Confused Dr. Jeffrey Long thinks his book proves there’s an afterlife

Dr. Jeffrey Long is a doctor who helps terminal cancer patients deal with their illness. He’s been fascinated with Near Death Experiences for a long time, and he’s recently written a book about them called Evidence of the Afterlife: The Science of Near-Death Experiences. He has interviewed thousands of people, and because of the remarkable similarity of their experiences, he’s concluded it must be proof there is an afterlife. I think it just proves he’s a fucking idiot.

Dr. Long has obviously decided to abandon his objectivity, and I find his use of the word “Science” in his title extremely misleading. When you do science, you have to explain how even your own theories might be disproved; in his case, all that is necessary is evidence that the reason we experience similar effects during death is because of the way the brain reacts when it dies.

The effects of NDEs have been recorded for a long time, and most serious scientists compare them with what we experience during lucid dreaming (this is where people are aware they are dreaming, but still have very realistic experiences). Dr. Long is either unaware of these studies, or has already concluded that the only viable explanation must be there is a supernatural world that people escape to during death. It’s a pretty weak conclusion, and it’s obviously not very scientific. Perhaps he’s never heard of Occam’s Razor; is it more logical to assume people’s brains are freaking out and releasing a potent cocktail of chemicals to calm them down, or that a spiritual world beyond our comprehension exists so our minds can live forever in some fantasy land paradise? I feel fucking stupid just proposing the latter, and so should he.

He claims he’s a better physician now that he’s written this book. I would disagree, since he now foolishly believes he has enough proof to tell his patients they don’t need to feel frightened about death since they will live forever in a magical playland created by a loving sky daddy. Maybe not everyone feels it’s very healthy to endorse obvious wishful thinking. Sounds to me like he’s actually gotten worse…

NOTE: I mistook Long for a clinical psychologist, but was disturbed to find he’s actually a medical doctor. How exactly does he think his skills have improved with his acceptance of fantasy?

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Comments (81)

  • avatar

    Ben Taylor

    What I’d say to all that: “You know something is happening here and we don’t know what it is. Do we?” (Mr. Jones)

  • avatar


    I’m sure your religion of atheism will be alive an well for some time no matter what people discover. If you can prove you’re actually reading this email let the world know, because it’ll be the first piece of scientific evidence that is not a least somewhat of an approximation.

  • avatar


    The vast majority of physicians are not scientists. They have a few science course, but to be a competant researcher and qualify tor grants, one must have a Ph.D. in a science.

    Physicians are diagnosticians using abductive reasoning with a preexisting list of medical conditions having lists of symptoms. They do not propose hypotheses or models that are testable.

    Where Jeffry Long concludes that there is only one conclusion from his “studies” is not scientific in that there are always alternatives, even if they are not currently known. Scientists are best off testing multiple hypotheses. Physicians who do this often miss condtions that are not on those lists and are rare, and they do not creatively investigate other medical possibilities. They often blame undiagnosable conditions are “mental” problems. This is despicable!

    If Long were right, then no science would be possible, since immaterial, disembodied entities are excluded (though not theoretical entities for theories). SUch entities violate the principle methodological assumption of all of science: methodological naturalism.

    Furthermore, personal accounts do not constitute data for science.

    Personal accounts, supernaturalism, and abductive reasoning from a preexisting list of conditions or personal testimony signal nonscience.

  • avatar


    some one mentioned Occam’s Razor- id go by that- after all being in practical medicine,trusting in diagnostic parsimony helped me more than thinking of Hickum’s dictum….. we are not even at the fringe border of understanding brain chemicals..let alone its awesomely complex neuronal wiring…OBE and NDE probably is just a lucid manifestation of its metabolism firing wrongly during complex wiring function..akin to sometimes perceiving vived dreams as reality ….

  • avatar


    If you are born blind and wish to see for the first time and in a far superior manner, and the same if you are born deaf, then wait till your brain goes WRONG and spews chemicals into a body with no pulse – than ZAP! You have it. I want my brain to fail please so that my senses in a pulseless body can be improved!!! If I can attain this I will become an ignorant atheist.

  • avatar


    When one studies ones own mind, one comes to realise how fragile it really is. look up research on the reliability of eye witnesses. If courts understood this they would never accept an eyewitnesses account. we are all so easily duped. Now on to near death experiences, the word is NEAR not dead! so the person is still alive but undergoing an event which without medical intervention would have resulted in death. by definition the person did not die. Therefore these experienced sensations can be the result of the trauma being endured. The body has an array of tools to defend itself against extreme circumstances. The release of these chemical tools could easily account for the “lucid dreaming”. So what about the common thread? well one common thread is we are all human. The other is these people discuss their experiences with others of the same ilk. Given the unreliable witness factor their stories start to align.

    While Dr J Long may be a great doctor he has not used any scientific method in his book. Therefore simply calling it the science of NDE is itself deceptive. so in other words the book starts with a lie. I cant see it getting any better from there.

    Only people who “want to believe” will believe this prattle. but then they believe a lot of nonsense already.

    Always keep this in mind…

    “50% of all people have below average intelligence, and average is pretty ordinary if you ask me!”


  • avatar


    I doubt if anyone has done real research on brain activities. Isn’t it funny that everything we do is shaped by brain and how it functions and we have spent so little digging into this important issue? I have never seen a paper or a book that scientifically and comprehensively tell us how brain works. I am disappointed by reading books talking about the brain symptoms but never tangible research about the very root, which is the brain itself, how it functions, and what can be done to use it better. I hate to see that it remains as a mystery for a long time to come.

  • avatar


    And they laughed at people (Copernicus) who said the world was round, because there was no proof 400 years ago.

    And they laughed at those who said that atoms and matter were not solid, but were only waves of energy, until scientists agreed that nothing was solid.

    And so you are all allowed to laugh – that is your right. But just maybe, one day, there will be stronger proof. So I say let’s not be too strongly opinionate for or against at this stage.
    What is interesting to me is that some blind people (who had never seen colours before)described what they saw in their NDE and did so mentioning colours of things that could not know about. How do you describe red if you have never seen it…. just interesting.

  • avatar

    georeg davis

    Those born blind are completely unable to form concepts of colour, light & shade and perspective. Yet these blind subjects after expereincing NDE are completely able to understand and form concepts of the three mentioned. For example, if you tell a person born blind that buildings are smaller at a distance but always the same size at the same time at whatever distance, they are totally confused by the statement – but not after NDE. Some had 360 degree vision while the brain had quit giving signals. I suppose then to improve our sight we must shut the brain off!

  • avatar

    Lucy Abrams

    I appreciate the outrage of the author. I feel the same way but on differant points. I’ve listened to him several times and have come to the conclusion that
    Long is mixed up and clueless. He relates his own personal experiences regarding “buffalo nickles” and is completely unaware of what synchronicity is and how it occurs.

    Later in the interview i listened to he DREAMS he died and he calls this a “NDE”. Dreaming that you died is NOT AN NDE.

    NDE’s are intimately tied to clinical death .

    I listened to this interview like I said a few times before i came to some conclusions and throughout I felt he is a vain self-promoter and wants to insert himself into NDE studies and research without regard for the many senior members in the field.

    He’s a dope and I wouldn’t buy ANY of his books for all the tea in China.

  • avatar


    If you people want some hard scientific data to support the idea that consciousness is primal to the universe and not just some emergent property of some several ounces of meat called a brain, then may I suggest Robert Lanza’s BIOCENTRISM.Robert Lanza is a leading genetic engineer who is changing the world according to US News & World Report. He’s likened to the new “Einstein”. Are you changing the world with your “science”? Your atheism in no way is a statement of science but like the believer, it is an article of faith.

    And oh yeah, our most brilliant minds cannot deliberately and conscientiously build a protein or enzyme (of which a million can sit on the head of a pin)that unwinds our DNA let alone the DNA, tissue, organs, or organisms with brains and nervous systems intact by scratch. If this is so, what makes you think something as complex as you came about by the random crashing of molecules like classic billiard balls? Laws are only principles observed repetively by existing elements but a law has never created anything. 2 plus 2 = 4 is a mathematical law, but that has never deposited $4 into my bank account. You’ve got your heads stuck under the hood of your Bentley and arrogantly proclaim, “Why, there’s no need for a maker of this vehicle you oaf! It’s very obvious how this machine works-by internal combustion”! That’s the problem with you materialist reductionist practitioners of scientism, you err in logic by mistaking mechanism with agency. Internal combustion is the mechanism, man is the agent. In the words of Max Planck: “As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter”.
    Das Wesen der Materie [The Nature of Matter], speech at Florence, Italy (1944)
    This guy’s the father of quantum physics. If he believes, what allows you the license to call anyone else on this post stupid? Let’s see you lay bare the mysteries of the universe as this man has-SO ARROGANT! And it’s an unjustified arrogance!

    Now, until you can send me data on the physiological processes that account for qualia or the subjective experence of emotions along with this sense of “I” along a sequential time trajectory despite the fact our cells are replaced many times over in a lifetime, then you’re not exactly in a position to proclaim with certainty there is no continuation of consciousness.And when i say account for the hard problem of consciousness, I don’t mean the “easy problem” as shown by neuronal correlates. As for Occam’s Razor (sheesh you atheists tire me-so overused), the simplest explanation “tends” to be the correct one-that means, not always so. Also, the simplest explanation is the one that is true whether it is perceived that way by us or not.

