If you attended (or tried to attend, or thought about) a Seattle TSAD meetup, I’d love to hear your feedback!
Optimization Process
Karma: 748
(Thanks for your response! I’m pessimistic that this conversational subtree will lead to great insights for either of us, but am jotting down my scattered thoughts in case they’re of interest.)
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It seems to me that you can represent a sequential setting as a one-shot
SituationwhoseActiontype is a function from “observations so far” (in your +50%/-40% example,List<"win"|"lose">) to “action I take in that sub-situation” (in your example, the fraction of my bankroll I bet on the next flip.(...maybe you can’t do this transform if you violate dynamic consistency? But violating dynamic consistency seems Actually Crazy in a way that merely violating consequentialism isn’t. Something is deeply broken if you simultaneously think “I’m going to do X if Y happens” and “I know that after Y happens I won’t do X.”)
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In your “fair coin, +50%/-40%” example: if I have the opportunity to play this game for 10 rounds, and my life savings are $100k, then I agree “always bet everything” seems like a bad plan, and optimizing for my median net worth at the end seems pretty reasonable.
...but if $100k is just the contents of my wallet, and I have $X in illiquid assets that can’t participate in this game… and $X is much larger than ($100k)x(1.5^10)… then optimizing for my median net worth at the end no longer seems reasonable.
My best guess at your resolution to this is something like “in the second case, 10 rounds isn’t necessarily sequential enough, you need a number of iterations that depends on X”; but me having an extra $100T at home doesn’t affect my preference ordering of outcomes, and it seems to me that a median-utility-based decision theory should be insensitive to the magnitude of [my illiquid savings] vs [my bankroll].
No response required!
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A friend and I spent a day or two poring over… one of Ole Peters’s papers, I believe this one… a couple years ago, and came away feeling like we still didn’t “get it.” Reading this post, I, uh, well, I still don’t get it, but thank you for helping my confusion at least crystallize into an I-think-well-defined question:
type Situation<Action, Utility> = Action -> Map<Utility, Probability> // "If I take action A, what's the probability I get payout U?" type DecisionTheory<A, U> = Situation<A, U> -> A // "What action should I take in this situation?" ev_maximization: DecisionTheory<Any, RealNumber> = situation -> argmax( situation.actions, action -> sum(u * p for u, p in situation(action)) ) // There are of course many more decision theories; e.g. your "preference utility" is pointing at the set of decision theories whose only requirement of the Utility type is that it be totally ordered. coolness: (DecisionTheory -> RealNumber) = TODO // some obviously-reasonable objective function recommendation: DecisionTheory = TODO // some ergodic-flavored decision theory assert coolness(recommendation) > coolness(ev_maximization)What valid (coolness, recommendation) pair is most likely to make me say
Ah, yes, that coolness function seems like a reasonable candidate for The One True Metric By Which To Judge Decision Theories, at least as good as judging decision theories by how much they maximize my average utility.
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What anchors the reality of [whether Claude is being used for mass surveillance and/or autonomous weapons] to [the words published by Anthropic and the Pentagon]? (What stops Anthropic from folding and plausibly-deniably lying-in-ways-that-aren’t-technically-legally-lying about it?)
So your update is mostly correct, except that the droplets usually vaporize “inside the valve”, not “immediately after the valve”.
Oh, that’s very interesting. I’ll have to look into that more. (And learn more about Joule-Thomson, which I know… of… but was hoping I could ignore.)
Thanks again for the brain!
Thanks much for the brainpower! Agreed that this is easier to think about in terms of classical thermodynamics with its continuous fluids; I’m just on a bit of a stubbornly fundamentalist kick (ex).
If it entertains you to continue chatting, I have a couple clarifying questions:
They are in an environment where the pressure is low enough that [the droplets] can vaporize [...] the system is a vapor+liquid saturated equilibrium.
“Saturated equilibrium” sounds at odds with “pressure low enough that the droplets can vaporize.” Reconcile? (My best guess: you’re saying that the droplets evaporate enough to establish an equilibrium partial pressure very quickly after the expansion valve.)
the refrigerant droplets vaporize completely because of heat transfer from the outside in the evaporator, not vaporizing THEN absorbing heat from the outside.
IIUC: you’re saying that my diagram is incorrect in depicting the droplets vaporizing completely in the bulk of the gas; actually, the vaporization mostly (entirely?) occurs on the surface of the evaporator. Seems totally plausible. But, for heat to transfer from the exterior to the droplets, the droplets must be colder than the exterior; am I correct in identifying post-expansion-valve evaporative cooling as the reason the droplets are cold?
Trying to synthesize your response into my stubbornly-statistical-mechanical model, my update is:
immediately after the expansion valve, the droplets quickly evaporate enough to establish the equilibrium partial pressure;
that evaporation results in the liquid+vapor mixture being cold;
cold droplets (which, contra my diagram, have not mostly evaporated) settle on the surface of the evaporator;
heat conducts from outside into those droplets, which consequently finish vaporizing
(Tongue partly-but-not-entirely in cheek: if you painstakingly prepare a second box of gas with the exact same initial conditions as the first, it will have exactly the same temperature; corollary, if you painstakingly prepare a second person with the exact same initial conditions as the first, they will have exactly the same free will.)
