The Absolute Self-Selection Assumption

The post mentioned some problems/issues with this approach that remain to be resolved. Here are some additional ones.

My brain has preferences between probability distributions built into it.

Your brain is built to intuitively grapple with distribution over future experiences, like your example "I have a 50% chance of remaining me, and a 50% chance of becoming my copy." Unfortunately UDASSA doesn't give you that. It only gives you a distribution over observer-moments in an absolute sense (hence the "A" in ASSA), and there is no good way to convert such a distribution into a distribution over future experiences. (Suppose you're copied at time 0, then the "copy" is copied again at time 1. Under UDASSA this is entirely unproblematic, but it doesn't tell you whether you should anticipate being the "original" at time 2 with probability 1/2 or 1/3.) The "pure" UDASSA position would be that there is no such thing as "remaining me" or "becoming my copy", and you just have to make your choices using the distribution over observer-moments without "linking" the observer-moments together in any way.

What I want is a probability distribution over all possible experiences (or "observer-moments"), so that I can use my existing preferences to make intelligent decisions in a universe with more than one observer I care about.

Do you consider this probability distribution an objective measure of how much each observer-moment exists? Or is it just a (possibly approximate) measure of how much you care about each observer-moment? I'm still going back and forth on these two positions myself. See What Are Probabilities, Anyway? where I go into this distinction a bit more. (The former is what I usually mean when I say UDASSA. Perhaps we could call the latter UDT-UMC for Updateless Decision Theory w/ Universal Measure of Care, unless someone has a better name for it. :)

UDASSA implies that simulations on the 2 atom thick computer count for twice as much as simulations on the 1 atom thick computer, because they are easier to specify.

Does this not seem counterintuitive to you? Suppose you find out you are living in a simulation on a 2 atom thick computer, and the simulation-keeper gives you a choice of (a) moving to a 1 atom thick computer, or (b) flipping a coin and shutting down the simulation or not based on the coin flip, would you really be indifferent? Under UDT-UMC, we can say that how much we care about an observer-moment is related to its "probability" under UD, but not necessarily exactly equal and could be influenced by other factors. If we accept the complexity of value thesis, then there is no reason why the measure of care has to be maximally simple, right? (This post is also related.)

1. In an infinite universe, there are infinitely many copies of you (infinitely many of which are Boltzmann brains).

This is a meme I keep seeing, and it's just not true. You need a lot more assumptions to justify that, such as "randomly generated", or very very strong versions of the cosmological principle.

The real line is infinite, but there's only one copy of the number 7.

The shortest description of me is a pair (U, x), where U is a description of my universe and x is a description of where to find me in that universe.

It might not be possible to describe U without making some arbitrary choices concerning "co-ordinates" (and other acts of "gauge-fixing"). And then when they're chosen, we're going to want to 'throw them away' once we've located the observer (since the co-ordinates are not physically meaningful and certainly don't form part of the observer's "mental state".)

So really, it's better to talk about a "centred universe" whose co-ordinates are specially chosen to have the observer in the middle, rather than an uncentered ("objective") universe plus a pointer.

Anyway, I still want to know whether being close to a 'landmark' (like a supermassive black hole) is going to significantly increase one's probability. And whether, if tons of copies of you are made and sent far and wide, you should 'anticipate' waking up close to a landmark.

The "Born Probabilities" section was 11 dang paragraphs of "they're the best fit to our observations and Occam's razor." :(

For example, if the last (truly random) coin I saw flipped came up heads, then in order to specify my experiences you need to specify the result of that coin flip. An equal number of equally complex descriptions point to the version of me who saw heads and the version of me who saw tails.

This is not necessarily true. The sequence HHHHHHHHHH has a lower Kolmogorov complexity than HTTTTHTHTT. So this weighting of observers by complexity has observable consequences in that we will see simpler strings more often than a uniform distribution would predict. But we don't, which makes this idea unlikely.

