Draw a line through any two points in space. Does that represent a dimension - or a direction? In a Universe with no background and no centre, the direction you chance upon might be ‘inward’, or it might be ‘outward’ which is just the converse of ‘inward’. The technical difference between a Dimension and a Direction is that Dimensions, such as those of space: height, width and breadth, are generally accepted to be orthogonal to each other. I wouldn’t argue with that although as we shall see, that may not be the whole story.
Time is usually considered the fourth Dimension (see the next section), but the 'fifth dimension' of popular culture is closer to the idea of orthogonality. You can still see Rod Serling's 'The Outer Limits' on TV. As in many other stories, the 'fifth dimension' is one you can reach just as easily as by stepping through a door. Wouldn't that be great? Just as Serling’s 'fifth dimension' is much more exotic than the world we know and have fully mapped, how we could conjure with, say, a ninth dimension!
The 'portal to another world' has been inspiring awe in children for generations, from C S
Lewis' world of Narnia, through the wardrobe, to another Lewis: Lewis Carroll's 'Through the Page 7
Looking Glass', and on to Harry Potter. It very much helps if we can keep a strong visualization of these ideas. To describe things visually is to understand them, the way clever people understand numbers by using them through formulae. Even the simple visualisation of a boat at sea gives a useful starting point. The best visualization I can think of does come from my childhood, and I want to draw our attention to it now. It comes from the world of comics, by the artist Steve Ditko.
To digress briefly, I first started reading comics as a teenager. This medium of the imagination was to feed my sense of wonder for my whole life. As an adult, I could be left cold by Tate Modern and Damien Hirst, but I could be moved to a gasp by comics, as I was when I first saw the covers of Dave McKean, for ‘Sandman’. As a teenager, my father had made me burn my collection of pornographic magazines after my mother discovered them under my bed. Some of these erotic images live fondly on in my memory today, but they are alongside the beauty of Marie Severin’s images, for Marvel. This colleague of Steve Ditko showed me, for example, what it might look like if a man was strong enough to scoop up a castle by its corner (the Hulk), and teased my imagination with images I couldn't even try to describe to you now (Zom, The Living Tribunal).
(I cannot resist adding, whilst we are talking about dimension, that of course the comic page is a 2D representation of 3D. Think about the attraction to the artist of the ease with which one can draw a stretching limb (Mr Fantastic, Plastic Man) or a man picking up a castle by its corner (Hulk) or a man shrunk to ant-size or grown to giant-size. These tasks were rendered far easier by drawing on the flat page than they could possibly be in three dimensions – at least before CGI. But then think about the challenge to pure imagination in putting these to story).
When at last I had the chance for my own essay entirely on this subject, I set out to write what I had always wanted to read: just one typical fans experience of the art-form for posterity. But of course there is a serious point to be made as well on behalf of a theory of everything and everyone about the psychological principles that perhaps underlie an extraordinary success. The resulting essay is free of charge below.
http://whatistheshapeoftheuniverse.co.uk/6_OtherResources/Art%20-
%20An%20Essay.pdf
Marie Severin illustrated Dr Strange, amongst others, but it was Steve Ditko who was the co-creator and artistic force behind this character, a 'Master of the Mystic Arts'. Ditko's first stories showed Strange routinely travelling through portals he was able to open to other Page 8
The Shape of the Universe
worlds and dimensions. The illustration below shows Strange traveling through the portal he is able to open to a place which appears to be many-dimensional.
The Marvel comic-book character Dr Strange travels through what appears to be a two-dimensional shape apparently having a different third dimension, acting as a shortcut, in this ‘world’.
Ditko then reveals to us, in all its glory, this world? - space? area? Universe? - notice how the visualization is so strong it challenges us to find the words to match it. The creators, Stan Lee and Steve Ditko himself, came to describe this as a ‘realm’, or 'domain' ( the Domain of Dormammu, the Domain of Nightmare), recognizing that the normal terms like ‘country’,
‘world’ or even ‘dimension’ did not match the intuitive and logical sense of what I will be calling poly-dimensionality. But that is to come.
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As the story progresses, Dr Strange is attacked by minions of the ruler of the domain he has entered.
Intriguingly, they can attack him through portals of their own devising. It is as if they can create or at least access the dimensions in which they are almost next to Strange, and have only to take a single step to be right beside him.
