# Where Experience Confuses Physicists

post by Eliezer Yudkowsky (Eliezer_Yudkowsky) · 2008-04-26T05:05:01.000Z · score: 20 (24 votes) · LW · GW · Legacy · 29 comments**Continuation of**: Where Physics Meets Experience

When we last met our heroes, the Ebborians, they were discussing the known phenomenon in which the entire planet of Ebbore and all its people splits down its fourth-dimensional thickness into two sheets, just like an individual Ebborian brain-sheet splitting along its third dimension.

And Po'mi has just asked:

"Why should the subjective probability of finding ourselves in a side of the split world, be exactly proportional to the square of the thickness of that side?"

When the initial hubbub quiets down, the respected Nharglane of Ebbore asks: "Po'mi, what is it *exactly* that you found?"

"Using instruments of the type we are all familiar with," Po'mi explains, "I determined when a splitting of the world was about to take place, and in what proportions the world would split. I found that I could not predict *exactly* which world I would find myself in—"

"Of course not," interrupts De'da, "you found yourself in *both* worlds, every time -"

"—but I could predict *probabilistically* which world I would find myself in. Out of all the times the world was about to split 2:1, into a side of two-thirds width and a side of one-third width, I found myself on the thicker side around 4 times out of 5, and on the thinner side around 1 time out of 5. When the world was about to split 3:1, I found myself on the thicker side 9 times out of 10, and on the thinner side 1 time out of 10."

"Are you *very sure* of this?" asks Nharglane. "How much data did you gather?"

Po'mi offers an overwhelming mountain of experimental evidence.

"I guess that settles that," mutters Nharglane.

"So you see," Po'mi says, "you were right after all, Yu'el, not to eliminate 'subjective probability' from your worldview. For if we do not have a 4/5 subjective anticipation of *continuing into* the thicker side of a 2:1 split, then how could we even *describe* this rule?"

"A good question," says De'da. "There ought to be *some* way of phrasing your discovery, which eliminates this problematic concept of 'subjective continuation'..."

The inimitable Ha'ro speaks up: "You might say that we find ourselves in a world in which the *remembered* splits obey the squared-thickness rule, to within the limits of statistical expectation."

De'da smiles. "Yes, excellent! That describes the evidence in terms of recorded experimental results, which seems less problematic than this 'subjective anticipation' business."

"Does that really buy us anything...?" murmurs Yu'el. "We're not limited to memories; we could perform the experiment again. What, on that next occasion, would you *anticipate* as your experimental result? If the thickness is split a hundred to one? Afterward it will be only a memory... but what about beforehand?"

"I think," says De'da, "that you have forgotten one of your own cardinal rules, Yu'el. Surely, what you *anticipate* is part of your map, not the territory. Your degree of anticipation is partial information you possess; it is not a substance of the experiment itself."

Yu'el pauses. "Aye, that is one of my cardinal rules... but I like my partial information to be *about* something. Before I can distinguish the map and the territory, I need a concept of the territory. What is my subjective anticipation *about*, in this case? I will *in fact* end up in both world-sides. I can calculate a certain probability to five decimal places, and verify it experimentally—but what is it a probability *of?*"

"I know!" shouts Bo'ma. "It's the probability that your *original* self ends up on that world-side! The other person is *just a copy!*"

A great groan goes up from the assembled Ebborians. "Not this again," says De'da. "Didn't we settle this during the Identity Wars?"

"Yes," Yu'el says. "There is no copy: there are two originals."

De'da shakes his head in disgust. "And what are the odds that, out of umpteen billion split Ebbores, *we* would be the originals at this point?"

"But you can't deny," Bo'ma says smugly, "that my theory produces good experimental predictions! It explains our observations, and that's all you can ask of any theory. And so science vindicates the Army of Original Warriors—we were right all along!"

"Hold on," says Yu'el. "That theory doesn't actually *explain* anything. At all."

"What?" says Bo'ma. "Of course it does. I use it daily to make experimental predictions; though *you* might not understand that part, not being a physicist."

Yu'el raises an eye. "Failure to explain anything is a hard-to-notice phenomenon in scientific theories. You have to pay close attention, or you'll miss it. It was once thought that phlogiston theory predicted that wood, when burned, would lose phlogiston and transform into ash; and predicted that candles, burning in an enclosed space, would saturate the air with phlogiston and then go out. But these were not *advance* predictions of phlogiston theory. Rather, phlogiston theorists saw those results, and then said 'Phlogiston did it.' Now why didn't people notice this right away? Because that sort of thing is actually surprisingly hard to notice."