    And before I depart and to satisfy your sense of entitlement, here’s the math behind the near death experience. And before you retort with a “That’s not proof”, crap, I already know that. It’s EVIDENCE-there’s a difference. Heres a quote and the math-you figure it out:
    “It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning (Many Worlds in One [New York: Hill and Wang, 2006], p.176)”.
    -Alexander Vilenkin / Professor of Physics and Director of the Institute of Cosmology at Tufts University
    The math:
    Physicist Uses NDEs To Clarify The Nature Of Time
    by Paul Bernstein, Ph.D.
    This year at professional conferences in Oxford, Paris and Prague, as last year at academic gatherings in Germany, Italy, and Greece, European astrophysicist Metod Saniga explained to his scientific colleagues how the NDE research of Raymond Moody, Kenneth Ring and PMH Atwater has helped him to develop a mathematical model of time that seems to offer solutions to problems that have vexed scholars since Einstein.
    Poster announcing the international Advanced Research Workshop on the natureof time, co-directed by Dr. Saniga.
    In brief, Dr. Saniga takes seriously the testimony of NDErs when they describe being in a realm where “time stops”, and where some of them “see the past, present, and future all at once.” To this occurrence of what he calls “the Pure Present”, Dr. Saniga adds the experience of mystics, clairvoyants and others who’ve experienced suddenly being in the future, and still others who describe being drawn involuntarily back into the past.1 Saniga uses these “anomalous experiences” to show that a single mathematical model can account for both the conventional and the extraordinary ways that humans experience time. Yet the model also remains compatible with what is known about time throughout the physical universe, and even sheds interesting light on the possible nature of time and space at the very early period of our Universe just after the Big Bang.2
    Because the same mathematical principles can connect all these different experiences—both physical and psychological— Dr. Saniga asserts that any attempt to dismiss non-ordinary states of consciousness like NDEs “as pure hallucinatory phenomena would simultaneously cast a doubtful eye on the very role of mathematics in our understanding of Nature. To the contrary, it is mathematics itself…that tells us that it is far more natural to expect all these ‘unusual’ perceptions of time to be simply as real as our ordinary (‘normal’) one.”3
    Dr. Saniga’s model cannot be fully described without using the specialized mathematics known as ‘algebraic projective geometry’. And since most of us have not been trained in that math, I am forced to risk oversimplifying his explanation a little bit here, in order to share it with the general public.
    Recall how we all commonly think of time, as we go about our daily lives: time seems to be a simple ‘arrow’ or straight line running from the past, through the present, and pointing toward the future. However,
    Geometric representation of NDErs’ experience of time as “pure present”
    as Dr. Saniga points out, the fundamental equations of physics do not really insist on such a one-directional experience of time:
    It is a well-known fact that the fundamental equations of physics are time-reversible, i.e. they do not distinguish between the past and future. Moreover, the very concept of the present, the now, has no proper place in the temporal of physics at all; this holds true whether one is talking of classical physics, quantum mechanics, or relativity theory.4
    In other words, our “arrow of time always moving forward” experience, seems to be strongly related to what we humans create as our experience of time, not to any invariable aspect of physical time itself.
    So in order for Dr. Saniga to encompass within one model both the conventional notions of physical time and the subtleties of human ‘subjective’ time, he found it necessary to expand beyond the simple line model of time. Consequently, instead of representing each event as simply a single point along a line of time, he found that a single event can more accurately be represented as a curved line within a group of “conics” (curves like parabolas and hyperbolas). And to express that most precisely, most scientifically, Dr. Saniga found that he should use both geometry (which is the mathematics for describing shapes like those curves) and algebra (which is the mathematics for describing relationships among such shapes).
    To his surprise and delight, this combined ‘algebraic-geometry’ description then accurately predicted many variations in time that scientists have already observed in both the physical and the psychological worlds. The resulting model is a series of diagrams and equations that embrace the “ordinary” and the “anomalous” manifestations of time, including the following near-death experiences Dr. Saniga selected from the writings of NDErs and their researchers:
    (1) “After…going through this long, dark place, all of my childhood thoughts, my whole entire life was there at the end of this tunnel, just flashing in front of me….Not one thing at a time, but …everything at one time. It was just all there at once.” [An experiencer quoted in Dr. Raymond Moody’s 1975 book, Life after Life5].
    (2) “Personal flash-forwards…take place while an individual is undergoing an NDE…It is as though the individual sees something of the whole trajectory of his life, not just past events…To the NDEr they represent events of a conditional future — i.e., if he chooses to return to life then these events will ensue. In this sense, a personal flash-forward may be likened to a “memory” of future events. [Dr. Kenneth Ring, in his 1984 book, Heading Towards Omega6].
    When Dr. Saniga moves from such human experiences of time to cosmological conditions of time, his model suggests what might have occurred during the creation of our universe. “There is a growing suspicion among physicists,” he reports, “that the Universe might have been born with a different dimensionality than what we observe [today].” Specifically, instead of the 3 dimensions of space and 1 dimension of time that we are used to, the early Big Bang situation would seem to have been the opposite: only one dimension of space—accompanied by three dimensions of time.7 And instead of this startling notion having to remain a mere speculation, Dr. Saniga states that his model can, in principle, be tested by astronomers in the near-future, once sensing devices that look into deep space become more sensitive— because his equations predict that one of our current three dimensions of space should be slightly different from the other two spatial dimensions.8
    Just as intriguing, this understanding of physical dimensionality matches some views of spiritual psychology, as expressed for example in a book by psychology-philosopher Michael Washburn, professor at Indiana University, and summarized years before Dr. Saniga had published his works, as follows:
    Washburn asserts that who we ordinarily think we are (our ego) is only a part of our experience. The vaster part he calls the Dynamic Ground, in which he unites what others call our unconscious, our instincts, our libido, and the spiritual forces that inspire us. …
    Because the ego will cause its own misery if it remains closed to the Dynamic Ground (which it made unconscious during early childhood), people can hardly avoid a spiritual life eventually. The everso- common ‘mid-life crisis’, like the ancient’s ‘dark night of the soul’, is the opening of the ego to the forces it had closed itself off from, during its earlier (and necessary) stage of development.
    Our ego, in other words, is good enough at operating in the 3- dimensional world of matter and unilinear time, but cannot of itself encompass the world of eternity in which this 3-dimensional world is suspended.9
    In agreement with this psycho-spiritual understanding, Saniga’s equations show that our 3-dimensional ‘time-bound’ world might indeed be suspended within a much vaster, endless, world of eternity. He adds a particular category of mathematics called “Cremona transformations” to reveal that our usual world of 3 spatial dimensions and 1 time dimension may very well be just an “island” in a much larger “sea” that is its opposite. As Dr. Saniga expressed this mathematical discovery to his academic colleagues:
    There exists a totally amazing 3-to-1 splitting in the character of…fundamental elements. . . .The far prevailing mode is…one spatial dimension…and three time dimensions. The …. [everyday] configuration of 3 spatial with 1 time dimension can be seen as a mere ‘island’ in the ‘sea’ of 1+3’s.10
    How have his colleagues responded to this model? “The reaction has been positive,” he wrote me, “but so far not many people have delved deeply into the ideas behind it.” Jonathan Smith, mathematician at the University of Iowa, said, “I’m skeptical at the moment—but I’m willing to be convinced.” At the same time, one Harvard astrophysicist wrote:
    Saniga demonstrates that there are coordinate systems within a simple transformation of our present system that explain the broad range of time phenomena found in the psychiatric literature. Of course the demonstration that this is possible does not prove that it is true, but it does explain a lot of ‘data’. And that is all you can ever ask of such a theory, so it deserves to be read and pondered.
    Consider an analogy to the Einstein relativity principle, which showed that you do some transformation of the time and space coordinate systems to produce the result that the velocity of light is always constant, and all mass has an equivalence principle where the gravity associated with mass is equivalent to acceleration. The report by Saniga reads a lot like Einstein’s Special Theory of Relativity, while the part equivalent to the General Theory of Relativity remains to be discovered.
    Dr. Saniga (kneeling in center, hand on lawn) with international research colleagues
    retired Air Force colonel from Texas wrote to Dr. Saniga:
    I was most interested in your work on ‘dimensionality of space’ . …In 1957 when I was 13 years old, I was electrocuted with 7,200 volts and had the classic NDE experience. From that accident, and to this day, I am convinced … our world is not [just] a 3-dimensional one. …The conventional distortion is the construct of a “past”, a “now”, and a “future”… At the earliest level of my NDE journey…that human construct fell away, that ‘arrow of time’. …Then followed a series of increasing levels of consciousness. I clearly recall the joy of additional dimensionality, of wanting to pause and celebrate the arrival of each [additional dimension], …the blooming and opening up of another one….
    At around the eighth level…I was beyond any joy I have ever known….But I was becoming distracted by the approach of the Light….The engulfing of the Light around me, the Being, and my Exchange with this Being, I strongly sense took place at a 10th or perhaps higher level of dimensionality.11
    Back in [our daily] three-dimensional existence, I see those [other] levels reduced to something like the presence of multiple panes of glass you view through, to see your sweetheart approach in her car outside your office. You see your sweetheart and her smile, oblivious of the 12 panes of glass you are viewing her through. It is not germane to the human experience, but we coexist in this multidimensional world just as a cube drawn on a blackboard exists in ours….
    I sense, Dr. Saniga, that you are perhaps far more courageous to present this to your peers than I was when I came forward finally in 1981 to discuss my 1957 NDE. What excites me is your apparent suspicion that science in its present structure and approach is wholly ill-prepared to address this domain….Your discipline in the sciences combined with your tolerance and appreciation of this material is very powerful.
    Because Dr. Saniga continues to gather NDEs for his research, you may email him at if you wish to tell him about the role of time in your own particular near-death experience.

  • avatar


    Another point:
    The near death experiencers born blind from birth can see for the first time during their NDE. It is a physical impossibility for the blind from birth to see any images in their dreams or any drug induced hallucination. They have no prior images to borrow from to reconstruct an image in their visual cortex and thus never enter REM intrusion. And yet, they can see for the very first time during an NDE. Now Gerald Woerlee likes to argue that they are assembling tactile experiences to construct an image, but there is no science to support that (just conjecture by a desperate atheist) and it still begs the question why is their seeing for the first time unique to the NDE? Why not have that experience in a dream, or better still, a nightmare which may parallel the trauma? Answer that for me and then we’ll talk.

  • avatar


    Oh yes, there are examples of pilots who have suffered anoxia and also had an NDE at a later date and there was NO similarity between the two. The one is foggy and confused while the other is super clear. So don’t give me the oxygebn deprived brain thing as an explanation-please!

    As for Persinger’s God Helmet, it has never illicited a parallel NDE in the classic case and this materialist has recently announced that he has proven telepathy is real in his lab. He also said he suspects the materialists and old style paradigm adherents will never be able to accept this.

    As for Ketamine, even the pioneer of this field, Dr Jansen, who originally believed ketamine reduced NDE’s to physical brain junk, has recanted and says he believes NDE’s may, in fact, be evidence for a soul. Here’s his words:

    “I am no longer as opposed to spiritual explanations of near-death phenomena as my article . . . would appear to suggest. Over the past two years . . . I have moved more toward the views put forward by John Lilly and Stanislav Grof: namely, that drugs and psychological disciplines such as meditation and yoga may render certain ‘states’ more accessible [and toward] those who see drugs as just another door to a space, and not as actually producing that space. After 12 years of studying ketamine, I now believe that there most definitely is a soul that is independent of experience. It exists when we begin, and may persist when we end. Ketamine is a door to a place we cannot normally get to; it is definitely not evidence that such a place does not exist.”

  • avatar


    And if anyone here can explain the double slit experiment while leaving consciousness out of the picture, do two things for me:
    1) Post that evidence here on this site
    2) Publish your findings and win the Nobel Prize overnight.

  • avatar


    And oh yeah, Jim:
    Rather than call me a moron, educate me on the science and go out and win that nobel prize that resolves the problem of the double slit experiment. Reduce that to a Newtoniam Paradigm that fits into your neat classic world. And I’m still waiting for you to create a protein from scratch that can unwind a DNA helix. What? You can’t do what blind unguided forces can do? That brilliant mind so sharp and so keen-the product of billions of years of evolution cannot replicate even the most mundane of of scientific wonders with focused and deliberate intent? You can’t do what particles randomly bumping into each other can do? Maybe you’re the scientific moron! Admittedly, I can’t make that stuff either which makes me a scientific moron too. The difference is, I know it. You are actually proof that you have an identification that lies outside your brain so you ought to be the first in line to believe in NDE’s: your immaterial ego is far larger than your material brain. There’s no match! Your dualistic nature must be true! Youre’ a dark soul Jim-constantly berating other’s for their faith. Do you spend as much time berating the Easter Bunny? Personally, I think you’re just pissed off at God. Why spend so much time berating what doesn’t exist? Why devote a website to the debunking of something that isn’t real? Talk about a waste of time! Talk about unscientific! You should be in a lab somewhere figuring this stuff out rather than posting blogs. Notice that the true great minds are not posting here. Ooops! I guess that means me too.

