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Saturday, January 25, 2014

116. Econophysics



A financial market is a complex system in which a large number of traders interact with one another, and also react to information, and determine the ‘best’ price for a given item. The time evolution of the price and the number of transactions of a traded item is generally unpredictable.



The time series indicating the price variation of an item is found to be essentially indistinguishable from a stochastic or random process. Like other complex systems, financial markets are open systems with many interacting subunits, and the subunits interact nonlinearly.


In the study of stock markets, the so-called efficient-market hypothesis serves as a useful benchmark. An efficient market is defined as one in which all the available information is processed instantly when it reaches the market, and in which this fact is immediately reflected in new values of prices of the traded assets. The efficient-market hypothesis (EMH) makes the idealized stipulation that any market is highly efficient in determining the most rational price of a traded item or asset. It was originally formulated in the 1960s. There are two assumptions involved here:
(i) the market is efficient; and
(ii) the behaviour of traders is strictly rational.
As we shall see below, this is only an idealization.

Why does the time series of returns appear to be random? This is because it carries so much information that there are no readily discernible regularities in it. It is, by and large, a 'non-redundant' time series, meaning that the information it carries is almost irreducible, or algorithmically incompressible, for most practical purposes (cf. Part 23). The EMH requires that the concerned time series for market prices has a 'dense' amount of non-redundant information. Since there are limits on the speed and capacity of our computers, a time series carrying this information is almost indistinguishable from a totally random time series. Of course, analysis of the deviation from a totally random time series is a good way of testing the degree of validity of the EMH in a given situation.


Suppose there is good demand for a commodity because of its attractive existing price. Naturally, the price will increase. This will then reduce the demand. And a reduced demand will entail a lowering of the price, and so on, till the demand and the price have reached a state of equilibrium. Thus negative feedbacks tend to stabilize an economy, as per conventional economic theory. This law of diminishing returns implies a single equilibrium point for an economy, and such situations are amenable to analytical control.



By and large, resource-based economic activities (e.g. agriculture and mining) tend to follow the law of diminishing returns. By contrast, knowledge-based parts of an economy are generally governed by the law of increasing returns or positive feedback.


As demonstrated by the pioneering studies of Brian Arthur during the 1990s, positive feedbacks often occur in an economy, with the resultant multiple equilibrium points. Small shifts in the economy can get amplified, rather than smothered out. The economy evolves like any open, nonlinear complex system. There can be multiple bifurcations in phase space, and it is difficult to predict which bifurcation branch will be chosen by the market forces. What is more, once the random events select a particular branch or path in phase space, the choice tends to get locked-in, regardless of the advantages of the alternatives.

An example is the history of the VCR industry. The market started out with two competing formats, VHS and Beta, selling at about the same price. (It appears, in hindsight, that Beta was technically superior.) In the beginning there were increasing returns for each format, as their market shares increased. For example, a large number of VHS recorders in the hands of consumers motivated the vendors to stock more prerecorded tapes in the VHS format. This encouraged more people to buy VHS recorders. The same law of increasing returns operated for the Beta format also. In the beginning there were fluctuations in the fortunes of the two competing brands, attributable to factors such as external circumstances, ‘luck’, and corporate manoeuvring. Then, perhaps by chance, increasing returns on early gains by VHS (reduced production costs per unit on increased volumes of production) tilted the game in favour of VHS, driving the other technology out of the market. This is something which could not have been predicted in the beginning.

The law of increasing returns can go beyond the product with which a company started (Arthur 1990): ‘Not only do the costs of producing high-technology products fall as a company makes more of them, but the benefits of using them increase. Many items such as computers or telecommunications equipment work in networks that require compatibility. When one brand gains a significant market share, people have a strong incentive to buy more of the same product so as to be able to exchange information with those using it already.’



Path dependence

In a positive-feedback economy, although the individual transactions are small and essentially random events, they can accumulate by the positive (nonlinear) feedbacks. A number of characteristics or historical antecedents of positive-feedback economies can be listed:

1. In a particular industry, there is often a clustering of firms in a specific geographical location. A different location would have been better, but there is a kind of freezing of historical accidents in what has actually happened. Why? The first firm chooses a location for some logical (or even illogical) reason. The choice of the second firm depends not only on the (real or perceived) merits of that region, but also on the fact that it is profitable to be near the first firm. There is a cascading effect because the third firm may be influenced more by the presence of the first two firms in that region, than by the absolute merit of that region; and so on.

