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One of the major end-the-world-in-2012 theories is Timewave Zero, which purports to produce mathematical evidence that there is a singularity at the end of 2012. A singularity is a point beyond which something cannot be known. It may foretell a physical catastrophe, or it may foretell a Rapture of the Nerds – or anything in between.  Is it likely that this theory, which occupies pages of formulae and can be bought on a computer program, is predicting the end of the world as we know it?
Timewave Zero was proposed by Terence McKenna and Dennis McKenna in their book, "The Invisible Landscape". "Timewave Zero" is the McKenna brothers' way of representing the flow of "novelty" over time. The graphic representation is derived from the standard sequence of hexagrams of the I Ching in what is known as the King Wen sequence. At one point, the graph dives through the axis – this is presumed to be infinite 'novelty' – and ends. This is the end of history. It is not necessarily a violent or final end of humanity, but a point after which a discussion of changes in 'novelty' becomes useless.

The book is about more than a mathematical theory. The first part is about the relationship between the nervous system and the physical universe via the linking mechanism of quantum mechanics (or at least electron spin resonance), a discussion which appears to be intended to show that consciousness is more than an accidental spark of the human nervous system. Quantum Mechanics, which fundamentally depends on a conscious observer, leads the most rigorous and mathematical minds into hair-tearing frenzies as they then need to have fundamental definitions for consciousness and observerdom. (c.f. Penrose, p 1031 to 1033) In the hands of the less rigorous, there can be even more to say on the subject, as in this book.

The book begins with the relationship between Shamanism and mind-altering substances. The authors claim that drug molecules in the neurons which cause the hallucinations of the shaman slip inside the spiral of DNA, altering its electron spin resonance. If you take these drugs and sing, the electromagnetic field produced by your singing, they go on, could affect these drug/DNA complexes, and this could produce a hologram of an idea, which is a sort of flying saucer. They call this the "apparent functioning of the audilely induced intercalation of harmine into the genetic matrix." (p. 121) (Harmine is a drug molecule.)

Accordingly, then, the brothers took drugs, which made them believe an insect was guarding them. They felt schizophrenic and met bizarre life-forms. This apparently proved their point. "In the wake of our experiment there have been, besides enormous disruptions of statistical norms in the form of accumulations of meaningful coincidences, instances of physical phenomena absolutely beyond current understanding. Telepathic phenomena especially, in our subjective judgment, were manifest several times during this period…[some] may violate the usual laws of conventional physics."

They then have a "sharp shift of focus" for part II, and discuss the I Ching in detail. The I Ching is an oracle, but the brothers do not use it as an oracle. They discuss the layout of the pieces of the oracle in their standard sequence. (Think of it as describing the pieces on a chess board before the game begins.) The I Ching "pieces" are 64 hexagrams or designs of six lines in a vertical column. Each line can be broken or unbroken. Because there are two states (broken or unbroken) and six lines, there are 2^6 combinations, or 64 different possible hexagrams. In this arrangement, the King Wen sequence, the 64 are arranged in 32 pairs and the differences between the pairs can be described in shorthand as the number of lines which change between the first and the second member of the pair. To stress the point again, the King Wen is the standard or book sequence of the hexagrams, not part of a divinatory activity.

To the McKennas, the I Ching is related in a fundamental way to a calendar they postulate for the Ancient Chinese. A lunar year is 13 months of 29.53 days (384 days). 384 is 64 multiplied by 6. The I Ching has sixty four hexagrams. Furthermore,

29.53 days X 6 is 384 (one lunar year)
384 X 64 is 67 solar years and 124 days or two sunspot cycles (McKenna says the Ancient Chinese were aware of the sunspot cycle)
7 solar years, 124 days X 64, is 4306 years, about two Zodiacal ages
4306 years X 6 is 25, 836 solar years or about one precession of the equinoxes.

