The Whole Megillah
The Road to Reality: A Complete Guide to the Laws of the
Universe. Roger Penrose. xxviii + 1099 pp. Alfred Knopf, 2004. $40.
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. The text will seem gloriously variegated to some readers
but frustratingly inaccessible to others. It's a physically huge
book, but every ounce of the content was designed with great care.
There is no single road here, though; rather, Penrose has provided a
bundle of interlaced narratives that must be teased out by the reader.
The first half of the book is devoted to mathematics and the second
to physics. The math portion is pure delight. Penrose starts with
the simplest ideas, such as counting, and builds gradually, with
great care, until he has taught us most of the kinds of math that
physicists wield these days (covering, for example, Riemann surfaces
and complex mapping, hypercomplex numbers, manifolds of n
dimensions, symplectic groups and tensors). It is simply astounding
that he has accomplished this feat. He does invoke equations, but
they are perfectly chosen for explanatory power and simplicity.
Reading this math section is eerily liberating. It is shocking that
so much can be explained so well. The obvious comparisons are to
The Feynman Lectures on Physics or George
Gamow's One, Two, Three . . . Infinity, but the achievement
here is greater, because the 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.
All readers will profit from being swept upward by Penrose, even if
only for a fraction of the journey, and beginners will be amazed at
how far Penrose can take them. Even so, it's unlikely a novice
reader will get through more than perhaps the first hundred pages of
the book without help.
Mathematicians will find Penrose's unconventional presentations of
familiar ideas amusing and will be introduced to new gems and
curiosities. Computer scientists and other technical readers who
haven't used this sort of math since school days will enjoy both the
review Penrose provides and the overview of recent advances.
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. There is a sense of
drama as modern mathematics is reconstructed. An early brush with
true love is depicted when Penrose explains in an utterly simple way
why the "almost mystical" formula
-1=eiπ is true. Consummation awaits in the
chapter about hyperfunctions.
Penrose uses illustrations frequently. Peculiar yet perfect, the
drawings in some cases look as though they might have been sketched
by the underground comic artist R. Crumb. 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.
Penrose takes absolutely nothing about numbers for granted. For
example, he expresses profound doubts about the most basic counting
numbers and wonders whether aliens might find a different way to be
mathematical. This attitude comes as no surprise, because he has had
one of the most eccentric careers in the sciences, combining
superlative contributions to physics and mathematics with excursions
into philosophy and speculative neuroscience. The constant returning
to first principles may not be to everyone's taste. For Penrose it
is a source of inspiration and part of a quest for clarity, whereas
for others it might come off as an ivory-tower indulgence. I loved it.
The Road to Reality is 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. I was reminded of
Camille Paglia's Sexual Personae: Art and Decadence from
Nefertiti to Emily Dickinson. Both are big books that at
turns amaze and infuriate many readers.
To get to the infuriations, we must turn to the second half of the
book, which is devoted to physics. This portion reads more like a
suspense novel than a romance. Right at the end the reader becomes
aware of elaborate setups put in place hundreds of pages back, in
anticipation of the spectacular climax—the unveiling of
Penrose's best shot at promoting further research into his twistor
theory. Despite that structure, this 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.
Penrose veers into irony in the lengths to which he goes to point
out where his ideas deviate from the mainstream. He is then
excruciatingly polite as he eviscerates concepts he believes to be
overrated, such as string theory and M theory. Why all this high
drama? Through no fault of Penrose's, theoretical physics has become
a rough sport lately. Heated debate is nothing new—one recalls
the immortal put-down attributed to Wolfgang Pauli: "This isn't
even wrong." And yet something new does seem to be happening,
in that a mob mentality is taking hold.
For those who haven't been keeping score, here's a very quick
summary: Quantum field theory and the theory of general relativity
have such superb power that no experiment yet has shown a crack in
either of them, even though they both predict wildly
counterintuitive properties in physical reality. And yet the two
theories seem to be deeply at odds with each other, which suggests
that there must be some other as-yet-unknown theory that
incorporates them both in a consistent way, a theory of quantum
gravity. It is fervently sought. The mainstream, and extremely
cocky, school of thought is that string theory or M theory is
inevitably going to be accepted as this unifying theory.
The second-most-studied approach is loop quantum gravity. There has
sometimes been an almost thuggish dismissal of it by the string
crowd. As it happens, loop quantum gravity makes extensive use of
some of Penrose's ideas, such as spin networks. Penrose, however,
has been most identified with yet a third approach, twistor theory,
which was intensely studied in the late 20th century but has been on
a back burner for most physicists lately, although not for Penrose.
This makes him twice the outcast, yet he is still one of the most
creative and productive individuals in his field.
A quick look at responses to Penrose's book on the Internet turns up
some—a noisy minority—that are shockingly negative in
tone. Science is always under siege by charlatans, and theories of
gravity are among the most attractive to con artists and
self-deceiving megalomaniacs. But to dismiss someone like Penrose in
harsh tones is to diminish the power of such language when it is
applied to more appropriate targets.
One gets the impression 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. If that's the problem,
help is on the way, because measurements of cosmic background
radiation and ingenious new experiments will soon present a new
generation of physicists with beguiling data.
Why did Penrose put all these elements together into such a big
book? His presentation of the whole megillah makes a point that, had
Penrose stated it explicitly (which he does not), might have gone
something like this: "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." I found him persuasive.
Finally, Penrose presents us with a cosmic, romantic sense of human
history fused with his technical autobiography. To him, the great
adventure of history is the quest to understand what is going on in
this weird reality we find ourselves in, and his personal story is
that same quest in miniature. The book opens with a fantasy about an
artisan in ancient Egypt who wonders about the cosmos, and it closes
with another fantasy, about a young woman sometime in the future who
is on the verge of the next big intuition about quantum gravity.
Penrose gives us something that has been missing from the public
discourse on science lately—a reason to live, something to
look forward to. After all, why should religious types be the only
ones to offer this? 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.