Future tension

Beginning of sunrise over dark horizonWill the sun rise? Photo taken from the ISS on 1 March 2016. Photo courtesy NASA

Facts about the past and present are either true or false. Can knowledge of the future offer the same degree of certainty?

by Anthony Sudbery is professor emeritus of mathematics at University of York. His research focuses on quantum theory. He lives in York.

Que sera sera
Whatever will be will be
The future’s not ours to see
Que sera sera.

So sang Doris Day in 1956, expressing a near-universal belief of humankind: you can’t know the future. Even if this is not quite a universal belief, then the universal experience of humankind is that we don’t know the future. We don’t know it, that is, in the immediate way that we know parts of the present and the past. We see some things happening in the present, we remember some things in the past, but we don’t see or remember the future. 

But perception can be deceptive, and memory can be unreliable; even this kind of direct knowledge is not certain. And there are kinds of indirect knowledge of the future that can be as certain as anything we know by direct perception or memory. I reckon I know that the sun will rise tomorrow; if I throw a stone hard at my kitchen window, I know that it will break the window. On the other hand, I did not know on Christmas Eve last year that my hometown of York was going to be hit by heavy rain on Christmas Day and nearly isolated by floods on Boxing Day.

In the ancient world and, I think, to our childhood selves, it is events such as the York floods that make us believe that we cannot know the future. I might know some things about the future, but I cannot know everything; I am sure that some things will happen tomorrow that I have no inkling of, and that I could not possibly have known about, today. In the past, such events might have been attributed to the unknowable will of the gods. York was flooded because the rain god was in a bad mood, or felt like playing with us. My insurance policy refers to such catastrophes as ‘acts of God’. When we feel that there is no knowing who will win an election, we say that the result is ‘in the lap of the gods’.

Aristotle formulated the openness of the future in the language of logic. Living in Athens at a time when invasion from the sea was always a possibility, he made his argument using the following sentence: ‘There will be a sea-battle tomorrow.’ One of the classical laws of logic is the ‘law of the excluded middle’ which states that every sentence is either true or false: either the sentence is true or its negation is true. But Aristotle argued that neither ‘There will be a sea-battle tomorrow’ nor ‘There will not be a sea-battle tomorrow’ is definitely true, for both possibilities lead to fatalism; if the first statement is true, for example, there would be nothing anybody could do to avert the sea-battle. Therefore, these statements belong to a third logical category, neither true nor false. In modern times, this conclusion has been realised in the development of many-valued logic.

But some statements in the future tense do seem to be true; I have given the examples ‘The sun will rise tomorrow’ and, after I have thrown the stone, ‘That window is going to break.’ Let’s look at these more closely. In fact, no such future statement is 100 per cent certain. The sun might not rise tomorrow; there might be a galactic star-trawler heading for the solar system, ready to scoop up the sun tonight and make off with it at nearly the speed of light. When I throw the stone at the window, my big brother, who is a responsible member of the family and a superb cricketer, might be coming round the corner of the house; he might see me throw the stone and catch it so as to save the window.

We did not know that the sun would fail to make its scheduled appearance tomorrow morning; I did not know that my naughtiness would be foiled. But this lack of knowledge is not a specific consequence of the fact that we are talking about the future. If the Spaceguard programme had had a wider remit, we might have seen the star-trawler coming, and then we would have known that we had seen our last sunrise; if I had known my brother’s whereabouts, I could have predicted his window-saving catch. In both these scenarios, the lack of knowledge of the future reduces to lack of knowledge about the present.

The success of modern science gave rise to the idea that this is always true: not knowing the future can always be traced back to not knowing something about the present. As more and more phenomena came under the sway of the laws of physics, so that more and more events could be explained as being caused by previous events, so confidence grew that every future event could be predicted with certainty, given enough knowledge of the present. The most famous statement of this confidence was made by the French mathematician Pierre-Simon Laplace in 1814:

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

This idea goes back to Isaac Newton, who in 1687 had a dream:

I wish we could derive the rest of the phenomena of Nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards one another, and cohere in regular figures, or are repelled and recede from one another.

In this view, everything in the world is made up of point particles, and their behaviour is explained by the action of forces that make the particles move according to Newton’s equations of motion. These completely determine the future motion of the particles if their positions and velocities are given at any one instant; the theory is deterministic. So if we fail to know the future, that is purely because we do not know enough about the present…




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