Multifractal Financial Chaos in an Artificial Economy

Carlos Pedro Dos Santos Gonçalves 
UNIDE - ISCTE Business School - Lisbon University Institute

June 19, 2010

Abstract:      
A model is proposed of a population of competing companies that are in a coevolutionary race and whose evolutionary performance is evaluated by a financial market, composed of value investors and of a breed of arbitrageurs that perform bargain arbitrage, trying to identify 'bargains' in the form of relative misspricings and, acting accordingly, buying assets with higher value at lower prices and selling assets with lower value at higher prices.

The model's equations are based on coupled networks of nonlinear maps, in this way, the model is focused on a coevolutionary process between companies and financial market. It is shown that, for a wide range of dynamical couplings and parameters, Multifractal Self-organized Criticality (MSOC) takes place, with the emergence of patterns of turbulence that closely resemble actual financial turbulence. The relation between arbitrage and multifractal financial turbulence is addressed.

Keywords: Multifractal chaos, financial turbulence, multifractal self-organized criticality, evolutionary arbitrage theory, financial markets’ efficiency, tail risk, evolutionary finance, microscopic financial modeling

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1576990

From Eternity to Eternity…

By: Maria Odete Madeira

Being the being of the being the same being that is of the becoming, as being that becomes, and, thus, alterity of itself, in itself, fundamental issues are placed, in what regards the relations of scale and the laws of structure that may be perceptioned, apprehended and formalized towards fixed human languages, which, due to that fixity, are incapable of capturing the fundamental (co)dynamics of simultaneous permanence and change in a same being, a (co)dynamics in which the constituent and constitutive antithetical movement determines the dynamics of scale that displace themselves in percolating multifractal webs, dependent upon the systemic processing (co)implicated in the locality/nonlocality of the respective systems.

Having, also, to consider, in those same issues, that the limit to the formalization, on the part of the human agents, is processed at the level of the individuated limit of the system itself, as self-referent noumenon, dependent upon its preformative and formative initial conditions, inaccessible to possible algorithmic schemes, assembled from the systemic effects, observed in ontological situational contexts and processes that spill over towards eidetics that transcend the mathematical reason, as human language that develops and uses disciplinary tools made available towards effects of calculation and measurement.

Thus, other dynamics of cognitive processing will have to be introduced, such as, processes and arbitria of systemic synchronization, linked to autopoietic cognitive reasons and dynamics.

Quantum Game of Life I - Life and Death

By Carlos Pedro Gonçalves

The first version of the Quantum Life model is now published in Netlogo at the website:

http://ccl.northwestern.edu/netlogo/models/community/Quantum%20Life%20I


This is a model of a Quantum Game of Life with path-dependent local quantum computation, exemplifying a Quantum Cellular Automaton.


Each patch can be either vacant of life or occupied by a living entity.

At each round of the game, a patch can be actualized into one of the two alternatives: (1) vacant of life or (2) occupied by a living entity, with a certain probability amplitude defined by the local patch quantum (game) state.


There are two alternative rules through which this game is played:

(1) - The clustering rule;

(2) - The spatially and temporally independent rule.

In the first rule, there is the production of a flocking (or herding) phenomenon, that is, the birth of living entities tends to occur through clustering, making emerge, in the quantum game, a quantum gravitic mechanism where the birth and death of living entities tends to lead to clusters of living entities.


In the second rule, the flocking (or herding) phenomenon is absent, the birth and death of living entities occurs with a fixed local probability for each patch, such that there is a fixed local probability for a vacant patch to become occupied by a living entity and a fixed local probability for a living entity, residing in a certain patch, to die.

See also the following video for another version of the model, with a simulation of the clustering rule:

http://www.youtube.com/watch?v=14jdqWEe0wE

"Moral judgments can be altered ... by magnets"

By: Maria Odete Madeira

“Moral judgments can be altered ... by magnets (...) By disrupting brain activity in a particular region, neuroscientists can sway people’s views of moral situations.”

http://web.mit.edu/newsoffice/2010/moral-control-0330.html

In the above quoted article, it is imperatively stated that “Moral judgments can be altered ... by magnets” and that “By disrupting brain activity in a particular region, neuroscientists can sway people’s views of moral situations.”.

