Garden of Eden States

1The garden in Venice whose story I would tell was once a bank of mud. Unconscious of its sweet destiny

2In her is the end of breeding.

Her boredom is exquisite and excessive.

3Instrumentality is considered to be the fundamental characteristic of technology. If we inquire, step by step, into what technology, represented as means, actually is, then we shall arrive at revealing. The possibility of all productive manufacturing lies in revealing. Technology is therefore no mere means. Technology is a way of revealing. If we give heed to this, then another whole realm for the essence of technology will open itself up to us. It is the realm of revealing, i.e., of truth.

4It happens that under certain reasonable assumptions about the tessellation structure there will always exist configurations which cannot occur except at time T = 0. That is, these configurations are not only unstable, but they are nonconstructible in the sense that there is no configuration at time T - 1 which will give rise to the given configuration at time T by means of the function f which defines the rules for the transition from one state to another. Such a configuration will be called a Garden-of-Eden configuration.

5This term, from the Biblical account in the second and third chapters of Genesis, was suggested by John W. Tukey. Since a Garden-of-Eden configuration cannot be produced by any other configuration, no self-reproducing configuration can contain a copy of a Garden-of-Eden configuration.

6The conditions under which these Garden-of-Eden configurations can occur involve the ability to perform erasing. After a blackboard has been erased, it is no longer possible to tell what had been written there; and by analogy with this, the term erasing is used by the designers of memory units in digital computers. Erasing is an irreversible process whereby a given action produces a state from which it is impossible to determine the preceding states from which it could have arisen.

7For a tessellation structure for which there exist erasable configurations, there exist Garden-of-Eden configurations.

8Such a Garden-of-Eden configuration corresponds to a machine which cannot arise as the result of any past state of its universe, but can occur only at time T = 0. This also corresponds to a machine which cannot be built out of the available parts, but whose physical structure can be described as an arrangement of those parts.

9(1) The universe is homogeneous.

(2) Space and time take on only discrete integer values.

(3) Only local action can occur at any one time.

(4) The universe is in Euclidean N-space.

(5) The laws of behavior of the universe are deterministic.

(6) Erasing is possible.

From these six assumptions (and perhaps other hidden ones which I have not noticed) it can be concluded that Garden-of-Eden configurations exist.

10Thus we have proved that the existence of two indistinguishable configurations is a necessary as well as a sufficient condition for the existence of Garden-of-Eden configurations.

11Practical experience indicated that entry into the separate reality or the nonordinary reality of the shamanic cosmology was most easily achieved through the use of hallucinogenic tryptamines. To investigate this assumption, we organized, early in 1971, an expedition to the Upper Amazon Basin to locate sources of organic tryptamines and to explore their possible relevance to the search for liberation into eschatological time.

12In the ancient world, including Egypt, there was an eschatological schema, according to which a time of decline and despair heralded the advent of final time. The historical events were read into this schema, as conversely the event that seceded from time was read into history.

13Humans are regarded as leading a wholly profane existence within a wholly profane time, that is, within history; the reality of the sacred is denied or reduced to the level of psychology. In non-Western cultures, in primitive cultures particularly, humans are not conscious of living in historical time, but regard themselves as inhabiting a numinous sacral time. If these humans are conscious of history at all, it is of a mythical, paradigmatic history, a paradisiacal epoch that lies beyond the attritional influence of profane time.

14In the midst of the orgy, a man whispers into a woman’s ear: “what are you doing after the orgy?”

15Utopia is no longer the domain of transcendence, it is the domain of simulation.

16Human beings are therefore the natural agents for a compression that is building up in the temporal world toward transition into some higher dimension of existence. History is going to end. This is the astonishing conclusion that I draw out of the psychedelic experience. And all the scenarios of history’s ending that haunt human thinking on the matter, ranging from the Apocalypse of John down to the latest prophecies of the flying saucer cults, are attempts to grasp or come to grips with an intuition of transcendental departure from business as usual.

