Confessing Evangelical

In the comments to my previous post the other day, I rather ungraciously referred to Roger Penrose's book The Road to Reality as "Climbing Mount Unreadable". Since then, I've made it to about page 220, showing it's not as bad as all that; but it is still a challenging read. I was given it for Christmas 2004, and my first attempt at reading it ground to a halt by about page 100 (out of 1,045), but this time I'm making life easier for myself by skipping the exercises.

"Exercises"? Yes, indeed: unusually for a bestselling "popular science" book, Penrose doesn't stint on the "hard sums". The book was written out of his conviction that most popular books about cosmology and quantum physics are potentially misleading, because they skip over the mathematical concepts that are fundamental to understanding - and, more important, evaluating - the scientific concepts involved. So the first half of the book provides an overview of mathematical concepts such as geometry, complex numbers and topology.

This has given the book - which, remarkably, made it into the top-ten bestsellers list here in the UK - a reputation for being rather more purchased than read, which I imagine is pretty accurate. While the blurb says that the book "assumes no particular specialist knowledge on the part of the reader", it's difficult to see how a reader without mathematical training could make it through the first half without taking to drink. I'm a mathematics graduate, and I'm still finding it pretty tough going at times.

That said, Penrose does as good a job as anyone possibly could of making these fundamentally complex concepts comprehensible, and one of the real pleasures of the book is reading a section, finding it utterly baffling, then stopping to think, re-read a few sentences, and discovering that the concepts involved suddenly spring to life in one's head: what Penrose himself has been known to call an "A-ha!" moment. (This is particularly appropriate, given Penrose's conviction - expounded in his best-known book, The Emperor's New Mind - that understanding the "A-ha!" experience is fundamental to understanding human consciousness as a whole.)

There's an illuminating review of Penrose's "physically huge" book on the American Scientist website, by computer scientist (and composer, artist and author) Jaron Lanier, who starts his review by saying:

Roger Penrose's latest book, The Road to Reality, is so generous in scope that it is difficult to absorb the breadth of its offerings.

Though Lanier admits that while "the text will seem gloriously variegated to some readers", it will seem "frustratingly inaccessible to others".

Lanier describes the mathematics section as "eerily liberating":

It is shocking that so much can be explained so well ... [T]he book starts at such an elementary level and soars to such heights, without any glitches along the way. It's a magical escape from the bounds of gravity.

One of the most engaging aspects of the review is Lanier's insight into the human aspects of Penrose's book:

The first half of The Road to Reality can be read as a love story about a little boy who adored numbers - especially complex numbers - like life itself, and who never grew up. Penrose's warm, funny temperament comes across in an understated way, and the reader is able to feel a little of what it would be like to have his superlative mathematical ease and intuition.

This is helped along by Penrose's liberal use of illustrations, hand-drawn by himself:

Unlike the sterile draftsman's renderings usually seen in math books, these drawings present metaphors. Some of the sketches depict the cute mental mnemonics that Penrose employs to keep ideas clearly in his mind. When he shows us a little bubble universe with assorted junk flung about, bursting out of a representative point in a potato chip-like configuration space, we know he has shared an intimate thought with us.

(The diagram in question is displayed above - click the thumbnail for a full-size version, with caption in a new window.)

Lanier summarises Penrose's book as "the lifetime statement of a devoted thinker who has defied the mainstream and can cast powerful if unusual light on a canon of familiar thoughts". Lanier then takes a quick detour into Pseud's Corner as he compares the book to Camille Paglia's Sexual Personae, on the basis that "both are big books that at turns amaze and infuriate many readers".

The "infuriations" come from the second half of the book, in which Penrose turns from the mathematics undergirding modern physics to the physics itself:

[T]his second ascent to the heavens from scratch is almost as smooth and inviting as the brilliant math presentation that precedes it. The big difference is that here Penrose is giving us a tour of controversies, and he's in fighting form.

Theoretical physics "has become a rough sport lately", and Penrose is out of step with the prevailing fashion for regarding "string theory" as the most likely way in which quantum physics and general relativity can be reconciled (the biggest challenge currently facing theoretical physics). This has led to some "shockingly negative" responses to Penrose, some of which are so vehement they lead Lanier to conclude that "some physicists have gone for so long without any experimental data that might resolve the quantum-gravity debates that they are going a little crazy".

Lanier suggests that Penrose's status as something of an "outcast" in modern physics is one driver for his writing this book. He suggests that Penrose's motivation can be summed up as follows:

"I'm going to bypass the physicists who have succumbed to a mob mentality and make my case by addressing everyone else - whether they have the technical background to understand me or not. None of us really knows what the right theory of quantum gravity will turn out to be, and unfortunately it's hard to do experiments, so we'll have to be patient to work this out.

"But in the meantime, just look at what a creative thinker I am and how productive I've been, despite my inclination to explore the unusual. The fact that I can explain my ideas to novices also shows that I am thinking clearly. Are you really ready to close your mind off and believe those string people, who are so sure of themselves? None of us has real evidence, but I'm the kind of guy you want to pay attention to."

Lanier concludes by applauding Penrose's "cosmic, romantic sense of human history":

Penrose gives us something that has been missing from the public discourse on science lately - a reason to live, something to look forward to ... One of the problems with the pompous triumphalism of string theory is that it suggests a premature decrease in mystery. One can practically hear Peggy Lee singing "Is That All There Is?" If it's true that that is all there is, that message would be fine, but Penrose makes a persuasive case that we are still surrounded by a sea of inviting mystery.

Incidentally, if anyone reading this has an unfinished copy of The Road to Reality glowering down at them from the bookshelf, then apparently Penrose's recommendation is that, if the worst comes to the worst, you should just read the last chapter. I haven't got that far yet - I'll post another update in, ooh, October or so ;-) - so can't comment any further on that suggestion. But according to another review (PDF) it contains something of a "happy ending" - "late-breaking news" of a new proposed theory that could reconcile string theory with Penrose's own "twistor" concept, and thus finally bring the "twice outcast" Penrose back in from the cold.