Introduction
Much has been written about the nature of space and time. Unfortunately the esoteric delights of Quantum Theory and Relativity Theory are accessible to only a few, and most of us have neither the time nor the inclination to study the necessary mathematics and physics to understand the equations underlying the various models of space and time, (or of some combination of them). Also, while there may be some excellent non-technical books about these weighty matters, which make it a joy to ponder the indeterminate status of Schrodinger's Cat (poor thing!) as an alternative to counting sheep when insomnia prevails, there is little of practical use for most of us who are simply trying to make some sense of life's existence, and to better understand our place in the cosmos.
Most of us already understand enough about space and time to run our lives, at least at the level of knowing that in order to meet up with someone, it helps if you arrange to meet at the same place at the same time. Any failure to meet is not likely to be due to Quantum effects, or the misapplication of Relativity Theory. We have some idea of how to get around in space, and we understand that we are born, we grow older and we die, sooner or later. We can use calendars, clocks, maps and our memories to simplify dealing with space and time, and to increase precision, but this is a convenience rather than a necessity.
So why bother to look any further? Does it really make any practical difference to our lives whether space on the scale of the universe is flat or curved, whether the universe will expand forever following the Big Bang, whether Time is linear, cyclical, helical, multidimensional or whatever? I am asking here whether it really matters to the ordinary person.
Most people would probably say that, when compared with the importance of our daily activities, our families, friends, relationships and ambitions, these philosophical abstractions about space and time are pretty irrelevant.
With respect to Astrology, which is very involved with space and time, there are really three questions.
(1). Is it worth our expending energy on studying the nature of space and time at all, except out of a legitimate curiosity?
(2). Can Astrology make any useful contributions to our understanding of space and time from within its own discipline?
(3). If the answer to question (2) is affirmative, can these contributions be translated into terms that are easy to understand, and that make sense to the layman.
The answer to the first question must be a personal one in the first instance, but let us see how an understanding of Astrology might lead to some insights about space and time.
Astrology and Astronomy
There is sometimes considerable misunderstanding about the difference between Astronomy and Astrology, and for those who are not clear about the similarities and the differences I include a link in the bibliography.
At first sight, Astrological "space" involves of the surfaces of two spheres, the surface of the earth, (approximately spherical), and the surface of the celestial sphere. However, the two surfaces can be placed into one-to-one correspondence, in the sense that any unique point on the surface of the earth can be paired up with a unique point on the celestial sphere. One way of doing this is to relate each point on the surface of the earth to the equivalent point on the celestial sphere that is directly overhead. We can therefore make do with only one sphere, though in practice Astrologers tend to think in terms of the earth's surface when calculating the Angles and Houses in a chart, while considering projection on to the celestial sphere for the planets. It is worth mentioning here that the Astrologer needs to know the place of birth, (or of an event), in order to calculate the Angles and Houses in a chart, though it is not necessary for calculating the positions of the planets.
It is quite possible to draw up a 3-D horoscope on the surface of the earth, and/or to project this onto the celestial sphere. However this is not often performed, and most horoscopes are 2-D with the planets and house cusps being projected on to a Great Circle. This has the advantage of making a horoscope easier to read for many Astrologers, but it also leads to meaningless arguments as to which projection is the "correct" one!
We can leave aside for the moment the question of whether the surface of a sphere is a 2-D manifold, (where a point can be defined by just two coordinates, such as longitude and latitude), or whether the surface of a sphere is really "embedded" in 3-D space where 3 coordinates define a point, (e.g. along x,y,z axes).
Astrology, (and Astronomy, in so far as it is used in Astrological calculations), as we know them, appear therefore to be closely involved with the surface of a sphere as the relevant "space".
