To explain the phenomenal world to the last detail is what the scientific enterprise is all about. For this, one needs to adopt a course. That course, since the seventeenth century, includes instruments, experiments, definitions, theories and such. But there is something more: the laws of nature, as Galileo noted, are in the language of mathematics. The role of sophisticated mathematics in the physicist’s elucidation of phenomena is far more significant than its formulation in that abstract language. There are aspects of reality of which we cannot have the slightest inkling without the aid of mathematics. Mathematics is the most fruitful road to a coherent, consistent, and rational grasp of the magnificent simplicity that underlies the horrendous complexity of reality. This truth is amplified in the book under review.
Mathematical physicist Roger Penrose – well known for his thesis that the currently recognized laws of physics are incomplete and his call for a new theory to explain consciousness – begins his book with an essay on the conceptual framework of his reflections: The mind grasps the marvelous subtelies inherent in the mathematics that rules the phenomenal world; mathematics, in turn, has allowed, if not instigated, mind to evolve. After formulating these key principles, he offers a brief note on the Good, the True, and the Beautiful, reminding this reviewer of the Hindu notion of satyam-shivam-sundaram (Truth-Goodness-Beauty) which sees the Divine in this seamless triune.
The next fifteen chapters of the book treat the informed reader to the mathematical nuggets that serve as bricks for the edifice erected by physics in its grasp of the world. Penrose does this with erudition, insight, and flair, as also considered opinions on the state of physics. He takes us on a grand tour, à la Dante, of the abundant orchards of mathematics: from Pythagorean Greece with its irrational numbers and proofs of propositions, to transfinite numbers, Turing machines and Gödel’s theorem. He recalls for us complex numbers and logarithms, calculus, analytical continuation, Fourier series, hyperfunctions, and much more. But all this is a feast only for those who have benefited from advanced courses in mathematics. Contrary to what the flap invitingly says, this book is not for the lay reader, no matter how serious. One might as well browse though the Upanishads in sacred Sanskrit.
Next follow ten chapters dealing with practically every cog in the grand machine of twentieth century theoretical physics: relativity, quantum physics, Lagrangians, Hamiltonians, symmetry groups, quantum field theory, the standard model, and the Big Bang. Again the reader familiar with the topics will be charmed, but others will be jolted into the recognition of how little they know of ivory tower esoterica.
In the current formalism of quantum mechanics (QM), in any collection of micro-entities every part is inextricably linked to every other, somewhat as every member of a society is connected to all others. This inevitable holism is called quantum entanglement. Penroses’s chapter on quanglement (as he calls it) is one of the clearest technical discussions of the topic. We read here his own take on the associated issues. Quanglement is related to measurement theory which Penrose calls the measurement paradox because of the awkward puzzles that arise when one tries to be specific about the parameters associated with quantum states. This cannot be discussed without referring to the ubiquitous y function which has been subjected to varying interpretations, resulting in the nebulous ontology of QM. Penrose feels a clarification is urgent.
The standard model is a crowning achievement of twentieth century physics in its vision of the roots of matter and phenomena. In his non-standard discussion of this venerated paradigm, Penrose reminds the reader that this is not the “ultimate answer.” He also says that string theory “gains its support and chooses its directions of development almost entirely from aesthetic judgments guided by mathematical desiderata.” By describing the originator (Edward Witten) of string theory as a more remarkable mathematician than he realizes, Penrose subtly conveys his lack of enthusiasm for this theory and its variants which have been popularized by able exponents
Penrose contends that many currently respected theories of physics are highly speculative: a view shared by others beyond the ivory tower, but one that can be stated so bluntly and boldly only by a Penrose.
The decades-old attempts to synthesize gravity with other fundamental forces are presented at length, always with the caution that none of these is to be taken as the last word. Penrose is harsh on those who dream of a final theory when he says that “most physicists of the day (1920s) were not so foolish as to think that this (the physics of their time) could shortly lead to a ‘theory of everything’.”
Penrose talks about the role of fashion in physical theory: a post-modernist contention which may not sit well with many scientists. He says that in business concerns “it is the large ones that have a natural tendency to get larger at the expense of smaller ones,” and so it is in physics too. By implication, this is the reason why his own theory of twistors hasn’t received as much attention. He warns that “with ideas that are far from the possibility of experimental confirmation,” one “must be especially cautious in taking the popularity approach as any real indication of its validity.”
By the time I had waded through a thousand and odd pages, fascinated as I was by the conciseness and clarity with which all the magic of mathematical physics is presented, I had forgotten that I was supposed to be traveling on the road to reality. Then to my surprise I read the statement: “I do not believe that we have yet found the true ‘road to reality,’ despite the extraordinary progress that has been made … in the last few centuries.” I will admit that right from the start I did not resonate with the title of the book because there are after all different roads to different kinds of reality: the mystical, the poetic, the philosophical, to name a few. And within physics itself there is a multilemma as to which of the many roads it has to choose from. So it is not surprising that physics hasn’t found the road to reality. Mathematics is one road to it.
Penrose is not shy of using words like mystery and miracle qua scientist. In this humility he displays the wisdom that eludes some other creative minds. The crux of his message is that physics offers us many wonderful things through the mathematical channel; yet it would be a serious error to mistake creative mathematics for physical reality. Dante concluded his masterpiece with a gaze on the radiance, instigated by “the love that moves the sun and other stars,” Likewise, Penrose realizes in the end that morality and beauty are as much there as Platonic mathematics in the expanded vision of the human mind. As I interpret this, science without humanity is dry and lifeless. Aesthetics breathes charm into science, and ethics makes it human in an enlightened way.