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John D Barrow


Impossibility

Category: Science | Published: 1998 | Review Added: 23-08-2021

Rating: 4 - A top read

With every century that has passed, science and technology have given us more insight into, and control over, the world around us. The momentum seems to be towards an eventual understanding of everything that there is to be understood. Yet, as mathematician John D Barrow observes in the Preface to this book, final illumination seems always to recede beyond our grip:

A pattern has emerged in many spheres of enquiry in which a scientific theory becomes so successful in the quantity and quality of its accurate predictions that its practitioners start to wonder if the end is in sight - whether their theory might be able to explain everything within its encompass. But then something strange hjappesn. The theory predicts that it cannot predict. It turns out to be not simply limited in scope, but self-limiting. This pattern is so strikingly recurrent that it suggests to us that we can recognize mature scientific theories by their self-limiting character. Such limits arise not merely because theories are inadequate or inaccurate, or inappropriate: they tell us something profound about the nature of knowledge and the implications of investigating the Universe from within.

What, then, are the limits of human knowledge, of human capability, and more broadly, of the laws of physics themselves?

Barrow sets himself a sizeable challenge in trying to encapsulate, in a relatively short work, the notion of scientific impossibility. In the early chapters, he examines the history of the concept of impossibility in the fields of religion, philosophy and logic. For example, would an omniscient and omnipotent God be bound by the laws of mathematics and logic, or would any paradoxical "truth" be allowed Him, for example for two plus two to equal five? Is there any philosophical realm in which the logically impossible could be practically possible? As that author pithily puts it:

Logical descriptions of complex worlds contain within themselves the seeds of their own limitation. A world that was simple enough to be fully known would be too simple to contain conscious observers who might know it.

Barrow moves on from a historical perspective to consider practical limitations to human knowledge. The "low-hanging fruit" of scientific law, amenable to investigation via cheap and straightforward experiments by committed enthusiasts, was mostly picked by the end of the nineteenth century. The implications of Newtonian mechanics were fully researched and documented, and some scientists believed the holy grail of a complete mathematical description of the physical world to be in reach. But just as science seemed set to rest on its laurels, Max Planck discovered that beyond a certain limit, scientific measurement moves from continuity to granularity: at exceedingly small scales, we can no longer talk of definite positions and momentum of particles, but only of accumulations of their probabilities. Quantum mechanics was born, setting off a second scientific revolution, whereby, paradoxically, equations governing matter at the tiniest of levels yielded to humankind unprecedented power over the macroscopic world. The Twentieth Century was the era of the atom bomb, telecommunications and the computer.

The behaviour of matter and energy in natural earthly conditions now being well understood, scientific study had moved into the realm of physical extremes, experiments into which often required budgets of millions of pounds. These experiments also sometimes involved the creating of conditions - for example, the behaviour of fluids close to a temperature of Absolute Zero - that we can reasonably assume have never existed naturally in the history of the universe.

At some point - and perhaps this point has already been reached - science is going to be limited by practical and financial constraints. With the world's resources under unprecedented strain, investigation of esoteric phenomena that further human knowledge with little practical gain is likely to play second fiddle to more mundane research into sustainable energy use. Will our search for ultimate understanding be overridden by more pressing pragmatic needs?

Then there is the question of what such "ultimate understanding" might involve. Even supposing that we managed to whittle down the four fundamental physical laws to one "super-law", would that give us the deep understanding we seek? Is a succinct and elegant mathematical description of reality the same thing as an understanding of it?

Barrow returns occasionally to the observation that although the known laws of physics allow complex phenomena such as the appearance of self-organising life forms, they don't actually predict them. The emergence of a planet that could support life, and then the emergence of life on it, and then the emergence of self-concious beings from that life, are all allowed by the laws of quantum mechanics and relativity - but they are exceedingly improbable. There seems to be some hidden, pattern-forming law operating at a macroscopic level that is at present not only uninvestigated, but widely unacknowledged. It must be said that Barrow largely glosses over this scientific gap.

Later, the book moves onto the notion of cosmological unknowability. The speed of light will forever present a horizon to our observations, beyond which we cannot peer. No event whose light has not had time to reach us is visible, even in principle. On top of this, to look out into space is to look backwards in time: we will never be able to gain a snapshot of what the universe looks like now.

The universe beyond our observation might be similar to the universe available to it; but there is no reason to assume that this is the case. We can make educated guesses about the beginning of the universe, and the proto-laws that obtained there; but here, as so often, paradox creeps in:

If we can find an explanation for some (or even all) of the observed astronomical properties of the universe that does not depend on knowing the intial state of the unvierse (or whether it had an intial state), then, conversely, those same observations will be unable to tell us about the structure (or existence) of thie initial state. We can't have our cake and eat it.

Barrow rounds off his book with a return to his home territory, mathematics, and Gödel's Theorem, a logical proof that there "must exist statements of arithmetic whose truth or falsity cannot be established using the axioms and and decuctive rules of arithmetic." Since all science is founded upon mathematics, this suggests that science, ipso facto, cannot lead us to ultimate truth, in whatever that might consist.

Perhaps wisely, Barrow provides no technical detail of Gödel's Theorem; but he covers many of its implications, which inevitably leave the lay reader behind.

I have found this a difficult book to review. It covers such a huge amount of ground that it can't easily be summarised, and it doesn't arrive at a neat conclusion.

Perhaps this is the point: there is no limit to the study of limits, and whether one regards that possibility with frustration or with awe depends on one's temperament. Throughout the book, Barrow himself comes across as engagingly sanguine in his acceptance of a universe about which we can always know more, but not hope to know everything.

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