So8res(Nate Soares)

Karma: 5,179

So8res 5 Mar 2021 5:20 UTC
8 points
in reply to: AlexMennen’s comment on: I’m still mystified by the Born rule
Thanks! I expect I can stare at this and figure something out about why there is no reasonable notion of “triality” in Vect (ie, no 3-way analog of vector space duality—and, like, obviously that’s a little ridiculous, but also there’s definitely still something I haven’t understood about the special-ness of the dual space).

ETA: Also, I’m curious what you think the connection is between the “L2 is connected to bilinear forms” and “L2 is the only Lp metric invariant under nontrivial change of basis”, if it’s easy to state.

FWIW, I’m mostly reading these arguments as being variations on “if you put anything else than a 2 there, your life sucks”, and I believe that, but I still have a sense that the explanation I’m looking for is more about how putting a 2 there is positively natural, not just the best of a bad lot. That said, I’m loving these arguments, and I expect I can mine them for some of the intuition-corrections I seek :-)

So8res 5 Mar 2021 4:50 UTC
14 points
in reply to: Adele Lopez’s comment on: I’m still mystified by the Born rule
Thanks! This seems to me like another piece of the puzzle =D

In this case, this is one that I already had (at least, well enough for the hindsight bias to kick in :-p), and it’s on my list of trailheads next time I try to ground out the 2 in the Born rule. FWIW, some lingering questions I have when I take this viewpoint include “ok, cool, why are there no corresponding situations where I want to compare 3 vectorish thingies?” / “I see why the argument works for 2, but I have a sneaking suspicion that this 2 is being slipped into the problem statement in a way that I’m not yet quite following”. Also, I have a sense that there’s some fairly important fact about anointing some linear isomorphism between a vector space and its dual as “canonical” that I have yet to grasp. Like, some part of the answer to “why do I never want to compare 3 vectorish thingies” is b/c the relationship between a vector space and its dual space is somehow pretty special, and there’s no correspondingly special… triality of vector spaces. (Hrm. I wonder whether I can ground the 2 in the Born rule out into the 2 in categorical duality. That would be nuts.)

FWIW, one of my litmus tests is question “assuming we are supposed to measure distance in R2 using an L2 norm, why are we not supposed to measure distance in R3 using an L3 norm?”. And, like, I have a bunch of explanations for why this is (including “L3 isn’t invariant under most any change of basis” (per Alex’s argument above) and “b/c the natural notion of distance between two points in R3 factors into two questions of distance in R2, so using L2 in R2 pins down using L2 in Rn”), but I still feel like there’s some… surprising fixation on 2 here, that I can’t yet explain to the satisfaction of young-Nate who guesses that cuberute(x^3 + y^3 + z^3)=r is the equation for a sphere. Like, I still feel kinda like math said “proof by induction: starting in the case where n=2, …” and I’m like “wat why aren’t we starting at 0” and it’s like “don’t worry, n < 2 will work out as special cases” and I’m like “ok, sure, this argument is valid, but also wtf are you doing”. My wtfs aren’t all ironed out yet.

And, maybe I’m chasing shadows (eg, seeking a logical explanation where there is none, which is the sort of thing that can happen to a poor sap who lacks an explicit understanding of logical causality), but my suspicion is that I’m still missing part of the explanation. And both this route (which I’d gloss as “understand why it’s so important/natural/??? to have/choose/determine a canonical isomorphism between your vector space and its dual, then appeal to bilinearity”, with a prereq of better understanding why we have/care-about duality but not triality in Vect) and Alex’s (which I’d gloss as “explain why 2 obviously-should-be the balance point in the Lp norms”) both feel like good trailheads to me.

(And, in case this wasn’t clear to all readers, none of my assertions of confusion here are allegations that everyone else is similarly confused—indeed, Alex and Adele have already given demonstrations to the contrary.)

<3 hooray.

So8res 5 Mar 2021 3:44 UTC
8 points
in reply to: evhub’s comment on: I’m still mystified by the Born rule
Cool, thanks. Yeah, I don’t have >50% on either of those two things holding up to philisophical progress (and thus, eg, I disagree that future theories need to agree with UDASSA on those fronts). Rather, happeningness-as-it-relates-to-multiple-simulations and happeningness-as-it-relates-to-the-simplicity-of-reality are precisely the sort of things where I claim Alice-style confusion, and where it seems to me like UDASSA is alledging answers while being unable to dissolve my confusions, and where I suspect UDASSA is not-even-wrong.

