Re point 1, 2: Check this out. For the specific case of 0 to even bits, ??? to odd bits, I think solomonoff can probably get that, but not more general relations.Re: point 3, Solomonoff is about stochastic environments that just take your action as an input, and aren't reading your policy. For infra-Bayes, you can deal with policy-dependent environments without issue, as you can consider hard-coding in every possible policy to get a family of stochastic environments, and UDT behavior naturally falls out as a result from this encoding. There's still some op... (read more)
Ah. So, low expected utility alone isn't too much of a problem. The amount of weight a hypothesis has in a prior after updating depends on the gap between the best-case values and worst-case values. Ie, "how much does it matter what happens here". So, the stuff that withers in the prior as you update are the hypotheses that are like "what happens now has negligible impact on improving the worst-case". So, hypotheses that are like "you are screwed no matter what" just drop out completely, as if it doesn't matter what you do, you might as well pick actions t... (read more)
"mixture of infradistributions" is just an infradistribution, much like how a mixture of probability distributions is a probability distribution.Let's say we've got a prior ζ∈ΔN, a probability distribution over indexed hypotheses.If you're working in a vector space, you can take any countable collection of sets in said vector space, and mix them together according to a prior ζ∈ΔN giving a weight to each set. Just make the set of all points which can be made by the process "pick a point from each set, and mix the points together according to ... (read more)
The concave functional view is "the thing you do with a probability distribution is take expectations of functions with it. In fact, it's actually possible to identify a probability distribution with the function (X→R)→R mapping a function to its expectation. Similarly, the thing we do with an infradistribution is taking expectations of functions with it. Let's just look at the behavior of the function (X→R)→R we get, and neglect the view of everything as a set of a-measures."As it turns out, this view makes proofs a whole lot cleaner a... (read more)
Sounds like a special case of crisp infradistributions (ie, all partial probability distributions have a unique associated crisp infradistribution)Given some Q, we can consider the (nonempty) set of probability distributions equal to Q where Q is defined. This set is convex (clearly, a mixture of two probability distributions which agree with Q about the probability of an event will also agree with Q about the probability of an event).Convex (compact) sets of probability distributions = crisp infradistributions.... (read more)
You're completely right that hypotheses with unconstrained Murphy get ignored because you're doomed no matter what you do, so you might as well optimize for just the other hypotheses where what you do matters. Your "-1,000,000 vs -999,999 is the same sort of problem as 0 vs 1" reasoning is good.Again, you are making the serious mistake of trying to think about Murphy verbally, rather than thinking of Murphy as the personification of the "inf" part of the EΨ[f]:=inf(m,b)∈Ψm(f)+b definition of expected value, and writing actual equations. Ψ&nb... (read more)
There's actually an upcoming post going into more detail on what the deal is with pseudocausal and acausal belief functions, among several other things, I can send you a draft if you want. "Belief Functions and Decision Theory" is a post that hasn't held up nearly as well to time as "Basic Inframeasure Theory".
If you use the Anti-Nirvana trick, your agent just goes "nothing matters at all, the foe will mispredict and I'll get -infinity reward" and rolls over and cries since all policies are optimal. Don't do that one, it's a bad idea.For the concave expectation functionals: Well, there's another constraint or two, like monotonicity, but yeah, LF duality basically says that you can turn any (monotone) concave expectation functional into an inframeasure. Ie, all risk aversion can be interpreted as having radical uncertainty over some aspects of how the environment... (read more)
Maximin, actually. You're maximizing your worst-case result.It's probably worth mentioning that "Murphy" isn't an actual foe where it makes sense to talk about destroying resources lest Murphy use them, it's just a personification of the fact that we have a set of options, any of which could be picked, and we want to get the highest lower bound on utility we can for that set of options, so we assume we're playing against an adversary with perfectly opposite utility function for intuition. For that last paragraph, translating it back out from the "Murphy" t... (read more)
I found this Quanta magazine article about it which seems to indicate that it fits the CMB spectrum well but required a fair deal of fiddling with gravity to do so, but I lamentably lack the physics capabilities to evaluate the original paper.
