One more century goes by, one more millennium is closed, requiring from this planet an evaluation of the results achieved up till now in wisdom and consciousness, a trial balance of humanity's long journey throughout the ages, burdened with its living history of sorrow and bliss. It's the flowing of time, in the direct and unavoidable feeling of daily existence. It's the presence of Chronos, the greatest of all masters, in his endless commitment to bring forth experience and knowledge, devouring his students afterwards: we, all of us, his offspring of transitory beings, however secretly eternal.

Human beings, supposedly bounded to the tracks of time, questions and interrogates ceaselessly. Pain and joy are companions that spur their expectations, their findings and their illusions. However, humankind's impulse to discovery, to reach far into mystery, is stronger and greater than all hindrances of life. We live in time but we don't know what it is. Speculations come from very far away, from ancient ages, in this time of always being. From Classical Antiquity to the Middle Ages, from the dawn of scientific thought to the inconclusive paradoxes of contemporary science, time continues, hieratically enduring as the greatest of all mysteries, even greater than the riddles of love and death, because the mystery of time is of the same lineage of the mystery of God.

Humanity works out elaborate calendars and scrutinizes nature's cycles. We use our speculative intelligence and our poetic sensitiveness, our imagination and our refined physical and mathematical tools. Many distinctions were already done (to know is to distinguish), many propositions were formulated, many hypothesis, many theories and a few doubtful certainties are the meager outcome. The mystery of time is so deep and serious that not even what has been thought about it can be refuted or replaced by something new that turn obsolete the older ideas. Everything which was already said about time continues to be valid - or doesn't have any validity at all. On suspect that the study of time is something like an endless skein: wherever we approach it, its end, if there's any, can be the same point where we started. Birds fly in the air and cannot see it. Fishes swim in water and are not aware of it. The human spirit is immersed in time but is not able to comprehend it.

In the West, our means to interpret the world are still based on Greek outlines. Our way of thinking and understanding was structured in Ancient Greece, and the models we adopt for reality were built there; these models have been readjusted and rearranged along the centuries, although they remain essentially the same. Plus ça change, plus c'est la même chose. The Hellenic world has generated, among many others, the remarkable genius of Euclid, author of The Elements, the most divulged book of all times after the Bible, and the most influent treaty in the history of science. For fifteen hundred years Euclidean geometry organized the perception of space in a clear and intuitive frame, which even today seems to be indispensable to a proper understanding of the objective world. Euclid have shown that length, width and height are the necessary and sufficient dimensions to insert an object in space, the empirical reality we live in. To localize anything in space we don't need a fourth or much less a fifth or sixth dimension: there is not even a place for them. Stephen Hawking, the English scientist, observed that "If there were more than three dimensions in space the planets orbits around the Sun [...] would be unstable and tend inwards following a spiral path".

From 18th century on several alternative geometries were proposed by Gauss, Riemann, Lobatchevski and others. However, they are only variations on that one by Euclid, be it so for their behavior in very large or very small scales or to their number of dimensions - which can be any, in the abstract propositions of mathematics. We should remember, however, that everyday world, the world of things and physical objects, the world where we live and move is undeniably the Euclidean three-dimensional world: any additional dimension is superfluous to properly characterize empirical space. It's naive to suppose that all abstract formulations of mathematics correspond to anything geometrical, and much less to anything physical or belonging to other parts of wholeness. If we can argue that a four-dimensional tesseract octahedroid could "exist" somehow, what could a solid of seven, 19 or 1322 dimensions mean? Such speculation should be as inane as looking for the meaning of a temperature of 450 Celsius negative, or what should have occurred in the universe 180 billion years ago or to wonder about the properties of the world in a scale of 10-340 cm.

While we drive along a road or travel by train, just one parameter will be sufficient to spatially localize ourselves: if we know the kilometer where we are we will be perfectly situated, since we move along a line which is one-dimensional space. However, if we're sailing in the Caribbean and wish to give our position, two numbers are necessary: we need to know the longitude and latitude of the point where we are, since we move in a surface, a space of two dimensions. Otherwise, if we drift in the wind aboard a balloon, three numbers shall be necessary to localize our position, since we will need to add our altitude to the longitude and latitude of the point over where we are, because the space where the balloon, the airplane, the condor and the albatross soar is the full three-dimensional space.

This is the Euclidean space, the empirical space, the world of life, action and movement. However, as we can perceive by the notion of movement, space is not everything. Since the Greeks, and much before, humans acknowledge the natural succession of the events, of the cycles of day and night, the phases of the Moon, the seasons, the sequence of birth, childhood, maturity, old age and the unavoidable encounter with death at the end of our journey. The mystery of the origins, the mystery of love that renovates and death which closes, the mystery of changes in things, places and people, the succession of wars, kingdoms, conquests and empires that end with a bang or in a whimper, all these are archetypal themes since the remote past and probably they will accompany the human drama in the near future.

