Apr 25, 2008
Once upon a time, there was an alien species, whose planet hovered in the void of a universe with laws almost like our own. They would have been alien to us, but of course they did not think of themselves as alien. They communicated via rapid flashes of light, rather than sound. We'll call them the Ebborians.
Ebborians reproduce by fission, an adult dividing into two new individuals. They share genetic material, but not through sexual recombination; Ebborian adults swap genetic material with each other. They have two eyes, four legs, and two hands, letting a fissioned Ebborian survive long enough to regrow.
Human DNA is built in a double helix; unzipping the helix a little at a time produces two stretches of single strands of DNA. Each single strand attracts complementary bases, producing a new double strand. At the end of the operation, a DNA double helix has turned into two double helices. Hence earthly life.
Ebborians fission their brains, as well as their bodies, by a process something like how human DNA divides.
Imagine an Ebborian brain as a flat sheet of paper, computing in a way that is more electrical than chemical—charges flowing down conductive pathways.
When it's time for an Ebborian to fission, the brain-paper splits down its thickness into two sheets of paper. Each new sheet is capable of conducting electricity on its own. Indeed, the Ebborian(s) stays conscious throughout the whole fissioning process. Over time, the brain-paper grows thick enough to fission again.
Electricity flows through Ebborian brains faster than human neurons fire. But the Ebborian brain is constrained by its two-dimensionality. An Ebborian brain-paper must split down its thickness while retaining the integrity of its program. Ebborian evolution took the cheap way out: the brain-paper computes in a purely two-dimensional way. The Ebborians have much faster neuron-equivalents, but they are far less interconnected.
On the whole, Ebborians think faster than humans and remember less. They are less susceptible to habit; they recompute what we would cache. They would be incredulous at the idea that a human neuron might be connected to a thousand neighbors, and equally incredulous at the idea that our axons and dendrites propagate signals at only a few meters per second.
The Ebborians have no concept of parents, children, or sexuality. Every adult Ebborian remembers fissioning many times. But Ebborian memories quickly fade if not used; no one knows the last common ancestor of those now alive.
In principle, an Ebborian personality can be immortal. Yet an Ebborian remembers less life than a seventy-year-old human. They retain only the most important highlights of their last few millennia. Is this immortality? Is it death?
The Ebborians had to rediscover natural selection from scratch, because no one retained their memories of being a fish.
But I digress from my tale.
Today, the Ebborians have gathered to celebrate a day which all present will remember for hundreds of years. They have discovered (they believe) the Ultimate Grand Unified Theory of Everything for their universe. The theory which seems, at last, to explain every known fundamental physical phenomenon—to predict what every instrument will measure, in every experiment whose initial conditions are exactly known, and which can be calculated on available computers.
"But wait!" cries an Ebborian. (We'll call this one Po'mi.) "But wait!", cries Po'mi, "There are still questions the Unified Theory can't answer! During the fission process, when exactly does one Ebborian consciousness become two separate people?"
The gathered Ebborians look at each other. Finally, there speaks the moderator of the gathering, the second-foremost Ebborian on the planet: the much-respected Nharglane of Ebbore, who achieved his position through consistent gentleness and courtesy.
"Well," Nharglane says, "I admit I can't answer that one—but is it really a question of fundamental physics?"
"I wouldn't even call that a 'question'," snorts De'da the Ebborian, "seeing as how there's no experimental test whose result depends on the answer."
"On the contrary," retorts Po'mi, "all our experimental results ultimately come down to our experiences. If a theory of physics can't predict what we'll experience, what good is it?"
De'da shrugs. "One person, two people—how does that make a difference even to experience? How do you tell even internally whether you're one person or two people? Of course, if you look over and see your other self, you know you're finished dividing—but by that time your brain has long since finished splitting."
"Clearly," says Po'mi, "at any given point, whatever is having an experience is one person. So it is never necessary to tell whether you are one person or two people. You are always one person. But at any given time during the split, does there exist another, different consciousness as yet, with its own awareness?"