17Soma is the light at the beginning and end of history. This is the notion. It infuses history. History is a process that it created for its own purposes. We are involved in a symbiotic relationship with a biological creature that is like a god because it is so advanced, different, and in possession of such a peculiar body of information compared with ourselves.

18History is the shock wave of eschatology. Something is at the end of time and it is casting an enormous shadow over human history, drawing all human becoming toward it. All the wars, the philosophies, the rapes, the pillaging, the migrations, the cities, the civilizations all of this is occupying a microsecond of geological, planetary, and galactic time as the monkeys react to the symbiote, which is in the environment and which is feeding information to humanity about the larger picture. I do not belong to the school that wants to attribute all of our accomplishments to knowledge given to us as a gift from friendly aliens. I’m describing something I hope is more profound than that. As nervous systems evolve to higher and higher levels, they come more and more to understand the true situation in which they are embedded. And the true situation in which we are embedded is an organism, an organization of active intelligence on a galactic scale.

19These are the apocalyptic concrescences that haunt the historical continuum, igniting religions and various hysterias, and seeping ideas into highly tuned nervous systems.

For the Eschaton, positioned in eternity, all things are somehow coexistent in time or outside of time. All events have already happened.

20All these images — the starship, the space colony, the lapis — are precursory images. They follow naturally from the idea that history is the shock wave of eschatology.

21Are the eternal laws of nature still evolving? Is there a realm beyond space and time that grants the patterns and the conditions for creativity, organization, and emergent evolutionary process or does the universe make itself up as it goes along? Are the causes of things in the past or are they in the future? Is there some hyperdimensional, transcendental Object luring us forward? Is history but the shadow cast backward by eschatology? Are we humans the imaginers or the imagined; or is history in some way a co-creation an unsettled, chronically evolving, funky partnership between ourselves and the hyperdimensional Pattern Maker?

22Imagination is a kind of eschatological object shedding influence throughout the temporal dimension and throughout the morphogenetic field.

23RUPERT: Your description of the imagination emanating from the cosmic attractor sounds to me like a combination of Plato, Thomas Taylor, and Teilhard de Chardin. It resembles the Omega Point that, according to Teilhard, is the attractor of the whole evolutionary process. Everything is being drawn toward this end point. This is like Aristotle’s conception of God as the prime mover of the revolving heavenly spheres. According to him, the heavens were not being pushed by God, they were being pulled by God. God is so attractive that the heavens keep on going round and round, eternal rotation being the closest they can come to the divine state of eternal bliss.

24Why the apocalypse is such a strong attractor is an interesting question. The attractor beyond all the doom may be another state of being that is extraordinarily blissful compared with anything we know here, as well as more perfect. This is the fantasy of the recovery of Eden, the Promised Land. There’s something quite magical and infinitely attractive about this idea that has motivated the entire historical process.

25ESCHATOLOGY: A branch of theology dealing with the “four last things”: death, judgment, heaven, and hell.

26OMEGA POINT: The state of complex unity toward which everything is developing, according to the philosophy of the evolutionary mystic Teilhard de Chardin, who described it as “a distinct Centre radiating at the core of a system of centres … a supremely autonomous focus of union.”

27TELEOLOGY: The study of ends or final causes; the explanation of phenomena by reference to goals or purposes.

28All the pain and suffering and war and desperation would somehow be repaid and made right through the intercession of the mystery of higher dimensions and a backward flowing logic of time that somehow undoes what has already happened. The wave of understanding that had been gaining strength since the twenty-seventh of February was so strong as to be nearly visible in everything around me. The lenticular shape of the approaching philosopher’s stone seemed to be everywhere that I looked. Every shape and form around me was pregnant with its unearthly, opalescent depths.

