The Allure of Speculative Cosmology

Our Mathematical Universe:  My Quest for the Ultimate Nature of Reality

Max Tegmark

Vintage Books, 2014
My shelves are littered with many books like this one—I have long harbored an interest in astronomy, astrophysics, cosmology, quantum mechanics, and so on.  My grandmother first introduced me to the night sky with a pair of binoculars (I still own them) and rudimentary star charts, and the love took hold.  In fact, responding to my keen interest, my college astronomy professor once mapped out an entire physics curriculum, and I sometimes muse about how things might have turned out had I gone that path.

Every year or two I pick up the recent work of a prominent scientist or scientific author, to follow his or her particular tour through historical and modern physics and cosmology, enjoying and profiting from a slightly different take on the web of theories and observations that compose the field.  Tegmark’s book had been out for some time without my notice, and I was delighted to discover it under the tree last Christmas.

The thesis of the book is simple, but its defense is so expansive as to stagger the attempt to sum it up succinctly.  Cosmology, the primary topic here, typically draws from many disciplines and ranges widely, from subatomic particles to microwave background radiation.  This is no different.  Tegmark weaves together concepts from astrophysics, quantum mechanics, information theory, thermodynamics, relativity, cognitive theory, inflation and others to illustrate and support his primary point:  the universe is a mathematical structure.  Not merely described by a mathematical structure, but actually a mathematical entity, like some super-complex cube from high-school geometry come to life.  Mathematics IS reality, not simply a useful tool for describing it.

Philosophers of science have sometimes contemplated the utility and ‘spooky’ success of mathematics, not only for describing scientific results but frequently predicting them, leading the way.  For example, nineteenth century mathematicians explored strange non-Euclidean geometries, with no reference to or interest in any known physical phenomenon, inadvertently creating the exact tools Einstein needed to describe spacetime decades later.  It is also common throughout the natural and physical world for objects to exhibit mathematical symmetries and ratios.  Today’s extant scientific theories, moreover, are constructed around a mere 32 numerical constants, and the intrinsic properties of subatomic particles are purely mathematical in nature.  All of this suggests to Tegmark that the utility of mathematics goes beyond mere description.

Tegmark organizes the book around several themes to make his case.  First, an historical account of modern science and the successful theories that have emerged, from Galileo to Newton to Einstein to Schrodinger to Hubble to Gamow to Guth and many others.  Scientists discovered that the universe is both large and expanding, that it likely emerged from a ‘Big Bang’ nearly 14 billion years ago, that space and time are relative concepts, that the behavior of the fundamental particles composing everything is ‘probabilistic’, and that at certain times space itself has been stretched prodigiously with significant consequences.  The tale is fascinating, over time repeatedly swinging from confidence to crisis, from new discovery to renewed breakthrough.  And that cycle is likely to continue indefinitely, even as science gradually achieves greater understanding.  In recent decades, for example, the science community has begun to grapple with so-called ‘dark’ energy and matter, the presence of which are known through their effects, but which no one has observed directly and which may in fact comprise about 96% of the mass of the universe.

Predictions borne out by observation and experiment are the basis for scientific success, yet Tegmark notes that the major theories also predict phenomena that have not yet been verified observationally.  Such predictions must be taken seriously (albeit with some scepticism too) since they arise from theoretical frameworks whose other predictions have indeed been verified.  For example, theory predicted black holes decades prior to proof of their existence—only recently have research teams successfully imaged one.

