Thursday, 17 May 2007

Our linear and non-linear lives

     Describe the ways changes propagate in our lives, under the constant cause and effect relationships between the conditions of the environment and features of the agents in a system. Conditions and features vary, they are variable. Variables of either features or conditions, become connected with one another by the cause and effect relationships.

     The variable that causes a change in another variable is the independent variable and the variable the effect is directed to the dependent variable. The changed dependent variable acts further as an independent variable, and becomes the cause for change in other dependent variables. These, in turn, affect other variables and so on, creating chain reactions that propagate within the state space of a particular system.

     Affected variables change the conditions and features in a system. The system undergoes a transformation. The transformation is either linear or non-linear. Whether a certain transformation is linear or non-linear is consequent to the position of the independent variable in the dependency hierarchy. The lower in the hierarchy the independent variable is, the greater the transformation effected upon the state of the system, as it will affect a great many variables in the chain-wise fashion, and the greater the effect, the greater the transformation, a greater amount of change. It is described as an exponential function and in a graph is drawn, not with a straight line but with a curved line, a hyperbola, therefore the non-linear term.

     Linear transformation takes place when the independent variable is found higher in the dependency hierarchy of variables in a system therefore it affects a smaller number of variables, a limited effect, a smaller size of transformation. In a graph its effect is shown by a straight line, a linear transformation. Most of the transformations in real life phenomena are linear transformations.

     The linear or non-linear mode of transformation effected by interacting variables is universal and apply to all systems in each end of the scale, from the microscales to the macroscales. John Gribbin mentions about the expansion of the Universe: "That, today the Universe is expanding at a more or less steady rate, in a linear fashion. It is like a walk down the road, in which each step takes you the same distance as the previous step. But in the very early Universe, the scalar fields that we have mentioned caused exponential expansion. This is like taking a walk in which the second step takes you twice as far as the first step, the third step four times as far, the fourth step eight times as far, and so on".
     So in a linear transformation, the dependent variable matches step by step the independent variable whereas in the non-linear transformation a step in the independent variable can be matched by hundreds of steps by the dependent variable.

     In our lives this can be seen in the events that surround the beginning of romantic relationships as is accompanied by excitement anticipation and fervour, when we first meet the person we start a relationship with, the non-linear phase. Later on as this is followed by a settling down period, we enter the linear phase. If at the weekend we stay home and relax then we are content being in a linear state, whereas if we go out have fun and enjoy ourselves we enter the non-linear phase. We always make choices in life in what path to follow, linear or non-linear; what mode to engage into at any time. We lead either linear or non-linear lives.


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