Roger Penrose Is Smarter Than All Of Us
The experience of reading Roger Penrose’s “Fashion, Faith and Fantasy in the New Physics of the Universe” is much like attending an advanced physics lecture at a prestigious university. The subject matter is intensely difficult, the logic can be thin and leave much as an exercise for the reader, and the quirky professor goes off on minimally-helpful tangents about his own advanced research. With all that said, at the end, you feel that something of crucial importance has been imparted, an insight about the fundamental nature of reality, a beautiful pearl of wisdom unparalleled in its rigor and elegance… and if your IQ were 40 points higher, you might actually be able to appreciate it.
“Fashion, Faith and Fantasy”—“FFF” hereafter—is hard. The book is about the thorniest controversies at the frontiers of modern physics. Penrose, a Nobel Prize-winning physicist with an illustrious career spanning multiple decades, wants to express some bold positions, explaining why he rejects mainstream views in certain fields. But in order to do so, he first has to explain what he’s talking about, which means some tough physics. Even though Penrose wants FFF to be accessible to laymen, these explanations are sufficiently dense that fairly often, I found myself wondering whether Penrose was using Euler’s method of persuasion—known more generally as Proof by Intimidation. The book is hard.
Each part of the book expresses a different objection to a modern physical theory. Chapter 1 deals with the “Fashionable”, but not all that substantive, string theory; Chapter 2 deals with the excessive “Faith” some have in the scalability of quantum mechanics; Chapter 3 identifies various views in cosmology that qualify as “Fantasy”, chiefly cosmic inflation; and Chapter 4 briefly expresses Penrose’s own views on those topics, contrasting with what he’s critiqued in the prior sections. (I’ll wrap the relevant sections of Chapter 4 into my discussion of the other three, so as to discuss the same topics at the same times, rather than revisiting e.g. string theory at the very end.)
Even though the subject matter is heavy, you shouldn’t need to understand much physics to get something from this review. I’m hardly equipped to understand string theory, so I’m not even going to try explaining it. My summary of Penrose’s arguments will mostly take the form of imperfect visual metaphors and lossy oversimplifications, like a sloppy science journalist.
This cat is confused by strings, but you don’t have to be!
On the other hand, if you know a great deal about physics, and you see something obviously wrong in what I’ve written, please assume that it’s an error in my oversimplification, rather than assuming it’s an oversight in Penrose’s work. Unlike me, Penrose uses a careful, cumulative approach to ground his arguments and undermine his opponents’, incorporating scientific knowledge from across his illustrious career in theoretical physics. Oh, and incorporating math. Uh, a lot of math. Let’s start there.
The Mathematical Appendix
You Should Have Paid More Attention in Linear Algebra
Some books try to make you feel dumb. They bludgeon you with complex theories and arcane terminology which they expect you not to understand. They browbeat you with those arcana until you’re thoroughly Eulered, intimidating you into uncritical acceptance of the author’s assertions.
Even though it’d soothe my bruised ego, I can’t dismiss FFF as one of these books. To the contrary, it’s desperate to make its reader feel smart. Penrose wants even a layman to be able to pick up FFF and appreciate at least the outlines of its arguments, which is why Appendix A is a patient exposition of the mathematical concepts and terms those arguments depend on. Even if you’ve never heard the term “Harmonic Analysis”, or don’t know what it means for a “vector space” to be a “bundle of fibres” with a “twist”, the tools are there for you to get up to speed.
Given the subject matter of the book, I knew the math would be no joke. But I figured it’d be manageable for me. I did well in undergraduate multivariable calculus, linear algebra, and set theory. I took introductory classes on quantum mechanics and relativity. I expected I’d have some catching up to do, but that overall, I’d be fine.
