Having broached Dimension we will move on to studying the poly-dimensional whole of our subject, but let’s make the effort first to consider time in its own right, as that has been the single most significant suggestion for an additional dimension made so far. I want to enlist the aid of a real physicist, Richard Feynman, in the understanding of time.
Feynman is one of the most famous physicists of the 20th Century of course, but he also wrote for the layman, as a teacher. That’s how I happened to read a book of his (QED: The Strange Theory of Light and Matter) which observes that experiments made at different points of time t0, t1, t2, etc. clearly show sub-atomic particles and events reversed in time, happening at t2, then t1, then t0, etc.
The particle appears to have travelled in time, as effect precedes cause.
Extract from Richard Feynman’s book’QED – The Strange Theory of Light and Matter’
Page 38
The Shape of the Universe
This extract is from Page 99 of the online PDF version of Feynman’s book showing sub-atomic time-travel. Feynman is discussing the interaction between a photon (wavy line) and an electron (straight line). In Fig 63 he has given three possibilities and here, in Fig. 64, he identifies where, as a Positron, a sub-atomic particle moves backward in space and time – from time t3 to t5 – where it meets itself coming forward as an electron in space and time.
If I look at my watch, it says the time is 1 minute past 10 on Sunday morning. It also has the date: 17th. Just imagine if, instead of changing my watch, the time on my watch changed what time it actually was!
I could wind the hands backward to set an earlier time and day, or forward to set a later one.
Nowadays, it may be easier to imagine that time is a dimension than to imagine it is not. Yet, time-travel is an impossibility. It would mean I would meet myself – or my father, and accidentally kill him... How do we resolve this paradox? How can we understand time, in a way that includes this phenomenon of it being a dimension?
To come back to the watch on my wrist, it shows me the time of day, the day of the week, and the day of the month, but it does not show which month it is. For that, I'd need an electronic watch, to keep track of the day and the year. If I was on a desert island, with no battery, I could learn to tell the date from the stars. In ages past, that is how people have agreed what date it was. Knowledge of the Zodiac arose through studying the passing of time.
Page 39
But the Zodiac partly repeats every year so that everyone born in August is Leo, like me. All stars visible with the naked eye from Earth are within the Milky Way galaxy. It takes about a quarter of a billion years for Earth to rotate once around the Galactic Centre – a Galactic Year – but the Zodiac of visually familiar stars repeats itself after only 27,000 years. There is no clock other than the one we make, so if we take away every external measurement of time, what tells us that time is passing? That is, can we tell that time is still passing, or might it seem as if time were repeating?
There are times when I am awake that time seems to slow down, and times when it seems to speed up. Fortunately I know logically that these are subjective sensations. I do not need a watch to tell me that time is passing at a steady rate. It is easy to tell that time is passing while I am awake.
It is much less easy to tell, while I am asleep. I have no real perception that time has passed after I awaken from sleep. The memory of dreams may be a clue, but in dreams, when I am falling asleep, I never feel that less is happening, it always feels like more is happening. My theory about why we do not remember dreams is not because they make no sense and are too difficult to recall, it is that too much happens too fast. Instead of cause and effect chained together, it seems like causes have multiple effects and effects have multiple causes. The dream overwhelms recall.
When you see it like that, travel into the future along a dimension of time becomes less interesting. Travelling forward in time does not need a time machine, just suspended animation.
We are all getting older. There are physical changes both outside and inside the body which show this, and eventually we will all die. Yet that is intellectual knowledge. Internally, I don't feel old. I don't feel a particular age. I don't know what dying means. The human race will go on and, I feel, so will I. But if I had no watch, I would still be accumulating experience. It is the steady accumulation not just of experiences, but of experience itself, which tells me that I have lived out a life. When I was young there were many things I did not know. Whether it was falling in love, qualifying for a degree, or starting a business from a hobby. Some of these I now know, but not all. My experience changes me permanently, without necessarily changing you, as yours does. We become defined.