  • avatar


    Maybe you atheists can get back with me and tell me if you think astrophysicist Metod Saniga is “confused”. You want science? Chew on this…

    R. Buccheri et al. (eds.); Endophysics, Time, Quantum and the Subjective; 245{272
    °c 2005 World Scienti¯c Publishing Co. All rights reserved.
    Astronomical Institute, Slovak Academy of Sciences,
    SK-05960 Tatransk¶a Lomnica, Slovak Republic
    Abstract: The paper presents, to our knowledge, a ¯rst fairly comprehensive and math-
    ematically well-underpinned classi¯cation of the psychopathology of time (and space).
    After reviewing the most illustrative ¯rst-person accounts of \anomalous/peculiar” ex-
    periences of time (and, to a lesser degree, space) we introduce and describe in detail their
    algebraic geometrical model. The model features six qualitatively di®erent types of the
    internal structure of time dimension and four types of that of space. As for time, the most
    pronounced are the ordinary \past-present-future,” \present-only” (\eternal/everlasting
    now”) and \no-present” (time \standing still”) patterns. Concerning space, the most
    elementary are the ordinary, i.e., \here-and-there,” mode and the \here-only” one (\om-
    nipresence”). We then show what the admissible combinations of temporal and spatial
    psycho-patterns are and give a rigorous algebraic geometrical classi¯cation of them. The
    predictive power of the model is illustrated by the phenomenon of psychological time-
    reversal and the experiential di®erence between time and space. The paper ends with a
    brief account of some epistemological/ontological questions stemming from the approach.
    Keywords: Mental Space-Times { Pencil of Conics/Lines { Cremona Transformations
    1 Introduction
    Time | \the supreme law of nature” after Sir Arthur Stanley Eddington,
    a world-famous astrophysicist of the last century | is undoubtedly one of
    the deepest mysteries science has ever faced. Indeed, one would hardly ¯nd
    something that is, on the one hand, so intimately connected with our ex-
    perience and yet, on the other, so di±cult to come to grips with. Nothing,
    perhaps, can better illustrate this point than a large group of phenomena
    that are collectively referred to as the psychopathology of time, that is, all
    \anomalous/peculiar” experiences of time as invariably encountered and
    reported in various mental psychoses, drug-induced states, deep meditative
    and mystical states as well as in many other \altered” states of con-
    sciousness [1{7]. For such peculiar fabric of psychological time comprises,
    as we shall see in more detail, such bizarre, paradoxical and mind-boggling
    forms as \eternity, everlasting now,” \arrested/suspended” time, time \go-
    ing backward,” and even \disordered/fragmented” time, to mention the
    most pronounced of them.
    246 A Geometrical Chart of Altered Temporality (and Spatiality)
    Up to date, there exists no acceptable psychological/neurological model
    capable of properly dealing with these fascinating time constructs and un-
    derpinning any logical classi¯cation of them. The reason why this is so
    rests, in our opinion, upon the following two facts. First, these extraor-
    dinary experiences of time (and, of course, space as well) are inherently
    participatory, non-reproducible and subjective and, so, seriously at odds
    with current methodologies/paradigms of science, which strive for repro-
    ducibility and objectivity. Second, the most pronounced departures from
    the \consensus” reality are so foreign to our \waking” mind that their
    properties defy our common sense logic and cannot be adequately commu-
    nicated in words; an interested scholar has to go through a large number
    of relevant ¯rst-hand accounts/narratives and acquire the ability to read
    between the lines in order to spot an(y) underlying conceptual pattern. We
    are therefore convinced that further progress in our understanding of these
    phenomena will inevitably entail a serious shift in the corresponding scien-
    ti¯c paradigms to reveal their true epistemological/ontological status and
    be accompanied by the increasing use of su±ciently abstract mathematical
    concepts to properly grasp their qualitative properties.
    Our study of psychopathological (space-)times has, from the very be-
    ginning, been pursued in accordance with this strategy [7{9]. The model
    discussed in the second part of the paper thus features not only a fairly high
    level of abstraction, but it also poses a serious challenge to some generally
    accepted dogmas in natural sciences. Formally, it employs advanced geo-
    metrical concepts, like a projective space and/or Cremona transformations.
    Conceptually, it relies on a daring and far-reaching assumption that the
    anecdotal, ¯rst-person descriptions of extraordinary states of consciousness
    are on a par with standard observational/experimental evidence in natural
    sciences. It is this \abstract geometrization of the ¯rst-person perspective”
    that gives our approach a remarkable unifying and predictive power and
    makes it a very promising conceptual step towards the ultimate unveiling
    of the riddle of time. The purpose of the paper is to demonstrate this.
    The presentation is focussed on conceptual issues rather than mathemati-
    cal technicalities, the latter being reduced to the extent that also the reader
    with a comparatively slight mathematical background can easily follow the
    main line of reasoning.
    2 Mental (Space-)Times: Most Illustrative Cases
    We shall start with a compact, yet comprehensive enough, review of the
    most distinguished forms of \anomalous” experience of time. This review
    Metod Saniga 247
    is unique in that it consists solely of ¯rst-person accounts/narratives, three
    or four per each mode. This way even the uninitiated reader can get a fairly
    clear idea about the nature of experiences involved and realize the source
    and character of possible di±culties one is likely to face when attempting
    to mathematically model these experiences.
    2.1 \Eternity,” alias \eternal/everlasting now”
    This is perhaps the most pronounced and in the literature best-documented
    kind of profoundly \distorted” sense of time. It is a sort of compressing,
    telescoping of past, present and future into the present moment that is
    experienced as \eternal/everlasting now.” One of the best portrayals of
    what this experience looks like is found in the following account [10, p. 46]:
    I woke up in a whole di®erent world in which the puzzle of
    the world was solved extremely easily in a form of a di®erent
    space. I was amazed at the wonder of this di®erent space and
    this amazement concealed my judgement, this space is totally
    distinct from the one we all know. It had di®erent dimensions,
    everything contained everything else. I was this space and this
    space was me. The outer space was part of this space, I was in
    the outer space and the outer space was in me. . .
    Anyway, I didn’t experience time, time of the outer space and
    aeons until the second phase of this dream. In the cosmic °ow
    of time you saw worlds coming into existence, blooming like
    °owers, actually existing and then disappearing. It was an end-
    less game. If you looked back into the past, you saw aeons, if
    you looked forward into the future there were aeons stretching
    into the eternity, and this eternity was contained in the point of
    the present. One was situated in a state of being in which the
    \will-be” and the \vanishing” were already included, and this
    \being” was my consciousness. It contained it all. This \being-
    contained” was presented very vividly in a geometric way in
    form of circles of di®erent size which again were all part of a
    unity since all of the circles formed exactly one circle. The
    biggest circle was part of the smallest one and vice versa. . .
    This narrative is remarkable in a couple of aspects. Not only does the sub-
    ject try to understand his uncanny experience of time in terms of a simple
    geometrical model, but he also pays particular attention to the spatial fabric
    of his extraordinary state, which also di®ers utterly from what is regarded
    248 A Geometrical Chart of Altered Temporality (and Spatiality)
    as a normal/ordinary perception of space; in fact, the subject ¯nds himself
    to be one/fused with space!
    Another description of the same kind of mental space-time structure is
    taken from Atwater [11, Chpt. 2]. It is based on one of many author’s near-
    death experiences, which was also accompanied by a fascinating archetypal
    This time, I moved, not my environment, and I moved rapidly….
    My speed accelerated until I noticed a wide but thin-edged ex-
    panse of bright light ahead, like a \parting” in space or a \lip,”
    with a brightness so brilliant it was beyond light yet I could
    look upon it without pain or discomfort. . . The closer I came
    the larger the parting in space appeared until. . . I was absorbed
    by it as if engulfed by a force ¯eld. . . Further movement on my
    part ceased because of the shock of what happened next. Before
    me there loomed two gigantic, impossibly huge masses spinning
    at great speed, looking for all the world like cyclones. One was
    inverted over the other, forming an hourglass shape, but where
    the spouts should have touched there was instead incredible rays
    of power shooting out in all directions. . . I stared at the specta-
    cle before me in disbelief. . . As I stared, I came to recognize my
    former Phyllis self in the midupperleft of the top cyclone. Even
    though only a speck, I could see my Phyllis clearly, and super-
    imposed over her were all her past lives and all her future lives
    happening at the same time in the same place as her present life.
    Everything was happening at once! Around Phyllis was every-
    one else she had known and around them many others. . . The
    same phenomenon was happening to each and all. Past, present,
    and future were not separated but, instead, interpenetrated like
    a multiple hologram combined with its own re°ection. The only
    physical movement anyone or anything made was to contract
    and expand. There was no up or down, right or left, forward
    or backward. There was only in and out, like breathing, like
    the universe and all creation were breathing | inhale/exhale,
    contraction/expansion, in/out, o®/on.
    The last example, but by no means less astounding than the former two, is
    borrowed from Braud [12] and depicts in great detail and clarity a gradual
    transformation of our ordinary, waking sense of time (and space) into that
    of \eternity” (and \omnipresence”):
    Metod Saniga 249
    I get up and walk to the kitchen, thinking about what a timeless
    experience would be like. I direct my attention to everything
    that is happening at the present moment | what is happening
    here, locally, inside of me and near me, but non-locally as well,
    at ever increasing distances from me. I am imagining everything
    that is going on in a slice of the present | throughout the
    country, the planet, the universe. It’s all happening at once.
    I begin to collapse time, expanding the slice of the present, ¯ll-
    ing it with what has occurred in the immediate \past.” I call
    my attention to what I just did and experienced, what led up
    to this moment, locally, but keep these events within a slowly
    expanding present moment. The present slice of time slowly
    enlarges, encompassing, still holding, what has gone just be-
    fore, locally, but increasingly non-locally as well. By now, I
    am standing near the kitchen sink. The present moment con-
    tinues to grow, expand. Now it expands into the \future” as
    well. Events are gradually piling up in this increasingly larger
    moment. What began as a thin, moving slice of time, is be-
    coming thicker and thicker, increasingly ¯lled with events from
    the \present,”\past,” and \future.” The moving window of the
    present becomes wider and wider, and moves increasingly out-
    wardly in two temporal directions at once. It is as though things
    are piling up in an ever-widening present.
    The \now” is becoming very thick and crowded! \Past” events
    do not fall away and cease to be; rather, they continue and oc-
    cupy this ever-widening present. \Future” events already are,
    and they, too, are ¯lling this increasingly thick and full present
    moment. The moment continues to grow, expand, ¯ll, until it
    contains all things, all events. It is so full, so crowded, so thick,
    that everything begins to blend together. Distinctions blur.
    Boundaries melt away. Everything becomes increasingly homo-
    geneous, like an in¯nite expanse of gelatine. My own boundaries
    dissolve. My individuality melts away. The moment is so full
    that there no longer are separate things. There is no-thing here.
    There are no distinctions.
    A very strong emotion overtakes me. Tears of wonder-joy ¯ll my
    eyes. This is a profoundly moving experience. Somehow, I have
    moved away from the sink and am now several feet away, facing
    250 A Geometrical Chart of Altered Temporality (and Spatiality)
