R E S P I R O N O N - F I C T I O N

Time, the Sphinx

by Paul Doru Mugur

A. We do not perceive time directly so where does the idea of time come from? Time is created by comparison, time is an abstraction inferred from the observation of movement, time is a mental image, a metaphor, a little poem that our mind creates by inference and analogical thinking. Movement is the background for the idea of time. For us humans, there is always something that moves, that changes outside or inside our body. Even when nothing moves outside the body, the thoughts come and go and the heart continues to beat so there is always movement and change associated with human existence. On further analysis, in order to perceive movement and change you need some kind of neurological devices to memorize and compare different sensory inputs. The perception of movement is build up from comparisons between sensory data and it needs a certain type of memory (immediate memory). We are born with the perceptual apparatus for movement and the sensation of movement itself; although not primary this sensation is innate. On the other side, what we call time, contrary to what Kant have thought is not aprioric, time is a psychological and social construct that is different between individual and between cultures. This inner, personal time is not simply a distorted mirror of some external, mysterious entity but it is also relatively independent of it; complex relationship between different time domains stirred a millennia long debate between philosophers around its nature.

We build up the meaning of time in a certain language from our direct experiences; time is like the elephant in Rumi`s poem: our sensations, our perceptions and our immediate, short or long term memory capture different aspects of it from which then we attempt to reconstruct the whole.

Time has a complex structure and if we would compare it to an animal it does not, in fact, resemble an elephant but looks more like a sphinx, a chimera, a combination of several animals in one being and if we continue this comparison we can think of the different parts of this chimerical being, time, as being linked to different neuronal networks/mental systems. Time is like the scattered pieces of a puzzle or several puzzles that we try to fit together. I compared it to a sphinx but in fact we can never know its real form, we can never perceive it entirely in all its aspects.

-Time as present, as now. Linked to attention.

-Time as a fleeting process, as an ongoing action. Linked to attention and the perception of movement.

-Time as past. Linked to different types of memory.

-Time as duration. Linked to memory.

-Time as future. Linked to imagination.

-Time as simultaneity. Linked to memory and attention.

-Time as “as before and after”. Linked to memory and attention.

-Time as causality. Linked to our logical mind.

The paradoxical nature of time that combines in one notion movement and rest, presence and absence has fascinated the western mind since Zeno of Elea with his “arguments against movement” that Aristotle has tried to solve by defining movement using dual concepts as actuality and potentiality. For Aristotle, time is intimely related to movement and he defined it as ”the number of movement with respect to earlier and later. Time is therefore not movement but movement insofar as it has a number." Aristotle tried desperately to get away from the purely qualitative aspect of movement to find something that he could pinpoint, an objective quantity that is measurable. The development of physics to our date is a continuation of his idea that “Time is the number of movement” bluntly ignoring the fleeting aspects of time and concentrating only on its measurable aspects.

From this idea of numbers or strings of numbers separated only by the distinction between “earlier and later” comes the image of the time as a point on a straight line and as time running monotonously and continuously as it does in a well behaved clock. But the true nature of time does not have anything to do with the comforting/discomforting image of a ticking clock.

The paradoxical nature of time surfaces in microphysics when we attempt to obtain simultaneously a precise measurement of the position of a particle and it`s movement. At the heart of this impossibility predicted by Heisenberg indeterminacy principle lays exactly the dual nature of time that appears as static when we measure it as position and as dynamic when we consider it as movement. Classical physics took as granted time to be a measurable number and ignored its fleeting and unpredictable nature that is not only fundamental but it is also a source of perpetual novelty and complex outcomes as the modern developments in thermodynamics and chaos theory have shown.

In order to visualize this quantitative aspect of time we can change this image of a natural number on a straight line with other more complicated mathematical figures or more sophisticated type of numbers but, fundamentally, we should ask always ourselves:

Is time a number? Can time be measured at all?

Any serious investigation of time should take into consideration also its qualitative aspects.

B. We can attack the problem of time from different angles, using different conceptual tools: we can investigate syntactically the use of word “time”, we can look semantically for the different meanings of this word, we can search its etymology, we can analyze the different metaphors used to illustrate it but are all these intellectual games of construction/deconstruction going to tell us what time is?