De'da performs an elaborate quiver, the Ebborian equivalent of waving one's hands. "When the brain splits, it splits fast enough that there isn't much time where the question would be ambiguous. One instant, all the electrical charges are moving as a whole. The next instant, they move separately."
"That's not true," says Po'mi. "You can't sweep the problem under the rug that easily. There is a quite appreciable time—many picoseconds—when the two halves of the brain are within distance for the moving electrical charges in each half to tug on the other. Not quite causally separated, and not quite the same computation either. Certainly there is a time when there is definitely one person, and a time when there is definitely two people. But at which exact point in between are there two distinct conscious experiences?"
"My challenge stands," says De'da. "How does it make a difference, even a difference of first-person experience, as to when you say the split occurs? There's no third-party experiment you can perform to tell you the answer. And no difference of first-person experience, either. Your belief that consciousness must 'split' at some particular point, stems from trying to model consciousness as a big rock of awareness that can only be in one place at a time. There's no third-party experiment, and no first-person experience, that can tell you when you've split; the question is meaningless."
"If experience is meaningless," retorts Po'mi, "then so are all our scientific theories, which are merely intended to explain our experiences."
"If I may," says another Ebborian, named Yu'el, "I think I can refine my honorable colleague Po'mi's dilemma. Suppose that you anesthetized one of us -"
(Ebborians use an anesthetic that effectively shuts off electrical power to the brain—no processing or learning occurs while an Ebborian is anesthetized.)
"- and then flipped a coin. If the coin comes up heads, you split the subject while they are unconscious. If the coin comes up tails, you leave the subject as is. When the subject goes to sleep, should they anticipate a 2/3 probability of seeing the coin come up heads, or anticipate a 1/2 probability of seeing the coin come up heads? If you answer 2/3, then there is a difference of anticipation that could be made to depend on exactly when you split."
"Clearly, then," says De'da, "the answer is 1/2, since answering 2/3 gets us into paradoxical and ill-defined issues."
Yu'el looks thoughtful. "What if we split you into 512 parts while you were anesthetized? Would you still answer a probability of 1/2 for seeing the coin come up heads?"
De'da shrugs. "Certainly. When I went to sleep, I would figure on a 1/2 probability that I wouldn't get split at all."
"Hmm..." Yu'el says. "All right, suppose that we are definitely going to split you into 16 parts. 3 of you will wake up in a red room, 13 of you will wake up in a green room. Do you anticipate a 13/16 probability of waking up in a green room?"
"I anticipate waking up in a green room with near-1 probability," replies De'da, "and I anticipate waking up in a red room with near-1 probability. My future selves will experience both outcomes."
"But I'm asking about your personal anticipation," Yu'el persists. "When you fall asleep, how much do you anticipate seeing a green room? You can't see both room colors at once—that's not an experience anyone will have—so which color do you personally anticipate more?"
De'da shakes his head. "I can see where this is going; you plan to ask what I anticipate in cases where I may or may not be split. But I must deny that your question has an objective answer, precisely because of where it leads. Now, I do say to you, that I care about my future selves. If you ask me whether I would like each of my green-room selves, or each of my red-room selves, to receive ten dollars, I will of course choose the green-roomers—but I don't care to follow this notion of 'personal anticipation' where you are taking it."
"While you are anesthetized," says Yu'el, "I will flip a coin; if the coin comes up heads, I will put 3 of you into red rooms and 13 of you into green rooms. If the coin comes up tails, I will reverse the proportion. If you wake up in a green room, what is your posterior probability that the coin came up heads?"
De'da pauses. "Well..." he says slowly, "Clearly, some of me will be wrong, no matter which reasoning method I use—but if you offer me a bet, I can minimize the number of me who bet poorly, by using the general policy, of each self betting as if the posterior probability of their color dominating is 13/16. And if you try to make that judgment depend on the details of the splitting process, then it just depends on how whoever offers the bet counts Ebborians."
