The Beginning of Infinity: Explanations That Transform the World (74 page)

The Character of Physical Law
(1965)

Among other things, Feynman forgot that the very concept of a ‘law’ of nature is not cast in stone. As I mentioned in
Chapter 5
, this concept was different before Newton and Galileo, and it may change again. The concept of levels of explanation dates from the twentieth century, and it too will change if I am right that, as I guessed in
Chapter 5
, there are fundamental laws that look emergent relative to microscopic physics. More generally, the most fundamental discoveries have always, and will always, not only consist of new explanations, but use new modes of explanation. As for being boring, that is merely a prophecy that criteria for judging problems will not evolve as fast as the problems themselves; but there is no argument for that other than a failure of imagination. Even Feynman cannot get round the fact that the future is not yet imaginable.

Shedding that kind of parochialism is something that will have to be done again and again in the future. A level of knowledge, wealth, computer power or physical scale that seems absurdly huge at any
given instant will later be considered pathetically tiny. Yet we shall never reach anything like an unproblematic state. Like the guests at Infinity Hotel, we shall never be ‘nearly there’.

There are two versions of ‘nearly there’. In the dismal version, knowledge is bounded by laws of nature or supernatural decree, and progress has been a temporary phase. Though this is rank pessimism by my definition, it has gone under various names – including ‘optimism’ – and has been integral to most world views in the past. In the cheerful version, all remaining ignorance will soon be eliminated or confined to insignificant areas. This is optimistic in form, but the closer one looks, the more pessimistic it becomes in substance. In politics, for instance, utopians promise that a finite number of already-known changes can bring about a perfected human state, and that is a well-known recipe for dogmatism and tyranny.

In physics, imagine that Lagrange had been right that ‘the system of the world can be discovered only once’, or that Michelson had been right that all physics still undiscovered in 1894 was about ‘the sixth place of decimals’. They were claiming to
know
that anyone who subsequently became curious about what underlay that ‘system of the world’ would be enquiring futilely into the incomprehensible. And that anyone who ever wondered at an anomaly, and suspected that some fundamental explanation contained a misconception, would be mistaken.

Michelson’s future – our present – would have been lacking in explanatory knowledge to an extent that we can no longer easily imagine. A vast range of phenomena already known to him, such as gravity, the properties of the chemical elements, and the luminosity of the sun, remained to be explained. He was claiming that these phenomena would only ever appear as list of facts or rules of thumb, to be memorized but never understood or fruitfully questioned. Every such frontier of fundamental knowledge that existed in 1894 would have been a barrier beyond which nothing would ever be amenable to explanation. There would be no such thing as the internal structure of atoms, no dynamics of space and time, no such subject as cosmology, no explanation for the equations governing gravitation or electromagnetism, no connections between physics and the theory of computation . . . The deepest
structure
in the world would be an inexplicable,
anthropocentric boundary, coinciding with the boundary of what the physicists of 1894 thought they understood. And nothing inside that boundary – like, say, the existence of a force of gravity – would ever turn out to be profoundly false.

Nothing very important would ever be discovered in the laboratory that Michelson was opening. Each generation of students who studied there, instead of striving to understand the world more deeply than their teachers, could aspire to nothing better than to emulate them – or, at best, to discover the seventh decimal place of some constant whose sixth was already known. (But how? The most sensitive scientific instruments today depend on fundamental discoveries made after 1894.) Their system of the world would for ever remain a tiny, frozen island of explanation in an ocean of incomprehensibility. Michelson’s ‘fundamental laws and facts of physical science’, instead of being the beginning of an infinity of further understanding, as they were in reality, would have been the last gasp of reason in the field.

I doubt that either Lagrange or Michelson thought of himself as pessimistic. Yet their prophecies entailed the dismal decree that
no matter what you do, you will understand no further
. It so happens that both of them had made discoveries which could have led them to the very progress whose possibility they denied. They should have been seeking that progress, should they not? But almost no one is creative in fields in which they are pessimistic.