In English time is mostly used as a noun but can also behave like a verb (we can “time” smth).

On the other hand, in the process of time passage, time is both the agent, the instrument and the action itself. “Time passes” but how? “Who” passes and “how” and “where” or “when”?

A la Wittgenstein, each time when we use the word “time”, we should analyze the precise context in which we use the word because “time” may take dozens of different meanings in different circumstances.

The word for time in English goes back at least 6 millenia to the Indo-European “dai”. In sanskrit “daya” means “to divide”, “to allot”, “to possess” but also, interestingly, “to have compassion”, “to sympathize with” so even in the original etymology the word had the paradoxical meaning of both “to divide”, “to split” and “to sympathize with” . “Dai” was taken into Germanic language as two words “tidiz” (a division of time) that became “tide” in English and “timon” that became approximately 1000 years ago “tima” (appropriate time) in Old English. Then, in Middle English “tima” became “tyme” from which our word “time” was derived. Note that in Sanskrit the word for time was “kala”. Note that in the North Germanic languages the word "tímon" became “hour”: Swedish: timme ("hour"), Danish: time ("hour") Norwegian: time ("hour").

In English, time has a more general meaning and the older sense of "appropriate time" only survives in expressions like "It is time to go," or "It is time for dinner".

Using the approach of Lakoff and Johnson from “Metaphors we live by” we can look at the metaphors related to the word “time” in different cultures. For example, the Aymara people, an indigenous group that lives in the Andes highlands, use for time a spatial metaphor that is exactly opposite to the one used by everybody else in the world. For us, the “past” is somewhere “behind” and the future lies somewhere “in front”. Aymara language uses “nayra,” the basic word for “eye,” “front” or “sight,” to mean “past” and “qhipa,” the basic word for “back” or “behind,” to mean “future.” which is exactly opposite to what we do. Logically, their metaphor makes a lot more sense because we can visualize the past but we don`t know anything about the future.

C. From the perception of the movement we build up the concept of a flow responsible for all the changes in our world and we attribute to this flow different characteristics:

1.unicity 2.continuity 3.universality 4.uniformity 5.order 6.direction 7.independence

1. Unicity

Is time really unique? During their recent history as rational beings on Earth, humans have given very similar answers to phenomena that, on one hand they considered essential for their existence, on the other hand they did not understand.

It is interesting to note that man has a similar relationship with time as he does with God (in some old cultures like Iranian, for example, time, Zurvan, was in fact God) so I think we can borrow a religious terminology and talk about monochronistic, polichronistic, bichronistic, trichronistic, achronistic and agnostic answers to the question: is there a time out there and if the answer is yes: is this time unique?

In philosophy and physics the idea of different times with more than one dimensions/ directions has been around for a while and there are several alternatives to the Kantian aprioric model of a unique time responsible for both change and causality.

It is interesting to note that man has a similar relationship with time as he does with God (in some old cultures like Iranian, for example, time, Zurvan, was in fact God) so I think we can also talk about monochronistic, bichronistic, trichronistic, polichronistic, achronistic and agnostic answers to the question: is there a time out there and if the answer is yes: is this time unique?

Achronism

-Since Parmenide (Julian Barbour, re-loaded) proposed the idea of a-temporality: no time. In this line of thought time is simply absent, change, motion and process are meaningless. There can be no interactions in this immobile, a-temporal world.

Bichronism

-If the now moves in time, there must be a second time, wrote John Dunne¹ in1927 in his famous book “An Experiment with Time” in which he describes several premonitions he had while he was dreaming. Then, in 1951, H. A. C. Dobbs² proposed another type of two-dimensional time based on the distinction between its transitory and extensional aspects. His assumption of a second time-dimension implies that there exists a second way of ordering the constituents of a temporal process, by means of a relation similar in structure to the relation of “before (or after) “or “earlier (or later) than.” The two time-orders thus generated would have the same complete logical independence, or mutual orthogonality, as the three extensive aspects of space relations commonly described by three orthogonal Cartesian coordinate axes.” In order to avoid the infinite regression trap of Dunne, Dobbs carefully noted immediately after: “This does not entail that the “becoming” aspect of time is two-dimensional.”

Then there are several philosophical models of many time dimensions Jack W. Meiland³ (1974) and G. C. Goddu⁴ (2003), etc.