"In this case," continues Yu'el, "you have given us a rule that the *original* Ebborian has a probability of ending up in a world-side, which is proportional to the squared thickness of the side. We originally had the mystery of where the squared-thickness rule came from. And now that you've offered us your rule, we have the *exact same mystery* as before. *Why* would each world have a squared-thickness probability of receiving the original? Why wouldn't the original consciousness *always* go to the thicker world? Or go with probability *directly* proportional to thickness, instead of the square? And what does it even *mean* to be the original?"

"That doesn't matter," retorts Bo'ma. "Let the equation *mean* anything it likes, so long as it gives good experimental predictions. What is the meaning of an electrical charge? Why is it an electrical charge? That doesn't matter; only the numbers matter. My law that the original ends up in a particular side, with probability equaling the square of its thickness, gives good numbers. End of story."

Yu'el shakes his head. "When I look over the raw structure of your theory—the computer program that would correspond to this model—it contains a strictly superfluous element. You have to compute the square of the thickness, and turn it into a probability, in order to get *the chance that the original self goes there.* Why not just *keep that probability* as the experimental prediction? Why *further* specify that this is the *probability of* original-ness? Adding that last rule doesn't help you compute any *better* experimental predictions; and it leaves all the original mysteries intact. Including Po'mi's question as to when exactly a world splits. And it adds the new mystery of why original-ness should only end up in one world-side, with probability equal to the square of the thickness." Yu'el pauses. "You might as well just claim that all the split world-sides except one vanish from the universe."

Bo'ma snorts. "For a world-side to 'just vanish' would outright violate the laws of physics. Why, if it all vanished in an instant, that would mean the event occurred non-locally—faster than light. My suggestion about 'originals' and 'copies' doesn't postulate unphysical behavior, whatever other criticisms you may have."

Yu'el nods. "You're right, that was unfair of me. I apologize."

"Well," says Bo'ma, "how about this, then? What if 'fourth-dimensional thickness', as we've been calling it, is actually a *degree of partial information* about who we *really* are? And then when the world splits, we find out."

"Um... *what*?" says Yu'el. "Are you sure you don't want to rephrase that, or something?"

Bo'ma shakes his head. "No, you heard me the first time."

"Okay," says Yu'el, "correct me if I'm wrong, but I thought I heard Nharglane say that you had to do things like differentiate the fourth-dimensional density in order to do your experimental calculations. That doesn't sound like probability theory to me. It sounds like physics."

"Right," Bo'ma says, "it's a quantity that propagates around with wave mechanics that involve the differential of the density, but it's *also* a degree of partial information."

"Look," Yu'el says, "if this 4D density business works the way you say it does, it should be easy to set up a situation where there's no *possible* 'fact as to who you really are' that is fixed in advance but unknown to you, because the so-called 'answer' will change depending on the so-called 'question'—"

"Okay," Bo'ma says, "forget the 'probability' part. What if 4D thickness is *the very stuff of reality itself?* So how *real* something is, equals the 4D thickness—no, pardon me, the square of the 4D thickness. Thus, some world-sides are quantitatively *realer* than others, and that's why you're more likely to find yourself in them."

"Why," says Yu'el, "is the *very stuff of reality itself* manifesting as a physical quantity with its own wave mechanics? What's next, electrical charge as a degree of possibility? And besides, doesn't that violate -"

Then Yu'el pauses, and falls silent.

"What is it?" inquires Po'mi.

"I was about to say, wouldn't that violate the Generalized Anti-Zombie Principle," Yu'el replies slowly. "Because then you could have a complete mathematical model of our world, to be looked over by the Flying Spaghetti Monster, and then *afterward *you would need to tell the Flying Spaghetti Monster an *extra* postulate: *Things are real in proportion to the square of their fourth-dimensional thickness.* You could change that postulate, and leave everything microphysically the same, but people would find... different proportions of themselves?... in different places. The difference would be detectable *internally*... sort of... because the inhabitants would *experience* the results in different proportions, whatever that means. They would see different things, or at least see the same things in different relative amounts. But any third-party observer, looking over the universe, couldn't tell which internal people were *more real,* and so couldn't discover the statistics of experience."