If there's something wrong with some theory, isn't it quite odd that looking around at different parts of the universe seems to produce such a striking level of agreement on how much missing mass there is? If there was some out-of-left-field thing, I'd expect it to have confusing manifestations in many different areas and astronomers angsting about dramatically inconsistent measurements, I would not expect the CMB to end up explained away (and the error bars on those measurements are really really small) by the same 5:1 mix of non-baryonic matter vs baryon... (read more)
Yes, pink is gas and purple is mass, but also the gas there makes up the dominant component of the visible mass in the Bullet Cluster, far outweighing the stars.Also, physicists have come up with a whole lot of possible candidates for dark matter particles. The supersymmetry-based ones took a decent kicking at the LHC, and I'm unsure of the motivations for some of the other ones, but the two that look most promising (to me, others may differ in opinion) are axions and sterile neutrinos, as those were conjectured to plug holes in the Standard Model, so they... (read more)
I'd go with number 2, because my snap reaction was "ooh, there's a "show personal blogposts" button?"EDIT: Ok, I found the button. The problem with that button is that it looks identical to the other tags, and is at the right side of the screen when the structure of "Latest" draws your eyes to the left side of the screen. I'd make it a bit bigger and on the left side of the screen.
So, first off, I should probably say that a lot of the formalism overhead involved in this post in particular feels like the sort of thing that will get a whole lot more elegant as we work more things out, but "Basic inframeasure theory" still looks pretty good at this point and worth reading, and the basic results (ability to translate from pseudocausal to causal, dynamic consistency, capturing most of UDT, definition of learning) will still hold up.Yes, your current understanding is correct, it's rebuilding probability theory in more generality to be sui... (read more)
So, we've also got an analogue of KL-divergence for crisp infradistributions.
We'll be using P and Q for crisp infradistributions, and p and q for probability distributions associated with them. DKL will be used for the KL-divergence of infradistributions, and dKL will be used for the KL-divergence of probability distributions. For crisp infradistributions, the KL-divergence is defined as
I'm not entirely sure why it's like this, but it has the basic properties yo... (read more)
It is currently disassembled in my garage, will be fully tested when the 2.0 version is built, and the 2.0 version has had construction stalled for this year because I've been working on other projects. The 1.0 version did remove CO2 from a room as measured by a CO2 meter, but the size and volume made it not worthwhile.
Potential counterargument: Second-strike capabilities are still relevant in the interstellar setting. You could build a bunch of hidden ships in the oort cloud to ram the foe and do equal devastation if the other party does it first, deterring a first strike even with tensions and an absence of communication. Further, while the "ram with high-relativistic objects" idea works pretty well for preemptively ending a civilization confined to a handful of planets, AI's would be able to colonize a bunch of little asteroids and KBO's and comets in the oort cloud, and the higher level of dispersal would lead to preemptive total elimination being less viable.
I will be hosting a readthrough of this sequence on MIRIxDiscord again, PM for a link.
Reno has 90F daily highs during summer. Knocking 10 degrees off is a nonneglible improvement over Las Vegas, though.
So, here's some considerations (not an actual policy)It's instructive to look at the case of nuclear weapons, and the key analogies or disanalogies to math work. For nuclear weapons, the basic theory is pretty simple and building the hardware is the hard part, while for AI, the situation seems reversed. The hard part there is knowing what to do in the first place, not scrounging up the hardware to do it.First, a chunk from Wikipedia
Most of the current ideas of the Teller–Ulam design came into public awareness after the DOE attempted to censor a magazine ar
Person in a room: - 35 g of O2/hr from roomPerson in a room with a CO2 stripper: -35 g of O2/hr from roomHow does the presence of a CO2 stripper do anything at all to the oxygen amount in the air?
Do you think this problem is essentially different from "suppose Omega asks you for 10 bucks. You say no. Then Omega says "actually I flipped a fair coin that came up tails, if it had come up heads, I would have given you 100 dollars if I predicted you'd give me 10 dollars on tails"?(I think I can motivate "reconsider choosing heads" if you're like "yeah, this is just counterfactual mugging with belated notification of what situation you're in, and I'd pay up in that circumstance")
Maximin over outcomes would lead to the agent devoting all its efforts towards avoiding the worst outcomes, sacrificing overall utility, while maximin over expected value pushes towards policies that do acceptably on average in all of the environments that it may find itself in.Regarding "why listen to past me", I guess to answer this question I'd need to ask about your intuitions on Counterfactual mugging. What would you do if it's one-shot? What would you do if it's repeated? If you were told about the problem beforehand, would you pay money for a commitment mechanism to make future-you pay up the money if asked? (for +EV)
Yeah, looking back, I should probably fix the m- part and have the signs being consistent with the usual usage where it's a measure minus another one, instead of the addition of two signed measures, one a measure and one a negative measure. May be a bit of a pain to fix, though, the proof pages are extremely laggy to edit.Wikipedia's definition can be matched up with our definition by fixing a partial order where (m′,b′)≥(m,b) iff there's a (m∗,b∗) that's a sa-measure s.t. (m,b)+(m∗,b∗)=(m′,b′), and this generalizes to any closed c... (read more)
We go to the trouble of sa-measures because it's possible to add a sa-measure to an a-measure, and get another a-measure where the expectation values of all the functions went up, while the new a-measure we landed at would be impossible to make by adding an a-measure to an a-measure.Basically, we've gotta use sa-measures for a clean formulation of "we added all the points we possibly could to this set", getting the canonical set in your equivalence class.Admittedly, you could intersect with the cone of a-measures again at the end (as we do in the next post... (read more)
Can you elaborate on what you meant by locally distinguishing between hypotheses?