McKenna knows that there is little direct evidence that this proposed calendar was actually used in Ancient China, and so he says things like, "It is possible to suggest that in Neolithic China the sequence of 64 hexagrams X 6 was actually known and used as a calendar, " (p132) and that this "suggests a possible historical speculation". McKenna goes to great lengths to explain that this calendar, if it were ever used, would be a very accurate one. "The relative clumsiness of the traditional Chinese calendar seems to lend support to this idea that it conceals an older, reformed lunar calendar. [It] had an average length of 360 days into which two intercalary months were inserted every five years. This means that a lunar year of 12 months would have 354.4 days per year, which is short of the average duration of 360 days. The solar year, on the other hand is 5.25 days longer than the 360-day year. When 10.85, the sum of 5.25 and 5.6 is taken times 5 (the five years into which the two intercalary months are inserted), the result is 54.26 days, which is approximately five days less than exactly two lunar months. These calculations show that, in spite of the insertion of the two extra lunar months every five years, this calendar…would still gain 4.8 days every five years; compare this to the loss of one day every 454.5 lunar yeas for a thirteen month lunar year of 384 days, in only one intercalary day every ten years. This latter represents a level of accuracy improved by a factor of many thousands. Even in comparison with [our calendar] this calendar is accurate by a factor well over one hundred. [Even without intercalation, it is twice as accurate as ours.] (p. 133)

McKenna is taken with the concept of 64. He points out that there are 64 codons in nucleic acid. This is true, and it's true for the same reason as the number of hexagrams in the I Ching – very simple arithmetic. There are four 'letters' in DNA and each 'word' is three letters long. So there are 4^3, or 64 possible words in DNA. He does not mention that most of these 'words' are 'redundant' – variant spellings for the same amino acids. There are approximately 20 amino acids and a stop codon and a start codon. The other 'words' call up the same amino acids. For instance, Tryptophan only has one spelling: UGG. But UUA, UUG, CUU, CUC, CUA and CUG all spell "Leucine". The genetic code behaves exactly as you would expect something to behave that was parsimonious (uses as few letters as possible). 4^2 (16) would be too few, and 4^4 would be far too many; 4^3 is just right. More bizarrely, he also says that the number of folk taxonomies or 'conceptual categories' also equals 2^6, or 64. This is like reading one of those books that say there are seven basic plots, or five basic plots or three – the number of folk taxonomies in the world probably exceeds the number of categories in this particular folk taxonomy. Are there really '64' – no more, no less – ways you can divide up reality? I think Jorge Luis Borges probably did more than that all by his self – for fun! The rationale seems to be that you can't think about more than six orthogonally related binary dimensions. Maybe so, but I don't think it is an actual limit, like the number of codons in DNA or the number of hexagrams in the I Ching.

The King Wen sequence is artificial, in the sense that the hexagrams are not arranged in random pairs. There was thought behind the sequence, just as there was thought behind the arrangement of chessmen on a chess board. It's easier to see this as a diagram. There is a vast number of "logical orders" that a series of hexagrams can be in, for instance, if the first line is complete, then broken, then the second line is complete, then broken and so on. Or you can have a one be "right way up" and the next one be the same one "upside down". The reason behind the King Wen sequence isn't known, but it has been thought out. For instance, a type of difference called a "five" (five lines are different between pairs) never appears; the type of difference called a "two" appears twenty times and the type of difference called a "six" appears nine times. "Even" to "odd" transitions appear three times more often than odd to even. The McKennas found that there was a logical beginning and end to the sequence – and this occurs at the standard King Wen beginning and end – which is not random. Millions of tries with a random number generator only found a few sequences with this type of logic. It clearly isn't due to chance. If the first order of difference (number of line changes between pairs) is graphed, McKenna found a "singularity" – the first three and last three differences are identical, so the graph can be joined up at that point.

So far so good. The sequence is graphed, from beginning to end, and then reversed and the reversal laid over the first graph. Then the McKennas start saying things like, "We will consider the space-time continuum as a modular wave-hierarchy. This hierarchy is composed of waves that have, on the most simple level, the configuration that is generated by figure 18b [the two graphs put together running backward and forward from the singularity]. The energy map of changes plotted backward upon itself forms pairs that, when added together always equal 64. The graph was seemingly constructed to be superimposed backward upon itself, suggesting to us that time was understood to function with the same holographic properties that have long been an accepted part of the phenomenon of the perception of three-dimensional space." (p. 146) This isn't meaningful – the changes do add to 64, obviously, but "energy pairs" doesn't mean anything here – they are drawings. The graph wasn't "seemingly constructed" at all, since the McKennas themselves constructed it for a reason and have no need to assume anything – the Ancient Chinese probably didn't construct it at all. (The McKennas even say on p. 143 "whether they graphed the first order of difference, as we have done…is moot".) And "holographic properties" are not really "an accepted part of the phenomenon of the perception of three-dimensional space" – despite a chapter earlier on holograms, this statement is a stretch and has no mathematical basis. Further on they say, "We have called the quantized wave-particle, whatever its level of occurrence within the hierarchy or its duration, eschaton". By now, they are simply manipulating words. The "eschaton" is a religious term, not a physics or biological one.

