3/30/22

Is it possible, even in principle, to know everything? Is there a limit to the places science can take us, not because there are mystical realms accessible only by mystical means, but because complete comprehensibility just isn't built into the nature of things? Barrow discusses some of the more obvious, scientifically-established limits to what we can know, such as Heinsenberg's Uncertainty Principle (although that actually gets surprisingly little coverage), the fact that the unbreakable speed of light limits how much of the universe we can ever see, and the way Gödel's Incompleteness Theorem tells us there are some mathematical truths that cannot be arrived at mathematically. But much of the book deals with more abstract, even philosophical questions. Is it possible that the universe, despite what physicists like to believe, is so infinitely complicated that the closer we look, the more we'll see, forever? Is the human brain, which, after all, evolved to help us survive and reproduce and has only produced our ability to do math and science as a sort of side effect, even capable of truly understanding the universe? Will human knowledge continue increasing forever, or is the absolute best we can hope for a future in which it takes more and more effort to discover less and less? And so on.

It makes for a somewhat rambling trip through a wide variety of subjects, some of which seem more relevant to the main thrust of the book than others. Some sections are clear and fascinating. Others, I think, are just a bit too dense, while still others feel oddly lacking in substance. Ultimately much of what Barrow has to say is, by its very nature, unsatisfying, because on many of these subjects, all one can really do is pose the question, stare at it for a while, and then shrug and walk away. Far too often we don't even know what it is we don't know. But it is certainly a wide-ranging and thought-provoking journey that Barrow takes us on in the course of contemplating all these unknowns. ( )

Our study of the limits of science and the science of limits will take us from the considerations of practical limits of cost, computability, and complexity to the restrictions imposed on what we can know by our location in the middle of the Nature's spectra of size, age, and complexity. We shall speculate about our possible technological futures and locate our current abilities on the spectrum of possibilities for the manipulation of Nature in the realms of the large, the small, and the complex. But practicalities are not the only limits we face. There may be limits imposed by the nature of our humanity. The human brain was not evolved with science in mind. Scientific investigation, like our artistic senses, are by-products of a mixed bag of attributes that survived preferentially because they were better adapted to survive in the environments they faced in the far distant past. Perhaps those ambitious origins will compromise our quest for an understanding of the Universe? Next, we shall start to pick at the edges of possible knowledge. We shall learn that many of the great cosmological questions about the beginning, the end, and the structure of our Universe are unanswerable. Despite the confident exposition of the modern view of the Universe by astronomers, these expositions are invariably simplified in ways that disguise the reasons why we cannot know whether or not the Universe is finite or infinite, open or closed, of finite age or eternal. Finally, we delve into the mysteries of the famous theorems of Godel concerning the limitations of mathematics. We know that there must exist statements of arithmetic whose truth we can never confirm or deny. What does this really mean? What is the fine print on this theorem? What are its implications for science? Does it mean that there are scientific questions that we can never answer? We shall see that the answers are unexpected and lead us to consider the possible meaning of inconsistency in Nature, of the paradoxes of time travel, the nature of freewill and the workings of the mind. Finally we explore some of the strange implications of trying to pass from the consideration of individual choices to collective choices. Whether it is the outcome of an election or the making up of one's mind in the face of the brain's competing options, we find a deep impossibility that may have ramifications throughout the domain of complex systems.