    in the opposite direction, standing near the dining room table.
    I am out of time and in an eternal present. In this present is
    everything and no-thing. I, myself, am no longer here. Images
    fade away. Words and thoughts fade away. Awareness remains,
    but it is a di®erent sort of awareness. Since distinctions have
    vanished, there is nothing to know and no one to do the knowing.
    \I” am no longer localized, but no longer \conscious” in the
    usual sense. There is no-thing to be witnessed, and yet there is
    still a witnesser.
    The experience begins to fade. I am \myself” again. I am pro-
    foundly moved. I feel awe and great gratitude for this experience
    with which I have been blessed. . .
    2.2 Time \standing still,” alias \arrested/suspended” time
    Another well-documented and quite abundant anomalous temporal mode.
    A couple of examples are found in Tellenbach [13, p. 13]:
    I sure do notice the passing of time but couldn’t experience it.
    I know that tomorrow will be another day again but don’t feel
    it approaching. I can estimate the past in terms of years but I
    don’t have any connection to it anymore. The time standstill is
    in¯nite, I live in a constant eternity. I see the clocks turn but
    for me time does not °ow. . . Everything lies in one line, there
    are no di®erences of depth anymore. . . Everything is like a ¯rm
    plane. . .
    and [ibid, p. 14]
    Everything is very di®erent in my case, time is passing very
    slowly. Nights last so long, one hour is as long as usually a
    whole day. . . Sometimes time had totally stood still, it would
    have been horrifying. Even space had changed: Everything is
    so empty and dark, everything is so far away from me. . .
    I don’t see space as usual, I see everything as if it were just a
    background. It all seems to me like a wall, everything is °at.
    Everything presses down, everything looks away from me and
    laughs. . .
    Both reports are given by depressive (melancholic) patients. It is worth
    noticing here that when time comes to a stillstand, perceived space seems
    Metod Saniga 251
    to lose one dimension, becoming thus two-dimensional. A slightly more
    detailed description of this time pattern we succeeded in ¯nding in a paper
    by Muscatello and Giovanardi Rossi [14, p. 784]:
    Time is standing still for me, I believe. It is perhaps only a
    few moments that I have been so bad. I look at a clock and
    I have the impression, if I look at it again, that an enormous
    period of time has passed, as if hours would have passed instead
    only a few minutes. It seems to me that a duration of time is
    enormous. Time does not pass any longer, I look at the clock
    but its hands are always at the same position, they no longer
    move, they no longer go on; then I check if the clock came to
    a halt, I see that it works, but the hands are standing still. I
    do not think about my past, I remember it but I do not think
    about it too much. When I am so bad, I never think about
    my past. Nothing enters my mind, nothing. . . I did not manage
    to think about anything. I did not manage to see anything in
    my future. The present does not exist for me when I am so
    bad. . . the past does not exist, the future does not exist.
    The following vignette is taken form a treatise on mescaline-induced exper-
    imental psychoses by Beringer [15, p. 311]:
    The strangest thing was that every once in a while my normal
    time-awareness, as far as these ¯gures were concerned, got to-
    tally lost; time was no longer a stream, which °ew away and
    whose °ux could have been measured, but it was rather similar
    to a sea, which as a whole stood still and which was in itself only
    a chaotic and utter jumble. I was no longer able to understand
    the continuous becoming of the ¯gures as a sequence in a cer-
    tain time direction, but sometimes the colours and forms °ew
    into an indescribable jumble, as if the previously alternating
    ¯gures were now experienced all simultaneously. Had I previ-
    ously seen these ¯gures in a constant motion, so now it was only
    a colorful and inexpressible manifold there in which I was not
    able to perceive any motion anymore. When I totally sank into
    the show of the ¯gures, it happened every now and then that I
    also sank into this time-still-standing, where the succession was
    transformed into a still standing present. Not only am I now
    not able to formulate these interruptions of the normal time
    experience, I am also almost unable to imagine my experience
    252 A Geometrical Chart of Altered Temporality (and Spatiality)
    of them any more. When I tore myself away from these ¯gures
    and violently turned myself to the outer world, this anomalous
    time experience was no longer here, but this disturbance of the
    sense of time found its expression in a form of illusion that an
    immense long time must have passed since my last waking-up.
    2.3 Time \going/°owing backward”
    This kind of time pathology is very often found in mental psychoses [1,2,5,16{
    18]. Here is a representative case, communicated by a schizophrenic patient
    of Fischer [19, p. 556]:
    Yesterday at noon, when the meal was being served, I looked
    at the clock: why did no one else? But there was something
    strange about it. For the clock did not help me any more and
    did not have anything to say to me any more. How was I going
    to relate to the clock? I felt as if I had been put back, as if
    something of the past returned, so to speak, toward me, as if I
    were going on a journey. It was as if at 11:30 a.m. it was 11:00
    a.m. again, but not only time repeated itself again, but all that
    had happened for me during that time as well. In fact, all of
    this is much too profound for me to express. In the middle of
    all this something happened which did not seem to belong here.
    Suddenly, it was not only 11:00 a.m. again, but a time which
    passed a long time before was there and there inside | have I
    already told you about a nut in a great, hard shell? It was like
    that again: in the middle of time I was coming from the past
    towards myself. It was dreadful. I told myself that perhaps the
    clock had been set back, the orderlies wanted to play a stupid
    trick with the clock. I tried to envisage time as usual, but I
    could not do it; and then came a feeling of horrible expectation
    that I could be sucked up into the past, or that the past would
    overcome me and °ow over me. It was disquieting that someone
    could play with time like that, somewhat daemonic. . .
    A brief and concise description of \psycho-time-reversal” is found in Laing
    [20, p. 148]:
    I got the impression that time was °owing backward; I felt that
    time proceeded in the opposite direction, I had just this ex-
    traordinary sensation, indeed… the most important sensation
    Metod Saniga 253
    at that moment was, time in the opposite direction…. The per-
    ception was so real that I looked at a clock and, I do not know
    how, I had the impression that the clock con¯rmed this feeling,
    although I was not able to discern the motion of its hands….
    A similar depiction is also furnished by a depressive patient of Kloos [21,
    p. 237]:
    As I suddenly broke down I had this feeling inside me that time
    had completely °own away. After those three weeks in a sick-
    camp, I had this feeling that the clock hands run idle, that
    they do not have any hold. This was my sudden feeling. I did
    not ¯nd, so to speak, any hold of a clock and of life anymore,
    I experienced a dreadful psychological breakdown. I do not
    know the reason why I especially became conscious of the clock.
    At the same time, I had this feeling that the clock hands run
    backward. . . There is only one piece left, so to speak, and that
    stands still. I could not believe that time really did advance,
    and that is why I thought that the clock hands did not have any
    hold and ran idle. . . As I worked and worked again, and worried
    and did not manage anything, I simply had this feeling that
    everything around us (including us) goes back. . . In my sickness
    I simply did not come along and then I had this delusion inside
    me that time runs backward. . . I did not know what was what
    anymore, and I always thought that I was losing my mind. I
    always thought that the clock hands run the wrong way round,
    that they are without any meaning. I just stood-up in the sick-
    camp and looked at the clock | and it came to me then at
    once: well, what is this, time runs the wrong way round?!. . . I
    saw, of course, that the hands moved forward, but, as I could
    not believe it, I kept thinking that in reality the clock runs
    backward. . .
    2.4 \Disordered/fragmented” time
    The following experience, voluntarily induced by mescaline, is the most
    representative one we have been able to ¯nd in the literature available [22,
    p. 295]:
    For half an hour nothing happened. Then I began feeling sick;
    and various nerves and muscles started twitching unpleasantly.
    254 A Geometrical Chart of Altered Temporality (and Spatiality)
    Then, as this wore o®, my body became more or less anaes-
    thetized, and I became \de-personalized,” i.e., I felt completely
    detached from my body and the world. . .
    This experience alone would have fully justi¯ed the entire ex-
    periment for me. . . , but at about 1.30 all interest in these visual
    phenomena was abruptly swept aside when I found that time
    was behaving even more strangely than color. Though perfectly
    rational and wide-awake. . . I was not experiencing events in the
    normal sequence of time. I was experiencing the events of 3.30
    before the events of 3.0; the events of 2.0 after the events of
    2.45, and so on. Several events I experienced with an equal de-
    gree of reality more than once. I am not suggesting, of course,
    that the events of 3.30 happened before the events of 3.0, or
    that any event happened more than once. All I am saying is
    that I experienced them, not in the familiar sequence of clock
    time, but in a di®erent, apparently capricious sequence which
    was outside my control.
    By \I” in this context I mean, of course, my disembodied self,
    and by \experienced” I mean learned by a special kind of aware-
    ness which seemed to comprehend yet be di®erent from seeing,
    hearing, etc.. . . I count this experience, which occurred when, as
    I say, I was wide awake and intelligent, sitting in my own arm-
    chair at home, as the most astounding and thought-provoking
    of my life….
    And here is another mescaline-borne episode of a very similar time’s sense
    [15, p. 148]:
    While walking upstairs, a sudden and as if nailed-down picture
    of this moment, the momentary view of Dr. M., Dr. St. and
    myself in space, attracted my attention. This repeated itself
    on di®erent stairs. At the top of the stairway there seemed to
    be no continutity of time at all, the whole course of events was
    only a mess of separate situations without any connection. And
    these situations, in case of active work, could later have been
    connected in the same way in which one can observe a celluloid
    ¯lm. Yet at the same time these situations | in both experi-
    encing and a direct reproduction of the happening afterwards |
    carried the character of the independent and disconnected. A
    Metod Saniga 255
    strange next-to-each-other-ness, not a one-after-the-other-ness;
    they have no position in time, time has no sense here. . .
    From these ¯rst-hand accounts it is quite obvious that the fabric of psycho-
    logical time is so intricate, complex and multifarious that, at ¯rst sight, it
    may seem to lie completely beyond grasp of any mathematical framework.
    Yet, the contrary is true. In what follows we shall introduce and describe in
    detail a simple algebraic geometrical model that not only is capable of qual-
    itatively accounting for all the \non-ordinary” time structures mentioned
    above, but also predicts some novel forms of these.
    3 Pencil Dimensions of Time/Space and Their Mental
    3.1 Time dimension viewed as a pencil of conics and its
    (mental) patterns
    A cornerstone of our model of the perceived time dimension is conics and
    their simplest, i.e., linear and single parametrical, aggregates, usually called
    pencils [23{25]. A conic is an algebraic curve analytically de¯ned by a
    second order (i.e., quadratic) equation. It is composite (singular) or proper
    according as this equation is factorable or not. A hyperbola, a parabola
    and an ellipse are all familiar (and the only) examples of proper conics
    (with a non-empty image). A composite conic consists of either a pair of
    (straight-)lines, which can be distinct or coincident, or of a single point.
    Two distinct conics lying in the same plane have, in general, four points in
    common (see Fig. 1, left); these, of course, need not be all distinct and/or
    real. Any two coplanar conics de¯ne a unique pencil of conics, viz. the
    totality of conics that pass through each of the points shared by the two
    conics (see Fig. 1, right); these common points are called base points of