Time is a god, says the human intuition since we appeared on Earth. Perhaps, almost surely, he is the most powerful of all gods. In a rare exception among world mythologies, Judeo-Christian is a culture which do not identify its god with time. According to our traditions, time was created together with the universe, non in tempore sed cum tempore incepit creatio, as stated Saint Augustine. By the same token, on the conception of time flow and the existence of spiritual creatures, Judeo-Christian myth diverges from most traditions. Time is seen as a linear, non-returning current, and the spiritual existence of each one of us is a unique non-repeated experience. Anthropological studies, however, show that in most cultures time is conceived as cyclical, sometimes in very long periods, as much as the lives of a sole spiritual entity are seen as repeated in many incarnations. Throughout the entire Bible - the Ecclesiastic, whose time is circular, is a notable exception - time is conceived as one single linear flow, with a unique beginning in the divine act of Creation and also an end of the times, when we all shall return to damnation or eternal bliss "forever".

The flow of time is not recognized as such in some cultures, and the notions of past, present and future do not constitute always the frame used to understand the world. This happens among the Australian aborigines, whose hundreds of diverse languages don't have even one word to signify time. But the most curious example is found in Arizona, with the Hopi Indians. They assort the events according to their degree of "credibility", being so the facts that happened in the near past or not far away are more credible than others more distant in time or space, considered less trustful.

However, in spite of examples as the Hopi Indians that show diverse perceptions of time in different cultures, the contemporary frame adopted worldwide, even in the occidentalized East, is the Judeo-Christian model, of Greek origins. Today, this linear non-cyclical time flow consolidates the theory of the big bang, the modern account of the creation of the Universe in contemporary science. Such a myth of the science of our days, however, is all but universally accepted, in spite of some findings of observational astrophysics that give support to it. There are many uncertainties, some of them capable of turning upside down the standard conception of the physical universe or, more widely, of wholeness. This term, more embracing than Universe, has been adopted to designate not only the physical universe acknowledged by astronomers as their field of study, but also the non-physical world of mind, which resides in the interior of subjectivities. Beyond that, it also comprises the hidden realm of the factors that act on the random events and accidents of the physical world, the inscrutable world of the ideal forms of Plato (where mathematical entities float), and also the "world 3", proposed by Karl Popper: the existential locus of the outcome of human mind such as the works of art; the social institutions; ethical values; symphonic music; the contents of books; scientific and philosophical problems and all theories - including the erroneous, silly and absurd.

A cosmologist's most fascinating doubt concerns to the uniqueness of the Universe. Up till now there is no way to know for sure if this is the only universe ever created or, alternatively, if it is part of a cyclical existence, whose present expansion phase is only a pulse of a much longer existence in an immeasurable time flow. The clearing up of this point absorbs many researchers attention and care who, in the labyrinths of particles laboratories and in the depths of radio telescopes explorations try hard to discover if the universe is "open" or "closed". Or, in other words, if it will continue to expand forever towards an inglorious thermal death or, instead, slow down the expansion rate to a halt, initiating then a long contraction phase to be ended billions of years later in a catastrophic big crunch, when all matter and energy will fall inwards, imploding spectacularly into a single point: the dreadful Doomsday black hole. It should be a kind of reversed fiat lux, a colossal apocalypse of unthinkable proportions, the most radical manifestation of the Lord's wrath, annihilating His entire creation in extreme iconoclastic desperation.

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2 – Insufficiency of linear time

However, there is still a remote hope in the possibility that such supreme hecatomb, that horrible ultimate holocaust be only the end of a cycle, just the preparation for a new attempt of the bewildered god trying to succeed with a Cosmos that finally satisfies him.

It's noticeable that the same duality about the conception of time comes out not only in contemporary science of the experiments and laboratories but also in recurrent traditions and myths of pre-scientific cultures. Nevertheless, this is not the greatest doubt: if time is a unique flow, without any new opportunities to repair a possible divine failure, or if creation repeats itself in a succession of cycles, as an incompetent god's attempts to improve his creation in each new trial. A conclusive answer to this question is improbable and certainly shouldn't be a solution to the problems of metaphysics and cosmology. Under a closer look we find out that this is not the dilemma and that the real question is of another nature. It only can be considered as a scientific problem if we abandon the narrow view of contemporary physicists and cosmologists, who cannot get a glimpse of anything beyond the universe they circumscribed as their field of study and research. The central question about time concerns to its dimensional nature.

If we scrutinize this question about the way time flows we verify that wholeness cannot be circumscribed in none of the hypothesis proposed by particles physicists, astrophysicists or cosmologists. First of all, it is mostly evident that it's indispensable to widen the narrow conception of Universe adopted by physical science and astronomy, in order to incorporate the vastness of the subjective world and the imaginary slope of being, the ineffable essence of the spirit that each of us is, or that Is us.

Since this point is well established, it will become evident that the linear conception of time as a continuous flow from the past to the future - or, otherwise, from the future to the past, in another possible reading - be it so cyclical or non-cyclical, cannot explain the psychical face of being, the mental world, the subjectivity centered in each one of us as a mirror of the objective world of things, events and living. Linear time simply cannot contain wholeness, in the sense we describe it.

There are unaccountable recorded facts that show meaningful ruptures in the apparently continuous flow of the river perceived by Heraclitus. Let us see, as examples, some of the premonitions recorded only in the literary outcome.