Consider a computer which is 2 atoms thick running a simulation of you. Suppose this computer can be divided down the middle into two 1 atom thick computers which would both run the same simulation independently. We are faced with an unfortunate dichotomy: either the 2 atom thick simulation has the same weight as two 1 atom thick simulations put together, or it doesn't.

UDASSA implies that simulations on the 2 atom thick computer count for twice as much as simulations on the 1 atom thick computer, because they are easier to specify.

I think the answer is that the 2-atom thick computer does not automatically have twice as much measure as a 1-atom thick computer. I think you're assuming that in the (U, x) pair, x is just a plain coordinate that locates a system (implementing an observer moment) in 4D spacetime plus Everett branch path. Another possibility is that x is a program for finding a system inside of a 4D spacetime and Everett tree.

Imagine a 2-atom thick computer (containing a mind) which will lose a layer of material and become 1-atom thick if a coin lands on heads. If x were just a plain coordinate, then the mind should expect the coin to land on tails with 2:1 odds, because its volume is cut in half in the heads outcome, and only half as many possible x bit-strings now point to it, so its measure is cut in half. However, if x is a program, then the program can begin with a plain coordinate for finding an early version of the 2-atom thick computer, and then contain instructions for tracking the system in space as time progresses. (The only "plain coordinates" the program would need from there would be a record of the Everett branches to follow the system through.) The locator x would barely need to change to track a future version of the mind after the computer shrinks in thickness compared to if the computer didn't shrink, so the mind's measure would not be affected much.

If the 2-atom thick computer split into two 1-atom thick computers, then you can imagine (U, x) where x is a locator for the 2-atom thick computer before the split, and (U, x1) and (U, x2) where x1 and x2 are locators for the different copies of the computer after the split. x1 and x2 differ from x by pointing to a future time (and record of some more Everett branches but I'm going to ignore that for this) and to differing indexes of which side of the split of the system to track at the time of the split. The measure of the computer is split into the different future copies, but this isn't just because each copy is half of the volume of the original, and does not imply that a 2-atom thick computer shrinking into 1-atom of thickness halves the measure. In the shrinking case, the program x does not need to contain an index about which side of the computer to track: the program contains code to track the computational system, and doesn't need much nudging to keep tracking the computational system when the edge of the material starts transforming into something else not recognized as the computational system. It's only in the case where both halves resemble the computational system enough to continue to be tracked that measure is split.

Jacques Mallah's paper on the Many Computations Interpretation seems relevant here.

Should

serious problems with Boltzmann machines

instead read

serious problems with Boltzmann brains

?

I sheepishly admit to not having followed this particularly well on the first read-through.

That said, it seems very well-structured, so I suspect that my inability to follow it is a symptom of not having sufficient familiarity with its prerequisites.

In any event, the sentence:

I am simply not going to try to be selfish (I don't know how).

....in context, was worth the price of admission of the entire essay.

UDASSA implies that simulations on the 2 atom thick computer count for twice as much as simulations on the 1 atom thick computer, because they are easier to specify. Given a description of one of the 1 atom thick computers, then there are two descriptions of equal complexity that point to the simulation running on the 2 atom thick computer: one description pointing to each layer of the 2 atom thick computer. When a 2 atom thick computer splits, the total number of descriptions pointing to the experience it is simulating doesn't change.

But those 2 descriptions are going to be nearly identical to each other. Shouldn't two descriptions that differ by very little, together, be less than two descriptions that differ a lot? It seems to make very little sense to me to give same weight to 10 beings each of which is unique, and to 10 beings which differ by 4 bits, especially when those bit are not going to propagate through into rest of the being.

Surely, most of us would strongly prefer a world where you have different people, to a world where one person is running on a very thick and inefficient computer.

I still don't get why people have to use all these indirect abstractions like measure rather than just thinking in ambient control on the multiverse directly.

Consider the randomized algorithm A: compute the state of the universe at time t, then sample a classical configuration with probability proportional to its squared inner product with the universal wavefunction.