(In fact, you listing those two things causes me to believe that I failed to convey the intended point in my analogy above. I lean towards just calling this ‘progress’ and dropping the thread here, though I’d be willing to give a round of feedback if you wanna try paraphrasing or otherwise falsifying my model instead. Regardless, hooray for a more precise articulation of a disagreement!)

So8res 4 Mar 2021 21:44 UTC
14 points
in reply to: AlexMennen’s comment on: I’m still mystified by the Born rule
<3, this is exactly the sort of thought I claim to be missing when I say I still don’t know how to trace the 2 in the Born rule back to its maker. This is a step I didn’t yet have. It doesn’t feel like the last piece I’m missing, but it does feel like a piece—eg, now I can focus some attention on “why precisely is this crossover point at 2 / where is that 2 coming from?”. Thanks!

(And ofc there’s still a question about why we use an Lp norm, and indeed why we pass out gaze along the walls in a way that factors through the shadow on that wall, but I am fairly happy rolling most of that into the “what are we to learn from the fact that reality has the quantum nature” bundle.)

So8res 4 Mar 2021 14:26 UTC
4 points
in reply to: AlexMennen’s comment on: I’m still mystified by the Born rule
When you’re using TMs to approximate physics, you have to balance the continuity of physics against the discreteness of the machines somehow. The easy thing to do is to discuss the limiting behavior of a family of machines that perform the simulation at ever-finer fidelity. I was doing this implicitly, for lack of desire to get into details.

And as I’ve said above, I’m not attempting to suggest that these naive approaches—such as sampling a single classical state and reporting the positions of some things with arbitrary fidelity in the limit—are reasonable ideas. Quite the opposite. What I’m trying to point out is that if all you have is a quantum state and the Born rule, you cannot turn it into a hypothesis without making a bunch of other choices, for which I know of no consensus answer (and for which I have not seen proposals that would resolve the problem to my satisfaction, though I have some ideas).

I agree that the correct way of making these choices will almost surely not involve recording any observation with infinite precision (in the limit).

So8res 4 Mar 2021 6:54 UTC
8 points
in reply to: evhub’s comment on: I’m still mystified by the Born rule
Neat! I’d bet against that if I knew how :-) I expect UDASSA to look more like a red herring from the perspective of the future, with most of its answers revealed as wrong or not-even-wrong or otherwise rendered inapplicable by deep viewpoint shifts. Off the top of my head, a bet I might take is “the question of which UTM meta-reality uses to determine the simplicity of various realities was quite off-base” (as judged by, say, agreement of both EY and PC or their surrogates in 1000 subjective years).

In fact, I’m curious for examples of things that UDASSA seems to get right, that you think better theories must improve upon. (None spring to my own mind. Though, one hypothesis I have is that I’ve so-deeply-internalized all the aspects of UDASSA that seem obviously-true to me (or that I got from some ancestor-theory), that the only things I can percieve under that label are the controversial things, such that I am not attributing to it some credit that it is due. For instance, perhaps you include various pieces of the updateless perspective under that umbrella while I do not.)

So8res 4 Mar 2021 5:14 UTC
6 points
in reply to: TAG’s comment on: I’m still mystified by the Born rule

How could an SI compare a deterministic theory to a probablistic one?

The deterministic theory gets probability proportional to 2^-length + (0 if it was correct so far else -infty), the probabilistic theory gets probability proportional to 2^-length + log(probability it assigned to the observations so far).

That said, I was not suggesting a solomonoff inductor in which some machines were outputting bits and others were outputting probabilities.

I suspect that there’s a miscommunication somewhere up the line, and my not-terribly-charitable-guess is that it stems from you misunderstanding the formalism of Solomonoff induction and/or the point I was making about it. I do not expect to clarify further, alas. I’d welcome someone else hopping in if they think they see the point I was making & can transmit it.

So8res 4 Mar 2021 5:09 UTC
11 points
in reply to: evhub’s comment on: I’m still mystified by the Born rule

Absolutely no effect does seem pretty counterintuitive to me, especially given that we know from QM that different levels of happeningness are at least possible.

