flatland
Before Orwell's masterpiece novel, 1984, about a dystopian society and what politically motivated and propaganda-induced groupthink looked and sounded like, another Englishman by the name of Edwin Abbott Abbott wrote a semi-satirical, allegorical sci-fi novella called Flatland: A Romance of Many Dimensions, in 1884. In his story, Abbott ingeniously uses flat geometric shapes to represent different strata of society in his contemporary experience of Victorian England. Taking aim at his era's biases, prejudices and social mores, Abbott satirizes the thought processes and modes of oppression towards those who would begin to consider other, higher, levels of reality, and allegorizes the reception of divine inspiration using a mathematical conceit that may have more reality to it than perhaps even Abbott supposed.

On this week's MindMatters we discuss Flatland in all its cosmological glory. Like a dimensionally flattened, but fleshed-out, Plato's cave, we delve into the book's significance as a profound allegory, its many intricately bound insights, and what Edwin Abbott was entertainingly imploring us to think about and consider. In a world where ever greater numbers of people actually believe that the world is flat, we'll be thinking on a story which suggests that higher dimensions are not only possible - but probable - if only one can open one's mind enough to 'see' it.


Running Time: 01:01:04

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See also: Here's the transcript of the show:

Elan: Hello and welcome back to another MindMatters show. Today we're going to be discussing a book that was written in 1884 by an English school master named Edwin Abbott Abbott. The book is called Flatland, and it's a book that we touched upon sometime ago when our brand was the Truth Perspective. It was part of a show discussion on Unlocking the Secrets of Consciousness: Hyper Dimensional Attractors and Frog Brains - yes that was the title of it - and that was a discussion of a book called Consciousness: Anatomy of the Soul, written by Peter Walling and Kenneth Hicks.

As part of that discussion, we looked at the writings of Edwin Abbott Abbott and this book called Flatland, which is a short book that is at once a kind of cultural satire of Victorian England, a mathematical enquiry and a sci-fi novel. I think most importantly, it's a call towards reason and towards thinking outside of our expanded perceptions of space, of dimensions, of those constructs that we've been taught to think about and view our reality within.

So that's just a rough outline. The book really begins with an incredibly detailed description of a strata, of a flatland society where you have a hierarchy of individuals who are made up of different geometrical figures. So you have men who were 'squares'. The protagonist of the story is a square. You have polygons and hexagons, isosceles triangles, and women are needles basically, kind of uni-dimensional. And there's a strict hierarchy among these various geometrical figures that suggest a lot of the social conditions of Victorian England at the time. It's quite funny in places, but also pretty serious in other places because one can recognise the prejudices and the oppression that may exist among different strata of society, if you can think about it in those terms.

So it works on that level. I think one of the more important reasons for discussing the book today, as I was saying, is this limitation that many people or individuals as illustrated in the book, have in being able to view reality outside two dimensional terms. So, our protagonist is a square. He runs a household, he has a wife and children, he's got servants and he's visited one day by a circle who ends up being a sphere. This sphere is from the dimension of space. I don't think that's exactly how it's termed but it's this higher dimensional area and the sphere is visiting the square because of this time period every thousand years or every millennium that there's this opportunity to have this kind of message being brought down to Flatland about the fact that there is another dimension, there is a 3D universe that the flatlanders have been kept largely ignorant of.

So there's a lot of struggle on the part of square to understand the message that sphere has come down to explain to him and to impart to him, in the hopes that square will become a prophet for a new perception, a new reality. That may be a good place to leave it off and jump off from.

Harrison: Like you said, it's a story with many dimensions, no pun intended. If we focus on the first just for a second, on the nature of the social commentary or social satire, I thought it was interesting that when the book first came out over a hundred and thirty years ago, there were charges against Abbott for being sexist because, of course, in the story, like you said, the women are lines, sharp pointed lines. They don't have angles. They're not triangles - in a sense the lowest of the shapes that live in Flatland. He of course depicts them with all of the Victorian era, but not limited to that time or place stereotypes of women. He responded to that after the publication by saying: "Well it actually was a satire, that's how I intended it. I didn't intend to argue for those positions but the narrator himself, the square, is a product of his society. So square himself has those prejudices and stereotypes".

