In a broad sense of that term, reading Max Tegmark's Our Mathematical Universe is akin to a religious experience. I would not be at all surprised if Tegmark felt a similar sense of excitement in writing this massively learned yet wonderfully accessible book. For by the book's close, he found himself talking about the universe as a form of transcendence and advocating for the solemn ethical responsibilities humanity must undertake as likely one of the very few self-aware species in the galaxy.
On the level of my own religious perspective, I was deeply moved by Tegmark's work. But it is probably best first to recapitulate the main points of his argument. His claims go beyond ambitious -- they are truly audacious. Everything, he says -- our universe, and the many other universes with which it coexists -- are not only explainable mathematically but are in fact mathematical structures.
This sounds like a book that only a nerd would love. But that is not true. As Tegmark builds his narrative he makes his case in lucid prose, remarkably free of the equations and calculations that only a select few will ever comprehend. He nevertheless succeeds in building a compelling case that moves gradually from what we all know to be true about the universe until it finally pushes hard against the outer boundaries of human knowledge.
He begins with a couple of important premises. First, where cosmology is concerned, we must always be prepared to be counter-intuitive. It is not obvious to the casual observer that the earth should be round, or that it is in constant motion around the sun, or that all matter is composed of minutely-small subatomic particles. Careful observation, however, coupled with the willingness to break free of the conventional and obvious ways of thought, made these insights possible. Second, Tegmark insists that we should realize that the limits of what we know are constantly expanding -- the solar system was once the limit of our understanding, then the galaxy, and now the universe as demarcated by the cosmic background radiation left over from the Big Bang.
But, Tegmark continues, there is a reality lying beyond these observable limits. Theoretical physics points to the existence of a vast number of other universes that may never come into contact with ours but whose existence we may nevertheless infer.
Tegmark commences his explanation for how these other universes came to be with a discussion of "cosmic inflation." Inflation began as a hypothesis that sought to explain certain irregularities in the standard account of the Big Bang. It still rests upon a well-grounded assumption: "that once upon a time, there was a tiny uniform blob of a substance whose density was very hard to dilute" (p. 100). Because this primordial matter could not dilute, because its density remained nearly the same as it grew larger, it was capable of explosive, exponential growth. And while inflation remains a hypothesis today, empirical verification of its role in the formation of our universe is inching closer.
Our observable universe, Tegmark indicates, took its shape as inflation began to slow at least in our small corner of existence. But inflation, which is incessant, could reasonably be assumed to continue elsewhere and is still bringing into being countless other universes. And since its growth is exponential, the number of these other universes continues to double and to double again at an ever-increasing pace. Not all, or even most of these universes, likely obey the same physical laws as ours, and most are probably hostile and forbidding places. Still, their existence can be inferred from what we know about our own.
It is through inflation that we gain an awareness of the vastness of the cosmos and what Tegmark calls "Level One" and "Level Two" universes. Level One universes are those universes, scattered throughout the cosmos, whose physical laws resemble our own. We may never encounter them directly since inflation continually expands the distances between us and them, but it is likely that a process which continues to spawn universes at an exponential rate will bring into being other universes similar to our own. Level Two universes, like the first type, are also created by inflation, but are governed by different effective rules of physics than our own.
After probing the depths of space, Tegmark directs the reader's attention to the smallest bits of matter -- subatomic particles. It had been known for nearly a century that the smallest particles -- electrons and the like -- did not obey classical rules of physics. Had they, all atomic structure would have collapsed soon after the Big Bang. Something was responsible for preserving atomic structure, but what, exactly?
Tegmark draws on theories of quantum mechanics to assert that subatomic particles possess the capacity of being in more than one place at the same time, a phenomenon called "superposition." The movement of such particles, furthermore, is governed by the "wavefunction," which "describes the extent to which [they're] in two different places" (p. 179).
Why, then, do we not observe such behavior in our daily lives? The traditional answer, proposed by Niels Bohr and Werner Heisenberg, is that the act of observation collapsed the wavefunction "so that you find the object only in one place" (p. 178).
Tegmark, however, rejects the traditional account in favor of a more radical version of quantum mechanics. Why can't we more directly observe this sort of subatomic behavior? It has nothing to do with what we as observers bring to the process. Rather, it is the interaction of particles with one another that causes them to appear fixed in a process known as "decoherence." But, in optimal circumstances, it has become possible to detect electrons being in two places at one time: "if you pump out as many air molecules as possible with a good vacuum pump, an electron can typically survive for about a second without colliding with anything, which is plenty enough time for it to demonstrate funky quantum-superposition behavior" (p. 199).
These conclusions lead Tegmark to endorse Hugh Everett's controversial "many worlds" theory -- that in a process that remains undetectable subatomic particles "hive off" and bring into being new worlds that are almost exact copies as our own but that might differ in some crucial respect. Thus in some worlds we might be dead while in others we are the kings and queens of some exotic land. These many worlds Tegmark labels "Level Three" universes.
Tegmark has now prepared his readers for the final step in his reasoning. Subatomic particles, he asserts, are mathematical structures. And if they are mathematical structures, then everything which they support and form and order must also be a mathematical structure. Thus Tegmark is led to his "mathematical universe hypothesis."
Having now reviewed Tegmark's claims, I'd like to return to the dimension of religion. I am a Christian with some specialized training in ancient and medieval philosophy. And I find in Tegmark's arguments echoes of some very old ways of explaining existence.
The Greek philosopher Democritus (c. 460-370 BCE) proposed that all of existence was formed of invisible atoms. He even suggested the possibility of a multiplicity of worlds and universes that might be found on the far side of the firmament of stars we see in the night sky. By the second and third centuries BCE, we find the Stoics suggesting that this body of scientific knowledge reflected the existence of a God who was reason.
Early Christian writers borrowed this idea and made it a backbone of their own understanding of the universe. God is reason. Hence no science is alien to God. Many great medieval minds would have concurred -- thinkers like Albert the Great (c. 1200-1280) and Robert Grosseteste (c. 1175-1253) among many others. (None of this is to diminish the Church's role in sometimes violently stifling scientific inquiry as when Giordano Bruno was burnt at the stake.)
When I read Tegmark, I see traces of this very old way of understanding the divine. What else is mathematics but reason in its pure form? This is a commitment I share. God is reason. And since God is reason, there is no branch of inquiry where a believer should fear to tread.
This traditional account of God as reason has been obscured in a contemporary American context that is convulsed between dueling schools of fundamentalism -- simplistic, literal-minded religious zealotry on the one hand, and cool dogmatic atheism on the other. We must revive our commitment to a God that is reason if there is to be any hope of reconciling religion and science.
But if God is reason, there is yet one more thing that the Scriptures add. For revelation tells us that God is also love. While mathematics may tell us the form and shape and logic of all existence, it is as yet incomplete without love. For it is love that makes humanity a community, that calls for self-sacrifice and the sublimation of the personal for the good of something larger. If, as Tegmark argues, human life has meaning and significance even in the face of cosmic vastness, it is because we are, at least in our better moments, cooperative creatures capable of loving our neighbors as we do ourselves.
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