29If we trigger the eschatology, we will appear to act in the role of the Anti-Christ, but the real Anti-Christ is history’s distorted reflection of the Christ at the end of time — the cosmic Adam-anthropos. The eschatological Christ is Anti-Christ only from a historical perspective.

30The Other plays with us and approaches us through the imagination and then a critical juncture is reached. To go beyond this juncture requires abandonment of old and ingrained habits of thinking and seeing. At that moment the world turns lazily inside out and what was hidden is revealed: a magical modality, a different mental landscape than one has ever known, and the landscape becomes real.

31At one point I picked up a stick and in the sandy soil of our living area I scratched the shorthand symbol for “and.” I called it “the ampersand.” I found its binding fold in one corner of a quaternary Structure to be very satisfying. I began to imagine this symbol as the symbol of the condensation of the alchemical lapis. To me it appeared to be the natural symbol for a four-dimensional universe somehow bound into a 3-D matrix.

I spoke of it as the ampersand for several days, then I called it “the eschaton.” This I imagined as a basic unit of time; the combination and resonance among the set of eschatons in the universe determined which of the possible worlds allowed by physics would actually undergo the formality of occurring. “The formality of actually occurring” was a phrase from Whitehead that kept echoing through my thoughts like the refrain of a half-forgotten song. I imagined that at the end of time all the eschatons would resonate together as a unity and thereby create an ontological transformation of reality—the end of time as a kind of garden of earthly delights.

32But really, what Eros means in the Greek sense is a kind of unity of nature, a kind of all-pervasive order that bridges one ontological level to another.

33Eschaton comes from the Greek word εσχ, which just means “the end.” The eschaton is the last thing, the final thing.

It’s very important to science to eliminate from its thinking any suspicion that this eschaton might exist. Because if it were to exist, it would impart to reality a purpose, you see? If the eschaton exists, then it’s like a goal, or an attraction point, or an energy sink toward which historical process is being moved.

34Reality is accelerating toward an unimaginable Omega Point.

35Dense. Technical. Fascinating. Infuriating. Marvelously weird.

36This strange insectoid intelligence gently directed our authors to study the King Wen sequence of the I Ching, which just happens to be the oldest sequence in that ancient divinatory tool. What they found there was a pattern, a rhythm, a rhythm moving through time, maybe the key to time itself — a rhythm that danced its way through the millennia toward an omega point that the McKennas calculated to be the year 2012.

37In Greek mythology and in the German intellectual tradition, Dionysus is the proleptic god par excellence. He is “the coming god,” not merely in the sense that his coming is anticipated in the future for example, every destructive-creative springtime but also in the strong sense that his primary attribute is defined in terms of coming and recoming, not actual arrival. The true essence of the demigod consists in perpetually coming toward humanity from the future but not necessarily ever arriving.

38post festum (after the celebration), “which indicates an irreparable past, an arrival at things that are already done.” Post festum speaks of a kind of ontological belatedness “which is always late with respect to itself.”

39In such retroactive and repetitive compulsions does the neurotic history of the present produce—and reproduce—the future.

40However, if we look too far into the future, there is no future (at least not for us, as the punks affirmed so noisily).

41The years 2000, 2001, and 3001, the Millennium, the Eschaton, Utopia, Heaven, and the Level above Human: however we describe the object that lies at the end of history, it inevitably becomes the focus for intense cathexis—the libidinal transference of value. We project our most powerful fantasies onto the symbolic logic of these utopian artifacts. Just as the black monolith is stroked by early simians in Stanley Kubrick’s version of 2001: A Space Odyssey, so too the apocalypse is invested libidinally with a neo-Freudian reconfiguration of desire and transcendence. The millennium has become the ultimate seductive model, beckoning us toward the exquisitely elusive process of revelation.

42The word apocalypse derives from the Greek apokalupsis and apo-calyptein, meaning to “uncover,” “unveil,” or “reveal”: hence Revelation.