Throughout description of the Flatland world, he is arguing for their social system, giving all the justifications for it and the reason why it is a great form of social order and arguing on behalf of the system even though he is one of the enlightened ones that receives the message from above, the gospel of space, of the third dimension.

So that's one aspect where you see how Abbott constructs this world. There's no one-to-one ratio for all of the different features of Victorian society, but he manages to inject them into this world in a way that's kind of plausible. The more facets you have to your shape, the more angles you have, the more edges you have, the higher your status, the higher your class. The circles, or the ones that come to approximate the closest to a circle, having a very high number of angles, like a polygon with many sides to it - the closer you get to a circle, at least to be able to be called a circle, you become the priestly class, the closest to perfection.

The people on the lower end of the spectrum are these isosceles triangles, or the triangles with irregular angles to them. They don't have two equal length sides to them. I believe those ones were the criminal class, the low class, and there are various comments throughout the book on the nature of the criminal class and how when you're born into that class, you're just going to be a criminal anyway. It's a very, almost Darwinian eugenicist's view of humanity and social interaction in class warfare. So the higher classes are always socially manipulating and socially planning in order to quell any rebellions from below. There's a description of politics in there too and the nature of social control, the nature of state control and all of those things.

So when you have this presentation of a specific society, and like you said, he is primarily modelling this on the Victorian era, you have this description of a society and the kind of the moral of the story is that there is a higher world. There is a higher perspective. That comes to be imparted to him by this sphere, this three dimensional being from the higher dimension that comes to him to try to explain. At first, like you said, he doesn't understand, he can't understand. He ends up physically assaulting this cross section of the sphere as a circle that appears in his room one day, and has to be physically pulled out of his two dimensional space to be shown his world in order to finally get it. And then, for the rest of his life, he tries to remember that vision that he was given of being pulled out of space, and then to impart it to others too, and ends up getting arrested and thrown in prison and he writes Flatland from prison.

I mentioned the eugenicist aspect to it. There's a lot of state murder in the story. If you deviate from regularity you'll be executed. They have trials where, for instance in the square's trial, everyone involved in the trial will then be executed afterwards so that they can't spread what they heard about the trial. So like you said, it's a very dystopian kind of totalitarian system of social control is in there but yet we see it from the perspective of someone who believes in this system because it's just self evident, these truths, that the polygons are smarter and more spiritually evolved and developed than the lower classes who have practically no ability to raise themselves. In theory they do but in practice they don't. The classes are kept very rigid.

So once there is this perception of a higher knowledge of the nature of reality, the wider nature of reality, forces square or any inhabitant of Flatland to think outside the square, and to actually envision the box, to be able to see the box. That puts the first part of the book into perspective, I think because I think one of the goals that Abbott had, or one of the messages in this book, is that it really is in part an allegory or a symbol for the reception of a spiritual message. It was probably specifically a Christian message, the receiving of the Gospel, and then preaching the Gospel and then being persecuted because of it. It's a fairly standard storyline.

But the message that even the square doesn't fully get, doesn't fully understand, is that his entire society, his entire self-conception and self-image, is two dimensional, that everything, all of his social interactions, all of his social mores and customs are all on a low level, on a basic level and that there's much more to the world, much more to reality, and basically the truth if he were to know it completely, would completely relativize that society, that understanding of reality, to the point where it is itself unreal, in a sense. The real or the true is the perspective that he had for a glimpse of a moment when the sphere raised him out of his two dimensional life and showed him the third dimension. That's really the state that most of us are in, or that all of us are in.

We in our third dimensional reality, with our third dimensional societies, cultures and customs, are just as two dimensional as they are in Flatland, and we don't see it. We come up with justifications for why our culture is the best, our way of life is the best, things like that, and don't see that we really are the product of a bunch of average people. Every society is the product of a bunch of average people doing an average thing, but there's always a higher level.