There is an appendix of the book detailing the mathematics which go into changing this simple line into "Timewave Zero". The appendix is on line here: What isn't discussed in McKenna's book at all is what is called The Half Twist, or the Watkins Objection. Nowhere in the book, but buried in the user manual for the computer program is an unexplained mathematical operation.

I'll copy Watkins' objection here at length.

"The formula is really quite inelegant, and I personally found it hard to believe that if a map of temporal resonance was encoded into the King Wen sequence, it would look like this. In any case, my main concern was with the powers of -1. These constitute the "missing step" which isn't mentioned in The Invisible Landscape, but which turns up as a footnote of the TimeExplorer software manual. On p.79 we find Now we must change the sign of half of the 64 numbers in angle_lin[] as follows (snip) When reading this, I immediately thought "WHY?", as did several friends and colleagues who I guided through the construction. There is no good reason I could see for this sudden manipulation of the data. Without this step, the powers of -1 disappear from the formula, and the "data points" are a different set of numbers, leading to a different timewave. McKenna has looked at this timewave and agrees that it doesn't appear to represent a map of "novelty" in the sense that the "real" timewave is claimed to. It is possible that by changing the "zero date"
Dec. 21, 2012, one could obtain a better fit, but there's no longer any clear motivation to attempt this, as the main reason for taking the original timewave seriously were McKenna's (often very convincing) arguments for historical correlation. These would all be rendered meaningless without the aforementioned step. The footnote associated with this step reads: This is the mysterious "half twist". The reason for this is not well understood at present and is a question which awaits further research. This struck me as absurd. After all, why introduce such a step into an (already overcomplicated) algorithm whilst admitting that the reason for doing so is "not well understood at present"? I confronted McKenna on this issue, and he immediately grasped the significance of my challenge. He would have to either (1) justify this mysterious "half twist" or (2) abandon the timewave theory altogether."

McKenna did not respond adequately at the time, and Watkins concluded: "Therefore we see that not only is the inclusion of the "half twist" failing to guarantee the "preservation" of some geometric property to which McKenna has referred, but the failure is precisely because of its inclusion. McKenna's stated reason for this (crucial) step of the construction is unacceptable. As a mathematician who has met and talked with him, who is sympathetic with the majority of his other work, and who is only interested in spreading clarity, I must conclude that the "timewave" cannot be taken to be what McKenna claims it is."

In fact, McKenna addresses this much later and says, "The revised wave is very similar in shape but its values are generally more Novel." Note: very similar in shape. He does not himself go on to address whether similar is as good as identical.

Sheliak's paper on the resolution of the Watkins Objection gives the correlation as "comparisons ranged from a low of 0.73 to a high of 0.98 with an average correlation of 0.86." For the non-mathematically inclined, a correlation of 0.86 is good, if say, you wanted to compare the days you eat an apple compared with the days the doctor stays away. For a complicated graph that is supposed to predict things down to the events of one day in 20 billion years, it is not a good correlation.

Once all the transformations are done on the data, what one can see is a complicated line. It dives down (increases "novelty") at the end. The reason why the line should represent "novelty" is not well explored. The definition seems fuzzy. Habit and routine are hills on the graph. Valleys are increases in "novelty". The axis is marked in units, but a given unit of "novelty" is not defined. The line is said to be fractal, so in the general overview, the entire history of the universe is said to be represented, and variations in "novelty" are Big Units. In a close-up, only a few years are shown at once, and the line now represents "novelty" only on Earth, and, generally speaking, only where "novelty" affects the
United States of America. The units of novelty are smaller.

McKenna explains the fractal scaling of the wavy line (waveform) generated by these processes. Briefly, fractal scaling means that a magnification of a small portion of the wavy line looks exactly like the overall wavy line. McKenna's table, on p. 154, goes from 72 X 10^9 years (billion years) to 1.597 X 10 ^-27 of a second, which he calls in the "range of Planck's constant". Note that this is based on a lunar calendar that may or may not have been used, which only needs a day intercalating every few hundred years. This is very accurate by our leap-year-every-four-years standards. Remember the part above where it is well over one hundred times more accurate? One hundred is one followed by two zeros. The range of the graph is from billions of years to one and a half xontoseconds (as I am assured by Wikipedia is the proper word for one octillionth or one quadrilliardth). The "very accurate calendar" that's one hundred times as good as ours is scalable over a range of one to one followed by 42 zeros without any kind of adjustment. This seems unlikely.