What about time? Well, Astrologers cannot draw up a horoscope at all if they do not know the time, if time is meant in the normal way - year, month, day, hour, minute and seconds. However knowing the time of an event to within a few minutes normally allows an accurate chart, and ideally the time should be known as accurately as possible. Assuming for the moment that time is linear, and that for present purposes we are concerned with horoscopes for events between, say, 5000 B.C. and 25000 A.D., (which ought to satisfy most people), we need only to know, (as accurately as possible), where during that 30000 year period our particular time is situated. Although there are many possible times within this period, they all lie at unique points along this long time line. Astrology therefore uses just one dimension of time, in this sense.
Yet there is a paradox here. In addition to natal Astrology, or the study of the birth chart itself, set up for a given time, astrologers also use charts cast for different times, and use them to forecast trends or events. A common and logical technique is to examine the transits, that is to compare the positions of the planets now with their positions in the natal horoscope, looking for some relationship between the two sets of positions. What is seemingly less logical, at first sight, is the use of primary directions and secondary progressions, and even converse directions and progressions. These methods rely on drawing up charts for times other than the birth time or the present moment. It is not intuitively obvious that a chart drawn up for a time 30 days after birth should bear any relation to the life of a person aged 30, yet the successful use of secondary progressions suggests that there must be a link somewhere.
In one sense only one time dimension is involved, but in another sense it is as though there are several dimensions of time that are independent yet linked in some way. And somehow one can go "backwards", as it were, if converse techniques are valid.
In the case of some techniques, units of time and units of space can almost be interchanged in a sense. A horoscope drawn up for 2 hours after a birth time, (equivalent to age 30 using primary directions), is almost exactly the same as a chart drawn for the original birth time at a place 30 degrees to the west (at the same latitude). the Moon will have moved a degree or so, and some of the planets a few minutes of arc, but that is all. The house cusps will be the same.
Whatever the reality, Astrology certainly appears to treat space and time as though they can be dealt with rather more flexibly than ordinary experience would suggest.
Consciousness, Space and Time
Over the last few hundred years, advances in optics have enabled us to extend our normal visual abilities to study distant objects through telescopes, and small objects through microscopes. In this sense, some of the limits on our ability to explore space have been removed. When it comes to time, technological advances allow us to see models of protracted processes occurring very quickly, or of brief processes being slowed down. We can press the fast forward button, or we can view frame by frame.
While these advances have given us better insights into the evolution of life's processes, and allowed us to examine space and time at different scales, has this progress really increased our understanding at a personal level? Does it increase our understanding of subjective time, of the apparent quickening of the passage of time as we grow older for example? Not in any obvious way, to my mind.
While individuals who are interested in the philosophy of Astrology may indeed ponder space and time, the materials with which they are closely involved, and may form their own models to aid their understanding, they would still probably find it hard to argue with the layman who suggests, (perhaps), that time appears to go twice as fast at age 60 as it does at age 30 because, in percentage terms, two years at age 60 is equivalent to one year at age 30. The layman might be right or wrong, but it would be difficult to use understandings gleaned from Astrology to affirm or to refute his plausible explanation.
No, I think it is better to go about exploring time in an entirely different way. We can come back to Astrology later.
On December 2nd 1875, the Author J. W. Dunne was born, and in 1927 his seminal work "An Experiment with Time" was published. I first came across this book when I was about 18, when browsing in a library. I was foolish enough to lend the copy I bought to someone who had the sense to hang on to it. I currently have the 1964 edition, and have not made the mistake of lending this copy to anybody! "An Experiment with Time" was out of print for many years, but I have discovered that the book is now available again. I would recommend that anyone with an interest in time read "An Experiment with Time".
The book is written in such a way that it is difficult to convey the compelling nature of Dunne's well-argued case, and his work might seem more like detective fiction rather than fact, at first reading. If I were to be asked to select the one book that had had the most influence on the way I live my life, and on my attempts to understand the human condition, I would unhesitatingly choose "An Experiment with Time".
In a nutshell, (and in an informal way), here is the gist of the story. Dunne describes how he appeared to have a disturbing ability to have dreams in which he dreamed about events that occurred while he was awake. Nothing too abnormal about that you might think. Most of us are aware of at least some of our dreams, and can remember some of them upon waking. The vast majority of people must have had the experience of doing something out of the ordinary during the day, and then dreaming about it again during the ensuing night. The problem for Dunne was that he sometimes had this sort of dream the night before the waking event.