If hospitals are overwhelmed, it's valuable to have a component of the hospital treatment plan for pneumonia on-hand to treat either yourself or others who have it especially bad. One of these is oxygen concentrators, which are not sold out yet and are ~$400 on Amazon. This doesn't deal with especially severe cases, but for cases which fall in the "shortness of breath, low blood oxygen" class without further medical complications, it'd probably be useful if you can't or don't want to go to a hospital due to overload. http... (read more)
I found a paper about this exact sort of thing. Escardo and Olivia call that type signature a "selection functional", and the type signature (A→B)→B is called a "quantification functional", and there's several interesting things you can do with them, like combining multiple selection functionals into one in a way that looks reminiscent of game theory. (ie, if ϵ has type signature (A→C)→A, and δ has type signature (B→C)→B, then ϵ⊗δ has type signature ((A×B... (read more)
Oh, I see what the issue is. Propositional tautology given A means A⊢pcϕ, not A⊢ϕ. So yeah, when A is a boolean that is equivalent to ⊥ via boolean logic alone, we can't use that A for the exact reason you said, but if A isn't equivalent to ⊥ via boolean logic alone (although it may be possible to infer ⊥ by other means), then the denominator isn't necessarily small.
Yup, a monoid, because ϕ∨⊥=ϕ and A∪∅=A, so it acts as an identitity element, and we don't care about the order. Nice catch.
You're also correct about what propositional tautology given A means.
Yup! The subscript is the counterfactual we're working in, so you can think of it as a sort of conditional pricing.
The prices aren't necessarily unique, we set them anew on each turn, and there may be multiple valid prices for each turn. Basically, the prices are just set so that the supertrader doesn't earn money in any of the "possible" worlds that we might be in. Monotonicity is just "the price of a set of possibilities is greater than the price of a subset of possibilities"
If there's a short proof of ϕ from ψ and a short proof of ψ from ϕ and they both have relatively long disproofs, then counterfacting on ϕ, ψ should have a high value, and counterfacting on ψ, ϕ should have a high value.
The way to read ⊢ is that the stuff on the left is your collection of axioms (A is a finite collection of axioms and A,ϕ just means we're using the stuff in A as well as the statement ϕ as our axioms), and it proves some statement.
For the first formulation of the va... (read more)
Yup, this turned out to be a crucial consideration that makes the whole project look a lot less worthwhile. If ventilation at a bad temperature is available, it's cheaper to just get a heat exchanger and ventilate away and eat the increased heating costs during winter than to do a CO2 stripper.
There's still a remaining use case for rooms without windows that aren't amenable to just feeding an air duct outside, but that's a lot more niche than my original expectations. Gonna edit the original post now.
Also, a paper on extremely high-density algal photobioreactors quotes algal concentration by volume as being as high as 6% under optimal conditions. The dry mass is about 1/8 of the wet mass of algae, so that's 0.75% concentration by weight percent. If the algal inventory in your reactor is 9 kg dry mass (you'd need to waste about 3 kg/day of dry weight or 24 kg/day of wet weight, to keep up with 2 people worth of CO2, or a third of the algae each day), that's 1200 kg of water in your reactor. Since a gallon is about 4 kg of water, that&apos... (read more)
[EDIT: I see numbers as high as 4 g/L/day quoted for algae growth rates, I updated the reasoning accordingly]
The numbers don't quite add up on an algae bioreactor for personal use. The stated growth rate for chlorella algae is 0.6 g/L/day, and there are about 4 liters in a gallon, so 100 gallons of algae solution is 400 liters is 240 g of algae grown per day, and since about 2/3ds of new biomass comes from CO2 via the 6CO2+6H2O->C6H12O6 reaction, that's 160 g of CO2 locked up per day, or... about 1/6 of a person worth of CO2 in a 24 hour peri... (read more)
I have the relevant air sensor, it'd be really hard to blind it because it makes noise, and the behavioral effects thing is a good idea, thank you.