So I don't know if Abbott would have looked at another society, or a future society, maybe in the last hundred and thirty years and say "Oh, this is objectively better than my society that I was satirizing in Flatland". He may do so. He might look at our world and say "It's so great that we've got rid of this this this and this", but that doesn't mean that we're that much better. We're different but we're the same at the same time because there's always a higher level, and there will always be a perspective from which all human societies are two dimensional.

And that is in Flatland the third dimension. So from our perspective it would be a fourth dimensional reality. This is something that I think Square even proposes to the sphere, and the sphere rejects it. He's like "Oh, that's ridiculous, I live in space, there's nothing higher than space". Again, that shows that the same applies on each level, so even in the third dimension the sphere can't comprehend that there might be four dimensional space.

Elan: Well he later recants a little bit...

Harrison: Yeah.

Elan: ...and says "You know what, I misspoke and occasionally even we get prophets from the fourth dimensional space and we're struggling to understand this higher area."

I wanted to get to a point you made about what Abbott would think or experience had he lived today, because I think it's a good observation. As you were mentioning that, Harrison, I was thinking about this recent war, this information and knowledge war that we're seeing regarding intelligent design. I don't know how aware people are of the fact that there are publications out there that are calling for outright censorship of the science, of the writing of and about intelligent design.

This is very interesting to me and I think is almost a perfect analogy with Flatland. There are scientists or people out there who call themselves scientists, who are practicing what Chittick might call scientism - that is really pseudo science - that don't want us to be thinking about higher dimensional realities that might have had a hand in informing our reality.

So that comes to mind. And I wanted to say that it's interesting also that people would put Abbott under fire for his satire because English literature had a fine tradition of satire. You had Jonathan Swift writing a couple of hundred years prior to Abbott and putting out essays that were full of satirical information that drove the point home. One of the best writers that we see on Sott, Signs of the Times, is C. J. Hopkins whose articles about contemporary fascistic thinking are driven home by some fantastic satire in a way that a more dry and straight forward article doesn't always convey certain thoughts.

Harrison: Maybe to move on to some of the mathematical parts of the story, for those who either didn't listen to our show on the consciousness book or haven't read Flatland or anything about the four dimensions, a bit of an analogy from Flatland itself might be able to give an idea of what we mean when we talk of the fourth spatial dimension.

So in Flatland it's like a sheet of paper, or the surface of a liquid. It's a flat surface and everything that exists, exists on that surface, so nothing has a third dimension to it. It would be like the shapes that you draw on paper had their own existence. So they can only comprehend two dimensions and can't comprehend stepping out of that third dimension. Now when you have a sheet of paper, and you have a sphere, when this sphere passes through that paper as it does in Flatland, it first appears as a point and then a small circle and then the circle grows, and as it completely passes through the circle, then gets smaller and smaller until it disappears.

So you have a crosssection of a higher dimensional object which appears as a two dimensional object. So two dimensional shapes are crosssections of a third dimensional object. So an analogy in the third dimension would be if you would see a small point appear and then a sphere that's very tiny that gets larger and larger, maybe a beach ball, and then shrinks and shrinks until it disappears again. So you'd have a point appear from nowhere, grow, shrink, and then disappear. That would be a hypersphere entering three dimensional space, passing through it, and then disappearing. It's the same thing with a cube and you could imagine any shape like that.

Now another way of representing a hypercube for instance, would be to unfold it. When you unfold the sides of a cube, you get that cross shaped shape. You have six squares. You fold them all up and you get a cube. A hypercube would be composed of cubes stacked on top of each other that you then fold together. You have to fold them in hyperspace in the fourth dimension - you can probably search on YouTube for visualization of a hypercube and you can see the rotations of it. Oftentimes one of the ways of looking at it is a cube. They don't look like cubes but they're connected to other six-sided figures and then it can rotate through itself and you see it undulating.

In the fourth dimension, each of those would be a perfect cube. I think the way it works is that each corner of the cube is connected to a corner of the other cubes and somehow that works in the fourth dimension. We can't visualize it in the third dimension very well. We can kind of visualize it but it's not geometrically accurate.