How could Jonathan Swift foresee, in his Gulliver's Travels, that planet Mars has two moons which revolve in opposite directions, more than a century before science discovered that? How did Jules Verne know in his novel From the Earth to the Moon, with an anticipation equivalent to Swift's, that the conquest of the Moon would be attained by an American vehicle with a three men crew that should depart from Florida for a three day trip and in its return would splash down in the sea? How could H.G. Wells, in his book The World Set Free, describe a war that would take place in the 1950s, where football sized atomic bombs were dropped from aircraft with explosive power to destroy an entire city? This was written in 1913, when no one had an idea of what a chain reaction could be, nor that atoms could be disintegrated yielding fantastic energy. Finally, to stop an endless series of examples, how could the obscure American writer Morgan Robertson, in a 1898 novel named Futility, describe the wreck of a brand-new liner named Titan, sunk in its maiden voyage between England and the United States, after a collision with an iceberg, with hundreds of casualties due to the lack of life-boats? This book describes with such a wealth of details the ship, the travel and what came to happen in 1912, in the sinking of the Titanic, that it should be a serious object of consideration by everyone who intends to study what time really is. The flood of premonitions that occur - and the press reports - related to happenings that result in collective emotional shock have been studied in many universities and research centers. A sweeping new conception of time certainly will come up from these studies with important effects on science and philosophy.

We live in a very meaningful epoch of humanity's history. This Symposium is an eloquent evidence that science, the arts, philosophy and religious mythology can and should unite as in Classic Antiquity and in many ancient cultures not committed to Judeo-Christian set of assumptions and all its unfolding into the metaphysical basis of Western science. I am sure that this merger will happen without a need of science to abandon the rigor of its methods, without the arts having to lose its creative freedom, without philosophy having to adjust itself to ideological molds and without many fertile religious myths of all peoples continue to be disdained as irrelevant fantasies.

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3 – Do we need crazy  ideas?

Presently, in most scientific circles there is a growing rejection of the standard four-dimensional space-time lattice as proposed in my good friend Albert Einstein's special theory of relativity. This uneasiness has been manifested in several scientific fields through some of their most representative voices. There is a diffused consensus that such a dimensional framing cannot be adjusted even to the phenomena studied in the laboratory experiments of quantum physics. Some awkward proposals have been made lately in the context of scientific theories that surge and disappear in the almost desperate trials to understand the elementary constituents of the universe - if these constituents really exist. One of these propositions admits that each subatomic particle has its own set of space dimensions, what would give as a result that an object formed by 1035 particles should be situated in a structure of 1035 3 dimensions. This is surely absurd, except to the mind which conceived such an idea.

The crop of theories in the science marketplace included, by the end of the century, the so called great unified theories (GUTS), supergravity theory, the largely praised superstrings theory, the never attained theory of everything and several others. This rapid succession reflects very well the headaches faced by those who meddle in the intimate parts of matter and the universe. The results have been disappointing. The late scientist Heinz Pagels, who was the President of the New York Academy of Sciences, desolately declared in his 1985 book Perfect Symmetry: "Most people who work [in these theories] feel that some crucial idea is missing; without it theories simply do not describe the real world" . What could be this crucial idea? Should it be something still more awkward than some crazy ideas which became fashionable after he logical crisis started by the bewildering paradoxes of experimental physics?

Wolfgang Pauli, one of the founding fathers of quantum physics, and a most respected 20th century scientist, once came to Columbia University to give a lecture upon a new theory of elementary particles, proposed by Heisenberg. I was in the audience and also was Niels Bohr - who can be considered the pope of modern physics. After the lecture Bohr remarked that the new theory couldn't be correct because it wasn't crazy enough. Soon, both men were sitting at opposite ends of a table with Bohr arguing that "The theory is not crazy enough!" and Pauli insisting loudly that "It is crazy enough to be true!". It should be very difficult to someone passing by to understand that it was a discussion between two great scientists, not a quarrel between two deranged old men.

It's my position that such a race for crazy ideas is leading us to nowhere, in spite of the seductive mathematical formalisms and misleading experimental clues that allure some physicists suggesting they are in the right track. Sometimes I wonder if the good Lord amuses Himself on the naive trials of those who hope to spot Him concealing His hand, or hiding the secret blueprints He used to create the universe. Albert himself once confessed that his wildest dream was "to discover the plans God used to make the world. The rest are details".

Stephen Hawking recently expressed his view that very little is missing to complete an all explaining "theory of everything", which would throw scientific research into the dull task of filling up the lacking details of the picture . Hawking doesn't show to be aware that he repeats the same illusion of science one century ago, when it was supposed that everything which was to be known about the physical world was already discovered, "remaining only the detailing of minor aspects to be done". This happened at the same time Lord John Rayleigh was calculating the spectrum of a black-body, discovering the annoying phenomenon called the ultraviolet catastrophe, which cracked from top to bottom the whole building of classic physics. Rash statements like these show the force of the standard paradigm in certain phases of the scientific development, capable to lead men of brilliant intelligence to state foolish ideas, somewhat obvious to those who are not committed to the paradigm enticements.

Under a benevolent view, a paradigm can be defined as a constellation of assumptions and beliefs, scales of values, techniques and concepts shared by the members of a certain scientific community in a moment of its history. In a more accurate description, a paradigm is the set of accepted proceedings, usual ways of thinking or vices of thought, of logic-metaphysical prejudices that block the scientific development in a certain epoch. These hindrances confine the scientists of a community into a limited universe of study, with a previously established spectrum of acceptable truths and conclusions. Thomas Kuhn have shown how paradigms establish a priori what can or cannot be accepted as true, in a certain epoch of the history of science. The bondage to a paradigm have leaded respectful researchers to reject entire segments of their own experiences, to deny evident results of experiments, or to neglect facts and possibilities which a less committed look or judgment wouldn't let to escape.