I was not fine. Clocking in at 70 pages, the appendix touched on what I’d learned in those classes, but with twists and turns that weren’t covered in any course I’d taken. In particular, one of the critical concepts that Penrose wants to communicate—which is fundamental to many of his arguments—is “functional freedom”. Functional freedom provides a measure of how many states a physical system can take (i.e. the size of a phase space), without invoking cardinality of infinities. It’s similar to the idea of “degrees of freedom” and the dimension of a space. But as far as I can tell, Penrose’s extension of those ideas into “functional freedom” is totally original. It’s not the toughest material in the appendix, but there’s no wiki page about it, and no helpful math Stack Exchange threads on the topic. The terminology and notation Penrose chooses for it appear to be his own creations, and a reader won’t have encountered them outside his works. Not great for accessibility.
Wait, his notation uses power towers of infinities? I’m calling the math police.
On top of covering apparently-original topics in mathematics, the appendix covers topics in preexisting math that I hadn’t covered in any detail the first time around, and a few topics I’d never run into at all. It was a significant challenge, as I think it would be for most readers. By the end, I was re-reading practically every page, sometimes multiple times, trying not to get completely lost. I definitely didn’t grasp more than two-thirds of what Penrose was trying to communicate.
But even when I was struggling, I didn’t get the sense that I was being intentionally Eulered. Penrose probably could have expressed some of the ideas better, but mostly, the linear algebra concepts discussed are just intrinsically difficult. And when I did grasp new concepts, they often came as flashes of insight which resolved lingering confusions for me. For example, the appendix taught me how patchworks of local coordinate systems can cover a surface with no well-behaved global coordinate system—something I’d heard about when learning about relativity, but had never before grasped at the level of insight. The appendix might not be perfect, and I might not have understood it all, but I’m convinced it’s meant to be helpful instead of intimidating; and the smarter the reader, the more they’ll get from it.
The appendix also features many original illustrations, which are peppered through the book. Virtually all of the illustrations in the book (save a few computer-generated ones) were drawn by Penrose himself, and he has a real talent. His diagrams always manage to be both illuminating and beautiful. FFF has art as well as argument; it’s definitely the kind of book you could leave open on a coffee table to impress visitors. As an added bonus, at a glance, some of the illustrations look like they could have come from either a geometry textbook, Lovecraftian horror, or the Voynich Manuscript.
When you gaze long enough into the w-plane, it also gazes back
In all, my biggest problem with the appendix is precisely that it is an appendix. If I had been Penrose’s editor, I would have told him to put it at the beginning. It should be considered a required introduction to the book, not an optional addition. Laying the conceptual groundwork for your arguments in an appendix is bad form.
If you pick up FFF, start with the math; and if you struggle with it, join the club. Once you finish, be prepared for more confusion ahead, as Penrose launches his first salvo against the vapid bandwagoning of mainstream physics.
Fashion
Beating Up Particle Physics and Taking its Lunch Money
Chapter 1 of FFF is all about string theory and its alleged inadequacies. Before launching into his criticisms, Penrose begins with a whiplash tour through “fashionable” scientific theories of the past 3000 years. The usual outmoded theories from the history of science are mentioned: Platonic solids and the four elements; the geocentric model of the solar system; the phlogiston theory of combustion before proper chemistry; Newtonian gravity before general relativity. All of these theories were great while they were the best on offer, but they’ve since been superseded by more developed theories. FFF doesn’t reference Thomas Kuhn’s “The Structure of Scientific Revolutions” directly, but it’s covering the same ground.
String theory came about through a revolution in Quantum Field Theory, or QFT, in the 60s and 70s. It promised to resolve some anomalies involving infinities. QFT described some particle interactions using “Feynman diagrams”, basically just tracing the paths of particles over time. But when the diagrams had loops in them, QFT’s math could get really weird. Sometimes calculations even diverged, producing infinite answers. The actual energies involved are definitely finite, so a new approach was needed. String theory offered that new approach by transforming the lines of Feynman diagrams (figure 1-10) into surfaces and tubes (1-11).
Penrose’s illustrations are just the right blend of information and aesthetics.
