On the Non-Linear Origins of Consciousness Part II: Eternity versus Infinity 1.3.0

Abstract Eternity is a key concept in religious thought, infinity a key concept in scientific thought, and it is a common thing for people to equivocate between them. In particular scientists have the idea that consciousness is because of its attachment to the body and the brain of finite extent, which is to be contrasted with the orthodox Christian view that consciousness can exist independently of the brain, and is of infinite extent. Both parties see infinite consciousness as something that starts at some point on a time line and extends for an interminably long period, with scientists typically denying that consciousness has this property, and Christians and others affirming it. Here we carefully define eternity, and the notions of infinity in common usage by mathematicians scientists, and explain why they are not the same.


Eternity and Infinity

Mathematicians and scientists, and perhaps most people, have a notion of the infinite as something very long or very short, or very big or very small. This notion is common to all orthodox mathematical thinking, and pervades all orthodox physical theories. What it boils down to is thought that there is something greater than any specified quantity (1, 2, 3…) and/or that is or that there is something smaller than any specified quantity (1/2, 1/2, 1/3…).

David Lodge in his book The Picture Goers (1) writes

Think of a ball of steel as large as the world, and a fly alighting on it once every million years. When the ball of steel is rubbed away by the friction, eternity will not even have begun.

Like many, Lodge has taken “eternity” to be another word for an endlessly long period of time.

In the arena of problem solving -most especially when a problem is very difficult to solve- it is sometimes the case that the reason for a problem is, not that no one is smart enough to think of an answer to a question that is available, but that the answer isn’t available because the question hasn’t been correctly posed. Suppose for example if I ask whether a man has stopped beating his wife in the circumstance that the wasn’t beating their wife in the first place. That question cant possibly be correctly answered. Nor -I assert- can the vexed question of the finitude or the infinitude of consciousness construed as something that exists on a linear time, line and divides materialists from non-materialists when it comes to the subject of the nature consciousness, and life after death, some of the most important questions that can possibly be posed. The problem in the wife-beating example is the false assumption of wife-beating, the problem in the dispute between the materialist and the orthodox Christian is the false assumption that eternity is linear. If eternity is linear, then anyone who claims that consciousness is eternal is claiming that it is infinitely long in the mathematicians sense of an infinitely long number or time line. From here, the Atheist Materialists loudly proclaim that consciousness is not eternal, and Christians, Muslims, some Jews (not Hasidic Jews of Kabbalists (2)) no less loudly proclaim that it is eternal, where both parties to the dispute have the idea fixed in their heads, expressed by Lodge in The Picture Goers, of consciousness as travelling on a line that has a beginning and stretches indefinitely into the distance.


The Theory of Relativity

To see that this is quite the wrong way to look at it, and that neither Atheist Materialists nor modern day Christians know what they’re talking about, consider the Special Theory Relativity. Its essence can be most easily explained by reference to the famous train thought-experiment. The figure below depicts a train, and a light source located in the center of a carriage. It shows that from the point of view of an observer inside the train, light emitted from the center of the carriage reaches the front and the rear of the carriage simultaneously, but that from the point of view of an observer outside the train, the light reaches the front of the carriage first.

One of the following principles then must be false:

1. There is a perfectly isomorphic relationship between the time lines of observers regardless of their states of motion

2. The fundamental laws of physics are the same for all observers (in uniform motion)

3. Light is propagated at the velocity c regardless of the state of motion of the emitting body

(2) and (3) are apparently true, meaning that (1) is false. According to SR then, observers traveling at different velocities literally inhabit different spatio-temporal environments, different times and spaces (3, 4). In particular, space contracts and time slows in the direction of motion. But there is a subtlety here that has been completely overlooked, and that we can reveal by considering General Relativity, Einstein’s extension of SR to gravity. At root of GR is the idea that mass curves space-time (4, 5), and the fact that this is a half-truth is suggested by the implication of local infinities (6), the lack of a coherent mathematical framework for both large scale and small scale objects (7), and by the flat rotation curves of distant galaxies. The last is the motivation for the idea of dark matter (8):

