The Watkins Objection is Not Fatal
By Peter Meyer
This was written in response to the publication in November 2010 on Reality Sandwich of Matthew Watkins' article 2012 and the "Watkins Objection" to Terence McKenna's "Timewave Theory" and appears among the comments on that article.
Some people may believe that the Watkins Objection refutes or invalidates the theory of Timewave Zero. This is not so, as I shall now explain.
First we should distinguish between the timewave as a mathematical construct and its interpretation (that is, the use to which Terence put it). There are two parts to the construction of the timewave: (1) Beginning with the King Wen Sequence of hexagrams and ending with a set of 384 numbers (which in themselves have no meaning). (2) Beginning with those numbers and ending with a function which associates any real number not greater than some real number Z with a non-zero real number. Then (3): That function is interpreted as associating any point in time not later than the "zero point" (Z) with a quantity or quality which Terence called "novelty".
In his article Derivation of the Timewave from the King Wen Sequence of Hexagrams Terence provided a less-than-clear explanation of part (1) and an even-less-clear allusion to part (2), so from that article it is impossible to understand exactly how the timewave is constructed. The details of (1) and (2) are made explicit in my "Derivation of the Original 384 Numbers" (on the CD-ROM) and The Mathematics of Timewave Zero respectively. All the steps in the construction of the timewave from the King Wen Sequence are thus set out and the associated mathematics is sound, so the timewave is a well-defined mathematical object.
There are basically two types of objections to the Timewave Zero theory: (a) The construction of the timewave begins from an arbitary starting point and is itself arbitrary. (b) The theory is vague and untestable. There is some merit to (b) insofar as the concept of "novelty" is hard to define in a way which would allow novelty values to be assigned to historical events and thus allow their correlation (or lack of it) with properties of the timewave to be studied. Whether a theory which is untestable can be claimed to be nevertheless true is one which philosophers have debated.
The Watkins Objection is of type (a). It is stated in the section "The Objection" in Matthew's "Autopsy" article. In essence it may be stated as follows: (i) In the 1975 edition of The Invisible Landscape a set of 384 numbers is given (in Appendix II), which is said to be derived from the King Wen Sequence and to be an intermediary in the construction of the timewave. (ii) In his "Derivation" article Terence described the construction of these 384 numbers from the King Wen Sequence, and asserts that the construction elegantly conserves certain numerical qualities associated with the hexagrams. (iii) In 1994 I discovered that there is a step required in the construction of these numbers (that is, the numbers given in The Invisible Landscape) which is not mentioned in Terence's explanation of the construction, namely, the so-called "half-twist" (which is described in my article "Derivation of the Original 384 Numbers"). (iv) According to Matthew, the inclusion of the half-twist destroys the conservation of the numerical qualities extolled by Terence as a virtue of the 384 numbers (upon which the timewave is based). (v) Matthew then concludes that if the half-twist cannot be incorporated into the construction of the 384 numbers so as to preserve some set of desirable numerical qualities (and Terence could not do this, having no recollection of any such half-twist) then the theory is fatally flawed. Or as Matthew put it, Terence "would have to either justify this mysterious 'half twist' or abandon the timewave theory altogether."
There are two ways to avoid the conclusion of the Watkins Objection that the Timewave Zero theory is fatally flawed. The first way is simply that to claim that (v) is unjustified. Terence's description in his "Derivation" is sufficiently complex and convoluted that a little more complexity and convolution might allow incorporation of the half-twist in such a way that the 384 numbers of The Invisible Landscape regain their respectability. It must be admitted, however, that this has not been done and is not likely to be done.
The second way can actually be implemented. The origin of the half-twist is not known. Terence claimed not to know of it. It is thus possible, as mentioned in Matthew's article, that it was introduced into the process of constructing the 384 numbers by Terence's FORTRAN programmers, Royce and Kelley. (Where are they now?) Perhaps they were all stoned when Terence was explaining it, and some misunderstanding crept in. In any case, if the half-twist is eliminated from the construction then a slightly different set of 384 numbers results, which I have named the "Watkins" number set in recognition of Matthew's contribution to the subject. The original set of numbers (those given in The Invisible Landscape) I have named the "Kelley" number set (see The Four Number Sets).
Step (2) in the construction of the timewave (from the 384 numbers to the fractal function) works equally well for either set of numbers, and the two timewaves generated are quite similar, though not identical. Thus the evidence which Terence presented in support of his theory, concerning correlations between the timewave and historical events, might or might not remain cogent when the Watkins timewave is used instead of the one that Terence used, the Kelley timewave. This is something which can be investigated by the use of the Fractal Time software in conjunction with Terence's books and tapes. If the Watkins timewave is found to be in accord with historical vicissitude at least as well as the Kelley timewave then the Watkins Objection, rather than invalidating the theory, will be seen to have pointed the way to a more accurate version.