N-space, M-space, and Consciousness

Part 1

There's an idea I've brought up quite often on my blog – the notion that the underlying reality of our world is a field of pure information, a cosmic database combined with a vast information processing system. By analogy, this informational substrate is similar to the code that underlies a virtual-reality environment in a computer game. Just as the virtual reality of the game reduces ultimately to ones and zeros – pure information – so the apparently real world around us in all its dimensions may reduce ultimately to pure information.

This raises an obvious question: what renders the information to generate our "real" world? After all, the data in the computer would just sit there, useless for game-playing purposes, unless the computer was able to render the data as images and sounds. By what means do we render our world?

One possible answer is: our minds. Not our brains, please note; our brains are physical objects and thus are part of the rendered, multidimensional, multisensory imagery we call reality. It is our minds that (just possibly) translate the informational code into the world of experience. 

Let's suppose this is true. If the mind is what does the rendering, then each individual mind renders its own "virtual-reality" world out of the same information matrix. And each "world" will be slightly different from all the others, because it will depend on our particular point of view – our focus, our choice of what to tune in to and what to ignore.

Here I'm going to introduce a little jargon. Let's call the information matrix N-space. The N stands for noumenal, or, if you prefer, number. (It works either way.) And let's call our individual, personal, subjective world M-space, with M standing for mind. We all live in our own M-space, and we are all rendering N-space in order to generate our M-space. 

Notice that neither of these things is really "space" in any physical sense. We might think of them as fields or matrices. However we wish to describe them, both N-space and M-space are nonphysical. 

So each mind renders its own "real" world, but all minds draw from a common source – the N-space database/information processor. Mind somehow takes pure information and translates it into an experiential world, which is subjective but grounded in objective data. By objective, I mean that N-space exists independent of the observer; by subjective, I mean that M-space exists only in respect to the observer.

We have, then, three aspects of reality: N-space, which is pure information and information processing; M-space, which is reality as each of us subjectively experiences it; and the mind, which serves to render N-space into M-space.

If there is a place for God in this scheme, God would be seen as a kind of primal or cosmic mind, which wrote the code that constitutes N-space. Our own minds would presumably be small offshoots or rivulets of this larger mind.

Now here, to me, is the really interesting thing. In this scenario, there is no physical space at all.

There is N-space, which is a nonphysical matrix of data, and there is M-space, which is subjective experience, and there is the mind – which, whatever it is, is not physical.

So there is no physical space or physical world. There is only information rendered by various minds into subjective virtual realities for purpose of creative exploration.

We might visualize M-space as a thought bubble in a comic strip. And we might visualize all the M-spaces of humanity as a vast froth of bubbles on the surface of a dark sea. On the seafloor, hidden from sight, there is N-space, the source of it all.

Matter and energy are rendered from data. Data are nonphysical. The minds that do the rendering are also nonphysical. The resulting rendered "images" appear to be physical, but they are only experiential constructs, the equivalent of avatars and icons on a computer screen, or the shadows on the wall of Plato's cave.

Now, is this pure subjectivism? I don't think so, because all minds render their virtual realities from the same database/information processing system.

In other words, we can retain the distinction between objective and subjective in this scheme. While the objective/subjective distinction breaks down in terms of M-space, it applies, in a somewhat different way, to the interaction of the mind and N-space. As mentioned above, N-space is objective in the sense that it is independent of the observer, while M-space is subjective in that it is dependent on the observer. 

So we can still talk about objective reality, but what we're talking about is not M-space – our personal experience – but N-space, the information matrix that serves as the ground of being.

It would seem that people who have had epiphanies – e.g., the "cosmic consciousness" episodes recounted by Richard Maurice Bucke, or many near-death experiences – have been able to temporarily break out of M-space and tap into N-space directly. They often feel they were exposed to all knowledge, which would be the case if N-space constitutes all the data and programming that underlie what we call "the world." But they cannot retain most of the details when they return to ordinary consciousness, because they are back in M-space again.

It is probable that many psychic events take place because the mind is able to tap into N-space in a small way and access the "code" directly. N-space, being nonphysical, is also nonlocal; information that is readily accessible in the matrix may pertain to physically distant "objects," just as information in a computer may pertain to objects on any part of the screen. So remote viewing (clairvoyance), telepathy, precognition, and other seemingly unthinkable abilities become quite possible. 

