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Light Hole versus Black Hole:

A black hole, in conventional scientific terms, is where an enormous amount of mass is accumulated at a single dimensionless point – a singularity – giving rise to infinite density. Time stops. All distances are reduced to zero.

The realm of light – the arena for photons and all other particles travelling at light speed – is where time stops and distances are zero i.e. it has the same characteristics as a black hole singularity, the one glaring difference being that the realm of light – the Light Hole, so to speak – has no mass. (But, of course, we should always bear in mind that Einstein’s most famous equation, E = mc2, makes mass and energy different forms of the same thing, related by the square of light speed.)

In other words, the Light Hole is the massless equivalent of a black hole. The Light Hole is the defining speed limit of the universe. Black holes are the mass limit of the universe. If particles accelerated to light speed acquire infinite mass (i.e. ALL of the mass created by the Big Bang) then by accelerating the cosmos to light speed, we would be combining the Light Hole and the Genesis Singularity in one entity. Isn’t it remarkable that the physical universe always returns to itself? If you push it too far in any direction, you invariably come back to a dimensionless domain outside space and time, associated with zero and infinity. The physical dimensional universe – the finite – is hardwired to the dimensionless mental universe – the infinite. The wiring is provided by light.

The term “black hole” is one that has validity only from the perspective of observers not travelling at light speed, but, to something that is travelling at light speed, there’s no such thing as a black hole. Moreover, the expression “travelling at light speed” is meaningless from the point of view of any particle travelling at light speed because it’s not actually travelling anywhere (since it’s not in space and time, and all distances are zero).

When the finite and the infinite come together, paradox is inevitable. Alfred Weber, discussing Hegel’s approach to the infinite and the finite, said:

“The contradiction found in the idea of being is resolved in the notion of becoming. Being becomes i.e. determines itself, limits itself, defines itself. But determinate or finite being continues ad infinitum; the finite is infinite; nothing compels thought to assign limits to it. Here we have a new contradiction, which is resolved in the notion of individuality (being-for-self, Fürsichsein). The individual is the unity of the finite and the infinite. To consider these two terms as excluding each other is to forget that the infinite, excluded by the finite, would be limited by the finite, or would be finite itself. If the infinite begins where the finite ends, and if the finite begins where the infinite ends, so that the infinite is beyond the finite, or the finite on this side of the infinite, it would not really be the infinite. The infinite is the essence of the finite, and the finite is the manifestation of the infinite, the infinite existing. Infinity determines itself, limits itself, sets boundaries to itself; in a word, it becomes the finite by the very fact that it gives itself existence. Existence is possible only under certain conditions, in certain modes, or within certain limits. Existence is self limitation. Existence is finite being. Finite being, the individual, the atom, is infinity existing in a certain manner, limited infinity: quality becomes quantity.”

There are a couple of key phrases here: 1) “The individual is the unity of the finite and the infinite.” That’s a perfect description of the union of a mortal body and an immortal soul. 2) “Infinity determines itself, limits itself, sets boundaries to itself; in a word, it becomes the finite by the very fact that it gives itself existence.” This is the appropriate response to the scientists who think that infinities are some threat to the fabric of the cosmos, that infinity represents a potentially fatal puncture of the finite. In fact, it is the nature of the infinite to set boundaries to itself and become finite. A circle is a perfect symbol of infinity represented in a finite form. Infinity is never a threat to the finite. Indeed it is the origin of the finite. There is no such thing as uncontrolled infinity. When an equation of physics produces an infinite result, it is a sign that something fascinating is happening: that the interface of r > 0 and r = 0 has been reached. It is no cause for the horror that afflicts physicists when they see infinity rearing its head. The final challenge facing mathematicians and physicists is to produce a technique for seamlessly integrating infinity with the finite rather than treating infinity as some sort of disastrous discontinuity. Everything between, and including, minus infinity to plus infinity is part of a smooth continuum. We never reach the “end of the world” and fall off the edge.