I also have that counterintuition, fwiw :-p

I have the sense that you missed my point wrt UDASSA, fwiw. Having failed once, I don’t expect I can transmit it rapidly via the medium of text, but I’ll give it another attempt.

This is not going to be a particularly tight analogy, but:

Alice is confused about metaethics. Alice has questions like “but why are good things good?” and “why should we care about goodness?” and “if goodness is not objective, can I render murder good by deciding it’s good?”.

Bob is not confused about ethics. Bob can correctly answer many of Alice’s questions: “good things are good b/c they result in good things such as, eg, human flourishing”, and “because we like good consequences, such as human flourishing”, and “no, because murder is not in fact good”. (...I’m only subtweeting Sam Harris a little bit, here.)

The problem with these answers is not that they are incorrect. The problem with these answers is that they are not deconfusing, they are not identifying the box that Alice is trapped in and freeing her from it.

Claire is not confused about metaethics. Claire can state correct answers to the questions that Alice did not know she was asking, such as “Alice!goodness is more-or-less a fixed logical funtion; Alice!goodness is perhaps slightly different from Claire!goodness but they are close enough as to make no difference against the space of values; this fixed logical function was etched into your genes by eons of sex and death; it is however good, and other logical functions in its place would not be.”

The problem with these answers is not that they are incorrect, as answers to the questions that Alice would have been asking were she freed from her box (although, once she’s glimpsed the heretofore hidden degree of freedom, she’s unlikely to need to actually ask those questions). The problem with these answers is that they are not meeting Alice at the point of her confusion. To her, they sound sort of odd, and do not yet have a distinguishable ring of truth.

What Alice needs in this hypothetical is a bunch of thought-experiments, observations, and considerations that cause her to percieve the dimension along which her hypotheses aren’t yet freed, so that the correct hypothesis can enter her view / so that her mind can undergo a subtle shift-in-how-she-frames-the-question such that the answers Claire gives suddenly become intuitively clear. She’s probably going to need to do a lot of the walking herself. She needs questions and nudges, not answers. Or something. (This is hard to articulate.)

I claim that my state wrt various anthropic questions—such as the ol’ trilemma—is analogous to that of Alice. I expect that becoming deconfused about the trilemma to feel like a bunch of changes to my viewpoint that cause the correct hypothesis to enter my view / that cause my mind to undergo a shift-in-how-I-frame-the-question such that the correct answer to snaps into focus. (This is still hard to articulate. I don’t think my words have captured the core. Hopefully they have waved in the right direction.) More generally, I claim to know what deconfusion looks like, and I can confidently assert that UDASSA hasn’t done it for me yet.

Like, for all I know, the odd shit UDASSA says to me is like the phrases Claire says to Alice—correct, topical, but odd-seeming and foreign from my current state of confusion. Perhaps there’s a pathway through the valley of my confusion that causes me to shift my understanding of (eg) the trilemma, such that the problem falls away, and I start emitting UDASSA-like sentences on the other side, but if so I have not yet found it.

And, as someone in the Claire-state wrt the problem of metaethics, I claim that I would be able to go back and walk Alice through the valley, to the point where she was happily emitting Claire-statements all her own. (Or, at least, I’d have a pretty good hit-rate among particularly sharp friends.) And I have not been able to cause any UDASSA-er to walk me through the valley. And also a number of the UDASSA-moves smell to me like missteps—perhaps b/c I’m bad at requesting it, but also perhaps b/c UDASSA doesn’t do the thing. All told, my guess is that it’s making about as much progress at resolving the core confusions as it looks like it’s making—ie, not much.

(To be clear, I have managed to get UDASSA to tell me why I shouldn’t be confused about the trilemma. But this is not the currency I seek, alas.)

So8res 4 Mar 2021 4:44 UTC
4 points
in reply to: TAG’s comment on: I’m still mystified by the Born rule
Yeah yeah, this is the problem I’m referring to :-)

I disagree that you must simulate collapse to solve this problem, though I agree that that would be one way to do it. (The way you get the right random numbers, fwiw, is from sample complexity—SI doesn’t put all its mass on the single machine that predicts the universe, it allocates mass to all machines that have not yet erred in proportion to their simplicity, so probability mass can end up on the class of machines, each individually quite complex, that describe QM and then hardcode the branch predictions. See also the proof about how the version of SI in which each TM outputs probabilities is equivalent to the version where they don’t.)