Another thing: to conserve processing power, computer programs do not render images that are not on the screen. If you are playing a computer game and looking "north" at a mountain, the computer will render the mountain in all its detail. But it will not render the city that is directly behind you, to the "south." If you turn to face south, the computer will obediently render the city on the screen, but it will no longer render the mountain. In a virtual-reality environment, to be is to be perceived, as Bishop Berkeley liked to say.

Does this mean that in the "real world," mountains and cities disappear if you're not looking at them? Here is my answer: they do disappear from your particular reality bubble, your personal, subjective M-space. Your mind is not rendering those particular data at that moment. However, if the mountain or city is being observed by some other mind, then it is rendered in that mind's M-space. Moreover, the data that are the ultimate constituents of the mountain or city always exist in N-space independent of any observer.

To ask an old question: Does the moon disappear if no one is looking at it? In this scenario, if literally nobody – no mind anywhere – is observing the moon, then the moon is not currently being rendered in anybody's M-space, and in that sense it has "disappeared." But the data that give rise to the moon in the first place, the data of N-space, are still there and are ready to be rendered by any mind at any time. So the moon is still there in N-space, but it is not presently being rendered in any M-space.

I'm not, of course, insisting that all this is true, or that there is any way of testing it or proving it. But I find it interesting to think about. And it may provide some kind of model by which to understand anomalous phenomena a little better. 

Part 2

I'd like to excerpt a few passages from Norman Friedman's 1997 book The Hidden Domain: Home of the Quantum Wave Function, Nature's Creative Source and briefly comment on them in light of the scenario I sketched out above. I'm also going to include a few excerpts and ideas from a fascinating online essay by Brian Whitworth, "The Emergence of the Physical World from Information Processing," arguing that the universe can best be understood as a virtual-reality environment.

Friedman, page 23: 

Einstein ... rejected Newton's notion of an absolute space, at rest and immovable, relative to which all objects in the universe are moving. Einstein suggested that this description of space be discarded because any observer, in whatever frame of reference, could say that he or she was at rest at all else was moving relative to them.

M-space, or what we call the "physical world," is a projection of a virtual reality tailored to the point of view of our particular consciousness. Therefore, each of us is the focal point of our own private M-space, and from our point of view, everything else is in motion relative to our fixed vantage point. By analogy, the VR environment of a computer game typically moves relative to the point of view of the user's avatar.

Freidman quotes a private communication from physicist Jack Sarfatti, page 34:

Einstein's original four-dimensional space-time is now understood to be a projection, or a shadow, of a larger higher-dimensional space called the "fiber bundle." The elementary particles and nongravitational forces are then interpreted as geometric structures in the higher dimensions beyond Einstein's space-time.

M-space is a projection or shadow of the larger higher-dimensional N-space. Elementary particles areinterpreted as informational structures in N-space.

Friedman, page 45:

The uncertainty principle leads to the idea that one electron (or any particle) is in principle indistinguishable from any other. 

The best comment on this is from Whitworth's essay, linked above:

Quantum equivalence: All quantum entities, like photons or electrons, are equivalent. Digital equivalence: Every digital "object" created by the same code must be equivalent. 

Or as Whitworth put it in an earlier version of his essay (I'm paraphrasing): Every digital symbol calculated by the same program is identical to every other, just as every photon is identical to every other photon because each is created by the same digital calculation. 

Friedman, page 49:

Thus, it would seem that we live in a world of at least two levels: the wave function is on one level and correlates with object of affection in the other level, which is ordinary three-dimensional reality. 

N-space, corresponding to the wave function, is one level, and M-space is what we call three-dimensional reality.

Friedman on the two-slit experiment, page 254: 

If we duplicate this experimental arrangement throughout the world with many experimenters, each firing just one electron at a given prearranged time, with each individual photographic plate showing the arrival of the one electron, and the results from all the plates are added together, then, amazingly, the interference pattern shows up again! These experiments are arranged so that no signal can travel between them at less than the speed of light, so there can be no physical communication between the electrons. Just how does each electron know where to strike the plate so that in the interference pattern appears? 

The electrons know where to strike the plate because the calculations have already been performed in N-space. The fact that the experiments are being carried out in different labs is irrelevant, since N-space is nonlocal. Since it is all one experiment (albeit broken up into different parts), the outcome is determined by a single set of calculations in N-space.