Some people ask the question: Why isn’t the speed of light infinite? As we have seen, it can be interpreted as infinite in its own frame of reference. It appears as finite in our frame of reference for exactly the reason just stated: infinity limits itself. Space and time are finite dimensions. Therefore anything perceived from the perspective of these dimensions will appear finite. If we wore green goggles, we would see everything as green. Similarly, if we wear spacetime goggles, everything appears in terms of space and time, of finite quantities. It cannot be emphasized enough that infinity filtered through finite dimensions must appear as finite.

The electromagnetic wave equation that describes light is time dependent. If light speed was infinite, it would have no time dependence since it would be everywhere at once. Hence the equation would fall apart, and the whole universe would be permanently blindingly bright. Light, as we understand it, would not exist. Space and time allow the infinite to be tamed, to provide scope for the type of lives we lead. Space and time are finite filters through which everything, including the infinite, is forced to appear finitely. The infinite speed of light is converted into the constant finite speed with which we are familiar.

Our universe is an extraordinary arena in which, just as Hegel contends, the infinite is able to become finite, to become individual and self-limiting. But via black holes and the Light Hole, the finite returns to the infinite. Individuation is extinguished in black holes – one thing cannot be distinguished from another. The same is true in the dimensionless realm of photons in their own frame of reference. In some sense, all photons are the same. Leibniz said that the universe is based on an infinite number of dimensionless mental entities called monads. Just like photons, they are in some sense all the same since they are not differentiated in space or time. We could just as easily treat infinite separate monads as one Monad. Thus infinity becomes finite and indeed singular. The many and the one are intimately and inextricably related.

We could almost talk of a single Photon, the light of the entire cosmos concentrated in one single super light particle. If the Monad is the Mind of God then the Photon is his Divine Light with which he illuminates existence.

Gnostic enlightenment is all about entering into union with the Monad via the cosmic light. Is there any more glorious image? Is it not infinitely more inspiring than the “vision” of the Abrahamic slave religions, where humanity is forever on its knees, with its eyes cast downwards through fear, worshipping a dim light far, far away, with which it will never come into communion.
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4Di – Space is not 3D:

The key to reality is the imaginary number, i. Imaginary numbers based on i are usually contrasted with so-called real numbers, which are the familiar numbers of the 3D world. (Numbers that contain both real and imaginary parts are known as “complex” numbers.)

How many dimensions of space are there? Three? That’s what common sense says. Wrong. There are four. Why? Because mathematics says so, and mathematics always takes priority over common sense. Here’s why there are four dimensions of space rather than three:

1) What is 1 x 1 (i.e. 1 “squared”)? Answer = 1.
2) What is -1 x -1 (i.e. -1 squared)? Answer = 1.

Notice anything odd? Squaring 1 or -1 gives the same answer. In fact, squaring any negative number always gives a positive number. So, although there is a set of positive numbers and a matching set of negative numbers, there is no such matching set when it comes to the squares of positive and negative numbers. The squares are always positive, whether or not they are derived from positive or negative numbers. But why should the universe exclude a matching set of negative square numbers? This contravenes the Pythagorean principle of mathematical completeness.

All sorts of things that could be accomplished via negative square numbers are impossible in a universe in which only positive square numbers are possible. Why should negative square numbers be prohibited? Is there any fundamental mathematical reason for it, or is just a consequence of limited mathematical knowledge? If -1 is OK, what’s wrong with -1 as a squared number? Symmetry demands that there should be a way of addressing this problem. There must be a set of negative squares forming the mirror image of the set of positive squares.

Mathematicians themselves were painfully slow to grasp what had to be done. Even when they stumbled upon the answer, it took them centuries to properly comprehend and develop it. They too were victims of the prejudices of common sense. They couldn’t see anything physical that negative squares would apply to, so they largely ignored them.

The key to the problem of negative squares was i, the imaginary number. This is defined as the square root of -1. When i is squared the result is -1 i.e. i2 = -1. From i we can generate all of the negative squares e.g. 5i squared = -25; 10i squared = -100. Mathematical symmetry is restored at a stroke. Mathematics is “complete” once more.

