PRINT May 1991


Three Spaces

WE ARE LIVING TUBES (WORMS). The world flows in through one of our openings (the mouth) to flow out again through the other opening (the anus). This is why we can distinguish between “forward” and “backward.” Most of us are bilaterally symmetrical, and this is why we can distinguish between “right” and “left” (though some of us, like sea urchins, are too many-sided to do so). Originally we all crawled forward and backward, and left and right, on the beach of some Precambrian ocean, and thus there was no need or possibility for us to distinguish between “upward” and “downward.” Somewhat later some of us (the birds and insects) took off from the ground, and some others (the cephalopods and humans) stood upright, though still sticking to the surface. For those who had taken off, a sphere of dimensions like “up to the right” or “down behind” opened up; for those who began to stand upright it was instead a hemisphere that became accessible to locomotion. This may be taken to be a description of vital space, of which all other kinds of space are either derivatives or abstractions.

If you consider the hemisphere of human space you will find that it looks more like a box than a bowl, because it is shallow. We can measure the length and breadth of the space we cross in thousands of miles, but until quite recently the height of our space only measured a few yards and its depth but a few inches. This wide and long but shallow box that is our vital space is better suited for geometry (measurement of the ground) than for topology (science of space), because it consists of two dimensions to which a third has been added. We upright worms think geometrically; equations of the third degree make us nervous, and we had better leave topology to birds, bees, and angels. If we divide our vital space (Lebensraum), we divide it into areas, and we never fight about cubic miles (even if we have an air force). Of course we may extend that flat box of ours indefinitely by drawing a Cartesian cross, and it will then have three dimensions. Still it will not have become “real space,” because it will continue to be a geometrical (not a topological) construct.

This flat box of ours stands still, and things move around within it. You might say that those things move with time, and that time blows through space like the wind through a room with open windows. Philosophers have thought deeply about time, and about how it relates to space, yet nobody will deny that time and space can be easily distinguished. Nobody will mistake a watch for a yardstick, unless he’s crazy. Sometimes we do have a curious feeling about distances: is this place two miles away or two hours? You might also say that the distance between New York and Paris is $1,000. But these are unnecessary, idle reflections. The fact is that we live in a rigid space to be measured in miles, and that we move with a time to be measured in hours. Or at least this has been true so far.

But we humans have the curious ability to put ourselves in the place of somebody else: we are capable of abstraction. We can, for instance, ask ourselves how space looks from the point of view of a galaxy (of which we know, of course, that it cannot look but can only be looked at). And if we ask such a question, we find to our surprise that we cannot answer in words but only in numbers. The reason is that words are used to articulate vital space, while numbers are more abstract. (This is, by the way, a very curious reason.) Now if we articulate how space looks if seen by a galaxy, we will have to formulate equations of the fourth dimension. This is very uncomfortable, because even three dimensions like cubic miles make us nervous. But we now dispose of apparatuses that may help us to perceive such equations. They are called “plotters,” and they can generate synthetic images out of numbers and show them on computer screens: we can see for ourselves what space looks like from a galaxy’s point of view. We call this “outer space” or “cosmic space,” and we even build vehicles to explore those regions closest to where we are.

This is not good enough, however. We may calculate cosmic space, we may imagine those calculations on screens, and we may even send machines and people there, but we cannot really understand it as long as we cannot say what it is in the words of some human language. So we must make an effort to find words to name those equations. This, unfortunately, results in monsters like “curved space-time,” an E.T.-monster (which is more horrible than anything shown in science-fiction movies) that must somehow be incorporated into common speech.

The result looks more or less as follows: space is just as big as it is old, namely about fifteen billion years old and fifteen billion light years in diameter. It expands with time until time is exhausted, and this will happen when everything in space is evenly distributed. Because although space is empty, it is full of possibilities for things to happen accidentally, and for the results to be there for a time and then disappear again. The things that happen there (like the galaxies at which we look, and like ourselves) are curves within the field of the possibilities of space-time. For instance, the planet Earth is a curve within the field of gravitation of the sun, which again is a curve within the field of the gravitation of a galaxy, which again is a curve, and so forth. You can calculate all of this in algorithms, and you can show it on a computer screen, and now that you have uttered it in so many words, you can understand it. But do you?

