Posts
Comments
One overriding perspective in Max and my approach is that we need to design our systems so that their safety can be formally verified. In software, people often bring up the halting problem as an argument that general software can't be verified. But we don't need to verify general software, we are designing our systems so that they can be verified.
I am a great proponent of proof-carrying code that is designed and annotated for ease of verification as a direction of development. But even from that starry-eyed perspective, the proposals that Andrew argues against here seem wildly unrealistic.
A proof-carrying piece of C code can prove that it is not vulnerable to any buffer overflows, or that it will never run motor 1 and motor 2 simultaneously in opposite directions. A bit more ambitiously, it could contain a full proof of a complete behavioral specification, proving that the software will perform a certain set of behaviors at all times, which as a corollary also implies that it is proof against a large body of security threats. This is not something we can really manage in practice yet, but it's well within the extrapolated range of current techniques. We could build a compiler that will only compile software that contains a proof matching some minimum necessary specification, too.
Now imagine trying to prove that my program doesn't perform any sequence of perfectly innocuous interactions that happens to trigger a known or unknown bug in a mysql 5.1.32 server on the internet somewhere. How would you specify that? You can specify that the program doesn't do anything that might affect anything ever (though this leads to the well-known boxing problems); but if I want my program to have some nonzero ability to affect things in non-malicious ways, how would you specify that it doesn't do anything that might break something in some other part of the world in some unexpected way, including any unknown zero-days in mysql 5.1.32 servers? Presumably my proof checker doesn't contain the full code of all other systems on the internet my software might plausibly interact with. How could I specify a requirement like this, let alone prove it?
Proving that a piece of software has the behavior I want, or the behavior I allow, is something that can be done by carefully annotating my code with lemmas and contracts and incremental assumptions that together build up to a proof of the behavior I want. Proving that the software will have the behavior I want no matter what conditions you could possibly throw at it sounds harder but is actually mostly the same problem -- and so I would expect that proofs of almost-perfect security of a piece of software would not be that difficult either. But that is security of the software against attacks that might threaten the desired behavior of the software. Demonstrating that the software is not a threat to something else somewhere is another matter entirely, as this requires first knowing and encoding in the proofs all the ways in which the rest of the world might be negatively affected by actions-in-general. Not just superficially, either, if you want the proof to rule out the mysql 5.1.32 zero-day that just uses a sequence of normal interactions that should be perfectly innocent but in practice aren't. This is proving a negative in the worst possible way; to prove something like this, you would need to quantify over all possible higher-order behaviors the program doesn't have. I don't see how any of the real-or-imagined formal verification techniques I have ever heard about could possibly do anything even vaguely like this.
All the above is the world of software versus software, where even the external environment can be known to the last bit, with crisp behavior that can be analyzed and perfectly simulated even to the point where you can reproduce the mysql 5.1.32 bugs. Doing the same thing with biology would be a whole other order of magnitude in challenge level. Proving that a certain piece of synthesized DNA is not going to form a threat to human biology in some indirect way is essentially analogous to the mysql exploitation problem above, but much, much harder. Here, too, you would need to have a proof that quantifies over all possible higher order behaviors the piece of DNA doesn't have, all applied to the minor inconvenience that is the much murkier world of biology.
Unless I missed some incredible new developments in the field of formal verification, quantification over all possible higher order patterns and consequences of a system being analyzed is something that is absolutely out of reach of any formal verification techniques I have heard of. But if you do know of any techniques that could challenge this barrier, do tell :)
This seems very confused.
What makes good art a subjective quality is that its acceptance criterion is one that refers to the viewer as one of its terms. The is-good-art() predicate, or the art-quality() real-valued function, has a viewer parameter in it. What makes good physics-theory an objective quality is that its acceptance criterion doesn't refer to the viewer; the is-good-physics-theory() predicate, or the physics-theory-accuracy() real-valued function, is one that compares the theory to reality, without the viewer playing a role as a term inside the function.
Sure, both of these functions are in the end computed by human brains, which adds a level of subjectivity to the imperfect physical act of actually evaluating these functions. But that doesn't mean that the ideal things-that-these-brains-are-supposedly-evaluating are themselves subjective. A human brain evaluating how accurate a certain physics theory is results in a subjective assessment of an objective truth; a human brain evaluating whether a certain painting is art results in a subjective assessment of a subjective property. The act of assessment by an imperfect brain adds a layer of subjectivity over something that may or may not be objective in the abstract; but that abstract ideal of that which these brains are supposedly evaluating has a real difference in kind that is well beyond mere consensus.