In the old diagrams, particles had been represented by points, tracing out lines over time; in the new theory, particles had to be represented by little lines and loops, which would trace out surfaces and tubes over time, like filament coming off a 3D printer. These line-particles were termed “strings”, and a new string-y theory of QFT—“string theory” for short—had been born.
Changing particles into strings solved some of QFT’s big problems. It also had some really neat, elegant mathematical features. String theory’s tubes and surfaces could be modeled with certain well-behaved, well-understood sets of complex numbers called Riemann Surfaces. It seemed possible that, if string theory were pursued to its conclusions, the laws of physics could be shown to emerge from the beautiful mathematics of these surfaces. An elegant Theory Of Everything™ could be in the offing.
Everyone—Penrose included—was excited and intrigued by these developments. But like the theories before it, string theory came with anomalies of its own. When combined with the rules of quantum mechanics…
Something bad happened? An “essential…parameter invariance” was threatened, “without [which] the mathematical description of the string failed to make proper sense as a theory of strings…” OK, I’m out of my depth. Let’s stick with “something bad happened,” and whatever the exact problem was, it threatened to undermine the mathematical elegance that had been part of string theory’s appeal.
String theorists had a fix, but it was pretty outlandish. The math could be made to work out again… if the strings were allowed to travel through extra dimensions in space. String theorists eventually came up with models that required only 6 extra dimensions (on top of the normal 4), but their original model required a total of 26 dimensions!
If that alarms you, you’re in good company—Penrose thinks that this “solution” creates far more problems than it solves. Adding extra dimensions involves introducing far more “functional freedom”, that mathematical concept he introduced in the appendix, and that’s bad because…
Because…
Crap, am I getting Eulered? Penrose lays out a series of problems with the 10-dimensional approach, all of which seem damning enough. Apparently, the theory conveniently can’t be tested at available energies; there are multiple versions of the theory, none with any clear advantage over the others; string theory may even fail to resolve those troublesome divergences in QFT it was invented to address! The allegations are serious. However, the reasoning he supports them with is uncharacteristically thin. For one of his objections, Penrose doesn’t present reasoning at all, and merely cites one of his own papers (co-authored with Stephen Hawking), nakedly asserting that the paper proves a high-dimensional string universe would “crumple” almost instantly.
Part of me is grateful that Penrose didn’t make the math even more complex by carefully backing up each of his arguments. And if he had, it’s not as if I would be qualified to evaluate them. But it was still demoralizing to feel totally unable to engage with what he was saying. The joy of reading FFF usually comes from Penrose’s ability to accessibly explain complex ideas within a coherent narrative. Judging by that metric, this was a low point in the book.
In any case, because of the various objections he raises, Penrose believes that string theory is overdue for retirement, or at least de-emphasis. Enough problems and inconsistencies have built up within it that the best way forward is to throw out some of string theory’s assumptions and change tacks entirely. (In Kuhnian terms, the paradigm of string theory has built up enough anomalies that a revolution is in order.) And yet, instead of being reconsidered, string theory is ignoring its inadequacies while sucking up more money and attention than all its rivals combined, like a zombie leech on particle physics’ neck.
My words, not his.
While reading, I began to be skeptical about how dominant string theory really is. Among everyone I know who cares about physics, it’s something of a frequent punching bag for being “unfalsifiable”. Starting in 2006, a full ten years before the publication of FFF, legendary nerd cartoonist Randall Munroe (aka XKCD) was penning strips mocking string theory, calling its adherents brainless, and making fun of extra dimensions. String theorists seem like the butt of every joke in physics; if so, is it really possible they could wield so much power?
Having asked around, it seems like the answer is somehow a resounding yes. Everyone I asked said that string theorists get their studies funded, their articles published, and tenure-track positions offered, winning the intense competition for those critical career milestones. One of my relatives has a PhD in physics, and said one of the principal reasons he didn’t want to continue in academia was because of this dominance of string theory.
