On one of my visits to Nepal in the late 1970s I met an Indian swami by the name of Shri Mahant Ganesh, or Ganesh Baba for short. Unlike most Indian swamis known in the West at that time, he was sympathetic to the many hippies who had traveled to India, and to their use of LSD for spiritual advancement. In 1979 he traveled to San Francisco for an operation to remove eye cataracts (which was successful). We shared a cottage in Oakland for a few months, where, most evenings, he regaled his admirers (who knew him from India) with his teachings about Kriya Yoga. Later he went to stay with his other admirers on the U.S. East Coast.

At that time a good friend of mine gave me a copy of the book The Invisible Landscape by Terence and his brother Dennis. The first half of this book concerns the brothers' expedition to the Amazon in the early 1970s (looking for an obscure native psychedelic snuff) where they unexpectedly found an abundance of psilocybin mushrooms. The second half of this book concerns Terence's attempt (no doubt influenced by their mushroom consumption) to develop a theory of time, or rather, of events in time, based on his fascination with the Chinese I Ching method of divination.

In 1986 Ganesh Baba returned to San Francisco at the invitation of his admirers, and since he was known as "the psychedelic swami" I wished to arrange a meeting between him and Terence (which unfortunately did not occur, as Baba had to leave the U.S. a short time later). I phoned Terence and was invited to meet him at his home in Occidental. As soon as he discovered that I was a computer programmer he proceeded to enlist me in his project to develop software to illustrate his theory of time, which was then known as "System Zero" but soon after as "Timewave Zero". The history of this software, from an early version for the Apple //e computer to the later version for MS-DOS and Windows, is described in detail in History of the Timewave Zero Software.

The theory of the Timewave was developed by Terence partly based on his mushroom experiences in the Amazon, and it was already mostly conceptualized when I met him. My contribution (in addition to writing the software) was to take his graphical intuition of the structure of the Timewave and put it on a solid mathematical basis, whereupon it turned out to be a genuine fractal (exhibiting unlimited self-similarity under magnification).

Terence used the Timewave to explain, or at least to understand, the occurrence of events in time, and to support his view that time (and we who are immersed in time) is leading up to a final point, which (adopting the word from Christian doctrine) he called "the Eschaton". This is the idea that time will come to an end and the world will be transformed into something purely spiritual.

Below is a screenshot of the Timewave Zero software showing the final 25 years leading up the Eschaton. The values on the vertical axis represent "novelty", or more accurately, the inverse of novelty, since this value is zero at the end point (here December 21, 2012) when novelty as experienced becomes infinite.

The idea of an end of the world occurs in several cultures and esoteric teachings, including the Irish/Celtic, with which Terence (being of Irish descent) was familiar. Somewhere he mentions the Irish benediction, "May you be alive at the end of the world", which suggests that "the end of the world" will be something marvelous to behold (maybe angelic choirs and celestial music, or something even more astounding).

Before modern science arose, people who thought of time usually thought of it as cyclic. This was a plausible inference from the observation of the cyclical behavior of the heavenly bodies. The Sun rises and sets, and this constitutes a "day". A few tens of thousands of years ago humans discovered that it always took about 29 days for the Moon to complete a cycle from full to invisible and back again to full. The periodicity of the visible planets was recognized, at latest, by the Babylonians, who kept records of celestial events.

The idea of a "week" of seven days arose some thousands of years ago despite the fact that no period of seven days occurs in Nature. The cycle of seven days in a week almost certainly derives from the fact that seven heavenly bodies were known to the Babylonians — the Sun, the Moon, Venus, Mars, Mercury, Jupiter and Saturn. (For more on this see Why Seven Days in a Week?)

Building on the work of the Greek astronomer Ptolemy, European mathematicians and astronomers, around 1600 CE, developed a theory of "celestial mechanics" to explain why the heavenly bodies were observed to move as they did, and this culminated in Isaac Newton's theory of universal gravitation. Newton's physics assumed that time (whether earthly or heavenly) is simply pure duration, without any inherent structure. One October is, in itself, the same as any other October. Only what happens during a particular October is different.