Modifiers and subjectivity-affecting operations can be applied to both objective and subjective criteria, of course. The degree to which a theory of physics reflects reality is an objective measure; the degree to which a reader likes a theory is a subjective measure. The degree to which a viewer considers a painting to be art is a subjective measure; the degree to which the average human viewer considers a painting to be art is an objective measure, because the viewer parameter has been aggregated out. But these complications only obscure the basic distinction, they do not fundamentally challenge it.
This was my experience studying in the Netherlands as well. University officials were indeed on board with this, with the general assumption being that lectures and instructions and labs and such are a learning resource that you can use or not use at your discretion.
I would say that some formal proofs are actually impossible
Plausible. In the aftermath of spectre and meltdown I spent a fair amount of time thinking on how you could formally prove a piece of software to be free of information-leaking side channels, even assuming that the same thing holds for all dependent components such as underlying processors and operating systems and the like, and got mostly nowhere.
In fact, I think survival timelines might even require anyone who might be working on classes of software reliability that don't relate to alignment to actually switch their focus to alignment at this point.
Does that include those working on software correctness and reliability in general, without a security focus? I would expect better tools for making software that is free of bugs, such as programs that include correctness proofs as well as some of the lesser formal methods, to be on the critical path to survival -- for the simple reason that any number of mundane programming mistakes in a supposedly-aligned AI could easily kill us all. I was under the impression that you agree with this ["Assurance Requires Formal Proofs"]. I expect formal proofs of security in particular to be largely a corollary of this -- a C program that is proven to correctly accomplish any particular goal will necessarily not have any buffer overflows in it, for this would invoke undefined behavior which would make your proof not go through. This does not necessarily apply to all security properties, but I would expect it to apply to most of them.
Yes, I agree with this.
I cannot judge to what degree I agree with your strategic assessment of this technique, though. I interpreted your top-level post as judging that assurances based on formal proofs are realistically out of reach as a practical approach; whereas my own assessment is that making proven-correct [and therefore proven-secure] software a practical reality is a considerably less impossible problem than many other aspects of AI alignment, and indeed one I anticipate to actually happen in a timeline in which aligned AI materializes.
Assurance Requires Formal Proofs, Which Are Provably Impossible
The Halting Problem puts a certain standard of formalism outside our reach
This is really not true. The halting problem only makes it impossible to write a program that can analyze a piece of code and then reliably say "this is secure" or "this is insecure". It is completely possible to write an analyzer that can say "this is secure" for some inputs, "this is definitely insecure for reason X" for some other inputs, and "I am uncertain about your input so please go improve it" for everything in between. In particular, it is completely possible to have a machine-checkable proof system going along with executable code that can express proofs of extremely strong security properties for almost every program you might wish to run in practice, which can then judge "I can confirm this is secure" or "I can not confirm that this is secure which may or may not indicate an actual problem so go fix it".
Pulling this off in practice is still fiendishly difficult, of course, and progress in this field has been frustratingly slow. But there is no theoretical reason to suspect that this is fundamentally out of reach. (Or at least, not in the halting problem; Löb's theorem does provide some real limitations here that are particularly relevant for AI correctness proofs. But that is fairly niche relative to the broader notion of software correctness and security proofs.)
We see this a lot on major events, as I’ve noted before, like the Super Bowl or the World Cup. If you are on the ball, you’ll bet somewhat more on a big event, but you won’t bet that much more on it than on other things that have similarly crazy prices. So the amount of smart money does not scale up that much. Whereas the dumb money, especially the partisans and gamblers, come out of the woodwork and massively scale up.
This sounds like it should generalize to "in big events, especially those on which there are vast numbers of partisans on both sides, the prediction markets will reliably be insane and therefore close to useless for prediction purposes". Is that something one sees in practice for things like the World Cup?
One way the World Cup and Super Bowl differ from the election is that in a championship match, only a modest fraction of the people interested in the tournament as a whole will be partisans for the two contestants participating in the championship match; whereas in the election, I would expect the partisan coefficient to be much higher than that. Would that affect the degree to which the dumb money will overwhelm the smart money? I would expect so.
I do not think you are selling a strawman, but the notion that a utility function should be computable seems to me to be completely absurd. It seems like a confusion born from not understanding what computability means in practice.
Say I have a computer that will simulate an arbitrary Turing machine T, and will award me one utilon when that machine halts, and do nothing for me until that happens. With some clever cryptocurrency scheme, this is a scenario I could actually build today. My utility function ought plausibly to have a term in it that assigns a positive value to the computer simulating a halting Turing machine, and zero to the computer simulating a non-halting Turing machine. Yet the assumption of utility function computability would rule out this very sensible desire structure.