    the pencil. Any pencil of conics in the real plane contains at least one
    composite conic, and maximum three (not necessarily distinct and/or of
    the same type). Given a pencil of conics, a point of the plane that is not a
    base point of the pencil lies on exactly one (possibly composite) conic of the
    pencil, henceforth called the \on-conic.” The remaining proper conics of the
    pencil (\o®-conics”) are found to form two di®erent, in¯nitely large disjoint
    families: one family comprises those proper conics which have the point
    (henceforth the \reference point”) in their interior (\in-conics”), while the
    other features those conics which have this reference point in their exterior
    (\ex-conics”). For a given proper conic, a point, not on the conic, is its
    exterior or interior point depending on whether or not it lies on a line
    256 A Geometrical Chart of Altered Temporality (and Spatiality)
    Figure 1. Two distinct conics (ellipses) in the real plane (left) de¯ne a unique pencil
    (right). This pencil, which is the most general one, features four distinct base points
    and three distinct composite conics (each being a pair of distinct lines). Out of its
    in¯nite number of proper conics only nine are shown: four ellipses, one circle and four
    tangent to the conic (see Fig. 2); the exterior/interior of the conic is thus
    the set of all its exterior/interior points.
    Figure 2. An interior (left) and exterior (right) point (small circle) of a given proper
    conic (drawn as an ellipse); the right hand side of the ¯gure also illustrates existence of
    (two distinct) tangent lines issued from the point to the conic. If the point in question
    is regarded as the reference point, then the conic on the lef-hand side is an in-conic,
    whereas that on the right-hand side | an ex-conic.
    Why do we pay so much attention, and ascribe so much importance,
    to this con¯guration? Simply because in the case when the reference point
    falls on a proper conic this con¯guration lends itself as an enunciation of our
    ordinary experience/sense of time (dimension). To spot this correspondence
    [26] we take the reference point as a representation of the observer/subject
    and conceive each conic of the pencil as a single event/moment of time, with
    the understanding that the ex-conics represent events of the past, the in-
    conics stand for events of the future, and that the unique on-conic answers,
    naturally, to nothing but the present moment, the \now” | as depicted in
    Metod Saniga 257
    Figure 3. A non-trivial structure within a pencil of conics induced by a generic position of
    the reference point (small circle) and qualitatively reproducing our common perception
    of time. The single proper on-conic (solid curve, the present moment) separates the
    proper o®-conics into two distinct domains; the domain of the in-conics (dotted, events
    of the future) and that of the ex-conics (dashed, events of the past). In both the cases,
    only a few conics are drawn.
    Fig. 3. It is important for the reader to realize at this point a fundamen-
    tal di®erence between the conventional, physical concept of time dimension
    and that of ours. While the former portrays time, loosely speaking, as a
    line and labels events by points on this line, our theory regards time as
    a nontrivial geometrical con¯guration consisting of a given point and an
    in¯nite collection of conics, each event being represented by a pair com-
    prising the very point and a conic of the set. In other words, in our model
    an event/moment of time, rather than being a structureless element/point,
    possesses itself an intrinsic geometrical structure, in virtue of which we are
    able to introduce a qualitative distinction between individual events (or,
    better, groups thereof). And our next task is to show that this distinc-
    tion is very sensitive to the position of the reference point with respect to
    the distinguished objects of the set. And, indeed, apart from the \past-
    present-future” pattern, our model gives rise to other two prominent, in a
    sense dual to each other, structures. These correspond, as the reader may
    have noticed, to the cases where the reference point coincides with a base
    point of the pencil (Fig. 4b), or falls on one of its composite conics (Fig. 4c).
    In the former case, clearly, all the proper conics are on-conics, whereas in
    the latter case the pattern is lacking any such conic, being endowed with
    ex- and in-conics only. Hence, the corresponding time dimension, in the for-
    mer case, consists solely of the present moments (the \present-only” mode),
    whilst, in the latter case, it comprises only the past and future, being devoid
    258 A Geometrical Chart of Altered Temporality (and Spatiality)
    Figure 4. The three qualitatively di®erent patterns of the pencil-borne temporal dimen-
    sion according as the reference point (a small circle) is (a) incident with a proper conic
    (see Fig. 3), (b) coincides with one of the base points, or (c) falls on a composite conic
    of the generating pencil. In the case b, out of an in¯nity of conics incident with the
    reference point only (the segments of) a few of them are illustrated. The pencil is, as in
    Fig. 1, of the most general type.
    of the proper moment of the present (the \no-present” mode). Let us try to
    rephrase these two unusual temporal arrangements in terms of pathological
    temporal constructs listed in the previous section. We readily ¯nd out that
    the present-only pattern accounts for nothing but experiences of \eternity,”
    \everlasting now.” The no-present design is seen to be a proper ¯t for the
    time \standing still” mode; for our feeling that time \°ows,” \proceeds” is
    unequivocally tied to the notion of the present moment, the \now,” as the
    linking element between the past and future and so it is only too natural to
    assume that the absence of this element in the pattern should correspond
    to a complete suspension/cessation of the (sense of) time’s °ow.
    At this point, it is instructive to make a slight digression and discuss a
    very interesting feature of our approach that has a serious bearing on the
    very meaning of the term \pathological” when it comes to the concept of
    time. This feature tells us about a relative probability of the occurrence of
    the above-discussed three patterns of time in the realm of psychopathology.
    This probability should not be understood in a strict sense of the word,
    but rather in a looser, algebraic geometrical sense. The reasoning goes as
    follows. The conics of any pencil sweep up the whole plane and as the
    latter contains 12 (double in¯nity) of points, there are 12 of potential
    past-present-future patterns. Next, as our pencil features three composite
    conics, each of these is a pair of distinct lines, and a line possesses 11
    (single in¯nity) of points, we have 3£2£11 = 6£11 ¼ 11 of no-present
    modes. And, ¯nally, as our pencil features four base points, there are
    just four present-only structures. We see a clear predominance of the past-
    Metod Saniga 259
    Figure 5. The three distinct types of \line-related” pencil-patterns of time in dependence
    on whether the reference line is incident with (a) zero, (b) one, or (c) two base points of
    the pencil. In each case, every illustrated point (a small circle) of the line is accompanied
    by a drawing of a small portion of the conic incident with this particular point.
    present-future mode within the group; no wonder that it corresponds to our
    \ordinary,” \consensus” experience of time. Equivalently, this explains why
    experiences of \eternity” and/or time \standing still” are regarded/referred
    to as \anomalous/peculiar;” for the relative probability of their occurrence
    with respect to our \ordinary” experience of time is truly negligible.
    Let us examine next the other conceivable forms of generic pencil-time.
    We shall assume that instead of a single reference point there is a whole
    in¯nity of them, and these are, for simplicity, taken to form a line. What
    di®erent kinds of time dimension do we ¯nd in this case? Remarkably, there
    are, like in the previous case, three of them. They di®er from each other, as
    depicted in Fig. 5, in the position of this line with respect to the base points
    of the generating pencil of conics, being in the sequel labelled, respectively,
    as a zero-, one- and two-point pattern according as the reference line hits
    no, one or two of the base points. Obviously, these line-related temporal
    structures can each be regarded as composed of an in¯nite number of basic,
    point-related patterns. This composition reads:
    type past-present-future present-only no-present
    zero-point in¯nity none six
    one-point in¯nity one three
    two-point none two in¯nity
    The numbers in the ¯rst two columns are readily discernible from Fig. 5 and
    the de¯nition of the corresponding elementary modes. It is only the last
    (no-present) column that requires a word of explanation. Thus, the number
    in the ¯rst line (six) is the number of intersections of the reference line with
    the composite conics of the pencil; it follows from the facts that our pencil
    260 A Geometrical Chart of Altered Temporality (and Spatiality)
    features three composite conics, each of these is a pair of distinct lines,
    and in a projective plane every line is incident with any other line. The
    number in the second line (three) answers to the fact that if the reference
    line passes through a single base point, the latter absorbs three of these six
    points. Finally, when the reference line joins two base points, it becomes a
    component of a composite conic, i.e., every point of it lies on the composite
    conic in question. We further see that, among the composites, only one,
    the one-point mode (Fig. 5b), features all the three types of elementary
    patterns, and, similarly, only one, the two-point mode (Fig. 5c), lacks the
    most familiar of them. On the other hand, there is only one elementary
    pattern, the no-present one, that enters all the three kinds of composites,
    and only one, the present-only mode, whose number is always ¯nite. It is
    very intriguing to see that there is no homogeneous composite.
    What are the phenomenological counterparts of these composite tem-
    poral patterns? Clearly, each of them must be a mixture/superposition
    of the time’s experiences we have found to correspond to the elementary
    patterns involved. And these are strange constructs indeed. Thus, the zero-
    point mode corresponds to such an uncanny state of consciousness where
    the subject encounters an in¯nite tangle of \ordinary” experiences of time,
    di®ering from each other in the location of the moment of the present and,
    consequently, in the spans of the regions of past/future, this perception be-
    ing accompanied by the sense of time \standing still.” The one-point case
    is even more complex, as it includes, on top of the above, also the feeling
    of \eternity.” And these experiences are very much like those of \disor-
    dered/fragmented” time given in the previous section! But what about the
    two-point structure, an intricate blend of the sense of \eternity/everlasting
    now” and that of time \standing still”? This kind of experience was pri-
    vately communicated to one of us by Linda Howe [27], an instructor in the
    \akashic records” technique:
    One common scenario is when the sense of the self is so ex-
    panded, beyond any physical boundary…. In this aspect, the
    awareness of being one with, or a part of, all that is can be
    profound. The illusion of separation can be perceived as dis-
    solving and, at the same time, the awareness of the oneness,
    or unity,…becomes heightened, sometimes acutely so… In this
    the experience of time is dramatic in its expansion and simul-
    taneous contraction. There is a sense that there is only one
    moment, that all of time/eternity is held in that instant, very
    compressed and as powerful as one’s imagination can conceive.
    Metod Saniga 261
    Simultaneously, there is a sense that there is no time in the ex-
    pansion. That all is holding still. Not even slow motion, but no
    motion. A total suspension of time is experienced. This is the
    all time/no time paradox.
    There remains only one mode to be explained, namely the experi-
    ence/sense of time \going/°owing backward.” To this end, we shall return
    to our ordinary, past-present-future pattern (Fig. 4a) and examine what
    happens to this pattern as the reference point starts \moving” away from
    its original position. This \motion,” as delineated in Figs. 6a-c, is assumed
    to take place in such a way that the point always remains incident with one
    and the same conic. As it is quite obvious from this ¯gure, the qualitative
    structure of the original pattern (Fig. 6a) is preserved until the reference
    point, en route, hits a base point (Fig. 6b), in which case the pattern ac-
    quires its present-only type. Further motion of the reference point clearly
    leads to re-establishment of the original type, but with one remarkable
    di®erence { with the in-conics and ex-conics having swapped their roles