But many mathematicians found the imaginary number bizarre and repulsive. One mathematician described it as, “void of meaning, or rather self-contradictory and absurd.” Another said it was “uninterpretable”, and another “an untrustworthy intruder.” Another called it “fictitious.” Such people thought it had no practical applications and was just some odd mathematical irrelevance. In fact, it is arguably the most important number of all, holding the key to breaking through the barriers of “common sense” that block our path to the truth.

In 1831, the brilliant German mathematician Gauss wrote of imaginary numbers: “If this subject has hitherto been considered from the wrong viewpoint and thus enveloped in mystery and surrounded by darkness, it is largely an unsuitable terminology which should be blamed. Had +1, -1 and the square root of -1, instead of being called positive, negative and imaginary (or worse still impossible) unity, been given the names, say, of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity.”

You will never understand reality unless you appreciate the very real significance of the imaginary number. It is the crucial antidote to common sense. One might even call it the God Number since, as we shall see, it is the imaginary number that creates the scope for God, souls, heaven and an afterlife.

If x, y and z are the normal Cartesian coordinate axes (perpendicular to each other) of the three-dimensional space of common sense with which we are all familiar (left and right, backwards and forwards, up and down) then the “imaginary” axis for imaginary numbers is perpendicular to these three in a four dimensional space (that we can’t visualize, of course, since our senses are stuck in 3D).

It is precisely because we can’t picture 4D-space that “common sense” is so shocked by it and tries to resist it. It seems intrinsically wrong. Yet it is fundamental and essential to a true understanding of the universe, as will become clear.

The starting point is the famous theorem of Pythagoras which states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the famous “3, 4, 5” triangle, 32 + 42 = 52. So, the length of the hypotenuse = square root (side1 squared + side2 squared)

If two points (x1, y1) and (x2, y2) are placed on a 2D plane then we can calculate the distance between them by using Pythagoras’ theorem: distance = square root ((x2-x1)2 + (y2-y1)2). This is the general technique for calculating the distance between any two points. The same technique can be extended to two points in any dimensional space. In 4D (including the “imaginary” axis), each point is specified by four points: (x1, y1, z1, w1) and (x2, y2, z2, w2).

Using mathematical terminology, we write ds2 = dx2 + dy2 + dz2 + dw2 where “d” is shorthand for the distance or difference between the respective coordinates (e.g. dx = x2 – x1). However, because the values of “w” lie on the imaginary axis, this means that every value is multiplied by i, the imaginary number. If w1 = 2i and w2 = 8i then dw = 8i – 2i = 6i and dw2 = 6i2 = -36.

This ability of i to generate negative square numbers is one of the most important results conceivable. It is of such crucial significance because it means that in a 4D space, with one axis being imaginary, negative square numbers, which can be used in calculating distances between any two points, now become part of the mix. (In the traditional 3D universe, this is impossible – there are no negative squares involved in any distance calculations.)

To reflect that we have moved from 3D space to 4D space with an imaginary axis, we will henceforth use the designation “4Di”. Here are the astonishing consequences of reality being based on 4Di rather than 3D:

1) If the negative number produced by dw2 exactly balances the three positive numbers provided by dx2 + dy2 + dz2 then the overall result (ds2) will equal 0 i.e. it is possible, in 4Di space, for the distance between two different points (the square root of ds2) to be ZERO! In 3D space, the only way to get the distance between two points to be zero is for the two points to be the same. In 4Di space, thanks to the imaginary axis, two points that may be very far apart if we compare their respective x, y, z and w coordinates, can actually be separated by no distance at all. Hence, at a non common-sense level, the two points are actually the same despite being distinct, since no distance separates them. In quantum mechanics, we encounter the bizarre idea that a particle can be in two places at once. Here, we encounter the equally bizarre idea that two particles can be at the same place at once (in the sense of being at two distinct points but separated by no distance).