So there are these mathematical shapes that exist abstractly, and a whole hyperspace that exists abstractly, at the very least for the mathematician who's doing the equations and doing mathematics in four dimensions. But the idea is that perhaps this is actually true, or an actually real space. This is what we got into in our show on the consciousness book - that what those guys found and what they argued is that brain activity, when graphed mathematically, that graphical representation is a crosssection of a four dimensional shape, or a higher dimensional shape. Read the book for the details because you need to work through it in order to have it all make sense.

But what they argue is that consciousness is a hyperdimensional phenomenon. So consciousness is actually taking place in higher dimensions and then getting translated into third dimension through these cross-sections of brain activity. It's basically being constructed or put together again or re-membered in the brain activity, but that the consciousness itself is a hyperdimensional phenomenon.

So there are a few different ideas to bring together here and a bunch of possibilities as well. One of the implications that a lot of mathematicians derive from not only Flatland, but all these representations of the fourth dimension, is that there is a sense in which the fourth spatial dimension is time. Some disagree and say time is its own dimension, and the fourth spatial dimension is separate, but others say that they're integrally related somehow.

So just as those cross-sections of the sphere show up as circles, that in our third dimension any given point in time or slice of time, is the cross-section of a hyper dimensional figure, or shape. So your existence - if we just bring it down to the level of one being -- your existence from conception to death, each moment in your life is a cross-section of a higher dimensional you that encompasses all of the you's that sequentially took place, like an infinite number throughout your lifetime.

The same could be said for the entire universe. Each slice of time is a cross-section of the hyper dimensional universe.

Elan: I want to interrupt you Harrison, because what you just said has a lot of implications for how we perceive reality. If these are slices, if any moment in time is but a slice, or two dimensional, or even a line version of our time, what are the implications for reality itself, if it's not only the mind that has a connection to other dimensional realities, but our entire existence? It would seem to suggest that there is far more to us. Without getting too far into it, we've discussed reincarnation, the possibility of afterlife existence, high strangeness, all of these otherworldly ideas that tend to get poo-pooed so automatically by scientists.

So I think in the very acknowledgement of a fourth dimensional space or reality, if we allow ourselves to consider the possibilities here - this is what the consciousness book is basically alluding to, it's what it's pointing to - then we can try and be as rigorous about it as possible. We don't want to go too far off into one direction or another and assume all things but we can allow ourselves to be open to the possibility that time as we experience it and understand it - point A to point B - is really just a construct that we've been inculcated with and biologically focused on, given our physicality. But there's really just a lot more to it, in theory.

And I think that that creates an opening for entertaining, at the very least, where our three dimensional reality begins and where a fourth one may start.

Harrison: One of the implications in a lot of these writings, and not just Flatland, is that there's nothing that's strictly a one dimensional, two dimensional, or three dimensional object or being, that everything exists in a hyperdimensional reality and that we only see part of it. There are no sentient squares, but there might be two dimensional consciousnesses, for example, that exist in three dimensions but only experience a two dimensional reality. For us, we experience a three dimensional reality but are actually part of a four dimensional whole. So there wouldn't be these rigid divisions. Everything is a more or less limited expression of a hyperdimensional whole.

I've got two books here. One is P. D. Ouspensky's Tertium Organum where he deals with a lot of the fourth dimensional stuff. He finished it in 1915 or 1914, something like that, so it's about a hundred years old. And then, another book by Rudy Rucker called The Fourth Dimension, published in 1984, a hundred years after Flatland. Rucker himself was influenced by Flatland. He really liked it as a kid and then wrote this book about all the mathematics and implications.

It's been years since I read this book but I still recommend it. It's funny, it's easy to read, and it's got funny diagrams too, drawings to show all of the points. So I randomly flipped it open. Here is what I was talking about with the representation of the hypercube. [shows diagrams from the book] You've got the central cube and then all of those shapes coming out the side are also perfect cubes but they can't be represented as perfect cubes in three dimensions but that's one representation of a hypercube.

So he goes through all of it and there are various excerpts of his own fictional continuation of Flatland with a square. So if you want to get into it, I'd recommend this one too. But I wanted to read something from Tertium Organum about our 3D reality being a slice or a cross-section of a higher dimension. I'm going to read a page from chapter five of the book, Ouspensky writes:

"Four-dimensional space, if we attempt to represent it to ourselves, will be the infinite repetition of our space - of our infinite three-dimensional sphere - just as a line is the infinite repetition of a point.

