Today (14th March 2018), Stephen Hawking, possibly the most famous scientist of modern times, passed away. Hawking was a celebrity physicist, known for his books such as A Brief History of Time, which popularised the science of cosmology – the study of the universe.
To mark Hawking’s death, we republish here an extract from Alan Woods’ Reason in Revolt. In this passage, Alan, discusses Stephen Hawking’s ideas from the perspective of Marxist philosophy, putting forward a dialectical materialist analysis of the cosmos and the concept of black holes.
In 1970, Stephen Hawking put forward the idea that the energy content of a black hole might occasionally produce a pair of subatomic particles, one of which might escape. This implies that a black hole can evaporate, although this would take an unimaginably long period of time. In the end, according to this view, it would explode, producing a large amount of gamma rays.
Hawking’s theories have attracted a lot of attention. His well-written best seller A Brief History of Time, From the Big Bang to Black Holes, was perhaps the book that more than any other drew the attention of the new theories of cosmology to the public’s attention. The author’s lucid style made complicated ideas seem both simple and attractive. It makes for good reading, but so do many works of science fiction.
Regrettably, it appears to have become fashionable for the authors of popular works about cosmology to sound as mystical as possible, and to put forward the most outlandish theories, based on the maximum amount of speculation and the minimum amount of facts. Mathematical models have displaced observation almost entirely. The central philosophy of this school of thought is summed up in Stephen Hawking’s aphorism “one cannot really argue with a mathematical theorem.”
Hawking claims that he and Roger Penrose proved (mathematically) that the general theory of relativity “implied that the universe must have a beginning and, possibly, an end.” The basis of all this is that the general theory of relativity is taken as absolutely true. Yet, paradoxically, at the point of the big bang general relativity suddenly becomes irrelevant. It ceases to apply, just as all the laws of physics cease to apply, so that nothing whatsoever can be said about it. Nothing, that is, except metaphysical speculation of the worst sort. But we will return to this later.
According to this theory, time and space did not exist before the big bang, when all the matter in the universe was alleged to have been concentrated at a single infinitesimally small point, known to mathematicians as a singularity. Hawking himself points out the dimensions involved in this remarkable cosmological transaction:
“We now know that our galaxy is only one of some hundred thousand million that can be seen using modern telescopes, each galaxy itself containing some hundred thousand million stars…We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating; the stars in its spiral arms orbit around its centre about once every several hundred million years. Our sun is just an ordinary, average-sized, yellow star, near the inner edge of one of the spiral arms. We have certainly come a long way since Aristotle and Ptolemy, when we thought that the earth was the centre of the universe!” 1
In point of fact, the very large quantities of matter mentioned here give no real idea of the amount of matter in the universe. New galaxies and super-clusters are being discovered all the time, and there is no end to this process. We may have come a long way since Aristotle in some respects. But in others, it seems that we are far, far behind him. Aristotle would never have made the mistake of talking about a time before time existed, or claiming that the entire universe was, in effect, created from nothing. In order to find ideas like these one would have to go back several thousand years to the world of the Judaic-Babylonian creation myth.
Whenever someone attempts to protest against these proceedings, he is instantly ushered into the presence of the great Albert Einstein, as a naughty schoolboy is dragged to the headmaster’s study, and given a stern lecture on the need to show greater respect to general relativity, informed that one cannot argue with mathematical theorems, and sent home duly chastened.
The main difference is that most headmasters are alive, and Einstein is dead, and therefore unable to comment on this particular interpretation of his theories. In fact, one would look in vain in all the writings of Einstein for any reference to the big bang, black holes and the like.