To play devil’s advocate—is this dominance really all that bad? Scientific revolutions are warranted now and then, but Kuhn thought most progress happened when scientists had a common frame of assumptions to work from, allowing “normal science” to occur. Maybe string theory is providing that right now, and there’s still plenty of normal science to do before changing paradigms! Penrose brings up new ideas in string theory, with fancy names like “AdS/CFT correspondence” and “M-Theory”, and says they don’t resolve the problems he’s pointing out. But this could indicate that string theory still has room to grow. The theory isn’t fully developed; isn’t that just all the more reason it should continue developing? Maybe the dominant paradigm still has the potential to bear fruit.
Moreover, if the paradigm were to shift, there’s no clear answer as to what it should shift to. If string theory is like the Newtonian theory of gravity, where is the superior theory of relativity to replace it? Penrose has his own favored approach, “twistor” theory, which I couldn’t understand at all. Even given that twistors have advantages, is the theory yet mature enough to support productive science? The following story from Chapter 4 is what most made me pause and reflect on the potential benefits of string theory as a common paradigm to work from, even if it’s flawed. Emphasis is mine:
Following the first of my Princeton lectures, as I recall, I was approached by a prospective graduate student in theoretical physics who seemed evidently troubled about what line of research he should pursue, and he wanted some advice…Like many others, he had found the ideas of string theory to be enticing; but he had been somewhat discouraged by the negative assessment in my talk…I was reluctant to suggest my own area of twistor theory as an appropriate alternative, not only because there appeared to be no one he could work with on the subject, but also because it was a difficult area for a student with aspirations to make some real progress.
Twistor theory has apparently developed since then—in part with assistance from some string theory ideas!—and I would guess that Penrose would unreservedly recommend twistors to that student today. But this might express part of the reason why agitating for a paradigm shift too early could cause more harm than good for the progress of science.
Penrose’s critiques of string theory ultimately ring true to me, especially because they echo the same critiques that have been repeated elsewhere. Nonetheless, it’s possible the main problem might not be the string theorists, and the burden is on non-string theorists to offer a definitively better alternative. Ultimately, Chapter 1 felt like the weakest in the book.
Faith
In Which Eliezer is Counted Among the Righteous
Having alienated the most powerful faction in physics with his salvo against string theory, Penrose next sets his sights on one of the most tested and respected theories in all of modern physics: quantum mechanics (QM).
Have I mentioned how great Penrose’s illustrations are? Oh, a couple of times now? Good.
I have far more familiarity with QM than string theory, but I won’t try to summarize it fully here, especially when there are far better resources available which I can reference for that purpose. I highly recommend this series from MIT OpenCourseWare on YouTube. The first few lectures, given by the highly engaging Professor Allan Adams, give an excellent overview of what’s weird about quantum mechanics, in more than enough detail to engage critically with Chapter 2 of FFF. Alternatively, longtime readers of this blog and members of the rationalist community might turn to the first four entries in Eliezer Yudkowsky’s QM sequence on LessWrong, which seeks to teach many of the same basic lessons about QM. But go any deeper into the sequence than that, and things get awkward.
The fifth entry of Yudkowsky’s sequence begins as follows (emphasis mine):
“Macroscopic decoherence—also known as ‘many-worlds’—is the idea that the known quantum laws that govern microscopic events simply govern at all levels without alteration.”
Yudkowsky thinks this is true. From the force of his language, he perhaps even thinks it should be an obvious truth to anyone who knows enough about QM. He rejects theories which postulate some “collapse” on “measurement” of a quantum superposition. Instead, he thinks that the universe is a wave-function, which frequently splits into different “worlds”, and that measurement simply lets us discover what part of the wave-function we’re in.
