Saturday, April 04, 2009
Neo-classicists and the Neocons are not Economists but Phsyicist and Mathematicians Lost in the Maze of the Real Economy
All these so called economist from Debreu on, Nobel for his 'The Theory of Value', knew nothing whatsoever about the economy or economics. Debreu himself said on many occasions that he was not an economist. His Nobel prize winning work is a well crafted piece of differential topology, an existence theorem, to prove a solution exists to Walras' hypothesis, of a hundred years previously that prices could adjust by a process of trial and error, 'tattonement', to converge to a General Equilibrium - a set of prices such that that all markets cleared, i.e. supply equaled demand in every market.
His work is a beautiful demonstration of the wrongness not the rightness of General Equilibrium Theory and the Neo-Classical Economics that has now so catastrophically failed us. It is in fact a proof of what utter nonsense this perspective is. He shows that for General Equilibrium to be possible. There needs to be a set of markets defined over a complete, differentiable measure space defined over all time from the day of Genesis, the Big Bang, to the Present for all goods each of which must exist at all points of continuous time and between all points of time for this result to hold. His mathematics is beautiful but what arrant nonsense as economics.
For General Equilibrium to Exist even as an aspiration the universe has to be in stasis for eternity. Beautiful math that proves that economics based on the idea of tattonement leading in the limit to General Equilibrium is complete and utter nonsense. Instead his success with his Nobel acclamation charted a route that other followed in the Journal of Economic Theory, etc.
Marshal, the First Professor of Economics at Cambridge and Lord Keynes a successor were both excellent mathematicians, Keynes wrote a well respected treatise on probability theory but math never ever appeared in their published works in economics although it is clear they used it to discipline their thinking about the real economy, that especially Keynes practically knew so well. Keynes became very rich as did his College from his understanding of the stock market. Note that David Ricardo the second great economist, after Adam Smith, became very rich too from playing the markets in the early 19th Century - his father threw him out at 26 because he married a gentile. He retired to write around ten years later on what he made trading bonds on the London market.
Keynes summed it up in his General Theory to paraphrase "it is impossible to keep all necessary partial differentials you are holding constant at the back of your head when solving an economics problem" The relatively stable environment it is possible to create in physics both as a thought experiment and in the laboratory is simply non-existent in economics. Politics, society, human psychology and the natural environment co-evolve in a complex way with economic change such that it is impossible to truly keep track of where we are using mathematical formalism. The tradition of economics was to except the impossibility of uselessly formalizing the formalism you might choose to discipline your thinking in the background but which Debreu proves and Keynes recently vindicated "General Theory" demonstrates tend to obfuscate the economics.
Economics was a great discipline but we have now got to accept it has been wrong headed in its driving mentality for the last half century and seek other ways to pursue the study of the economy consonant with the traditions that died with Hicks Pigou and Schumpter and has not yet died in the person of Paul Samuelson whose beautifully crafted piece on Economic Analysis makes two things very clear. One if you cannot explain it to a wife uneducated in economics it is definitely bad economics and if anyway comparative static analysis which the General Equilibrium people revel in is only a tiny tiny part of the economics discipline which needs to embrace dynamics,in smooth, stochastic and historic spaces where completeness, differentiability and ceteris parabus writs do not run.
Thursday, November 29, 2007
The Mobius Field Theory of Love the Universe and Everything
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I have had a significant response from Luke Luke.W.Friendshuh@seagate.com about my response to Lynne's lynnras@maui.net very important issue about the need to address failure. The point I made and which is not yet truly challenged is that failure is ubiquitous and if far more in need of explanation than what i would call evolutionary success. WE should therefore not therefore try to infer things from the VERY particular cases of successes but must deal with the conditions that permit of many failures but in a context where given the interaction between a newly emergent source of a fast process we generally call "energy" and a slower process we call "material" we get an emergent unfolding in the general dynamic of evolution which we call a structure and generally allocate a name to its result which we generically call a form. In this universe there is however only process (dynamics) there is no form in any permanent sense whatsoever everything is always flowing including that which we have chosen to call inanimate, and what we sense is always the interactions between two processes one a fast and one slow.
As we have seen this term the universe has infinite variety because every element of it can be described by the connection between a function which is best described on the set of complex numbers which are observationally two series of interconnecting real numbers "fractals" which are stable and so the form of a genus or species if their modulus is less than 2. To be the totality that analytical sciences, the arts and social sciences deal with we only have to accept the McIntyre janet.mcintyre@flinders.edu.au conjecture that the universe in total is derivative of one process only which has to flow (have a rate of change with respect to time) continuously in three dimension. this object is by definition a mobius strip. It is the only thing that is one sided, with one edge but can only exist in three dimensions.
The physics high and low energy are beautifully simple. If space time was a circle flow, a circular field, the outer surface of the filed would have to travel faster than the inner surface - the circumference of a bigger circle being longer than the circumference of the inner one if the field of force is to stay cohesive therefore the infinity of its "substance" would have to move faster on the outside of the curve than it did on the inside. This is disruptive and such a process would quickly separate out and continue to separate out until it was a sequence of zero depth circles all embedded within each other with no sensual form other than the fact that each successive one was traveling slightly faster or slower than those it was adjacent two. However such a universe would be not be fractal and can easily be constructed in two dimension not three.
