An Eccentric Calculation
Measures and Units
So much for the Ages of Gaia, but what is the age of Gaia, the planet Earth, considered as a living organism? The question here is not, How old is Gaia in geological terms? That question has been answered by geoscientists and paleontologists: about 4.5 billion years old. Fine, but I have in mind another question.
I propose that we ask, How old is Gaia in her own time, as she lives it? The 4.5 billion year estimate universally accepted by science today is computed in Earth-years—that is, in the seasonal cycles of the orbital revolution of the Earth, measured by the time it takes to circle the Sun. The length of the terrestrial year is 365.2424 days. The day is also a terrestrial unit, marking the length of time it takes for the Earth to rotate once on its axis: 24 hours. This is anthropocentric measurement, a way of computing Gaia's time in terms of the human experience of days and years.
This is fine as far as it goes. We have to start somewhere, with some measure we can comprehend, but I want to proceed to another way of reckoning Gaian time. To help with the eccentric calculation, let's distinguish a measurement from a unit. 365.2424 days is a measurement of the terrestrial year. This is a measurement of time, duration. The measurement of the mean circumference of the Earth is about 24,000 miles. This is a measurement of space, distance. The unit of this spatial measurement is one mile, but a mile is also a measurement. A measurement always states a measurable dimension of space or time or matter (weight, mass) in specific figures. The measurement of your waistline in inches, for instance, is a specific figure (say, 38 and 1/2 inches) stated in uniform units, inches. It is a number that can be verified by instruments such as a tailor's tape-measure.
A unit may also be a known, calculated measure—for instance, the unit of a mile used to measure distance: 5280 feet—but unlike a measurement a unit can stand alone, independent of what it measures. A unit has autonomous properties, hence the magic of numbers. Some measurements are also used as units, but units cannot be equated with, or reduced to, measures. 365.2424 days is a measurement used as a unit in calculating geological time. As such, it is a provisional unit, not a pure unit. A pure unit is 360. This number is an expression of the sexigesimal system or base-six system. 6 and 360 are pure base units, not measurements of physical dimensions of time and space. Neither 6 nor 60 nor 360 is a measurement, except in geometrical terms. 24 is also a unit related to the base-six system. In geophysical terms, the measurements that come close to such units are nevertheless distinct from them. The measurement of a day on Earth is actually just under 24 hours. The closest pure unit is 24. When we say that the day has twenty-four hours, we are referring to a unit and not the true measurement. You can do things with the pure unit 24 that you cannot do with the exact measurement of a day. The unit is not merely more convenient; it has generative properties.
In my eccentric calculation we will look at existing measurements, but not remain restricted to them. We will use unit-numbers in a particular way, in order to develop a different scale for the standard measurements of geological time. The aim of this exercise is to develop a timescale that will allow us to imagine how Gaia lives in her own time, how she experiences the phases of her life in an organic and developmental sequence.
Eons and Geons
It is appropriate to measure the life of the Earth in terrestrial cycles of time. But let's imagine that Gaia's own sense of time might be computed in a different way, working from these Earth-based figures, of course—they are all we have to go on—but permutating or converting them. How can we proceed with such an exercise?
Mythologist Joseph Campbell noted that the current estimate of 4.5 billion terrestrial years (TY) for the lifetime of the Earth is very close to the pure unit 4320 found in Hindu mythology and other cosmological systems. 4320 occurs in several variations. By one reckoning, 4,320,000 years is one "Day of Brahma," that is, one vast cosmic cycle. Ancient calculations extrapolate 4320 into tens and hundreds of billions of years. 4320 is also the breakdown of the four Yugas or cosmic ages in sacred Hindu (Brahmanical) chronology. I will not go into the arcane properties of the sacred unit 4320 because that would be a digression, but I assure you that they are fascinating. In esoteric chronology, 4320 is a canonical number. It is not a measurement of anything, it is a sacred unit that converts measurements. For instance, 72 years is the measurement of Zodiacal time (or precession, see below). 4320 = 72 X 60, or sixty degrees of precession in the Zodiac. 4320 combines units from a base-six system (60) and units produced when the circle of 360 degrees is divided by 5. This is how the sacred or canonical numbers work, as tools of conversion.
