Next: Physics
Up: Table of contents
Previous: Complexity in Various Domains

The emergence of traffic jams from single cars

The traffic simulation [17,18] is an ideal laboratory for the study of complexity: the network of streets is highly documented and the cars motion can be measured and recorded with perfect precision. Yet the formation of jams is not well understood to this very day. In fact in some of the current projects it became necessary to introduce details not only of the car motion but also of the location of the workplace and home of the driver and passengers, their family structure and their life-style habits. Providing all this realistically for a population of 1 M people is an enormous computational and human time load and sometimes it seems that even this level of detail is not sufficient. Simpler, but not less important projects might be the motion of masses of humans in structured places, especially under pressure (in stadiums as match ends, or in theaters during alarms). The social importance of such studies is measured in many human lives.

From customers to markets

After loosing a fortune in a bubble (triggered by the South Sea Co.) in 1720 at the London Stock, Sir Isaac Newton was quoted to say: 'I can calculate the motions of the heavenly bodies, but not the madness of people.' It might seem over-ambitious to try where Newton has failed but let us not forget that we are 300 years later, have big computers and had plenty of additional opportunities to contemplate the madness of people.

The traditional approach in the product diffusion literature, is based on differential equations and leads to a continuous sales curve. This is contrasted with the results obtained by a discrete model that represents explicitly each customer and selling transaction [19]. Such a model leads to a sharp (percolation) phase transition [20] that explains the polarization of the campaigns in hits and flops for apparently very similar products and the fractal fluctuations of the sales even in steady market conditions.

The emergence of financial markets from investors

The financial economics has a long history of using precise mathematical models to describe the market behavior. However, in order to be tractable, the classical market models (the Capital Asset Pricing Model, the Arbitrage Pricing Theory, the Option Valuation Black-Scholes formula) made assumptions which are found invalid by the behavioral finance and market behavior experiments. By using the direct computer representation of the individual investors’ behavior, one can study the emergence of the (non-equilibrium) market dynamics in the presence of completely realistic conditions. The simulations performed until now [21][22] have already suggested generic universal relationships which were abstracted and then taken up for theoretical study in the framework of stylized models.

The emergence of the Immune Self from immune cells

The immune system is a cognitive system [23]: its task is to gather antigenic information, make sense out of it and act accordingly. The challenge is to understand how the system integrates the chemical signals and interactions into cognitive moduli and phenomena. Lately, a few groups adopted the method of representing in the computer the cells and enzymes believed to be involved in a immune disease, implement in the computer their experimentally known interactions and reactions and watch the emergence of (auto-)immune features similar with the ones observed in nature [24]. The next step is to suggest experiments to validate/ amend the postulated mechanisms.

The emergence of Perceptual Systems

The micro-to-macro paradigm can be applied to a wide range of perceptual and functional systems in the body. The main steps are to find the discrete microscopic degrees of freedom, their elementary interactions and to deduce the emergent macroscopic degrees of freedom and their effective dynamics. In the case of the visual system [25] this generic program is quite advanced. By using a combination of mathematical theorems and psychophysical observations one identified the approximate, ad-hoc algorithms that the visual system uses to reconstruct 3 D shapes from 2 D image sequences. As a consequence, one predicted specific visual illusions that were dramatically confirmed by experiment [26]. This kind of work can be extended to other perceptual systems and taken in a few directions: guidance for medical procedures, inspiration for novel technology, etc.

Microscopic Draws and Macroscopic Drawings

The processes of drawing and handwriting (and most of the thought processes) look superficially continuous and very difficult to characterize in precise terms. Yet lately it was possible to isolate very distinct discrete spatio-temporal drawing elements and to put them in direct relation to discrete mental events underlying the emergence of meaningful representation in children [27]. The clinical implications e.g. for (difficulties in) the emergence of writing are presently studied. This realization that there are intermediate (higher than neuron) scale 'atoms' in the cognitive processes is very encouraging for the possibility to apply complexity methods in this field.

Conceptual Structures with Transitive Dynamics

Dynamical networks were mentioned as a candidate for a 'lingua franca' among complexity workers. The nodes are fit to represent system parts / properties while the links can be used to represent their relationships. The evolution of objects, production processes, ideas, can then be represented as operations on these networks.

By a sequence of formal operations on the initial network one is lead to a novel network. The changes enforced in the network structure amount to changes in the nature of the real object. The sequence of operations leading to novel objects is usually quite simple, mechanical, well defined and easy to reproduce.

It turns out that a handful of universal sequences (which have been fully documented) are responsible for most of the novelty emergence in nature. Incidentally, ideas produced by a computer that applied one of these sequences obtained (from double-blind humans) higher inventiveness marks than the ideas produced by (a second group of) humans [28].

The basic dynamical element in this conceptual dynamics seems to be 'the diagonal link' or the 'transitive connection' (the emergence of a link between A and C if there are already links between A and B and between B and C). This object has been found in recent measurements to be highly correlated with crucial conceptual events as identified by competent humans. Moreover the density of 'diagonal links' has been found to be h3ly correlated with the salience of the text [29].

Next: Physics
Up: Table of contents
Previous: Complexity in Various Domains