The extrapolation process is a divergent and speculative generalization made from a minimal conceptual simplification or from a sampled data-base of evidence. It is a process whereby the simplifications which individuals use in order to understand and model existence are often overblown for the purpose of promoting some sort of cosmic universality. It frequently even takes the form of a global perspective judgement which is promulgated with a quasi-religious fervour in order to promote self interest in the guise of altruism. In imagery terms, it is symbolized by the simple idea of a rectangle multiplied, manipulated and materialized into a tottering house of cards. It teeters on the edge of a bending cantilever, supported wherever possible by whatever Dali-sticks can be found to delay the ultimate collapse.
Extrapolations are attempted in almost every aspect of life. At the social organizational level, simple moral injunctions are postulated...like "thou shalt not kill"...and then promoted as inviolable principles with universal application. Cosmologists would be severely handicapped without using the process. They extrapolate the models of daily experience from a position within the known universe, where the insides and outsides of things are pragmatic realities, to the absurdity of contemplating the universe as an entity with an interior but no exterior. They extrapolate from the obvious fact that there is a universe, to pointing out that there is thus at least one universe, to the suggestion that there could therefore possibly be multiple universes, to the final breathtaking assertion that there are multiple universes existing in parallel. They extrapolate from the pragmatic existential condition that three measurable parameters can assist in modelling space and the fact that there is no limit to the number of dimensions that can be mathematically manipulated, to the ludicrous concept of multiple folded spatial dimensions.
Since prediction is in fact an extrapolation, many of the hypotheses of science are often nothing more than the precarious inverted pyramid of cards depicted above. Population growth data is extrapolated into the future from the historical pattern of populations census totals, assuming that all the factors contributing to the recorded data continue to have the same significance. It is virtually certain that factors hitherto ignored will confound many such predictions. Climate change extrapolations have been made from a small section of a chaotic periodic process by assuming a linear or exponential simplification model instead of a periodic fourier model. The briefer the time-scale focussed on by the prophets, the less merit their predictions have.
Some extrapolations are worth persevering with nevertheless. On the weather front, as many patterns as possible of measurable physical factors in the atmosphere, are modelled into computation machines and a prediction about future meteorological conditions is extrapolated from present data. The intrinsically chaotic nature of the atmosphere will ensure that a deterministic model will always be unattainable but as the relative significance of the factors is refined and the power of the computation machines grows, such an extrapolation as this will become increasingly useful.
The underlying condition remains however, that any simplification-extrapolation process can barely hope to survive the chaotic reality of nature.