Einstein himself, although he initially tended towards philosophical idealism, was implacably opposed to mysticism in science. He spent the last decades of his life fighting against the subjective idealist views of Heisenberg and Bohr, and, in fact, moved close to a materialist position. He would certainly have been horrified that mystical conclusions should be drawn from his theories. The following is a good example:
“All of the Friedmann solutions have the feature that at some time in the past (between ten and twenty thousand million years ago) the distance between neighbouring galaxies must have been zero. At that time, which we call the big bang, the density of the universe and the curvature of space-time would have been infinite. Because mathematics cannot really handle infinite numbers, this means that the general theory of relativity (on which Friedmann’s solutions are based) predicts that there is a point in the universe where the theory itself breaks down. Such a point is an example of what mathematicians call a singularity. In fact, all our theories of science are formulated on the assumption that space-time is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of space-time is infinite. This means that even if there were events before the big bang, one could not use them to determine what would happen afterward, because predictability would break down at the big bang. Correspondingly, if, as is the case, we know only what has happened since the big bang, we could not determine what happened beforehand. As far as we are concerned, events before the big bang can have no consequences, so they should therefore cut them out of the model and say that time had a beginning at the big bang.”
Passages such as this forcefully remind one of the intellectual gymnastics of the Medieval Schoolmen, arguing about the number of angels who could dance on the end of a pin. This is not meant as an insult. If the validity of an argument is determined by its internal consistency, then the arguments of the Schoolmen were as valid as this. They were not fools, but highly skilled logicians and mathematicians, who erected theoretical constructs as elaborate and perfect in their way as medieval cathedrals. All that was necessary was to accept their premises, and everything fell into place. The problem is whether the original premise is valid or not. This is a general problem with all mathematics, and its central weakness. And this entire theory leans very heavily on mathematics.
“At the time which we call the big bang…” But if there was no time, how can we refer to it as “a time” at all? Time is said to have begun at that point. So what was there before time? A time when there was no time! The self-contradictory nature of this idea is glaringly obvious. Time and space are the mode of existence of matter. If there was neither time, nor space, nor matter, what was there? Energy? But energy, as Einstein explains, is just another manifestation of matter. A force field? But a force field is also energy, so the difficulty remains. The only way that time can be got rid of is if before the big bang there was— nothing.
The problem is: how is it possible to get from nothing to something? If one is religiously minded, there is no problem; God created the universe from nothing. This is the doctrine of the Catholic Church, of Creation ex nihilo. Hawking is uncomfortably aware of this fact, as he says in the very next line:
“Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention. (The Catholic Church, on the other hand, seized on the big bang model and in 1951 officially pronounced it to be in accordance with the Bible.)”
Hawking himself does not want to accept this conclusion. But it is unavoidable. The whole mess arises out of a philosophically incorrect concept of time. Einstein was partly responsible for this, since he appeared to introduce a subjective element by confusing the measurement of time with time itself. Here again the reaction against the old mechanical physics of Newton has been carried to an extreme. The question is not whether time is “relative” or “absolute”. The central issue to be addressed is whether time is objective or subjective; whether time is the mode of existence of matter or an entirely subjective concept existing in the mind and determined by the observer. Hawking clearly adopts a subjective view of time, when he writes:
“Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the other stays at sea level. The first twin would age faster than the second. Thus, if they met again, one would be older than the other. In this case, the difference in ages would be very small, but it would be much larger if one of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned he would be much younger than the one who stayed on Earth. This is known as the twins paradox, but it is a paradox only if one has the idea of absolute time at the back of one’s mind. In the theory of relativity there is no unique absolute measure of time that depends on where he is and how he is moving.” 2
That there is a subjective element in the measurement of time is not in dispute. We measure time according to a definite frame of reference, which can, and does, vary from one place to another. The time in London is different from the time in Sydney or New York. But this does not mean that time is purely subjective. The objective processes in the universe take place whether we are able to measure them or not. Time, space, and motion are objective to matter, and have no beginning and no end.
Here it is interesting to note what Engels had to say on the subject:
“Let us continue. So time had a beginning. What was there before this beginning? The universe, which was then in a self-identical, unchanging state. And as no changes succeed one another in this state, the more specialised idea of time transforms itself into the more general idea of being. In the first place, we are not in the least concerned here with what concepts change in Herr Dühring’s head. The subject at issue is not the concept of time, but real time, which Herr Dühring will by no means rid himself of so cheaply. In the second place, however much the concept of time may be converted into the more general idea of being, this takes us not one step further. For the basic forms of all being are space and time, and being out of time is just as gross an absurdity as being out of space.