The idea of a space-time curved by mass readily takes us back to an initial condition of the universe such that all the mass of the universe is compressed to a point, and this same infinite compression of mass is, by the terms of the theory, also to found at the centers of black holes. But the singular nature of the initial condition of the universe represents the beginning of the time, while the singularities at the centers of black holes in some sense represent the end of time, and these forms of curvature should therefore be quite distinct. More particularly, it should not be the case that both are attributable to the infinite action of the force of gravity – this is the theory breaking down, and a sign of a false assumption. Yes, everyone can see that the singularity “preceding” the big bang is not the same as the singularities “inside” black holes, but there is missing mathematics, and whether we like it or not, GR paints a picture of the universe that begins and ends in an identical state (infinite gravity is infinite gravity) when, clearly, there is throughout the universe as we know it an arrow of time leading from an energetic contracted state to an exhausted expanded one. In so far as it so much as makes sense to speak of infinite gravity, these can’t both be the result of infinite gravity. If we give up this idea that curvature is due to mass (which is a combination of light and space), and employ instead the idea that curvature is due to imbalances of light and space (where the classical world is balanced, the atomic world is unbalanced in the direction of light, and black holes are unbalanced in the direction of space), we will find that we can solve this and other problems. Mathematically, we capture what it is to be balanced, and what it is to depart from balance, thereby producing curvature, by re-expressing the tradition equation for a circle of area 1 (\pi \sqrt{\frac{1}{\pi }}^2=1) as

\lim_{x\to \infty } \left(e^{2 \gamma } \sqrt{\frac{1}{e^{2 \left(\sum _{n=1}^x \frac{1}{n}-\int_1^x \frac{1}{n} \, dn\right)}}}\right){}^2=1

Where the traditional equation fails by implying that an energy source located at the center of this area unit-circle is undiminished from center to circumference (it has either a zero or an infinite radius), the second provides us with a potentially infinite hierarchy of energy levels that are necessarily non-infinite and non-zero. Given that gamma is a spacial case of

\zeta (s)-\frac{1}{s-1} for s = 1, we can go from \lim_{x\to \infty } \, e^{2 \gamma } \sqrt{\frac{1}{e^{2 \left(\sum _{n=1}^x \frac{1}{n}-\int_1^x \frac{1}{n} \, dn\right)}}}{}^2=1 to the more general

\lim_{x\to \infty } \left(e^{(s+1) \left(\zeta (s)-\frac{1}{s-1}\right)} \left(\left(\frac{1}{\exp \left((s+1) \left(\sum _{n=1}^x \frac{1}{n^s}-\int_1^x \frac{1}{n^s} \, dn\right)\right)}\right){}^{\frac{1}{s+1}}\right){}^{s+1}\right)=1

Let s be a positive integer greater than 1 and let

\left(\frac{e^{2 \gamma } \left(e^{-\left(\zeta (s)-\frac{1}{s-1}\right)}\right)^2}{\hbar =e^{2 \gamma } \left(e^{-\left(\zeta (s)-\frac{1}{s-1}\right)}\right)^2-e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^7 \frac{1}{n^s}-\int_1^7 \frac{1}{n^s} \, dn\right)}\right){}^2}\right){}^{1/s} = the critical line/radius on the one side of which curvature in the direction of light is classical.
and on the other is non-classical

and we see something like this:

Let s be a positive real number less than 1, and let

\left(\frac{e^{2 \gamma } \left(e^{-\left(\zeta (s)-\frac{1}{s-1}\right)}\right)^2}{\sigma =e^{2 \gamma } \left(e^{-\left(\zeta (s)-\frac{1}{s-1}\right)}\right)^2-e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^7 \frac{1}{n^s}-\int_1^7 \frac{1}{n^s} \, dn\right)}\right){}^2}\right){}^{1/s} = the critical line/radius on the one side of which curvature in the direction of space is classical
and on the other is non-classical

and we have the following model:

Since the initial condition of the universe is, in this model, massless -since it involves no space and time, and an infinite concentration of light- it follows that absolutely speaking light has no speed, and that the apparent speed of light is due to the expansion of space. Hence we have