2. Railroad gauges are what they are at present because, once a particular choice was made (even arbitrarily), it was economical to stick to that choice everywhere in that region. There is a self-enforcement effect operating here.

3. The initial advantage possessed by a country or a multinational corporation can snowball into total dominance at the global level, until a better or cheaper product overcomes the monopoly. This highlights the importance of industrial research in any knowledge-based economy. Another important factor is the timing of release of a product.

In the language of evolution of the phase-space trajectory, what we are seeing here are random bifurcations in phase space (cf. Part 30). Once a branch of a bifurcation gets selected for further time-evolution, there is no going back; there is only a locked-in trajectory along a particular path in phase space. Thus the evolution of a positive-feedback economy has a strong path dependence. This can cause even hitherto successful economies to become locked into inferior paths of development. There is always a danger that a sound technology, with good long-term potential, may get rejected just because it has a long gestation period and slow initial growth. Similarly, when two new technologies compete, the one with a better initial acceptance by people may oust the other from the market, even when the other technology is inherently better (as shown by later events). Early superiority or ‘selectional advantage’ is no guarantee of long-term fitness. Arthur (1990) cites the example of how the U.S. nuclear-power programme got ‘phase-locked’ into the light-water-cooled reactors option, even though the high-temperature, gas-cooled, reactor designs may be inherently superior.

The bottom line is that, unlike negative-feedback economies, positive feedback economies do not head for a unique equilibrium; their phase-space trajectory is not path-independent. Like in a chaotic system, even identical-looking initial conditions can lead to divergence in trajectories, simply because even small events or errors may get hugely amplified as time passes. Long-term accurate forecasting then becomes difficult, if not impossible.

Kurzweil (2005) has made an interesting point about the long-term predictability of stocks of companies dealing with information technologies. Such technologies are highly influential in just about every industry now. 'With the full realization of the GNR revolutions in a few decades, every area of human endeavour will essentially comprise information technologies and thus will directly benefit from the law of increasing returns'. [Here GNR stands for Genetics-Nanotechnology-Robotics.] This should mean that it makes sense to make long-term investments in the stocks of companies dealing with such technologies (provided the companies are managed well !).


***
The emergence of humans has sharply accelerated the rise of the overall complexity of our Earth. This has happened, and is still happening at an ever-increasing pace, because of the evolution of cultural complexity. A major reason for this is the very high level of intelligence possessed by humans. I shall discuss the nature of intelligence in the next few posts. That will be the final topic in this series of blog posts under the label 'Understanding Natural Phenomena'.

Saturday, January 18, 2014

115. Memes and Their Evolution - 2





Memes (cf. Part 114) are specified by their 'representational content'. As representations of a portion of information, memes have a certain content. A representation in the human mind is some piece of our ‘mental furniture’ that carries information about the world. For example, a thought that ‘the object on my desk is a book’ is a mental representation of a bit of the world (namely that book). Therefore ‘representational content’ refers to the information that is included in the content of our representations.

It is representational content which accounts for the mechanisms of memetic heredity and for the influence of memes over their phenotypic effects. Distin (2005) uses the term memetic DNA for the representational content. It provides the mechanism for memetic evolution, just as DNA provides the mechanism for genetic evolution.

How is the representational content fixed in our brains? Replicators preserve and copy specific portions of information. For memes, we should be able to identify precisely which bits are carried in each replicator. This means pinpointing the exact content of any representation, and this is something determined partly by the various properties of the object or situation being represented. Yet representational content is determined by other factors as well, e.g. by the capabilities and history of the organism doing the representing.

Some organisms are capable of forming representations the content of which is determined by a combination of the relevant properties of that which is represented, and the organism’s own individual and social learning capacities. Such organisms are able, in other words, both to preserve information and to transmit it among themselves.