Terence McKenna, following the pre-Newtonian concept of time present in traditional cultures (in particular, the Chinese) declined to accept the Newtonian assumption that time itself lacks any structure. He posited that every instant of time (itself a modern concept) possesses a property that he called "novelty". The Cambridge Dictionary defines this word as "the quality of being new and unusual; something that has not been experienced before and so is interesting." Terence took the concept from philosophers such as Teilhard de Chardin and Alfred North Whitehead, who held that the Universe is endlessly creative. Rather than attribute this creativity to God, Terence held it to arise from the inherent nature (or structure) of time itself. However, Terence did not explain what time is. Perhaps he shared the view of St. Augustine, namely, "I know what time is when I don't think about it; but when I do think about it, I don't."

Terence claimed that in principle the degree of "novelty" associated with each point in time could be calculated. He found what he thought was a precedent for this in the ancient Chinese oracle called the I Ching, where the "calculation" is not done with numbers but rather is done by the throwing of a set of yarrow stalks (or later, of three coins). The yarrow stalks are thrown several times, and how they fall determines a particular so-called "hexagram" (or sometimes a pair of hexagrams).

A hexagram consists of six lines, one above the other. Some lines are in two parts — a "broken line". Clearly there are 2^6 =64 possible hexagrams (see here). When arranged consecutively in a single line we have a "hexagram sequence" (or, if the last hexagram is seen as following the first, we have a hexagram cycle). In traditional China there was one such sequence, used with the I Ching, known as the "King Wen Sequence", supposedly used in divination by an ancient Chinese emperor, King Wen. The first eight hexagrams are:

To arrive at the Timewave Terence first attended to the difference between successive hexagrams, that is, given a hexagram in the sequence, how many lines in that hexagram differed from the corresponding lines in the next hexagram. He called these 64 numbers the set of "first orders of difference". From this sequence of numbers he eventually derived (by a highly complex process) another set of 384 numbers, ranging in value from 0 to 79), shown in Table 2, which is copied from Terence's explanation given in Derivation of the Timewave from the King Wen Sequence of Hexagrams.

I was able to implement this derivation of the 384 numbers, starting from the hexagrams in the King Wen Sequence, in computer code (in the C language). Those interested should see my article "WEN_GRPH: Software for Generating Sets of 384 Numbers" on the Timewave Zero flash drive (which also contains the software that it describes).

A function w() is defined such that w(x) is the x-th number in that set of 384 numbers, counting forward in the set, but backward along the x-axis (in the Cartesian plane). This set of 384 numbers is then copied to x=-384, x=-768 and so on (backward along the x-axis), so that the function w() is defined for any negative integer. The points so-defined in the xy plane are then joined by straight lines to give a saw-tooth wave.

We can then define a function f(x) for any negative real number x, whose value for a given x is the sum of an infinite number of terms. This function is, or specifies, the Timewave. For more detail see The Mathematical Definition of the Timewave and The Mathematics of Timewave Zero. The latter article states the mathematical formula for the Timewave thus:

Terence then supposed that one day corresponds to one line in a hexagram. A hexagram (made up six lines) then corresponds to 6 days. The 64 I Ching hexagrams comprise 64*6 lines, for a total of 384 lines. Since the sequence of hexagrams can be seen as cyclic, we thus have a basis for seeing a period of 64*6 = 384 days as a cycle of days. Since temporal cycles (e.g. the cycle of the seasons) are repetitive, we can thus convert the Western linear view of time to a cyclic view, with time composed of repeated cycles of 384 days. Longer cycles are formed by successive multiplication by 64, thus:

64*384 days = 24,576 days = 67.29 years 64*64*384 days = 1,572,864 days = 4,306.36 years 64*64*64*384 days = 100,663,296 days = 275,606.74 years and so on.