43All apocalyptic philosophies must acknowledge and respond to this technological paradox—a secular eschatology merely unveils a void. Eros and Thanatos must therefore permit a third term: Techné.

44In the end was the word, and the word was Baudrillard.

45This “something” at the end of time is the Eschaton, a necessarily ambiguous transcendental object at the end of history. Like the millennium itself, the Eschaton is a floating symbol, equally as seductive and opaque as Arthur C. Clarke’s monolith in 2001. According to McKenna, the means to reach it is as vivid and psychedelic as Stanley Kubrick’s famous climactic sequence at the end of the film; in fact, it is much more so, thanks to the magic mushroom and other potent hallucinogens.

46The Eschaton is an enigmatic name applied to a transcendental object which lies at the end of history. It is the last of the Last Things.

47If G is not surjective then there exist Garden-of-Eden configurations, that is, configurations without a pre-image.

• Theorem 6 (Garden-of-Eden theorem, Moore [53] and Myhill [55]). GF is injective if and only if G is surjective.

48It was determined already in 1972 by S. Amoroso and Y. Patt that it is possible to decide if a given one-dimensional CA is reversible [2]. In the same paper, they also provided an algorithm to determine if a given CA is surjective:

• Theorem 9 (Amoroso and Patt [2]). There exist algorithms to determine if a given one-dimensional CA is injective or surjective.

49In higher-dimensional spaces the questions are, however much harder. It was shown in [38,41] that

• Theorem 10 (Kari [41]). There are no algorithms to determine if a given two-dimensional CA is injective or surjective.

50In order to create a Garden of Eden (i.e., a pattern with no parents) in Conway’s Game of Life, we greedily proceed as follows: Consider one cell. If it is ON it has 140 parents, and if it is OFF it has 372 parents. Therefore we set it ON so as to have a smaller number of parents. Then we consider an adjacent cell. If it is ON then the two-cell pattern has 417 parents, and if it is OFF then it has 703 parents. Therefore we set it ON so as to have a smaller number of parents. We continue in this way, considering cells one at a time in a pattern that spirals around the starting cell. For each cell, we choose it to be ON or OFF based on which of those options results in the pattern having fewer parents. This algorithm eventually produces a Garden of Eden — that is, a pattern with no parents. This happens when adding cell 266.

51A generation that cannot evolve from a previous generation by following the rules of Life is called a Garden of Eden. An orphan is a minimal subset of cells of a generation that has no predecessor. In other words, each generation that contains an orphan is a GoE.

Several orphans have been discovered [11]. The smallest known orphan was found by Beluchenko and is shown in Figure 1. There exists no orphan fitting in a 6×5 bounding box.

52Checking whether a given generation is a GoE is difficult because Life is not reversible; instances of Life can have multiple predecessors or none. No automaton is known which can perform the reverse step. The reversibility problem scales exponential with the size of the input grid: a given generation of an n×m grid has 2(n+2)(m+2) possible previous generations. Of course, only a fraction of these generations are predecessors. This explosion of possible previous generations makes it difficult to verify an orphan.

53Garden of Eden (GOE) states in cellular automata are grid configurations that have no precursors; that is, they can only occur as initial conditions. Finding individual configurations that minimize or maximize some criterion of interest (e.g., grid size, density, etc.) has been a popular sport in recreational mathematics, but systematic studies of the set of GOEs for a cellular automaton have been rare.

54The content of Theorem 1 is most easily understood in its contrapositive form, ¬ (f pre-injective) ⇔ ¬ (f surjective), which can be written as ∃c1 ≠ c2 f(c1) = f(c2) ⇔ ∃c |f^-1(c)| = 0. In words, a function f fails to be pre-injective if there exist two distinct finite configurations of the same size that are mapped to the same configuration by f. Such pairs of configurations are called twins. A function f fails to be surjective if there exist configurations without precursors, that is, GOE configurations. Thus, the theorem states that a cellular automaton possesses GOEs if and only if it has twins.