The Four Number SetsBy Peter Meyer

 Ever wonder where the TWZ bloggers get screenshots of the timewave (without ever telling you how they got them)? They use the Fractal Time software, which you too can obtain — click here to find out how.
It is sometimes said that there are four (or more) versions of the Timewave. This is true in the following sense: A timewave is a "fractal transform" (as explained in The Mathematics of Timewave Zero) of a simple function which is defined in terms of a set of 384 numbers. (Not just any set of 384 numbers, but only some sets satisfying certain conditions.) There are at least four such sets which have been used to generate timewaves. These four are named as follows: Kelley, Watkins, Sheliak and Huang Ti.

The Kelley number set is the original set of 384 numbers which appeared in an appendix to the 1975 edition of The Invisible Landscape. Until 1994 this was the only number set used to generate a timewave. In 1994 Peter Meyer discovered an inconsistency between (a) Terence McKenna's description of the generation of the Kelley set from the King Wen Sequence of I Ching hexagrams and (b) the actual computational algorithm needed to generate the Kelley set. A slight modification of the algorithm to conform to the description (specifically, the removal of the "half-twist") resulted in a second (very similar) number set, one which generated a slightly different timewave. (For exact details see the article "WEN_GRPH: Software for Generating Sets of 384 Numbers" on the CD-ROM and USB flash drive.)

By 1998 two more number sets had emerged: the Sheliak and the Huang Ti sets. These have no relation to the Kelley and Watkins number sets (they are discussed in the article on the WEN_GRPH program). When naming the four sets Peter Meyer gave the name "Watkins" to the Kelley number set without the half-twist, since he felt it would be immodest to name it after himself, and Matthew Watkins had made a contribution to Timewave Zero theory by condensing the construction (from the I Ching) of the numbers in the Kelley set to a single formula (stated in terms of the programming language MAPLE).

It should be noted that the construction of the fractal timewave is a two-step process: (i) The construction of the 384 numbers from the King Wen Sequence and (ii) the construction of the fractal timewave by a 'fractal transform' of those numbers. The Watkins formula (given in his article Autopsy for a Mathematical Hallucination?) captures only the first step. The second step is explained in detail in articles by Peter Meyer contained on the CD-ROM and flash drive.

In his article Matthew Watkins quotes the footnote in the user manual that Peter Meyer wrote in 1994 for an earlier version of the Timewave Zero software:

This is the mysterious "half twist". The reason for this is not well understood at present and is a question which awaits further research.

Matthew Watkins concludes that, because no reason could be given (by Terence McKenna or by anyone else) for the existence of the half-twist in the algorithm used in 1975 to generate the Kelley set, "the 'timewave' cannot be taken to be what McKenna claims it is." But since he does not say exactly what McKenna claims it is, we are left not knowing quite what to make of this conclusion.

Peter Meyer has suggested a way in which Terence McKenna could have escaped "the Watkins Objection" in a footnote which he added to the "Autopsy" article for the CD-ROM edition.