The adherence to a paradigm is essential to any responsible scientific undertaking. However, the risk is that a rigid commitment to its limitations block - as it usually does - the free interpretation of facts which cannot be understood within the field previously established as acceptable. Wholeness offers a multiplicity of diverse aspects to observation and understanding. So, what results of a non-critical acceptance of a paradigm is the jettisoning of entire continents of human experience as improper to scientific approach. Another consequence of such unrestrained adoption of a paradigm is the establishment of specific forms of questioning nature, limiting and conditioning the answers it should yield. An important advice was made by Heisenberg when he remarked that in scientific experiments we do not see nature itself, but rather nature submitted to our peculiar way of inquiring it.

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4 – What Einstein couldn't see

With respect to the specific subject of time, the central theme of this lecture, curious things have been happening as a consequence of the constraints imposed by the standard paradigm. First, we notice a specific blindness in some of the most outstanding personalities of science to certain results of their own experiments. Then, a repeated refusal to acknowledge obvious interpretations of facts emerging from experiments, if the case requires a basic reformulation of some aspects of the standard paradigm.

First of all, let's see my friend Albert Einstein's refusal to admit that time, being an imaginary value - as suggested in his special theory of relativity, and more clearly stated in Minkowsky's considerations - should be understood as something connected to the subjective world, something imaginary, which appears in the physical-spatial world as a projection of a geometric nature. Albert "saw" time has to be imaginary, but he didn't realize its subjective, non-physical character, so he could not develop the unfolding of this remarkable finding. Through this particular point - which passed unnoticed as a consequence of the Newtonian-Cartesian materialistic paradigm - science could jump over the metaphysical wall which averts physics of accepting the imaginary, the spiritual, the vastness of our inner world that forces its presence in the recent paradoxical experiments of quantum inquiries.

Minkowsky, in his paper "Space and Time" - presented to the 80th Assembly of German Natural Scientists and Physicists, which has taken place in Koln, September 21st, 1908 - introduces imaginary time in his proposal:

We can determine the ratio of the units of length and time beforehand in such a way that the natural limit of velocity becomes c=1. If we introduce, further, Ö -1´t = t (tau)  in place of t, the quadratic differential expression d2 = dx2 dy2 dz2 ds2 thus becomes perfectly symmetrical in x, y, z, s; and this symmetry is communicated to any law which does not contradict the world-postulate. Thus the essence of this postulate may be clothed mathematically in a very pregnant manner in the mystic formula: 3´10⁵km=Ö-1 secs (our italics).

Some years later, Albert repeated in his book Relativity, the Special and General Theory:

... Minkowsky's discovery [...] must be found mainly in the fact of his acknowledgment that the four-dimensional continuum of relativity [...] shows a pronounced relationship with the 3-dimensional continuum of Euclidean space. However, to give the right importance to this relationship we should replace the usual coordinate t with an imaginary value t=Ö -1´ct proportional to it. In such conditions, natural laws that satisfy the special theory of relativity exigencies assume mathematical forms where the time coordinates act precisely in the same way as space coordinates*.

However, in spite of the acknowledgment that t needs to assume its condition of imaginary value to satisfy its own theory propositions, this was not interpreted - either by Albert or any of his successors - as a clear indication that time is an imaginary subjective dimension which insinuates in the physical world through a projection. This is an ancient proposal of philosophy, of poetry and of the thought known as "mystical", that for centuries hold their own views on this mysterious and basic field.

Another aspect of the nature of time also discerned by Minkowsky and Einstein but ignored by later science concerns to the linear flow, usually associated to a line, as Heraclitus' river, which he saw as a projection of a more complex dimensional set. What puzzles me sometimes is that science, so many times beneficiary of cunning mathematical artifices, inserted in its interpretations and equations as esthetic resources didn't notice and reject the strange and asymmetrical dimensional organization of the world formed by three dimensions of space and only one of time.

It's a well known fact that Maxwell's equation for the unified electric and magnetic fields in its final form wasn't obtained through strictly mathematical deduction processes. Dissatisfied with the equation deduced by "honest" mathematical analysis, Maxwell considered it esthetically poor and introduced an "illicit" alteration which changed its form to a more elegant configuration. With this "dirty trick", Maxwell obtained a nice and balanced equation which responded more perfectly to the observed phenomena. This was not the only case of sleight-of-hand in mathematical deductions applied to physics, sometimes with excellent and unexpected results. Unfortunately, my limitations of time in this lecture (here it is, present and imposing its conditions!) doesn't permit to extend into other examples.

Anyway, I wish to remark that for me it seems curious that physicists' sense of esthetic didn't react to such a painfully unattractive structure of a lattice which has three dimensions of space and only one of time. What could limit or thwart someone's proposal for a more symmetrical framing, something esthetically more appealing, as Maxwell surely would do? Should 20th century physicists be less sensible than their predecessors? Certainly not. The remarks by Paul Dirac on the esthetic of nature and physics are well known: "God used beautiful mathematics to make the universe" and "it's more important to have beauty in equations than to adjust them to experience" . More recently, the physicist-clergyman J.C. Polkinghorne almost reaches an ecstasy of esthetic pleasure in his book The Quantum World: "Schrödinger's equation is one of the most beautiful differential equations ever conceived by a physician. Everything in it is mellowness and continuity..."