So, if this timewave can describe the "novelty" in the universe on scales from xontoseconds to billions of years, and it comes to an end at the certain point, how do we determine the exact date of that endpoint? The answer is surprising. You guess at the endpoint, based on how you think things fit. McKenna says, "First let me explain that we chose the end of the Mayan Calendar as the "end date" for this graph because we found good agreement between the events that comprise the historical records and the wave itself when this end date was chosen." There is no actual predicted end date for the timewave – the end date is based on people examining the up and down slopes and assigning dates to each one based on how much "novelty" they believed existed in the universe/earth/United States on any given epoch/year/day. Although McKenna does not say it in this edition of the book, his original assumption was that the final 67.29 year cycle of the timewave began on the most "novel" day he could think of, the atomic bombing of
Hiroshima. Now, this makes two assumptions – first it is assumed, without any real justification, that our planet is already in the final cycle – and it is further assumed that Hiroshima was a 'novel' event in a universally meaningful way. This would put the end date of history in mid-November 2012. When McKenna heard about the Mayan calendar, he apparently decided that the date should be moved later, to 2012-12-21, to coincide with it. Ref:

Others have also noted this assumption. Calleman, in his criticism of John Henry Jenkin's Mayan Calendar theory, says, "On this point some words should also be said about the work of the late Terence McKenna, who wrote the foreword to Jenkins book. Based on the I Ching McKenna developed a Time-Wave function that he claimed would come to an end at the end of the Long Count,
December 21, 2012. Unfortunately, McKenna is not here to respond, but Peter Meyer who developed the mathematics of the Time-Wave in the McKennas’ book The Invisible Landscape, pointed out already in his life-time that McKenna’s time wave, that had been anchored in human history merely by the choice of one single event, the Hiroshima Bombing, actually did not end on December 21, 2012, but on November 18, 2012. Since McKenna chose not to respond to this very serious criticism, we can only assume that it was wishful thinking that had led McKenna to say that the end of his time-wave coincided with the end-date of the Mayan Long Count."

So the chosen end date for the dive into infinite novelty was 2012-12-21. It is not a prediction, but an assumption. One usually tests a theory by making predictions. Normally, a theory that correctly predicts a future event is regarded very highly. It is possible for a theory to be highly regarded if it "predicts" something in the past, if that past is not yet known (i.e. the discovery is in the future). For instance, a theory that says an asteroid hit the earth and wiped out the dinosaurs in a certain range of years (in the past) is predictive if it says that you can dig in a certain stratum and find an Iridium layer –if someone does dig there, and does find an Iridium layer, it supports the theory.

What does the Timewave Zero graph predict? Actually, not very much. It "predicts" that the end of the Reagan years (in the past) would be followed by a period of sharply increasing "novelty". This is not very persuasive. First, the event is in the past. You're looking at the graph with a history book in front of you, and secondly, you are consciously or unconsciously making assumptions about what is "novelty" and whether you've had a lot of it or a little. The graphs are in units of novelty, but a unit has no exact value even at a given scale. How novel is
Tiananmen Square? How novel was 1968? Was the invasion of Kuwait more or less novel than the fall of the Berlin wall? Does Tiananmen square increase or decrease novelty, and does the fall of the Berlin wall do the same, or the opposite? On the larger scales, isn't a large-scale extinction event a decrease in novelty? I can certainly make a case that it has a potential to spur a great deal of novelty, but in itself, what is it? The development of language was probably an increase in novelty, but what does a broad peak on a graph labeled "possible language acquisition" actually mean? How can the Sixties be a time of steadily decreasing novelty, with the change coming in 1968? Why does the Black Death occur at the end of an astonishing increase in novelty and reverse it? I mean, I can see why it reverses it, but what caused the increase just before it broke out? You can read a large number of these "predictions" about past events at (note: this is the web archive as the original has been taken down. The Wayback Machine does not always answer on the first call, so you may have to click more than once).

There is a video of McKenna going through recent (to him) history on YouTube here.

