Diagram 1: Space is bent around a massive object such as a star

The star is shown by the dimple. To an observer from a distance, distances have been shortened, and time is also running a little slower. Light (shown by the A-C line) passing nearby is bent from the straight path indicated by the the A-B line.

We will discuss how Einstein revolutionised our concepts of time and space in the course of this survey. But to anticipate these arguments slightly, let us take a moment to consider what this remarkable concept means. A star, like our sun, bends space and time – something that has been routinely confirmed by observation since 1919.

Light travelling to earth from a star will be bent if it passes close to an intermediate star or galaxy. Space and time are bent by the great mass of this intermediate star or galaxy, and light passing through this bent space and time behaves just as if it was going though a gigantic lens. Today, this is routinely observed and quantified. It can give rise to gravitational lensing, an extremely useful tool in astronomy, in which a galaxy or other object in front of a distant object acts like a giant magnifying glass.

In the same way, the mass of all the stars in the universe collectively, together with other matter, have the effect of bending the space and time of the entire universe – and if there is enough mass, it could be bent right round back on itself in various ways. Current observations, however, suggest that there is not enough mass for this to happen.

We should point out that Woods calls this result of Einstein’s general theory of relativity a “regression to the mediaeval world outlook of a finite universe”, in a short passage particularly densely populated with false ideas. (pp382-3) But we should also point out that earlier in Reason in

Revolt, Woods has already unintentionally endorsed the idea of space-time bending, not once but twice: “This was proved in 1919, when it was shown that light bends under the force of gravity.” (p106) Later, Woods presents both his viewpoints on the same page, first appearing to deny or at least denigrate Einstein’s theory and then going on to say that:

“… [Einstein] predicted that a gravitational field would bend light rays…

In 1919… Einstein’s brilliant theory was demonstrated in practice.”

(p154)

Woods seems to fail to grasp here that the 1919 experiment attempted to show that space and time are distorted by the existence of a massive body and that the effect of gravity is a consequence of this distortion. Arthur Eddington’s famous 1919 observations, taken during an eclipse on the island of Principe off the West African coast, showed that light from a star that passed very close to the sun was indeed bent by the mass of the sun.

Eddington’s grand expedition was the first experimental test of Einstein’s general theory of relativity. His measurements were soon improved upon, and much more accurate measurements have confirmed his result – the confirmation of Einstein’s prediction that space and time is warped. Newton’s theory of gravity can also be used to suggest that light bends by a certain amount. But Einstein’s theory predicts that the gravitational effect on light should cause it to bend by roughly twice as much as predicted by Newtonian science – and light does, indeed, bend by the amount predicted by the general theory of relativity as it follows the curvature of space-time.

When scientists today speculate about other ‘island universes’ they may envisage universes governed by different laws which lie beyond the space-time of our universe and which, therefore, could not be measured in distances and times from our universe. Such universes might not be gravitationally attracted to one another or to the matter in our universe and may have none of the basic ‘constants’ as Rees calls them, of our universe – or even, some suggest, the same space-time dimensions. Science stands on the very first stepping-stone of a path to the possible discovery of other universes, in the same way that Kant anticipated a vast enlargement of our horizons when he speculated about other ‘island universes’.

So the term ‘the universe’ today can either refer specifically to our universe or, more broadly, to our universe and anything that may lie beyond it. But Woods is defending the old Newtonian notion of an essentially unchanging universe comprised of infinite time and space with “galaxies and more galaxies stretching out to infinity”.

What is infinity?

What does Woods mean by infinity? In the section, Does the Infinite Exist? Woods suggests that:

“The idea of the infinite seems difficult to grasp, because, at first sight,

it is beyond all human experience.” (p353)

An infinite universe would indeed be “beyond all human experience”. As the physicist Brian Greene says: “Experimenters never measure an infinite amount of anything. Dials never spin round to infinity. Meters never reach infinity. Calculators never register infinity.” (The Fabric of the Cosmos, p335)

But this raises precisely the question we will address in this survey: how did the universe come to be reckoned to be infinite?

After all, science, which is instinctively materialist, bases itself on human experience (including, of course, through the use of scientific instruments of all kinds), not on what is “beyond all human experience”. This raises a second question: how can Woods’ claim that the universe is infinite be a materialist claim?