It's not currently with me.
I think the next thing to do is build the 2.0 design, because it should perform better and will also be present with me, then test the empirical CO2 reduction and behavioral effects (although, again, blinding will be difficult), and reevaluate at that point.
I have the relevant air sensor, it'd be really hard to blind it because it makes noise, and the behavioral effects thing is a good idea, thank you.
Just randomizing would be useful; obviously, your air sensor doesn't care in the least if it is 'blinded' or not. And if it's placed in a room you don't go into, that may be enough. As well, maybe you can modify it to have a flap or door or obstruction which opens or closes, greatly changing the rate of CO2 absorption, and randomize that; or if you have someone willing to help, they can come in every n time u
Good point on phase 6. For phase 3, smaller changes in velocity further out are fine, but I still think that even with less velocity changes, you'll still have difficulty finding an engine that gets sufficient delta-V that isn't fission/fusion/antimatter based. (also in the meantime I realized that neutron damage over those sorts of timescales are going to be *really* bad.) For phase 5, I don't think a lightsail would provide enough deceleration, because you've got inverse-square losses. Maybe you could decelerate with a lightsail in t... (read more)
Very good point!
I'd be extremely interested in the quantitative analysis you've done so far.
See if this works.
I'm talking about using a laser sail to get up to near c (0.1 g acceleration for 40 lightyears is pretty strong) in the first place, and slowing down by other means.
This trick is about using a laser sail for both acceleration and deceleration.
Yeah, I think the original proposal for a solar sail involved deceleration by having the central part of the sail detach and receive the reflected beam from the outer "ring" of the sail. I didn't do this because IIRC the beam only maintains coherence over 40 lightyears or so, so that trick would be for nearby missions.
For 1, the mental model for non-relativistic but high speeds should be "a shallow crater is instantaneously vaporized out of the material going fast" and for relativistic speeds, it should be the same thing but with the vaporization directed in a deeper hole (energy doesn't spread out as much, it keeps in a narrow cone) instead of in all directions. However, your idea of having a spacecraft as a big flat sheet and being able to tolerate having a bunch of holes being shot in it is promising. The main issue that I see is that this approach is ... (read more)
Whoops, I guess I messed up on that setting. Yeah, it's ok.
Actually, no! The activation energy for the conversion of diamond to graphite is about 540 kJ/mol, and using the Arrhenius equation to get the rate constant for diamond-graphite conversion, with a radiator temperature of 1900 K, we get that after 10,000 years of continuous operation, 99.95% of the diamond will still be diamond. At room temperature, the diamond-to-carbon conversion rate is slow enough that protons will decay before any appreciable amount of graphite is made.
Even for a 100,000 year burn, 99.5% of the diamond will still be intact at 1900 K.
Th... (read more)
Agreed. Also, there's an incentive to keep thinking about how to go faster until the marginal gain in design by one day of thought speeds the rocket up by less than one day, instead of launching, otherwise you'll get overtaken, and agreeing on a coordinated plan ahead of time (you get this galaxy, I get that galaxy, etc...) to avoid issues with lightspeed delays.
Or maybe accepting messages from home (in rocket form or not) of "whoops, we were wrong about X, here's the convincing moral argument" and acting accordingly. Then the only thing to be worried about would be irreversible acts done in the process of colonizing a galaxy, instead of having a bad "living off resources" endstate.
Edited. Thanks for that. I guess I managed to miss both of those, I was mainly going off of the indispensable and extremely thorough Atomic Rockets site having extremely little discussion of intergalactic missions as opposed to interstellar missions.
It looks like there are some spots where me and Armstrong converged on the same strategy (using lasers to launch probes), but we seem to disagree about how big of a deal dust shielding is, how hard deceleration is, and what strategy to use for deceleration.
Yeah, Atomic Rockets was an incredibly helpful resource for me, I definitely endorse it for others.
This doesn't quite seem right, because just multiplying probabilities only works when all the quantities are independent. However, I'd put higher odds on someone having the ability to recognize a worthwhile result conditional on them having an ability to work on a problem, then having the ability to recognize a worthwhile result, so the multiplication of probabilities will be higher than it seems at first.
I'm unsure whether this consideration affects whether the distribution would be lognormal or not.