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Anathem
Neal Stephenson
Atlantic hardcover £18.99

review by George Berger

Since the 1930s, three questions have dominated basic thought in mathematics, physics, and psychology. (1.) Are mathematical entities - like numbers - discovered, or are they constructs of our minds? (2.) Does the correct interpretation of quantum mechanics require reference to acts of observation? (3.) What is consciousness? These questions are now under intense debate by scientists and philosophers, but no generally accepted answers have been forthcoming. They saturate today's science fiction, wherein tropes such as AI, parallel worlds, and augmented mental abilities help fictionalise these problems.

While narratives concerning any one of these have filled entire novels, it is the genius of Neal Stephenson to have written Anathem, an absorbing novel with the implicit assumption that the right solution of any one of them requires correct solutions to the other two. As philosophers say, they form a 'conceptual package.' Stephenson's package contains so much science and philosophy that it concerns the nature of all reality. Anathem explores these complex questions through a delightful story featuring some engaging personalities and their fascinating society.

Anathem begins with a global ruling elite (the Saecular Power) exerting a tight, but benevolent, grip on the Earth-like planet Arbre's human inhabitants, following long periods of strife, societal collapse, and re-organisation. Most live more or less as we do, while some reside in rather closed 'concents', groups of several 'maths'. Each math contains thinkers (theors) interested in mathematics, logic, the natural sciences (theorics) and/ or philosophy (metatheorics, i.e. metaphysics). They form its avout class. A math's ita are technicians who maintain the math's digital computers (syntactic devices) and Internet (reticulum) contact with the outside. Strict routines, rituals, and codes govern the men and women (fraas, suurs) of each math. The division into math and technological (praxic) surrounding society was considered a fair resolution after centuries of conflict over divergent beliefs and practices.

The easy-to-remember neologisms help make reading Anathem a pleasure. Its narrator, Fraa Erasmas, of the concent of Saunt Edhar, relates how he and others are ordered by the Saecular Power to leave the concent and travel to a meeting of avouts but not told why. His travelling companions include Fraa Orolo, Fraa Jad, and Suur Ala (to whom he is attracted). Earlier, in their math, Orolo discovered an orbiting alien spaceship. For his own reasons, connected with his discovery, he slopes off to visit a distant archaeological site. Fraa Erasmas joins him there later; the others eventually reach their original destination.

The account of these travels is wonderful. Unfortunately, reviews often focus on Anathem's beauty, to the detriment of the important science and philosophy I think the author desires to communicate. In these instances I feel Stephenson's ambition has failed. Hence I shall address the concepts rather than the action, as my way of doing justice to Stephenson's attempts to tackle the three questions.

The ship comes from another cosmos and holds humanoids from four of very many parallel worlds (cosmi), ideas of which serve to answer the three questions. (Increasing numbers of scientists now think along similar lines.) Stephenson's cosmi form a directed acyclic graph (DAG), a 'plurality of worlds' so related that information flows, say, from cosmos A to cosmos B, but not vice versa, for any cosmi A and B that are appropriately related, and in which there is no sequence of cosmi such that information from one cosmos can return to that cosmos by traversing that sequence. This is one example of what cosmologists call a multiverse. Stephenson's version is inspired by David Deutsch's influential 1997 book, The Fabric Of Reality. Deutsch uses the notion of related parallel worlds to solve fundamental problems in quantum mechanics. Since 2001 he has used information to relate worlds and to answer the second question in the negative. His controversial solution does not invoke DAGs.

Stephenson's multiverse is an original contribution to speculative science and SF. Anathem assumes that information flow from A to B makes knowledge of A available to conscious inhabitants of B. This attacks one part of the consciousness question: what is knowledge and how do we acquire it? Information flow also provides a means of inter-cosmic travel. The spaceship traverses four cosmi and eventually reaches the cosmos of Arbre. Since the multiverse is a DAG it cannot return home. This jump from knowledge to travel is one of those improbabilities that one must accept while reading SF. I won't spoil things by disclosing the reason for the trip, but can say that it involves an application of multiverse theory developed by Deutsch's collaborator, the philosopher Michael Lockwood.

Stephenson describes this manner of acquiring knowledge in some detail, and so drives Anathem into very deep philosophy, while keeping the story moving along. When Erasmas and the others finally arrive at the meeting of minds, the full theory becomes clear. The theors accept the multiverse theory and use it to come to terms with one of Arbre's main social problems. For centuries Arbre's thinkers were torn between two views of knowledge. One is that people can get 'upsights,' flashes of (e.g.) mathematical knowledge that seemingly come from another domain. This is the doctrine of Platonism in today's philosophy of mathematics. The theors decide that an upsight is the reception by a conscious brain of information from another cosmos.

Since information flow is, Deutsch claims, needed to understand quantum mechanics, the 'conceptual package' is complete. True accounts of mathematics, quantum mechanics, and one kind of conscious knowing are all needed to correctly describe the multiverse. Such is the philosophy of Anathem. Its acceptance by the theors implies their rejection of the notion that brains are syntactic devices that acquire or construct knowledge purely by the manipulation of brain states that act as symbols lacking intrinsic meaning. According to one computer doctrine of consciousness, mathematics is a 'game' played with neural items according to the brain's rules.

This is one version of our doctrine of formalism in the philosophy of mathematics. The upshot is that this book is a fictionalisation of our debate between Platonism and formalism, in which Platonism wins out. Today this issue is up for grabs. To write an interesting SF novel about it that instructs the reader is a magnificent achievement. The conclusion uses these concepts and cannot be understood without them. It is a novel of ideas and closed intellectual communities, as is Hermann Hesse's 1945 Nobel prize winning novel, The Glass Bead Game (aka: Magister Ludi).

Anathem has two serious deficiencies, one conceptual, the other literary. They are connected. First, its notion of information flow from cosmi to minds does not capture what philosophers understand by Platonism. Stephenson stresses upsights of complex mathematical structures and everyday events taking place in some cosmos. But Platonists hold that many upsights - which they often call 'intuitions' - are quite elementary, say that 2+2=4. By downplaying this sort of upsight, Stephenson neglects the Platonist's view that knowledge of complex mathematics is somehow dependent on knowledge of simpler mathematical facts. (He inherits this error from cosmologist Max Tegmark.) Moreover, I know of no contemporary Platonist who thinks that minds can access physical events by intuition. Yet both notions are central to the philosophy and drama of Anathem. Hence readers are misinformed about a significant academic debate, whose recent major players were the philosopher Edmund Husserl and the mathematical logician Kurt Gödel.

Second, its literary deficiency rests on Anathem's distinctive linguistic invention, wordplay, superfluous passages, and narrative zest. All this is delightful and readily accessible (the book has a glossary). But this makes it easy to overlook the philosophical and scientific content. For me it's clear that Stephenson's chief purpose was not to provide more than 900 pages of linguistic wonders, but to use the latter to seduce us into learning the basics of today's most daring approaches to the three questions with which I began this review.

Anathem by Neal Stephenson

Anathem cover



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