A great deal of what has been said earlier will become much clearer for us if we take as our standpoint the view that the fourth dimension should be looked for in time.

It will then become clear what is meant by saying that a four-dimensional body may be regarded as the trace of the movement in space of a three-dimensional body in a direction not contained in it.

The direction, not contained in three-dimensional space, in which every three-dimensional body moves, is the direction of time. By existing, every three-dimensional body moves in time, as it were, and leaves the trace of its motion in the form of a time-body, or a four-dimensional body.

Because of the properties of our perceiving apparatus, we never see or sense this body; we only see its section, and this we call a three-dimensional body. Therefore, we are greatly mistaken in thinking that a three-dimensional body is something real.

It is merely the projection of a four-dimensional body - its drawing, its image on our plane. A four-dimensional body is an infinite number of three-dimensional bodies.

In other words, a four-dimensional body is an infinite number of moments of existence of a three-dimensional body - of its states and positions. The three-dimensional body which we see is only a figure on a cinema film, so to speak, one of a series of snapshots.

Four-dimensional space - time - is actually the distance between the forms, states and positions of one and the same body (and of different bodies, i.e. bodies which appear different to us).

It separates those forms, states and positions from one another, and it also binds each one into some whole incomprehensible for us. This incomprehensible whole may be formed in time out of one physical body, or it may be formed out of different bodies."

So that's how Ouspensky represents it. Like I said, Rudy Rucker is one who argues that time is not equivalent to the fourth spatial dimension as Ouspensky seems to be arguing -- that there are just different ways of representing different dimensions.

So I'm not sure where I stand on the debate, but one of the implications of fourth dimension as time is like Ouspensky said - it's like your life is a film that plays itself out. And the way that I visualize that, which is a very deterministic model is let's say you have a video file that you open in 'quick time', or something. You can click on the slider and then move it forward and back, so you watch the video go forward and backwards and it is this deterministic whole that's like a two dimensional representation that is the entire time series of the life of whatever is in that film. So you've got the beginning to the end.

You could create, hypothetically, a 3D film of a four-dimensional object and do the same thing. You've got the slider so there's your conception. You can fast forward to your death, go backwards to your first career, forward, back, and it's the same film played over and over again - you just cycle through it, rewind or fast forward.

But that's a very deterministic view of the world. That's one of the things that Ouspensky deals with in one of those early chapters in Tertium Organum - is this question of free will and determinism. I believe Tertium Organum was written before any of the real work was done on quantum physics and especially before it entered into the popular imagination. But, like Ouspensky argues, either determinism or total free will are both bad options, they're too extreme. The truth is somewhere in between both of them.

The world isn't a deterministic - how do the scientists call it, the physicists? - a block universe, that's what it's called. The block universe is like a cube. Every cross section of which is a moment of time for the entire universe, and each moment of time is just stacked one on top of the other and you get this cube. That's just how they represent it for whatever reason.

You could go anywhere in space which is anywhere on one of those cross-sections, and then time is moving through that sphere. So you could trace an atom from the beginning of the time series through space, through that cube to the end of the universe at the top. Again, that's just the representation of it.

But, Ouspensky and me too, would say "Well no, that doesn't seem to capture the nature of reality". On some of the shows that we did on philosophy, some of which I think were in some of the shows we devoted to Jordan Peterson's ideas, that doesn't seem to be the way the universe is structured. The universe seems to be structured with an element of free will, or an element of accident, or an element of the possibility of novelty being introduced to the universe so that the future can't be completely predicted.

Ouspensky says something similar in Tertium Organum. He says that you can't totally predict the future but what you can do is predict based on complete knowledge of everything of the present - the way things will go without the introduction of some novelty, of something new.