A real time-machine, so to speak, would be one in which I could go back to not having had the experience I do have. I do not feel any older. I do not feel any particular age. But I do recognise the many differences that experience has made to me, and whilst going back to the Page 40
beginning would in one way be a new start, in almost all other ways, and in all the ways that matter, it would not be something I would want.
This gives me a sense of purpose to go with the sense of time passing. Although my life will end and perhaps a different life begin, the human race of which I am part is greater than death and has a greater purpose to which I contribute. The sense of purpose through experience is my proof that time is not cyclical and repeating. It matters.
I can imagine replacing the 'magic' of time-travel with a science I might call 'experience-travel'. Time-travel looks like fun and might be something I would want to do. Experience-travel is a rather different proposition. It seems much more like a one-time choice: a stark choice of whether to forge ahead for good or ill, or start again completely. If I had regrets about the way I had spent my life then I might be tempted by an offer of a completely different life. But if I am proud of the efforts I have made, and particularly if it was difficult at the time, then I'd be very reluctant to give up my hard-won experience - as indeed I am.
What is the best way to understand time? Is it indeed a solid, tangible fourth Dimension? Is it
"a flowing stream that you can never step into twice"? Or is it external at all, is there such a thing as 'time'? I'd like to argue for a new understanding that embraces all of these, but replaces them with a new metaphor. One which we can recognise subjectively well enough that it makes for a useful contra-posit when we get onto an objective shape for the Universe.
If we look at time as if it were a tree, then the past might be the solid, tangible trunk at the centre of the tree, with the future the infinitesimally-spreading, but bounded canopy of leaves and twigs.
The trunk does not extend upward forever and there is not only one future. We do not believe in a future that is predetermined by the past - it is not pre-destined. Neither does the canopy extend outward infinitely. We do not believe in a future that is entirely divorced from the past.
God does not play dice, and we believe in destiny, whatever name we give it. If my destiny branches in front of me like an Ash tree and your destiny were more like an Oak tree, we would not argue that one was better than the other.
It is a significant discovery that there are parts of the Universe which are further away than they should be according to the age of the Universe. The Universe is 14 billion years old, but 46 billion light-years wide, in every direction. In the tree metaphor I might understand this by understanding that the past is not a single trunk, breaking suddenly into a canopy of leaves, but one that branches first, again and again. Those parts of the Universe that are now so far away were once closer, everyone agrees. They are now not reachable in this Universe even if Page 41
one could travel indefinitely at the fastest possible speed. Time really does have all three elements that we associate with a tree: the trunk, the branches and the leaves.
We presume to think that time started at time 0, but this is just the same as thinking the Universe finishes at the edge. There is no time 0. Time did not start. From inside the Universe, the edge has infinitesimal detail – it can never finish. Although we can conceive of time Zero, for us inside the Universe, time continues back indefinitely getting infinitesimally close to zero, but only reaching it at infinity. To be glib about it, time did not start, as that would require time.
Indeed, this same thinking has led us to make the mistake of thinking that there was a 'Big Bang' - which then ended. This is a bit like looking at a tree and thinking it stops where the earth begins, simply because you cannot see the roots. We cannot see past the Cosmic Microwave Background Radiation, circa 380,000 years away from time Zero/immeasurably small, so that must be the result of the Big Bang’s ending, you could say. (I don’t know if you could; I’m being naughty...).
The Earth hides the roots, but it is not the roots. They are just as significant to the tree as the leaves, without which it cannot survive. We failed to see that the Big Bang never ended - it is still going on. That is *simpler* than the idea that it ended, not more complicated. I’d see that in my visualization as the roots of a tree of time.
Can I relate a tree to Feynman’s experimental observations? Approaching the tree from the other direction, top down, what we see is very different: a sea of branching twigs and stems, seemingly expanding into ever thicker sticks and branches, from the very small to larger and larger. I mentioned his book, QED : The strange theory of light and matter3, where Richard Feynman describes the series of measurements he makes on a subatomic particle. Each measurement gives a two-dimensional measure of movement (the x and y of a hypotenuse) which he then simply adds to give a final position, collapsing the dimensions (in my words).
