to be, but is not, flat. The appearances can be robust. They can persist, even when the truth about them is known.
The moon illusion and the appearance of a flat Earth can be explained, and in that sense resolved. Other cases are more disquieting. The universe appears to be full of things, including us, that persist, move about, and undergo changes over time. Time passes. We entertain thoughts of the past and future, but we find ourselves always in the present, a present always advancing toward the future and away from the past, a “moving present.”
If we are always in the present, however, what are we experiencing when we experience time’s passing? Some have found it useful to think of time as a river. You are in a boat drifting downstream. The present is wherever the boat happens to be. What is present now – a willow on the river’s bank – will soon be past, replaced by a granite outcropping currently downstream.
Row, row, row your boat gently down the stream, merrily, merrily, merrily, merrily, life is but a dream
A pleasing metaphor, but one that ultimately proves unhelpful. Consider that granite outcropping downstream. It is there, awaiting your approach. Is this how the future is? Is the future “out there” anticipating the arrival of the present? And what of the willow you passed moments ago? Is the past like that? Does the past persist once you have moved on? In that case, then, given that you were there in the past, the past would have to include a past you in a past boat. How would that work?
Even if you have ready answers to these questions, you can see that the river of time metaphor is internally incoherent. Were your experience of the passage of time analogous to your experiencing the scene passing before you as you drift downstream, you would be a spectator, not yourself a part of that scene: you are in the boat, not on the riverbank. You, however, the real you, the you reading these words, are very much a part of the passing scene in which we all find ourselves. That puts you on the riverbank, not in the boat, thereby subtracting the element of passage.
2.1 The A Series and the B Series
The river of time implicitly conflates two ways of representing time and its passage that were made salient a century ago by J. M. E. McTaggart (1866–1925) in the course of a discussion of temporal passage. Something that occurred yesterday is in the past, an occurrence today is in the present, and an occurrence tomorrow lies in the future. Tomorrow will be, before long, today, and then, some hours later, yesterday. Representing time in this way is to represent time’s passing. Yesterday, today, and tomorrow belong to what McTaggart calls the “A series.”
Suppose you are here, and here is San Francisco. St Louis is there, to the east. When you travel to St Louis, St Louis is here; San Francisco is no longer here, but there to the west. This is to represent spatial locations indexically, that is, by reference to here, here being wherever you happen to be.
The A series orders temporal locations indexically by reference to now, to the present. If now is Tuesday, Monday lies back there in the past and Wednesday is ahead in the future. When Wednesday comes, Wednesday is in the present, Wednesday is now, and Tuesday lies in the past. Here and now travel with you as you move through space and time.
The A series affords a now-centered representation of locations in time analogous to here-centered representations of locations in space. Spatial locations can be specified without a here, however. St Louis is 2,816 km (1,750 miles) east of San Francisco. This is so whether you are in San Francisco or in St Louis, or anywhere else for that matter. Might there be an analogous way of ordering occurrences in time?
Imagine that, on Tuesday, May 19, 2020, you had lunch five hours after you had breakfast and six hours before you sat down for dinner. In putting it this way, you would be locating your actions at intervals along a temporal dimension comparable to your locating St Louis 1,750 miles east of San Francisco. This, McTaggart’s “B series,” is fixed and unchanging. The thought that, on Tuesday, you have lunch after breakfast and before dinner is “eternally” or “timelessly” true: it is true on Monday, and remains true on Tuesday and Wednesday.
McTaggart observed that the B series leaves us with a frozen “block” universe. The B series admits of no change. For change to occur, for a tomato to ripen and change from green to red, for instance, you need something that is green today and red tomorrow. In a block universe, however, objects do not move through time and undergo changes. Everything is fixed, once and for all.
The same holds for motion: change in spatial location. For that you need something to be here – that is, wherever it happens to be – at one time, there, and not here, at a later time. Motion through both space and through time, then, appear to require the A series.
McTaggart argued that anything deserving to be called time would have to include temporal passage, and temporal passage involves the A series. Certainly, the A series is what comes to mind when we think of our experience of time and its passage. The A series is internally inconsistent, however. So, McTaggart concluded, time must be unreal. (Metaphysics in action!)
To appreciate McTaggart’s reasoning, focus on the time of a particular occurrence – the moment Neil Armstrong set foot on the moon (July 21, 1969, 2:56 UTC). You, the reader, can say truly that this occurrence is past. For his part, Armstrong, stepping onto the Moon, can say truly of this moment – July 21, 1969, 2:56 UTC – that it is present, and anyone, prior to July 21, 1969, could have said truly that it is in the future. As far as the A series is concerned, it is true of this moment that it is past, present, and future! Were time real, were time “out there,” every moment of time would have to be past, present, and future, and that, McTaggart insisted, makes no sense.
You can see how the argument works by considering a spatial analogue. The A series places you in the boat, a spectator on the passing scene as you float down the river. Upstream, the willow is afore (ahead of you), later it is abeam (directly opposite you), and, still later, abaft (behind you). Its being true of the willow that it is ahead, abeam, and abaft reflects the fact that, in describing the willow as ahead, abeam, or abaft, you are not describing features of the willow. Subtract you from the picture and it would make no sense to say that the willow, or anything else, is ahead, abeam, or abaft.
This leaves us with the B series, which, in effect, places you on the riverbank, adding you to the scene, undermining any sense of temporal passage. The appearance of time’s passing must be in us, a mere appearance with no foundation in reality. So says McTaggart.
2.2 A Fourth Dimension
This talk about the passage of time is all well and good, but if the goal is to understand time, why not ask the experts? Physicists, after all, have had a good deal to say about time. Time, they tell us, is a “spacelike” fourth dimension inextricably bound up with space. The universe is a four-dimensional McTaggartesque block. Its occupants can be at temporal distances from one another analogous to spatial distances. Your passing the willow and subsequently passing a granite outcropping are both there, at a temporal, as well as spatial, distance from one another. You, as you read these words, are really a stage or temporal part of a you extended in both space and time.
This should remind you of McTaggart’s unchanging, B series universe, which lacks the resources to accommodate temporal passage. The passage of time would seem to belong only to the appearances, not to reality.
As McTaggart observed,