Initially he was concerned that he might be going barmy, but fortunately he investigated other individuals and found that some of them apparently also had dreams relating to events that occurred in the future. Somewhat relieved that he was not alone, he asked himself why this sort of phenomenon only occurred in dreams. He then realised that he was begging the question, and he demonstrated that under certain conditions this apparent "seeing into the future" could occur when awake.
Dunne gave detailed instructions in his book, for those who wanted to look into matters for themselves. Basically this involves 4 steps.
(1). Have some dreams.
(2). Record the dreams in writing when you wake up, before you forget them.
(3). Review the record of the dreams a day or two later.
(4). See if an unusual waking event, described in the record, has occurred since the related dream.
This looks simple, but as Dunne points out, the mind plays all sort of tricks on the would be researcher, where dreams are involved. Note that only unusual events count. There would be no prizes for dreaming of driving to work, since such a dream could just as easily relate to a previous commuting trip, as to a future one. Dunne stresses the importance of detail in recording your dreams. Dreaming of seeing a car accident, and then seeing a car accident the following day would not necessarily be convincing. However, dreaming of seeing an upside-down yellow truck, with green mudguards, by the side of the road, with a tall man wearing a striped blue and pink anorak standing beside the front of the truck, would be convincing, (provided that you had recorded this detail in the dream, and noticed it again in the waking experience the following day).
Essentially Dunne found that most of his experimental subjects have some dreams that clearly relate to previous waking events, a similar number of dreams that clearly relate to "future" waking events, and many dreams that don't appear to relate to anything very much at all in waking life.
Armed with these results, Dunne set about developing a theory to explain his findings. Essentially he arrived at a model where there is more than one dimension of time, indeed he found that there is an infinite regress involving an infinite number of dimensions of time. However he argued that the significance of each further dimension decreases, so that for practical purposes three dimensions of time are probably sufficient.
Dunne argued that when we are awake, our consciousness keeps our focus of attention firmly in the here and now, paying attention to what is going on around us. When we are asleep, there is not normally much in the way of stimulation in the here and now, and the focus of attention shifts to "now" in the second dimension of time. As Dunne pointed out, the whole time-length of the first dimension of time is accessible, (rather like a dimension of space), when attention is moving along the "now" of the second time dimension, hence an explanation of his "dream effect".
Dunne goes on to discuss the implications of there being several time dimensions in his model. He argues persuasively that if his model is correct, (or even along the right lines), there is a highly convincing argument in favour of immortality. OK, we may die in the first dimension of time, but we live on in the second and higher dimensions of time. It will be a bit confusing at first, just as dreams are confusing if we expect ordinary rules of behaviour to apply.
Dunne also discusses the false antithesis between Free Will and Determinism. Some of his critics were quick to argue that his model demonstrated that the future was "fixed" or predetermined in all dimensions if his model was accurate. Dunne was well able to argue that this was not the case, and his arguments were certainly no weaker than those put up by other supporters of Free Will.
Those of you lucky enough to have experienced (and recorded) the phenomenon of having a dream, then of "waking up" into what gradually turns out to be another dream, and finally waking up into consciousness have probably experienced awareness in the third dimension of time, a curious world where things might have happened, (but didn't), and might happen in the future, (but probably won't, unless you are a Determinist, in which case they definitely won't!)
If you have a headache by now, this is probably a sign of good mental health! Most of us are thoroughly unaccustomed to thinking along these lines. Things get easier from now on.
Back to Astrology
We looked at the celestial sphere as Astrology's space, and we cheated a bit by leaving Astrology for a detailed look at Dunne's model of time. Dunne's model of time involves many dimensions of time, at right angles to each other in a Euclidean sense. How does this fit in with Astrology, if it fits in at all?
Well, provided we make one small refinement, Dunne's model works very well with Astrology.