1.* There is a perfectly isomorphic relationship between the time lines of observers regardless of their states of motion

2.* The fundamental laws of physics are the same for all observers

3. * Space expands at the velocity c regardless of the state of motion of the body in space

Recalling that balanced classical regions of moderate curvature are governed by the equation \lim_{x\to \infty } \, e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^x \frac{1}{n}-\int_1^x \frac{1}{n} \, dn\right)}\right){}^2=1, we can associate this concept of physical inertia to one of mathematical inertia and we can re-express 1.* – 3.* in this way:

1.** There is a perfectly isomorphic relationship between the number lines of observers regardless of their states of motion

2.** The fundamental laws of arithmetic are the same for all observers

3.** The prime-density of an arithmetic progression is governed by \lim_{x\to \infty } \left(e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^x \frac{1}{n}-\int_1^x \frac{1}{n} \, dn\right)}\right){}^2\right)=1

If (2**) and (3**) are true, then we can preserve the symmetry of the laws of arithmetic and the balance of prime-density and sparsity only at the cost of the symmetry of the unit. We might say that everyone has a clock governing their lives that runs at a slightly speed to anyone else’s clock because the prime-based asymmetry between the underlying number lines. But the equation \lim_{x\to \infty } \left(e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^x \frac{1}{n}-\int_1^x \frac{1}{n} \, dn\right)}\right){}^2\right)=1  , and the balance of density and sparsity implied by e^{2 \gamma } and by the Generalized Riemann Hypothesis (9), places a strict limit on the extent of the disagreement between one number line and another – between one clock and another- thereby preventing such things as the Twin Paradox (10) and other strange consequences of SR. It follows from the switch from the usual space-centric perspective to the absolute light-centric perspective (the God’s Eye View rather than the Man’s Eye View) that inertia is to be defined as the speed of the uniform expansion of space -c- and any departure by an object from c requires the action of a force. From here we deduce Newton’s laws of motion (11):

  1. Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it.
  2. Force is equal to the change in momentum (mV) per change in time. For a constant mass force = mass times acceleration.
  3. For every action there is an equal and opposite reaction.

Gravity and all of the official forces of nature can be reduced to the thought that a force is the curvature of space-time resulting in the departure from c in the direction of the acceleration (an imbalance of space) or the de-acceleration of the expansion (an imbalance of light) of space. Since the expansion of space is accelerating as a function of time, “accelerating” up to c is the same thing as decelerating to the degree that the gap between the acceleration and the uniform speed of the expansion of space -c- is bridged and therefore decelerating to the degree that -locally speaking- acceleration is suspended and time ceases.


The Shroud of Turin and Eternity

We can well-illustrate this idea of eternity by reference to the Shroud of Turin and the resurrection of Jesus of Nazareth.Physicist Joe Jackson holds a theory of image-creation known as the “cloth-collapse” theory according to which “the cloth collapsed through the underlying body, radiation emitted from all points within that body discolored the cloth so as to produce the observed image.” (12). But this theory is fairly easily disposed of by reference some typical criticisms leveled at the authenticity of the Shroud by deniers. For example, philosophy professor David Kyle Johnson, who writes a Psychology Today blog, observes that the hair of the man on the Shroud defies gravity (13):

It is parallel with the man’s body, as if he is standing, instead of falling to the back of the head as it would if was the body were lying flat…

He goes on to say that

Shroud enthusiasts – “shroudies,” as they like to be called – insist that the image on the shroud was produced by some kind of energy (like radiation) emitted by Jesus’s body as he rose. But the image on the shroud could not be produced by such an event. (A) Radiation can’t leave an image in cloth (false). (B) Even if it could, since radiation emits in all directions, at best it would just leave a blurry silhouette, not a clear cut face with features (false). (C) Even if it could produce a clear cut face with features, that face would be distorted. A cloth wrapped around someone’s head lays flat against their nose, eye sockets and ears. If someone’s face somehow ‘radiated’ and recorded an image on such a cloth, when flattened out the cloth would depict whole representations of each part – nose, eye socket, and ears\[LongDash]all pointing in the same direction (true, assuming the presence of gravity)…