Penrose thinks this is false. He’s a bit more polite about it, saying at one point, “I do appreciate why many of those who hold unshakably to a total faith in the physical truth of the quantum formalism are led to holding such a standpoint.” Nonetheless, the bolded text above is the exact principle which he’s set against in Chapter 2, and which he thinks is motivated by that unjustified faith in the universal scalability of QM. He thinks that common experience, scientific precedent, and general relativity all imply certain limits which will prevent quantum laws from operating on macroscopic objects.
To defend this view, he first describes what QM is, and how it works. Again, to actually understand QM well, I highly recommend the MIT lectures above. But here’s a shorter, worse explanation for anyone without 25 hours to spare.
Sometimes, in well-isolated systems of small objects, it seems like different possible states of a system can interfere with one another. In one classic experiment, electrons are shot, one at a time, at a wall with two slits in it. After passing through, they hit a back wall. If we block one slit, electrons simply pass through the other one and strike the back wall in a smooth bell curve behind it. But if both slits are open, the pattern created on the back wall is weird and wavy. This wavy distribution is what we’d expect if we shot many particles at once and they interfered with one another, acting like a wave, perhaps because of electrical repulsion or bouncing off each other. But again, each electron was shot one at a time, so it seems like each one interfered with… itself? To speculate wildly—did it somehow become a wave in the middle? Did it deflect from another possible version of itself which took the other path? Did it go through both at once, and only decided which version of its history to “keep” once it hit the back wall? Or is asking what the electron does before being measured meaningless, since you can’t test it?
Physicists don’t agree about what the electron is doing as it passes through the slits, but they have an agreed-upon formula for predicting where it will end up. This formula involves treating both possible paths through the slitted wall as “superimposed”, so that a “wave-function” representing the electron is neither passing through slot A, nor slot B; it’s in a combined “here-or-there” state. If we put more obstacles in the electron’s way, there’s math we can do to the wave-function which will give us the odds of where we’ll locate the electron. But notably, once we “measure”—once we find it “here”—the “here-or-there” superposition state vanishes, and the “there” branch of it ceases to interfere with our reality.
Whether, how, and why this “here-or-there” superposition state “collapses” upon “measurement” may be the biggest open question in quantum mechanics: the Measurement Problem. The scare quotes around “collapse” and “measurement” are necessary; we’re in metaphysics territory now, so everyone disagrees about what the proper words to use are, and what they correspond to. Penrose is taking this problem on and proposing an answer.
Penrose contrasts his view with people like Yudkowsky (without naming him, of course). Many-worlders, or “Everettians”, believe that there is no “collapse” of the wave-function. Instead, measurement simply provides us information about which chunk of the wave we’re in, where the “chunks” represent different worlds where different possibilities are realized; and this coincides with “decoherence” of a previous world into two or more new non-interfering worlds, which continue to be superimposed behind the scenes.
This has always seemed far-fetched to me. We are supposed to believe that worlds remain superimposed (as linearity requires they must be), but don’t appear to interfere with one another. How can this be, when interference terms naturally arise from the quantum formalism starting from a superimposed state? Decoherence requires either a great coincidence canceling out those interference terms, or the discovery of some hitherto-unrecognized effect suppressing them. Yudkowsky appears to believe something like the second, whereby decoherence naturally occurs when only some of a superposition’s amplitude interacts with a larger environment, causing apparently-classical behavior without the loss of linearity and without a discontinuity.
(I know this has gotten significantly more technical and less accessible, and I apologize. Given that I’m criticizing a prominent rationalist’s views on a rationalist blog, I feel a need to go into more detail here than in the rest of the review.)
It seems like Penrose has similar concerns to mine about linearity being preserved in complex systems, and he cites precedents in science to back up his case. He says:
...universal linearity is highly unusual in physical theories. It was noted [earlier] that Maxwell’s equations for the electromagnetic field are linear, but it should be pointed out that this linearity does not extend to the classical dynamical equations of an electromagnetic field together with charged particles or fluids that are interacting with it. The complete universality of the linearity demanded by the [quantum]-evolution of present-day quantum mechanics is utterly unprecedented.
