by Max Tegmark
It’s then quite natural that the SAS will perceive only those aspects of the external reality that are useful for attaining its goals. For example, migratory birds perceive Earth’s magnetic field because it’s useful for navigation, whereas star-nosed moles are blind because visual perception isn’t useful for their underground lifestyle. Although what’s useful and thus perceived varies among species, certain basic considerations appear to be shared among all life-forms. For instance, it’s only useful to perceive aspects of the world that exhibit enough stability and regularity that information about them can help predict the future. If you’re looking out over a stormy ocean, perceiving the exact motions of trillions of water molecules would be rather useless because they tend to collide with each other and change directions within less than a trillionth of a second. On the other hand, perceiving that a humongous wave is headed your way is quite useful, because you can predict its future motion several seconds in advance and use this prediction to avoid getting flushed out of the gene pool.
In the same way, it’s useful for an SAS to perceive itself as being localized and unique, because information can be processed only locally. Even if there exists an identical copy of you a googolplex meters away, or in a decohered part of the quantum Hilbert space, no information can be transferred between the two of you, so both of you might as well keep things simple and act as if the other copy doesn’t exist.
We perceive that for which awareness is needed
Because the parts of our brain that model the world and our place in it (and give rise to consciousness) are very useful and in high demand, their use is mostly reserved for computations/decisions that really require them. Just as you wouldn’t use a supercomputer to run a word processor, your brain doesn’t use its consciousness module for mundane tasks such as regulating your heartbeat—they’re instead outsourced to other brain regions whose workings you’re not consciously aware of. This suggests that if a future robot becomes self-aware, it might remain unaware of self-contained rote tasks that don’t require access to its reality model (multiplying numbers together, say). The consciousness framework envisioned by Giulio Tononi explains how such unconscious cognitive outsourcing can work.
For us humans, I find it interesting that our bodily defense against microscopic enemies (our highly complex immune system) doesn’t appear to be self-aware even though our defense against macroscopic enemies (our brain controlling various muscles) does. This is presumably because the aspects of our world that are relevant in the former case are so different (e.g., smaller length scales, longer time scales) from that of the latter that sophisticated, logical thinking and the accompanying self-awareness aren’t needed.
When Are You?
Previously, we discussed how a mathematical structure can contain self-aware observer moments, such as the one you’re having right now, and we explored the challenges of finding these observer moments and figuring out how they subjectively feel. You exist in a mathematical structure containing some sort of spacetime, so to make physical predictions, you should try to learn what kind of mathematical structure you’re in and your current observer moment’s location in it: where in space and when in time are you? As we’ll see, the “when” part is even more subtle than the “where” part, particularly when the number of yous changes over time.
Beyond Popper’s Two-Timing
To me, science is all about understanding reality and our place in it. From a pragmatic perspective, it’s about building a model of reality that lets us predict our future as successfully as possible, so that we can choose to do what we predict will have the best outcome—my guess is that it’s to help accomplish this task that we’ve been fortunate enough to evolve consciousness. Thinkers throughout the ages have tried to formalize this scientific process, and I think most contemporary scientists agree that it boils down to this:
1. Make predictions from assumptions.
2. Compare observations with predictions, update assumptions.
3. Repeat.
We scientists often call a collection of assumptions a theory. In the MUH context, the key assumptions that go into the model of reality are what mathematical structure we inhabit and which particular observer moment therein is the one you’re experiencing right now. Karl Popper emphasized the second item on the list, arguing that assumptions that can’t make testable predictions aren’t scientific. Although he placed particular emphasis on falsifiability, i.e., that it should in principle be able to test whether scientific assumptions are false, there’s a beautiful mathematical toolkit known as Bayesian decision theory which generalizes the true/false dichotomy to allow shades of gray: each possible assumption gets assigned a number between zero and one, the probability with which you think it’s correct, and there’s a simple formula for how to update these probabilities whenever you make new observations.
As elegant and well accepted as it is, there’s a problem with this approach to science: it requires two connected observer moments. In the first, you make your prediction, and in the second you contemplate what you’ve observed. This works well in the conventional situation where there is, was and always will be at most one copy of you (Figure 11.8, left), but breaks down for any parallel-universe scenario where you have alter egos. As we saw in Chapters 6 and 8, this breakdown can lead to novel effects such as subjective immortality and subjective randomness (Figure 11.8).
In the MUH context, we’ve argued that the perceptions of time flowing and of assumptions and observations having been made, exist in every single observer moment that we experience. This means that we must transcend Popper’s two-time approach to science with a one-time approach that can be applied to a single observer moment. I like to imagine that I have this awesome pocket-sized remote control for reality itself. When attending a dull meeting, I can press the Fast-Forward button. When I experience something amazing, I can rewind and replay it as many times as I want. And to transcend Popper, I simply press Pause. Now I can, in the spirit of Horace, truly seize the moment, taking it in, absorbing it and reflecting on it without feeling rushed on toward the future. In particular, I can reflect on what I assume and what I observe. If my brain is working well, then I’ll find that my internal-reality model agrees well with the latest news that my senses are reporting from the outside world. And if my scientific-reasoning algorithm is good, then I’ll find that the predictions I remember making for this moment are in decent agreement with what’s actually happening. While my senses are hard at work recording new information to be consciously perceived in future observer moments, the conscious part of my mind is busy using my scientific-reasoning algorithm to update my assumptions about more subtle and abstract aspects of reality.
