# Difference between revisions of "States"

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*the initial speed given the ball by the experimenter, that is to say, how 'hard' it is thrown | *the initial speed given the ball by the experimenter, that is to say, how 'hard' it is thrown | ||

*the initial direction given the ball by the experimenter | *the initial direction given the ball by the experimenter | ||

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+ | Provided we know these three exogenous variables, and provided we ignore all other possible causes of where the ball might be such as wind, magnetism, or somebody else getting in the way, we can work out where the ball will be at any point in time after it is thrown. | ||

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+ | The ball then passes through a series of states, each given by its speed and height. | ||

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+ | At any given moment in time, its speed and height constitute its ''state''. |

## Revision as of 02:23, 26 February 2015

## definition

The state of a dynamic system is most rigorously defined in state space theory but is applied widely in the physical sciences. In particular it is to be found in mechanics and its interface with quantum mechanics, but is in quite general use in describing electromagnetic and other physical phenomena. The notion of state features widely in economics although it is rarely subjected to critical examination.

In the above contexts, the state of a system refers to the magnitude of a definite and usually finite set of variables at a definite point in time, which are considered to describe or represent some aspect of reality which can be treated, for the purpose of study, as relatively autonomous, or self-contained.

In state space theory these variables are divided into the two general categories of exogenous and endogenous. Loosely speaking the exogenous variables are those whose magnitudes are defined (in a simulation) or caused (in reality) in ways that cannot be accounted for by any set of mathematical relations between the remaining, endogenous variables.

## example

If an experimenter throws a ball in the air, then the trajectory of the ball is uniquely described by two variables, its speed and its height. What happens to the ball after it is released depends only on

- gravitational acceleration
- the initial speed given the ball by the experimenter, that is to say, how 'hard' it is thrown
- the initial direction given the ball by the experimenter

Provided we know these three exogenous variables, and provided we ignore all other possible causes of where the ball might be such as wind, magnetism, or somebody else getting in the way, we can work out where the ball will be at any point in time after it is thrown.

The ball then passes through a series of states, each given by its speed and height.

At any given moment in time, its speed and height constitute its *state*.