(See in particular Pages 25-27 of the online PDF).
Imagine you are an ant on a leaf trying to get to another leaf. Now, the random short branching out from the thinnest twigs and stems requires a ‘dance’ for you to navigate from any 3D position to any other 3D position still within the tree; a dance through many smaller Dimensions as I may choose to think of the twigs. If the ant were smaller than an electron, and the twig thinner than it, then the tree would better approximate Feynman’s observations than either a river, or a path; any kind of line. (In fact, the reference to a 'dance' is Feynman 3 A simple Google search should provide a download link
Page 42
himself’s preferred description for what I would describe as a movement through poly-dimensional space.)
It is so difficult to imagine the far future with any degree of credibility that I approached doing so through video rather than with an essay. Although it is a long prospect at over 90 minutes, in fact I am very serious about a way to imagine an indefinite future for Earthly Humanity by straightforward extrapolation. I thought it was worth building my case in full and so I begin by looking backwards 100 years, to then look forward the same period. I follow by doing the same for 1000 years. Of course we don’t yet have a history to look back to for longer times so I am proposing an extrapolation from what we do know again to the same distance forward.
The video essay might live up to the “long” in its title, but it certainly lives up to the name: Billion!
Billion: The Long History of Time4
Let me return to the illustration by Steve Ditko from earlier where we see Dr Strange being attacked by the minions of Dormammu. It is not made clear in the story-telling whether the minions who command magical powers create the portals they step through to reach Strange, or whether the portals are simply an aspect of the domain of Dormammu being multi-dimensional. It doesn't matter to us in the Ditko story and I think it does not matter to us in understanding Feynman's story. We don't need to prove that at some point the three-dimensional cause-and-effect Universe becomes the multi-dimensioned, quantum Universe, since we simply observe that it does. The sub-atomic particle appears to dance because it moves through a series of pathways, each of which is a separate dimension, like the dimensions being created/discovered to reach Strange. And on the smallest scale, time turns out to be one of those dimensions; but on the smallest scale, only.
The great strength of a river or a path may be as a comparison to the flow or travel of time, but this is true of the tree as well. A tree grows outward at the same time as upward. It is, in some ways, born fully-formed, becoming more like itself with each year that passes. We are so used to thinking of time as a mechanism that it is extremely useful to be reminded it could possibly be thought of like an organism. The Universe may well be 14 billion years old, but that doesn’t mean that every year has to be exactly identical with every other year, in human terms. It is, after all, always ‘now’.
4 https://www.youtube.com/watch?v=vyWB377zGTI&t=176s Page 43
The Shape of the Universe
If the trunk of the tree is, in some way, the past, and the future is like the canopy of the tree, then ‘now’ is more than just the intersection between them, it is also the bark that for my purposes covers every part of the tree. As the surface, the bark separates tree from not-tree.
‘Now’ does not just separate the past from the future, it is also of course what gives the meaning to either.
The different types of tree are all derived from fractal mathematics underlying their different shapes.
Points of Similarity of tree with time
1
6
Twigs reflect Feynmans partial
7
1
dimensions
2
Branches make tree wider and taller
3
Trunk corresponds to Past
2
4
Bark corresponds to Now
5
Roots like Big Bang
3
4
Shape of tree both smallest and largest
6
5
scale is fractal
7
Alive, mortal
(You Physicists don’t necessarily need a better visualization of time than Einstein’s and even if you did, a tree might not be it. Einstein’s great achievement was in showing the inverse relation between speed and time. If you are stopped, time travels forward at maximum speed.
As you move, and your velocity approaches the speed of light, external time moves slower and slower, until you reach the limit of light speed, and it stops. But this is not really a fourth dimensional view of space-time as a uni-dimensional view of it – remember that earlier we talked of the current buzz-phrase ‘going forward’ as being the opposite of standing still? It is just a useful way to suggest everybody is moving in the same direction without having to state what direction that is.)
