John D. Barrow, New Theories of Everything, Oxford University Press, 2007.
Both of the present bloggers have enjoyed Barrow’s previous works. Bailey was so enthralled with Barrow and Tipler’s 1988 book The Anthropic Cosmological Principle that he read every word of its 736 pages multiple times. Borwein (with his brother Peter) wrote a favorable review of Barrow’s 1992 book Pi in the Sky for the publication Science.
Barrow’s latest book, New Theories of Everything, does not disappoint. In this wide-ranging work, Barrow examines the notion of viewing science as the search for algorithmic compression of observed data. In other words, the best scientific theory is the one that explains the most data precisely in as crisp a manner as possible.
Barrow examines this proposition from many different angles, including physics, cosmology, mathematics, mathematical logic, computer science, biology, history, philosophy and religion. This material is so well organized, and so lucidly written, that readers are bound to learn many things of interest, no matter what their backgrounds. Advanced knowledge of these fields is not required (although it will help).
Here are a few excerpts from this fascinating work:
[pg 11] On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting – the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic [pg 12] behind the Universe’s properties that can be written down in finite form by human beings.
[pg 52] [quoting Freeman Dyson] Godel proved that the world of pure mathematics is inexhaustible; no finite set of axioms and rules of inference can ever encompass the whole of mathematics; given any set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. I hope that an analogous situation exists in the physical world. If my view of the future is correct, it means that the world of physics and astronomy is also inexhaustible; no matter how far we got into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness, and memory.
[pg 113] [quoting Albert Einstein] however, we select from nature a complex [of phenomena] using the criterion of simplicity, in no case will its theoretical treatment turn out to be forever appropriate. … But I do not doubt that the day will come when that description [the general theory of relativity], too, will have to yield to another one, for reasons which at present we do not yet surmise. I believe that this process of deepening the theory has no limits.
[pg 121] There is no reason why life has to evolve in the Universe. Such complex step-by-step processes are not predictable because of their very sensitive dependence upon the starting conditions and upon subtle interactions between the evolving state and the ambient environment. All we can assert with confidence is a negative: if the constants of Nature were not within one percent or so of their observed values, then the basic buildings blocks of life would not exist in sufficient profusion in the Universe. Moreover, changes like this would affect the very stability of the elements and prevent the existence of the required elements rather than merely suppress their abundance.
[pg 138] Somehow the breathless world that we witness seems far removed from the timeless laws of Nature which govern the elementary particles and forces of Nature. The reason is clear. We do not observe the laws of Nature: we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves. This is the secret which reconciles the complexity observed in Nature with the advertised simplicity of her laws.
[pg 222] That is, the physicist likes to learn from particular illustrations of a general abstract concept. The mathematician, on the other hand, often eschews the particular in pursuit of the most abstract and general formulation possible. Although the mathematician may think from, or through, particular concrete examples in coming to appreciate the likely truth of very general statements, he will hide all those intuitive steps when he comes to present the conclusions of his thinking to outsiders. It presents the results of research as a hierarchy of definitions, theorems and proofs after the manner of Euclid; this minimizes unnecessary words but very effectively disguises the natural train of thought that led to the original results.
[pg 231] In practice, the intelligibility of the world amounts to the fact that we find it to be algorithmically compressible. We can replace sequences of facts and observational data by abbreviated statements which contain the same information content. These abbreviations we often call “laws of Nature.” If the world were not algorithmically compressible, then there would exist no simple laws of nature. Instead of using the law of gravitation to compute the orbits of the planets at whatever time in history we want to know them, we would have to keep precise records of the positions of the planets at all past times; yet this would still not help us one iota in predicting where they would be at any time in the future. This world is potentially and actually intelligible because at some level it is extensively algorithmically compressible. At root, this is why mathematics can work as a description of the physical world. It is the most [pg 232] expedient language that we have found in which to express those algorithmic compressions.