De'da laughs. "Sounds like a crushing objection to me."

"Only," says Yu'el, "is that really so different from believing that you can have the whole mathematical structure of a world, and then an *extra* fact as to whether that world happens to *exist* or *not exist*? Shouldn't *that* be ruled out by the Anti-Zombie Principle too? Shouldn't the Anti-Zombie Principle say that it was logically impossible to have had a world physically identical to our own, except that it *doesn't exist?* Otherwise there could be an abstract mathematical object structurally identical to this world, but with *no experiences in it*, because* it doesn't exist*. And papers that philosophers wrote about subjectivity wouldn't prove they were conscious, because the papers would also 'not exist'."

"Um..." says an Ebborian in the crowd, "correct me if I'm mistaken, but didn't you just solve the mystery of the First Cause?"

"You are mistaken," replies Yu'el. "I can tell when I have *solved* a mystery, because it stops being mysterious. To cleverly manipulate my own confusion is not to dissolve a problem. It is an interesting argument, and I may try to follow it further—but it's not an *answer* until the confusion goes away."

"Nonetheless," says Bo'ma, "if you're allowed to say that some worlds exist, and some worlds don't, why not have a degree of existence that's *quantitative?* And propagates around like a wave, and then we have to square it to get an answer."

Yu'el snorts. "Why not just let the 'degree of existence' be a complex number, while you're at it?"

Bo'ma rolls his eyes. "Please stop mocking me. I can't even *imagine *any possible experimental evidence which would point in the direction of *that* conclusion. You'd need a case where two events that were real in opposite directions canceled each other out."

"I'm sorry," says Yu'el, "I need to learn to control my tendency to attack straw opponents. But still, where would the squaring rule come from?"

An Ebborian named Ev'Hu suggests, "Well, you could have a rule that world-sides whose thickness tends toward zero, must have a degree of reality that also tends to zero. And then the rule which says that you square the thickness of a world-side, would let the probability tend toward zero as the world-thickness tended toward zero. QED."

"That's not QED," says Po'mi. "That's a complete non-sequitur. Logical fallacy of affirming the consequent. You could have all *sorts* of rules that would let the reality tend toward zero as the world-thickness tended toward zero, not just the squaring rule. You could approach the limit from many different directions. And in fact, *all *our world-sides have a thickness that 'tends toward zero' because they keep splitting. Furthermore, why would an indefinite tendency in the infinite future have any impact on what we do now?"

"The frequentist heresy," says Yu'el. "It sounds like some of their scriptures. But let's move on. Does anyone have any *helpful* suggestions? Ones that don't just shuffle the mystery around?"

Ha'ro speaks. "I've got one."

"Okay," Yu'el says, "this should be good."

"Suppose that when a world-side gets thin enough," Ha'ro says, "it cracks to pieces and falls apart. And then, when you did the statistics, it would turn out that the vast majority of *surviving* worlds have splitting histories similar to our own."

There's a certain unsettled pause.

"Ha'ro," says Nharglane of Ebbore, "to the best of my imperfect recollection, that is the most disturbing suggestion any Ebborian physicist has ever made in the history of time."

"Thank you very much," says Ha'ro. "But it could also be that a too-small world-side just sheds off in flakes when it splits, rather than containing actual sentient beings who get to experience a moment of horrified doom. The too-small worlds merely fail to exist, as it were. Or maybe sufficiently small world-sides get attracted to larger world-sides, and merge with them in a continuous process, obliterating the memories of anything having happened differently. But *that's* not important, the *real* question is whether the numbers would work out for the right size limit, and in fact," Ha'ro waves some calculations on a piece of paper, "all you need is for the minimum size of a cohesive world to be somewhere around the point where half the total fourth-dimensional mass is above the limit -"

"Eh?" says Yu'el.

"I figured some numbers and they don't look too implausible and we might be able to prove it, either from first-principles of 4D physics showing that a cracking process occurs, or with some kind of *really clever* experiment," amplifies Ha'ro.

"Sounds promising," says Yu'el. "So if I get what you're saying, there would be a *completely physical* explanation for why, when a typical bunch of worlds split 2:1, there's around 4 times as many cohesive worlds left that split from the thicker side, as from the thinner side."

"Yes," says Ha'ro, "you just count the surviving worlds."