So, why should we accept that awkward structure that looks like a strange animal with three legs in the right side and just one in the left? The answer, in my view, is the sacrosanct paradigm. Why the standard paradigm rejects any proposition for a more pleasant frame - a six-dimensional lattice, for instance, with three dimensions of space and three dimensions of time - if particle theories admit even greater number of dimensions (some of them quite unlikely) to their formulation? The Kaluza-Klein theory, which for several decades disputes its place as an explanation of the universe, requires eleven dimensions to be mathematically formulated. We surely agree that number eleven, prime and unpleasant, is devoid of any symmetry that appeals to our esthetic taste. I think the answer to these questions is related to the same mental blocking that prevented my dear Albert from seeing the world of the spirit in the imaginary character of time, in spite of his good personal feelings, prone to a deep spiritual relationship with his fellow creatures, and with the supreme cosmic order - which he used to identify with his conception of Divinity.

In spite of the refusal of physics to accept something so simple and clear as a system with three dimensions of space and three of time to support the cosmic wholeness, this proposal frequently shows up in the hazy world of quasi-scientific speculations. Such six-dimensional frame can be found in thesis and ideas of men considered as respectful among their followers, nonetheless seen with despise - or, at least, with distrust - by the scientific establishment. I refer to those authors who thrive in a shadowy region of doubtful and controversial knowledge, relegated to the condition of "mystics" by the learned elite, a word uttered almost as an offense, with a heavy negative charge while used by a scientist proud of his status and eager for the reverence of his colleagues. This pride and eagerness is the real cement that consolidates the standard paradigm in the scientific community.

The Italian mystic Pietro Ubaldi, in his pretentious work The Great Synthesis, and P.D. Ouspensky, disciple of the notorious Gurdjieff, both propose six-dimensional structures for their intuitive models - in many ways, wrong - of the universe. Apparently they didn't know each other's work, but both settle three dimensions of space and three of time to hold together their systems. I do not endorse this kind of speculation, usually devoid of basic information and lacking trustful methodological approach, nor I have any particular sympathy for these gentlemen; nevertheless I must admit that most creative ideas that later became science have flown in by intuitive channels. Both authors, who are not scientists, and several others - such as Pierre Weil, whose status is less clear - propose a six-dimensional lattice to hold together their universes but do not extend any explanations about its consequences and how should such frame adjust to the understanding of wholeness.

That's what I intend to do now.
____________
* This revealing text shows how Albert recognizes both imaginary character of time and its dimensional plurality. The unanswered question is: why didn't he develop this finding in his later work?

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5 – Six-dimensional spacetime

I want to show how a structure formed by three dimensions of space and three dimensions of time can account for all phenomena and possibilities contained in wholeness, at least until the horizons our intelligence, intuition and feeling permit us to reach.

First of all I wish to confirm my initial statements on space, which I see as Euclidean and 3-dimensional, albeit it can assume hyperbolic or elliptical variations at the whim of the scientist who studies it in special conditions or scales . However, I discard Hilbert's n-dimensional spaces as entirely abstract entities, essential to many mathematical formulations but devoid of any factual correspondence to the empirical world where we live in. I also discard the remote worlds of quarks and quasars whose existence is, to my view, entirely instrumental, without any relationship to our living experience of greed and bliss, my basic reference in our path to knowledge and true wisdom. About such distant entities I dare to say that even the verb to exist should be well qualified when applied to them.

I propose that Euclidean 3-dimensional space adjusts to the objective face of wholeness, that one we call real, the existential locus of matter and objects that physical science recognizes as such. On the other hand, time, which is also 3-dimensional, is the existential locus of the subjective contents - the subjects - that we identify to the imaginary face of Being, whose center is inside each one of us. Each incarnated spirit, or subjectivity living on Earth, human or not-human, is a complex entity, formed by a real or corporeal part, and another psychical or imaginary. This outline doesn't deny the existence (should existence be the proper word?) of entirely imaginary sentient beings, or entities whose "real" face hardly would be recognized as such by our means of perception. Our body occupies space and our soul - the mind, or psyche - is a creature of time . As complex beings, we inhabit 6-dimensional space-time in spite of not being aware of such dimensional frame in its completeness.

Linear time of clocks and calendars, such as recognized by physics, is only an expression of 3-dimensional time shrunk by a geometrical projection, a forced reduction which compresses the imaginary world by reason of the cultural conditioning of our perception. Sometimes we represent space by a coordinate axis and time by another, in some concise graphics of scholar books, unaware that if 3-dimensional space can be compressed into just one line, the same can be true for time. So we could be unconsciously doing this. About graphics, it's worth to remark that all of them use geometric projections, a useful resource for some needs but which make others difficult. It's noticeable that if we can easily draw a graphic which resumes 3-dimensional space in one axis and time (secretly 3-dimensional) in another, we hardly could draft a graphic representing a point - or event - in the relativistic 4-dimensional system. Simply, such a projection is not possible or, at last, it should result confusing if we try it.