    (Fig. 6c)! This means nothing but that the time’s arrows generated by
    the two past-present-future patterns, although sharing the same present
    moment, point in the opposite directions! One could hardly ¯nd a more
    elementary explanation of time-reversal.
    3.2 Space dimension viewed as a pencil of lines and its
    (mental) patterns
    It is evident that that the concept of a pencil, with conics as its constitut-
    ing elements, turns out to be an extremely fertile framework for getting a
    Figure 6. An elementary explanation of the phenomenon of a psychological time-reversal
    in terms of our pencil-borne model of time dimension. As in Fig. 3, the heavy curve(s)
    is (are) the on-conic(s), while those drawn as dotted/dashed represent the in-/ex-conics.
    A little arrow indicates the direction of the motion of the reference point (a small circle).
    262 A Geometrical Chart of Altered Temporality (and Spatiality)
    deeper qualitative insight into the ¯ne structure of psychological time di-
    mension. Motivated by this ¯nding, it is only too natural to address also
    the structure of psychological space in a similar fashion, i.e., retaining the
    concept, replacing only its constituting elements. As to our senses, space
    appears to have a less complex structure than time, and a line is a simpler
    geometrical object than a proper conic; we shall take a spatial dimension
    to be represented by a pencil of lines [8,9,25,26,28]. Our reasoning will par-
    allel that of the previous (sub)section, which will enable us to see how our
    approach gets to grips with the fundamental di®erence between time and
    space at the perceptual level. Two distinct lines in a plane su±ce to de¯ne
    a unique pencil, i.e., the set of all lines of the plane that pass through the
    point shared by the two (the point in question being called the vertex of the
    pencil). As any two lines in a projective plane have always one, and only
    one, point in common, there exists only one type of a pencil of lines; this
    is the ¯rst fundamental di®erence from the case of conics. Given a pencil
    of lines, a point of the plane (the reference point) that is di®erent from the
    vertex of the pencil is incident with exactly one line of the pencil (Fig. 7a);
    this line will henceforth be called the on-line, the remaining lines of the
    pencil being termed o®-lines. This particular a-pencil-of-lines-and-a-point
    con¯guration qualitatively mimics our \ordinary,” \here-and-there” sense
    of space, with the on-line standing for \here” and o®-lines for \there.” It
    is a spatial counterpart of the \ordinary,” past-present-future pattern of
    time (Fig. 4a). However, it must be pointed out here that, unlike o®-conics,
    o®-lines have all the same footing with respect to the reference point; this
    feature thus serves as a nice explanation why, in our \ordinary” state of
    consciousness, perceived space has a rather trivial structure when compared
    to that of perceived time. Another point-related spatial pattern is the one
    where the reference point is identical with the vertex of the pencil (Fig. 7b);
    as now all the lines of the pencils are on-lines, we get the \here-only” struc-
    ture. Being a twin of the \eternity,” \everlasting now” mode (Fig. 4b),
    this structure must necessarily be inherent to those \non-ordinary” states
    of consciousness that are characterized by feelings of \omnipresence,” or
    \fusion/oneness” with the universe. These here-and-there and here-only
    modes are obviously the only elementary patterns of pencil-space; for a line
    is so simple an object that there exist no singular forms of it and, so, there
    does not exist any spatial analogue of the no-present pattern. And as there
    are 12 potential here-and-there modes, but just a single here-only one, it is
    only natural that it is the former that underlies our \consensus” perception
    of space.
    Metod Saniga 263
    Figure 7. The two qualitatively di®erent elementary patterns of the pencil-borne space
    dimension depending on whether the reference point is di®erent (a) or not (b) from the
    vertex of the generating pencil of lines; in the latter case, out of an in¯nity of lines
    passing through the reference point only (the segments of) several of them are shown.
    Compare with Figures 4a and 4b, respectively.
    Figure 8. The two composite modes of space pencil-borne dimension, di®ering from
    each other in the position of the reference line (illustrated as a range of small circles)
    with respect to the vertex of the generating pencil of lines. Similarly to Fig. 5, every
    illustrated reference point goes with a drawing of a small part of the line incident with
    this particular point.
    The cases with the reference line are also structurally simpler than those
    of time dimension. There are, as the analogy suggests, a couple of them ac-
    cording as the line avoids the vertex (Fig. 8a) or is incident with it (Fig. 8b).
    As it can easily be recognized from Fig. 8, the former case is a compound of
    a single in¯nity of sole here-and-there modes, whereas the latter features a
    combination of both the elementary modes, with the preponderance of the
    more familiar of them. Accordingly, a subject experiencing the \avoiding-
    vertex” mode feels to be localized at every point (\multipresent”) along the
    particular space dimension, while that in a state backed by the \hitting-
    vertex” mode should feel to be both localized at a particular position of
    and simultaneously stretched out along the dimension in question.
    264 A Geometrical Chart of Altered Temporality (and Spatiality)
    4 Pencil-Borne Space-Time and the Varieties of its Internal
    So far we have treated time and space as two completely unrelated dimen-
    sions, which is of course in marked contrast to how the two aspects of reality
    are perceived to exist. Moreover, we have dealt with a single space dimen-
    sion only, while our senses tell us that there are (at least) three of them. So
    we have to re¯ne our model accordingly to comply with these constraints.
    To furnish this task, it is necessary to move from the (projective) plane
    into the (projective) space and | following and extending our recent work
    [26,28] | consider a speci¯c geometrical con¯guration comprising three
    distinct, non-coplanar pencils of lines (generating spatial dimensions) and
    a single pencil of conics (time). The planes carrying the pencils of lines are
    taken to be collinear, i.e., having a line in common, and none of the vertices
    of the pencils (denoted as Bi, i=1; 2; 3) is assumed to lie on this shared line
    (LB). The pencil of conics is, naturally, situated in the plane de¯ned by
    the three vertices (as these are assumed not to lie on a line), and its base
    points are these vertices and the point (L) of incidence of the plane and the
    line LB, as portrayed in Fig. 9. The reader may get an impression that our
    option for this con¯guration is completely arbitrary. This is, however, not
    the case, for this con¯guration plays a prominent role in the theory of so-
    called Cremona transformations between two projective spaces of dimension
    three.a For what follows it su±ces that the reader shares our intuitive belief
    that there is indeed something special to the above-described four-pencil
    con¯guration so that Nature found it worth making use of [26,28]. It is
    evident that this remarkable con¯guration, as it stands, can represent only
    a bare space-time, i.e., the space-time devoid of any subject/observer. So,
    in order to introduce the latter into our model, the con¯guration has to
    be endowed with an additional geometrical object. This can, of course, be
    done in a number of ways, one of the simplest being in terms of a single line
    (denoted as L¤ in Fig. 9). Armed with this premise and the postulates and
    ¯ndings of the previous section, we are able to ¯nd out which kinds of spatial
    and temporal patterns discussed above are mutually compatible (i.e., can
    form and \live together” on a single manifold) and thereby arrive at a ¯rst
    fairly comprehensive and mathematically well-underpinned classi¯cation of
    the psychopathology of time and space. It is not hard to see that this task
    aA proper explanation of what a Cremona transformation is and what kind(s) of distin-
    guished structures it entails would, however, take us too far a¯eld from the main topic
    of this paper: the interested reader is therefore referred to consult our above-mentioned
    papers [26,28] and/or a | though for ¯rst reading a bit di±cult | book by Hudson [29].
    Metod Saniga 265
    Figure 9. A particular geometrical con¯guration comprising three pencils of lines and a
    single pencil of conics, the latter being located in the plane de¯ned by the vertices of the
    pencils of lines. Out of an in¯nity of lines, only several are drawn in each of the three
    pencils; similarly, only a few proper conics (all being ellipses) are shown in the pencil of
    conics. The symbols are explained in the text.
    simply boils down to examining all possible positions of the reference line L¤
    within this con¯guration that lead to qualitatively di®erent arrangements
    of pencil-patterns induced by the point(s) of intersection of the line with
    the four pencil-carrying planes.
    We shall, of course, start with the case when the reference line is in
    a generic position with respect to the four planes. As it is obvious from
    Fig. 9, in this case the line cuts each of these planes in a unique point. As
    this point is clearly di®erent from any of the three vertices and from the
    point L as well, it speci¯es in each of the three planes BiLB (henceforth
    simply l-planes) a unique line, and in the B1B2B3-plane (c-plane) a unique,
    in general proper, conic (see Fig. 9; the three lines and the conic in question
    being drawn bold). Each of the three pencils of lines thus generates the
    here-and-there mode, and the pencil of conics features the past-present-
    future pattern. So, our generic pencil-borne space-time is, as expected, the
    space-time as perceived in our ordinary state of consciousness.
    In order to facilitate our subsequent discussion, we shall compactify our
    notation for di®erent kinds of pencil-borne patterns. For each elementary
    pattern we shall reserve one letter, uppercase for time and lowercase for
    266 A Geometrical Chart of Altered Temporality (and Spatiality)
    Figure 10. A diagrammatic sketch of an algebraic geometrical classi¯cation of pencil-
    borne space-times. Each sub¯gure features the reference line, the four \fundamental”
    planes and, in each of the latter, those fundamental elements that are \picked up” by
    the reference line; the cases where the reference line is incident with all the fundamental
    lines of a given l-plane and/or with an in¯nite number of the fundamental conics in
    the c-plane, are illustrated by drawing several lines and/or conics, respectively. The
    remaining symbols and notation are explained in the text.
    space; a composite mode will then bear several letters, corresponding to the
    elementary modes it consists of. As for time pencil-patterns, we shall adopt
    the following symbols: \A” for the ordinary, past-present-future mode (the
    \arrow” of time); \E” for the present-only (\eternity”) mode; and \S” for
    the no-present (time \standing still”) mode. The composite modes will
    then have the following abbreviations: \¹A¢S” for the zero-point mode;
    \¹A¢S¢E” for the one-point mode; and \S¢E” for the two-point mode, with
    ¹ standing for \multi-” and signifying that the number of modes denoted by
    the letter immediately following this symbol is unlimited/in¯nite. Concern-
    ing space patterns, we shall use \h” for the ordinary, here-and-there mode
    and \o” for the here-only (\omnipresence”) mode. Its composites will ac-
    cordingly be denoted as \¹h” (vertex-avoiding) and \h¢o” (vertex-hitting).
    Metod Saniga 267
    So what are possible kinds of our pencil-borne, \Cremonian” psycho-
    space-times? From an algebraic geometrical point of view, there are alto-
    gether 19 di®erent types of them, as depicted in Fig. 10. And they are seen
    to form a truly remarkable sequence, once being grouped into distinict rows
    according to their number/abundance (the ¯rst column) and into distinct
    columns according to the number of dimensions of localizability (the low-
    ermost row) and/or the character of the Cremonian image of the reference
    line in the second projective space (the uppermost row). As easily dis-
    cernible from the ¯gure, the individual sub-¯gures di®er from each other in
    the position of the reference line and each of them is accompanied by four
    of the above-introduced labels/acronyms so that the reader can readily ¯nd
    out the corresponding internal pattern of each spatial dimension and time
    as well. The number/abundance of a particular type within the structure
    is, as above, of a geometrical origin. Thus [30], there are 14 (quadruple
    in¯nity) of lines in a three dimensional projective space and out of them
    13 are incident with a given line, 12 with two di®erent (possibly incident)
    lines, and 11 pass through a given point and simultaneously lie in a given