Dr Strange is a Master Sorcerer – a ‘Master of the Mystic Arts’
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In describing these sub-dimensions of course, I am imposing my verbal understanding onto a visual storytelling. Ditko might respond that it is 'just magic' (and I am overcomplicating it).
In long-established metaphysical thinking, Heaven is a place rather like 'the Fifth Dimension'.
Although it is a place one can never visit physically, it exists alongside, and in addition, to the physical plane of the Universe. Even now, there is no reason that we know of that 'the Heavens', which is to say the stars, could not actually contain Heaven. You certainly cannot visit the Sun physically, as you cannot visit Heaven physically; it is 'up', being gravitationally at the centre for us, as Heaven is likewise 'upward'; and it is composed of plasma, a fourth state of matter with different properties than either solid, liquid or gas, as Heaven is a different place.
Personally, I would not argue for Hell as a place that really exists, and it is not my hope to convince you here that Heaven does either. But I have personally benefited from the principle that Heaven is not a proposition to ‘reward good children’ but a serious mystery that repays adult individual consideration. It turns out there is, after all, ‘something to know’. As a subject, it became my first free essay.
http://whatistheshapeoftheuniverse.co.uk/3_Religion/Religion.htm If you don’t read this, what I really want now, is to draw your attention to the long-standing terminology that Heaven is 'onward' and 'upward'. Whether your view is that the corollary of
'onward and upward' is 'backward and downward', or whether you share my view that is actually 'stationary', the point is that this is a two-dimensional characterisation of the larger metaphysic.
We make use of this dimensional meta-simplification all the time. Leaders no longer speak of onward and upward, but of 'the way forward'. When they do, it is not in comparison to the way left or even the way backward, it is really in comparison to the way not forward, i.e. at a standstill. In psychological terms also – that is, in the metaphysical world of the mind – we speak of 'moving on' in the same sense.
Why does this matter? Because I say, there is a tension between what is known and what is believed. As I write these words, the New Scientist has the cover below.
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Here is how the article begins:
"THE ONLY way is up." An earnest student of our physical realities might find room to dispute this jollying phrase. There is also down, and, for that matter, left, right, forwards and backwards. Six ways to go. Then again, the further up you go, the less down you are, and similarly for left and right, forwards and backwards. So that's three independent directions to move in – gravity and local obstacles permitting.
It is a fact so bald that we rarely stop to ask an even balder question: why?
Physicists have wrestled with this perplexing question of space's essential three-ness for a good while now – not, it must be said, with much success.
Our best theories of nature supply no clue as to why space might have three dimensions, rather than two, four or 5.2.
I'd like to read the rest of this article but for its notoriety rather than its implication. (The New Scientist is good news but it is not always free of ideological spin).
Of course physicists are the ones who have taught us that we cannot simply talk of three dimensions. They have taught us 'space-time', and that time is a dimension. We have all become reasonably comfortable with that. Although impossible it has been exotic, rather than threatening, to think of traveling backward in time. It is physicists who have pushed on to ask Page 12
if there are more than these four dimensions and in recent times some physicists have suggested there may in reality be as much as eleven dimensions.
What we know for sure is that the Universe is infinite, and the number of dimensions it has is infinite – or in my terminology – infinitesimal, like the digits of Pi (and for the same reason).We have not found any dimension is more important than, or even as important as, the three we usually consider: not even time. All the directions of space are a product of three dimensions in the same way all the shades of colour can be defined as some combination of a mix of red, blue and green - or another colour model.
Yes, the Universe is many dimensional but let’s refer to it as no more than that. Let’s refer to the Universe as poly-dimensional.
Now I can tie together the physics and the maths with a useful definition. When I was at school I was taught to use an oblong symbol for the Universal set, but I can redraw this more accurately, I think:
Diagram Redacted
Old Universal Set
Better Universal Set
I use a thick perimeter to indicate that the set has an infinitesimal boundary – it goes on forever and ever getting smaller and smaller, so this more accurately describes mathematically and visually what is trans-finite, i.e. connected to infinity, like Pi, e, me, you and the Universe.
So how is the Universe physically infinitesimal on the largest possible scale i.e. at the edge?