If the natal horoscope is the starting point for all work, then transits measured along the time line would correspond to the first dimension of time. Progressions could work along a second dimension of time, directions along a third, and so on, for example.
Unfortunately if the time dimensions are strictly at right angles in a Euclidean sense, this set up will not work. Any movement along one axis will occur entirely independently of movement along any other axis.
You will perhaps remember that earlier in this article I said that "We can leave aside for the moment the question of whether the surface of a sphere is a 2-D manifold, (where a point can be defined by just two coordinates, such as longitude and latitude), or whether the surface of a sphere is really "embedded" in 3-D space where 3 coordinates define a point, (e.g. along x,y,z axes)."
Let us choose another system of coordinates for the spherical surface that represents the earth. We could equally apply the system to surface of the celestial sphere, as the two surfaces can be placed in one-to-one correspondence, but it is possibly easier to visualise using the surface of the earth.
Consider the origin of the x,y,z system of Cartesian coordinates to be at the North Pole, (for the sake of simplicity).
Let the x-y plane be tangent to the earth's surface at the North Pole, with the z axis passing through both poles in a straight line through the centre of the earth, and extending beyond the earth's surface in a straight line in both directions.
Let the x axis lie tangent to the surface of the earth in such a way that when viewed from directly above the North Pole the x axis looks as though it lies along the longitude 0 degrees and longitude 180 degrees circle.
Let the y axis lie tangent to the surface of the earth in such a way that when viewed from directly above the North Pole the y axis looks as though it lies along the longitude 90 degrees east and longitude 90 degrees west circle.
Now let us change the rules a bit and say that although the x, y and z axes are at right angles at the origin, (the North Pole), the x axis and the y axis follow the surface of the earth round the great circles that they project onto. The infinite straight lines in Euclidean space that were the x and y axes, are now great circles in positively curved spherical space. Those who speculate about the structure of space-time commonly produce models involving positive or negative curvature, so I have no problem with accepting this modification. (The z axis might be positively curved as well, but for the moment let us assume that if there is any curvature, the z axis is locally straight in the Euclidean sense, so that it passes through both poles and the earth's centre).
Now let us perform a similar act for the first three dimensions of time. Let us suppose that two of these three time axes follow geodesics on a 2-D (mathematical) spherical surface, again with the origin at the North Pole of this rather ghostly time-sphere surface. (Again for the moment let us assume the third axis is locally straight in the Euclidean sense).
At last we have a rationale for the progressions. Movement along our new x axis, (now a great circle), is no longer independent of movement along the z axis. If we travel theta radians from the North Pole along the 0 longitude line, (the x axis), we shall, by virtue of the properties of any sphere, inescapably move a short distance along the z axis as well. This distance will be numerically equal to 1 - cosine theta, (a fairly small distance for small theta, but a distance nevertheless). Under these circumstances, it might make sense to use a "day for a year" progressions, since the "day" would be measured along a different axis from the "year". the point is that movement in along the two axes would be inextricably connected.
One could speculate that the primary directions involve a third dimension of time. It is interesting that the progressions involve a day for a year (365 to 1 ratio), while the primary directions involve four minutes for a year (360 times 365 to 1 ratio). Those figures of 365 and 360 are not very different.
How about the hastening of the passage of time with age? Well, a model like this gives a rate of change equivalent to sine theta, which for small angles is approximately equal to theta. So the rate at which you age depends on how much you have aged already. Maybe the layman could be right after all!
Conclusion
While I have long been familiar with the concept of many dimensions of time, I have only recently started to look at the implications of one or more of these dimensions having curvature. Further updates to follow as I explore further.
Relevant Links
Amazon for books, including J. W. Dunne's "An Experiment with Time"
Lucidity.Com for much useful info about dreaming, including being consciously aware whilst dreaming
J. W. Dunne - a site that looks at the first chapters of the book
The Science of Time - an excellent site featuring, inter alia, clocks in several dimensions.....
Astronomy and Astrology - a brief article about their similarities and differences
Page created 21st April 2001
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