Friedman, page 56: 

An explanation for this strange wave-particle duality, called the Copenhagen interpretation, was presented by Bohr in 1927 at the fifth Solvay conference in Brussels. The simplest statement of Bohr's view is this: the quantum world is not real. Bohr recognized that the quantum world is completely different from our normal everyday world governed by the familiar laws of classical physics. Though we have mathematical formalisms to describe it, the unreal world of the quantum relates to the real world only by an act of measurement. 

I would prefer to flip this around and say that M-space is not fully real, while N-space – the underlying information realm – is what is ultimately real. However, it depends on how you look at it. The key point is that the two dimensions of "reality" are qualitatively different, and that N-space can be understood only in terms of "mathematical formalisms," which makes sense given that it is a realm of pure information and information processing.

Friedman, page 58: 

In classical physics, mathematics is used to represent the attributes of a system. The formulae are taken at face value and assumed to be actual descriptions of the evolution of the system. In quantum theory, the situation is quite different. Here the mathematics is an algorithm for calculating the results of experiments, at least as far as the Copenhagen interpretation is concerned. Actuality is no longer considered, but has evaporated into the mists of the mystical.

I would look at this differently, and say that N-space is the actuality, while our three-dimensional "physical" world is, in a sense, part of the "mists of the mystical" – in the sense that it is a projection of consciousness.  

Friedman describes his own point of view on page 62:

It is our thesis that the wave function is not merely a symbol to be used in a calculational procedure. Rather, it has real meaning and describes a hidden domain that is the creative source of our three-dimensional world.

This, unlike the views quoted earlier by Friedman, is essentially the same as the M-space/N-space idea. N-space is the "hidden domain that is the creative source of our three dimensional world," and "is not merely a symbol to be used in a calculational procedure." Rather, the calculational procedures are the basis of what we call reality.

Friedman, footnote on page 64:

Some scientists think the space continuum may actually be grainy, which implies a universal minimum length, usually estimated to be 10 [to the power of] -33 cm. Every gravitational wave in space has a zero-point energy and because of that, the lengths below 10 [to the power of] -33 become undefinable. 

The universal minimum length in a virtual-reality universe would correspond to a single pixel on a computer screen, the smallest image that can be displayed. The universal minimum time would correspond to the length of time between screen refreshes.

Friedman, page 68:

We can conjecture that there are two types of time. One type describes a sequence of actual events brought about by the collapsing wave function, which is the time we are aware of in the three-dimensional universe. The other kind of time, used to create space-time in Einstein's relativity theory, refers to the evolution of possibilities in the Schrodinger equation. Since possibilities are not real events, that type has been called imaginary or virtual time.

The "time" that applies to N-space is qualitatively different from the "time" that we proceed in M-space. This is why precognition and retrocognition are possible; these abilities apparently involve tapping into N-space directly. 

In what way are the mathematical formulae of N-space "rendered" into the multidimensional, multisensory images of M-space? Friedman discusses how the probabilties of the "hidden domain of the quantum wave function" can be translated into what we know as realities. This is a little complicated, so I will summarize in a series of steps.

1. Schrodinger's equation expresses the quantum wave function as a complex equation, i.e., a mixture of real numbers and imaginary numbers. This wave can be written as a sum of sine waves using Fourier's equations, but the sine waves are also complex functions (with imaginary numbers). 

2. Imaginary numbers cannot be plotted as coordinates in physical space. Therefore Schrodinger's equation cannot tell us the location of the subatomic particle in space.

3. Is there any way to convert imaginary numbers into real numbers and thus locate the particle in physical space? Yes. If you multiply an imaginary number by its complex conjugate, the result is a real number.

4. What is the complex conjugate of the quantum wave function? All waves can be understood as "retarded waves," which travel forward in time, and "advanced waves," which travel backward in time. The advanced quantum wave is the complex conjugate of the retarded quantum wave; the product of these two waves gives us a wave function that can be expressed purely in real numbers, and which thus provides us with a location in physical space. 

In terms of our scenario, we might think of N-space as consisting of complex equations - a mix of real numbers and imaginary numbers. What we call "rendering" would consist of multiplying these equations by their cognates. The result would be real numbers only, or "physical reality." Note that this process can be understood either in terms of mathematical calculations (multiplication) or wave interactions. N-space, then, could be said to consist of "complex equations" or of "quantum waves" - two different ways of lookingat the same thing. Equations relate better to the computer analogy, while waves relate better to the hologram analogy. The two analogies (or metaphors, or modekls) are very similar, since a hologram can be created entirely by a computer, and since the wave interference patterns on a holographic plate can be translated into data. 

