# Re: The increasing transformation problem

From: Paul Cockshott (paul@COCKSHOTT.COM)
Date: Tue Jun 10 2003 - 17:50:42 EDT

```Paul Bullock wrote:
this is the difference between us in the understanding of Marx's method,
value is a social relation, the price is the quantitative expression of
a form of appearance of value, as a thing. How do you measure the
'distance' between a relation and its 'thingified' expression, between
quality and quantity?

1. Is it appropriate to speak of value as quality rather than
quantity - I dont think so since Marx constantly deals with
it as a quantitative concept - ideas like rate of surplus value
would make no sense unless it is quantitative. It is defined
in terms of a quantity of socially necessary labour. There
is nothing mysterious about that, it is in principle measurable
given enough information about the conditions of production.

2. Which is a relation?  Is it not exchange value? This is a relation
between
two commodities. Price as a generalisation of exchange value
is also a relation, specifically an equivalence relation between
a commodity and money. At the level of the national i/o tables
what you have is a relation between the aggregate output of an
industry and a quantity of money. If we abstract from the output
itself we are left with a vector of money.

3. If you invert the i/o matrix you can extract the direct and
indirect labour required to produce each industries output, this
is a vector of labour hours.

4. Given two vectors one can correlate them to get a measure of
similarity, or alternatively normalise them and measure the
cosine of the angle between them using the dot product.
This measures the distances between the system of prices and
the system of values.

5. More generally what is a relation?
A binary relation is a set of pairs such that some predicate
holds. The exchange relation analysed in vol 1 of capital with
its relative and equivalent forms is just such a set of pairs.
Extending beyond binary relations, a relation is a set of
tuples such that some predicat is true, or alternatively we
can take the extension of the set to define the predicate.

6. When you say that value is a relation what do you mean?
What order of relation is it, what are the domains in the
relation? One response would be to say that it is a binary
relation with the domains being quantities of a product in
the first case and quantities of labour in the second case.

7. This relation is induced by a more complex structure which is
not itself a relation: namely the aggregate technical conditions
of production, and the social conditions under which these
are operated.

> Paul,
>
>    From: Paul Cockshott
>
>      To: OPE-L@SUS.CSUCHICO.EDU
>      Sent: Monday, June 09, 2003 9:50 AM
>      Subject: Re: The increasing transformation problem
>       Paul Bullock wrote:
>
>     >   Your idea that  there is a 'distance' between values and
>     > prices cannot apply to any factually observable realm...
>     > since values are only expressed in market  prices, which
>     > themselves can be explained as being 'regulated' by prices
>     > of production.
>
>      This is simply wrong. With the advent of I/O tables one can
>      work
>      back to get estimates of values and compare these with
>      prices.
>      There is a lot of econometric literature doing this.
>
>     >
>
>      --
>      Paul Cockshott
>      Dept Computing Science
>      University of Glasgow
>
>
>
>      0141 330 3125
>
>
>
```

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