Even Given Eyes To See, We Know Nothing About What We're Looking At...,

cheniere  |  In the light of other past researches, we were very much attracted when we first saw his typescript last year, by the author's perceptive treatment of the operational‑theoretic significance of measurement, in relation to the broader question of the meaning of negative entropy. Several years ago ¹ we had constructed a pilot model of an electro‑mechanical machine we described as the Critical Probability Sequence Calculator, designed and based on considerations stemming from the mathematical principles of a definite discipline which we later² called chronotopology: the topological (not excluding quantitative relations) and most generalized analysis of the temporal process, of all time series ‑ the science of time so to speak. To use a popular word in a semi‑popular sense, the CPSC was a 'time‑machine,' as its input data consist solely of known past times, and its output solely of most probable future times. That is, like the Hamiltonian analysis of action in this respect, its operation was concerned only with more general quantities connected with the structure of the temporal process itself, rather than with the nature of the particular events or occurrences involved or in question, although it can tell us many useful things about those events. However, as an analogue computer, it was built simply to demonstrate visibly the operation of interdependences already much more exactly stated as chronotopological relationships.

That situations themselves should have general laws of temporal structure, quite apart from their particular contents, is a conclusion that must be meaningful to the working scientist; for it is but a special example of the truth of scientific abstraction, and a particularly understandable one in the light of the modern theory of games, which is a discipline that borders on chronotopology.

One of the bridges from ordinary physics to chronotopology is the bridge on which Rothstein's excellent analyses also lie: the generalized conception of entropy. And in some of what follows we will summarize what we wrote in 1951 in the paper previously referred to, and in other places. We will dispense with any unnecessary apologies for the endeavor to make the discussion essentially understandable to the intelligent layman.

Modern studies in communication theory (and communications are perhaps the heart of our present civilization) involve time series in a manner basic to their assumptions. A great deal of 20th century interest is centering on the more and more exact use and measurement of time intervals. Ours might be epitomized as the Century of Time‑for only since the 1900's has so much depended on split‑second timing and the accurate measurement of that timi ng in fields ranging from electronics engineering to fast‑lens photography.

Another reflection of the importance of time in our era is the emphasis on high speeds, i.e. minimum time intervals for action, and thus more effected in less time. Since power can be measured by energy‑release per time‑unit, the century of time becomes, and so it has proved, the Century of Power. To the responsible thinker such an equation is fraught with profound and significant consequences for both science and humanity. Great amounts of energy delivered in minimal times demand

a) extreme accuracy of knowledge and knowledgeapplication concerning production of the phenomena,

b) full understanding of the nature and genesis of the phenomena involved; since at such speeds and at such amplitudes of energy a practically irrevocable, quite easily disturbing set of consequences is assured. That we have mastered (a) more than (b) deserves at least this parenthetical mention. And yet there is a far‑reaching connection between the two, whereby any more profound knowledge will inevitably lead in turn to a sounder basis for actions stemming from that knowledge.

No longer is it enough simply to take time for granted and merely apportion and program it in a rather naively arbitrary fashion. Time must be analyzed, and its nature probed for whatever it may reveal in the way of determinable sequences of critical probabilities. The analysis of time per se is due to become, in approximate language, quite probably a necessity for us as a principal mode of attack by our science on its own possible shortcomings. For with our present comparatively careening pace of technical advance and action, safety factors, emergent from a thorough study and knowledge of the nature of this critical quantity 'time,' are by that very nature most enabled to be the source of what is so obviously lacking in our knowledge on so many advanced levels: adequate means of controlling consequences and hence direction of advance.

Chronotopology (deriving from Chronos + topos + logia) is the study of the intra‑connectivity of time (including the inter‑connectivity of time points and intervals), the nature or structure of time, 0 if you will; how it is contrived in its various ways of formation and how those structures function, in operation and interrelation.

It is simple though revealing, and it is practically important to the development of our subject, to appreciate that seconds, minutes, days, years, centuries, et al., are not time, but merely the measures of time; that they are no more time than rulers are what they measure. Of the nature and structure of time itself investigations have been all but silent. As with many problems lying at the foundations of our thought and procedures, it has been taken for granted and thereby neglected ‑ as for centuries before the advent mathematical logic were the foundations of arithmetic. The "but" in the above phrase "investigations have been all but silent” conveys an indirect point. As science has advanced, time has had to be used increasingly as a paramimplicitly (as in the phase spaces of statistical mechanics) or explicitly.

Birkhoff's improved enunciation of the ergodic problem ³ actually was one of a characteristic set of modern efforts to associate a structure with time in a formulated manner. Aside from theoretical interest, those efforts have obtained a wide justification in practice and in terms of the greater analytic power they conferred. They lead directly to chronotopological conceptions as their ideational destination and basis.

The discovery of the exact formal congruence of a portion of the theory of probability (that for stochastic processes) with a portion of the theory of general dynamics is another significant outcome of those efforts. Such a congr        uence constitutes more or less suggestion that probability theory has been undergoing, ever since its first practical use as the theory of probable errors by astronomy, a gradual metamorphosis into the actual study of governing time‑forces and their configurations, into chronotopology. And the strangely privileged character of the time parameter in quantum mechanics is well known – another fact pointing in the same direction.

Now Birkhoff's basic limit theorem may be analyzed as a consequence of the second law of thermodynamics, since all possible states of change of a given system will become exhausted with increase of entropy ⁴ as time proceeds. It is to the credit of W.. S. Franklin to have been the first  specifically to point out ⁵ that the second law of thermodynamics "relates to the inevitable forward movement which we call time"; not clock‑time, however, but time more clearly exhibiting its nature, and measured by what Eddington has termed an entropy‑clock ⁶. When we combine this fact with the definition of increase of entropy established by Boltzmann, Maxwell, and Gibbs as progression from less to more probable states, we can arrive at a basic theorem in chronotopology:

T₁, The movement of time is an integrated movement toward regions of ever‑increasing probability.

Corollary: It is thus a selective movement in a sense to be determined by a more accurate understanding of probability, and in what 'probability' actually consists in any given situation.

This theorem, supported by modern thermodynamic theory, indicates that it would no longer be correct for the Kantian purely subjective view of time entirely to dominate modern scientific thinking, as it has thus far tended to do since Mach. Rather, a truer balance of viewpoint is indicated whereby time, though subjectively effective too, nevertheless possesses definite structural and functional characteristics which can be formulated quantitatively. We shall eventually see that time may be defined as the ultimate causal pattern of all energy‑release and that this release is of an oscillatory nature. To put it more popularly, there are time waves.