Friedman sums up the sequence of steps outlined above, page 73: 

The basic tenet of Cramer's transactional interpretation of quantum theory (as it is called) is that every quantum event involves a kind of 'handshake' between the past and the future, so that in some way, the future is affecting the past.

In other words, the retarded wave and the advanced wave "shake hands" across time - something that's hard to visualize in our three-dimensional world (M-space), but easier to understand in the context of N-space, where time behaves differently. 

Some additional points made by Brian Whitworth's essay. (The following are not verbatim excepts but paraphrases and abridgements.) 

Processing load effects could explain relativity effects. Space and time arise from a fixed information processing allocation, so the sum total of space and time processing adds up to the local processing available.

In other words, time appears to expand and space appears to contract as you approach light speed because the information processing system is reaching the limit of its processing load. (See Whitworth's essay for details.)

The algorithmic simplicity of fundamental physical laws and constants is explained by the needs of the information processing system. In a virtual reality, the basic rules must be simple because they must be constantly calculated and recalculated.

If complementary object properties use the same memory location, the object can appear as having either position or momentum, but not both at once. (See the website The Bottom Layer for a step-by-step discussion of this point.) 

In a VR universe, all object movement would be expected to be by state transitions.

Quantum jumps and quantum tunneling are known examples of state transitions - i.e., discontinuous movement, in which a particle shifts its energy level or its position or from one state to another without passing through the intervening state. This is difficult to explain in terms of objective reality, but easy enough to understand if the transitions reflect calculations taking place in N-space. The particle does not need to pass through the intervening states, because it simply shifts from one state to another as a result of a behind the scenes calculation. The new state shows up as soon as the virtual-reality screen is refreshed.

A virtual-reality system may start with a sudden influx of information as the virtual-reality universe boots up. This corresponds to the apparent origin of the universe out of nothing, as posited by the Big Bang theory.

Finally, Whiteworth asks: 

Given the speed of light is a universal maximum, what is simpler, that it depends on the properties of featureless space, or that [it] represents a maximum network processing rate?

In this view, the speed of light as an absolute maximum simply indicates the maximum speed at which the information processing system can crunch the numbers. In the M-space/N-space scenario, the limit may also involve the maximum capacity of the render engine. Note that the rendering is done individually for each observer, so the render effects would be apparent only to an observer(s) who was approaching light speed in his particular M-space. The render effects would not be apparent to anyone not approaching light speed, because that person's unique M-space would not be under an unusually high processing load. 

Part 3

Musing further on this notion of M-space and N-space, I found myself wondering which philosophical tradition it would fit most closely. The obvious choice might be Plato, with his famous image of reality as shadows on the wall of a cave. But I think the best match is probably the metaphysics of Immanuel Kant.

Now, I am certainly no expert on Kant. And I know that his philosophy is notoriously complex and difficult to decipher. It's always possible that I am misunderstanding his position. Nevertheless, based on descriptions and excerpts that I found in the Stanford Encyclopedia of Philosophy, I think the Kantian metaphysics, in its "two-worlds" interpretation, aligns pretty closely with the N-space/M-space idea. 

Here is how the encyclopedia describes Kant's view: 

Perhaps the central and most controversial thesis of the Critique of Pure Reason is that human beings experience only appearances, not things in themselves; and that space and time are only subjective forms of human intuition that would not subsist in themselves if one were to abstract from all subjective conditions of human intuition. Kant calls this thesis transcendental idealism….

The sensible world, or the world of appearances, is constructed by the human mind from a combination of sensory matter that we receive passively and a priori forms that are supplied by our cognitive faculties…. 

If “we can cognize of things a priori only what we ourselves have put into them,” then we cannot have a priori knowledge about things whose existence and nature are entirely independent of the human mind, which Kant calls things in themselves. In his words: “[F]rom this deduction of our faculty of cognizing a priori [...] there emerges a very strange result [...], namely that with this faculty we can never get beyond the boundaries of possible experience, [...and] that such cognition reaches appearances only, leaving the thing in itself as something actual for itself but uncognized by us.”

It is simple enough to rewrite the above in terms of the ideas we've been discussing on this blog:

Human beings experience only M-space (mental space), not N-space (the information matrix); space and time are only subjective forms of human perception operating in M-space and would not subsist in themselves if one were to abstract from all subjective conditions of human experience, i.e., if one were to get outside M-space and access N-space directly.