2) And if dw2 is larger (as a negative number) than the three positive numbers provided by dx2 + dy2 + dz2 then it means that the overall result ds2 will be less than 0 i.e. it is possible for the squared distance between two distinct points to be negative. (This means that the distance, the square root, will be imaginary.) In other words, in 4Di space, it is possible to get squared distances greater than zero (as in ordinary 3D space), less than zero and exactly equal to zero. Or, in terms of distance, to get real, imaginary and zero distances. In the 3D world of our everyday experience, this is impossible since the distance between two distinct points is always real. We can take a ruler and physically measure the distance in 3D space. But no “common sense” ruler will help us to measure an imaginary length or no length at all. Yet it turns out that imaginary and zero distances dictate our world.

3) If, to emphasize the different character of w compared with x, y and z, we write iw instead of w then d(iw)2 = -dw2. Hence our original equation of ds2 = dx2 + dy2 + dz2 + dw2 can be rewritten as ds2 = dx2 + dy2 + dz2 + d(iw)2 which, in turn, becomes ds2 = dx2 + dy2 + dz2 – dw2. So, the critical function of the imaginary axis is to introduce a negative sign into the calculation of distances, thus counteracting the normal positive signs. The squares of the three real spatial axes x, y and z have the same positive sign, while the square of the imaginary axis w is preceded by a negative sign. Our lives are dominated by the fact that one “square” axis in 4Di space has a different sign from the others. Our minds separate out the three positive axes and call them 3D “real” space.

To characterize the universe as a 4Di space rather than a 3D space is revolutionary. We now begin to see the glimmerings of something utterly profound: our ability to experience “reality” is severely restricted. If it is the case that our senses have evolved to be attuned to a 3D physical space but we actually inhabit a 4Di space then our senses will constantly deceive us since they are lacking awareness of an entire dimension. Hence much of our inability to grasp reality would stem from this problem. “Common sense” i.e. placing our trust in the direct evidence provided by our senses is our worst enemy because our senses are cut adrift from one of the four dimensions in which we live.

It’s hard to believe that we could successfully ignore an entire dimension without disastrous effects. In fact, we don’t. The effects of the “missing” dimension based on the imaginary spatial axis manifest themselves to us in an entirely different way from those associated with the traditional three spatial axes. We experience these effects as the basis of TIME.

Einstein himself, and everyone who followed him, failed to understand this astonishing truth: time has its origins in imaginary space. Time is not a primary dimension, but secondary, being based on distance. Or rather on imaginary distance.

A light particle, a photon, has no mass. What governs its path and speed? Will it follow an “imaginary”, “real” or “zero” distance path through 4Di space? In fact, it takes the simplest, shortest path of least resistance between two points. What is that path? It is the most obvious, least complicated option, the path of least resistance: the “zero” path i.e. where there is no distance between any points on this path.

The zero path traced out by a moving, massless particle through 4Di space has a unique significance: it is the limiting speed of the universe. No particle travelling along an imaginary path can ever exceed the speed of a particle following the zero path (i.e. the zero path speed is the speed limit for particles on imaginary paths) and no particle travelling along a real path can ever travel at less than that zero path speed. The zero path speed is the universal speed limit for any particle following any other path; it is the lowest speed attainable for any real path particle and the highest speed attainable for any imaginary path particle. We know this special speed by another name. It is the speed of light.

This unique speed is invariant. No matter what frame of reference is used, the speed of light always has the same value. Every observer, no matter what speed they are moving at, will always obtain the same value for the speed of light. Even someone travelling at 99.999% of the speed of light will, if they switch on a torch, find the light beam racing away from them at the speed of light, exactly as would happen if they were standing still. We can now understand why this should be so: light is following a unique, invariant zero path. (Note that we are referring to the speed of light in a vacuum; light travels more slowly through other media such as water.)

Einstein famously wondered what would happen if he were travelling at the speed of light while holding a mirror in front of himself. Since both he and the mirror would be travelling at the speed of light, how could the light from his face catch up with the mirror in order to be reflected back? Wouldn’t his reflection disappear? The answer he arrived at with the special theory of relativity was that a) he could never attain light speed and b) he would always see his reflection.