It's very important to be aware that time and space are different things, although they can be converted in each other, as Albert have shown. After relativity, it's a commonplace to believe that pairs like time and space, or matter and energy, are one sole thing. This is not exact, and to believe that can be more confusing than enlightening. Time and space are convertible one into the other in special circumstances; however, they are distinct ways we use to perceive the world , in the same sense that matter and energy - explosively convertible in each other - are different contents of this world.
Length, width and height are not distinguishable in their own and they only take these names when we ascribe to them. Length has not different intrinsic qualities from width or height, except in a specific referential frame which requires some subjective assumptions to make them distinguishable. We cannot see such dimensions of space as separate entities, unless we use deliberate criteria to do it. We perceive space as a whole and length, width and height are our spirit's constructs just for a better management of it. These obvious considerations turn to be necessary because in my proposition they are not valid for the three dimensions of time.

But - we can argue - if our perception of space is actually of a volume, which contain or may accommodate volumes, 2-dimesional surfaces or lines, why don't we feel something similar about time? Why the mental picture we make of time is always that of a river which continuously runs, a chariot which makes it's way in a road, something that flows steadily, irrevocably, linear? I reply that such view is a shortcoming of our cultural conditioning that shaped our cerebral structure throughout many centuries. As I said before, the three dimensions of time, such as those of space, are around us, we are immersed in them although we are not aware of them. The metaphor of the linear flow of history as a river is embedded in our minds confining the world we can see as much as the linguistic structures we impose on reality, molding and shaping the world to make it understandable. The contrast is that such an imprisonment of 3-dimensional time in its linear cage is still more deep, once it's the linear time of sequential speech that conditions and models linguistic structures.

Today, linear time has the tremendous force of an archetype and the sweeping power of a god. It's true that we are subject to many of its constraints but this is also valid for space. We cannot move without encumbrance along linear, or 2-dimensional nor 3-dimensional time. But the same happens to space: even if we acknowledge its broad 3-dimensionality which unfolds up to the clouds and interstellar space, we are not free to move in it as one pleases. We are constrained by physical limitations, bounded to the Earth's surface, to the size of our ship or to the bars of a jail. The prisoner sees the blue sky and the far away mountains through the rails of the window, but he can only move in the tiny world of his cell.

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6 -- Two-dimensional time

First, we need to know what 2 and 3-dimensional time really are, and then to study a way - and by which means - we could move in these realms. It seems clear that we can figure out what one-dimensional time is. I just have to look at the seconds hand in my watch or at the maze of my wrinkles in the bathroom mirror to have a feeling of linear time. But, what could be a 2-dimensional time? What should be the metaphor that could adjust to it, or what kind of mental picture can we make of it? Why doesn't 2-dimensional time appear in the instruments and observations of physicists?

To understand what 2-dimensional time is (and also 3-dimensional) it's necessary to accept its imaginary - hence subjective -character, as bounded to the imaginary face of wholeness, which discloses only through subjectivities: spirits or sentient beings, human or other. It's necessary to become aware that time is something essentially subjective, which manifests in the space of physical things as a projection of geometrical nature. It's essential to understand that transformation, even when it occurs in physical things of space, doesn't imply time, and that time is transformation being perceived by some subjectivity . Without a participation of the subjective and imaginary slope of wholeness there is no time nor movement - although there can be transformation. I recall Ernst Mach's still valid remark in his classic book The Science of Mechanics: "It is utterly beyond our power to measure the changes of things by time. Quite contrary, time is an abstraction, at which we arrive by means of the change of things." Without its subjective and imaginary face the universe would be only an immense decaying corpse, and the transformation that could occur there should be only a kind of rottenness - by reason of entropy.

This is unthinkable to a "hard-nose" physicist, usually prone to smile condescendingly from inside his cage. But his smirk may vanish when he recollects the notion of a particle's proper time, which is basic to the formulation of general relativity and to qualify any quantum object: "an absolute concept of metaphysical flavor" as quantum physicist Bruno Bertotti once said to me. Many quantum scientists consider this basic notion - a very difficult one for mathematical treating -, as a key for unexpected doors to the subjective and imaginary slopes of wholeness, doors that no one dared to open really wide, up to now. And that smile certainly will disappear if he becomes aware of the utter implications of linear time as definitely bounded to the observer, the way special relativity puts it, demolishing the Newtonian concept of simultaneity. At last, maybe something awakens in this physicist's spirit if he concedes to face open-heartedly the longtime controversy between the physicists' notion of time and the more widely spread psychological time of the rest of humanity.

Time is imaginary and subjective. The notion of 2-dimensional time emerges when we get aware that each subjectivity has its own proper time, its exclusive worldline, also defined by Minkowsky in that very paper already a century old, where he has shown the imaginary character of time.
Surface-time can be conceived as the sideways move of an individual worldline through the subjectivities that crowd the universe, human or otherwise, incarnated or not, whichever terrestrial or inhabitants of far away cultured celestial bodies , even unlikely odd beings of interstellar clouds or abiding unsuspected regions of Tartarus and Elysium. In this conception, disembodied spirits have no "existence" in 3-dimensional space, only in time. Channeling phenomena of interaction with alive humans or several kinds of materialization should be taken as similar to geometric projections yet to be studied.