Trees do live a very long time, but they do not live forever. The last reason for we metaphysicists for choosing a tree to represent time is that a tree dies.
Page 44
The oldest individual trees that we have found have lived for thousands of years. One can see that a tree deserves respect for the life it lives out, rather as we honour animal life to a degree. The purpose of time is not time, itself. The tree of time is not immortal because (if you choose to believe in Him) then God is obviously not here yet.
He must be coming. (Spoiler alert: please see “Where is Heaven”, previously referenced.)
~ • ~
Let me pause again here to take stock. At this point readers may not know whether or not what I have written is true, but it is evident I believe it to be so. Let me also pause to ask what difference does it make? There is a big difference between Einstein and me. Einstein's work led indirectly to the Atomic bomb. He was pushing the edges of physics; in fact, some argue, he was extending the 80% of classical physics described by Newton to the 99% of physics resulting in the bomb, and the observations of Feynman.
Even if time finds me accepted, there will be no great prediction, test and verification to come out of my comments as there has been repeatedly for Einstein. There will be no 'warp drive'
or 'wormhole' from my work, in fact if anything, the opposite. This is a simplification, even more than an increase in knowledge, as I am arguing that we are closer to 99.99% in our understanding of physics.
There will not be any travel outside our galaxy by us in the foreseeable future. I do not think there will ever be any travel at or anywhere near the speed of light – yet that is a good thing!
For those who want to go it will take the combined efforts of even the very least of us to succeed. For those who want to go to other Stars it can only ever be a one-way trip.
More on this later. For now, I want to go on to ask what is the physical shape of this Universal Transfinite Set? Can something that is infinite be meaningfully said to have a shape?
Part D: THE POLYDIMENSIONAL SHAPE OF THE UNIVERSE
To paraphrase a quote from Nikola Tesla: “The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite eccentric.”
To quote myself from 2006: “To think deeply is also to think quickly. To think clearly, takes time.” Here is what I also wrote then:
“The word for a shape that is finite but unbounded is 'transfinite'.
Page 45
If you draw a circle, with the area representing finity and the outside representing the infinite you have one representation of the Universe.
Another is a square box, which is the mathematical symbol for the Universal Set.
How else would you draw this, or represent it in any way? Well, however it is done, one way to conceive of such a model (to use the scientist's term) is as an explosion. Since the finity is unbounded, it pushes toward or is otherwise drawn to, the infinite
Now, if this is a correct representation, is it the best representation? I would suggest not. For is it not more profound to consider a finity outside the infinite? Literally, in-finite?
This too can be drawn. Simply draw a circle for a set (as in school) and put a dot at the centre, to represent the infini
3 te
3 s
w in
or g d u s l a
R r e it d y a . c i t .e e . d 'o' with . at the
33 words Redacted
centre... This is the definition.
This is a shape to ponder for a long time. There is a profound difference between the centre and the edge, as well as a profound similarity. They are both infinite, but whereas the edge is unchanging and infinitely uninteresting, the centre is constantly growing ever becoming more than itself but never changing into something else ...
ii) The perimeter of the shape goes on forever, but is not infinite. If you try to examine it outwards, then you find it getting smaller, not bigger - just like Zeno's frog in reverse. What word in English is used to define something that goes on forever, getting smaller and smaller...?
iii) The pleasing and stable configuration is for infinity to be at the centre. If infinity is not at the centre, the balance is eccentric. We see eccentricity in the human mind. Furthermore (as a Church Hymn I know put it), the mind is an avatar of the Universe. The Universe of mind may be considered as three dimensional, as the universe of matter is best considered as three dimensional. The three dimensions of mind (here in the West) are those of Transactional Analysis. Is this also so in the East?
iv) Although numbers, like Pi, arguably go on forever and ever, and people, like Michelangelo, arguably live on indefinitely, in spirit; the greatest of all Page 46
infinities is surely the one, true God. Do we have a decent proof of the existence of God? If the most recent is St Anselm's nearly a thousand years ago, isn't it about time there was another one?”