That the speed of light is constant in all frames of reference is one of the truly momentous facts of existence. Just consider how truly weird it is. If a man at the front of a train that is travelling at 100 kilometres per hour throws a rock out of the window at 50 kilometres an hour in the same direction as the travelling train, then a stationary observer will measure the rock as travelling away from him at 150 kilometres per hour i.e. the sum of the speed of the train and the speed of the rock. Likewise, common sense says that if a man travelling at 0.9 light speed switches on a torch and the light beam shoots away at light speed, then a stationary observer should measure the light beam as travelling at 1.9 times the speed of light, but common sense is completely wrong. Light, no matter who observes it in whatever context, is always measured to have exactly the same value in a vacuum. An observer standing still and an observer travelling at near light speed will both obtain exactly the same result for the speed of light. How can it be that relative motion between the stationary and moving observer makes no difference at all to how they measure the speed of light?

Imagine that the speed of light is 100 km per hour, and a man on a train travelling at 90 km per hour switches on a torch. We would expect a stationary observer to see the light beam travelling at 90 + 100 = 190 km per hour, but in fact the observer would see it travelling at 100 km per hour. How is this possible? Speed is distance over time. After one hour, the man on the train has travelled 90 km, and, relative to him, the light beam has travelled a further 100 km. So, he measures the speed of light to be 100 km divided by 1 hr = 100 km per hour. Relative to a stationary observer, the light beam has seemingly travelled 190 km in the hour so its value should be 190 km per hour, but it’s still in fact 100 km per hour. As Einstein realized, the only credible way for this to be true for both the stationary and moving observers is for distance and time to change in some proportionate way as our speed alters so that it will still seem as if the light beam has travelled only 100 km in an hour.

For distance and time to alter as speed alters means that they are not primary, absolute properties of existence; they are dependent on how objects move. The ramifications are astounding. The idea that anything has definite, measurable dimensions in any absolute sense is rendered meaningless. An object viewed by a stationary observer will have different dimensions depending on the object’s speed relative to that of light. So, what are its “true” dimensions? Can it be said to have any? Because we never move at speeds significant in relation to light speed we never notice any strange changes in the dimensions of objects as they move relative to us, but we would if the speed of light were similar to the speeds we move at. If light speed were 1000 km per hour, we would notice weird effects all the time. We would no longer have a vocabulary based on solid, unchanging objects with fixed dimensions.

When a particle moves in “Zero space”, it does not experience time and it has no mass. What about particles moving through “imaginary” space? That’s when they do experience time and they have a positive mass. What about particles moving through “real” space? That’s when they experience “imaginary time” and have “imaginary mass”. In the language of relativity theory, the zone we live in is called “timelike” and only subluminal speeds are possible, while the zone associated with real space is called “spacelike” and only superluminal speeds are possible.

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In a typical textbook treatment of Einstein’s special theory of relativity, you will encounter the equation: ds2 = dx2 + dy2 + dz2 -c2dt2 where c is the speed of light. How does this compare with the equation we have used of ds2 = dx2 + dy2 + dz2 -dw2? The equations are identical except for -dw2 (based on the imaginary axis) and -c2dt2. The square root of -c2dt2 is icdt since (icdt)2 = i2 x c2 x dt2. In other words, the imaginary axis is at the heart of -c2dt2, just as it is at the heart of -dw2. In fact, the only difference between -c2dt2 and -dw2 is the constant c2.

The imaginary axis that we have labelled “w” uses units of distance i.e. spatial units. The speed of light, c, has units of distance divided by units of time (since speed = distance divided by time). Hence the time axis, t, multiplied by c has units of distance since (distance/time) x time = distance because the time units cancel out. Thus the term cdt has space rather than time units and is now on a par with dx, dy and dz, which are also measured in distance units. So, dw is directly proportional to cdt since both are measured in distance units and c is a constant.

To state it explicitly, the time axis (t) and the imaginary axis (w) are directly related, via c the speed of light, the “natural speed” of the cosmos. We have thus demonstrated the astonishing fact that time is intimately related to imaginary space, the two being linked by the invariant speed of light. The mathematics of 4Di space are IDENTICAL to the mathematics of what the German mathematician Minkowski called 4D spacetime, where space and time are fused together, with time leading to squared distance expressions that have the opposite sign to the squared expressions of the conventional spatial axes of x, y and z. One of the central enigmas of existence can, in some sense, be attributed to this difference of a negative sign being matched against three positive signs, leading to real, imaginary and null zones instead of just real zones.