Apparently, Newtonian gravity has a similar loss of linearity in complex systems. The basic formulas satisfy linear equations, but the motion of three or more bodies cannot be predicted or described by linear equations. By analogy, even if the simplest description of the wave-function’s evolution is linear, that doesn’t mean that QM will remain fully linear in more complicated systems. The emergent behavior can be non-linear.
Penrose also advances a far simpler argument against Everettian views: we do not perceive ourselves to be in superpositions. He invokes the old example of Schrödinger’s Cat, asking what someone observing a superimposed cat would experience, and commenting:
…It is argued (not very logically, in my view) that the observer’s experiences “split” into two coexisting individual un-superposed experiences. My problem, here, is that I do not see why what we call “experiences” need to be un-superposed. Why should an observer not be able to experience a quantum superposition?
We don’t seem to interact or interfere with other possible versions of ourselves, or anything of the sort, nor do we seem to experience a superposition between two experiences at the same time. Along with Penrose, I think a many-worlds picture should imply that some of those things happen. An additional explanatory burden, then, is placed on many-worlders to explain why such things don’t seem to happen.
“Yes, of course, cats should be in the most super positions.”
After expressing this skepticism about universal linearity, Penrose outlines a theory which he thinks can better explain when and why collapse, or “spontaneous decay”, of a superimposed state occurs. The evolution of the wave-function happens over time. But in general relativity, time coordinates are defined differently for objects based on their gravitational fields. So for two potential outcomes in a quantum superposition, the more their mass is displaced from one another, the more out of whack their time coordinates will be, destabilizing the superimposed state until it eventually collapses. This offers a well-defined, testable reason why massive objects on macro scales don’t do weird quantum stuff. I have no idea whether it will pan out experimentally, but I find myself somewhat optimistic about the theory.
All in all, Penrose’s discourse on QM was positively enlightening. Parts of it brought on that miraculous feeling of seeing my own half-formed thoughts given beautiful expression, making Chapter 2 the highlight of FFF for me. It helps that Penrose took a comprehensible position on a well-defined issue—and I found myself fully convinced.
Perhaps not coincidentally, out of the three fields Penrose discusses, I know QM the best. This is my strongest data point in favor of the book not Eulering me. The more I know about a topic, the more reasonable Penrose’s arguments sound! It’s like the opposite of Gell-Mann Amnesia. Because his arguments seem stronger the more I know, it seems likely that his arguments are uniformly strong, and if/when they seem weak, the real problem could be my ignorance.
However, Chapter 2 isn’t all sunshine and roses on the comprehensibility and accessibility front. Penrose spends a subchapter or two talking about functional freedom in the context of QM, and it’s totally incomprehensible to me. Just when things were going so well. C’est la vie, let’s move on.
Fantasy
Why Inflation is Ruining Everything
A friend once joked to me that physics is the study of things that are either very very small or very very large. Having spent two-thirds of FFF dealing with very small scales, Penrose now sets his sights on the big side of things, seeking to correct the record in cosmology.
Penrose’s mandate for Chapter 3 is taking on “fantastical” ideas in cosmology which have more of a wishful than a rational basis. Eventually, he’ll reach the main target of his criticism: the theory of cosmic inflation.
No, not THAT inflation.
He takes his time getting there, though. On the way, he touches on what seems like every major idea in cosmology, embarking on a wide-ranging survey of the universe’s history, shape, and fate, taking pot shots at unlikely views as he goes. I’ll give an overview of some major points.
The topology or “shape” of the overall universe, as well as its size (finite? infinite?), appear to be open questions. The shape is important, since the curvature of the shape can determine whether a universe expands indefinitely, remains stable, or eventually “crunches” back down into a singularity. However, because of a positive “cosmological constant” 𝛬 in our universe, these geometrical effects are totally overridden, and physicists expect that the universe will expand at an accelerated pace as time passes. And even if it were to “crunch”, Penrose finds the idea that it could then “bounce” into a new Big Bang and new universe implausible. It would most likely just collapse down into a singular state (like a black hole) and stay there.