“The Hegelian ‘timelessly past being’ and the neo-Schellingian ‘unpreconceivable being’ are rational ideas compared with this being out of time. For this reason Herr Dühring sets to work very cautiously; actually it is of course time, but of such a kind as cannot really be called time; time does not in itself consist of real parts, and is only divided up arbitrarily by our understanding—only an actual filling of time with differentiable facts is susceptible of being counted—what the accumulation of empty duration means is quite unimaginable. What this accumulation is supposed to mean is immaterial here; the question is whether the world, in the state assumed here, has duration, passes through a duration in time. We have long known that we can get nothing by measuring such a duration without content, just as we can get nothing by measuring without aim or purpose in empty space; and Hegel calls this infinity bad precisely because of the tedium of this procedure.” 3
Do singularities exist?
A black hole and a singularity are not the same thing. There is nothing in principle that excludes the possible existence of stellar black holes, in the sense of a massive collapsed star where the force of gravity is so immense that not even light can escape from its surface.
Even the idea is not new. It was predicted in the 18th century by John Mitchell who pointed out that a sufficiently massive star would trap light. He came to this conclusion on the basis of Newton’s classical theory of gravitation. General relativity did not enter into it.
However, the theory advanced by Hawking and Penrose goes far beyond the observed facts, and, as we have seen, draws conclusions that lend themselves to all kinds of mysticism, even if this was not their intention.
Eric Lerner considers the case for supermassive black holes at the centre of galaxies to be weak. Together with Anthony Peratt, he has shown how all the features associated with these supermassive black holes, quasars, etc., can be better explained by electromagnetic phenomena. However, he believes the evidence is considerably stronger for the existence of stellar sized black holes since this rests on detecting very intense X-ray sources which are too big to be neutron stars. But even here the observations are far from proving the case.
The abstractions of mathematics are useful tools for understanding the universe, on one condition: that we do not lose sight of the fact that even the best mathematical model is only a rough approximation of reality. The problems start when people begin confusing the model with the thing itself. Hawking himself unwittingly reveals the weakness of this method in the passage already quoted. He assumes that the density of the universe at the point of the big bang was infinite, without giving any reasons for this, and then adds, in a most peculiar line of argument, that “because mathematics cannot really handle infinite numbers” the theory of relativity breaks down at this point.
To this, it is necessary to add, “and all the known laws of physics”, since it is not only general relativity which breaks down with the big bang, but all of science. It is not just that we do not know what occurred before this. It is that we cannot know.
This is a return to Kant’s theory of the unknowable Thing-in-Itself. In the past, it was the role of religion and certain idealist philosophers, like Hume and Kant, to place a limit upon human understanding. Science was permitted to go so far, and no further. At the point where human intelligence was not allowed to proceed, mysticism, religion and irrationality commenced. Yet the whole history of science is the story of how one barrier after another was removed. What was supposed to be unknowable for one generation became an open book for the next. The whole of science is based on the notion that the universe can be known. Now, for the first time, scientists are placing limits on knowledge, an extraordinary state of affairs and a sad comment on the present situation in theoretical physics and cosmology.
Consider the implications of the above passage: a) since the laws of science, including general relativity (which is supposed to provide the basis for the whole theory) break down at the big bang, it is impossible to know what, if anything, occurred before it, b) even if there were events before the big bang, they have no relevance to what happened afterwards, c) we cannot know anything about it, and so, d) we should simply “cut it out of the model and say that time began at the big bang.”
The self-assurance with which these assertions are put forward is truly breathtaking. We are asked to accept an absolute limit on our ability to understand the most fundamental problems in cosmology, in effect, to ask no questions (because all questions about the time before there was time are meaningless) and that we should just accept without more ado that time began with the big bang. In this way, Stephen Hawking simply assumes what has to be proved. In the same way, the theologians assert that God created the universe, and when asked who created God, merely answer that such questions are beyond the minds of mortals. On one thing we can agree, however; the whole thing does indeed “smack of divine intervention”. More than that, it necessarily implies it.