But - it can be argued - aren't these entities known to be discrete, individual, discontinuous? Certainly not! They are not separate. All subjectivities that aspire to the right of existing (whatever this may mean) are dots in a vast continuity, like the countless emerging peaks of a gigantic submersed mountain range. We are the islands this ridge forms, deceptively separated from each other in our bodies and our vanity. Such continuity is the oneness of spirit, the imaginary slope of uncountable complex beings that pervade the entire cosmos embedded in its 6-dimensional lattice.

Sideways motion in surface-time cause short-circuits between subjectivities, perceived in our vicinity as synchronicities or telepathy. Telepathy doesn't imply time or energy because there isn't any transmission or reception of anything. The phenomena we call telepathic are just the fortuitous sharing of the same thoughts, feelings or information by two or more subjectivities not linked by physical communication media. So, what really happens is a kind of sudden and surprising short-circuit in surface-time. Unexpected motion of a spirit or its "sensing organs" along its own worldline, or in a bundle of worldlines, explain presages, omens and premonitions. The vehicle for these movements is emotion, when it surpasses a certain critical limit yet to be studied. That's why most authentic prophets become weary and suffer great loss of psychical energy of an emotional nature when they wield their powers too intensively. It's also for that reason that events that cause waves of premonitions almost always are a kind of happenings able to trigger strong collective emotions, such as catastrophic earthquakes, large shipwreck or the murder of important and esteemed personalities.

It's usual in literature that a fiction book, after some years of its publication turn out to be a foresight of actual facts to happen later. This occurs because creative imagination is a name given to the freedom an artist-writer's spirit have to move along the superior dimensions of 2 and 3-dimensional time, capturing other epochs and boundless collective experience. They access past memory as well as future foresight, reaching the sources of a permanent knowledge sometimes called transpersonal unconscious. It's a mistake to say that an artist is like an aerial or antenna, once nothing is transmitted or received. An artist is a free being, able to ride short-circuits and soar over unexplored or remote regions of imaginary time, bringing with him that experience to share with others through his artistry.

The metaphor of the sideways movement of a worldline, as a resource to understand 2-dimensional time is a clear analogy with the generation of a surface in Euclidean space through the lateral motion of a line. This way, 2-dimensional time is the fabric of countless subjectivities that pervade the universe, each one bearing its proper time, individual and linear.

But - someone could ask - how can the time we see in clocks and calendars seem the same, common to everyone? Initially I reply this is not exact, as states quantum physics, as well as relativity. Then I add something new: I am convinced of the existence of a principle of consistency, which allows the compatibility of interacting subjectivities' individual times. This new principle of science, which comes out to join others discovered in the beginnings of quantum physics, states that interacting subjectivities' individual times connect to each other in such a way a perfect illusion is created: clock time seems to be the same for all of them, as if they were sharing a common good. But this can occur only among interacting subjectivities, only if they are in touch or, in a sense, communicating by physical means. Non-interacting subjectivities can be bounded to very different individual times. Or, in other words: to look for an equivalence between individual times of non-interacting subjectivities doesn't make sense, once they are bounded to universes that actually are not communicating. I think most of the scientists who listen to me now acknowledge this proposal as not far from an extension of quantum and relativistic long lived findings.

Three-dimensional time, however, remains beyond human skill for abstract thinking and imagination. Three-dimensional time is the realm of gods. But a glimpse of its structure can be attained by the same geometrical expedient we used to understand 2-dimensional time, and should be seen under the strict limits of a metaphor: 3-dimensional time can be generated by a dislocation of 2-dimensional surface-time - formed by the weaving of many subjectivities - in a direction perpendicular to that "surface". This way we create something similar to a "volume", an inconceivable imaginary volume, the absolute volume that engulfs the evolution of wholeness, which contains everything and has no limits nor outside. Three-dimensional time is the most close equivalent we can conjecture of God's mind, as well as three-dimensional boundless space - the universe - could be a metaphor for the locus of his physical body. In one of his texts the Christian theological philosopher Thomas Aquinas said:

In spite of all events manage to become real successively, God doesn't know them as we do, that is, in the sequence of their happening. He knows them simultaneously. All things are present to God, in eternity, because His look sees everything as present.

Later, he said:

The soul is part of time, existing above time, in eternity: it encompasses nature but surpasses physical movement as measured by time. Time is the measure of transformation; eternity is the measure of permanence.

Here we touch the ineffable borders of Eternity. Whoever can freely move in these premises is a god - or Himself.
Closing this Gnostic journey to the fringes of the knowable we see, with awe and disbelief, that time, as the physicists see it, this time where entropy abides, our common linear time of clocks and calendars, of erosion and wrinkles, this quotidian time which drip drip drip drip drip drip drip ceaselessly, unending, is nothing more than a tiny leak in the immeasurable tank of Eternity.

That's what I had to say. I wish to thank you all for your attention and patience.