M-space, or the world of appearances, is constructed by the human mind out of pure information rendered or modeled into "objects" by means of consciousness. 

We cannot have direct knowledge of N-space, or "things in themselves." N-space is something actual but uncognized by us. 

Kant wrote of "the objects, or what is the same thing, the experience in which alone they can be cognized (as given objects)." This profound statement encapsulates the often overlooked fact that all experience is subjective experience, and that what we call "physical things" are ultimately sensory images in our field of awareness - images in M-space. 

Kant also wrote: 

We have therefore wanted to say that all our intuition is nothing but the representation of appearance; that the things that we intuit are not in themselves what we intuit them to be, nor are their relations so constituted in themselves as they appear to us; and that if we remove our own subject or even only the subjective constitution of the senses in general, then all constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us. We are acquainted with nothing except our way of perceiving them, which is peculiar to us, and which therefore does not necessarily pertain to every being, though to be sure it pertains to every human being.

Which could be translated as:

All our perceptual awareness is nothing but the rendering of objects in M-space. The things we perceive are not in themselves – i.e., in N-space – what we perceive them to be, nor are their relations so constituted in N-space as they appear to us in M-space. If we could remove our awareness, i.e., get outside of M-space altogether, then all relations of objects in space and time, indeed space and time themselves, would disappear, as would all appearances – all sensory images – since such appearances cannot exist in themselves, but only in our field of awareness. What these objects ultimately consist of when abstracted from consciousness is entirely unknown to us. We are acquainted with nothing except our way of perceiving them in our own M-space, which is peculiar to our mode of consciousness, and which therefore does not necessarily pertain to every being, though it surely pertains to every human being. 

Below is the encyclopedia's summary of Kant's view (in the two-worlds interpretation), with my comments in brackets and yellow text: 

Things in themselves [the informational properties of N-space], on this interpretation, are absolutely real in the sense that they would exist and have whatever properties they have even if no human beings were around to perceive them. Appearances, on the other hand, are not absolutely real in that sense, because their existence and properties depend on human perceivers [whose consciousness renders them as objects in M-space]. Moreover, whenever appearances do exist, in some sense they exist in the mind of human perceivers [i.e., in M-space]. So appearances are mental entities or mental representations. This, coupled with the claim that we experience only appearances, makes transcendental idealism a form of phenomenalism on this interpretation, because it reduces the objects of experience to mental representations. All of our experiences – all of our perceptions of objects and events in space, even those objects and events themselves, and all non-spatial but still temporal thoughts and feelings – fall into the class of appearances that exist in the mind of human perceivers. These appearances cut us off entirely from the reality of things in themselves, which are non-spatial and non-temporal [all experience takes place in M-space, or more precisely, experience simply is M-space, so we cannot experience anything outside it]. Yet Kant's theory, on this interpretation, nevertheless requires that things in themselves [N-space information and information processing] exist, because they must transmit to us the sensory data from which we construct appearances. In principle we cannot know how things in themselves affect our senses [we cannot get outside M-space to examine N-space], because our experience and knowledge is limited to the world of appearances constructed by and in the mind [our experience and knowledge are limited to M-space]. Things in themselves are therefore a sort of theoretical posit [N-space cannot be proved, only posited], whose existence and role are required by the theory but are not directly verifiable.

The article also makes this important point: 

Kant denies that appearances are unreal: they are just as real as things in themselves but are in a different metaphysical class.

Similarly, it is not that M-space is unreal; it is real for us. But it is not ultimately real; it is not the ground of being. M-space and N-space are qualitatively different; they are in "different metaphysical classes." 

The Stanford Encyclopedia article also brings up an objection to Kantian metaphysics: 

But if there is no space, time, change, or causation in the realm of things in themselves, then how can things in themselves affect us? … It seems, rather, to be incoherent that things in themselves could affect us at all if they are not in space or time.

Conceivably the M-space/N-space idea could supply an answer, or at least a lead to an answer, to this objection. 

First (and apparently contrary to Kant), there would have to be change in N-space, because the information is continually processed. This does not necessarily mean there is "time" as we understand it. By definition, N-space is outside the parameters of what we understand as space, time, and causation, because it is outside of M-space, which is the only environment we know. 

Second, things that are outside of space and time as we understand them could still affect us - if they provide the data that our consciousness renders or models into space-time objects and events. By analogy, a computer program is a very different thing from the experience of playing a video game. The program is nothing but ones and zeros, while the virtual-reality environment of the game is full of color and texture and movement and action. Yet the program gives rise to the virtual environment in which the game is played.  