So8res 4 Mar 2021 4:35 UTC
5 points
in reply to: interstice’s comment on: I’m still mystified by the Born rule
^_^

Also, thanks for all the resource links!

So8res 4 Mar 2021 4:20 UTC
2 points
in reply to: TAG’s comment on: I’m still mystified by the Born rule
To be clear, the process that I’m talking about for turning a quantum state into a hypothesis is not intended to be a physical process (such as a measurement), it’s intended to be a Turing machine (that produces output suitable for use by Solomonoff induction).

That said, to be clear, I don’t think this is a fundamentally hard problem. My point is not “we have absolutely no idea how to do it”, it’s somehing more like “there’s not a consensus answer here” + “it requires additional machinery above and beyond [the state vector + the born rule + your home address]” + “in my experience, many (non-specialist-physicist) people don’t even register this as a problem, and talk about the Born rule as if it’s supposed to fill this gap”.

I agree that there are a bunch of reasonable additional pieces of machinery you can use to get the missing piece (such as choice of a “measurement basis”); my own suspicion is that the right answer looks a bit different from what I’ve seen others propose (and routes through, eg, machinery that lets you read off the remembered history, as opposed to machinery that picks some subbasis to retain); my guess is that there are experimental differences in theory but they’re probably tricky to create in practice, but I haven’t worked through the details myself.

So8res 4 Mar 2021 4:10 UTC
7 points
in reply to: interstice’s comment on: I’m still mystified by the Born rule
I agree that the problem doesn’t seem too hard, and that there are a bunch of plausible-seeming theories. (I have my own pet favorites.)

So8res 4 Mar 2021 4:07 UTC
6 points
in reply to: evhub’s comment on: I’m still mystified by the Born rule
This is precisely the thought that caused me to put the word ‘apparent’ in that quote :-p. (In particular, I recalled the original UDASSA post asserting that it took that horn, and this seeming both damning-to-me and not-obviously-true-for-the-reason-you-state, and I didn’t want to bog my comment down, so I threw in a hedge word and moved on.) FWIW I have decent odds on “a thicker computer (and, indeed, any number of additional copies of exactly the same em) has no effect”, and that’s more obviously in contradiction with UDASSA.

Although, that isn’t the name of my true objection. The name of my true objection is something more like “UDASSA leaves me no less confused, gives me no sense of “aha!”, or enlightenment, or a-mystery-unraveled, about the questions at hand”. Like, I continue to have the dualing intuitions “obviously more copies = more happening” and “obviously, setting aside how it’s nice for friends to have backup copies in case of catastrophe, adding an identical em of my bud doesn’t make the world better, nor make their experiences different (never mind stronger)”. And, while UDASSA is a simple idea that picks a horse in that race, it doesn’t… reveal to each intuition why they were confused, and bring them into unison, or something?

Like, perhaps UDASSA is the answer and I simply have not yet figured out how to operate it in a way that reveals its secrets? But I also haven’t seen anyone else operate it in a way that reveals the sort of things that seem-like-deconfusion-to-me, and my guess is that it’s a red herring.

So8res 4 Mar 2021 3:46 UTC
6 points
in reply to: evhub’s comment on: I’m still mystified by the Born rule
I agree that the Born rule is just the poster child for the key remaining confusions (eg, I would have found it similarly natural to use the moniker “Hilbert space confusions”).

I disagree about whether UDASSA contains much of the answer here. For instance, I have some probability on “physics is deeper than logic” being more-true-than-the-opposite in a way that ends up tossing UDASSA out the window somehow. For another instance, I weakly suspect that “running an emulation on a computer with 2x-as-thick wires does not make them twice-as-happening” is closer to the truth than the opposite, in apparent contradiction with UDASSA. More generally, I’m suspicious of the whole framework, and the “physics gives us hints about the UTM that meta-reality uses” line of attack feels to me like it has gone astray somewhere. (I have a bunch more model here, but don’t want to go into it at the moment.)

