Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott

From: Paul C (clyder@GN.APC.ORG)
Date: Tue Sep 21 2004 - 16:55:42 EDT


Alejandro Valle Baeza wrote:

>
>
> Paul Cockshott wrote:
>
>> Recently Steedman (1998) proposed to measure such deviations by the 
>> angle between market price and value vectors, as pointed out by 
>> Cockshott. Nobody uses Euclidian distance to measure value-price 
>> deviation. Nevertheless is not clear to me if according to Paulís 
>> paper are all of them wrong? Could Paul explain practical 
>> implications of his paper for measuring labor value-price deviations?
>>
>> ---------------------------------------------
>>
>> I think that Steadman's measure is probably wrong, and that mean 
>> absolute deviation
>>
>> is a more appropriate measure.
>>
>> ---------------------------------------
>>
> This is very important to me because you are finding bases to 
> intuitive approaches for measuring value price deviations. Could you 
> tell us more about why MAD seems more convenient than angle proposed 
> by Steedman?
>
>> Alejandro Valle Baeza
>>
At first when I looked at the problem of testing the similarity of 
prices and values I hit on a measure similar to
Steadmans - the normalised dot product of the two vectors which is the 
cosine of their angle. It was only later
that I thought that such calculations of angles assume that you are 
operating in a euclidean space. If the
metric of distance is different in your space then such measures are not 
appropriate. On the other hand
the sum of absolute differences does correspond to the metric formula 
for distances in commodity space.
It follows that the mean absolute difference - which is derived from the 
sum of absolute differences,
also follows the same form, and as such is an appropriate measure of 
distance in commodity space.


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