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Tallis in Wonderland

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Draining the River and Quivering the Arrow

Raymond Tallis against the ‘flow’ and ‘direction’ of time.

Readers with long memories may recall previous articles in which I have argued that placing time on a par with the three dimensions of space as the ‘Fourth Dimension’ misrepresents it, howsoever useful this proves for predicting and manipulating the material world. The idea of time as a dimension analogous to space is particularly tenacious because temporal relations are universally represented as lines (in space). For example, time is the x axis on graphs portraying the unfolding of physical processes; and histories are presented as ‘time-lines’.

The dimension metaphor is so powerful that it can live alongside other quasi-spatial images of time, even though these additional images are at odds with time being thought of as a dimension. Time, we are told, flows; or, if it does not actually flow, is unidirectional – pointing one way rather than another. Thus the origin of the ‘rivers’ and ‘arrows’ of time. On the face of things, these ‘dis-analogies’ should bring comfort to those who want to rescue time from the bad company it has fallen into: length, height and breadth don’t flow; nor do they have a direction. While together they enable a movement to have a direction, in themselves they don’t move or point one way rather than another. Insofar as spatial dimensions do have a ‘direction’, it is simply a relative one in which each is at 90º to the other two. But alas, no comfort is forthcoming from the ‘flow and direction’ dis-analogies, because these distinctively unspatial properties ascribed to the Fourth Dimension are illusory. I want to here consider why.

Against The Flow

We often speak poetically of the ‘flow’ of ‘the river of time’. This is clearly wrong, because rivers, unlike the water in them, do not flow – otherwise maps would be continually out of date, with all rivers disappearing into the ocean. But couldn’t time move like the water in the river? Let’s leave aside the question – not as daft as may seem – of whether ‘water’ here means all the water in the river or the water at a specific place, and focus on the more obvious problems. If time flows, what does it flow in? Stuff such as water flows in space, relative to other stuff in space (such as banks) that flow not at all, or more slowly. This is clearly not something that time could manage: time could not flow in or relative to time in the way that spatially-extended, located matter such as water flows between other bits of spatially-extended matter. Besides, how quickly would it flow? The obvious answer, one second per second, demonstrates the vacuity of the very notion of ‘time on the move’. Velocity or rate cannot have the same dimension on both the numerator and the denominator.

Nevertheless, the idea of temporal flow is irresistible. It gets a bit of a boost from the way the calendar makes us think of time in lumps. On Friday at noon, my doctor’s appointment next Wednesday noon is five days away. On Saturday at noon, Wednesday noon will be four only days away. Wednesday, it seems, is coming nearer, bearing the dreaded appointment in its belly.

Doesn’t this show time on the move? No. In order for Wednesday to come a day nearer to now, now has to move by a day towards Wednesday. Friday and Wednesday remain separated by an unchanging amount. So there is no genuine, or net, movement of time – unless we allow the peculiar and self-contradictory notion of time moving towards itself in two opposite directions.

There are other ways of retaining the notion of time as dynamic without resorting to an idea as evidently vulnerable as that of flow. For some, what is on the move is not time itself, but ‘now’, which picks out successive moments. With characteristic floweriness, George Santayana speaks of “the essence of ‘nowness’” that “runs like fire along the fuse of time.” (Realms of Being, 1942.) This only multiplies the problems of the dynamic idea of time. It separates now from time, in order that time-in-waiting can be picked out by now skipping along it. The notion of the present as a ‘moving spotlight’, giving successive instants their instant in the sun, is even more problematic. It requires time to move in a dimension which is both distinct from itself and inseparable from it.

There have been many attempts to construct objection-proof dynamic ideas of time. Some writers have replaced ‘flowing’ with ‘growing’: time is like a tree which gets bigger but overall stays in the same place, and the present is the ‘growing tip’ of time. This raises the question of what it is growing into. It can hardly be growing into the future, which doesn’t exist until it has been grown into. Others think of time as a ‘growing block’, reflecting the apparent observation that as time ‘passes’ there is more of it, preserved in an increasing accumulation of events. Every year that passes adds another year’s worth of The Past. This, of course, confuses time itself with events that have happened in time, or rather, the record of them. The diary of my life will get fatter as I get older because more pages will be filled, and these pages can co-exist. The days in which the events happened do not, however, co-exist, any more than the events themselves do. So time does not increase like a growing heap of days and their contents.

Missing The Point

There is a last ditch position for those who can’t entirely shake off the notion of the ‘passage’ of time; namely, that although time doesn’t actually move, it at least has a direction – that (unlike, say, a simple line) it is asymmetrical. Even when it is not moving, an arrow is differentiated into the head pointing where it might be going to, and the tail marking where it has come from. This has prompted a search for a so-called ‘arrow of time’ to explain why there is a irreversible passage from something that was once future to something that will be past.

