During correspondence (published in 1999 as a DuVersity pamphlet; see www.duversity.org/link.html ) conducted during 1962-63 between physicist David Bohm and British philosopher J. G. Bennett, Bohm elaborated a notion of “the three kinds of time”. Quoting Bohm (letter dated 3rd February, 1962):

…So now there are two kinds of time, which I denote by t and t respectively. The time parameter, t, refers to the wave function and therefore to the continuously changing potentialities.

But we need a third kind of time. For if a certain quantum state, h, dies out exponentially, the system will disappear from existence unless another quantum state, h, surges up and takes its place. This is the time of repetition, or hyparxis, which I shall denote by T.

Evidently, the three kinds of time must be related. The movement will take place in the following way:

  1. the potentialities are prepared (this is detailed by the parameter, t)
  2. the present actuality dies out, while another actuality arises within the new potentialities to take its place (this is described by the parameter t)
  3. the repetition of time, T, is the parameter of hyparxis. It represents roughly the number of periods, t, of exponential decay of actuality that are needed before the new (or repeated) actuality arises again. (Emphasis added.)

Evidently, the ratio t /T represents the “ability to be”. For if the ratio is small, the system finds it difficult to repeat its existence after it dies out, so that its existence is relatively “tenuous” and weak. On the other hand, if t /T is of the order of unity, it is a really “solid ” kind of existence.

The canonical equation of the Paine-Pensinger model of superconductant DNA has three terms, each with its own class of temporal operator. These temporal operators are formalizations of the three kinds of time Bohm refers to. Compare the following statement (THE MOON OF HOA BINH, Vol. II, p. 331, 1994), describing this canonical equation, with Bohm’s statement given above:

…In term #3, the quantum of information to be exchanged is defined by the linear-time taken by a parcel of p-electrons in transiting ToÛTc. The inverse of this period establishes the fundamental frequency of this quantum. The number of such transits establishes the number of quanta to be read. Term #2 evaluates the time taken to receive these quanta -- which themselves exist as a sinusoidal function of time -- within the structure of the DNA molecule… Term #1 evaluates the time taken by the embedding environment to receive the signal represented
by term #2. (Emphasis added.)

Three-fold operator-time, acting (at limiting velocities, accelerations, and time rates of change of acceleration of given limited spacetime domains) as a composite logical operator, decomposing and recomposing a multivalued reference space, is a generalization of the above described “three kinds of time” and an extension of Bohm’s notion of “active information”. It must be understood, however, that repetition in time, T, the parameter of hyparxis, is not the “everyday” sort of repetition associated with cyclic motion of a physical object in ponderable x,y,z-space relative to the (as commonly regarded) passive linear-time reference parameter, t. T is a larger context than that of t. T does not exist in t; t exists in T. The same applies to the relationship of t to t; t is a larger context than that of t. t does not exist in t; t exits in t . t repeats itself in t ;t repeats itself in T. t repeating itself in t can be imagined as analogous to a spinning circular disc moving continuously around the interior of the inner tube (a torus) of a turning automobile tire. t repeating itself in T can be imagined as analogous to a twisting cylinder moving continuously around the interior of a non-orientable, self-reentrant, spinning Klein bottle. These are chronotopological analogies only valid as viewed through the perspective established by a single-valued logic, whereas the reality of the involved relationships, as viewed through the perspectives established by m-valued logics, is that of 3-fold operator-time acting as composite logical operator to decompose and recompose a multivalued reference space.


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