Figure 11.8: When each observer moment can be uniquely linked to a predecessor and a successor, we perceive subjective causality (left). When some but not all successors disappear, we may perceive subjective immortality. When several subjectively distinguishable successors share the same predecessor, we perceive subjective randomness.
Why Aren’t You an Ant?
So how should you reason in your observer moment, once you’ve pressed the Pause button? You need a good framework for this not only to get by in a multiverse, but also, as we’ll see, for making sense of the so-called doomsday argument and other famous philosophical conundrums. If you believe in the Mathematical Universe Hypothesis, then you should try to figure out which mathematical structure you inhabit. If that structure contains many observer moments that subjectively feel like yours, then you could be any one of them. Unless there’s something in the mathematics that somehow breaks the symmetry and favors some over others, you’re equally likely to be any one of them. Therefore, as I argued in my 1996 mathematical universe paper, you reach the following conclusion:
You should reason as if your observer moment is a random one among those it could be.
The past two decades have seen a vigorous and fascinating discussion of various alternative modes of reasoning in the philosophy liter
ature, triggered in part by the doomsday argument (which we’ll explore shortly) and related puzzles. The basic idea that we should expect to find our consciousness not in a random place (as per the Copernican principle) but in a random observer has a long history; we saw in Chapter 6 that Brandon Carter formulated it as his weak anthropic principle, and Alex Vilenkin from Chapter 5 has formulated it as the principle of mediocrity. Contemporary philosophers such as Nick Bostrom, Paul Almond and Milan C´ircovic´ have explored it extensively, and in 2002, Bostrom coined the now standard terminology of the Strong Self-Sampling Assumption.
Strong Self-Sampling Assumption (SSSA): Each observer moment should reason as if it were randomly selected from the class of all observer moments in its reference class.
The subtlety here is how reference class should be interpreted, and philosophers who accept the SSSA often argue about this. If you use the maximally restrictive option and limit the reference class to other yous’ observer moments that feel subjectively indistinguishable from your own, you recover my old approach. However, we’ll see that you can often reach additional interesting conclusions by being more liberal: you’ll still reach correct conclusions even if distinguishable observer moments are allowed, as long as the way they subjectively feel different doesn’t bias the answer you’re seeking. To get a feeling for how this works, let’s consider an example of the SSSA in action—Nick Bostrom’s Sleeping Beauty puzzle:
Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details. On Sunday she’s put to sleep. A fair coin is then tossed. If the coin comes up heads, Beauty is awoken and interviewed on Monday only. If the coin comes up tails, she’s awoken and interviewed on Monday and Tuesday, but when she’s put to sleep again on Monday, she’s given a dose of an amnesia-inducing drug that ensures she can’t remember her previous awakening. Any time Beauty is awakened and interviewed, she’s asked, “What odds would you give that the coin landed heads?”
After a large number of publications on the subject, the philosophy community is now split between the “halfers” and the “thirders,” who feel that she should assign probabilities of 1/2 and 1/3, respectively. In the MUH framework, there’s no such thing as true randomness, so let’s replace the coin by a quantum measurement that realizes both outcomes equally in two Level III parallel universes. There are now three subjectively indistinguishable observer moments in the mathematical structure that correspond to her being interviewed, and they’re all equally real:
1. The coin landed heads and it’s Monday.
2. The coin landed tails and it’s Monday.
3. The coin landed tails and it’s Tuesday.
Since only one of the three corresponds to the heads option, she should assign a probability of 1/3 to this and will experience the corresponding subjective randomness once she finds out.
Now suppose the experimenters secretly decided to repaint her fingernails in a color depending on the quantum-measurement outcome. This means that the observer moments aren’t all indistinguishable, but as long as she doesn’t know the color code, the odds she gives shouldn’t change. In other words, we’re free to broaden the reference class as long as it won’t bias the results.
This conclusion has radical implications: it suggests that no matter how vast and crazy a multiverse may exist out there, we humans are likely to be rather typical among all observers asking this sort of question! For example, it’s extremely unlikely that typical solar systems contain quadrillions of hominids similar to us, because if that were the case, we’d be about a million times more likely to find ourselves in such a populous solar system rather than in our own with its measly 7 billion denizens. In other words, the SSSA allows us to make statements about what’s going on even in places that we can’t observe.