    plane; a line is uniquely de¯ned by two distinct points (their joint) or two
    di®erent planes (their meet). Non-localizability in a particular dimension
    means that the reference line does not de¯ne a unique line in the corre-
    sponding l-plane, or a unique conic in the c-plane; this, obviously, happens
    when the reference line passes through a base point (or the point L), or lies
    completely in an l-plane/the c-plane. Hence, \o”, \¹h” and \h¢o” are non-
    local patterns of space dimensions, while \E”, \¹A¢S,” \¹A¢S¢E” and \S¢E”
    are those of time; in Fig. 10, the former/latter are illustrated by drawing
    several lines/conics in the corresponding l-planes/c-plane so that they can
    readily be recognized.
    A number of intriguing facts can be revealed from Fig. 10. First, and
    perhaps the most crucial fact, is that our consensus space-time (represented
    by the sub-¯gure in the top left-hand corner; this sub-¯gure is a fully equiv-
    alent version of Fig. 9) is, as expected, by far the most abundant type in
    the hierarchy, as there are 14 of its potential cases. On the other hand,
    there is just one potential case of space-time where the subject is completely
    non-localized (the sub-¯gure in the bottom right-hand corner; the reference
    line is here identical with the line LB). Next, it is fairly obvious that the
    most numerous patterns are those where the subject is completely local-
    ized (the \all” column); as the number of dimensions of non-localizability
    increases (i.e., as we move in the ¯gure from left to right), the number of
    potential cases decreases (i.e., we move from the top to the bottom of the
    268 A Geometrical Chart of Altered Temporality (and Spatiality)
    ¯gure). Further, we notice that if there are at least two dimensions of non-
    localizability (the last three columns), one of them is always time. Also, for
    the two non-ordinary elementary patterns of time, the S-mode prevails over
    the E-mode. The most variegated row is seen to be the 12-one (featuring
    six di®erent types of space-time patterns and spanning three di®erent levels
    of non-localizability), the least variegated being the top and bottom ones.
    It is also worth stressing that out of the spatial modes it is the h-one that
    occurs most frequently, while amongst the temporal patterns it is the S-
    and E-modes that enjoy this property. Also, there exists no pencil-borne
    space-time whose space dimensions would be all of the o- or h¢o-type. In-
    terestingly, the least frequently encountered patterns are h¢o (space) and
    S¢E (time). Finally, there are pairs of patterns which are incompatible with
    each other: the o-mode with the ¹h-one, the S¢E-mode with the ¹h-one
    and the S-pattern with the o-one.
    From the information gathered in Fig. 10 and the ¯ndings of the previous
    section(s) it will represent no di±culty for the reader to infer and analyze
    the \experiential contents” for each type of space-time. We only add the
    following note. One of the most distinguished features of a great majority
    of extraordinary states of consciousness is a seriously altered sense of indi-
    viduality, ego, or self-hood. In particular, the greater the departure from
    our consensus reality, the lesser the sense of ego; ultimately, in the most
    abstract states, the subject feels to completely transcend/surpass his/her
    sense of ego, and, so, the dichotomy between subject and object. That
    important feature, too, has a proper place in our model, once we identify
    the \degree” of the sense of ego with the level of localization of the subject
    in our pencil-borne space-times. From Fig. 10 we then readily discern that
    our consensus experience of space-time is characterized by the strongest
    sense of the self. As we move across the ¯gure from left to right, the sense
    of ego accompanying the individual types of space-times (or, better, the
    corresponding states of consciousness) gradually \melts/dissolves,” until it
    completely vanishes in the state represented by the sub-¯gure located at
    the very bottom of the ¯gure. Here is a recently found ¯rst-person account
    that describes in great detail not only this transformation of the sense of
    \I,” but also accompanying profound changes in the perception of both
    time and space, and which dovetails very nicely with the implications of
    our model [31]:
    For twelve hours I moved in and out of dimensions of both space
    and time. The incomprehensible became comprehensible. Re-
    alities within realities blossomed and faded. From the in¯nitely
    Metod Saniga 269
    large to the in¯nitely small, unbounded and unfettered mind
    °ashed across landscapes of incredible depth and beauty…. I
    was looking into the source of my very being, and without ques-
    tion, my creator. And then I came to realize too that I was at
    the interface between individual mind and absolute mind.
    Entheogens, or in my case psilocybes, provide the pivotal role
    of interfacing between individual consciousness and universal
    consciousness. It is the crucial link or conduit that bridge the
    two at a single point. That point then begins to widen, and
    both entities slowly merge. As the interface grows, what were
    initially two now opens into one. It’s not just a random happen-
    ing though, an alignment process between the two takes place.
    Actually it’s more a matter of one aligning itself to the other.
    This is not a conscious operation, although consciousness is wit-
    ness to it…. To experience this phase of the psychic event was
    an absolute revelation with all the glory and beauty imaginable.
    With my minds eye I was able to see the outline of the inter-
    face where the two became the One, where duality merged into
    unity…. I had the pleasant ability at the center of the interface
    to merge in and out at will. In one moment I was myself, a
    separate thinking entity with all my individual thoughts; as I
    merged out my self-hood ceased to exist; my individuality gone;
    my thoughts as unique things ceased to be, given way to abso-
    lute thought. Time and space played an interesting part in this
    experience. While in myself time existed, time °owed, there was
    past and future, but while merged in unity time ceased, there
    was no past or future. Everything was in a single instant; what
    Plotinus called the \Eternal Now.” In myself space had dimen-
    sion, there was up and down, limitations existed. Merged in the
    other, there was no up, no down, no limitation, all was in¯nite
    and absolute. This gave rise to another incredible phenomenon;
    with time suspended and space without boundary omniscience
    came into full awareness; yes, all things known; no limitations
    to knowledge…. Omnipotence, and omnipresence also became
    an awesome recognition, but not related to me personally since
    the I had ceased to be; they were aspects of that great Oneness
    that was the universe of consciousness. Merging back into my
    own ego left me with only a memory of being present to it all….
    270 A Geometrical Chart of Altered Temporality (and Spatiality)
    5 Conclusion
    A few weeks before his death, in a letter of condolence to the family of his
    life-time friend Michele Besso, Albert Einstein wrote [32]: \For us believing
    physicists the distinction between past, present, and future is only an illu-
    sion, even if a stubborn one.” We have, however, rigorously demonstrated
    that this \illusion” and its most pronounced \peculiarities/anomalies” are
    underlaid by a de¯nite algebraic geometrical pattern. Does it mean that
    our math is a sort of illusion, too? Or, rather, is it physics that falls short of
    grasping the true nature of time [33]? To tackle this dilemma, we perhaps
    need a new conceptual framework for physics [34,35], like, for example, the
    relational blockworld proposed recently by Stuckey et al. [36]. The lat-
    ter inverts the conventional physics paradigm/hierarchy by taking relations
    (modelled by matrix variables) to be fundamental to relata (modelled by
    single-valued variables) and viewing matrix variables as having no counter-
    part in diachronic/trans-temporal objects, i.e. not having ontological status
    as \real things.” This inverted paradigm is perfectly in the spirit of, and
    lends support to, our model once we regard individual states of conscious-
    ness (\mental space-times”) as relations not needing to have counterparts
    in the \material world,” and so in the brain in particular. And this is
    a truly powerful paradigm shift, supported by a number of extraordinary
    human experiences, like the following one [37, pp. 26,27]:
    I experience myself as beyond everything, literally everything,
    . . . I am a silent witness, vast and unchanging, beyond time and
    all space. . . The recognition, which is a direct perception, is that
    everything is in me. The body, the universe, essence, person-
    ality, everything that can become an object of perception, is
    not me, but is in me. I am pure awareness, mere witnessing,
    where everything arises and passes away. . . I am beyond space
    and time; both space and time are within me. All of time is
    a movement within me. Personality, or more accurately, the
    personal experience or soul, is time. Time is the °ux of this
    personal consciousness. Essence is timelessness. I see time as
    the movement of the timeless within me. All of time, the time
    of the body and of all of physical existence, is a small process
    within me. I am beyond time and timelessness. I am the be-
    yond, beyond all and everything.
    Metod Saniga 271
    I am very grateful to Mr. P. Bend¶³k for painstaking drawing of the ¯g-
    ures and Dr. R. Kom·z¶³k for the help with conversion of the latter into
    postscript form. I would also like to express my cordial thanks to Miss D.
    Veverkov¶a and Mr. P. Hahman for translating into English all the excerpts
    taken from journals written in German. This work was supported in part
    by the 2001{2002 NATO/FNRS ARF \Algebraic Geometrical Structure
    of Spacetime,” the 2000{2002 NATO CLG PST.CLG.976850 \Structure of
    Time and Quantum Computing,” the joint 2001{2003 CNR{SAV research
    project \The Subjective Time and Its Underlying Mathematical Structure”
    and a 2004 SSHN Physics Fellowship of the French Ministry of Youth, Na-
    tional Education and Research (# 411867G/P392152B).
    1. Cutting, J., and Silzer, H. (1990) Psychopathology of time in brain disease
    and schizophrenia, Behavioural Neurology 3, 197{215.
    2. Hartocollis, P. (1983) Time and Timelessness, or the Varieties of Temporal
    Experience, International Universities Press, New York.
    3. Heimann, H. (1990) Zeistrukturen in der Psychopathologie, in J. Ascho® et al.
    (eds.), Die Zeit: Dauer und Augenblick, Piper, MÄunchen, pp. 59{78.
    4. Jaspers, K. (1923) Allgemeine Psychopathologie, Springer, Berlin.
    5. Melges, E.T. (1982) Time and the Inner Future: A Temporal Approach to
    Psychiatric Disorders, John Wiley and Sons, New York.
    6. Minkowski, E. (1933) Le Temps V¶ecu | ¶ Etudes Ph¶enom¶enologiques et Psy-
    chopathologiques, Gauthier, Paris.
    7. Saniga, M. (2000) Algebraic geometry: A tool for resolving the enigma of
    time?, in R. Buccheri, V. Di Gesµu, and M. Saniga (eds.), Studies on the Struc-
    ture of Time: From Physics to Psycho(patho)logy, Kluwer Academic/Plenum
    Publishers, New York, pp. 137{166.
    8. Saniga, M. (1998) Unveiling the nature of time: Altered states of consciousness
    and pencil-generated space-times, Int. J. Transdisc. Studies 2, 8{17.
    9. Saniga, M. (1999) Geometry of psycho(patho)logical space-times: A clue to
    resolving the enigma of time?, Noetic Journal 2, 265{273.
    10. Huber, G. (1955) Akasa, der Mystische Raum, Origo Verlag, ZÄurich.
    11. Atwater, P.M.H. (1988) Coming Back to Life. The After-E®ects of the Near-
    Death Experience, Dodd, Mead and Company, New York.
    12. Braud, W.G. (1995) An experience of timelessness, Exceptional Human Expe-
    rience 13, 64{66.
    13. Tellenbach, H. (1956) Die Raumlichkeit der Melancholischen: I. Mitteilung,
    Nervenarzt 27, 12{18.
    14. Muscatello, C.F., and Giovanardi Rossi, P. (1967) Perdita della visione mentale
    e patologia dell’esperienza temporale, Giornale di Psichiatria e di Neuropa-
    tologia 95, 765{788.
    272 A Geometrical Chart of Altered Temporality (and Spatiality)
    15. Beringer, K. (1969) Der Meskalinrausch, seine Geschichte und Erschein-
    ungsweise, Springer, Berlin.
    16. Israeli, N. (1932) The psychopathology of time, Psychol. Review 39, 486{491.
    17. Lehmann, H.E. (1967) Time and psychopathology, Annals of the New York
    Academy of Sciences 138, 798{821.
    18. Schilder, P. (1936) Psychopathology of time, Journal of Nervous and Mental
    Disease 83, 530{546.
    19. Fischer, F. (1929) Zeitstruktur und Schizophrenie, Zeitschrift fÄur die gesamte
    Neurologie und Psychiatrie 121, 544{574.
    20. Laing, R.D. (1968) La Politica dell’Esperienza, Feltrinelli, Milano.
    21. Kloos, G. (1938) StÄorungen des Zeiterlebens in der endogenen Depression,
    Nervenarzt 11, 225{244.
    22. Ebin, D. (1961) The Drug Experience, Orion Press, New York.
    23. Berger, M. (198