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*

7 – Appendix – The eight mistakes of Albert Einstein

The brotherly friendship which joined us in life, and the great respect I have for the memory of Albert Einstein as a man and a scientist, are not hindrance to impede me to relate, in the name of truth, a few points where his extraordinary intuition wasn't enough to make him aware of some facts of science as they really are, and later research proved to be different of the master's view:

a) After being one of the founding-fathers of quantum physics, in 1905, even inventing basic terms as quantum and photon, he didn't accept its philosophical consequences, specially the probabilistic character of the world at quantum scales, and the non-existence of an objective reality apart from the observer.

b) To conceive, in 1930, with Podolsky and Rosen, a mind experiment (Gedanken-experiment) to "prove" the absurdity of non-locality which, years later in laboratories, proved precisely the opposite of his expectations.

c) Not to accept Friedmann's solutions for his equations of general relativity, that have shown a non-static universe which should be necessarily under a process of expansion or contraction. This finding sounded unacceptable, leading him to conceive a hypothetical force (lambda) which would balance the universe turning it into a static system. Today we know that the universe is expanding and lambda force doesn't exist.

d) To release, in 1950, a theory of the unified field which intended to unify the four basic interactions of physics, which concluded with four equations equal to zero that were not correct. In his calculations, Albert has done a division by zero without perceiving it. This is a mistake in mathematics because it leads to false results or absurdities.

e) To have admitted, for the developing of his general theory of relativity, the seminal notion of proper-time, (tau), originally introduced by Minkowsky some years before, without noticing that a revolution was contained in that proposition. Not even Minkowsky got aware that by connecting to each point - which means each particle - a proper time, he was accreting a new dimension to the time order, and its imaginary character would definitely bound time to the observing subject.

f) To have insisted in the irreversibility of time flow, even when quantum physics showed that it is reversible at quantum scales and Gödel demonstrated this reversibility in the cosmic level, in 1949, with his solution to the equations of general relativity.

g) To try to prove that black holes couldn't exist, in a paper published in the Annals of Mathematics, in 1939, although black holes are a logic result of his equations for general relativity.

h) To discover the possibility of "gravitational lenses" - a phenomenon already discovered by astronomers - however forecasting that science would never be capable of using them to observe distant objects, as they are today.

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Further reading:

• Aquinas, Thoma. Philosophical Texts. London: Oxford University Press, 1952.
• Bergson, Henri. Durée et Simultanéité. Paris: Presses Universitaires de France, 1968.
• Borges, Jorge Luis. História de la Eternidad. Buenos Aires: Emecé Editores S.A., 1953.
• Davies, Paul. Superforce. Glenister Gavin Ltd., 1984.
• Duncan, Ronald and Miranda Weston-Smith, edit. The Encyclopaedia of Ignorance. London: Pergamon Press Ltd., 1977.
• Eddington, Arthur Stanley. Space,Time and Gravitation. Cambridge, 1920.
• Einstein, Albert, H. Minkowsky, H.Weyl et al. The Principle of Relativity – A Collection of Original Memoirs on the Theory of Relativity. Translated by W. Perret and G.B. Jeffery, with notes by A. Sommerfeld. New York: Dover Publications, 1952.
• Einstein, Albert. Relativity, The Special and General Theory. Translated by R.W. Lawson, 4^th ed. London: Methuen & Co.
• Einstein, Albert. Mein Weltbild. Zurich: Europa Verlag, 1953.
• Ekeland, Ivar. Le Calcul, l'Imprévu. Editions du Seuil, 1978.
• Eliade, Mircea Le Mithe de l'Éternel Retour. Paris: Editions Gallimard, 1969.
• Franz, Marie-Louise von. Time – Rhythm and Repose. Thames and Hudson, 1978.
• Gribbin, John. Timewarps. New York: Delacorte, 1979.
• Hawking, Stephen. Is the End in Sight for Theoretical Physics? Cambridge University Press, 1980.
• Hovis, R. Corby and John A. Montgomery. "P.A.M. Dirac and the Beauty of Physics", Scientific American. May, 1993.
• Kaufmann, William J. The Cosmic Frontiers of General Relativity. Little, Brown and Company, 1977.
• Kuhn, Thomas S. The Structure of Scientific Revolutions. The University of Chicago Press, 1962.
• Lessa, Adelaide Peters. Precognição. São Paulo: Livraria Duas Cidades, 1975.
• Morris, Richard. Time's Arrows – Scientific Attitudes toward Time. New York: Simon and Schuster, Inc., 1985.
• Ouspensky, P.D. Um Novo Modelo do Universo. translation by Daniel Camarinha. São Paulo: Editora Pensamento, s/ data.
• Pagels, Heinz. Perfect Simmetry. New York: Simon and Schuster, 1985.
• Pagels, Heinz. The Cosmic Code. New York: Bantam Books, 1983.
• Popper, Karl R. El Universo Abierto – Un Argumento en Favor del Indeterminismo. Madrid: Editorial Tecnos S.A., 1986.
• Prigogine, Ilya and Isabelle Stengers. Entre le Temps et l'Éternité. Paris: Librairie Arthème Fayard, 1988.
• Prigogyne, Ilya. La Nascita del Tempo. Roma-Napoli: Edizioni Theoria, 1988.
• Rucker, Rudy. The Fourth Dimension – A Guided Tour of the Higher Universes. Boston: Houghton Mifflin Company, 1984.
• Saint Augustin. The City of God. New York: Modern Library, 1950.
• Ubaldi, Pietro. A Grande Síntese. Translation by Mario Corbioli. São Paulo: Lake, s/ data.
• Weil, Pierre. As Fronteiras da Evolução e da Morte. Petrópolis: Editora Vozes Ltda., 1983.
• Whorf, Benjamin Lee. Language, Thought and Reality: Selected Writings of Benjamin Lee Whorf. Editado por John B. Carroll. Cambridge: MIT Press, 1966.

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