Roy Lisker

Relativity, Special and General represent Time as a linear dimension in a 4-diemnsional spacetime. However, one of the important ways in which time can be distinguished from space is through the examination of the distinguishing properties of clocks and r ulers. Clocks are irreversible dynamical systems subject to constraint by the laws of nature. Rulers are reversible systems which do not directly depend upon the laws of motion, but only on the principles of isometry. Axiom systems for homogeneous time, linear time, cyclic time and "cyclic-linear" time are proposed and given a thorough examination.

Non-intuitive ideas in science, such as the constancy of the speed of light in all reference frames or the hierarchy of transfinites, are always based on elementary observations and primitive notions which in some sense are considered to be self-evident. In all examples of non-intuitive concepts, a decision has been made to consider certain elementary observations more self-evident than others. If one inverts this order, the non-intuitive concept is replaced by another thus creating what may be called a dual image of science. In certain cases, the paradigm of image/dual-image may be a more adequate representation of physical reality than the postulation of either one of them alone.

This paper applies the ideas presented in "Time, Euclidean Geometry and Relativity" ID 1290 , to a specific problem in temporal measurement. It is shown that, under very natural assumptions, that if there is a minimum time interval T in ones collection of clocks, it is impossible to measure an interval of time 1/2T save by the accidental construction of a clock which pulses in that interval. This situation is contrasted to that for length, in which either the Euclidean Algorithm or a ruler and compass construction can be used to construct a lengh 1/2L from a length Lo.

Definitions of Causation are shown to be specific to particular sciences. Also, the idealized notion of causation that is maintained by scientists working in a given field frequently differs from that which is used in actual practice. All interpretationsof causation used in the sciences can be shown to have an algebraic structure, which we call a "Causal Algebra": a mathematical entity embodying the notions of Possibility, Impossibility and Actuality. The algebraic approach is applied to various branches of physics, biology, geology. cosmology. At the end of the article a model for causation from the Big Bang is proposed.