Our Mathematical Universe

by Max Tegmark

  Yet the complexity of all this pales in comparison to the patterns of information processing in your brain. As we discussed in Chapter 8 and illustrated in Figure 8.7, your roughly hundred billion neurons are constantly generating electrical signals (“firing”), which involves shuffling around billions of trillions of atoms, notably sodium, potassium and calcium ions. The trajectories of these atoms form an extremely elaborate braid through spacetime, whose complex intertwining corresponds to storing and processing information in a way that somehow gives rise to our familiar sensation of self-awareness. There’s broad consensus in the scientific community that we still don’t understand how this works, so it’s fair to say that we humans don’t yet fully understand what we are. However, in broad brushstrokes, we might say this: You’re a pattern in spacetime. A mathematical pattern. Specifically, you’re a braid in spacetime—indeed one of the most elaborate braids known.

  Figure 11.4: Complexity is a hallmark of life. The motion of an object corresponds to a pattern in spacetime. An inanimate clump of ten particles accelerating toward the left constitutes a simple pattern (left), while the particles that make up a living organism constitute a complex pattern (middle), corresponding to the complex motions that accomplish information processing and other vital processes. When a living organism dies, it eventually disintegrates and its particles separate from each other (right). These crude illustrations show merely ten particles; your own spacetime pattern involves about 1029 particles and is mind-blowingly complex.

  Click here to see a larger image.

  Some people find it emotionally displeasing to think of themselves as a collection of particles. Indeed, I got a good laugh back in my twenties when my friend Emil addressed my friend Mats as an atomhög, Swedish for “atom heap,” in an attempt to insult him. However, if someone says, “I can’t believe I’m just a heap of atoms!” I object to the use of the word just: the elaborate spacetime braid that corresponds to their mind is, hands down, the most beautifully complex type of pattern we’ve ever encountered in our Universe. The world’s fastest computer, the Grand Canyon or even the Sun—their spacetime patterns are all simple in comparison.

  Whereas many of the particles inside you are in the constant complex motion that corresponds to your being alive, others move only in less-elaborate ways, such as many of the ones that make up your skin and help keep the other particles from flying apart. This means that your spacetime tube is a bit like those electrical cables where the inner strands are braided together and the shared insulation on the outside resembles a hollow tube. Moreover, most of your particles get regularly replaced. For example, about three-quarters of your body weight is water molecules, which get replaced every month or so, and your skin cells and red blood cells are replaced every few months. In spacetime, the trajectories of these particles joining and then leaving your body make a pattern reminiscent of the familiar silk strands attached to a corncob. At both ends of your spacetime braid, corresponding to your birth and death, all the threads gradually separate, corresponding to all your particles joining, interacting and finally going their own separate ways (Figure 11.4, right). This makes the spacetime structure of your entire life resemble a tree: at the bottom, corresponding to early times, is an elaborate system of roots corresponding to the spacetime trajectories of many particles, which gradually merge into thicker strands and culminate in a single tubelike trunk corresponding to your current body (with a remarkable braidlike pattern inside as we described above). At the top, corresponding to late times, the trunk splits into ever-finer branches, corresponding to your particles going their own separate ways once your life is over. In other words, the pattern of life has only a finite extent along the time dimension, with the braid coming apart into frizz at both ends.

  All of the patterns we’ve discussed of course exist in four dimensions rather than three, and the metaphors about braids, cables and trees, shouldn’t be taken too literally. The key point is simply that you can be an unchanging pattern in spacetime—the specific details of this pattern are less important for the points we’re making. This pattern is part of the mathematical structure that is our Universe, and the relations between different parts of the pattern are encoded in mathematical equations. As we saw in Chapter 8, Everett’s quantum mechanics endows you with an even more interesting—but no less mathematical—structure, since a single you (the tree trunk) can split into many branches, each feeling that they’re the one and only you—we’ll return to this later.

  Living in the Moment

  Now we’ve discussed how space itself, the stuff in space and even you yourself can be a part of a mathematical structure. But this came at a price: we had to abandon the familiar feeling that time flows as a mere illusion, and instead think of time as a fourth dimension in an unchanging mathematical structure. So how can we reconcile this with our subjective experience that things change from one moment to the next?

  All your subjective perceptions exist in spacetime, just as every scene of a movie exists on its DVD. Specifically, spacetime contains a large number of braidlike patterns corresponding to subjective perceptions both at different places, corresponding to different people, and at different times. Let’s refer to each such perception as an “observer moment.” I coined a different name for this in my 1996 mathematical-universe paper, but I like observer moment better, and Nick Bostrom and other philosophers have established it as the standard term in recent years. You know from experience that some of these observer moments feel connected and fused together into a seemingly seamless sequence, corresponding to what you call your life. However, this feeling raises tough questions. How does the connecting work? Specifically, is there some sort of rule for which observer moments feel connected, and why does this connected sequence of observer moments subjectively feel like time flowing?