In his polemic against Dühring, Engels points out that it is impossible that motion should arise out of immobility, that something should arise out of nothing: “Without an act of Creation we can never get from nothing to something, even if the something were as small as a mathematical differential.”4
Hawking’s principal defence seems to be that the alternative theory to the big bang, put forward by Fred Hoyle, Thomas Gold and Hermann Bondi—the so-called Steady State theory—was shown to be false. From the standpoint of dialectical materialism, there was never anything to choose between these two theories. One was as bad as the other. Indeed the Steady State theory, which suggested that matter was being continuously created in space out of nothing, was, if possible, even more mystical than its rival. The very fact that such an idea could be taken seriously by scientists is itself a damning comment on the philosophical confusion that has bedevilled science for so long.
The ancients already understood that “out of nothing comes nothing”. This fact is expressed in one of the most fundamental laws of physics, the law of the conservation of energy. Hoyle’s claim that only a very small amount was involved makes no difference. It is a bit like the naïve young lady who, in order to placate her irate father who found out she was going to have a baby, assured him that it was “only a little one”. Not even the tiniest particle of matter (or energy, which is the same) can ever be created or destroyed, and therefore the Steady State theory was doomed from the outset.
Penrose’s theory of a “singularity” was originally nothing to do with the origin of the universe. It merely predicted that a star collapsing under its own gravity would be trapped in a region whose surface eventually shrinks to zero size. In 1970, however, he and Hawking produced a joint paper in which they claimed to prove that the big bang itself was such a “singularity”, provided only that “general relativity is correct and the universe contains as much matter as we observe.”
“There was a lot of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity.”
General relativity has proved a very powerful tool, but every theory has its limits, and one has the impression that it is being pushed to the limit here. How long it will be before it is replaced by a broader and more comprehensive set of ideas it is impossible to say, but it is clear that this particular application of it has led to a blind alley. As far as the amount of matter in the universe is concerned, the total amount will never be known, because it has no limit. Typically, they are so wrapped up in mathematical equations, that they forget reality. In practice, the equations have replaced reality.
Having succeeded in convincing a lot of people, on the basis that “one cannot really argue with a mathematical theorem,” Hawking then proceeded to have second thoughts: “It is perhaps ironic,” he says, “that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe—as we shall see later, it can disappear once quantum effects are taken into account.” The arbitrary nature of the whole method is shown in Hawking’s extraordinary change of mind. He now says there is no singularity in the big bang. Why? What has changed? There is no more actual evidence than before. These twists and turns all take place in the world of mathematical abstractions.
Hawking’s theory of black holes represents an extension of the idea of singularity to particular parts of the universe. It is full of the most contradictory and mystical elements. Take the following passage, which describes the extraordinary scenario of an astronaut falling into a black hole:
“The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must be a singularity of infinite density and space-time curvature within a black hole. This is rather like the big bang at the beginning of time, only it would be an end of time for the collapsing body and the astronaut. At this singularity the laws of science and our ability to predict the future would break down. However, any observer who remained outside the black hole would not be affected by this failure of predictability, because neither light nor any other signal could reach him from the singularity. This remarkable fact led Roger Penrose to propose the cosmic censorship hypothesis, which might be paraphrased as ‘God abhors a naked singularity’. In other words, the singularities produced by gravitational collapse occur only in places, like black holes, where they are decently hidden from outside view by an event horizon. Strictly, this is what is known as the weak cosmic censorship hypothesis: it protects observers who remain outside the black hole from the consequences of the breakdown of predictability that occurs at the singularity, but it does nothing at all for the poor unfortunate astronaut who falls into the hole.” 5
What sense can one make of this? Not content with the beginning (and end) of time for the universe as a whole, Penrose and Hawking now discover numerous parts of the universe where time has already ended! It has now been demonstrated that black holes exist (probably the remnants of massive collapsed stars), and contain tremendous concentrations of matter and gravity. But it seems extremely doubtful that this gravitational collapse could ever reach the point of a singularity, much less remain in this state forever. Long before this point was reached, such a tremendous concentration of matter and energy would result in a massive explosion.