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The New Scientist had a headline in 2008 (“Galaxy hints at fractal Universe”) in which the article began with these words:
Is the matter in the universe arranged in a fractal pattern? A new study of nearly a million galaxies suggests it is – though there are no well-accepted theories to explain why that would be so.
The article goes on to explain:
Nearly all physicists agree that on relatively small scales the distribution is fractal-like: hundreds of billions of stars grouptogether to form galaxies, galaxies clump together to formclusters, and clusters amass into superclusters.
The point of contention, however, is what happens at even larger scales.
According to most physicists, this Russian doll-style clustering comes to an end and the universe, on large scales, becomes homogeneous.
Here is what Wikipedia says about fractals:
A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers.
You’re familiar with a fractal from the example of a coastline. As you know, you can ‘zoom in’
indefinitely on a fractal pattern and always see more detail. Mathematically, I would say, a fractal is a set with an infinitesimal perimeter. Because you have already seen it in the case of Page 14
Pi, you know how an infinitesimal number can continue indefinitely without ever repeating.
You also know that Pi is a practical number with limited usage. It may be the work of God but it is not infinite; it is not God.
In exactly the same way, you can ‘zoom out’ on the Universe (of which we are all part), and always see more detail; but what you are looking at on these largest scales is the edge of the Universe which continues without repeat – but perhaps even meaninglessly2 – forever, as a fractal.
It is what you might expect to see at the horizon of space.
~ • ~
Now that we are here at the edge of space ok, let’s look back to our starting point (see page 7), the technical difference between a Dimension and a Direction is that Dimensions, such as height, width and breadth, are orthogonal to each other.
The easiest way to conceive of the Universe is as a sphere, so let’s begin with that.
This is interesting: We can conceive of the sphere as having a radius of 13.8 billion light-years distance. That is because the Universe is 13.8 billion years old so we are told, and the speed of light is the limit. You may also know that the observable Universe is 46 billion light years from end-to-end. The conventional explanation is because space has expanded during the time being measured, but is that right?
We are told that space is expanding but because there is no centre there is no frame of reference to determine whether it is expanding or contracting. Both are equally good interpretations of the observation. And if we were to say space is contracting on the largest scale then at some point it would come into balance.
I draw no conclusion other than to say that we need a starting point we can understand and so I propose the sphere. The Internet tells me the furthest you could travel at the speed of light, allowing for 'expansion', is 14.5 billion light-years. Although they don’t match exactly, I’m happy those figures are close enough to allow for experimental error (!) So my sphere would have a radius of between 13.8 billion and 14.5 billion. It gives us a basis for refinement.
2
This is an important point. For all its appeal in fiction - unlike Time-Travel, which we come on to later -
‘multiple Universes’ is not a meaningful idea.
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Let’s go back to the idea of a sea as a concept for infinity. We now understand that we are on the surface of the sea with a horizon that is between 13.8 and 14.5 bly ( billion light-years) away all around us. We understand why this sea has no exact edge – because it is infinitesimal
- and our position on it is entirely by chance: there is no objective centre.
In other words, our visualisation – our map – works for two out of the three Dimensions. If we want to move in space we can do so but we are moving on the surface of the sea. Unlike Dr Strange, we cannot go below or conversely, lift off from, the surface.
We’ve talked a lot about a fifth Dimension, enough to be fairly sure that if there was one, we would know it. It seems unlikely. I said that Time is the fourth Dimension and indeed, Time is both well understood and poorly understood, which gives me a golden opportunity to deal with it in a separate section on its own, below. An example is that, beloved as it is of fiction, nobody really thinks that time-travel is possible, and yet it is a proven aspect of physics (see Feynman’s book, and below). Be that as it may, for you or me, time travel is not possible. Time is not in reality a Dimension.
But we measure our distances against speed – the speed of light. Could speed be a Dimension? (Not really, I thought. What then about a dimension of scale?) In point of fact I have already pre-empted myself. I have said that there is no third Dimension!
But I haven’t justified that yet; there is a different possibility still to consider.
What about gravity? Could gravity possibly be a Dimension?
VOICEOVER
How does gravity operate at the centre of the Earth? Let’s Google to get the answer!
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The top link on Google right now is: https://futurism.com/what-would-happen-if-you-jumped-through-the-center-of-the-earth which is accompanied by the above graphic.
But is this the whole story?