Aside from their inability to get real human blood corresponding to the wounds of Jesus of Nazareth, and to place this blood beneath the body image, two properties of the real Shroud that expose every the faked-up-Shrouds as a fake are a) the undistorted nature of the original frontal and dorsal images -especially the dorsal image- regardless of their distance form the cloth and the orientation of the body and the cloth in space, and b) the random distribution of the degraded micro-fibers that produce these images, a distribution that implies that whatever it was that imposed itself upon the cloth to produce the image was imposed evenly. Below we see a comparison between the real Shroud image on the left and a recent attempt to recreate it using the technique known as bas-relief (when a cloth placed over and pressed against a body or statue) (14):

Note the unsubtlety of the fake image, its comparative lack of detail, and its distortion. And things are even worse for the would-be Shroud-forger than it may seem, for the Shroud image contains within the noise much more information than is usually seen. When even a little of this extra information is teased out, it becomes obvious that the bas-relief method, and various methods, cannot possibly reproduce the requisite level of intricacy:


A method that can produce such intricacy is one employed by art historian Nicolas Allen (15):

Below we see a comparison between the real Shroud-image (left and center) and Nicolas’ attempt to recreate this image using a form of photography that would theoretically have been available to a medieval forger:

The trouble now is -as can be clearly seen- is not distortion, and lack of detail, but the unevenness -the directionality- of the light used to make the image. There is no directionality to any light behind the Shroud-image. The problem with these fake-Shroud images -distortion or unevenness in the distribution of the light- is the same problem effecting cloth-collapse theories. Since the cloth in these theories isn’t flat with respect to the body that it wrapped, and body is itself the light-source, it is inevitable that any image produced in the manner described by Jackson will -like the Shroud imitations above- involve distortion and/or signs that it was lit in an uneven manner. A theory -the only theory- that is free from these defects came in its earliest form from artist Isobel Piczeg (16), always the most deeply thoughtful and eagle-eyed of sindonologists, who observed:

  • The lack of anatomical distortion of the naked Body projected on the Shroud.
  • It is clearly visible on the Shroud Images, especially on the Dorsal Image, that the muscles of the Body are not crushed and flattened against the stone bench of the tomb.
  • The Body is hovering between the upper and the lower sheet and there is NO TRACE OF GRAVITY.

  • The lack of gravity is also further proven by the Shroud linen. The linen does not fall on top of the Body, but remains in its unnaturally stretched condition at some distance from the body.

She proposes that there is an “interface between the projection of the Frontal Image and the Dorsal Image” onto the Shroud and that this is interface is an “event horizon that blocks every communication between the two sides of the image.”:


There is the hermetic separation of the two Images with no overlap. The Frontal Image is projected upward and the Dorsal Image downward, clearly describing a Horizontal Interface in between.The Interface seems to have the power of making the Shroud straight and taut and definitely forced to be parallel with this mysterious entity. Due to this condition of the Shroud the Image of the Body on both sides is visibly perfect and undistorted anatomically. The cloth is staying at some distance from the Body and does not fall on it. Also clearly visible is that the muscles of the Body are not flattened against the stone bench of the tomb. The body is weightlessly hovering between the two sides of the sheet. The fact that the upper side of the sheet did not fall on the Body and that the muscles are not crushed and flattened against the stone bench of the tomb clearly proves the total absence of gravity.All the above visible traces on the Shroud indicate that the new Entity, the mysterious Interface is significantly more than just an Interface. It has obviously great power of a special kind that indicates we are dealing with an Event Horizon. The lack of Gravity, however, introduces here a significant paradox. There is a great upsurge of energy with strong organizing power that would mean decreasing entropy. The immense energy released has the means to overpower Gravity while energizing the Event Horizon already in place. (here some new and different laws seem to present themselves that have to be studied).

The greatly divided Upper region and Lower region of the Isolated System of the Shroud each seems to have its own Event Horizon. Since energy has been added by entropy falling, the Event Horizons move closer and closer to each other, finally becoming one. Time collapses to Zero. Eventually they disappear, revealing the entity they were clothing so to speak, the Space-Time Singularity Big Bang style. Everything indicates that at the collapse of the Interface the Body is suddenly no longer in the tomb.