  An obvious guess could be that the connecting has to do with continuity: that two observer moments feel connected if they’re adjacent in spacetime and part of the same pattern. However, Figure 11.5 illustrates that the question is trickier than it first seems, and that the answer can’t be this simple. First of all, the observer moment (labeled C) corresponding to my waking up feels connected to the one (labeled B) corresponding to my falling asleep. Specifically, it feels to me as if C is the continuation of B, even though these two observer moments are nowhere near each other in spacetime. Second, there are many other observer moments (corresponding to perceptions of other people on my flight) that are much closer to C in both space and time, so why doesn’t C instead feel connected to one of those observer moments? Third, imagine a perfect clone of me being assembled while I’m sleeping, with all the particles in the same configurations, except located in another identical-looking airplane. Then the subjective perception of my clone upon awakening will be subjectively identical to the one I have at C, so by definition, it too feels connected to B even though its spacetime pattern isn’t.1

  Figure 11.5: My world line when flying to London. I take off (A), fall asleep shortly thereafter (B) and wake up (C) shortly before landing (D). Even though my conscious perception at (C) is at a different point than (B) in both space and time, it appears to connect seamlessly with my last conscious perception at (B), but not with the many other conscious perceptions (of fellow passengers) that are much closer to (C) than to (B) in both space and time.

  Click here to see a larger image.

  This suggests that the continuity business is a red herring, and that there simply is no new physical process to be discovered that somehow makes certain observer moments feel connected, thereby explaining our familiar feeling that time flows. Fortunately, there’s a simpler explanation that doesn’t require any new physics, which we’ll now explore. The Mathematical Universe Hypothesis combined with our subjective experience tells us that there are very complex braidlike structures in spacetime that are self-aware and subjectively feel like observer moments. We know that these structures can be quite localized both in space and in time: your brain occupies j
ust over a liter of volume, and the time it takes for your brain to have individual thoughts or sensations is typically about a tenth of a second, give or take a factor of ten. This means that how an observer moment subjectively feels depends only on what’s right there in that localized region of spacetime—not on what’s elsewhere in space (such as the external reality you see around you), and not on what’s elsewhere in time (such as what you experienced a few seconds ago). Yet crucial components of your conscious perceptions involve both of those: right now, you feel aware both of the book in front of you and of the sentence that you read five seconds ago, even though neither belong to the small spacetime region constituting your present observer moment. In other words, it appears that the way your observer moment subjectively feels involves what’s elsewhere in both space and time—even though it wasn’t supposed to involve either. How can this be?

  Figure 11.6: The subjective perceptions in spacetime (observer moments) of a diver and a skier at four separate times. Each film strip corresponds to a single observer moment, including both a clear image of what’s currently happening, and progressively hazier memories of what happened in the past. If I’d rearranged the eight strips in a random order, you could easily reconstruct the sequences because of relations between them: the current visual impressions (right frame) in some observer moments match memories in others.

  We discussed the spatial part of this paradox in Chapter 9, and concluded that your consciousness is actually observing not the outside world, but rather an elaborate reality model contained in your brain which is continually updated via input from your sensory organs to track what’s actually taking place in the outside world.2 So the spacetime pattern corresponding to your current observer moment includes the state of your reality model right now. As illustrated in Figure 11.6, it’s quite analogous for the temporal part: your world model includes not merely information about the present state of your surroundings, but also memories of how your surroundings were in the past. Each of the eight film strips represents a single observer moment. For each one, there’s a clear image of what’s currently happening, and progressively hazier memories of what happened in the past. You’re therefore aware of an entire time sequence of events right now at this very moment. Just as your spatial-reality model gives you the subjective feeling of looking at a three-dimensional space even though your mind is actually looking at the reality model in your brain, this temporal-reality model with its sequence of memories gives you the subjective feeling of time flowing through a sequence of events even while your mind is actually looking at the reality model in your brain in a single observer moment.

  In other words, your subjective feeling that time is flowing comes from the relations between these memories that you have right now. Imagine a thought experiment where a perfect clone of me is built asleep, complete with all my memories, and is only woken up long enough to perceive a single observer moment. He’d still feel that time flowed from a complex and interesting past, even though he got to experience only that one moment. This means that the subjective perceptions of duration and change are qualia, basic instantaneous perceptions just as redness, blueness or sweetness.