In that context, Penrose introduces a concept he’ll lean on throughout the rest of Chapter 3: that of entropy. A given system of particles has high entropy if there are lots of other configurations of those particles which look the same at a glance. In other words, low entropy states are “special”, whereas high entropy states have lots of closely similar states, and are usually more hot and chaotic. The Second Law of Thermodynamics, which is a feature of virtually every system we know of, says that entropy is overwhelmingly likely to increase with time, since the odds of a “special” state fluctuating into existence from a less special state is virtually nil.
These definitions create a thorny problem for cosmology. Hot and chaotic states have high entropy, and the Big Bang was the hottest and most chaotic of them all. So did the Big Bang have singularly high entropy? If so, wouldn’t going from there to the state of the universe today—a less hot, less chaotic state—violate the Second Law of Thermodynamics? The solution lies in the distribution of mass, which was apparently spatially uniform originally. Uniform distributions of space are low-entropy; gravity bringing mass together increases entropy. So while thermal entropy was high in the Big Bang, gravitational entropy was very low, and gravity makes a much greater contribution to overall entropy. As matter coalesced into stars, planets, and especially black holes, there was a vast increase in overall entropy, even as the universe cooled from its initial temperature.
After hitting on all of these topics, we finally arrive at cosmic inflation, Penrose’s main “fantastical” target of Chapter 3. The dominant account of the universe’s history currently includes inflation, to the point where cosmology classes and textbooks often teach it as established fact instead of one theory among others. And Penrose is careful to point out that, much like string theory, the theory solves some problems even as it creates others. He credits it with predicting that the universe has no curvature, which is supported by the most recent astronomical observations. But with all that acknowledged, he himself doesn’t believe in inflation.
Penrose’s objections mainly focus on entropy. Inflation was invented to try to explain some puzzling features of the universe, such as how the universe got as smooth in its distribution of matter as it appears to be today. The theory’s answer is that the universe, well, inflated—that for a very short period of time, the cosmological constant 𝛬 (from earlier, the one accelerating the universe’s expansion) suddenly became huge, expanding the universe greatly and “smoothing” things out. But as Penrose covered earlier, smooth, uniform distributions of matter have low entropy. For inflation to take a high-entropy “lumpy” state and turn it into a low-entropy “smooth” state violates the Second Law of Thermodynamics, which Penrose thinks makes the theory enormously implausible.
Penrose notes that some inflationists can respond by invoking the Anthropic Principle. Essentially, this says that even if the Second Law of Thermodynamics makes the random generation of an inflated region arbitrarily unlikely, in an infinite universe (or multiverse, though Penrose scorns that idea), such inflation will still occasionally happen. If this inflation is the only way to create a low-entropy area that can support life, then living organisms will always live in a post-inflation region, since however unlikely that region’s creation is, it’s a precondition for those observers to exist.
Penrose’s response? This proves too much; starting from the same assumptions, you can derive absurdities. If you think your region fluctuated into existence randomly, it is far more likely that it did so yesterday than a billion years ago, since by the Second Law of Thermodynamics, yesterday is a higher-entropy state, and therefore more easily randomly generated. What’s more, if “inflated regions” capable of supporting life can fluctuate into existence randomly, the exceedingly vast majority of such regions will be of the absolute minimum size necessary to support life. In the limit of this argument, you are overwhelmingly likely to not actually be a human, but to be a “Boltzmann Brain”, gray matter that popped into existence to experience only the illusion of the present moment before dying from cosmic exposure.
Even given the Anthropic Principle, an inflated universe filled with observers is exceedingly unlikely relative to one filled with Boltzmann brains individually inflated into existence.