"And if the Flying Spaghetti Monster ran a simulation of our universe's physics, the simulation would automatically include observers that experienced the same things we did, with the same statistical probabilities," says Yu'el. "No extra postulates required. None of the quantities in the universe would need additional characteristics beyond their strictly physical structure. Running any mathematically equivalent computer program would do the trick—you wouldn't need to be told how to *interpret* it a particular way."

Ha'ro nods. "That's the general idea."

"Well, I don't know if that's *correct,*" says Yu'el. "There's some potential issues, as you know. But I've got to say it's the first suggestion I've heard that's even *remotely* helpful in making all this seem any less mysterious."

Part of *The Quantum Physics Sequence*

Next post: "On Being Decoherent"

Previous post: "Where Physics Meets Experience"

## 29 comments

Comments sorted by oldest first, as this post is from before comment nesting was available (around 2009-02-27).

How come no one has yet investigated whether or not Ha'ro's suggestion can be proven or disproven from first principles?

I come from the future, bearing important news!

Probably the easiest way to show that Ha'ro's suggestion requires additional postulates is to use a toy model like a weighted quantum coinflip. Because flipping a coin is nice and simple, the extra step required to eliminate states of low amplitude squared really stands out. If you do a single flip, you get probabilities of 1/2 from counting states, even if the amplitudes squared are, say, 0.4 and 0.6. If you flip many independent coins, you should just be able to multiply the results together, which means counting states still gives the wrong answer - if something else supposedly happens, that's a property called "nonlinearity," which normal quantum mechanics provably does not have.

This can be quickly seen if you spend a lot of time on this stuff, which is why nobody has gotten a paper published about it specifically (though there are plenty of speculations about changing quantum mechanics to be nonlinear). Yhis is a case where no journal articles specifically on something doesn't mean it's "not investigated" - it just means no articles.

You have an exaggerated idea of how easy it is to get academics to spend *their* valuable time thinking about *your* ideas.

Rot13:

Anzrf: Cb'zv: Zvgpuryy Cbegre Aunetynar: Qba'g xabj lrg - vf vg nalbar? Qr'qn: Qnavry Qraarg Lh'ry: Gung'f lbh - Ryvrmre Lhqxbjfxl Un'eb: Ebova Unafba Ob'zn: Znk Obea Ri'uh: Uhtu Rirergg

Unir V tbg vg?

Mike Blume: hit Wikipedia for info on E.E. "Doc" Smith.

I am deeply honored to have my suggestion illustrated with such an eloquent parable. In fairness, I guess I should try to post some quotes from the now dominant opposing view on this.

Rot13:

V guvax Qr'qn vf Qnivq Qrhgfpu.

I think De'da is David Deutsch.

*How come no one has yet investigated whether or not Ha'ro's suggestion can be proven or disproven from first principles?*

As far as I know it *has* been disproven from first principles. If we should put an equal probability on all non-mangled worlds, then we should expect to find ourselves in a high-entropy world, unless I've misunderstood and the number of non-mangled worlds stays exactly constant under entropy increase.

I think it would be possible to prove that if you made a monkey type out a random program with the universe as input, it would output your mind with a probability proportional to the squared amplitude of your world. I think if you studied the orthodox Deutsch/Wallace/Greaves decision-theoretical account of probabilities in MWI, you would understand how to do this proof, even though they don't put it in these terms. But I'm not sure.

*cheerleads for orthodoxy*

Sorry for the triple-post, but I'm hoping to make my position a bit clearer --

I don't see why probabilities in many-worlds QM should produce any *new* mysteries that were not already present in ordinary functionalist philosophy. In functionalism, to turn a third-person view of the world into subjective anticipations, you need a criterion to determine whether the world *implements* a mind, and how many minds it implements, and/or to what degree. Once you have such a criterion, it should be straightforward to apply it to a branching quantum universe, and it doesn't seem obvious a priori that this criterion would say the branching quantum universe implements the same number of minds for every one of the structures that we happen to call a "world" (if there's even a reasonable way to decide when to call something one world and when to call something two worlds).

Mitchell Porter, I think, would say that the same problems of vagueness of existence/implementation/etc kill both functionalism and the MWI. I would say that the solution to these problems for functionalism will show us the way to a solution for the same problems in MWI, one that shows that we have to assign probabilities the Born way to begin with and not equally across worlds.

So out of curiosity, how much longer is the cutesy analogy thing going to go on for?

Steven: Mike Blume nailed them. Though your suggestion also had merit.