With this our capacity for abstraction is by no means exhausted. We may also abstract ourselves from our vital space and put ourselves in the place of the particles that compose us. Here the problem is different. In the case of the galaxies we may ask: what would space look like if the galaxies could look at it? But in the case of the particles we must ask: what would space look like if there were any particles we ourselves could look at? Because we may look at galaxies, but if we look for particles like quarks we see only traces. But, we might ask, if we cannot even see these particles, why should we try to put ourselves in their place? The answer is, we must do so, not only because of nuclear power and Chernobyl, but because we are able to calculate it. Now let this be put more carefully: since we cannot say exactly where a particle is, we should better say of that space not what or how it is but what and how it might be. This is why we should call it a“virtual space,” and only then try to understand it.

The equations that describe virtual space are even more exotic than those that calculate cosmic space, because they calculate probabilities, which is to say strictly nothing—at least nothing yet. Probability calculus states what might be, but it says even more than that. It says that reality (that which is) and unreality (that which is not) are the two horizons of probability, and that the space of particles somehow oscillates between the two. This is more or less what that monstrous term “probability wave” means. But if you try to imagine space as that sort of wave, you have not yet understood what virtual space means. You must consider two other things as well: first, anything you say about that space is more or less probable, that is, meaningless nonsense, and second, there is another monstrous term, namely, “quantic jump,” and it says that a particle may jump from one orbit to another without spending time while jumping. In other words, a particle may be simultaneously at two different places within that space. Do not try to imagine such a horror (you will not succeed), but admit instead that what we are talking about is virtual time within virtual space, a not-yet-space with a not-yet-time, which is to say: we are talking about a situation in which words fail.

Consider what has just been said about cosmic space and about virtual space, and then consider how people all around us talk about it. Every teenager talks about cosmic space, and every artist about virtual space, as if they and everybody else knew what those words mean. One thing is certain: they mean something that does not fit into our vital space, that long and broad but flat box wherein we live for the simple reason that we are upright worms. You might say that all those people use those words because they are worms with brains attached to their mouth end. And a brain is a well-known paradox: it contains the cosmic space of which it is a part, because particles jump within the brain over nerve synapses, which means that the brain contains the virtual space that contains the cosmic space that contains the vital space in which the brain lives. But if you said so in order to explain why teenagers and artists speak about the three spaces here discussed, you would have contributed to the confusion instead of simplifying the situation. And a different sort of effort is needed if we are to understand what is happening today.

It is a fact that for more than a century we have been learning how to fly, and that, although we have not yet learned to do it properly, we can already experience space more or less as birds do. Another fact is that for some time now we have had things that begin with the prefix “tele-,” which literally may mean “far” but which really means “to bring nearer.” Thus with the telescope we can bring things like the moon and the planets so near that they no longer look as if they are in cosmic space; thanks to the telephone we can approach people who cannot be heard and seen in vital space; thanks to the telegraph we can correspond with people over long distances as if they were in the same town in which we live; thanks to television we can see events as they happen in a quite different place within vital space; and thanks to telematics we can become neighbors with everyone equipped with the same type of apparatus. Thus that long, wide, and flat box we call our vital space is beginning to burst at its seams, and its lid is coming off to enable us to get up and leave it.

But there is another fact that may be even more decisive: we no longer have a feeling that we can trust our vital space or the time that blows through it. We are now capable of simulating things so perfectly that we can no longer distinguish them well from “true things.” For instance, we can no longer say for sure whether we are watching a real or a staged scene when looking at the TV screen, or whether that voice that speaks to us is human or the voice of an apparatus. On the other hand, the fad that we can be telepresent instantly all over the place makes us doubt whether we are truly present here and now, or whether we are only dreaming. This means that we can no longer distinguish well between fact and fiction, between science and art, between the real and the unreal. Now this is a feeling that accords very well with virtual space, where true and untrue statements have literally no meaning.

If you take those two sets of fads together—on the one hand, vital space is no longer closed but is opening up to cosmic space, and on the other hand, it is becoming as untrustworthy as virtual space—you begin to understand why all those people speak about cosmic and virtual spaces. They no longer feel at home within vital space, so they are beginning to crawl out into those other spaces that can be calculated, and that everybody can contemplate on computer screens, but that nobody can understand in the true sense of that term. The upright worm that we are is beginning to take off, but nobody can say as yet where it is going, or what it is plunging into. We cannot even say whether it is going to continue to be a worm, whether it is going to be crushed, or whether it is changing into a bird or an angel.

Vilém Flusser is a teacher of communications at São Paulo University and at the École Nationale de la Photographic, Arles. He contributes this column regularly to Artforum.