In the case of complex representations, which have links not only externally to perceptions and behaviour but also internally to other representations, the resultant behavioural flexibility can enable us to track down their content more completely. It should be possible to test all of the links, by altering the associations that the organism encounters, and observing the effects on its behaviour. Only representations with this determinacy of content can count as memes, since a crucial aspect of any replicator is the preservation of given information.

Thus memes are representations which preserve their content in a way that can be copied between generations. As representations, they are specifically those bits of our mental furniture which control our behaviour in response to the information they carry. In other words, the basis of memes in representational content is precisely what accounts for their ability to exert executive effects on the world.



Representations gain meaning from their context within a representational system (RS), and the uniquely human capacity that lies at the heart of culture is our ability to copy and develop RSs, as well as adding individual representations to our repertoire: the ability, in other words, to meta-represent. Natural languages, as also systems of mathematical and musical notation, are some examples of cultural RSs, and each is peculiarly appropriate to its particular cultural area. Human minds acquire replicators on an ongoing basis throughout their lives, and this means that they can acquire novel RSs as well as novel representations. Among these various RSs, the natural languages have primacy: they alone benefit from an innate device for their acquisition. Yet they benefit, too, from the innate ability to meta-represent – and it is this which allows us also to develop nonlinguistic RSs, whose diverse rules and structures are realized in media other than speech. Once these sorts of RS have been taken into account, it becomes clear that there are many concepts that are not available to us until the RS that supports them has been developed.

According to Distin (2005), humans are born with a degree of 'mindedness' that includes, for example, the ‘representation instinct’: an ability and tendency to learn and manipulate vast numbers of representations, as well as the various systems in which they are embedded. And this innate mental potential of an infant is realized as a result of exposure to the cultural environment.

Genes preserve and replicate biological information by building vehicles for their own propagation and protection. The effects of the genes are found in the machines that they build for their survival, and their replication also depends ultimately on this same machinery. Memes depend for their replication on a faculty of the human mind that is ultimately of a genetic nature, namely the representation instinct. Organisms, as well as minds, develop via interaction between the innate potential and the environment, and in the case of the mind a crucial part of that environment comprises of the memes.



A human mind is thus partly a product of the memes, but only because it has the innate potential to interact with and develop in response to these memes. And culture is the product of human minds, although the preservation of information in representational content ensures that the culture we see today is mostly the result of memes produced by human minds of long ago. The development of human minds depends on a combination of two types of processes: their innate potential is the result of an interaction between genes and the physical environment, and that potential is fulfilled as a result of interaction with memes.

The selfish meme?

'Memes are best thought about not by analogy with genes but as new replicators, with their own ways of surviving and getting copied' (Susan Blackmore).

Dawkins (1976) described the essence of his ‘selfish gene’ theory as the insight ‘that there are two ways of looking at natural selection, the gene’s angle and that of the individual’. The essence of his selfish meme hypothesis is the insight that there are two ways of looking at cultural change, the meme’s angle and that of the human individual.

One of the most significant implications of Dawkins’ selfish-gene theory is that the individual organism was not an inevitable outcome of genetic evolution: it so happens that genes have banded together to build survival machines, but the only crucial feature of any form of evolution is the replicator – the unit of selection. Although organisms clearly exist, and have a perspective from which the world of genes is irrelevant to their everyday lives, fundamentally their lives and evolution are determined by that world. According to Distin (2005), no analogous insight arises from the theory of the selfish meme, because memes do not build survival machines. Their replicative mechanisms, and the means of their variation and selection, lie in genetically determined human faculties, and not in vehicles that they themselves build.

Blackmore (1999), however, takes the view that we are meme machines, just as we are gene machines. Consequently, she argues that ‘there is no conscious self inside’ those machines; and that ‘a complex interplay of replicators and environment’ is all there is to life. Our sense of self may not be illusory, but our sense of control over the collective products of our minds may well be. Although our minds provide the mechanisms of memetic evolution, there is a very real sense in which the directions of that evolution are independent of us.

For more on memes, please click here.

