3. Fractal time and the I Ching
 10,000 years ago humans began domesticating plants and animals.
 500 years ago we invented the printing press.
 100 years ago we began driving automobiles.
 50 years ago we invented the computer.
 30 years ago we landed on the moon.
The speed of change is rapid. Population, computing power, speed of transport, the sheer amount of known information, and most other things that involve humans, are all increasing at an accelerating rate. The rate at which they are increasing is increasing. We are all part of it, with younger people thinking nothing of it, and the elderly commenting on it, but generally handling it okay. But if we were to transport King Arthur to modernday New York he’d most probably pass out from trying to grasp what was happening. But can it stop, slow down or reverse. No, for that is not in our nature.
Things will keep changing at a faster rate. Every 18 months the power of computers double. Soon they will be smarter than us, and we are already on the verge of cloning humans and close to using nanotechnology to create atomic size minimachines. Maybe there will come a time when the rate of change will reach such a speed that change is all that will exist. Various fringe scientists have tried to calculate this point of infinity, giving us calculated dates ranging from 2010 to 2050. Dates that many of us will live to see. Perhaps the date is Dec 22, 2012. Ethnobotanists and fractal time experts Terrence and Dennis McKenna believe so, and they present their ideas in Invisible Landscape: Mind Hallucinogens and the I Ching (1993).
Their studies began with the I Ching, which is composed of 64 hexagrams, or sixline figures. It struck them that 6 x 64 = 384, which is exceptionally close to the
number of days in 13 lunar months (29.5306 x 13 = 383.8978), and that maybe the I Ching was originally an ancient Chinese calendar. Further multiples had astronomical significance:
1 day x 64 
x 6 
= 384 days 
= 13 lunar months 
384 days 
x 64 
= 67 years, 104.25 days 
= 6 minor sunspot cycles (11.2 years each) 
67 years, 104.25 days 
x 64 
= 4306+ years 
= 2 Zodiacal ages 
4306+ years 
x 6 
= 25836 years 
= 1 precession of the equinoxes 
The McKenna brothers arrived at the 2012 end date by using fractals. Starting from a table of differences between one hexagram and the next, they developed a Mandelbrot fractal in which each level is 64 times greater then the one below it. They then laid this fractal pattern on top of a time scale. The peaks and troughs of the pattern relate to the level of connectedness or novelty in any span of time, whether it covers a day, millennia or even since the beginning of time. By matching the levels of the pattern with key periods in history, they determined it would fit best if the end of the time scale was December 22, 2012. This is the only point in which the level of novelty reaches its maximum, and everything that happens is new. Change feeds upon itself like nanomachines converting every atom in the universe into gold.
The final 80 or so pages of their Invisible Landscape (1993) describe the complicated mathematics and methodology they employed. A base period of roughly 67 years was discovered (all calculations are rough, but not inaccurate).
2012 minus 67 years = 1945, a year of great change
2012 minus 4,300 years (67×64) = 2300 BC, the beginning of historical time
2012 minus 275,000 years (4300 x 64) = the emergence of Homo sapiens
2012 minus 18 million years (275,000 x 64) = the height of the age of mammals
2012 minus 1.3 billion years = the beginning of life on our planet
About what may happen in 2012 they have this to say:
“Achievement of the zero state can be imagined to arrive in one of two forms. One is the dissolution of the cosmos in an actual cessation and unravelling of the natural laws, a literal apocalypse. The other possibility. the culmination of a human process, a process of toolmaking, which comes to completion in the perfect artifact: the monadic self, exteriorised, condensed, and visible in three dimensions; in alchemical terms, the dream of a union of spirit and matter”[i]
On top of all this they state that they calculated the 2012 end date in the early 1970′s, long before they had heard of the Mayan calendar. And to their credit, the original 1975 edition of The Invisible Landscape makes no mention of the Maya. If this is true, then it would be prudent to consider their result as much more than a coincidence, and to take their ideas seriously.
Also fitting the model of increasing novelty and the 2012 end date is the idea that on a subconscious level humans can sense a great change approaching. Unsure of what exactly to expect, but nevertheless feeling uneasy, we are doing the best we can to “get everything done” while we still have time. A last minute desperate attempt to achieve the peak of our potential. And if we are able to somehow sense a disturbance ahead, maybe birds and animals will pick up on it as well. Maybe in December 2012 the nonhuman species will suddenly hush, as they have demonstrated prior to earthquakes.
[i] Dennis J. McKenna and Terence K. McKenna, Invisible Landscape (1993), Harper Collins, p.188
[ii] John Major Jenkins, Maya Cosmogenisis 2012 (1998), Bear & Co, page 7
Note on Precession of the Equinoxes
The Earth spins on an axis, with the northern end at the North Pole. The spinning action is like that of a top; and like a top the Earth wobbles as it spins – but very slowly, with one wobble taking approximately 25,800 years. This causes the location in space that the North Pole points at to gradually change. At present it points to Polaris, the North Star. In 12,000 years time it will be pointing close to Vega. As the pole star changes, so does the position in the sky of all the other stars, relative to our wobbly spinning Earth. Astroarcheaologists mention the precession of the equinoxes a lot, for it explains how ancient stone circles and pyramids have lost their former accuracy in pinpointing astronomical events. It can also help determine precisely when these monuments were built.
The ancient Olmec (who predated the Maya) were very aware of this slow precession, and periodically realigned the pyramid at La Venta so that it could maintain its accuracy.[ii]
Note on Fractals
Fractal geometry is often called “the geometry of nature.” A fractal is geometric shape that is complex and detailed in structure at any level of magnification. Often fractals are selfsimilar each small portion of the fractal can be viewed as a reducedscale replica of the whole. Building fractals relies on a repeated formula. Below is one example of how a fractal “grows”. And beside it is an example from nature – the leaves of the fern are the same shape as the branch, which itself is the same shape as the entire fern. In nature the depth of detail is limited; in mathematics the depth is infinite.


Note on Nanotechnology
A nanometer is one billionth of a meter (3 – 4 atoms wide). Nanotechnology is the creation of minute objects, with the ultimate goal of using individual atoms as building blocks. Some engineers dream of creating selfreplicating nanobots – tiny devices that create replicas of themselves by manipulating atoms. A much quoted worry is that someone will create selfreplicating nanobots that refuse to stop – overnight the universe could contain nanobots and nothing else!