After time, due to the impulse of the time-like part of Singularity started to proceed in a new direction, it had to give forth the Image that was carried by the last time quanta and encoded, as we know, on the Event Horizon. It was the Image of the dead Body with a retrospective quality and recorded in two halves.

The space-like part of Singularity, as we have seen, explodes with everything all at once spreading its powerful Information Field. With its obvious assistance the Image recovered by time spreads itself on both sides of the cloth. The mechanism is extremely complex. The orthogonal projection is scarce. The oblique forms are transported in multi planes turning and turning, superposed and creating a Bas-relief effect with the mysterious Event Horizon as its impenetrable background. Another paradoxical quality of the Shroud is its semi-three-dimensional character, a two-dimensional encoded Image that can only translate itself in three dimensions, forever speaking about the presence of a real three-dimensional Body.

We have to remember also that the explosion of a singularity is an incredibly powerful event even in an Isolated System. One of these brought forth the Big bang. The tomb can contain and witness only the infinitesimal split duration of the explosion and action of the Singularity, hence the unknown and alien marks on the Shroud that no one could imitate.

Creation started out of a Singularity and its explosion. We call it the Big Bang. No matter how startling and how unbelievable it is, but this investigation led to a definite Singularity. The Second Creation has been started in the tomb and burst forth from there. The Shroud is an incredible Blueprint presented amidst the signs of a monumental sacrifice.

I close with the very fitting words of John Archibald Wheeler:

“Some day a door will open and expose the glittering central mechanism of the world in its beauty and simplicity”.
Who would have thought that this door will open through the Shroud of Turin!

These ideas are vague-sounding, expressed with words rather than numbers, and as indicated by Isabel herself, they don’t really make sense in the light of the General Theory of Relativity, and/or The Standard Model of Particle Physics (“paradox” is her term ). But they make good sense, and the paradox is resolved, in the light of the theory described above and illustrated below:

This picture shows that the resurrection took place, and image was projected onto the Shroud, at the split second the gap between the acceleration of the expansion of space and c was bridged by the de-accelerating body of Jesus of Nazareth, i.e. at the split second that gravity was suspended for that body and it entered the realm that we can call “eternity”. More generally, it shows how it is that the linear world of which we are conscious is not fundamental, has it origins in the non-linear world of eternity.



In the light of this mathematics, we can look to the research begun in 1960 by the late chairman of the department of psychiatry at the University of Virginia Dr Ian Stephenson (17). Stephenson’s overall thesis is that was that children’s possession of certain knowledge together with unusual abilities, philias, phobias, certain physical defects and illnesses, cannot not be fully explained by heredity or the environment, and that reincarnation provides a third and the best type of explanation (18). His research has been continued by Dr Jon Tucker, his replacement at the University of Virginia, and Tucker has uncovered compelling case for the reality of reincarnation concerns young boy born in 1998 -James Leininger- who from the age of two claimed to be the reincarnation of an American navy fighter pilot James Huston shot down and killed by the Japanese in 1945 (19). James (pictured at an older age below left) correctly identified the aircraft carrier from which he which James Huston (below right) was flying his missions and its location at the time Huston was killed, correctly identified one of Huston’s co-pilots, and correctly identified the manner in which Huston was shot down…

The skeptical objection is encapsulated by a comment appearing beneath a you-tube video telling this story:

This is ridiculous. I’ll throw out 3 explanations, what is the most logical:

1. His father is making the whole story up to try and become famous and earn a bit of money. Pretty logical. Everyone likes to make a buck. We didn’t even get to see James speak and be asked questions without his mother and father next to him. That would result in him not being able to answer questions except for the ones mentioned by his father there.

2. He somehow heard about this James Huston guy’s story somewhere. Seeing how he absolutely loved planes, it seems quite possible that some relative could have mentioned this story to him. He wouldn’t have to go in depth, he didn’t reveal that much.

3. When you die, your brain, which holds your memories by the way, somehow gets transfered into the child of a random boy born in the USA.

