Trajectory

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Summary

A trajectory of a temporal system is the entire set of states that it passes through between two points in time, the initial state and the end state. For a simulation, a state is defined by set of state variables describing the system. Thus for example in the capitalist simulation the state consists of everything that you see on your screen, while you are running the simulation. As time advances, the simulation moves from one state to the next. During the simulation, each successive state is recorded in an internal database. The database thus stores the trajectory of the simulation

Representation, trajectory, state and reality

Any mathematical or programmed trajectory is a representation of reality and is not the same thing as reality itself. Philosophers differ when they speak of the relation between a representation and reality; loosely speaking, the representation provides knowledge about reality which may either help understand or explain it, or possibly predict it. The term model is sometimes used by economists to describe the relation between a representation and reality, but scholars of the [Temporal Single System Interpretation]] (TSSI) school generally avoid this language because it contains an ideological payload arising from model illusion, confusing the two functions of understanding and representation. Many economic systems that are expressed as models, especially simultaneist or equiibrium models, become a substitute for understanding, or in fact impose understandings dominated by its conformity to the prejudices and private interests of the economist, who select models whose results re-enforce and support these prejudices, making them more acceptable to the class interests on whome the economists' livelihood depends.

Thus in equilibrium models, crisis is theoretically impossible. This is not necessarily a feature of reality; economists however frequently argue that because the model cannot contain crisis, neither can reality. Equilibrium models are therefore much more convincing to anyone whose interests are advanced, if it can be shown that that the capitalist system has no inherent tendency to crisis. Those whose interests are advanced by this conclusion contain capitalists themselves, but also those whose livelihood and status depend on the approval of capitalists, and the resources they provide. This largely accounts for the almost universal popularity of equilibrium models in economics.

To counter the risk of model illusion, no claim should be made that this simulation "models" reality in the sense that economics conventionally uses the word. A simulation is a representation. In addition, as explained in the next section, the simulations on this site represent theories; it is these theories that seek to explain reality, not the simulations which allow us to understand and study how the theories work.

Theory, simulation and model illusion

The various possible trajectories which can be produced using the simulation site are primarily representations of economic theories about reality. This is because their function is to assist understanding, which is not possible without theory.

The site, and this wiki, therefore pay a lot of attention to the work of writers who have studied capitalist reproduction. This includes temporal theorists like Karl Marx, Rosa Luxemburg, Otto Bauer, Grossman and Kalecki, and also [[simultaneist] theorists such as Leon walras, Ladislaw von Bortkiewicz, Paul Sweezy or Piero Sraffa. In the works of these writers we find theories of reality which are often expressed in numerical terms, speaking for example of price, value, quantity of use value, rate of profit, and so on. [[TSSI}} scholars divide these into two broad schools of thought - simultaneist and temporal.

All such writers, and in fact most economists, construct theories of the economy which represent it as a trajectory: a succession of states. They differ in two respects: the technical details of the calculation and the meaning to be attached to its results. In the first category we therefore find many differences about how the economy moves from one state to the next, which variables should be included in the state, and which of these variables should be treated as exogenous and which endogenous. However theorists also differ about the meaning of these variables, and such differences are frequently concealed especially in simultaneist expositions, especially when these expositions employ the concept of model. This is because such models impose a meaning which derives from the representation, rather than reality; in such expositions, meaning tends to be determined by the characteristics of the representation, rather than the characteristics of reality. This error can be summarised by the concept of model illusion.

Therefore, whilst there is often superficial agreement on the variables to be included in the state - so that for example, the price of each [commodity]] is included in almost all representations (although value is not always included - there are potentially enormous concealed differences about the meaning of these variables.

The simulation itself, viewed as a pure calculation, is simply a way of connecting sets of numbers at different points in time. In order to gain insight into reality from it, it should be recognised that it is a representation both of reality, and of theories about reality. Generally speaking, it is as much a tool for understanding other people's theories, than for understanding reality. If model illusion is to be avoided, therefore, the simulation cannot, and should not, be used as a direct attempt to represent reality independent of theory. Only a theory can assign meaning to the state variables in the simulation, and only a theory can assign meaning to the connection between state variables at different points in time, that is, to the trajectory of the simulation.

Creating, saving, retrieving and studying trajectories using the simulation

A trajectory is uniquely determined by the initial state of the trajectory and the transition rules which determine how it gets from one state to the next. Users of the simulation site can therefore create their own trajectories by defining both of these.

They can use existing trajectories which the developer, or other users, have created. They can also construct their own. This is done by saving and retrieving parameter files containing all the information needed to run one simulation for any desired time.

Details of how to do this are provided in the user guide