All of this stems from mathematical completeness, from the imaginary number i. Without it, all distances are real. With it, distances can be real, imaginary or zero. So, by ensuring that all of mathematics is used rather than a subset, we get the possibility of far more diverse phenomena. The Zero zone – the so-called infinitely narrow “luxon wall” – stands between the real and “imaginary” universes i.e. between the spacelike and timelike zones of existence. We have shown that time is born of imaginary space. Without imaginary space there would be no such thing as time. 4Di space is the basic entity, not 4D spacetime.

Isaac Newton believed in absolute space and absolute time. He envisaged space as an infinitely large 3D container, with time being measured by a cosmic clock that ticked at the same rate everywhere in the universe. This is the common sense view of space and time, and it works very well in our everyday environment. For Newton, space and time existed independently of any objects i.e. if you removed everything from the universe, space would continue to exist and time would continue to tick by.

Leibniz, with his “relational” view of time and space, opposed Newton. According to the relational view, space and time would not exist if there were no objects. Time and space describe relations between objects, and without objects then there are no relations to describe.

Einsteinian physics replaced Newton’s absolute space and time (each existing independently of the other) with a 4D spacetime where space and time are inextricably fused together. Einstein’s system is Leibnizian since space and time are dependent on the contents of the universe and how those contents move with respect to each other.

The Einsteinian/Leibnizian view only becomes obvious when objects are travelling at near lightspeed, hence why science remained resolutely Newtonian for so long.

However, the Einsteinian view of 4D spacetime is itself not the full story and ought to be replaced by the more fundamental 4Di space involving three real spatial axes and one imaginary spatial axis. Time comes into existence only because of 4Di space i.e. time is not a fundamental property of the universe but rather a secondary characteristic derived from the imaginary component of space. If space were not a 4Di domain then time as we know it would simply not exist.

Time results from how 3D objects move through 4Di space. Its nature changes depending on what path an object takes through space. Time does not “tell” an object how to move; rather, a moving object tells time how to tick, or indeed not to tick at all in the case of particles such as photons.

Moving objects are the fundamental reality of the dimensional universe, and “space” (4Di) defines the mathematical set of relations that all moving objects obey, thus giving rise to the laws of physics. Space does not exist as an independent, absolute physical entity; it is a mathematical construct that is given the appearance of reality by how objects move with respect to each other. Time is not an independent, absolute physical entity either, which is why time has always been so hard to define. People have been baffled by time because they have always attempted to make it a primary property of the cosmos. Once time is understood as a function of the mathematics of space and, in particular, of imaginary space then everything becomes clear. Even apparently stationary objects (in relation to space) are still moving – through time.

To reiterate, precisely as Leibniz first asserted, time and space do not exist in an absolute sense. Only moving objects exist. The dimensional universe, as we experience it, is the arena of physical objects in motion in space and/or time. There’s nothing more to it.

What is crucial to understand is that the frame of reference of any massless entity is outwith space and time. Everything that happens in the cosmos is instantly reflected in this unique reference frame. All possible information about the physical universe is instantaneously captured in the light domain.

When we describe the physical universe in terms of 4Di rather than 3D, at a stroke we get to the heart of the difference between common sense and reality. Common sense says that only 3D exists, but 3D is mathematically incomplete because zero and imaginary distances between two distinct points are prohibited. Physically, this seems to make sense, but mathematically it’s absurd. Why should zero and imaginary distances be excluded because of a mathematical feature that all negative numbers raised to an even power are positive? If another mathematical feature – imaginary numbers – can resolve this and allow a negative number to be generated when any such imaginary number is raised to an even power, why should nature ignore this complete version of mathematics in favour of a truncated version? Nature doesn’t. Nature is mathematical. Nature obeys the laws of complete, not incomplete, mathematics. It includes ALL numbers, not a subset of numbers. Numbers such as zero, infinity and the imaginary number are as “real” as 1, 2 and 3. They cannot be ignored or excluded or treated as less real or indeed as unreal.