David D: Cutesy analogy's done.

Robin and Eliezer, I do appreciate the significance of the proposed hypothesis, but I feel I must rethink this subject carefully. It used to be my favorite subject, a very long time ago though (pre-Deutsch). In this reply, at first I focus on your criticism of alternatives, but as a result of responding to you, a particular alternative will be shaped. (Sorry for the length.)

Ev'Hu suggests, "Well, you could have a rule that world-sides whose thickness tends toward zero, must have a degree of reality that also tends to zero. And then the rule which says that you square the thickness of a world-side, would let the probability tend toward zero as the world-thickness tended toward zero. QED."

Let me try an alternative with only one rule and without limits.

Sincere Question: Do we need a "rule" or hypothesis stating that *zero* transition amplitude between any two quantum states implies that either state is *impossible* to obtain from the other? (As opposed to somehow demonstrating or defending this proposition.)

Suppose that some general argument can be used to back the above proposition, else let us introduce it as a new axiom. (It would be in the same league as your hypothesis, but weaker.) Let us combine it with considerations of physical continuity, based on the observation that exactly zero transition amplitude is a mathematical idealization. Thus we need to form a new concept, "approximate impossibility", for actual pairs of states, without yet specifying how close to zero an amplitude must be in order for "approximate impossibility" to hold. Now note that the object "absolute value of a squared transition amplitude" shares the properties of mathematical measure *and* the subjective property that if it is small enough it implies approximate impossibility. It looks like a duck and it quacks like a duck! Conjecture: a full probability interpretation can be based on there two premises. At the end, if one cares, it will be possible to clarify the notion "approximate impossibility" (relative to a particular situation and particular practical concerns) but that would be mainly a consistency check rather than a useful excercise.

"That's not QED," says Po'mi. "That's a complete non-sequitur. Logical fallacy of affirming the consequent. You could have all sorts of rules that would let the reality tend toward zero as the world-thickness tended toward zero, not just the squaring rule. [...]

Conjecture: only the absolute value of the square of the transition amplitude has the properties of probability.

And in fact, all our world-sides have a thickness that 'tends toward zero' because they keep splitting.

Then let us deal with only one split at a time.

Furthermore, why would an indefinite tendency in the infinite future have any impact on what we do now?"

I think that the frequentist demons distracted you at this point. The main concern is not "what we do now"; the point is (as you hinted elsewhere) to account for the body of facts, both data and memories, which look just as if they were generated from random processes.

(Caveat: Although I did introduce "approximate impossibility", a patently subjective concept, it was only a crutch, in the way of demonstrating that the subjective interpretation of "absolute value of a squared transition amplitude" shares a common feature with the subjective interpretation of probability. That common feature was a foot in the door, to explain why this object *is* probability. Thus we can account for the observed frequencies being typically close to theoretical values.)

Thanks in advance for any back criticism! Also thanks for maintaining this wondrful weblogsite, which I noticed only yesterday and it has overstimulated my head. For that matter, I found a discussion somewhat related to the elusiveness of exact impossibility: <http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/>.

Steven is basically right about my views. Though the criticism of vagueness only matters so long as people insist on being vague. In principle there could be a functionalism in which the functional states are microphysically distinct natural kinds, and a many-worlds interpretation in which the worlds are exactly individuated and enumerated. But it's not an accident that functionalism and MWI try to tolerate vagueness; it arises naturally, given the theoretical entities which are asked to play the role of "mind" and "world".

Po'mi could ask Ha'ro, "How thin is thin enough?" (to fall apart). That's the counterpart, in the story, of the decoherence threshold that remains unspecified in mangled-worlds theory. As an exercise in saving the phenomena (in this case, the observed relative frequencies of experimental outcomes), it is fair enough to say "if it happens somewhere in this range, the numbers work". But the theory would still be incomplete, for the reasons Po'mi raises in part one.

Yes, functionalism has never had a well-defined boundary about which processes instantiate which computations, let alone which processes instantiate which conscious beings. I suspect it may be the concept of "instantiation" that's at fault - since it implies that there is an instantiated thing separate from that which instantiates it. Anytime you start looking for things that resemble bridging laws, you should suspect that you're on a zombie track. What you need are *identity* laws.

But, Mitchell, you end up with exactly the same questions when you consider an Ebborian with a splitting brain. You say that a definite fact should exist as to how many people there are. But it wouldn't seem terribly impossible to construct an Ebborian in real life - in which case the Ebborian is *definitely, visibly* splitting.