At the present time there are several scientific multi-dimensional time (2 or more).

First there are the 6 dimensions= 4 space+2 time models of Merab Gogberashvili⁵ and Itzhak Bars⁶.

Trichronism

Then there is the model of Xiaodong Chen⁷ (2005) that continues the ideas of G. Ziino⁸ (1985) of a three dimensional time.

Polichronism

In the theory of relativity there are countless possible times that vary in function of the observer but time itself has only one dimension.

Agnosticism

The agnostics suspend their judgments on the matter of time structure.

Calabi-Yau manifold

2. Continuity: Is time continuous or discontinuous?

In the theory of relativity Einstein postulated a continuous space-time manifold but in the quantum world space and time may be discrete. Chronons have been proposed By Paul Davies and K. J. Hsu as theoretical particles or atoms of indivisible intervals of time. More recently, Smolin in his loop-quantum gravity searches for a non-string TOE has also been speculating about a digital nature of space-time. But the model of chronons is difficult to support. As the paradoxes of Zenon point out, if chronons existed, physical continuity, motion and time (relative interval) would not be possible. But, maybe, as buddhists imagined, the chronons are like beads on a string that touch each other and thus maintain continuous contact with each other.

Or maybe, the structure of time is similar to an ourobouros, the mythic serpent biting its tail and resemble a Klein bottle and beyond the chronon, the shortest time structure there is the largest time time-structure that I called a metachronon (beyond the chronon), maybe the chronon is like a portal towards the metachronon, which contains all the time that ever existed and will ever exist. Such a closed structure kindly suggested by my friend, Dr. Florin Popescu, may resemble a Klein bottle and has been used in different attempts to describe the structure of the universe. (see for example the work of V.N. Yershov, a physicist from Pulkovo Observatory in St. Petersburg, Russia)

Klein bottle(exterior)

3. Universality

In the theory of relativity, both special and generalized, there is no universal time. In the early 30`s in several papers, the cosmologist Edward Arthur Milne introduced two different times, one cosmic, one local. Also in the model of J.T. Fraser, the president of the International Society for the Study of Time (1966) and the Founding Editor of KronoScope - Journal, there are different times at different levels of organization of matter. According to Fraser, time has different strata, or time scales, rather than a single cosmic time or universal clock. This model, with six levels, was proposed by J. T. Fraser in 1975 in Chapter 12 of “Of Time, Passion, and Knowledge”. The first three levels in Fraser`s hierarchical theory of time are atemporality, prototemporality and eotemporality all of which deal with physical reality: the absolute chaos of electromagnetic radiation at the time of the Big Bang, the realm of particle waves and massive objects such as planets and stars, respectively. The fourth level is biotemporality, which is the time associated with living organisms, and among the characteristics of which are short-term time horizons. Following biotemporality in this hierarchy is nootemporality, which is the time of the human mind with longer, open-ended time horizons. Atop the hierarchy is sociotemporality, the time of a society produced by social consensus. This theoretical model is described in a set of eight propositions (J.T.Fraser 99, pp26-43) the elaboration of which provide many of the model`s details, including the points that the hierarchy is a nested hierarchy and that the hierarchy is open-ended, meaning that there is no necessary logic that indicates the time of human societies is the final temporal form that will evolve with the universe.” (“The human organization of time” by Allen C. Bluedorn, p.24). In an extreme version of this hierarchical model of time, there might be an infinity of strata, with self-similarity across scales. Such a model was proposed in 1975 by the McKenna brothers in “The Invisible Landscape”. Thus, zooming into the microstructure of time one gets lost, as each new view is much like the last. This is the structure of the mathematical objects called fractals, which abound in the mathematical theory of dynamics.

4. Uniformity

Is there a uniform time that flows continuously like a metronome? As Einstein mentioned in his book “Relativity, The Special and the General Theory” we take for granted that “clocks go at the same rate if they are of identical construction”, and, also, clocks are build up with the assumption that indeed there is a uniform and monotonous flow. In reality, each entity in the universe may have its own time-flow and for some of these entities time does not flow monotonously. In fact, each moment of time is new and we take for granted that all moments are of the same duration regardless of their position on the timeline but is this assumption correct? Can we build up a model of non-uniform, non-monotonous time? I am a physician and I can certify that not all 80 years old are the same: biologically some of them are 65 others are 90 and psychologically some of them may be younger than 20 so nature build up this model for us already!

