of money space ( an interval since this is an order 1 space )
that is proportional to the degree of accuracy with which they
are quoted. I often have to order components for manufacturing processes
and my experience is that in practice the accuracy to which prices
are given in catalogues is less than 2 significant digits. Prices
are of course longer than this, something that costs $1200.00 is listed
to 6 figures but the last 4 are not significant. 

This is reinforced if one takes into account the variation between prices
quoted by different wholesalers. I thus estimate that the significant
part of the price could be encoded in a 6 bit binary number. I then allow
4 further bits to specify the power of 10 exponent, giving the number of
zeros after the leading number. This gives me my estimate of 10 bits.

In fact however, this figure of 10 bits is almost certainly an overestimate,
since not all prices are equally probable. If I order a common chip, say
a 22v10, I can by inspecting past catalogues predict the likely price
range in a new catalogue. I know that $1000 is unlikely, as is 10cents,
whereas $5 would be likely. A more precise specifiction from
information theory takes into account the probability density of
prices by multiplying the price interval by its probability, and
gives us a measure of information -log2 of the probability of the interval.

In most cases one can do well by assuming that todays price will be the
same as the previous price. It is only when prices change, that they come
close to encoding the full 10 bits of their numeric specification.


The effect of this is to reduce the information content of an individual
price in a price time series to well under 10 bits.

It is this paradox that chris is refering to but misunderstanding when
he says that the prices encode an almost infinite amount of information
to a knowlegeable individual. The correct formulation is that prices
almost no new information most of the time. When prices change, they
convey extra information, up to the limits described above. But since
the normal information content approaches zero, the relative information
content of even 10 bits when divided by zero seems infinite.

>     As for Paul's observation that "new technologies reduce
>the labour that is socially necessary," I remain critical of
>the somewhat arbitrary notion of the "socially necessary."
>Granted, there are certain existential factors, such as sex,
>food, clothing, and shelter, which are necessary for the
>reproduction of human life.  But the notion of the "socially
>necessary" can differ based on WHO is recognizing the social
>necessity of the product, and IN WHAT CONTEXT that
>recognition proceeds.  Not only do different societies have
>different "necessities," different people WITHIN societies
>act on the basis of vastly different judgments regarding what
>THEY believe is necessary to their well-being.  The richer
>approach of the Austrians is far better than the labor theory
>of value at grasping these valuational differences, and the
>vacillating prices that reflect - and are reflected by -
>these differences.
The notion of socially necessary labour is one phrase to denote two
concepts that are logically distinct.
1) The amount of labour that current best practice requires to make a thing.
2) The fraction of the social working day that should go into
   a given branch of production.
In neither case does it involve an outside theorist laying down what
is or is not socially necessary. In the first case it is dependent upon
the state of technology and in the second on a whole complex of social
factors which influence demand for commodities. These are too hetrogenous
for it to be possible to produce any general theory, though there may be
specific theories applicable to particular industries.


>     As for Paul's observation that the inventors are
>"fabulous beasts," and that the real contrast is between
>workers in design departments and workers in body shops, I
>think that he is greatly underestimating the role of the
>inventor in the genesis of production and in the creation of
>human values.  Invention is the application of theoretical
>knowledge to material reality.  I think that the Marxist
>"bias" against `capitalists,' sometimes obscures the role of
>the `capitalist' as entrepreneurial inventor.  To this
>extent, and even within the parameters of a labor theory, the
>`capitalist' QUA INVENTOR makes a substantial contribution to
>the PRODUCTION process and to all the individuals, both
>workers and other `capitalists,' who benefit from this
>application of knowledge.

I am notionally and inventor, since I am named as such on
a number of patents, but the inventions are the property of my
employer, essentially because they are the product of collective
labour whilst the employer paid my wages. The capitalist inventor
is, in modern society, a fable. Capitalists hire salaried engineers
to invent things for them. The inventions through patent law
become commodities, and their production is just another branch
of commodity production, itself governed by the law of value.

Paul Cockshott
Dept Computer Science, University of Strathclyde


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