  • avatar


    A little more science for the believers…
    In November 2006 I was invited to a meeting at the Salk Institute in La Jolla, California called “Beyond Belief” ( Other speakers and attendees were predominantly atheists, and harshly critical of the notion of spirituality. They included Richard Dawkins, Sam Harris, Patricia Churchland, Steven Weinberg (the least venal), Neil deGrasse Tyson and others who collectively vilified creationists and religious warriors. But the speakers also ragged on the notion of any purpose or meaning to existence, heaped ridicule on the very possibility of a God-like entity (and those who believed in such an entity), declared that scientists and philosophers should set society’s moral and ethical standards, and called for a billion dollar public relations campaign to convince the public God does not exist.

    Near the end of the first day came my turn to speak. I began by saying that the conference to that point had been like the Spanish Inquisition in reverse – the scientists were burning the believers. And while I had no particular interest in organized religion, I did believe there could be a scientific account for spirituality.

    After pointing out faulty assumptions in conventional brain models for consciousness and summarizing the Penrose-Hameroff theory, I laid out my plausibility argument for scientific, secular spirituality, suggesting cosmic connections and influence in our conscious thoughts occurred via quantum interactions in microtubules. I closed with a slide of the DNA molecule which emphasized it’s internal core where quantum effects rule, suggesting a Penrose non-computable influence in genetic mutations and evolution (aimed at Dawkins in the form of a quantum-based intelligent design).

    At the end a few people clapped loudly, but most sat in steely silence. The moderator and conference organizer Roger Bingham said I had enraged nearly everyone in the room. Indeed, I had raised a stink, and felt (happily) like the skunk at an atheist convention.

    Comments from the audience were negative, but off base. Physicist Lawrence Krauss said my suggestion of backward time effects in the quantum unconscious (indicated by experiments, and required to rescue consciousness from its unfortunate characterization as epiphenomenal illusion) were impossible. He was apparently unaware of the verification of Wheeler’s delayed choice experiments which precisely prove such backward time effects. Krauss also questioned the possibility of biological quantum computation at brain temperature, but I pointed to evidence for warm quantum coherence in biological photosynthesis. Neuroscientist Terry Sejnowski attempted to criticize my view, but floundered, unable to explain how his conventional approach could explain 40 Hz gamma synchrony EEG (the best measurable correlate of consciousness) without quantum effects.

    Our theory also chafes proponents of artificial intelligence (“AI”, including advocates of the so-called Singularity) who assume consciousness results from interactions among neurons with no consideration of deeper activities or quantum mechanisms. Along these lines I recently spoke at Google in Silicon Valley, my talk being titled A new marriage of brain and computer – Why the Singularity is bogus. That talk is at

    I am not by nature confrontational, but am happy to debate scientists and philosophers who oppose our theory. Atheism does not hold the scientific high ground. Secular spirituality based on quantum biology and the physics of spacetime geometry is a viable and important idea. I am not offering or suggesting any proof, just a plausibility argument.

  • avatar


    I read Dr. Long’s book. I thought that the fundamentalist Christians were anti science and dogmatic. yeah…looks like the atheists are even worse

  • avatar


    Damn people. I don’t quite agree with how the OP got his point across, however, I do agree with his point and several others made. Eye-witness accounts are just simply not evidence, it’s just that easy. There is an immense amount of empirical evidence AGAINST a life-after-death presented by actual scientists (Not an MD). The human brain is tailor-made to calm the body while it’s under intense stress, and I’d imagine being near death would be intense stress for the body. This “chemical cocktail” is released to ease the body to aid in healing or make death that much easier. To one woman (There may be others, if I missed you, you’re welcome to reply as well) who is using Occam’s Razor to state that the simplest answer is God; That’s utterly redundant. That just brings up a much larger question; What made God?

    Also, I’d like to add that I’m an atheist, and these people making absurd generalizations towards atheists are sadly disillusioned and prejudice. It’s to the same degree that some atheists group all religious people into the category of these Young-Earth Creationists. Leave your prejudice behind when science is the topic or you’ve already lost any argument or case.

  • avatar


    Science is as dogmatic as religion, currently.

    Qualitative measures and quantitative measures-are measures! the lack of openness to other understandings and considerations of what we are measuring is like a person who has never traveled but angry at those who don’t speak his (usually) language. Consciousness outside of the mechanical, or reductionistic models will not help our understanding of human experience, change, evolution- our human development. There are many realms of science, that live within the imagination. The extrapolation of statistical analysis and theoretical positions at the base of psychics; the understanding of the brain and consciousness; and the universe-prove scientific rhetoric wrong almost daily now. Every recent discovery proves the latest theory wrong, and lets not forget science community “politics”.

    Science today is limited by its focus on function and technology and not on exploring the imagination, the various sources of creativity and the many ways and possibilities of the origins of how that represents life.

  • avatar


    Er??? … He’s an oncologist. His patients are dying in pain. Does he give them grade A pharmaceuticals to deal with the pain? Ja’ think this may have something to do with visions?

    Ever hear of a Brompton Cocktail?

    Morphine, Pharmacy grade Coke and a few other things in brandy. That’s just a little something to take the edge off the pain.

    And you wonder why they see things?

  • avatar

    Angela Jurgensen

    Hi there,

    As a book critic, I must say that I was disappointed when I read your review. Your arguments against Dr. Long’s book are based purely on your experience with other Afterlife books — you have not read his book at all. Not that I have either, mind you; but I did read pass the blurb.

    How can you be objective and hold your own beliefs, if you do not take the time to read and consider someone else’s mind and body of work? The only intelligent, proper way to fight an “enemy” is to know it.

    You would have made a much stronger post if you had read the book, and not only the blurb. By reading past the blurb, you would be able to try and debunk some of the valid points the author makes — such as, how come blind people, who are blind since birth, have visual experiences when going through a NDE?

    Simply calling a doctor a “fucking idiot” just makes you look like you can’t hold an argument, and that you are a cement-enclosed brick, impervious to any kind of argument that contradicts your own beliefs.

    Think of it this way — by responding to a 224 page book with 4 paragraphs that don’t really mention anything specific to the book itself — only to the GENRE the book was written on — makes you seem close minded and lazy.

    And of course, makes people shake their heads and write here on your page — either saying “Hmmm, weak argument” or saying “YEAH that’s right, the doctor is a dumb ass, pass me the beer.”

    Maybe this is all you want for your website.

  • avatar


    My first impression is that “near death” is a very problematic phrase. It’s like nearly pregnant. You’re either dead or you’re not dead. Is an instant of death the same as being dead for twenty minutes or an hour or a year? The doctor who proposes the idea of life after death says, “Scientifically speaking, interviewing people that have permanently died is challenging.” Case in point.

    Next, the doctor uses the term “permanent death” in this interview. This tells me that whatever he has studied or read about that provides a clue to the survival of physical death has nothing to do with people who have died for any length of time. Further, what is “permanent death” if not permanent? Seems rather unambiguous to me.

    The notion of life after death and reincarnation is curious and offers much hope, including to the doctor in this interview who says that it helps him deal with cancer patients. However, for me it’s a quantum leap to say there is evidence for life after death when the evidence is inconclusive and so full of holes. They’re going to have to do better than testimonials and diagnostics on people who show no life signs for only a few minutes or so.

  • avatar


    You sound like a jackass! Keep talking!

  • avatar

    Paulo Garutti

    Angela, Bravo! You said everything! How can you expect to be respected by calling someone a “fucking idiot”…
    I also believe today’s science is as dogmatic as religion is. I do hope one day they will both merge into something fundamental. Today none of them are holding the proper answers.

  • avatar

    Fay Hill

    Hi Jacob Fortin,
    I am astounded that you use insults (not scientific proof) and vague references to dreams and the effects of brain chemicals produced by stressed people without having even read Dr Long’s book and seen that he has conducted a totally professional scientific research study and already addressed the dreams/brain chemical hallucination explanations in his book. You did not even know what is in the book, you didn’t even realise Long was a practicing medical doctor, and obviously you did not read his research methods in his book, yet you are quick to criticise. Why? I will tell you why because science is based on materialism/pysicalism, evolution is most definately based more than any other theoretical science, so an immaterial dualist theory busts a lot of science taught as fact today. Do that and out come the knives, scientists that have not even read your research report of any details just want to preserve their materialist/physicalist dogma and their theories even at the expense of several falsifications.
    Kind Regards

  • avatar

    greg deliver

    A lot of times science is just crap and yeah it does not have all the answers, its based on testing, placebo and other crap.

    I have read many studies on prolotherapy and science, they said it was flawed and did not work, science right there is bull because the studies where not done correctly.

    Has for NDE well how can it be wrong when there is no brain activity the heart is stopped and millions of people came back from the dead with the same story. It cannot all be brain wave activities.

    Science cannot explain everything and most of the time fails to explain everything.

  • avatar


    Dr. Michael Sabom is a cardiologist whose latest book, Light and Death, includes a detailed medical and scientific analysis of an amazing near-death experience of a woman named Pam Reynolds. She underwent a rare operation to remove a giant basilar artery aneurysm in her brain that threatened her life. The size and location of the aneurysm, however, precluded its safe removal using the standard neuro-surgical techniques. She was referred to a doctor who had pioneered a daring surgical procedure known as hypothermic cardiac arrest. It allowed Pam’s aneurysm to be excised with a reasonable chance of success. This operation, nicknamed “standstill” by the doctors who perform it, required that Pam’s body temperature be lowered to 60 degrees, her heartbeat and breathing stopped, her brain waves flattened, and the blood drained from her head. In everyday terms, she was put to death. After removing the aneurysm, she was restored to life. During the time that Pam was in standstill, she experienced a NDE. Her remarkably detailed veridical out-of-body observations during her surgery were later verified to be very accurate. This case is considered to be one of the strongest cases of veridical evidence in NDE research because of her ability to describe the unique surgical instruments and procedures used and her ability to describe in detail these events while she was clinically and brain dead.

    When all of Pam’s vital signs were stopped, the doctor turned on a surgical saw and began to cut through Pam’s skull. While this was going on, Pam reported that she felt herself “pop” outside her body and hover above the operating table. Then she watched the doctors working on her lifeless body for awhile. From her out-of-body position, she observed the doctor sawing into her skull with what looked to her like an electric toothbrush. Pam heard and reported later what the nurses in the operating room had said and exactly what was happening during the operation. At this time, every monitor attached to Pam’s body registered “no life” whatsoever. At some point, Pam’s consciousness floated out of the operating room and traveled down a tunnel which had a light at the end of it where her deceased relatives and friends were waiting including her long-dead grandmother. Pam’s NDE ended when her deceased uncle led her back to her body for her to reentered it. Pam compared the feeling of reentering her dead body to “plunging into a pool of ice.”

    Pam Reynolds interview about her NDE:
    Blind woman sees for the first time in her life during her NDE:

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