RE: [OPE] Dialectics for the New Century

Date: Thu Apr 03 2008 - 08:54:03 EDT

Hi Paul C:
All aspects of social relations of production can not be 
be expressed as 'calculi'.  That is, in part, because there
are essential aspects of  those relations  which can not 
be expressed  as *magnitude*  and are  
comprehensable merely through formal/mathematical calculi. 
How, for instance, is the changing 'balance of power'
among (and within) contending classes under capitalism calculated?
If class struggle is  calculi, can't it (at least in principle) be 
expressed as a quantitative *formula*?
I see the exclusive emphasis on 'calculi' as ... well ...
In solidarity, Jerry

“Calculi are rules for the manipulation of strings of symbols and these rules will not do any
calculations unless there is some material apparatus to interpret them. Leave a book on the
low-calculus on a shelf along with a sheet of paper containing a formula in the l-calculus and
nothing will happen. Bring along a mathematician, give them the book and the formula
and, given enough paper and pencil the ensemble can compute. Alternatively, feed the
l-calculus formula into a computer with a lisp interpreter and it will evaluate.” (Are There New Models of Computation? Reply to Wegner and Eberbach, Paul Cockshott and Greg Michaelson,, The Computer Journal 2007 50(2):232-247; doi:10.1093/comjnl/bxl062)
“And conversely, when we interpret
Turing’s theorem as a statement about what can and cannot be computed in
physical fact, we are adopting some of his tacit assumptions about physical
reality or equivalently about the laws of physics.
So where does mathematical effectiveness come from? It is not simply a
miracle, “a wonderful gift which we neither understand nor deserve” [17]
— at least, no more so than our ability to discover empirical knowledge,
for our knowledge of mathematics and logic is inextricably entangled with
our knowledge of physical reality: every mathematical proof depends for
its acceptance upon our agreement about the rules that govern the behavior
of physical objects such as computers or our brains. Hence when we im-
prove our knowledge about physical reality, we may also gain new means of
improving our knowledge of logic, mathematics and formal constructs. It
seems that we have no choice but to recognize the dependence of our math-
ematical knowledge (though not, we stress, of mathematical truth itself) on
physics, and that being so, it is time to abandon the classical view of com-
putation as a purely logical notion independent of that of computation as a
physical process. In the following we discuss how the discovery of quantum
mechanics in particular has changed our understanding of the nature of

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