Penrose treats this as absurd, and thinks any theory implying it must be false. The implication of Boltzmann Brains “points to the futility of seeking explanations of an anthropic type for the low-entropy requirements of our actual universe.” But I wish he’d justified that more carefully. Is a universe with Boltzmann Brains actually all that ridiculous? I confess that I’m torn on the question.
It would certainly be troubling. It would imply that everyone should always think they are almost certainly not who, what, or where they think they are. It would also imply that our experiences don’t result from our senses; most brains would fluctuate into existence experiencing and believing totally random things with no connection to reality. Perhaps this is sufficient reason to doubt the theory. Can you ever be warranted to believe something which implies that all your beliefs are unwarranted? I think not, and I lean towards rejecting the possibility of Boltzmann Brains for this reason. Nonetheless, not everyone likes pragmatic arguments like these, and there’s plenty of room for debate on the topic.
But perhaps it’s good that Penrose didn’t get sucked down that rabbit hole; Chapter 3 is already busy enough. In a word, I’d call it eclectic. Penrose bounces back and forth between the many views he wants to discuss and knock down, making for a somewhat chaotic read. I hardly covered half of the topics he touched on! At one moment, you’re reading about the topology of the universe; the next, you’re reading about how maybe 𝛬 doesn’t need a physical explanation; and then suddenly, you find yourself in the middle of what feels more like philosophy than physics.
Nonetheless, I loved Chapter 3. Everything it talks about is fascinating. In writing this review and deciding what I was and wasn’t going to cover, it was really difficult making cuts. I don’t blame Penrose for having a hard time narrowing down his subject matter too! For all its seeming distractibility, I think this is the chapter that the average rationalist-inclined reader would enjoy the most, especially in contrast with Nick Bostrom’s writings on the Anthropic Principle.
Finally—the ever-present question in this book: am I just getting Eulered? I still don’t think so. While the theories he’s discussing are complex, the core objections he makes are simple and accessible, such that they can be evaluated and critiqued even by laymen. And while Penrose speaks from authority in places in this chapter, I’m inclined to believe he’s earned that right. After all, he won the 2020 Nobel Prize in Physics for work in cosmology. If you’re going to trust anyone on this topic, it might as well be him.
Conclusion
2/10, functional freedom wasn’t mentioned enough
Would I recommend “Fashion, Faith, and Fantasy” to you? Before answering, I’d ask you two questions.
First, did you fall asleep before reaching the end of this review? If not, then you might not be the kind of person who would enjoy engaging with FFF. Books on theoretical physics have narrow appeal, and FFF is no exception. Still, Penrose works hard to make it fun throughout, with amusing asides and gorgeous art. If you’re still with me, you might enjoy a theoretical physics book, and this one is as entertaining as any other in the genre.
Second, do you know what the mathematical definition of a subspace is? If not, you might want to look elsewhere. For example, Penrose’s buddy Stephen Hawking wrote a book covering the same topics which is much more accessible; it goes lighter on the math and heavier on the illustrations. I realize this might sound condescending. “I don’t think you’re educated enough for Penrose. Here, try Hawking’s picture book!” But quite honestly, I wasn’t smart enough for FFF—not really—and I suspect that if you haven’t gotten through at least a linear algebra class, you won’t have any fun at all trying to read it. Even if I feel like an asshole, I’m obligated to ask whether you’re mathematically prepared for this book.
If you answered “yes” to both questions, I would wholeheartedly recommend it to you. Roger Penrose is really, really smart. If you want to be exposed to the inner workings of his gigantic wrinkly brain, and if you’re prepared to feel at least a little dumb yourself, pick up “Fashion, Faith, and Fantasy in the New Physics of the Universe.” Even if you get as lost as I did, you’ll at least see some beautiful illustrations on your journey through it.
The incorporated quotes and visuals are included for purposes of criticism, commentary, and transformative humor, all of which are purposes covered by “fair use”. Rights to said content remain reserved to their original holders. The cat is mine.