Also, the perception of time is non-uniform for people of different ages. As the poet Guy Pentreath wrote:

"For when I was a babe and wept and slept, time crept, and when I was a boy and laughed and talked, time walked, and as the years saw me a man, time ran, and as I older grew, time flew".

and there are several very interesting mathematical models describing the variation of subjective time with the chronological age. In one of these models, the variation of the psychological age is proportional with the square root of the chronological age (In “Time, Quality of Life and Social Development”: “A Mathematical Approach to the Psychological Age”, Jose Leniz, & Gonzalo Alcaino and “Speculation of Factors Concerning the Influence of Time on Well Being”, Mihai Dinu, 1982).

The presupposition of the uniformity of time definitively needs further investigation. In the theory of relativity Einstein implicitly assumes that the rate of time flow is constant in a clock that is not accelerated and is not influenced by a gravitational field and this postulate needs to be revisited. If the structure of the universe itself changes continuously with time it is possible that each moment in time is in fact not only irreversible but also unique.

5. Order

In our experience time is ordered, the “before” always precedes the “after” and the “cause” always precedes the “effect”. Apparently, every sequence of events has a determined temporal order. We experimentally verify that specific events occur before others and not vice-versa. Certain events (effects) are triggered off by others (causes), providing us with the notion of causality. Fundamentally, the concept of time is strongly related to the idea of order of events, for Leibnitz, in fact, time was the order of events. But can we imagine a different order or multiple orders of events? The radical reformulation of physics conjecture, in which one abandons the causal structure of the laws of physics and allows, without restriction, time travel, reformulating physics from the ground up is, in fact, possible. (Visser, M. Lorentzian Wormholes: From Einstein to Hawking, American Institute of Physics, New York, 1995).

As suggested by Frederick Turner, “time itself may contain two directions of causality, a strong forward one and a weak backward one (or, more precisely, forward causes and backward “correspondences” or “evidential constraints”), then a feedback loop can be completed and time itself may be considered to be nonlinear and perhaps self-organizing, as nonlinear systems tend to be”. So, in a certain sense, time itself may be alive.

The question about time`s uniformity and order are related to our representations of time: Does time ressemble the real line as in Zenon`s paradoxes? Or maybe because of its cuantic nature is more like the interrupted line on the highway? Is time fractal? Is it a sphere? Is time`s structure complex and convoluted like the Capadoccia caverns?

6. Direction

Universe, in latin Universum, from latin uni, one, + versum, derivative of versus, “turned toward” so universe means turned toward one. But does the universe have a temporal orientation? Does time have a preferential direction? Is time irreversible and if this is the case, why, how did the arrows of time came into being in the first place? Does time at quantum levels have also a direction? In Wikipedia are cited no less than seven arrows of time:

-Thermodynamic arrow of time, determined by the Second Law of Thermodynamics, which states that in an isolated system, entropy tends to increase with time. –Cosmological arrow of time, the universe expands - rather than shrinks - by definition. –Radiative arrow of time, waves expand outward from their source. -Causal arrow of time. A cause precedes its effect. -The particle physics (weak) arrow of time. Certain subatomic interactions involving the weak nuclear force rarely violate the conservation of both parity and charge conjugation. An example is the kaon decay. Such processes could have been responsible for matter creation in the early universe. -The quantum arrow of time. In quantum physics the wave function collapse is irreversible in time. -The psychological/perceptual arrow of time. We remember the past but not the future.

To these arrows Roger Penrose added the “black hole” arrow of time: there are no white whole around and Stephen J. Gould added the “biological aging” arrow of time.

Finally, all these arrows seem to be reducible to two: the thermodynamic arrow of time and the particle physics (weak) arrow of time. These two arrows are thought to be a direct consequence of the initial conditions in the early universe.

Is gravity the cause of this arrow of time? Lawrence Schulman of Clarkson University in New York State argued that after 380,000 years of existence the universe switched from a chaotic high-entropy ball of fire to a highly ordered state - the first time it became cool enough for the constituents of atoms to combine due to gravity. "What was a high-entropy, typical, state in the earlier regime became a low-entropy, special state in the later regime," says Schulman. Did an arrow of time exist before gravity came into play and pulled matter together to create galaxies, stars and planets? We don`t know yet.