So either it's *your* job to say definitely when one person becomes two - or you have to deny that the Ebborian could be conscious without new physics that would themselves settle the issue.

So, Mitchell, would you agree with the following statements?

1) "All criticisms that I have of MWI apply equally to any functionalist theory of consciousness."

2) "All criticisms that I have of MWI apply equally to any computable theory of physics."

3) "All criticisms that I have of MWI apply equally to any Copenhagen interpretation in which the collapse process is purely random and there are no new physics supporting consciousness beyond what is in the Standard Model."

I accept the second horn of the dilemma. Consciousness is not computation abstracted from substrate. Computational capabilities alone never imply consciousness. States of consciousness are what they are, objectively and intrinsically; states of computation depend on semantic imputation by an observer and on underdetermined coarse-graining of physical state space.

You *could* have a dualism with a bridging law which associated states of consciousness with a particular arbitrary refinement of a computational coarse-graining to the point of completeness, but (i) it would still not be identity (ii) it would be exceedingly complicated. So, especially given the hints of ontological nonlocality we get from quantum theory, I think it better to look for a new ontology in which the mind is not presupposed to be an aggregate of spatial parts to begin with. This may or may not involve new physics, in the sense of new *mathematics*; it may be that the change in perspective required involves no more extra formalism than does MWI. It does, very probably, require new biophysics and neuroscience, in the form of mesoscopic quantum phenomena in the brain that are functionally relevant to cognition. And it very definitely requires backing away from the attempt to reduce consciousness to combinations of known physical properties. If anything, we have to go the other way: understand consciousness in itself, to the extent that that is possible, and then use that to understand what physical properties actually "are", once the conscious mind has been identified with a particular part of the brain as formally described by physics.

None of that implies that the physics of consciousness is noncomputable, by the way, in the sense of being susceptible to exact simulation, so I will demur from statement 2. Consciousness involves a series of states; it can formally be described in terms of state transitions; and so it can be simulated on a Turing machine, unless there really is some Turing-busting basic cognitive operation, like Feferman reflection. But it won't *be* consciousness unless it's happening on the right substrate - e.g. one irreducible quantum tensor factor, rather than a product of them - that's the implication. But it's hard to see that if you think of the formal mathematical language - "tensor factor" - as being the fundamental description, and the psychologistic language - "intentionality" - as phlogiston-talk. The *actual* nature of consciousness is expressed by concepts like intentionality, qualia, etc., and any description in terms of Hilbert spaces (and so forth) will be purely formal and dynamical. This is why ontology is more fundamental than physics (as physics is presently understood).

I accept your warning (as Yu'el) that maybe things are radically other than I have ever imagined. I don't insist that this, for example, is *definitely* the right way ahead, far from it. But I have considerable confidence that most existing ideas about how to fit the mind into natural science are wrong, as they involve either spurious identities which break down on examination, or outright denial of phenomenological facts that are ontologically inconvenient.

*Anytime you start looking for things that resemble bridging laws, you should suspect that you're on a zombie track. What you need are identity laws.*

I don't think bridging vs identity laws makes much of a difference; might it not be possible to say something like, "the mind is identical to a structure in the physical world, and the degree to which a structure A exists in a structure B is proportional to the probability that a random program with input B puts out A"?

An Ebborian named Ev'Hu suggests, "Well, you could have a rule that world-sides whose thickness tends toward zero, must have a degree of reality that also tends to zero. And then the rule which says that you square the thickness of a world-side, would let the probability tend toward zero as the world-thickness tended toward zero. QED."

An argument somewhat like this except not stupid is now known. Namely, the squaring rule can be motivated by a frequentist argument that successfully distinguishes it from a cubing rule or whatever. See for example this lecture. The idea is to start with the postulate that being in an exact eigenstate of an observable means a measurement of that observable should yield the corresponding outcome with certainty. From this the Born rule can be seen as a consequence. Specifically, suppose you have a state like a|a> + b|b>, where = 0. Then, you want to know the statistics for a measurement in the |a>,|b> basis. For n copies of this state, you can make a frequency operator so that the eigenvalue m/n corresponds to getting outcome |a> m times out of n. In the limit where you have infinitely many copies of the state a|a> + b|b>, you obtain an eigenstate of this operator with eigenvalue m/n = |a|^2.