However if the field of flow is a mobius strip the above does not happen as described. The circular structure is still there but because it is only one surface with one edge the forces acting within it do not manifest in a separation our of its structure just in terms of its depth, though that occurs, and is what we call "procreation" at what we have chosen to call the biological level, but what is more important because the filed in three dimensional that the disruptive dynamics i have described due to the centrifugal forces inevitable in circular motion also occur within the length, the direction of the flow itself. This is on the curve inevitable in the mobius strip. The same edge on opposite "sides" (what can that mean) of the strip has to move faster than the other for it to stay cohesive but they are the same thing separated in relative time by the flow but so must flow at the same speed but they cannot because one is on the outside of the "circle" and the other is on the "inside". the only way out of this conundrum is the one described for the circle but here it ia absolutely imperative the flow must split in two along its direction of flow. In a mobius field this can only provide temporary relief because then the process has created a one sided field three space with two twists in it not one so the process of "construction" I have described must continue and the "double twisted mobius" strip must split again along its line of flow but this time this rupture will not produce one "quadruple twisted mobius strips" but two single twisted ones intertwined with each other. This is what i believe we call a "structure" a "form" and it always has two parts one flowing faster than the other to create the local basin of attraction we call form but which mathematically is a Mandelbrot set (highly fractal) defined by a function defined over a complex field that that from a particular perspective in time could be described as temporally stable.
I think one of these intertwined mobius strips we may chose to label as energy that always has the potential to disrupt the "form" and the other we might chose to call "information" which provides the apparent organisation that creates the autopeosis we attribute to a particular form that in biology we would perhaps describe as a species - please note that the entity is the species not the structural dichotomy we often introduce here between "male" and "female" or the dynamic dichotomy we chose to introduce by distinguishing between parent and child. this species will replicate itself like the concentric circles do ad infinitum as long as it energy keeps on being energised and its information keeps acting to retain its structure which it will.
However the process is continuous and never stops. We now call it evolution. New species and an occasional genus keep spinning out of the process but it is ONE process in three dimension where nothing every becomes disconnected from anything else but each element, "structure", within it MUST contain all the elements of all the previous processes in the unfolding hierarchy that is the way of the universe we inhabit.
The first two interconnected mobius strips are that between the universe we occupy and the anti-universe we cannot sense but that is its dual. Our universe then splits along its lateral axis into "strings" (the stuff of high energy physics) that then split again into matter and energy (nuclear physics) from which are formed elements which in turn form molecules which accrete out into the structures of our astrophysical universe, which produce within its field suns working on the basis of fast "electromagnetic style" energy and planets working on slow gravitational organising style energy that produces "solar" systems linking slow and fast energy to produce at one end of the spectrum suns pushing out huge volumes of fast energy from the interaction in their core between fast electromagnetic energy and slow gravitational energy and at the other planets with an insufficiency in size to become energy producing sources so act as a sink for their suns energy and the dissipation of their own residual electromagnetic energy held in abeyance to their sun to receive greater or lesser amount of electromagnetic energy from it determined by their distance from it.
The forces acting on the planets turn them into a huge mixing machine for all the elements and the molecules and their are billions upon billions of these and in some this mixing pot must inevitable produce yet another lateral rift in the fabric of the ever unfolding set of mobius strips that are our universe to produce what we call life which again is an interconnection between a fast "energy" source with a slower organising "information" source to produce a new form, a species. This entity this singleton, can then divide ad infinitum presenting as it dynamic structure parents and children and its formatting structure males and females but actually always being one thing.
I can go onto describe the process evolving to create the emergent processes we call societies etc but I will not.
On this model we have a system of systems processes (SSPs) which with no equivocation whatsoever everything is always connected to everything else but a huge variety of structures and forms (genus) are manifest within this ONE very very very simple process and within each of the elements the variety of species in form is equally massive and within all of these there is prior and posterior parents and children and conjunctive male and female for want of better labels – one has one process continuously generating isomorphies of itself consisting of the two linked local parts of the common singular flow, one fast and one slow we call a “structure” a term probably best attached to the singularity and so two “form” we could chose to call “male” and “female” or阴 ying and 阳 yang {by the way日is the character for the sun the giver of electromagnetic energy and月the character for the inert moon symbolic of gravitational organisational energy working alone while阝(fù yì) is simply singular for a place}
Now the structural mathematics of all this has all been worked out and proved mathematically in Rene Thom’s great but impenetrable book to the non-mathematician “Structural Stability and Morphogenesis”. This work is still VERY highly regarded by all the mathematicians in his peer group and has never been discredited for or by itself. It has been discredited by the use that has been made of it by uncomprehending non-mathematicians.
The key thing to know is that his mathematics is defined over a measure not a metric space. It can therefore never produce any quantifiable predictions that could be statistically tested. It only seeks to explain how ordered, fast and slow, smooth dynamic process can interact to produces the discontinuities (catastrophes) that create the huge variety of structures we sense and our brains construct out of what they believe, find useful to our survival, about the universe we occupy.