Although I would not write the same words today, in 2014, my choice eight years later would not be so great an improvement, I think. I was conscious of defining a shape (the ci 8r cl
w e
o rw
d ist h a
dot at
R t
e h
d e
a
c c
t e
e n
d tre) and thus giving a definition of the Universe which anyone could use. At the same time, I was trying to give a fuller explanation so that people who did not care about the definition would also understand it.
One of the interesting things that struck me at the time about the definition above is that it 40 words Redacted
describes a picture fully and completely using only words, that is, words and letters (an ‘o’, with a dot at the centre…). I was in the intriguing position of being able to say that I could define the Universe's shape in 29 words; but that it would take 430 words to explain it.
It would even be possible to encrypt the definition and reveal it at some point in the future, when perhaps, someone else had come up with the same conclusion and reasoning. In this way, it could become an entertainment; a great game. There is one Universe; it has one shape; what is it? Over the course of say, a single year, the prediction of a solution to the puzzle could be made. Clues could even be given. As time passed, interest would build, making the solution more difficult, not easier. Even if I were proven suddenly wrong, or somehow inappropriate, it seemed to me an admirable enterprise: rather more worthy than 'Pop Idol'.
Well, maybe. But meanwhile, I was entertaining myself thoroughly with another new type of creative game and in a way which bears on the subject.
If 'Pop Idol' represents the zenith of mass-market entertainment then 'Tomb Raider' had marked a similar zenith in computer games. I'd played and enjoyed that, and 'Doom' and 'Age of Empires' all of which represented a new experience for the keen games-player. But now I had come across a different product entirely, a free computer program called Bryce.
It is a remarkable thing when someone is able to create a program that generates employment for other people. Microsoft had done it with their Office products, and for many others like me directly with their Visual Basic programming tool. I would realise in coming years that Bryce had done something similar in graphic design as, in the computer press in articles and adverts I would frequently see Bryce images: visually appealing illustrations that could be quickly and easily generated in Bryce – if only someone had the imagination.
Page 47
The Shape of the Universe
Bryce is a ray-tracing program. It creates photo-realistic pictures by calculating the paths that rays of light would take through a virtual 3D world. The user can create objects and apply textures – even create a landscape picture with trees, mountains and buildings. They can then create things that only exist in imagination, like a pink sun, or purple seas. This is where I had gotten started. What does a plant look like inside a glass ball? What if you put the letters of a word into it?
It is one thing to see things that could exist, but don’t. I was engaged by seeing them rendered with photographic realism, but I’d been reading comics all my life, I was used to astonishing images. What was another thing entirely was to see things rendered with photographic realism that could not exist in real life. With Bryce you don’t need any wires so when you put a light inside a glass ball, it needs no power source. How do things reflect inside a perfect tube? In Bryce there is no gravity so I can suspend something in midair and have 360 degree reflection.
Of course I had been tempted by Bryce's ability to create a model of what I conceived the shape of the Universe to be. In two dimensions, you can only draw it as I have described. In four dimensions, it would look like a Klein bottle. What about in Bryce? Well, we can visualise it easily enough. Picture a balloon that i
5 s
3 pe
w r
o f
r e
d c
s tl
Rye s
d p
a h
cteri
d c
al, now push a pin into it, right to
the centre, but imagine it does not burst. Like a 3D Klein bottle, the edge sort of 'wraps round'
to meet the centre. I'd cut this in half in my imagination so as to get a look inside and that was what I was modelling in Bryce.
Until one day, I saw the same shape on the New Scientist website.
The Shape of the Cosmos
Diagrams Redacted
As modeled in the free 3D renderer, Bryce
From New Scientist
Page 48
The Picard topology had been identified as the shape of the Universe by some German
Physicists. Well, not quite the same shape. My pe
rfect bell had become a trumpet horn in the
hands of the Germans, but it was unquestionably
the same overall shape. Was it just that the
Germans didn't fully understand the difference be
tween infinite and infinitesimal?