In my comment where it says "where = 0", what it is supposed to indicate is that the inner product of |a> and |b> is zero. That is, the states are orthogonal. I think the braket notation I used to write this was misinterpreted as an html tag.

*Yu'el nods. "You're right, that was unfair of me. I apologize." *

This truly is an alien race.

They're rare, Ben, but they walk the Earth.

Because then you could have a complete mathematical model of our world, to be looked over by the Flying Spaghetti Monster, and then afterward you would need to tell the Flying Spaghetti Monster an extra postulate: Things are real in proportion to the square of their fourth-dimensional thickness. You could change that postulate, and leave everything microphysically the same, but people would find... different proportions of themselves?... in different places.

What if, when you change that postulate, you (or the Flying Spaghetti Monster) can no longer find any sentient beings? Because when you do that, a completely different subset of 3D worlds come into prominence, and those worlds just don't have the right properties for sentient beings to evolve. The worlds where the Ebborians exist are still somewhere in the resulting distribution on worlds, but they are now just about impossible to find.

Now suppose there was a fifth dimension, where at coordinate c, things are real in proportion to thickness^c. Then the above implies that most of the sentient life in this universe is going to be concentrated at coordinate c=2.

If this was true, wouldn't it explain the mystery just as well as if Ha'ro's "when a world-side gets thin enough, it cracks to pieces and falls apart" was true?

To expand upon this a bit more, consider:

- In standard anthropic reasoning, you should expect to find yourself at coordinate 2 with high probability before you've observed anything other than "I'm sentient", and also anticipate observing experimental results consistent with being at coordinate 2.
- Under SIA, you should expect to live in a world with measure proportional to thickness^2, even if the world has no fifth dimension.
- Under UDT, you care equally about every coordinate c, but will act
*as if*you care mostly about c=2, because that is where you can create the most value with your decisions. (And same for worlds without the fifth dimension.)

So this seems to be a perfectly good (possible) solution.

sentient

I think it would be a good habit for people here to take explicit notice whenever decision-making concepts and consciousness/sentience concepts occur in association. Other than that decision-makers can have preferences *about* consciousness/sentience, decision-making and consciousness/sentience don't obviously have anything to do with each other. (Not that I object to parent comment, I just needed a place to say this.)

Yes, I agree. In fact, in UDT, decision making doesn't depend on consciousness/sentience, but in the standard formulation of anthropic reasoning, it does. So I would count that as an advantage for UDT (and actually it was the original motivation for me to consider it).

Under UDT, you care equally about every coordinate c, but will act as if you care mostly about c=2, because that is where you can create the most value with your decisions. (And same for worlds without the fifth dimension.)

It seems to me that this is where proofs of the Born rule by philosophers lend strong further support. The proofs, if I understand correctly, depend on assumptions that don't quite seem *mandatory*, but without which any decision strategy is practically impossible to specify or carry out. For example, the defense of "branching indifference" in section 9 of this paper:

If we are prepared to be even slightly instrumentalist in our criteria for belief ascription, it may not even

make senseto suppose that an agent genuinely wants to do something that is ridiculously beyond even their idealised capabilities. For instance, suppose I say that I desire (ceteris paribus) to date someone with a prime number of atoms in their body. It is not even remotely possible for me to take any action which even slightly moves me towards that goal. In practice my actual dating strategy will have to fall back on “secondary” principles which have no connection at all to my “primary” goal — and since those secondary principles are actually what underwrites my entire dating behaviour, arguably it makes more sense to say thattheyare my actual desires, and that my ‘primary’ desire is at best an impossible dream, at worst an empty utterance.

Otherwise there could be an abstract mathematical object structurally identical to this world, but with no experiences in it, because it doesn't exist. And papers that philosophers wrote about subjectivity wouldn't prove they were conscious, because the papers would also 'not exist'.

didn't you just solve the mystery of the First Cause?

My take :

A universe is not just math, it also needs processing to run.

Existence is not in the software or the processor, but in the processing.

So long as that universe is not run/simulated, it's philosophers do not exist, and what they would write is unknown.

Processing is what you need to *embed* a mathematical process into your universe, I agree, but that doesn't necessarily imply that there is a Universal Processor in which our universe is embedded, or even that this hypothesis is meaningful. (For one, what universe does this processor live in? Processors *bridge* universes, in a sense - they don't explain existence, but pass it off to the "larger" world.)