I agree that these questions likely go to the heart of population ethics as well as anthropics :-)

So8res 4 Mar 2021 3:33 UTC
6 points
in reply to: TAG’s comment on: I’m still mystified by the Born rule
I agree that there’s a difference between “put a delta-spike on the single classical state you sampled” and “zero out amplitude on all states not consistent with the observation you got from your sample”. I disagree that using the latter to generate a sensory stream from a quantum state yields reasonable predictions—eg, taken literally I think you’re still zeroing out all but a measure-zero subset of the position basis, and I expect the momenta to explode immediately. You can perhaps get this hypothesis (or the vanilla delta spike) hobbling by trying to smooth things out a bit (eg, keep a Gaussian centered on each classical state in which you made the sampled observation), but I still expect this to be experimentally distinguishable from what really happens (eg by way of some quantum-eraser-style hijinks or other sizeable entanglements), though I haven’t checked the details myself.

So8res 4 Mar 2021 2:56 UTC
11 points
in reply to: So8res’s comment on: Are the Born probabilities really that mysterious?
Warning: the post doesn’t attempt to answer your question (ie, “can we reduce the Born rule to conservation of information?”). I don’t know the answer to that. Sorry.

My guess is that a line can be drawn between the two; I’m uncertain how strong it can be made.

This may be just reciting things that you already know (or a worse plan than your current one), but in case not, the way I’d attempt to answer this would be:
1. Solidly understand how to ground out the Born rule in the inner product. (https://arxiv.org/abs/1405.7907 might be a good place to start if you haven’t already done this? I didn’t personally like the narrative there, but I found some of the framework helpful.)
2. Recall the details of that one theorem that relates unitary evolution to conservation of information.
3. Meditate on the connection between unitary operators, orthonormal bases, and the inner product.
4. See if there’s a compelling link to be made that runs from the Born rule, through the inner product operator, through unitarity, to conservation of information.
Also, I find this question interesting and am also curious for an answer :-)
What links here?
- I’m still mystified by the Born rule by So8res (4 Mar 2021 2:35 UTC; 73 points)

So8res 4 Mar 2021 2:39 UTC
21 points
on: Are the Born probabilities really that mysterious?
I tried to commentate, and accidentally a whole post. Short version: I think one or two of the many mysteries people tend to find swirling around the Born rule are washed away by the argument you mention (regardless of how tight the analogy to Liouville’s theorem), but some others remain (including the one that I currently consider central).

I’m still mystified by the Born rule

So8res4 Mar 2021 2:35 UTC

73 points

40 comments10 min readLW link

So8res 3 Mar 2021 20:35 UTC
19 points
on: So8re’s Shortform Feed
Crossposted from Twitter, might not engage much with comments on LW and I may or may not moderate replies.
PSA: In my book, everyone has an unlimited number of “I don’t understand”, “plz say that again in different words”, “plz expand upon that”, and “plz pause while I absorb that” tokens.
Possession of an unlimited number of such tokens (& their ilk) is one of your sacred rights as a fellow curious mind seeking to understand the world around you. Specifically, no amount of well-intentioned requests for clarification or thinking time will cause me to think you’re an idiot.
I might conclude that there’s more ground to cover than I hoped; I may despair of communicating quickly; I might rebudget my attention. But asking for clarification or time-to-consider won’t convince me you’re a fool. (In fact, I consider it evidence to the contrary!).
If you ask loads of Qs, I sometimes get frustrated. Sometimes b/c my goals were frustrated, but more often it’s b/c I tend to feel strong visceral frustration when asked for clarification re a concept I kinda understand, don’t fully understand, and wish to understand. (I find this breed of frustration quite valuable—it tends to spur me to gain deeper understandings of things I care about. My apologies to those who ask me Qs, watch me get viscerally frustrated, and believe that the frustration is directed at them. Known rent-paying bug.)
I’m not saying that spending these tokens will never cost you. Noticing a big inferential gap can sap my desire to continue, which may sting, etc. etc. But if I do cease my attempts to convey, it will be with sadness—towards my lack of time, not your lack of smarts.
(Also, tbc, the usual outcome is not that I despair of communicating. In my experience, communicating w/ high caliber thinkers on technical topics involves regular and repeated expenditure of these tokens.)

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So8res31 Jan 2021 2:58 UTC

9 points

7 comments1 min readLW link

So8res(Nate Soares)

I’m still mys­tified by the Born rule

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I’m still mystified by the Born rule

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