Competing Arrows of Time

Courtesy Physics News Graphics

The same Lawrence Schulman (1999) imagined the possibility that in the universe there may be areas with a reversed time arrow. Above there is a schematic diagram showing the birth of the universe amid the Big Bang, the subsequent expansion of the universe, and an eventual re-contraction ending in a "Big Crunch." The white circles represent matter in our universe subject to the "arrow of time," according to which a wineglass, after it falls off a table, will never reassemble itself and jump back up on the table. The black circles represent matter associated with a hypothetical inverse arrow of time.

Another deep mystery is the incongruence between the quantum evolution, governed by the Schrödinger equation, which is time-symmetric and the macroscopic asymmetry of time. Solving this enigma may be synonymous with finding the Holy-Grail of Physics, the TOE.

7. Independence

• Macroscopically, in the Theory of Relativity, time is not independent: it is related to space and also it dilates with increased speed or gravity.

Microscopically, in the Loop Quantum Gravity theory, time depends on the particles themselves and does not exist by itself.

D. We are not born with an innate sense of time, we build up the meaning of time in a certain language from our experiences.

Given the fact that we do not have a special organ to see time as we have eyes to see space and, so, we do not perceive time directly we can let our imagination fly freely and dream about what time could be in some fantastic dream-like scenarios.

I. First dream: the idea of the rhythm as a cosmic glue.

Harmonia

As a physician I interact with patients of different ages and I realize that age itself is not only chronological (Mr Smith is 75 years old) but also biological (Mr Smith has the body of a 60 years old) and psychological (Mr Smith has the sharpness of a teenager).

In medicine and biology we deal all the time with periodic phenomena: the metabolical reactions inside the cells, the cell division cycle, the heart, the breathing, the brain. Inside the brain there is the suprachiasmatic nucleus, or nuclei, (SCN), a tiny region on the brain's midline in a shallow impression of the optic chiasm, is responsible for controlling endogenous circadian rhythms like a master clock that binds many rhythms together. The circadian rhythm in the SCN is generated by a gene expression cycle in individual SCN neurons. The circadian rhythm in the first place originated in the rhythmic alternance of night and day.

Human beings are symphonies of co-dependent biorhythms and they are connected with the universe through rhythms.

The idea of rhythm as a glue has been developed by Francisco Varella on his work on neuronal synchrony via coupled oscillators. The neuronal synchronization hypothesis that “a specific cell assembly of neurons emerge through a kind of temporal resonance or "glue" and postulates that it is the precise “coincidence of the firing of the cells that brings about unity in mental-cognitive experience”. Different aspects of time as for example the perception of the now, the lived present, emerge as a consequence of this “frame or window of simultaneity” of activation of synchronized neurons.

We can extrapolate the model of Varella to the entire universe seen as a rhythmic structure in which the connection of the different parts is realized through temporal resonance.

This vision of time and rhythm as a cosmic glue is not original. In the Chinese culture, as shown by Francois Julien, (Du "temps". Elements d'une philosophie du vivre, 2001) there are words for “moment” and “duration” but there is no word for time as an abstraction that contains both these aspects. The word “time” as we know it in the Western Culture appeared in China only in 1908 imported from Japan and it has been translated as shijian “between moments”. On another hand the ideas of rhythm and the synchronization between the human world and the cosmos has been extensively studied in China.

Also in the Ancient Greece, for Pytagora and his fellow searchers of the hidden harmony of the spheres, time was some type of cosmic glue. In fact, harmonia the key word of the Pythagoreans and meant primarily the joining or fitting of things together. Aristotle characterizes the Pythagorean as having reduced all things to numbers or elements of numbers, and described the whole universe as "a Harmonia and a number". Aristotle continued: "They said too that the whole universe is constructed according to a musical scale. This is what he (Pytagora) means to indicate by the words "and that the whole universe is a number, because it is both composed of numbers and organized numerically and musically. For the distances between the bodies revolving round the center are mathematically proportionate; some moves faster and some more slowly; the sound made by the slower bodies in their movement is lower in pitch, and that of the faster is higher; hence these separate notes, corresponding to the ratios of the distances, make the resultant sound concordant. Now number, they said, is the source of this harmony, and so they naturally put number as the principle on which the heaven and the whole universe depended."