Yu'el nods. "I can see what you are saying, De'da. But I just can't make myself believe it, at least not yet. If there were to be 3 of me waking up in red rooms, and a billion of me waking up in green rooms, I would quite strongly anticipate seeing a green room when I woke up. Just the same way that I anticipate not winning the lottery. And if the proportions of three red to a billion green, followed from a coin coming up heads; but the reverse proportion, of a billion red to three green, followed from tails; and I woke up and saw a red room; why, then, I would be nearly certain—on a quite personal level—that the coin had come up tails."
"That stance exposes you to quite a bit of trouble," notes De'da.
Yu'el nods. "I can even see some of the troubles myself. Suppose you split brains only a short distance apart from each other, so that they could, in principle, be fused back together again? What if there was an Ebborian with a brain thick enough to be split into a million parts, and the parts could then re-unite? Even if it's not biologically possible, we could do it with a computer-based mind, someday. Now, suppose you split me into 500,000 brains who woke up in green rooms, and 3 much thicker brains who woke up in red rooms. I would surely anticipate seeing the green room. But most of me who see the green room will see nearly the same thing—different in tiny details, perhaps, enough to differentiate our experience, but such details are soon forgotten. So now suppose that my 500,000 green selves are reunited into one Ebborian, and my 3 red selves are reunited into one Ebborian. Have I just sent nearly all of my "subjective probability" into the green future self, even though it is now only one of two? With only a little more work, you can see how a temporary expenditure of computing power, or a nicely refined brain-splitter and a dose of anesthesia, would let you have a high subjective probability of winning any lottery. At least any lottery that involved splitting you into pieces."
De'da furrows his eyes. "So have you not just proved your own theory to be nonsense?"
"I'm not sure," says Yu'el. "At this point, I'm not even sure the conclusion is wrong."
"I didn't suggest your conclusion was wrong," says De'da, "I suggested it was nonsense. There's a difference."
"Perhaps," says Yu'el. "Perhaps it will indeed turn out to be nonsense, when I know better. But if so, I don't quite know better yet. I can't quite see how to eliminate the notion of subjective anticipation from my view of the universe. I would need something to replace it, something to re-fill the role that anticipation currently plays in my worldview."
De'da shrugs. "Why not just eliminate 'subjective anticipation' outright?"
"For one thing," says Yu'el, "I would then have no way to express my surprise at the orderliness of the universe. Suppose you claimed that the universe was actually made up entirely of random experiences, brains temporarily coalescing from dust and experiencing all possible sensory data. Then if I don't count individuals, or weigh their existence somehow, that chaotic hypothesis would predict my existence as strongly as does science. The realization of all possible chaotic experiences would predict my own experience with probability 1. I need to keep my surprise at having this particular orderly experience, to justify my anticipation of seeing an orderly future. If I throw away the notion of subjective anticipation, then how do I differentiate the chaotic universe from the orderly one? Presumably there are Yu'els, somewhere in time and space (for the universe is spatially infinite) who are about to have a really chaotic experience. I need some way of saying that these Yu'els are rare, or weigh little—some way of mostly anticipating that I won't sprout wings and fly away. I'm not saying that my current way of doing this is good bookkeeping, or even coherent bookkeeping; but I can't just delete the bookkeeping without a more solid understanding to put in its place. I need some way to say that there are versions of me who see one thing, and versions of me who see something else, but there's some kind of different weight on them. Right now, what I try to do is count copies—but I don't know exactly what constitutes a copy."
Po'mi clears his throat, and speaks again. "So, Yu'el, you agree with me that there exists a definite and factual question as to exactly when there are two conscious experiences, instead of one."
"That, I do not concede," says Yu'el. "All that I have said may only be a recital of my own confusion. You are too quick to fix the language of your beliefs, when there are words in it that, by your own admission, you do not understand. No matter how fundamental your experience feels to you, it is not safe to trust that feeling, until experience is no longer something you are confused about. There is a black box here, a mystery. Anything could be inside that box—any sort of surprise—a shock that shatters everything you currently believe about consciousness. Including upsetting your belief that experience is fundamental. In fact, that strikes me as a surprise you should anticipate—though it will still come as a shock."
"But then," says Po'mi, "do you at least agree that if our physics does not specify which experiences are experienced, or how many of them, or how much they 'weigh', then our physics must be incomplete?"