To somebody who knew nothing about computers, it would be highly counterintuitive to think that the colorful world on the screen was produced by number-crunching strings of binary code. But this is in fact the case. Similarly, it is highly counterintuitive to think that our experience of reality is being modeled by our consciousness from moment to moment, out of data that arise from a nonphysical source. Still, it just might be true.

Part 4

Here are some interesting quotes from Seth Speaks, by Jane Roberts, interpreted in light of some of the ideas explored on this blog. All quotes are from Chapter 6. 

"Seth" was an entity allegedly channeled by Jane Roberts. The channeled material mainly involves issues like the nature of reality, the role of consciousness, and the potentialities of the soul. I cannot lknow for sure if this information really came from a discarnate source or from Roberts' subconscious, or from some combination of the two. Perhaps ultimately there is no sharp distinction between the subconscious, the hgher self, and other intelligences. In any case, the Seth material is complex and intriguing in its own right, and it may shed some light on the M-space/N-space idea. 

Seth tells us: 

You form physical matter and the physical world that you know. The physical senses actually can be said to create the physical world, in that they force you to perceive an available field of energy in physical terms, and impose a highly specialized pattern upon this field of reality.

There are no real divisions between the perceiver and the things seemingly perceived. In many ways the thing perceived is an extension of the perceiver. This may seem strange, but all acts are mental, or if you prefer, psychic acts.

Your universe is idea construction.

The world that you know is one of the infinite materializations taken by consciousness, and as such it is valid.

The soul's perceptions are not dependent upon time, because time is a physical camouflage and does not apply to nonphysical reality.

This seems to tie in reasonably well with the whole M-space/N-space thing. N-space, the information matrix, is "the available field of energy" that each mind "perceive[s] ... in physical terms." M-space is a kind of reality bubble created by the mind, and therefore "there are no real divisions between the perceiver and the things seemingly perceived," and "all acts are mental." Since every person has his own M-space, "the world that you know is one of the infinite materializations taken by consciousness, and as such it is valid." Space and time are properties of M-space but not of N-space (at least not in the same way), so "time is a physical camouflage and does not apply to nonphysical reality," i.e., to N-space. 

Seth on our physical reality: 

It is as if your present situation and all its physical phenomena were projected from within yourself outward, giving you a continuous running a motion picture, forcing you to perceive only those images that were being transposed. These seem so real that you find yourself in the position of reacting to them constantly…

They serve to mask other quite valid realities that exist at the same time, however, and actually from these other realities you gain the power and the knowledge to operate the material projections…

The inner senses are equipped to perceive data that is not physical. They are not deceived by the images that you project in three-dimensional reality…

Anything of which you are aware in three-dimensional existence is only a projection of a greater reality into that dimension. 

This matches up pretty well with the ideas of N-space and M-space that we've discussed earlier. Of course, the fact that the Seth material – or some of it – can be understood in terms roughly equivalent to the N-space idea doesn't mean that the N-space idea is correct. But it is at least intriguing to note the parallels.

Seth on apparitions: 

I have explained to some degree the way images are constructed out of an available field of energy. You perceive only your own constructions. If a "ghost" wants to contact you, therefore, he can do so through telepathy, and you can yourself construct the corresponding image if you desire. Or the individual might send you a thought-form at the same time that he telepathically communicates with you.

In our terms, the apparition's form is rendered in the M-space of the particular individual. Two or more individuals may render the equivalent form, each in his or her own subjective M-space. Another individual, whose consciousness is not telepathically in tune with that of the consciousness behind the apparition, may not render the apparition's form in his M-space at all. 

This might account for cases where two or three people see an apparition, while a fourth person in the room with them sees nothing. It might also account for the peculiar fact that an apparition (contrary to most movie ghosts) usually appears just as solid and three-dimensional as any other physical object, and is seen from the appropriate perspective by each observer– that is, one observer may view the apparition head-on, while an observer who is standing off on the side will see the apparition in profile. Light and shadow are also rendered appropriately. 

All of this is about what we would expect if the apparition is modeled in M-space like any other "real" thing. But since the rules (in the N-space program) governing the apparition are different from those governing other objects, the apparition can appear and vanish instantaneously, walk through walls, etc.

I'm not saying Seth's ideas line up perfectly with the ones we've been looking at, but there are some correspondences.

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