Saturday, January 11, 2014

114. Memes and Their Evolution - 1



'We are different from all other animals because we alone, at some time in our far past, became capable of widespread generalized imitation. This let loose new replicators  -  memes  -  which then  began to propagate, using us as their copying machinery much as genes use the copying machinery inside cells. From then on, this one species has been designed by two replicators, not one. This is why we are different from the millions of other species on the planet. This is how we got our big brains, our language and all our other peculiar ‘surplus’ abilities (Susan Blackmore 2000).



'Internet memes' is a familiar term these days. An Internet meme is an idea, style or action which spreads from person to person via the Internet. The good ones get viral, and ordinary or bad ones do not propagate because they are ignored by the netizens. Here are some examples of Internet memes:





It is information content that evolves in any type of evolution. The most basic aspects of evolution are replication of information (which also involves preservation of the replicated information), and the mode of transmittal of information. Genes preserve biological information, and they use DNA for this. What about culture?

Similar to the gene, which is the unit of biological inheritance, Richard Dawkins (1976) introduced the notion of the meme, which is the unit of cultural inheritance. A meme may be some good idea, a witty saying, a soul-stirring tune, a logical piece of reasoning, or a great philosophical concept. Dawkins visualized that two different evolutionary processes must have operated in tandem: the classical Darwinian evolution, and another one centred around intelligence, language, and culture. Memes are, roughly speaking, the cultural analogues of genes.

The genes that exist in many copies in a population are those that are good at surviving and replicating. Through a reinforcement effect, genes whose carriers in a population are good at cooperating with one another stand a better chance of surviving. Similarly, the fittest set of cooperating memes has a better chance of surviving to form the meme pool of the population. They replicate themselves by imitation or copying (Blackmore 1999), and also by a variety of other mechanisms (Distin 2005). Cultural evolution and progress occurs through a selective propagation of the fittest set of cooperating memes.

Memes evolve, just as genes evolve. In fact, any entities that can replicate, and that have a variation both in their specific features and in their reproductive success, are candidates for Darwinian selection. The coevolution of gene pools and meme pools (through language etc.) resulted in a rapid enlargement of the brain size of Homo sapiens. A large brain size, once attained, resulted in several other capabilities as well.

An important difference between memes and genes is that the speed of cultural evolution (development of ideas, customs, etc.) is far higher than the speed of genetic evolution. Nevertheless, there are several proposed analogies between the two. How far can we carry the gene analogy for understanding the nature of memes? This continues to be a subject of debate.

Distin (2005) has listed several characteristics of memes. One of them is the essential particulate nature of memes. The most efficient methods of replicating complexity are hierarchical (or modular or particulate). If variation were to be permitted in every element of a complex structure, then copying processes would lose much of their stability. In genetics, Mendel’s work established the particulateness of genes, namely the clear presence or absence of the effects of these replicators on the world. Something similar is necessary for memes in their role in the cultural evolution of complexity. This means that memes must be able to fit into established cultural assemblies without their own informational content being lost or blended in the process. That is, memes must have a certain degree of particulateness, so that the results that they produce are generally of a fixed nature. Their identity should be such that they are discernible packets of information (like the genotype). But, whereas the genotype is distinct and clearly definable, the phenotype (which is a manifestation of the genotype) in biological systems possesses a certain degree of flexibility and variability. Likewise, the manifestations of memes have a certain degree of flexibility that enables their effects to be produced in a variety of cultural contexts. Copied in these ways, information is given the stability to grow and develop in complexity. The breadth and depth of human culture is thus explained by the cumulative replication of particulate information.

In both genetics and memetics, the replicators carry information about the effects that they control. In the case of genes, their independence is maintained via the medium of DNA, which preserves biological information in a form that is replicable and can produce its effects in a variety of contexts. In the case of memes, this role is performed by ‘representational content,’ which is thus the memetic or cultural equivalent of DNA. More on this next time.

Till then, here is an interesting aside. The idea of free will has generated a lot of debate. I argued in Part 28 that free will is only an illusion. In a recent book Kurzweil (2012) makes an interesting point. He takes the view that the free-will idea is a useful meme (irrespective of whether it has a rational basis or not). For example, it enables us to fix responsibility for an act of crime.