Now which seems more logical…

This critic is grasping at straws (James’ father is a staunch evangelical Christian, unwaveringly upright, and initially very opposed to the idea of reincarnation, and James Huston’s story only became public knowledge after this case), but the response is typical of the skeptic of reincarnation: regardless of the strength of the evidence, there is something objectionable with the very idea of reincarnation that calls upon the “logical” person to look for alternative explanations.

These are the possibilities:

  1. Fraud by the reporter of the case.
  2. Fraud by the subject of the case: they guessed the details or they fabricated them based on knowledge and/or research.
  3. The subject somehow has access to a realm in which this information is available, although it isn’t the case that they are reincarnated.
  4. The subject really is reincarnated.

3 and 4 are out for the you-tube critic and skeptics, leaving them with 1 and 2 and with error and/or fraud. But what exactly is the problem with the other possibilities, and with the possibility that the subject is reincarnated? The answer is simply that the assumption that consciousness is in the brain regarded as a piece of machinery means that when the brain dies there is nothing left of consciousness. Stephenson’s most active critic was for a time was philosopher Paul Edwards, editor-in-chief of Macmillan’s Encyclopedia of Philosophy. From 1986, Edwards punished several articles on Stevenson’s work, and discussed Stevenson in his Reincarnation: A Critical Examination (20, 21). He argued that Stevenson’s views were “absurd nonsense” and that when examined in detail his case studies had “big holes” and “do not even begin to add up to a significant counterweight to the initial presumption against reincarnation.” Stevenson, he claimed, “evidently lives in a cloud-cuckoo-land.” Against Edwards, philosopher Robert Almeder points out in Death and Personal Survival (22) that the philosopher has begged the question by stating in advance that the idea of consciousness existing without the brain in the interval between lives was incredible, and that Edwards’s “dogmatic materialism” has forced him to the view that Stevenson’s case studies must be examples of fraud or delusional thinking… This point gets right to the point: Almeder finds that Edwards doesn’t have anything other than empty rhetoric with which to discredit Stephenson’s research, but if one assumes that consciousness can only exist in a functioning brain then what choice does one have but to dismiss afterlife and reincarnation? But from the mathematics above we see that it is a mistake to regard consciousness as residing in the brain, and Edwards negative stance toward reincarnation proves by reference to this mathematics to be unjustified. So also does the negative stance of Christians and Muslims and others, which like the stance of the Atheist Materialist, is based on a false conception of eternity and the relationship between eternity and infinity.

Download pdf


(1) Lodge, D (1960), The Picture Goers

(2) (26) Limmud Bay Area 2016: Judaism and Reincarnation

(3) Einstein, A (1905), On the Electrodynamics of Moving Bodies

(4) Einstein A. (1916), Relativity: The Special and General Theory

(5) O’Connor, J (1996), General relativity

(6) Wald, R (1997), Gravitational Collapse and Cosmic Censorship

(7) Wald, R (1984), General Relativity

(8) de Swart, J. et al (2017), How dark matter came to matter

(9) Davenport, H (2000), Multiplicative number theory

(10) Cowell, B (2000), The Modern Revolution in Physics

(11) Newton, I (1687), The Principia: Mathematical Principles of Natural Philosophy

(12) Jackson, J (1991), An unconventional hypothesis to explain all image characteristics found on the Shroud image

(13 Johnson, K (2014), Let Go of the Shroud

(14) Pullella, P (2009), Italian scientist reproduces Shroud of Turin

(15) Allan, N (1998), The Turin Shroud and the Crystal Lens

(16) Piczek, I, The Event Horizon of the Shroud of Turin

(17) Stephenson, I (1966), Twenty Cases Suggestive of Reincarnation

(18) Stephenson, I (1997) Reincarnation and Biology: A Contribution to the Etiology of Birthmarks and Birth Defects

(19) Tucker, J (2016), The Case of James Leininger: An American Case of the Reincarnation Type

(20) Edwards, P (1986/87), The Case Against Reincarnation

(21) Edwards, P (1996), Reincarnation: A Critical Examination

(22) Almeider, R (1992), Death and Personal Survival