Anything not forbidden is compulsory. Imaginary numbers are not forbidden, hence are compulsory. They are embedded in nature, but our common sense chooses to interpret them as non-spatial: as time, in fact. So, the profound mystery of why space and time exist is now explained by the underlying mathematical truth that there are two different types of numbers: real and imaginary. Real numbers underlie our conventional understanding of space; imaginary numbers underpin time. But, fundamentally, we are dealing with a single entity: all the numbers of mathematics, the complete set, none ignored or excluded. Nature operates according to Complete Mathematics. If it can exist mathematically then it will exist in reality. Anything not forbidden mathematically is compulsory.

Look at all of the things that fall into place when 4Di replaces 3D:

1) Instead of distances between two points always being real (as in 3D), it becomes possible to also have zero and imaginary distances. Three types of “reality” – three choices – become possible where only one was possible in 3D.

2) It transpires that Einstein’s famous special theory of relativity is based precisely on this division of reality into three distinct aspects. However, Einstein talked of a 4D spacetime rather than 4Di space. 4D spacetime and 4Di space obey exactly the same mathematical rules and framework. We choose to emphasise 4Di because it shows that the basic reality is spatial rather than spatial plus temporal. Time is derived from imaginary space; it is a secondary feature, not a primary one. Time could not exist if there were no imaginary space. Imaginary space, because it leads to zero and imaginary distances rather than just real distances, provides the crucial factor that makes life as we know it possible.

3) To reiterate, there are three zones of spatial reality: zero, imaginary and real. In the zero zone – “Null Space” – all distances and times are by definition zero. Everything is interconnected. Everything is One. This is the centre of the cosmic mystery, the transcendent realm that mystics have intuitively grasped. Since each point in our familiar 3D space can be matched up with an imaginary coordinate that can ensure that any two points in 4Di space are separated by zero distance then in Null Space all things are inextricably brought together in a single cosmic unity. This is the most profound mystery of all, and it is brought about by mathematical completeness. It cannot be stressed enough that in 4Di space, but not in 3D space, there is a null zone in which all things are connected. Our world of everyday common sense is locked into the illusion of 3D “reality” and, in this incomplete representation of existence, the differences between things are emphasized rather than their unity: individuation is stressed over communion. The great religion of Hinduism has always stressed that, under the power of Maya, human life is essentially illusory, and Buddhism makes the same claim that our reality is an illusion. But the illusion is one of incompleteness rather than false reality. To the extent that we experience 3D rather than 4Di, our view of reality is distorted, but it’s not fake or make-believe. It’s inaccurate, not wrong. It is lacking complete information. The world is absolutely real, but the 3D representation of it omits a critical component. The Absolute Truth lies in 4Di. Reason can lead us there, but not our common sense which leads us astray, and certainly not faith, which is useless.

4) The real and imaginary zones are like mirror images of each other, with the Null zone providing the mirror, the infinitely narrow luxon wall.

5) The Null zone is an extraordinary place where particles have no mass or size; where everything is interconnected and no time passes. It is the realm of the inverse twins, zero and infinity. The most extraordinary fact of existence is that zero and infinity can exist at the heart of 4Di spatial reality. Physicists are horrified and baffled by the Null zone. They don’t comprehend that it is the most critical feature of science and mathematics, and indeed of life itself. It is where the answer to every mystery ultimately lies.

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So, have we provided the answer to mathematical completeness? Does 4Di accommodate all possible numbers? Is the cosmos four dimensional (three real space dimensions and one imaginary space dimension)?

No, we have committed an error. Although 4Di has the right “shape” – which is why Einstein’s special theory of relativity works – it is not actually complete. Can you see what we have done wrong? Use your intuition. What number seems right for the total number of dimensions required for mathematical completeness? How many dimensions does the cosmos need?

Are you beginning to see the light?
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