125 words Redacted
The Picard topology, as described by New Scientist for lay-persons like me, had an infinitely long spike which at the top end flared out into a finite bell-shape. “If you left the Universe by flying out of the bell you'd rejoin it by finding yourself flying up the long spike back toward the bell.” NS described the shape as finite/infinite and I knew that wasn't right.
Let us consider all the possibilites, which seem to boil down to three or four: 1a) The Universe is finite
2b) The Universe is infinitesimal at the edge and infinite at the centre 2c) The Universe is infinitesimal at the centre and infinite at the edge 3d) The Universe is infinitesimal at both the edge and the centre I rule out 1 because although I have no proof, in my whole life it has been accepted wisdom that the Universe is infinite. No-one has ever seriously suggested otherwise.
I would combine c into b as 2. I do not know what difference it would make to anything if 2c were true instead of 2b.
I am left with 2b and 3d. Again I cannot choose between them, but again I do not need to make that choice for others. If God is infinite, then He is in the Universe and can only be at the centre. If God is infinite but outside of the Universe then both edge and centre are transfinite, bounded with an end that is not finite, but infinitesimal. If there is a personal God, then 2b is the Shape of the Universe. If not, then 3d is true.
Incidentally, observe what happens at the botto m of the spike: New Scientist describes the spike as being infinitely long and infinitely thin – but only that. At the bottom, the spike is that but it is more: it is infinitely stretching; infinitely f
alling away.
Picture how a raindrop forms: the perfect sphe re dropping off the spike. Now reverse that picture as if it were the spike falling1 o
4 f
4 f wth
o e
r d p
s eRrefe
d c
a tc t sep
d here. At the end of the spike the
Universe is infinitely long and infinitely thin and infinitely falling away, at an increasing rate.
You can replace the sphere with God, or with nothing, and that leaves the 'falling away' which is just the mechanism I was describing earlier as creating gravity. It is the same visualisation Page 49
as was used to say that: the centre has moved away from the two spheres through a poly-dimensional space.
3 Ways of Viewing the Big
This is the point in the text, I think, where the shape of Bang
the Universe comes fully into view.
As I had to admit earlier, it is not an Einsteinian insight, M1
M6
such as splitting the atom. It is – at the least - a compelling interpretation of the available data, but as the makers of Betamax video learnt, the best idea does
M2
M3
not always win out. Science, and physics more than anything, progresses by matching theoretical prediction
M4
M5
to observed phenomenon. Modern quantum theory did
this when it predicted and then observed the Higgs Boson. For many physicists, that may be just as
Acceleration away from a centre
could create the same gravity
compelling as what I have written.
as ‘Dark Mass’
An idea is, arguably, of its time. We see this when Newton and Liebnitz simultaneously and separately
discover a key building block of modern maths, in M1
M6
calculus. Again arguably, we see its absence when M2
M3
America does not instigate gun control. (With the M4
M5
wisdom of hindsight we might look back to the twenties
and see that the prohibition of alcohol which gave rise
to the mafia could also have been an era where gun control was seriously debated in the US, and decided Acceleration toward a centre
one way or another. By the time we reach the modern
could also make the Universe
era and my lifetime, it is in some ways too late for such expand.
an open debate. Gun control, as addressed by Michael Moore's 'Bowling for Columbine', has become a matter
M1
M6
of faith, not politics.)
M2
M3
Although what I have done is much less than
M4
M5
Einsteinian, it is also quite different. Einstein's information was a new discovery. He had stood on the
shoulders of giants and raised the ceiling, and it would Acceleration without a centre is
less obvious to see, but has
result in splitting the atom and perhaps, eventually, free the same effect.
energy from
Page 50
fusion. Einstein could not have made an entertainment out of Relativity since, as it was said, only twelve people in the world understood it at the time. In the end, I was not courageous enough to create the Internet-based entertainment I had dreamed of. I made the best entertainment I could from taking the time to complete this writing. This shape for the Universe is not a new complication out of the current situation, it is a simplification, I would like to think.
