If this assumption were correct, our world would return more and more to thermal equilibrium; but because the whole universe is so great, it might be probable that at some future time some other world might deviate as far from thermal equilibrium as our world does at present. Then the aforementioned H curve would form a representation of what takes place in the universe. The summits of the curve would represent the worlds where visible motion and life exist.
Boltzmann returned to this theme a year later, this time writing in German. The following is my translation:
One has a choice between two pictures. One can suppose that the complete universe is currently in a most unlikely state. However, one can also suppose that the eons during which improbable states occur are relatively short compared with all time, and the distance to Sirius is small compared with the scale of the universe. Then in the universe, which otherwise is everywhere in thermal equilibrium, i.e. is dead, one can find, here and there, relatively small regions on the scale of our stellar region (let us call them isolated worlds) that during the relatively short eons are far from equilibrium. What is more, there will be as many of these in which the probability of the state is increasing as decreasing. Thus, for the universe the two directions of time are indistinguishable, just as in space there is no up or down. But just as we, at a certain point on the surface of the Earth, regard the direction to the centre of the Earth as down, a living creature that at a certain time is present in one of these isolated worlds will regard the direction of time towards the more improbable state as different from the opposite direction (calling the former the past, or beginning, and the latter the future, or end). Therefore, in these small regions that become isolated from the universe the ‘beginning’ will always be in an improbable state.
Time Without Time (p. 29) In connection with my suggestion that the brain may be deceiving us when we see motion, it is interesting to note that, as Steven Pinker points out in his How the Mind Works, people with specific types of brain damage see no motion when normal people do see motion. In his words, they ‘can see objects change their positions but cannot see them move—a syndrome that a philosopher once tried to convince me was logically impossible! The stream from a teapot does not flow but looks like an icicle; the cup does not gradually fill with tea but is empty and then suddenly full’.
If the mind can do these things, it may be creating the impression of motion in undamaged brains.
CHAPTER 3: A TIMELESS WORLD
First Outline (p. 36) The philosopher best known for questioning the existence of time and its flow was John McTaggart, who is often quoted for his espousal of the ‘unreality’ of time and the denial of transience. The following argument of his is very characteristic of professional philosophers:
Past, present, and future are incompatible determinations. Every event must be one or the other, but no event can be more than one. If I say that any event is past, that implies that it is neither present nor future, and so with the others. And this exclusiveness is essential to change, and therefore to time. For the only change we can get is from future to present, and from present to past.
The characteristics, therefore, are incompatible. But every event has them all. if [an event] is past, it has been present and future. If it is future, it will be present and past. If it is present, it has been future and will be past. Thus all the three characteristics belong to each event. How is this consistent with their being incompatible? (McTaggart 1927, Vol. 2, p. 20)
Some thoughts here certainly match my own thinking, especially that ‘exclusiveness is essential to change’, but McTaggart’s arguments are purely logical and make no appeal to physics. Abner Shimony (1997)—to whom I am indebted for several discussions—compares McTaggart’s position with mine, but I think he has not quite understood my notion of time capsules, so I do not feel that his arguments force me to accept transience.
A typical example of theological thought about time is this extract from Conversations with God—An Uncommon Dialogue by Neale Donald Walsch (kindly sent me by Ann Gill):
Think of [time] as a spindle, representing the Eternal Moment of Now.
Now picture leafs [sic] of paper on the spindle, one atop the other. These are the elements of time. Each element separate and distinct, yet each existing simultaneously with the other. All the paper on the spindle at once! As much as there will ever be—as much as there ever was . . .
There is only One Moment—this moment—the Eternal Moment of Now (p-29).
Again, there is some overlap with my position. Walsch’s ‘leafs’, his elements of time, are my Nows. But the spindle of time, the Eternal Moment, is not at all part of my picture. My Nows are all constructed according to the same rule. There is no Eternal Moment, only the common rule of construction. I think Walsch is trying to grasp eternal substance where there is none, though I think he is right to say that the ‘leafs’ are all there at once and that this is a consoling thought. But we should not ask for more than we can get. Also, the image of time as a spindle is beautiful but misleading. In my view, the ‘leafs’ of time most definitely cannot be arranged along a single line, as the striking spindle image implies.
The Ultimate Arena (1) (p. 39) In this section I say that all structures that represent possible instants of time are three-dimensional. This is because the space we actually observe has three dimensions. However, in some modern theories (super-string theories) it is assumed that space actually has ten or even more dimensions. All but three of the dimensions are ‘rolled up’ so tightly that we cannot see them. In principle, my instants of time could fit into this picture. They would then have ten (or more) dimensions.
(2) This note is for experts. Platonia is a special type of configuration space known as a stratified manifold. The sheets, ribs and singular point that form the frontiers of Triangle Land are called strata. I believe that the stratified structure of Platonia is highly significant. Mathematicians and physicists really interested in this can consult DeWitt (1970) and Fischer (1970). The strata are generally regarded as something of a nuisance, since at them normal well-behaved mathematics breaks down. They are like grit in the works. But in the world’s oyster they may be the grit from which grows ‘a peal richer than all his tribe’: not Desdemona, but time (Chapter 22). (After Othello had strangled Desdemona and then realized his dreadful mistake, he said before stabbing himself that he was ‘one whose hand, Like the base Indian, threw away a pearl richer than all his tribe’.)
CHAPTER 4: ALTERNATIVE FRAMEWORKS
(1) (p. 61) I have written at considerable length about the early history of astronomy and mechanics and the absolute versus relative debate in my Absolute or Relative Motion? This has recently been reprinted as a paperback with the new title The Discovery of Dynamics (OUP, 2001). I still hope to complete a further volume bringing the story up to the present, and much has already been written, but my plans are in flux because of the developments mentioned at the end of the Preface and at various places in these notes. Readers wanting a full academic (and mathematical) treatment of the topics presented in Parts 2 and 3 of this book are asked to consult the above and the papers (Barbour 1994a, 1999, 2000, 2001), which cite earlier papers. For references to recent developments see p. 358 and my website (www.julianbarbour.com).