I remarked at the end of
Chapter 13
that the desirable future is one where we progress from misconception to ever better (less mistaken) misconception. I have often thought that the nature of science would be better understood if we called theories ‘misconceptions’ from the outset, instead of only after we have discovered their successors. Thus we could say that Einstein’s Misconception of Gravity was an improvement on Newton’s Misconception, which was an improvement on Kepler’s. The neo-Darwinian Misconception of Evolution is an improvement on Darwin’s Misconception, and his on Lamarck’s. If people thought of it like that, perhaps no one would need to be reminded that science claims neither infallibility nor finality.

Perhaps a more practical way of stressing the same truth would be to frame the growth of knowledge (all knowledge, not only scientific) as a continual transition from
problems
to
better problems
, rather than from
problems to solutions or from theories to better theories. This is the positive conception of ‘problems’ that I stressed in
Chapter 1
. Thanks to Einstein’s discoveries, our current problems in physics embody more knowledge than Einstein’s own problems did. His problems were rooted in the discoveries of Newton and Euclid, while most problems that preoccupy physicists today are rooted in – and would be inaccessible mysteries without – the discoveries of twentieth-century physics.

The same is true in mathematics. Although mathematical theorems are rarely proved
false
once they have been around for a while, what does happen is that mathematicians’ understanding of what is fundamental improves. Abstractions that were originally studied in their own right are understood as aspects of more general abstractions, or are related in unforeseen ways to other abstractions. And so progress in mathematics also goes from problems to better problems, as does progress in all other fields.

Optimism and reason are incompatible with the conceit that our knowledge is ‘nearly there’ in any sense, or that its foundations are. Yet comprehensive optimism has always been rare, and the lure of the prophetic fallacy strong. But there have always been exceptions. Socrates famously claimed to be deeply ignorant. And Popper wrote:

I believe that it would be worth trying to learn something about the world even if in trying to do so we should merely learn that we do not know much . . . It might be well for all of us to remember that, while differing widely in the various little bits we know, in our infinite ignorance we are all equal.

Conjectures and Refutations
(1963)

Infinite ignorance is a necessary condition for there to be infinite potential for knowledge. Rejecting the idea that we are ‘nearly there’ is a necessary condition for the avoidance of dogmatism, stagnation and tyranny.

In 1996 the journalist John Horgan caused something of a stir with his book
The End of Science
:
Facing the Limits of Knowledge in the Twilight of the Scientific Age
. In it, he argued that the final truth in all fundamental areas of science – or at least as much of it as human minds would ever be capable of grasping – had already been discovered during the twentieth century.

Horgan wrote that he had originally believed science to be ‘open-ended, even infinite’. But he became convinced of the contrary by (what I would call) a series of misconceptions and bad arguments. His basic misconception was empiricism. He believed that what distinguishes science from unscientific fields such as literary criticism, philosophy or art is that science has the ability to ‘resolve questions’ objectively (by comparing theories with reality), while other fields can produce only multiple, mutually incompatible interpretations of any issue. He was mistaken in both respects. As I have explained throughout this book, there is objective truth to be found in all those fields, while finality or infallibility cannot be found anywhere.

Horgan accepts from the bad philosophy of ‘postmodern’ literary criticism its wilful confusion between two kinds of ‘ambiguity’ that can exist in philosophy and art. The first is the ‘ambiguity’ of multiple true meanings, either intended by the author or existing because of the reach of the ideas. The second is the ambiguity of deliberate vagueness, confusion, equivocation or self-contradiction. The first is an attribute of deep ideas, the second an attribute of deep silliness. By confusing them, one ascribes to the best art and philosophy the qualities of the worst. Since, in that view, readers, viewers and critics can attribute any meaning they choose to the second kind of ambiguity, bad philosophy declares the same to be true of all knowledge: all meanings are equal, and none of them is objectively true. One then has a choice between complete nihilism or regarding
all
‘ambiguity’ as a good thing in those fields. Horgan chooses the latter option: he classifies art and philosophy as ‘ironic’ fields, irony being the presence of multiple conflicting meanings in a statement.