The entire universe is proof that the process of change is never-ending, at all levels. Vast tracts of the universe may be expanding, while others are contracting. Long periods of apparent equilibrium are disrupted by violent explosions, like supernovas, which in turn provide the raw material for the formation of new galaxies, which goes on all the time. There is no disappearance or creation of matter, but only its continuous, restless change from one state to another. There can therefore be no question of the “end of time” inside a black hole, or anywhere else.
An empty abstraction
The whole mystical notion derives from the subjectivist interpretation of time, which makes it dependent on (“relative to”) an observer. But time is an objective phenomenon, which is independent of any observer. The need to introduce the unfortunate astronaut into the picture does not arise from any scientific necessity, but is the product of a definite philosophical point of view, smuggled in under the banner of “relativity theory”.
You see, for time to be “real”, it needs an observer, who can then interpret it from his or her point of view. Presumably, if there is no observer, there is no time! In a most peculiar piece of reasoning, this observer is protected against the malign influence of the black hole, by an arbitrary hypothesis, a “weak cosmic censorship”, whatever that might mean. Inside the hole, however, there is no time at all. So outside, time exists, but a little distance away, time does not exit. At the boundary between the two states, we have the mysterious event horizon, the nature of which is shrouded in obscurity.
At least, it would appear that we must abandon all hope of ever understanding what goes on beyond the event horizon, since, to quote Hawking, it is “decently hidden from outside view.” Here we have the 20th century equivalent of the Kantian Thing-in-Itself. And, like the Thing-in-Itself, it turns out to be not so difficult to understand after all. What we have here is a mystical idealist view of time and space, fed into a mathematical model, and mistaken for something real.
Time and space are the most fundamental properties of matter. More correctly, they are the mode of existence of matter. Kant already pointed out that, if we leave aside all the physical properties of matter, we are left with time and space. But this is, in fact, an empty abstraction. Time and space can no more exist separately from the physical properties of matter than one can consume “fruit” in general, as opposed to apples and oranges, or make love to Womankind.
The accusation has been levelled against Marx without the slightest justification that he conceived of History as taking place without the conscious participation of men and women, as a result of Economic Forces, or some nonsense of the sort. In fact, Marx states quite clearly that History can do nothing, and that men and women make their own history, although they do not do so entirely according to their own “free will”.
Hawking, Penrose and many others are guilty precisely of the mistake that was falsely attributed to Marx. Instead of the empty abstraction History, which is, in effect, personified, and endowed with a life and a will of its own, we have the equally empty abstraction Time, envisaged as an independent entity which is born and dies, and generally gets up to all kinds of tricks, along with its friend, Space, which arises and collapses and bends, a bit like a cosmic drunkard, and ends up swallowing hapless astronauts in black holes.
Now this kind of thing is fine in science fiction, but is not very useful as a means of understanding the universe. Clearly, there are immense practical difficulties in obtaining precise information about, say, neutron stars. In a sense, in relation to the universe, we find ourselves in a position roughly analogous to early humans in relation to natural phenomena.
Lacking adequate information, we seek a rational explanation of difficult and obscure things. We are thrown back on our own resources—the mind and the imagination. Things seem mysterious when they are not understood. In order to understand, it is necessary to make hypotheses. Some of these will be found to be wrong. That in itself presents no problem. The whole history of science is full of examples where the pursuit of an incorrect hypothesis led to important discoveries.
