28 Oct 2009 @ 10:04, by John Grieve
Fixing Cartesianism
For many years commentators have said that the dualism of Descartes, his split between mind and body, is a form of alienation and symptomatic of the malaise that afflicts the Western mind. This is becoming more evident and the situation is approaching crisis point.
This is not just a problem of philosophy but, as I have tried to demonstrate, is something that's central to many aspects of our civilization. In this short piece I would like to suggest ways in which we can 'fix' the alienated mindset demonstrated in Descartes' mathematics and science.
In previous articles, and I will not restate all the arguments, I have asserted that there are serious weaknesses in the Cartesian project and the science associated with it, even to the point of taking issue with certain parts of relativity theory (space-time continuum)
It is evident to me that his system of cartesian coordinates does not like different scales, on the one hand, and discontinuities and infinities, on the other. It assumes everything is on the same scale and does not deal elegantly with exceptions to this. Likewise, in the area of discontinuities and infinities, the differential equations employed by this system, call for clumsy and tedious re-normalization techniques whenever problems are encountered. There must be an easier way.
I would suggest that the mathematics invented by the Chaos science is this easier way. The mathematics of maps,fractals, recursion, iteration and bifurcation. This Chaos maths is a natural successor to Cartesianism. It has no problem with different scales and its maps are in some ways a natural progression from co-ordinate geometry. Similarly, it can deal with infinities much more elegantly and without the need for normalization techniques.
Also,I believe, the days of the pre-eminence of the differential equation are coming to an end. In the technique of Chaos theory's iteration and re-iteration, we have, seemingly, another process of integration comparable to that of the calculus. If we can iterate differential expressions, then the days of solving millions of simultaneous differential equations on supercomputers will be over.
The Cartesian dualism is a name given to a whole reductionist, separatist mindset that positions us as observers 'over here' looking at an object 'over there' that we attach quantities to.
Becoming 'insiders' is a new way of being, and involves not only a holistic philosophy, but a new science and mathematics of integration as well.
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