However, unlike the postmodernists, Horgan thinks that science and mathematics are the shining exceptions to all that. They alone are capable of non-ironic knowledge. But there is also, he concludes, such a thing as
ironic science
– the kind of science that cannot ‘resolve questions’ because, essentially, it is just philosophy or art. Ironic science
can
continue indefinitely, but that is precisely because it never resolves anything; it never discovers objective truth. Its only value is in the eye of the beholder. So the future, according to Horgan, belongs to ironic knowledge. Objective knowledge has already reached its ultimate bounds.

Horgan surveys some of the open questions of fundamental science, and judges them all either ‘ironic’ or non-fundamental, in support of his thesis. But that conclusion was made inevitable by his premises alone. For consider the prospect of
any
future discovery that would constitute fundamental progress. We cannot know what it is, but bad philosophy can already split it, on principle, into a new rule of thumb and a new ‘interpretation’ (or explanation). The new rule of thumb cannot possibly be fundamental: it will just be another equation. Only a trained expert could tell the difference between it and the old equation. The new ‘interpretation’ will by definition be pure philosophy, and hence must be ‘ironic’. By this method, any potential progress can be pre-emptively reinterpreted as non-progress.

Horgan rightly points out that his prophecy cannot be proved false by placing it in the context of previous failed prophecies. The fact that Michelson was wrong about the achievements of the nineteenth century, and Lagrange about those of the seventeenth, does not imply that Horgan was wrong about those of the twentieth. However, it so happens that our current scientific
knowledge
includes a historically unusual number of deep, fundamental problems. Never before in the history of human thought has it been so obvious that our knowledge is tiny and our ignorance vast. And so, unusually, Horgan’s pessimism contradicts existing knowledge as well as being a prophetic fallacy. For example, the problem-situation of fundamental physics today has a radically different structure from that of 1894. Although physicists then were aware of some phenomena and theoretical issues which we now recognize as harbingers of the revolutionary explanations to come, their importance was unclear at the time. It was hard to distinguish those harbingers from anomalies that would eventually be cleared up with existing explanations plus the tweaking of the ‘sixth place of decimals’ or minor terms in a formula. But today there is no such excuse for denying that some of our problems are fundamental. Our best theories are telling us of profound mismatches between themselves and the reality that they are supposed to explain.

One of the most blatant examples of that is that physics currently has
two
fundamental ‘systems of the world’ – quantum theory and the general theory of relativity – and they are radically inconsistent. There are many ways of characterizing this inconsistency – known as the
problem of quantum gravity – corresponding to the many proposals for solving it that have been tried without success. One aspect is the ancient tension between the discrete and the continuous. The resolution that I described in
Chapter 11
, in terms of continuous clouds of fungible instances of a particle with diverse discrete attributes, works only if the spacetime in which this happens is itself continuous. But if spacetime is affected by the gravitation of the cloud, then it would acquire discrete attributes.

In cosmology, there has been revolutionary progress even in the few years since
The End of Science
was written – and also since I wrote
The Fabric of Reality
soon afterwards. At the time, all viable cosmological theories had the expansion of the universe gradually slowing down, due to gravity, ever since the initial explosion at the Big Bang and for ever in the future. Cosmologists were trying to determine whether, despite slowing down, its expansion rate was sufficient to make the universe expand for ever (like a projectile that has exceeded escape velocity) or whether it would eventually recollapse in a ‘Big Crunch’. Those were believed to be the only two possibilities. I discussed them in
The Fabric of Reality
because they were relevant to the question: is there a bound on the number of computational steps that a computer can execute during the lifetime of the universe? If there is, then physics will also impose a bound on the amount of knowledge that can be created – knowledge-creation being a form of computation.