Likewise, modern theory predicts the existence of various flavors of parallel universes, commonly referred to as the multiverse, and Tegmark arranges his argument around four distinct types.  Distant regions, beyond the reach of our most powerful telescopes, form the Level I multiverse.  Inflationary theory delivers Level II, a collection of ‘pocket’ universes forever separated from one another by newly inflating regions of space.  Schrodinger’s wave function provides the basis for the Level III multiverse.  In contrast to the so-called ‘Copenhagen interpretation’ of quantum mechanics, Tegmark (following his intellectual hero Hugh Everett) asserts that the wave function never collapses, instead hiving off a new universe into Hilbert space at each decision point (you’ll have to read the book for details).  Finally, Tegmark proposes the Mathematical Universe Hypothesis (MUH), the basis of what he refers to as the Level IV multiverse.  Since in his view the external reality is fundamentally mathematical, every known (as well as unknown) mathematical structure constitutes its own parallel universe.  Simple structures, like the high-school geometry cube, form dull and uninteresting universes, incapable of supporting intelligent life, for example.  More complex structures form more robust universes, including the one we happen to inhabit.  Our current understanding of that structure is only partial, but expanding as scientific theories converge.  In Tegmark’s view, the eventual ‘theory of everything’ that, for example, should unite quantum mechanics and gravity will in effect become the description of the mathematical structure in which we find ourselves.

For creatures that evolved on the savannah, with perceptual equipment and cognitive capabilities adapted for survival in that environment, parallel universes, wave functions, particle superposition and even mathematical structures are difficult to grasp and nearly impossible to visualize or comprehend since they have no apparent analogue or relationship to daily existence at human scale.  The second theme of the book, more subtle than the first, addresses this challenge while simultaneously advancing the case for the MUH.  Humans often fall into the trap of believing they are looking out on the world as it is.  Cognitive science, however, demonstrates that one’s ‘inner eye’ is really observing a model of the world maintained by the brain, a model that is updated by ‘qualia’, data from the senses.  Not only is this ‘internal reality’ subject to illusions and distortions stemming from errors of perception, it also requires humans to invent short-hand or approximations (human ‘baggage’ is Tegmark’s term) to describe and interact with the world outside.  We experience our ‘inner’ reality directly, and we associate with others through a ‘consensus’ reality—where we all generally agree that red is red, a chair is a chair, time flows forward, and so on.  Tegmark describes an entirely ‘external’ reality and proposes the External Reality Hypothesis (ERH), in which every element is described in a way that is completely free of ‘baggage’, concepts or even names.  All that exists here are abstract elements and the relations between them, mathematical structures in effect.  If one accepts the ERH—not too controversial in Tegmark’s opinion—then one should at least contemplate accepting the MUH.

This book covers a lot of ground—far more than one can reflect in a short essay.  Stating the thesis is relatively simple, but explaining how Tegmark justifies and defends his views requires exponentially more.  Along the way, Tegmark points out how the complete Mandelbrot set is described entirely by a single equation, or just a few bytes of information.  Chop off a small piece of it, however, and the description now requires many more bytes of information, possibly gigabytes.  The book is a bit like that.

So I have omitted discussion of many details and fascinating elements, including the final chapter, where Tegmark indulges a number of his existential fears and hopes and ends by begging the reader to adopt a ‘scientific lifestyle’.  It certainly lives up to its Adamsian title of ‘Life, Our Universe and Everything’, ranging far beyond mere summation of the prior twelve chapters, and becoming Tegmark’s manifesto, cri de coeur and call to arms.  If nothing else, it certainly raises a host of interesting side ventures to investigate, and could become the subject of an essay in its own right.

Am I convinced that our universe is one of perhaps infinite mathematical structures populating the external reality?  No, but I am intrigued and enjoyed the read.  Frankly, I’m not qualified to pass judgement on much of the argument, nor do I believe there is sufficient evidence to claim definitive proof.  Tegmark doesn't. But nor in my view is that really the point of such a book, or really any book that pushes the bounds.  While admittedly speculative, the thesis is at least plausible—proceeding logically from well-defended axioms—and the book remains an entertaining review of modern science.  In any event, if I’ve learned anything so far, it is to expect few to none in the way of certainties, and to resist such expectations in the first place.  For all its success and material benefits, the scientific endeavor remains (and should always remain) tentative.  Would that more of us adopted such an intellectual stance.

Highly recommended.