Now, to set the lifetime of the Earth at 4.320 billion years does not vary but a hair from "scientific fact." The variance of 4% between 4500 billion and 4320 billion may be regarded as too large by strict standards, but the exact moment when the Earth took globular form within the proto-planetary disk cannot be pinpointed with such accuracy. It is fair to say that 4.32 billion years ago was the threshold moment when the planet assumed form as a separate sphere distinct from the other planetary bodies forming in the whirling disk of primordial matter. I will use the canonical unit 4320, rather than the accepted measurement of 4500 million years, for calculating Gaia's Age in her own time.
This eccentric calculation requires only three simple steps. In the first step, I propose to convert 4320 million years to a base-ten figure. I'll call it 1000 Geons, defining a Geon as one geophysical age or epoch of Gaian time, though not yet expressed in Gaia's own time. Bear with me, folks. The Geon is just a contrivance, a device to reduce 4320 million years to a number of conceivable units.1 Geon = 4,320,000 terrestrial years (TY), or 4.32 million TY. The Geon is a handy mediating tool. It allows us to put the immense figure of 4320 million TY into a conceivable scale, but as a unit it is of no particular importance. 1000 is not a canonical number. We are just using the base-ten system to take an initial step into the eccentric calculation.
Conversion of complex, uneven measurements to a ten-base is a common way to put numbers into a workable scale. Scientists do this all the time. They use logarithmic scale, increasing by a factor of 10. 4,320,000,000 years—four billion, three hundred twenty million years—can be put into a ten-base as 4.32 X 10 to the 9th power. Every zero or decimal place equals a factor of 10 in the ten-base.
1000 Geons is a naive conversion of the measurement 4.32 billion into a ten-base, not a legitimate mathematical operation. I am simply assigning 1000 units to the given geological timespan. I am not concerned with mathematical correctness. What I am proposing might be called play math, compared to the hard math scientists use. The aim is of this childish exercise is to see what kind of results play math can yield. It will be pure foolishness to a professional mathematician or a scientist who uses equations to describe how the universe works, but, on the other hand, hard science cannot produce the kind of results that come out of play math. Scientists routinely ignore the canonical or sacred units and look only at what can be measured by instruments. But ancient systems of astronomy and geodetics used both measurements and pure units of measure, the canonical or archetypal numbers.
Now to the second step. In chaos theory, now called complexity theory, mathematicians use what are called iterations to generate fractal images on a computer screen. An iteration occurs when you set up a formula, feed data into it, and then feed the result generated by the equation back into the equation as more data. Iterations go into the millions and beyond. This is how stunningly complex, self-similar images such as the Mandelbrot set are produced.
Now, I am not going to propose a genuine iteration, but a kind of play iteration. In the second step, after having set up the equation, 4.320 billion years = 1000 Geons, we take the code number 4320 contained in the equation and feed it back into the equation. There are several ways to do this. Three choices, to be exact: either .432 or 4.23 or 43.2 can be fed back into the equation. I will try 43.2, just to see what results it will produce. So, let's divide 1000 Geons by the unit 43.2, which has no measurement value in this operation. The result is 23.15. Take a good long moment to register this unfamiliar number.
Such is my humble assumption as we hover between steps two and three of this brief, eccentric calculation. I assume a fractal principle operating in Gaia's time, such that, if we can detect it, we will be able to develop a sense of how the living planet senses time internally and organically, or her own terms. This would amount to discovering fractal, self-similar, internested units of timing in the geological timeframe. To do this we use play math. This is not my invention, and the method is not new. Play math or conversion with canonical numbers was common in ancient systems of calculation such as Hindu and Egyptian mathematics
Accepting 4.32 billion TY as Gaia's lifespan so far, let's assume that the unit 43.2 indicates the fractalization of her time, revealing how it unfolds—how Gaia evolves in her own time, you might say. In fractal timing, the unit 43.2 is a self-similar division of the measurement 4.32 billion years. Let's call this fractal unit 43.2 one division of organic time in Gaia's life. Having converted Gaia's lifespan of 4.32 billion years into 1000 Geons, we divided the measurement expressed in Geons by the fractal unit 43.2. The result is a new, odd-looking number that can be treated as a fractally derived unit of Gaian time: 23.15. Note how this number squeezes out of the naive, elementary math in an unexpected way. There are one thousand 4.32-million-year units in 1000 Geons, because each Geon, being 1000th of 4.32 billion years, has an assigned value of 4.32 million—a difference of three zeros, or ten to the power of 3. This is redundant and self-evident, of course. But when we divide the unit 43.2 back into the 1000, a different kind of number shows up. There are 23.15 units of 43.2 million years in 1000 Geons. 23.15 has the look of something we haven't seen until now.