Any living systems can be affected by electromagnetic fields. In what regards human organisms, of course that these are affected by electromagnetic fields in their cognition, of which the ethical judgment and the moral judgment are examples, this is not any Eureka moment.

Electromagnetic fields, a dog bite, an earthquake, hunger, the need to go to the toilet, common cold, a headache all of that affects an organism’s cognitive production, towards fundamental judgments. Anything that affects a body, affects the body’s cognitive functions. What's the surprise? Where’s the Eureka moment?

In an interconnected network a “disruption” of a local region of the network can have effects upon the whole system, but that does not legitimize a reduction of the system to that specific region, which is what is done in the research work that is reviewed in the article and reinforced by the review itself. This reduction is a scientific error.

What seems evident is that the people that have produced these experiments practice applied science, compromised by schemes of control, without considering the concepts and nature of the systems with which they are working.

Matters like the nature of human cognition, in proto-conscious and conscious aspects (reflection, reflexivity, reflexibility), towards judicative valorative judgments of survival, in situations of border with homeostatic processing, linked to mechanisms of risk evaluation for situational systemic self-references of rhythmic enactive intentionality, in abstract and concrete planes, articulated with the respective languages, none of this was considered in the research, nor in the article that reviewed it.

Other fundamental matters, linked to the nature of human cognition, such as the perceptive and affective porosity and the arbitriu, implicated in the systems of exchanges of matter, energy and information between an organism and the situational living web in which it is immersed, towards systemic effects of locality and nonlocality that are synthesized in any cognitive judgment, must be considered in any study that addresses human cognitive judgment, of which a moral judgment is an example. No human judgment can be reduced to black boxed input-output systems.

Conclusive statements like: “Moral judgments can be altered ... by magnets”, “By disrupting brain activity in a particular region, neuroscientists can sway people’s views of moral situations(...)” and “(...) You think of morality as being a really high-level behavior (...) To be able to apply (a magnetic field) to a specific brain region and change people’s moral judgments is really astonishing (...)”, all of these statements are scientific nonsense, “intellectual impostures” of an applied science that intermixes a bad Cartesianism with a bad Behaviorism, contaminated by an illusion of control.

on the strange loop...

By: Maria Odete Madeira

A strange loop is a feedback circle, linked to the systemic identity, as self-computable rotative dispositional dynamics, in which the system folds upon itself, without leaving itself, maintaining the constituent and constitutive systemic integrity.

A strange loop is rotatively projective. The projective rotativity is assumed, in the notion of systemic identity, at the level of the ontological dynamics of projectivity, intrinsic to the systems, signalized at the level of the effectivenesses that act upon the effects, and are postulated at the level of the causes, as formative capabilities that act upon the preservation of the integrity of the systems in survival interfaces.

On Parson’s Quasi-Concrete Objects

By: Maria Odete Madeira

Abstract existents are object/figures of thought and of reason, they may have, or not, simultaneously, correlationable concrete existence/examples.

In relation to the concrete/abstract the term “quasi” does not apply.

The term “quasi” can be applied to the relation between the potency/act, in which, in the potency, the intensity towards the act can generate, in the propension/tendency, displaced in the horizon of possibility, a situation or process of latent state, in which, in epistemological and ontological terms, the usage of the term “quasi-concrete” could be adequate.

But, regarding abstract objects, the term “quasi-concrete” is not applicable.

On the logos of the things...

By: Maria Odete Madeira

The things have to be “listened” to, perceptioned, interpreted and understood in their rotative topoi. We have to see what is in the things and not what we want or wish to think about them.

The sun has its logos, the stars, and the planets, an ant, a stone, a spider... each has its own logos that explains it, as such, and that logos does not depend upon us human observers... it is its logos and its truth.

If we interest ourselves, if we want to know what things are, we have to make an effort to synchronize our rotative rhythms with the rotative rhythms of the things that we want to know, to make emerge a gravitic point of systemic synchronization in order to listen to them... perceive them... understand them.