The basis of such arrows has been sought in overall trends in the physical world. The thermodynamic arrow reflects the fact that overwhelmingly we see a move from lower to higher states of entropy or disorder. The radiative arrow (probably another manifestation of thermodynamic asymmetry) is constructed upon the observation that outgoing waves from a source – such as a pebble dropped on a still pond – are coherent, whereas we do not see coherent incoming waves converging on a source. Alternatively, the supposed observation that an unknown, indeterminate future becomes a known, determinate past, is the basis for the arrow of information, expressed in the one-way accumulation of facts. The causal arrow draws on the fact that earlier causes bring about later effects, but not vice versa.

All of these attempts to derive a time-asymmetric world from the time-symmetric physical laws that govern it fail to deliver, as Huw Price demonstrates in his indispensable Time’s Arrow and Archimedes’ Point (1996). This is a topic for a future article, but it is sufficient for the present to note Price’s rigorously argued conclusion that there is nothing objective about temporal orientation. If you take a genuinely atemporal viewpoint, time would not be asymmetric. To put this another way, finding directionality in time requires us to establish in advance that states of the universe are ‘earlier’ or ‘later’ before we could notice that, say, the universe has a temporal trend towards increasing untidiness as we move from one state to the next. We cannot ground time’s arrow in anything other than time.

‘Time Permits The Universe To Be Restless’

It is not difficult, therefore, to demolish ideas of time that see it as dynamic or unidirectional. And given also that ‘flow’ and ‘direction’ are actually at odds with the idea of time as a quasi-spatial dimension, it may seem surprising that these ideas stick to our minds like burrs on Velcro. Perhaps it is because they express something absolutely central to experience; what Richard Gale in The Philosophy of Time (1968) has described as our being “immediately and poignantly involved in the whoosh of process” which we then translate into “the felt movement of one moment into the next.” Time is as it were the felt whoosh inside the whoosh of process and event. We project into time the dynamism of our restless universe, in particular the most fundamental and ubiquitous mode of that dynamism – motion.

This is not entirely irrational. Time can be seen as that which permits the universe to be restless, allowing change by heading off the logical impossibility of parts of it having incompatible properties. An object cannot be both in Position 1 and Position 2 (let’s leave quantum mechanics out of it for today) unless it is at Position 1 at time t1 and Position 2 at another time t2. So perhaps it is because time is the very condition of the possibility of change that we are inclined to ascribe to it the dynamism of change itself. This ascription is, however, self-contradictory for many reasons. The most obvious is that if time were not only the possibility of change but were in itself a change, or in some sense changing (flowing or whatever), then time would be required to make time possible.

Even so, the idea of the flow of time is difficult to shake off. And once we divide time up into parts – whether extended parts like days, or unextended parts like ‘nows’ – we are even more inclined to ascribe the properties of the changing universe to it. Successive days, or successive nows, or successive moments such as t1 and t2, borrow the character of events. The arrival of Wednesday noon and the arrival of my doctor’s appointment seem like two comparable, even analogous, happenings. Don’t we say, “And then The Great Day/The Appointed Time arrived”? And we reinforce the misunderstandings implicit in this idea of times as happenings with the calendrical view which makes days into event-containers moving towards ‘today’ like cable cars towards the stop.

It is also difficult to shake off ideas of flow and passage and arrows of time because we have no alternatives with which to replace them, and our minds abhor a vacuum. But the fact that time is not dynamic does not mean that it is static: that, for example, the universe is really frozen, and change is an illusion. Of course, there are many entities that are neither moving nor still; for example, prime numbers. (By the way, as J.J.C. Smart pointed out, the seeming stillness of the Block Universe of the Einsteinian four-dimensional manifold is only a reflection of the fact that it is an imagined sum-total of all events over all time. Nothing – no additional event – can be added to a total, by definition.)

If I seem to have taken what are only metaphors too literally, or too seriously, this is because we take them more literally and more seriously than we would like to admit. To break their spell, we need, as Wittgenstein put it in Philosophical Investigations (1953), to teach ourselves “to pass from a piece of disguised nonsense to something that is patent nonsense.”

Nonsense they may be; but the dynamic metaphors are not entirely empty. The idea of the ‘passage of time’ captures our sense of the loss of the past and of the implacability of change that propels us from birth to death, in respect of which we seem like logs on a river surging towards a cataract. Ridding ourselves of spatialised time, and quasi-spatial notions, therefore, requires constant vigilance against long-established habits. Did I not, after all, begin this article by referring to readers with long memories?

© Prof. Raymond Tallis 2013

Raymond Tallis’s article collection In Defence of Wonder [reviewed this issue] is out now from Acumen, and his Reflections of a Metaphysical Flaneur will be out soon, also from Acumen.


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