Geons of 4,320,000 years each are units of Gaian time useful for thinking about her total lifespan without getting lost in immense numbers. For instance, we can consider what happened in the 985th Geon, 15 Geons ago. This equates to 65 million years BP (before present), the moment of a mass extinction due to a meteor impact. In the 985th Geon, dinosaurs became extinct. The value of the Geon is to provide an apt proportional scale for trucking back and forth through the total 4.32 billion years of the Earth's life so far.
When we divide the unit 43.2 into 1000 Geons, we are simply asking how many 43.2 Geon units are contained in the entire period of 1000 Geons. The result, 23.15, is the current age of Gaia in her own years, if we allow that each 43.2-Geon unit is also a measurement, the extent of one Gaian year. One Geon is not a year in her time, 43.2 Geons are. Why do I say that 43.2 Geons is a year in Gaia's time? Well, 43.2 is the fractalization of 4.320 billion expressed as a division of 1000 Geons. Granted, it is not the only fractalization that can be construed, so it might well seem that this entire operation is arbitrary. I am deciding beforehand how I want to define a Gaian year, rather then deriving the length of the year from the figures. This may be considered as cheating, but at least I am cheating out in the open!
But seriously, there is more going on here than the mere foolishness it appears to be. In quest of Gaian timing, we must distinguish between the length of a Gaian year, and the number of years she has lived. The purpose of this exercise was to set up a scale showing the number of years she has lived in her own time. The fractal unit 43.2 is one of three choices, as we saw. I chose it for a reiteration to see how many years it would yield. Bear in mind, again, that the Gaian Year is not 43.2 million years or 4.32 million years, but 43.2 Geons. We express the Gaian Year in Geons first—this is the sleight of hand. In a moment we'll calculate it in terrestrial years.
So, Gaia's current age in her own time is 23 years. The standard geological timeframe makes Gaia appear to be immensely old, as she truly is in human terms, but in her own time she is still quite young. A mere lass of 23 and some months. This startlingly low figure introduces a totally new way to think about the evolution of the Earth.
I realize there are assumptions in these naive permutations that will not be self-evident on the first run through the exercise. Why assume that 43.2 Geons is one Gaian Year? In using play math, it is helpful to make as few assumptions as possible. The most elementary permutations will generate the most interesting results. 43.20 is a fractal unit of the measurement of Gaia's lifespan of 4.320 billion years, determined by a shift of one decimal place in the unit. The other shifts of the decimal, .4320 and 432.0, produce different results—but that is another exercise! It could be objected that I am not calculating Gaia's age at all, not in any legitimate way. I am arbitrarily choosing a unit to be a year of Gaian time, not deriving the length of the year from genuine calculations. Yes, that's true enough, but the interesting thing here is what the chosen unit does, the results it generates. I have selected 43.2 from three choices, I have not just pulled it out of the ether. To discover Gaia's age in years, we try out that unit for the duration of one year. I am assigning a value to the length of one of her years, in order to find out how old she is. To do so, I use the least complicated conversion that suggests itself.
I do not expect anyone who seriously understands mathematics to tolerate these operations. Those who understand it ludically might play along...
The Gaian Year
43.2 is a fractal variant of 4320, but considered as a measurement in Geons, it is also a period of real geophysical time. One Geon is 4,320,000 terrestrial years, 4.32 million TY. This is a reasonably apt figure, within the limits of human conception. Homo sapiens is thought to have emerged a little over 5 MYA (million years ago, or BP, before present). In other words, we've been around for just over one Geon. 1000 Geons is a manageable scale. Play math renders inconceivable periods of time into an apt framework. I believe this method was used by the ancients so that they did not get lost in vast, humanly meaningless arrays of numbers. The Maya used it to extrapolate into nontillions of years, yet their calenderics were as exact, and in some cases more exact, than modern time measurements. The fact that we use play math does not mean we are incapable of reckoning with real measurements.