So we are very deterministic and mechanical in our lives and the universe is the same way. So we can predict a probable future and we can predict possible futures, but at every moment there's the possibility of something new being introduced. It might be some form of inspiration, something that changes the action we take where we would have ordinarily, let's say, gone in this direction, but something new comes in to make us choose that direction, which couldn't have been predicted beforehand. Of course you could predict if this novel thing comes in, then this person might change and do this instead of that. But you can't predict the novelty. You can't say "Oh, this novelty will come here". There is an element of unpredictability in the universe and a space for free will, for changing the outcome. But things still progress causally. You can make predictions based on what you know but there's always the room for something you don't know, something new coming in.

So thinking about that in the last few days with Flatland, I was wondering about that because the universe doesn't seem to be a block universe. The future doesn't seem to be set in stone. There seems to be the possibility for new actions and novelty and unpredictable things happening. So how might this be represented in this fourth spatial dimension? What would a hyper human being look like, if the human life is a cross section of the time body as Ouspensky was putting it?

It wouldn't be that there's just me as a zygote and then my dead body, and everything that happens in between is just the inevitable progression of what will happen. So it's not just like a 3D MP4 file. There's something more to it. The way I kind of see it, at this point at least, is more like the fourth dimension is that there's an aspect of the simultaneity of all those time periods, all those slices, but also a simultaneity of all of the possibilities. 'So here's the way things will go for this body if these things happen', and 'here are all the ways that things might go if this happens', 'and this and this and this.' So not only do you just have all those cross sections of the one life that you will have lived when you die, but all of the possibilities that might have been, or that might still be if you're not dead and all of those possibilities form a time body, a possibility body.

Who knows? If any of this is true to any degree, maybe this is an even higher dimensional aspect that isn't strictly limited to the fourth dimension. Maybe it's a fifth or sixth dimensional thing, but, that there is a whole body of all of the possibilities for any individual - in this case human being - more than just that one life that you'll live. Maybe that one life that you'll live is the dominant tread in this web of possibilities, and maybe that's the life you live. And maybe there were all of these possibilities that you could have done, but for whatever reason you never achieved it. And maybe if we look into Flatland, maybe that's the life that all of these Flatlanders are living. It's that one possible life that is just the easy life, the path of least resistance that they take. 'If nothing new happens then this is the life you live', and that's the life they live because nothing new happened.

Probably more accurately - they didn't allow anything new to come in because of their prejudices, because of their closely held beliefs that they won't let go of, that they don't let go of in their lives. They're so identified with those aspects of themselves, their self image, their image of their society and their place in that society, that they don't let the things in that would let them break out of that MP4 file and live another one where maybe they get to experience that glimpse of the third dimension.

At least that's the way I'm looking at it, at the moment.

Corey: It's really interesting to think about and it's something that was really on the minds of a lot of very intelligent writers and authors like P. D. Ouspensky and Abbott and several others back in the late nineteenth century and very early twentieth century. It's kind of a shame that that movement towards hypothesizing that a lot of the inexplicable things about human existence that are objectively verifiable that do happen, the crazy stuff that does happen, trying to find a place for that somewhere in the universe using mathematics and science and trying to come up with ways to understand what it means to have more dimensions than what you are consciously able to experience. Abbott did a really good job of showing the limitations of that conscious experience of only two dimensions for these Flatland beings, and how the universe would look to them compared to the universe of space land and the spheres and us three dimensional beings.

There's no possible way you could understand it. It's just something that's so far outside of your experience, what you're capable of thinking and also what you assume is real and what you assume can exist. For the supreme crime of disobeying what is supremely assumed by all of your fellow two dimensional beings [laughter], the square ends up in jail. Which is funny because throughout the whole story, he's such a square, he's such an authoritarian follower. We have all of these dimensions and everything that goes along with the dimensions. If you've got enough angles then you're some supreme guy, super guy, and if you're not then you're like a lower caste, isosceles triangle type of thing. At the end of the day, he accepts the truth and feels that it's his duty to try to inform his grandson, and then he ends up in jail and imprisoned.

I like that analogy, especially for the large number of people out there who see something, who see that there's something amiss and it seems like there's something inexplicable happening in the minds of people, in world global politics and this and that, that can't be explained by just recourse to previous thought, old stale thought, logic, anything like that - that there's something much higher happening and we're kind of at the mercy of it, for whatever reason.