Consider the randomized algorithm B: compute the state of the universe at time t, then sample a classical configuration with probability proportional to its inner product with the universal wavefunction.

Algorithm A is arguably far, far simpler than Algorithm B, because the component

probability proportional to its squared inner product with the universal wavefunction.

is arguably simpler than the component

probability proportional to its inner product with the universal wavefunction.

The difference is the simplicity of normalization, which you need to perform in order to find the probability density. If I recall correctly (and see reference below), normalization of the classical wavefunction satisfying the Schroedinger equation is relatively easy with respect to squared inner product (modulus squared), because all you have to do is find a single constant which normalizes the wavefunction at any particular time (your choice). Once that has been done, then the wavefunction remains normalized forever, with respect to the modulus squared, i.e., with respect to Algorithm A.

I haven't checked the math, but I would be flabbergasted if normalization with respect to Algorithm B were anything like that simple. On the contrary, I would expect to need to find a new constant for each moment in time.

As long as we are reasoning from simplicity, which you seem to be doing, then this seems to provide us with a strong reason to favor Algorithm A over Algorithm B.

reference:

if a wave-function is initially normalized then it stays normalized as it evolves in time according to Schrödinger's equation.

Not being careful in making descriptive statements:

My brain has preferences between probability distributions built into it.

As humans using Solomonoff induction, we go on to argue that

Fundamental mental entities:

Rather than supposing that the probability of a certain universe depends on the complexity of that universe, it takes as a primitive object a probability distribution over possible experiences.

Unsubstantiated claims:

The shortest description of me is a pair (U, x), where U is a description of my universe and x is a description of where to find me in that universe.

My brain has preferences between probability distributions built into it.

Mine doesn't. Where can get a patch?

The first link in your post is broken (Hal Finney's entire site seems to be down) but there's a mirror here.

It eventually learns that the simplest explanation for its experiences is the description of an external lawful universe in which its sense organs are embedded and a description of that embedding.

That's the simplest explanation for our experiences. It may or may not be the simplest explanation for the experiences of an arbitrary sentient thinker.

Rather than supposing that the probability of a certain universe depends on the complexity of that universe, it takes as a primitive object a probability distribution over possible experiences. By the same reasoning that led a normal Solomonoff inductor to accept the existence of an external universe as the best explanation for its experiences, the least complex description of your conscious experience is the description of an external lawful universe and directions for finding the substructure embodying your experience within that substructure.

Unless I'm misunderstanding you, you're saying that we should start with an arbitrary prior (which may or may not be the same as Solomonoff's universal prior). If you're starting with an arbitrary prior, you have no idea what the best explanation for your experiences is going to be, because it depends on the prior. According to some prior, it's a Giant lookup table. According to some prior, you're being emulated by a supercomputer in a universe whose physics is being emulated at the elementary particle level by hand calculations performed by an immortal sentient being (with an odd utility function), who lives in an external lawful universe.

Of course, the same will be true if you take the standard universal prior, but define Kolmogorov complexity relative to a sufficiently bizarre universal Turing machine (of which there are many). According to the theory, it doesn't matter because over time you will predict your experiences with greater and greater accuracy. But you never update the relative credences you give to different models which make the same predictions, so if you started off thinking that the simulation of the simulation of the simulation was a better model than simply discarding the outer layers and taking the innermost level, you will forever hold the unfalsifiable belief that you live in an inescapable Matrix, even as you use your knowledge to correctly model reality and use your model to maximize your personal utility function (or whatever it is Solomonoff inductors are supposed to do).

On first skim - what's a "classical configuration"? There are 3000 or so Google results (in conjunction with "Born") but I don't immediately see an answer.

Thanks for this.

The Born probability explanation sounds a lot like Scott Aaronson's explanation for why the moon is round: because if it weren't, we would not be ourselves, but rather entities exactly like ourselves except that they live in a universe with a square moon.

I don't know whether that's an argument against that explanation, or whether this is one of those cases where the reductio ad absurdum turns out to be true.