43.2 Geons of 4.32 million terrestrial years each = 186,624,000 TY. This is the third result in the eccentric calculation, the third permutation so far. It states the length of a Gaian Year in terrestrial years. Anyone who studies planetary and lunisolar cycles will be immediately struck by this, the third-step result of the eccentric calculation. The cycle of the rotation of the lunar nodes is 18.6 TY. The figure 18.6 terrestrial years is a measurement. Curiously, the play math method of combining ten-base conversion with units of fractalization, foolish as it looks, now generates the module of a factual number.
Is it merely a coincidence that the length of one Gaian year (GY), stated in terrestrial years, is extremely close to the lunar nodal cycle times 10 to the 7th power? 18.6 X 10 to the 7th power gives the length of the Gaian year in terrestrial years, but it also relates Gaian time to the cycles of the moon. It is perhaps not surprizing that Gaia senses her own time in a fractal extrapolation of lunar cycles. This makes sense considering the intimate structural coupling of Earth and Moon. Life on Earth, including human life, responds to lunar cycles in all kinds of ways. Why shouldn't Gaia's own life-cycles over the long term reflect the microcosmic lunar rhythms? The eccentric calculation supports this assumption.
Considering the magnitude of the figures, the difference between 186,624,000 years (measurement of the Gaian Year) and 186,600,000 (lunar node cycle extrapolated) is minute, and 18.618, a variant of the lunar nodal figure, gives an even closer correlation. Canonical units were considered divine or magical because of the way they pervade and convert measurement numbers. Often the pure unit numbers are close to measurements, but they always retain a singular and autonomous quality. All this has been known for ages, and explained by sharper mathematicians than myself, but I am proposing a new angle on sacred mathematics by suggesting that canonical units can reveal fractal patterns in the measurements of cosmic time and the cycles of celestial bodies.
To summarize: 1 Geon = 4,320,000 terrestrial years (TY). There are 1000 Geons in Gaia's lifespan so far. 43.2 Geons = 186,624,000 TY. This is one year in Gaia's own time. A few other calculations consistent with this system:
1,000,000 TY = .2315 Geons
So, what other conversions are possible from the figures so far?
Look at Zodiacal timing, which can be measured by macrocosmic motion. Precession is the shift of the spring equinox against the background of the fixed stars, due to the slow spin of the Earth around its axial pole, like a top slowing down. It is an ancient and universal system for calculating long-term cosmic cycles such as the Zodiacal Ages, Arien, Piscean, Aquarian. (Note: The Ages run in reverse from the seasonal sequence of these constellations.) In short, calculation by stat time.
One precessional cycle is 25,920 TY. This is an important measurement of cosmic timing, applied in the long-term frame of many ancient systems of chronology. The true measurement is not exactly 25,920, for the rate of precession is somewhat variable over the long term. One measurement I used for many years is 71.632 years per degree of precessional shift. This is close to the pure unit 72 years. 72 X 360 = 25,920 years, the canonical figure for one complete cycle of precession in the Zodiac.
Above we noted above, 4320 years is 60 degrees of precession at 72 years per degree. The canonical units of Hindu chronology and Zodiacal precession are obviously internested. Now the question is, what happens if we convert one full precessional cycle (called a Kalpa) into Gaian time? 25,920 years, one full cycle of precession, is exactly .006 Geons. The canonical unit factored in Geons reverts to a base-ten figure, a three-point decimal, and, more significantly, it incorporates the base-six or sexigesimal system widely used for astronomical calculations. Crawling back through the decimal places we get this: ten cycles of precession is .06 Geons, 100 cycles of precession is .6 Geons, 1000 cycles of precession is 6 Geons. This is a pretty neat match, considering that I chose 1000 Geons more or less out of the blue, it seems. (Of course, these relations are nested in the canonical numbers and the six-base and ten-base systems, but how to discover them is what matters here.)