That's why I'm really glad that we read that book, and I hope that more listeners can get out there and find some of this material themselves because it's an exercise in understanding limitations and the pain of trying to understand the limitations of those below us and our own limitations. It's seeing that we kind of behave like we have the similar mental prison that the Flatlanders do. Obviously it's just a story, and it's just an analogy. I had a great professor and she told me that all analogies limp, they're never going to be quite perfect. But when you look at it in terms of what's just going on in our daily lives and what's been happening throughout history, there's how many countless people have said there's something terribly amiss? And that's where satire comes into play, right? It just satirizes our stale assumptions about the world and now more than ever we need more satirical glimpses at the stupidity of so many of our assumptions.

Elan: The struggle of the square, even as the sphere was explaining things to him and his railing against all of the sphere's explanations as to how there could be this three dimensional space, is explained with a lot of sympathy, in some ways I think. It's interesting that, in some ways, square was also in the position of sphere by visiting the lower dimensions in his dreams and trying to convey to 'Lineland' and 'Pointland' - these two even lower dimensions - that there was in fact a Flatland, in the best way that he could explain it.

There's a wonderful description of how the king, or president of Pointland was completely living within his own reality and couldn't possibly allow for any other explanation except for those that he had given himself. You just carry this analogy one step further, one step further, so you're seeing how this type of narrow thinking exists on all of these levels until, as we mentioned earlier, square says "Well, if there is a third dimension of space then there must be a fourth dimension of space". It's as though his perceptions have been completely blown open.

It's interesting also that Abbott has additional visitations by sphere and of the square's visitations to the lower levels, through his dreams, which is a suggestion that his consciousness is doing other things, is going to other places or areas. The suggestion is that there is something more to consciousness in learning that exists when we dream and when we're not in our consciousness state, necessarily.

I did want to get back to that idea that there is a 'thought police' regarding these areas of pursuit and this has been brought up on the show previously with scientists such as Rupert Sheldrake, most recently, and the large numbers of articles and things that have been put out there to squelch his ideas of just how broad consciousness can be.

Wilhelm Reich, in the 30's and 40's, had government organizations persecuting him because of his studies into consciousness and technology that suggested other 'somethings' [chuckles]. Otherness. He was limited and there are all sorts of stories. In the fields of medicine there are ideas that are being suppressed that I'm sure many of us are familiar with.

So this oppressive police state exists and is exemplified by the president in Flatland who not only throws the square into prison for trying to share some of these ideas, but even throws people into prison, like you were saying earlier Harrison, who were in the court witnessing and listening to the ideas. They can't be allowed to continue on with the knowledge that there may be another possibility to the reality that they exist within.

Harrison: There are just a few final ideas I want to try to formulate. One is that it seems this dimensional way of looking at things has resonance with the idea that you can only see, really, your own level of consciousness, or your own dimensional level and those below, but what is below can't see, can't comprehend what is higher. We can't really comprehend or see from a fourth dimensional perspective. But we can see and we can comprehend and think about second dimension or one dimension. It's easy.

This relates to something else. Do you remember in Flatland you guys, when he's encountering the sphere, there's talk about his 'inside'. Sphere was trying to get him to understand that there is another direction, neither north nor south but 'up', and he can't figure out what 'up' is. I can't remember what the connection with 'inside' was. Do you guys remember? Okay. First sphere said "Oh let me demonstrate for you, I will touch your insides", and square is "that's impossible, you can't touch my insides, you're outside of me". So he goes above and then plays with his 'insides' and he feels this sharp pain in his stomach and says " Oh my god, what are you doing?"

But there is this connection with what was on the inside. I think it was in his first encounter before he saw sphere that he felt a presence, that there was something else in the room and he felt it on his inside and the inside was how he felt the presence of this higher dimensional being.

That, combined with this idea of another direction -- because what is neither left, right, forward, back, or up and down - what is the other direction for us three dimensional beings? We do have a word for it because we do use directional words in a kind of symbolic way when we say something is higher. We don't mean that it's higher in the sky, higher above us, we don't mean that you look up and that's what we're talking about. 'Higher' means something else, it has an inner meaning.

