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I quite enjoyed Max Tegmark’s Our Mathematical Universe on a number of levels. While I thrilled at its concise and entertaining summaries of recent, consensus-backed theories about the observable universe — what a relief to finally understand the importance and implications of cosmic background radiation — I didn’t begin to grasp his much more personal ideas about reality’s ultimate nature until some weeks after finishing the book. This has given me a new, meditative model of the world and my place in it, and thinking upon it has provided a source of quiet comfort in turbulent times.
Tegmark doesn’t put it in so many words, but I understand the book’s eponymous conjecture this way: All of reality is a single, graphed-out equation, rendered in matter and energy rather than ink on paper.
A tiny equation like x = y describes, in three characters, a very simple yet boundless mathematical structure, in this case an infinite line: easy to conceive, predict, and work with, even if impossible to literally graph in its entirety. Tegmark, a physicist at MIT, feels certain that all of time and space, in its infinite vastness, maps to a mathematical structure with a similarly finite description — one short enough to fit on a T-shirt. (Clearly quite enamored with the notion of wearing the universal equation while a resident of said universe, Tegmark fantasizes about that T-shirt no fewer than three times within the book.)
In this view of reality having a single mathematical source, concepts like the flow of time, or motion, or randomness — or change of any kind — do not objectively exist. We subjectively perceive all these phenomena as living sub-structures within the whole super-structure, and in that sense, in our little line-segment view of our little slice of the graph paper, they are real and meaningful. But ultimate, objective reality contains every possible state of the universe, just like a graphed-out equation contains every possible point for which the equation holds true. These states exist outside of time, in the sense that time itself is just one axis of this graph.
In one latter part of the book, Tegmark invites the reader to consider the lifetime of an object — say, for example, the reader’s own body — as a collection of particles in three dimensional space, moving through time. Graph this phenomenon, and those punctiform particles stretch out along that fourth axis into noodles, all bound together so long as the object remains coherent. Now play it out further in either direction, and watch those noodles bind and braid together when the object comes into existence, and then fray out and go their separate ways when the object concludes its business, some distance upstream. In between these two ends, peer closely to see particle-noodles come and go as the object goes about its daily activity, taking in, transforming, or ejecting little bits of the universe.
If you feel up to it, you can try imagining the unimaginable fifth axis where each noodle bursts out into a fractal bush, representing every possible path through space that every particle can take, moment by moment, according to the law laid down by the one bit of math at the bottom of everything. Got that? Now zoom out a lot — all the way, keep going — so that the graph encompasses not just the one object’s little lifetime, with all its possibilities, but all the objects, everywhere, and everywhen, and everyhow. And when you arrive, there you have it: the single, unmoving, unchanging graph of everything. Bubble-trails in an infinitely complex but utterly static crystal. You are in it; every possible you is in it. And I am in it too, and every copy ever displayed of this blog post is in it (as well as every version I didn’t write but could have), and so’s Jesus and Buddha and Sappho and Carl Yastrzemski and everything that’s gonna happen to the memories of all of us, all together, forever.
To the best of my recollection, Tegmark avoids overt mention of any religion in Our Mathetmatical Universe, but it happens that I read this book in a period of exploration of religious traditions other than those I grew up with, made palatable through cultural filters nearer to hand. This includes Buddhist and Hindu thought as expressed by Alan Watts (discovered, yes, through the video game Everything), recent translations of ancient Chinese texts as guided by audio-book courses, and the color-saturated mashups up Eastern mysticism and contemporary cosmology found in Grant Morrison comics. None of these texts or teachers radically transformed the way I see reality, but I now feel that they made me pliable enough to consider Tegmark’s cosmic model, and find it surprisingly agreeable.
I may also have become more receptive due to some negative input: several months ago, I felt remarkably sour after listening to a radio piece about free will. The interviewer, using a narrow definition of the term, spoke to several physicists who all shot it down as a laughable or childish concept. They saw the universe as a complicated machine operating by wholly deterministic rules, each moment from the Big Bang until the Big Whatever entirely inevitable given the moment before, a ball rolling down a hill. The piece didn’t sit right with me, in part because I thought the question poorly asked, and I have yet to examine my distaste more deeply.
Why, then, does the superficially similar Tegmark model seem so satisfying to me? Clearly I dislike thinking of myself as riding through life on rails, fogged with the mere illusion of meaningful choice. But the alternate thought of every possible reality-state existing at once, which should also obviate the notion of choice, does not at all offend me in the same way.
I have long admired the hypothesis that the digits of π contain every conceivable number sequence, and thus every possible bit of numerically encodable information. The Tegmark model merely takes this one-dimensional concept and stretches it across a few additional directions, such that every possible universal snapshot might also be found, somewhere, in the graph of that elusive ultimate equation.
In this model, I don’t ride through life strapped into a mine-cart of irresistible physics. I don’t go anywhere. I just am, a static and eternal noodly swirl in a vast and unmoving map that is also its own territory that is the whole of everything that ever could be, according to a concise and immutable statement that one day I might indeed wear on a T-shirt.
And that makes me feel very peaceful.
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