The eccentric calculation suggests that the sexigesimal system used by the Babylonians, and still used today in astronomy, is congruent with the frame of Gaia's own time expressed in Geons. Fine, but let's recall that Geons are not real measurements of Gaian time, they are provisional units of geological time invented by John Lash. It certainly helps that 1000 cycles of precession equals 6 Geons because it correlates Zodiacal timing neatly to the standard geological timeframe, and we could play a lot with that correlation.... But what about the full Zodiacal cycle converted into Gaian Years? Lo and behold, that also works. 186,624,000 terrestrial years, one Gaian Year (GY), equals 7200 full cycles of Zodiacal precession. This is 72 (the key precessional number) times 10 to the power of 2.
The length of the Gaian Year may look arbitrary, and appear to have been computed in a naive manner, but the results are impressive. And there is more. Much more. Assuming that Gaia is 23 years old opens the way to an immense vista of empathic observations about the geophysical and biological evolution of the planet.
According to the current timescale, the first vascular plants appeared in the Silurian, around 418 MYA, or 418,000,000 years ago. This is looking back about 96 Geons into the past. To calculate ahead to the Silurian from the formation of the Earth (Gaia's birth moment), subtract 418 MY from 4320 MY. This give 3902 MYA. Divine 3902 by 4.32 (million years = 1 Geon) and you get 904 Geons. You could, of course, get the same figure by subtracting 96 Geons from the total 1000. It is easy to work back and forth on the timescale in Geons. When the Silurian began Gaia was 3902 million years old, reckoned by the geological timeframe. She had lived by that time into the 904th Geon. How old was she at that moment in her own time?
There are 43.2 Geons in a Gaian Year. 903 Geons divided by 43.2 = 20.9 years. The Silurian began as Gaia in her own time was reaching 21 full years, the age of adulthood in human development. Does this eccentric calculation make any sense? Well, in terms of organic maturity of the Gaian ecosystem— if that is how we define adulthood—the emergence of vascular plants was certainly the defining event. Today plant life constitutes more than 95 % of the entire biota of the Earth. Gaia is a plant-planet. The vast and diverse profusion of her plant-life is the predominant setting for all life. If it is acceptable to apply the analogy of geological time on the planet to developmental stages of human life, it would not be too ridiculous to imagine that adulthood for Gaia was determined by the emergence of vascular plants.
Is it surprizing that plant world—or, to be more precise, the foundation of the plant world existing today—emerges so late in her young life? The scheme of Gaian development follows the geological timeframe in this respect: a great deal of Gaia's lifespan transpired before life as we know it developed. The linear timescale shows slow development in geophysical and microbiological terms from 4500 MYA down to the Cambrian Age, 550 MYA. In other words, the first 872 Geons of Gaia's lifespan do not produce anything that supports life as we know it, but ti does, of course, produce the invisible microbial-molecular basis of life. No large animals or plants, no recognizable continental masses, evolve until after the Cambrian Age. The habitat and biota of the Earth today only began to develop after 895 Geons, approximately, counting from the formation of the Earth. In Gaia's own time, this is just as she attains the threshold age of twenty-one years.
The eccentric calculation may look preposterous to hardheads, but it can teach us many things about Gaian morphology. Even with the outrageous analogy between human and Gaian development—a gross act of anthropocentricism, to say the least—we can get a sense of Gaia's life process on her own terms. The method transcends itself by the results it yields. For instance, it shows us how different Gaia is from other large organisms and animals. Humans do not develop as a molecular-microbial mass and then, suddenly, around twenty-one, acquire the limbs, organs, and features characteric of a large animal. In fact, we acquire those features at an extremely accelerated rate, in the womb. But Gaia evolved in a different way, taking a long time before she brought the planet to its current configuration of continents, ecosystems, and biota.
The ultimate purpose of this eccentric calculation was to convert the geological timeframe into Gaian time. This done, we can look at how the Earth has evolved by analogy to the well-known stages of human development: birth, infancy, pre-puberty, puberty, adolescence, adulthood. Gaiology, as it might be called, is developmental psychology applied to the frame of geological ages.
In a companion essay to follow this one, I will sketch Gaiological development by correlating more key events in the standard geological timeframe, including periodic extinctions, to moments in Gaia's lifespan, considered in her own time.
jl: Nov 28, 2005
Material by John Lash and Lydia Dzumardjin: Copyright 2002 - 2018 by John L. Lash.