  This implication of the Mathematical Universe Hypothesis is pretty radical, so please pause your reading for a moment to take it in and think about it. What you’re aware of right at this moment feels not like a photo but like a movie clip. This movie isn’t reality—it exists only in your head, as part of your brain’s reality model. It contains lots of information about the actual external physical reality—as long as you aren’t dreaming or hallucinating—but still constitutes only a very heavily edited version of reality, akin to the evening news on TV, mainly featuring certain highlights of patterns nearby in space and time that your brain thinks are useful for you to be aware of.

  Just as when you watch news on TV, you’re not watching distant parts of space directly: you’re watching merely an edited movie about these parts of space. Similarly, you’re not watching the past, but an edited movie about the past. As opposed to watching the news during several minutes, you watch your internal newsreel all at once, thus being simultaneously aware of present and past events. A second later, you watch your internal newsreel once again, all at once, and it’s mostly unchanged like a TV rerun, but has been slightly re-edited to add another second of material at the end and shorten the remainder. In other words, even though an observer moment objectively occupies less than a liter of volume and a second of time, it subjectively feels as if it occupies all the space you’re aware of and all the time you remember. You feel as if you’re observing this space and time from here and now, but all that space and time are just part of the reality model that you’re experiencing. This is why you subjectively feel that time flows even though it doesn’t.

  * * *

  1If the assembly instructions for my clone were transmitted wirelessly from the body scanner that analyzed the original me, then the spacetime braids of me and my clone would still be connected by a very elaborate pattern in the electromagnetic field. But an identical copy of me waking up in the Level I multiverse of Chapter 6 would feel connected to C as well, without there being any information transfer between the two copies.

  2For a detailed discussion of time experience and the rich philosophical literature on the subject during the past two millennia, see http://plato.stanford.edu/entries/time-experience. In particular, the idea that key aspects of time perception such as duration can only be explained as perceptions of our memory were explored about 1,600 years ago by Saint Augustine; the Mathematical Universe Hypothesis gives such questions a new urgency.

  Self-Awareness

  Moreover, you too are in the movie, since your reality model includes a model of yourself—that’s why you’re not merely aware but also self-aware. This means that when you feel that you’re looking at this book, what’s really going on is that your brain’s reality model has its model of you looking at its model of the book, as illustrated in Figure 11.7. Which leads to the ultimate consciousness question: who’s looking at your brain’s reality model, to give rise to subjective consciousness? Here’s my guess: nobody! If there were another part of your brain that really looked at the whole reality model and became aware of all the information in it, then this brain region would need to physically transfer all that information into its own local copy. This would be a huge waste of resources from an evolutionary perspective, and there’s no evidence from neuroscience research of such wasteful duplication. Moreover, it wouldn’t answer the question: if a spectator is really needed, then this duplicate reality model would in turn need a spectator to be subjectively perceived, leading to another infinite regress problem.

  Figure 11.7: I think that consciousness is the way information feels when being processed in certain complex ways, and that the particular kind of consciousness that we humans subjectively perceive arises when your brain’s model of you is interacting with your brain’s model of the world. The arrows above indicate information flow. For example, information input from your senses continually helps your world model track key aspects of what’s actually going on in the external reality, and information output via your motor cortex controls your muscles to affect the external reality, say, by turning a page in this book.

  Rather, my guess is that the answer is beautifully simple: no spectator is needed, because your consciousness basically is your reality model. I think that consciousness is the way information feels when being processed in certain complex ways. Since the different parts of your brain interact with each other, different parts of your reality model can interact with each other, so the model of you can interact with your model of the outside world, giving rise to the subjective sensation of the former perceiving the latter. When you’re looking at a strawberry, your brain’s model of the color red feels subjectively very real—and so does your brain’s model of your mind’s eye as an observing vantage point. We already know that our brain is astonishingly creative in interpreting the same basic t
ypes of electrical signals in a bundle of neurons as qualia that subjectively feel completely different: we perceive them as colors, sounds, smells, tastes or touches, depending on whether the neuron bundle comes from our eyes, ears, nose, mouth or skin. The key difference lies not in the neurons that carry this information, but in the patterns whereby they’re connected. Although your perception of yourself and your perception of the strawberry are extremely different, it’s therefore plausible that they’re both fundamentally the same kind of thing: complex patterns in spacetime. In other words, I’m arguing that your perceptions of having a self, that subjective vantage point that you call “I,” are qualia just as your subjective perceptions of “red” or “green” are. In short, redness and self-awareness are both qualia.

  Predicting Your Future

  One of the key purposes of science, and indeed one of the key purposes of having a brain, is predicting our future. But if time doesn’t flow, then what do we even mean by predicting our future?