However, like any powerful tool, the SSSA must be used with caution. For example, why aren’t you an ant? If we take carbon-based life- forms on Earth as our reference class, our over ten quadrillion (1016) six-legged friends outnumber us bipeds by more than a million to one, so doesn’t that imply that your current observer moment is a million times more likely to be that of an ant than that of a human? If so, that would rule out your basic reality framework with 99.9999% confidence. Okay, we’ve neglected that humans live about a hundred times longer than ants, but that doesn’t change the troubling conclusion.
Instead, the resolution lies in the choice of reference class. As Figure 11.9 illustrates, you have many different choices of reference class, the most inclusive being all observer moments of all self-aware substructures and the most exclusive being only the ones that subjectively feel exactly like you do right now. If you ask the question “What sort of entity should I expect to be?,” then your reference class clearly needs to be restricted to entities that ask such questions—and ants don’t!
The business of using the right reference class corresponds to correctly using what statisticians call conditional probabilities, and botching this can cause epic failures. In 2010, a major poll failed to predict that U.S. Senate Majority Leader Harry Reid, would get reelected in Nevada because the robo-calling software hung up when the target didn’t speak English, thus losing the responses from pro-Reid Hispanic voters. In Chapter 6, we saw that a typical region of space might expect itself to be in a universe with too much dark energy to form any galaxies, and that a typical hydrogen atom in our particular Universe should expect to find itself in an intergalactic gas cloud or a star. But that’s not where you should expect to find yourself: “all points” or “all atoms” are irrelevant reference classes to you, because neither points nor atoms ask questions.
Why Aren’t You a Boltzmann Brain?
If you think it sounds crazy to have an extraterrestrial alien classmate in your reference class, you’ll be amused to know that some of my colleagues are busy arguing about even-more-exotic classmates: simulations and Boltzmann brains.
We’re living proof that atoms can be put together in an elaborate pattern that subjectively feels self-aware. So far, our physics research has turned up no evidence whatsoever suggesting that ours is the only possible path to consciousness. We therefore need to consider the possibility that there may be other kinds of atom arrangements that feel self-aware as well, and that some life-forms (perhaps even we or our descendants) will one day build such entities. They might be reminiscent of intelligent robots by having actual physical bodies that can interact with the world around them, or they might be simulations like characters in Star Trek: The Next Generation holodeck episodes or Agent Smith in The Matrix1 whose bodies are purely virtual, with lives playing out in the virtual reality of an extremely powerful computer. Some such simulations could have observer moments that subjectively feel exactly like you feel right now.
Figure 11.9: What’s the probability that [INSERT YOUR FAVORITE QUESTION HERE] given that I’m a …? What you replace the ellipsis by is your reference class, illustrated above. Under the Mathematical Universe Hypothesis, it’s always valid to reason as if you’re a random member of the most restrictive reference class, corresponding to all observer moments who subjectively feel like you do, but in some cases you can draw additional valid and interesting conclusions from broadening the reference class, say, to humans or other self-aware entities who are capable of asking the same question.
If this is the case, you clearly need to include the simulated yous in your reference class. Nick Bostrom and others have published extensively on this topic, concluding that there’s a reasonable probability that we’re in fact simulated. I’ll give a counterargument in the next chapter, but if you want to play it safe in the meantime, in the spirit of Pascal’s Wager, my advice is that you should live life to its fullest and do novel and interesting things. That way, in case you’re a simulation, whoever created you will be less likely to get bored and switch you off.…
Whereas simulations are purposefully created, so-called Boltzmann brains are created by coincidences. After pioneering the field known as statistical
mechanics about 150 years ago, the Austrian physicist Ludwig Boltzmann realized that if you leave a warm object alone for enough time, even most unlikely arrangements of atoms will occur by chance. The time it will take for the particles to spontaneously rearrange themselves into a self-aware brain is extremely long, but if you wait long enough, it will happen.
Now fast-forward to today’s Universe, and let’s consider its long-term fate. The accelerated expansion will eventually dilute away all the matter that currently fills our Universe, but if the cosmic dark-energy density remains constant (as current measurements suggest), then it will forever provide a very slight amount of heat energy. This heat comes from the same kind of quantum fluctuations that generated the cosmic microwave–background fluctuations in Chapter 5, and Stephen Hawking famously discovered that the faster our Universe expands, the higher this so-called Hawking temperature will be. The dark energy makes our Universe expand much more slowly than during inflation, so the temperature it provides is merely a millionth of a trillionth of a trillionth (10−30) of a degree above absolute zero.
This is hardly balmy, even by Swedish standards, but it isn’t absolute zero, which means that if you wait long enough, this heat energy will rearrange itself into anything you want. In the standard cosmological model, this random rearranging goes on forever, so it will randomly produce an exact replica of you who subjectively feels exactly like you do, complete with false memories of having lived your entire life. Much more often, it will replicate merely your disembodied brain, surviving just long enough to replicate your current observer moment. And then it will do it again, infinitely many times over, so that for every copy of you that has evolved and lived a real life, there are infinitely many delusional disembodied Boltzmann brains who think that they’ve lived that same real life.
