Autopsy for a Mathematical Hallucination? by Matthew Watkins
Editor's note: This article, which was written in 1996, is copied with the permission of the author from www.fourmilab.ch/rpkp/autopsy.html and is unchanged except for the addition of some minor details. It might be subtitled "The Watkins Objection". Eight footnotes have been added by Peter Meyer, the last of which suggests how the theory of Timewave Zero might be rescued from the Watkins Objection.
Introduction by Terence McKenna
Recently, while in Mexico at the classic Maya site of Palenque, I made the acquaintance of a young British mathematician and psychokinesiologist named Matthew Watkins. Watkins offered the strongest and most interesting critique of the timewave and the assumptions of its construction yet made. Watkins is confident that he has condensed the theory of the timewave into a formula (given below) and is further convinced that there is no rational basis for assuming that the timewave represents the fluctuation of any quantity which can be meaningfully understood as "novelty". Here in Watkins' own words is his formula and his objection.
The Meeting
I first became aware of the Timewave theory when I discovered a magazine article (in GQ) on Terence McKenna four or five years ago (in 1991 or '92). It briefly mentioned that he had developed a theory which involved mathematically modelling the historical ingression of "novelty" using a fractal generated from the King Wen sequence of I Ching hexagrams. The idea had been revealed to him whilst in an altered state of consciousness brought about by psilocybin mushrooms. I had been studying the I Ching for some time, was working on a PhD in mathematics, and had occasionally contemplated the role of psychoactive plants in ancient religious belief systems, so I was immediately fascinated and searched everywhere for more information. I discovered McKenna's writings and recordings, but although the theory was often referred to and used as a basis for some remarkable speculation, I was unable to find any detailed description of its foundations. Such a description had originally been published in The Invisible Landscape (Terence and Dennis McKenna) in the early seventies, an obscure book long out of print and almost impossible to find.
When, in 1994, I discovered that The Invisible Landscape had been republished, I immediately obtained a copy and studied it thoroughly. I was rather disappointed to find that the mathematical process which was applied to the King Wen sequence to generate the fractal "timewave" seemed worryingly arbitrary (no justification being given for many steps) and mathematically clumsy.[fn.1] Beyond that, the described procedure fails to give the same "data points" which appear in the appendix and which are used to ultimately define the fractal in question. More disappointing, I discovered that the December 21, 2012 date (now generally associated with McKenna's name) was in no way calculated — it was selected to give the timewave the "best possible fit" with the historical occurence of novelty as McKenna sees it. It was difficult to accept that such an exotic, imaginative idea could have such unsatisfactory foundations. I thought that perhaps McKenna had been unable to effectively communicate something very real which had been revealed to him, and decided to get in touch immediately.
We began an e-mail dialogue about a year ago (late 1994 or early '95), after he responded to a letter I sent offering mathematical advice (at this point I had completed my PhD on hyperspatial embeddings of differential manifolds). Little was achieved for many months. He referred to an idea he was exploring which related the distribution of large prime numbers to the timewave, but it was only when I received a copy of the Timewave software that I was able to look into this. I was unable to find any evidence to support the hypothesis, but I did find that the software manual gave a much more detailed account of the construction of the timewave than The Invisible Landscape had. The manual contained the actual source code which the software uses [fn.2], so I was able to study it with great care and formulate a detailed critique of the theory. We agreed to meet and discuss the issue in Palenque (in the Mexican state of Chiapas) in January, while he was teaching at a Botanical Preservation Corps conference in early 1996.
Terence and I had four lengthy, good natured, and most enjoyable discussions during the week I was in Palenque, and I was able to explain my critique step-by-step. By the final discussion he seemed to have fully grasped the nature of the problem, and had admitted that the theory appeared to have "no basis in rational thought". He claimed (and this struck me as sincere) that he was only interested in the truth, and that someone "disproving" the theory was just as a much of a relief to him as someone confirming its validity. He proposed that we collaborate on a piece provisionally entitled "Autopsy for a Mathematical Hallucination" in which we would carefully take the theory apart and see what had gone wrong. He claimed that I was the first person to approach him with a serious mathematical critique of his ideas, partly explaining why such an unjustifiable theory had not only survived for so long, but also attracted so much interest and attention.[fn.3]
Footnotes added 2010-07-16 by Peter Meyer
1. In saying that "the mathematical process which was applied to the King Wen sequence to generate the fractal 'timewave' seemed ... mathematically clumsy" Matthew presumably was thinking of the first stage of the construction of the timewave from the King Wen Sequence, the generation of the 384 numbers. The second stage, the generation of the fractal timewave from those numbers, is described in an appendix in the 2nd edition of The Invisible Landscape, and that description is mathematically rigorous and in no way clumsy.
2. The manual contained the C source code for the WEN_GRPH program, not for the program which calculated and displayed the timewave itself.
3. Matthew was "the first person to approach [Terence] with a serious mathematical critique of his ideas", but Terence had become aware of the basic problem already in 1994, when, upon my discovery of the "half-twist" (described later in the article), I asked him why he had not mentioned it in his explanation of the Derivation of the Timewave from the King Wen Sequence of Hexagrams, and he replied that he had no memory of it.
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