MATHEMATICS OF INTANGIBLES, cont'd


The standpoint of Nature is a reference frame in which everything exists in four dimensions -- three spatial dimensions and time. Nothing in Nature is three-dimensional.

Time can be taken as finite as space. However, just because it may be examined in finite durations does not mean it is any less a dimension than any of the three spatial dimensions. In Nature, space and time both are infinitely extensible. However, they are infinitely divisible only "in the abstract". The points and lines of Euclidean space do not exist in Nature. Nor in Nature can or does does delta-t head towards 0. Only within the framework of these abstractions does motion or displacement of mass in space exist or operate as a function of time varying independently. In Nature there is nothing, be it mass, energy or momentum, that operates as a function of time varying independently.

At any and every point, time t possesses the special and unique property of being consequential. That is: at time t-past there were certain data about particular masses, energies or momenta that no longer existed at time t-current; the same will be the case in time t-future with regard to particular masses, energies or momenta that exist in time t-present. This consequential property of time t is the one that is relaxed when space and time are abstracted to enable their infinite divisibility. It is relaxed so that only what should be expected to happen as a result of motion or displacement of some specific mass, energy or momentum in an abstracted finite space as a function of time varying independently may be predicted or examined.

The mathematics and analysis based on infinite divisibility of space and time and on functions of time taken as an independent variable are in their element when dealing with engineered space and engineered time. The point of engineering space and time by direct intervention, or "shock and awe" if you like, is precisely to suspend the consequential property of time as it actually passes in Nature. Indeed, precisely the degree to which physical natural phenomena associated either with causes or effects of the engineered intervention of interest can be rendered as functions of time varying independently may itself be taken the best measure of the extent to which this consequential property has been banished beyond the margins. The only time that counts for such engineered interventions is the duration of the engineered intervention itself.