We can all envisage an unending series of numbers, a series of numbers that continually grows greater in an infinite repetition of some additional amount. No matter how large the number gets, we can always add one more. A simple repetitive task, we imagine, at least in principle, can always be repeated in an infinite process that need never stop. In this sense, we cannot agree with Woods’ claim that the infinite seems “difficult to grasp”.

But it is important to realise that this infinite process of addition or repetition will never reach actual infinity. The number of repetitions, however large, will be a finite number, and will remain finite.

This infinite process is not the kind of infinity that Woods is talking about. “Infinity, by its very nature cannot be counted or measured.” (p353) “The idea of infinity cannot begin with one, or any other number. Infinity is not a mathematical concept.” (p218)

Potential and actual infinity

So we begin to see that, contrary to Woods’ assumption, there are two contrasting concepts of infinity which may concern us here. (We will glance at George Cantor’s contribution to this subject later.) The first is the familiar one, which can, in fact, begin with one, or any other number, where we can always imagine adding one more in an infinite process.

Woods does not accept this, but this is what Aristotle, the Greek philosopher of the fourth century BCE, termed “potential” infinity. It is a process that never leaves the finite – you never reach infinity – yet, at any particular stage under consideration, it is an infinite process. It is the only type of infinity which science recognises (in the real world, as opposed to mathematical methods such as calculus). The dial never reaches infinity even if the process appears to be infinite.

In this way, as we shall see later, Engels at one point envisaged a universe rolling out indefinitely in time and space, in an infinite process comprised only of finites, and never becoming infinite (Anti-Dühring, Part V, p67). Elsewhere, Engels envisaged the death of the universe, pointing out that at a certain point all the stars must exhaust their fuels.

The second concept of infinity – the only one that Woods recognises – is “beyond all human experience”. Aristotle calls this second type of infinity “actual infinity”. Woods claims that the infinite is quite distinct from the finite. Yet Aristotle and many philosophers and scientists, through the ages to the present day, have explained that the ‘actual infinite’, the infinite that is “beyond all human experience” according to Woods, is an ideal with ‘potential’ but no ‘actual’ reality.

Engels’ views

Before we start our historical survey let us address directly the question: is the universe – or for that matter, the ‘multiverse’ – infinite?

We answer this question in the course of this discussion, but to jump ahead, it may be useful to take a glimpse at Engels’ remarkable insight on this question. We will argue that among Engels’ insights, guided by dialectical considerations, are some that approximate to the position of modern science today.

As we will show, Engels discusses the coming into being of our universe and says that there must have been a cause to this event even if, at present, we have no idea what it is. In today’s terminology, science assumes that there must be a cause to the Big Bang and is searching for it.

But if one was to ask whether there must be an infinity of previous causes to the cause of the Big Bang, at another point Engels replies: infinity is a contradiction, and is full of contradictions (Anti-Dühring, PartV, p66). Engels was well

aware that Aristotle had shown that the actual infinite does not exist. It was common knowledge. It was also common knowledge that Aristotle discovered contradictions in the concept of actual infinity, and others, beginning with Galileo, have discovered many more. One such contradiction is called the infinite replication paradox, and simply follows from the fact that infinity can contain within it an infinite number of infinities.

Friedrich Engels (1820-1895)

Consider an infinity of people. With more than six billion people in the world, there are bound to be people who look very much like you. Famous people sometimes employ look-alikes to pretend to be them. Since antiquity it was understood that if the universe was infinite – a Newtonian universe or a multiverse of modern conception – there must be an infinite number of worlds (or universes) of every possible type, since even the most improbable worlds occur infinitely given an eternity of time and an infinity of space. Among them there will be an infinite number of worlds like ours, and even an infinite number of people like us living on these worlds – in fact, there must be an infinite number of people exactly like us, on these infinite worlds, doing exactly what you and I are doing right now.

As materialists, we must leave the actual infinite for what it is, a contradiction. As scientists emphasise, we have no material evidence for an infinite universe – just a sense that there must always be an endless chain of causes. Let us now place our discussion in its proper historical context.