However, we have a duty to attempt to ensure that hypotheses have a reasonably rational character. Here the study of philosophy becomes indispensable. Do we really have to go back to primitive myths and religion in order to make sense of the universe? Do we need to revive the discredited notions of idealism, which, in fact, are closely related to the former? Is it really necessary to re-invent the wheel? “One cannot argue with a mathematical theorem.” Maybe not. But it is certainly possible to argue with false philosophical premises, and an idealist interpretation of time, which leads Hawking to conclusions like the following:
“There are some solutions of the equations of general relativity in which it is possible for our astronaut to see a naked singularity: he may be able to avoid hitting the singularity and instead fall through a ‘wormhole’ and come out in another region of the universe. This would offer great possibilities for travel in space and time, but unfortunately it seems that these solutions may all be highly unstable; the least disturbance, such as the presence of an astronaut, may change them so that the astronaut could not see the singularity until he hit it and his time came to an end. In other words, the singularity would always lie in his future and never in his past. The strong version of the cosmic censorship hypothesis states that in a realistic solution, the singularities would always lie either entirely in the future (like the singularities of gravitational collapse) or entirely in the past (like the big bang). It is greatly to be hoped that some version of the censorship hypothesis holds because close to naked singularities it may be possible to travel into the past. While this would be fine for writers of science fiction, it would mean that no one’s life would ever be safe: someone might go into the past and kill your father or mother before you were conceived!” 6
“Time-travel” belongs to the pages of science fiction, where it can be a source of harmless amusement. But we are convinced that nobody ought to be afraid that their existence may be put at risk by some inconsiderate time-traveller doing away with their granny. Frankly, one only has to pose the question to realise that it is a patent absurdity. Time moves in only one direction, from past to future, and cannot be reversed. Whatever our friend the astronaut might find at the bottom of a black hole, he will not find that time has been reversed, or “stands still” (except in the sense that, since he would instantly be torn to pieces by the force of gravity, time would cease for him, along with a lot of other things).
We have already commented on the tendency to confuse science with science fiction. It is also noticeable that much of science fiction itself is permeated with a semi-religious, mystical and idealist spirit. Long ago, Engels pointed out that scientists who despised philosophy frequently fall victim to all kinds of mysticism. He wrote an article on the subject entitled Natural Science and the Spirit World, from which the following extract is taken:
“This school prevails in England. Its father, the much lauded Francis Bacon, already advanced the demand that his new empirical, inductive method should be pursued to attain, above all, by its means: longer life, rejuvenation—to a certain extent, alteration of stature and features, transformation of one body into another, the production of new species, power over the air and the production of storms. He complains that such investigations have been abandoned, and in his natural history he gives definite recipes for making gold and performing various miracles. Similarly Isaac Newton in his old age greatly busied himself with expounding the Revelation of St. John. So it is not to be wondered at if in recent years English empiricism in the person of some of its representatives—and not the worst of them—should seem to have fallen a hopeless victim to the spirit-rapping and spirit-seeing imported from America.” 7
There is no doubt that Stephen Hawking and Roger Penrose are brilliant scientists and mathematicians. The problem is that, if you begin with a wrong premise, you will inevitably draw the wrong conclusions. Hawking clearly feels uncomfortable with the idea that religious conclusions can be drawn from his theories. He mentions that in 1981 he attended a conference on cosmology in the Vatican, organised by the Jesuits, and comments:
“The Catholic Church had made a bad mistake with Galileo when it tried to lay down the law on a question of science, declaring that the sun went round the earth. Now, centuries later, it had decided to invite a number of experts to advise it on cosmology. At the end of the conference the participants were granted an audience with the Pope. He told us that it was all right to study the evolution of the universe after the big bang, but we should not inquire into the big bang itself because that was the moment of Creation and therefore the work of God. I was glad then that he did not know the subject of the talk I had just given at the conference—the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation. I had no desire to share the fate of Galileo, with whom I feel a strong sense of identity, partly because of the coincidence of having been born exactly 300 years after his death!” 8
Clearly, Hawking wishes to draw a line between himself and the Creationists. But the attempt is not very successful. How can the universe be finite, and yet have no boundaries? In mathematics, it is possible to have an infinite series of numbers which starts with one. But in practice, the idea of infinity cannot begin with one, or any other number. Infinity is not a mathematical concept. It cannot be counted. This one-sided “infinity” is what Hegel calls bad infinity. Engels deals with this question in his polemic with Dühring:
“But what of the contradiction of ‘the counted infinite numerical series’? We shall be in a position to examine it more closely a soon as Herr Dühring has performed the clever trick of counting it for us. When he has completed the task of counting from minus infinity to 0, let him come again. It is certainly obvious that, wherever he begins to count, he will leave behind him an infinite series and, with it, the task which he has to fulfil. Just let him invert his own infinite series 1+2+3+4…and try to count from the infinite end back to 1; it would obviously only be attempted by a man who has not the faintest understanding of what the problem is. Still more. When Herr Dühring asserts that the infinite series of lapsed time has been counted, he is thereby asserting that time has a beginning; for otherwise he would have been unable to start ‘counting’ at all. Once again, therefore, he smuggles into the argument, as a premise, what he has to prove. The idea of an infinite series which has been counted, in other words, the world-encompassing Dühringian Law of Determinate Number, is therefore a contradiction in adjecto, contains within itself a contradiction, and indeed an absurd contradiction.