Terence then assumed that the beginning and end points of each of these cycles must be marked in historical time by exceptionally "novel" events (with the longer the cycle the greater the novelty at the beginning and end). In particular the beginning and end of each 67.29-year cycle would be so marked.

So, he reasoned, we need to find a particular recent event which stand out for its novelty, and that is a likely candidate for the start of a 67.29-year cycle. Then by adding 24,576 days to the date of that event we obtain the date of the end of that cycle, which also will be exceptionally novel.

The use of a uranium fission bomb to kill 80,000 civilians on August 6, 1945, seemed to Terence the most likely candidate in recent history for such an event. Adding 67.29 years (24,576 days) to the date of the bombing of Hiroshima (August 6, 1945) brings one to November 18, 2012.

At this point Terence's construction of the Timewave goes off the rails. To explain why I have to elucidate the concept of the zero date.

The Timewave function f(x) is defined only for x≤0. Thus, according to Timewave theory, time ends when f(x)=0 because there can be no (ordinary) time without the Timewave, and the Timewave function f(x) is undefined for any x>0. When the x in f(x)) becomes zero, that is called the zero point. Time either ends at the zero point or time itself is transcended. Terence identified the zero point with the "Eschaton", when "novelty" becomes infinite.

To associate the Timewave with empirical time, the x in f(x) has to be associated with some point in historical time, such as 6 a.m. on December 21, 2012. Then the value of the Timewave at any temporal distance of x days prior to that date (that is, the "novelty" value) is given by the value of f(x).

A point that is often overlooked is that the Timewave theory does not specify the zero point, that is, the date of the Eschaton. In order to plot "noveltly" against time one has to specify an actual date for the zero point. When Terence began to speak publicly about the Timewave he first chose December 22, 2012, later revised to December 21, 2012, as the zero point, partly because this is the date of the winter solstice in 2012.

Another reason has to do with the fact that the Maya Calendar used a system of cycles-within-cycles (tuns, katuns and baktuns), the largest of which was a cycle of 13 baktuns, with each baktun consisting of 144,000 days, totalling approximately 5125.37 solar years. According to most scholars studying the Maya Calendar, the most recent cycle of 13 baktuns came to end on December 21, 2012.

As stated above, Terence looked for a recent event (this was in the 1970s) which could mark the beginning of a cycle of 24,576 days (one of the larger cycles posited by Timewave theory) and he deemed the first use of an atomic bomb against a civilian population on August 6, 1945, to be a likely candidate. He then added 24,576 days (67.29 years) to this date to arrive at November 18, 2012. Since this was only 33 days different from the date of the end of the 5125-year Mayan great cycle of 13 baktuns it seems that he decided to go with that date as the date of the Eschaton.

But the basic flaw in his reasoning is that the 24,576-day I Ching cycle (or rather, the 24,576-day period he constructed as part of the Timewave theory) that he looked at was the final such cycle prior to arrival at the zero point. He assumed that it was, and thus that the end of that 24,576-day period (whether November 18, 2012, or December 21) would be marked by the occurrence of the Eschaton, when the value of the Timewave function f(x) would at last become zero. There was no reason to suppose this, since after the end of that 24,576-day period (1945-2012) another one could ensue, and then another, until finally the Eschaton arrived at some time in the (possibly distant) future.

Since there was no basis for assuming that the date of the Hiroshima atomic bombing was the start date of the final 24,576-day period, there is no basis for assuming that the end date of that period is the date when the value of f(x) reaches zero (which is the supposed date of the Eschaton). Comparisons of the ups and downs of "novelty" (as shown in the graphs of the Timewave) with novel historical events was used by Terence as evidence of the truth of Timewave theory, but this evidence is flawed because there is no basis for claiming that the zero point is December 21, 2012, or any other date.