"No," says Yu'el, "I don't concede that either. Because consider that, even if a physics is known—even if we construct a universe with very simple physics, much simpler than our own Unified Theory—I can still present the same split-brain dilemmas, and they will still seem just as puzzling. This suggests that the source of the confusion is not in our theories of fundamental physics. It is on a higher level of organization. We can't compute exactly how proteins will fold up; but this is not a deficit in our theory of atomic dynamics, it is a deficit of computing power. We don't know what makes sharkras bloom only in spring; but this is not a deficit in our Unified Theory, it is a deficit in our biology—we don't possess the technology to take the sharkras apart on a molecular level to find out how they work. What you are pointing out is a gap in our science of consciousness, which would present us with just the same puzzles even if we knew all the fundamental physics. I see no work here for physicists, at all."
Po'mi smiles faintly at this, and is about to reply, when a listening Ebborian shouts, "What, have you begun to believe in zombies? That when you specify all the physical facts about a universe, there are facts about consciousness left over?"
"No!" says Yu'el. "Of course not! You can know the fundamental physics of a universe, hold all the fundamental equations in your mind, and still not have all the physical facts. You may not know why sharkras bloom in the summer. But if you could actually hold the entire fundamental physical state of the sharkra in your mind, and understand all its levels of organization, then you would necessarily know why it blooms—there would be no fact left over, from outside physics. When I say, 'Imagine running the split-brain experiment in a universe with simple known physics,' you are not concretely imagining that universe, in every detail. You are not actually specifying the entire physical makeup of an Ebborian in your imagination. You are only imagining that you know it. But if you actually knew how to build an entire conscious being from scratch, out of paperclips and rubberbands, you would have a great deal of knowledge that you do not presently have. This is important information that you are missing! Imagining that you have it, does not give you the insights that would follow from really knowing the full physical state of a conscious being."
"So," Yu'el continues, "We can imagine ourselves knowing the fundamental physics, and imagine an Ebborian brain splitting, and find that we don't know exactly when the consciousness has split. Because we are not concretely imagining a complete and detailed description of a conscious being, with full comprehension of the implicit higher levels of organization. There are knowledge gaps here, but they are not gaps of physics. They are gaps in our understanding of consciousness. I see no reason to think that fundamental physics has anything to do with such questions."
"Well then," Po'mi says, "I have a puzzle I should like you to explain, Yu'el. As you know, it was discovered not many years ago, that our universe has four spatial dimensions, rather than three dimensions, as it first appears."
"Aye," says Nharglane of Ebbore, "this was a key part in our working-out of the Unified Theory. Our models would be utterly at a loss to account for observed experimental results, if we could not model the fourth dimension, and differentiate the fourth-dimensional density of materials."
"And we also discovered," continues Po'mi, "that our very planet of Ebbore, including all the people on it, has a four-dimensional thickness, and is constantly fissioning along that thickness, just as our brains do. Only the fissioned sides of our planet do not remain in contact, as our new selves do; the sides separate into the fourth-dimensional void."
Nharglane nods. "Yes, it was rather a surprise to realize that the whole world is duplicated over and over. I shall remember that realization for a long time indeed. It is a good thing we Ebborians had our experience with self-fissioning, to prepare us for the shock. Otherwise we might have been driven mad, and embraced absurd physical theories."
"Well," says Po'mi, "when the world splits down its four-dimensional thickness, it does not always split exactly evenly. Indeed, it is not uncommon to see nine-tenths of the four-dimensional thickness in one side."
"Really?" says Yu'el. "My knowledge of physics is not so great as yours, but—"
"The statement is correct," says the respected Nharglane of Ebbore.
"Now," says Po'mi, "if fundamental physics has nothing to do with consciousness, can you tell me why the subjective probability of finding ourselves in a side of the split world, should be exactly proportional to the square of the thickness of that side?"
There is a great terrible silence.
"WHAT?" says Yu'el.
"WHAT?" says De'da.
"WHAT?" says Nharglane.
"WHAT?" says the entire audience of Ebborians.
To be continued...
Part of The Quantum Physics Sequence
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