We can imagine a model of the cosmos in which all the events are bound harmoniously together through rhythmicity in a vast temporal network and in which the entire universe participates in the occurrence of a local event. In this model the whole cosmos pushes the minutest event to happen and the law of causality is replaced by the law of cosmic co-dependence.

There is a striking similarity between the genesis of the universe and the development of the living organisms and human societies that raises the possibility that time itself contains self-similar sequences on different time-scales and thus it has a fractal-like nature. In biology there is the Haeckel law, “ontogeny recapitulates phylogeny” to which we may add: “ontogeny recapitulates phylogeny recapitulates cosmogony”.

For Plato “time was the image of inifinity”; it was cyclical and it did not evolve. Recently, Garret Lisi built-up an ingenious model of TOE useing the exceptional simple Lie group E8. As Plutarch mentioned, harmonia also meant "octave", the scale of eight and, maybe, E8 is indeed a graphical representation of the temporal structure of the universe.

E8 pattern

II. Second dream: the idea of metamorphosis and evolution of time itself.

Hypertime

Does it exist uniform time that flows continuously like a metronome? As Albert Einstein¹⁰ mentioned in his book “Relativity, The Special and the General Theory” we take for granted that “clocks go at the same rate if they are of identical construction”, and, also, clocks are build up with the assumption that indeed there is a uniform and monotonous flow. In reality, each entity in the universe may have its own time-flow and for some of these entities time may not flow monotonously. Each moment of time is new but we take for granted that all moments are of the same duration regardless of their position on the timeline but is this assumption correct? Can we build up a model of non-uniform, non-monotonous time? I am a physician and I can certify that not all 80 years old are the same: biologically some of them are 65 others are 90 and psychologically some of them may be younger than 20 so nature build up this model for us already!

Biological time flows with different rates at different stages of development. The human development starts with an embryonic stage in which a single cell clones itself very rapidly into billions of similar but non-identical copies followed by a progressive deceleration of this fast growth through the end of the childhood until and a plateau is reached and the rate between growth and programmed death is maintained constant in the adult.

Also, as the theory of kalpas in the Hindu religion and then later Vico suggested, the development of human societies may have different phases with distinct time qualities associated to each of it.

Similarly in the Big Bang model we find also that the cosmic time has different aspects at different times of development of the universe with an initial period of extremely fast growing followed by a progressive slowing down. Initially, at the beginning, as Weinberg⁷ wrote “it was light that then formed the dominant constituent of the universe,” then, subsequently, the elementary particles were created from light, and finally only when the universe cooled enough for them to exist, atoms and molecules appeared on the world stage.

According to J.T.Fraser¹², time has different strata, or time scales, rather than a single cosmic time or universal clock. This hierarchic time-model proposed by J. T. Fraser in 1975 in Chapter 12 of “Of Time, Passion, and Knowledge” has six levels: the first three are atemporality, prototemporality and eotemporality all of which deal with the physical realm: the absolute chaos of electromagnetic radiation immediately after the Big Bang, and the realms of particle waves and massive objects such as planets and stars, respectively. The fourth level is biotemporality, which is the time associated with living organisms, then, the next level in Fraser`s hierarchy is nootemporality, which is the time of the human consciousness and the last level is sociotemporality, the time of human societies.

When the universe cooled sufficiently to permit the collapse of energy into matter, that collapse included a change from temporal symmetry into temporal asymmetry, and, we can imagine that the nature of time itself changed from, borrowing J.T.Fraser terminology, atemporality to prototemporality and then progressed to eotemporality, the cosmic time that is still present on a universal scale.

In order to explain the birth of the universe and the apparition of time in the Big-Bang model Stephen Hawking and James Hartle proposed in 1983 the notion of a secondary time line, called imaginary time line, perpendicular to the direction of the real time, like the latitude and the longitude on the surface of the sphere.

In their model like in all the other multi-chronistic models the extra-dimensions of time are independent of each other.