Free will is like temperature: a useful tool for analyzing the behavior of certain systems which are too big and complicated to model in exact detail.
If you know the positions and velocities of every atom in a box of gas, with enough compute you can predict its future to arbitrary precision; does it “have a temperature”? Irrelevant! Technically yes, I guess, but it’s sorta an epiphenomenon, screened off from reality by your exact knowledge of the initial conditions and your willingness to throw compute at your model. But if you’re less-than-perfectly omniscient, it might be more convenient to consider the box as having a “temperature” and model it more abstractly.
Substitute “person+environment”/”free will” for “box of gas”/”temperature” and that’s all still true.
I see! Thanks for the thoughtful response. I think my problem is caused by not having brought enough neuroscience and psychology textbooks to my armchair, leaving me in too-many-plausible-hypotheses-land, rather than your too-few-. I’ll take another stab at this sequence if/when I collect more background knowledge!
I’ve read about half of this sequence, and it’s certainly the most palatable, well-founded-seeming discussion of consciousness I’ve ever encountered.
But… I’ve kind of run aground on the question: how would I tell if this is true? (Or, you know, all models are false etc., but how would I tell if this is useful?)
Three examples of how a theory can useful: “Hey, I came up with this new theory of blurtzian phenomena! …
Make predictions: ”...The literature has catalogued 347 kinds of blurtz, but under this model, there should be at least two more, with the following characteristics: [...]”
Distill: ”...The literature has catalogued 351 kinds of blurtz with various complicated characteristics, but under this model, all those complicated characteristics are pretty closely retrodicted by modeling each of the (3^3 choose 2) blurtzes as being the interaction of [...]”
Babble: ”...The literature has a couple different models of blurtzes, all with various open questions. Here’s one more. It’s not obviously right, but it’s another promising direction to go.”
This sequence doesn’t feel like (1) or (2) to me. Is it (3), or something else?
Heuristic: distrust any claim that’s much memetically fitter than its retraction would be. (Examples: “don’t take your vitamins with {food}, because it messes with {nutrient} uptake”; “Minnesota is much more humid than prior years because of global-warming-induced corn sweat”; “sharks are older than trees”; “the Great Wall of China is visible from LEO with the naked eye”)
It sounds like you’re assuming you have access to some “true” probability for each event; do I misunderstand? How would I determine the “true” probability of e.g. Harris winning the 2028 US presidency? Is it 0⁄1 depending on the ultimate outcome?
(Hmm. Come to think of it, if the y-axis were in logits, the error bars might be ill-defined, since “all the predictions come true” would correspond to +inf logits.)
Ah—I took every prediction with p<0.50 and flipped ’em, so that every prediction had p>=0.50, since I liked the suggestion “to represent the symmetry of predicting likely things will happen vs unlikely things won’t.”
Thanks for the close attention!
I like the idea, but with n>100 points a histogram seems better, and for few points it’s hard to draw conclusions. e.g., I can’t work out an interpretation of the stdev lines that I find helpful.
Nyeeeh, I see your point. I’m a sucker for mathematical elegance, and maybe in this case the emphasis is on “sucker.”
I’d make the starting point p=0.5, and use logits for the x-axis; that’s a more natural representation of probability to me. Optionally reflect p<0.5 about the y-axis to represent the symmetry of predicting likely things will happen vs unlikely things won’t.
(same predictions from my last graph, but reflected, and logitified)
Hmm. This unflattering illuminates a deficiency of the “cumsum(prob—actual)” plot: in this plot, most of the rise happens in the 2-7dB range, not because that’s where the predictor is most overconfident, but because that’s where most of the predictions are. A problem that a normal calibration plot wouldn’t share!
(A somewhat sloppy normal calibration plot for those predictions:
Perhaps the y-axis should be be in logits too; but I wasn’t willing to figure out how to twiddle the error bars and deal with buckets where all/none of the predictions came true.)
Random numbers! Code for the last figures.
That all of physics was perfectly beautiful and symmetric except for hyperspace, artificial gravity, shields and a few weapon types.
Oh, this is genius. I love this.
Ahhh! Yes, this is very helpful! Thanks for the explanation.
Question: if I’m considering an isolated system (~= “the entire universe”), you say that I can swap between state-vector-format and matrix-format via
. But later, you say...
If is uncoupled to its environment (e.g. we are studying a carefully vacuum-isolated system), then we still have to replace the old state vector picture by a (possibly rank ) density matrix …
But if , how could it ever be rank>1?
(Perhaps more generally: what does it mean when a state is represented as a rank>1 density matrix? Or: given that the space of possible s is much larger than the space of possible s, there are sometimes (always?) multiple s that correspond to some particular ; what’s the significance of choosing one versus another to represent your system’s state?)
Man, biology is both proof and disproof of God.
I’ve been greatly enjoying this series of animations of cellular processes—no expert I, but the individually rendered atom-lumps and the Brownian jostling make me think this guy cares about messy physical realism in a way my sterile textbook drawings have elided.
This bit about DNA-replication is my favorite so far.
How could such a mechanism possibly ever evolve?
Who would possibly ever design it like this?