So I think there's probably a way of putting all these ideas together, that the fourth dimension, the other direction (for us), for beings with a certain degree of consciousness, that is experienced first of all inside. It's an inner direction. When something happens inside you, inside your consciousness, that is the direction of the fourth dimension for us. It's not just forward in time or back in time, there's an inner dimension.

There's a scale of consciousness too, of higher and lower. And that might be a representation of, again, something dimensional going on. Because when we talked about the Consciousness book by Walling and Hicks, as they represented consciousness in these brain waves, there were levels of dimensionality to their analysis. So a low level of consciousness, a low dimensional number. And as the state of consciousness raised, you had a higher number, a higher dimensionality of consciousness.

So there might be an integral important link between states and levels of consciousness and dimensional numbers - a higher dimensional number is representative of a higher degree of consciousness. So if there is a growth in fourth dimension, that might be equivalent to spiritual growth, or the growth of consciousness, that what's actually growing is a fourth dimensional body. Again, this would be that novel road taken by the fourth dimensional whole, not the road less travelled, you could say, not the engrained groove of a trench that we're stuck in that's the path of least resistance. You can imagine a pebble or a ball rolling through a groove. It's stuck there because that's the path of least resistance. It can't jump out of the groove to find another groove maybe, or to form another groove just because it's easy. It's just following gravity.

If it does step out, that might be representative of a growth in consciousness, an inner growth, an inner growth that is higher, not higher in terms of altitude but higher in terms of the fourth direction, the fourth dimension, so an inner, upward growth that isn't literally 'up'. Just as for square, his development would be 'up', but not forward or back, or left to right, but a different 'up'. Not north or south.

So I just wanted to throw those ideas out there, that there seems that there could be a connection between all of those ideas and all of those ways of looking at things -- that real growth is inner growth and that might be hyper-dimensional growth. And to relate this to our last show, we were talking about the need for a kind of super intelligence to coordinate the progressive evolution of life itself, and the totality of life, and what that intelligence could be.

If consciousness and intelligence -- which might be related in some way -- are dimensional, that an intelligence that is higher than our own, then if the things that we've been saying are true must be hyper-dimensional. If the things we're saying about consciousness and its relation to two dimensions is true, then a hyper-intelligence would be a hyper- dimensional intelligence - something at either the level of a fully self-conscious fourth dimensional being, or fifth or sixth or however far it goes. With that level of intelligence, just like the sphere can look down on Flatland and see the entirety of Flatland and have a much greater breadth and depth of knowledge about Flatland, that the individuals themselves can't have - they can see it all in an instant. Whereas, square himself can only be aware of his tiny little life at one given time. He can learn about other things but the sphere can just view it all happening at the same time.

Maybe there's an equivalent from fourth to third -- an expanded field of vision combined with a vastly superior intellect, the ability to forecast, to predict, to see how things will work together or won't work together on a level that is just beyond our ability to conceive of. We can see the fruits of it. We can see it working out and kind of marvel at the complexity of it. But just as we, on its own level, can't see higher than itself, only lower than itself -- we can only guess and see the fingerprints. We can see...

Elan: The hints.

Harrison: ...the hints, the cross section maybe. That's about it.

Elan: As you were saying that, I wondered if, for those who are naturally open to the idea of higher dimensions, that there hasn't been some kind of interpenetration or experience of something that falls so far outside of the way that normal reality gets explained to us, whether it be synchronicities or déjà vous or strange dreams, or any number of things that are irrational by the agreed upon version of reality that we've been brought up thinking, that there are these interpenetrations or this kind of connection or touching of something higher, or just plainly different that is so inexplicable that once that contact has been made, then the opening and awareness of things that may or may not be connected to it, and the explanations like the fourth dimension, like Tertium Organum and any number of other texts that we've been looking at and discussing, we are quite willing to be the heretics in our Flatland and allow for a greater acknowledgement of a broader way of thinking about things, and understanding ourselves within a wider reality.

Well, if that's everything guys, we're going to say good-bye. We are glad you joined us today and we look forward to seeing you again next week. Thanks for listening.