I am introducing here for the first time the notion of hypertime and I suggest that time has a complex structure that mutates, evolves, changes gradually in a non-random way and far from being a linear, monotonous progression, it contains several layers of events and meta-events that are constantly interacting with each other creating a complex hypertime structure with several co-dependent dimensions.

Like the hands in Escher`s drawing, the hypertime dimensions have a dual paradoxical nature of being simultaneously real and virtual, events and meta-events generating each other continuously.

The structure of time may be a lot more complex than that captured by the Hawking-Hartle model. A suggestive metaphor for hypertime is Kali, the Hindu goddess of time and destruction, with its six arms:

Kali Mata Baijnath Shiva Temple

or even better, Avalokiteshvara Bodhisattva, with his one thousand arms and eyes:

The hypertime model suggests the presence of a complex network of inter-twinned dynamics perpetual active both at the personal and at the cosmic level: in this model, the notion of time line is replaced by the notion of hypertime matrix and the notion of moment with the notion of hypertime matrix configuration. Inner (subjective) and outer (objective) hypertimes are considered qualitatively different and co-dependent.

The grid of events (drawing by M.C. Escher)

Every single configuration of the global hypertime is unique; it is different both from the preceding and the following configurations. The number of dimensions of these configurations may vary in different local hypertime zones and, in a given local hypertime zone, this number may change and/or loop from (hyper)time to (hyper)time. Because of these continuous changes, clocks can never be 100% accurate and they indicate only one specific dimension of local hypertime with a very limited precision. Of course, these imperfections do not stop us from using clocks in our day to day activities but they may become extremely important at the Planck level at which clocks become useless. On the other hand, no hyperclock can measure global hypertime simply because global hypertime lacks a recursive pattern.

What are the consequences of this perpetual metamorphosis of temporal landscapes for us? An interesting possibility is that as we approach what several philosophers called the post-humanity our constructs of time may change and time for the post-human beings may be something very different then it is for us now. In the history of the universe there have been already, temporal singularities in which the nature of time changed suddenly like, for example, the moment when gravity appeared on the cosmic scene several hundred years after the Big Bang.

Maybe also for the even the notions of now, duration, past, present and future will suddenly change in the future in some type of psychological singularity and a new type of noo-temporality or noo-sphere will emerge.

Far from being a science-fiction speculation this shift in the human experience of time may be already present in certain special states. Ten years ago, Metod Saniga from the Slovak Academy of Science studied several patients with a distortion of the sense of time and discovered that their brains seemed to be hard-wired to perceive space and time as interconnected. "Pathology in time is always accompanied with a pathology of space, in a sense that space either loses dimensions or acquires other dimensions," Saniga declared in an interview for Wired Magazine¹³. "When time seems to stop, people often feel as if space becomes two-dimensional. On the other hand, when the subject feels they perceive the past, present and future (all at once), they simultaneously have the impression that space has infinite dimensions." In 1999 Saniga¹⁴ described these states as two forms of what he calls a "pure present" experience. In one case the present is completely frozen, while in the other the present seems to contain both past and future events as well. Saniga also gathered similar reports from people that have near-death experiences.

As announced by Ray Kurzweil and other singularity prophets another possibility is that due to the recent advances in the technology a new temporal level, an etemporality akin to that described in the Matrix movie series will suddenly appear with profound consequences for the human history.

Where does the Chinese Box of hypertime(s) ends? Is it possible for a model that contains both events and meta-events to avoid an infinite regression?

Hawking-Hartle`s stratagem has been to make different temporal dimensions perpendicular to each other and to define only one of them as real and consider the other (s) virtual. Another solution is to imagine that the structure of the global hypertime is a closed surface with a fixed geometry that itself does not evolve in time, similar to a Klein bottle. By using this ouroboros-like geometrical shape we may avoid the logical trap of an infinite regression, but this visual analogy is by no means a demonstration that beyond global hypertime there are no other superior (a?)temporal entities that may regulate it.

Tuba Mirum - the innards of a Klein Bottle Klein bottle (interior)

An earlier draft of this paper was presented in New York City on June 7, 2009 at the Tank Space at a multi-disciplinary conference on time.

References

1. J. W. Dunne An experiment with time. (1927) A. & C. Black, Faber & Faber.

2. H. A. C. Dobbs The Relation between the Time of Psychology and the Time of Physics; part I. (1951).

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