“It is clear that an infinity which has an end but no beginning is neither more nor less infinite than one with a beginning but no end. The slightest dialectical insight should have told Herr Dühring that beginning and end necessarily belong together, like the North Pole and the South Pole, and that if the end is left out, the beginning just becomes the end—the one end which the series has; and vice versa. The whole deception would be impossible but for the mathematical usage of working with infinite series. Because in mathematics it is necessary to start from determinate, finite terms in order to reach the indeterminate, the infinite, all mathematical series, positive or negative, must start with 1, or they cannot be used for calculation. But the logical need of the mathematician is far from being a compulsory law for the real world.” 9
Stephen Hawking carried this relativistic speculation to an extreme with his work on black holes, which leads us right into the realms of science fiction. In an attempt to get round the awkward question of what happened before the big bang, the idea was advanced of “baby universes”, coming into existence all the time, and connected by so-called wormholes. As Lerner ironically comments: “It is a vision that seems to beg for some form of cosmic birth control.” 10 It really is astounding that sober scientists could take such grotesque ideas for good coin.
The idea of a “finite universe with no boundaries” is yet another mathematical abstraction, which does not correspond to the reality of an eternal and infinite, constantly changing universe. Once we adopt this standpoint, there is no need for mystical speculations about “wormholes”, singularities, superstrings, and all the rest of it. An infinite universe does not require us to look for a beginning or an end, only to trace the endless process of movement, change and development. This dialectical conception leaves no room for Heaven or Hell, God or the Devil, Creation or the Last Judgement. The same cannot be said for Hawking who, quite predictably, ends up attempting to “know the mind of God”.
The reactionaries rub their hands at this spectacle, and use the prevailing current of obscurantism in science for their own ends. William Rees-Mogg, big business consultant, and James D. Davidson write:
“We think it is extremely likely that the religious movement we see at work in many societies across the globe will be strengthened if we go through a very difficult economic period. Religion will be strengthened because the current thrust of science no longer undermines the religious perception of reality. Indeed, for the first time in centuries, it actually buttresses it.” 11
Aristotle thought that everything on earth was perishable, but that the heavens themselves were changeless and immortal. Now we know differently. As we gaze with wonder at the immensity of the night sky, we know that every one of these heavenly bodies that light up the darkness will one day be extinguished. Not only mortal men and women, but the stars themselves that bear the names of Gods experience the agony and the ecstasy of change, birth and death. And, in some strange way, this knowledge brings us closer to the great universe of nature, from which we came and to which we must one day return.
Our sun has at present enough hydrogen to last for billions of years in its present state. Eventually, however, it will increase its temperature to the point where life on earth will become impossible. All individual beings must perish, but the wonderful diversity of the material universe in all its myriad manifestations is eternal and indestructible. Life arises, passes away, and arises again and again. Thus it has been. Thus it will ever be.