Here are a couple of screenshots with my annotations:  
timewave zero still from video

Another still:

timewavezero still from video 2

John Sheliak published a paper called Standard, Revised, and Random Generated TimeWave Results which go over the correlations of historical events with the timewave after the Watkins Objection has been addressed. These are graphs mentioned above with the 0.73 to 0.98 correlation to the old timewave. Some of the graphs on this new improved page are similar to the original graphs, but in at least one case, where the slope has been reversed, the explanation has been reversed also, to match the new slope. For instance, McKenna held a strong belief that war is habitual, not novel. Sheliak points out (with a graph) "Figure 19 shows the standard and revised TimeWave comparison graphs for the period 1935-1955, and there are obvious similarities and clear differences between the two waves. Both graphs show that WWII begins and ends during steep ascents into habit, but they describe somewhat diverging processes, for much of the middle period of the war. The revised TimeWave shows that a very novel process is apparently at work for much of the period of the war. The standard TimeWave does show novel influences, but it is neither as consistent nor dramatic as for the revised TimeWave. Some very potent novel process seems to be occurring during much of the war period, and that process may be suppressing a major ascent into habit that might otherwise be happening. Could this novel process be the development of nuclear science and technology, eventually leading to the production and use of nuclear weapons?" He goes on to suggest that it may seem offensive, but the knowledge of nuclear weapons is after all knowledge of how stars work, and not related to what use the knowledge is put. The use of the power is apparently on a steep uphill slope – a sign of habit. "Perhaps the process of becoming more aware of nature, and ourselves - is very novel indeed. It is the sacred knowledge of the shaman, who returns from an immersion into an aspect of nature, with guidance or healing for her or his people. We seem to have lost the sense of sacred knowledge with its accompanying responsibility, somewhere along the way. Perhaps it is time to regain that sense, and reclaim responsibility for our knowing." What use is a prediction, if the graph going either way can be explained by the same phenomenon?

Some of McKenna's other correlations seem like stretches. For instance, at his eschaton page, "Here are a series of interesting direct resonances. The explosion of new life forms in the Cambrian, the crucifixion of Christ and the murder of Anwar Sadat are in perfect resonance," says one web page. Cambrian, Christ and Anwar Sadat?
Graphs are here. Show me the assassination of President Kennedy instead – oh, it's not there.

One big event in the past we can all agree on increasing novelty was the Big Bang. When does the Big Bang occur in Timewave Zero? At 22 billion years ago. Scientists today calculate it as around 13.7 ± 0.2 billion years. This doesn't dismay the boosters of Timewave Zero. It's a chance to be proven right, eventually!

In summary, Timewave Zero is a wavy line derived from the arrangement of hexagrams in an Ancient Chinese book. You could assume that the vertical axis represents "novelty". The graph contains a singularity, where the line goes below the axis and cannot return. The McKennas assume that the end date is 2012-12-21. The graph does not "predict" this date. Rather, this date is an assumption of the theory. If you call this the end date, then you can count days backwards and see if the historical record shows 'novelty' or habituality at that time and compare it with the graph. Some people can see correlations with historical events.

I'll leave you with McKenna's own words from the book: "It is possible to suggest…in the wake of the closure of the vacuum fluctuation, the photonic forms existing and able for the first time to obey laws relevant to themselves as photonic holograms (forms) rather than as photonic holograms expressed through matter or antimatter, as objects or anti-objects. Such a process, though farfetched, would utilize a set of naturally occurring phenomena (vacuum fluctuations and higher dimensional matrices) to create the sort of basic ontological mutation in the nature of matter such as, we suggest, may characterize some future shift of epochs. The photonic shell, left in the wake of fourth-dimensional merging of holograms of matter, and of antimatter, may be the key to a clearer understanding of the archetype of a paradisiacal existence at time's end. The spiral implosion of time may entail the universe, and every entity in it, meeting and canceling its antimatter double to create, through this union of opposites, an ontological mutation from matter in a photonic form, which represents tremendous freedom."

Or of course it may not. I'm willing to bet that it doesn't.

1.The Invisible Landscape, Terence McKenna and Dennis McKenna, HarperSanFrancisco, 1994

2. Carl John Calleman on John Henry Jenkins' interpretation of the Mayan Calendar end date:

3. Roger Penrose, The Road To Reality, a Complete Guide to the Physical Universe, BCA, 2004

4. I Ching, Wikipedia general article,

5. King Wen sequence, Wikipedia general article,

6. Jorge Luis Borges on categorization,

7. Carl Johan Calleman, criticism of John Henry Jenkin's Mayan Calendar

8.Terence McKenna's site featuring graphs of the timewave and the historical events they match

9. Peter Meyer, The Zero Date, 1999-2006,

10. Terence McKenna, Timewave Zero video clip,

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