If I live in a Conway's Game of Life universe, there may be some chunk of universe somewhere that will eventually end up destroying all life (in the biological sense, not the Game of Life sense) in my universe. I assign lower utility to universes where this is the case, than to those were it is not. Is that computable? No.
More prosaically, as far as I currently understand, the universe we actually live in seems to be continuous in nature, and its state may not be describable even in principle with a finite number of bits. And even if it is, I do not actually know this, which means my utility function is also over potential universes (which, as far as I know, might be the one I live in) that require an infinite amount of state bits. Why in the world would one expect a utility function over an uncountable domain to be computable?
As far as I can see, the motivation for requiring a utility function to be computable is that this would make optimization for said utility function to be a great deal easier. Certainly this is true; there are powerful optimization techniques that apply only to computable utility functions, that an optimizer with an uncomputable utility function does not have access to in their full form. But the utility function is not up for grabs; the fact that life will be easier for me if I want a certain thing, should not be taken as an indication that that is want I want! This seems to me like the cart-before-horse error of trying to interpret the problem as one that is easier to solve, rather than the problem one actually wants solved.
One argument is that U() should be computable because the agent has to be able to use it in computations. If you can't evaluate U(), how are you supposed to use it? If U() exists as an actual module somewhere in the brain, how is it supposed to be implemented?
This line of thought here illustrates very well the (I claim) grossly mistaken intuition for assuming computability. If you can't evaluate U() perfectly, then perhaps what your brain is doing is only an approximation of what you really want, and perhaps the same constraint will hold for any greater mind that you can devise. But that does not mean that what your brain is optimizing for is necessarily what it actually wants! There is no requirement at all that your brain is a perfect judge of the desirability of the world it's looking at, after all (and we know for a fact that it does a far from perfect job at this).
This second claim sounds to me as being a bit trivial. Perhaps it is my reverse engineering background, but I have always taken it for granted that approximately any mechanism is understandable by a clever human given enough effort.
This book [and your review] explains a number of particular pieces of understanding of biological systems in detail, which is super interesting; but the mere point that these things can be understood with sufficient study almost feels axiomatic. Ignorance is in the map, not the territory; there are no confusing phenomena, only minds confused by phenomena; etc. Even when I knew nothing about this biological machinery, I never imagined for a second that no understanding was attainable in principle. I only saw *systems that are not optimized for ease of understanding*, and therefore presumably more challenging to understand than systems designed by human engineers which *are* optimized for ease of understanding.
But I get the impression that the real point you are shooting for (and possibly, the point the book is shooting for) is a stronger point than this. Not so much "there is understanding to be had here, if you look deeply enough", but rather a claim about what *particular type of structure* we are likely to find, and how this may or may not conform to the type of structure that humans are trained to look for.
Is this true? If it is, could you expand on this distinction?
If you are going to include formal proofs with your AI showing that the code does what it's supposed to, in the style of Coq and friends, then the characteristics of traditionally unsafe languages are not a deal-breaker. You can totally write provably correct and safe code in C, and you don't need to restrict yourself to a sharply limited version of the language either. You just need to prove that you are doing something sensible each time you perform a potentially unsafe action, such as accessing memory through a pointer.
This slows things down and adds to your burdens of proof, but not really by that much. It's a few more invariants you need to carry around with you throughout your proofs. Where in a safer language you may have to prove that your Foo list is still sorted after a certain operation, in C you will additionally have to prove that your pointer topology is still what you want after a certain operation. No big deal. In particular, a mature toolkit for proving properties about C programs will presumably have tools for automating away the 99% of trivial proof obligations involving pointer topology, leaving something for you to prove only when you are doing something clever.
For any such property that you can screw up, a language that will not allow you to screw it up in the first place will make your life easier and your proofs simpler, which is why OCaml is more popular as a vehicle for proven correct code than C. But if you are proving the correctness of every aspect of your program anyway, this is a pretty minor gain; the amount of stuff there is to prove about your object-level algorithms will be vastly greater than the requirements added by the lack of safety of your programming language. If only because there will be specialized tools for rapidly dealing with the latter, but not the former.
Not all those specialized tools exist just yet. Currently, the program correctness proof systems are pretty good at proving properties about functions [in the mathematical sense] operating on data structured in a way that mathematicians like to work with, and a bit rubbish at everything else people use software to do; it is no coincidence that Coq, Agda, Idris, Isabelle, and friends all work primarily with purely functional languages using some form of constructed types as a data model. But techniques for dealing with computing applications in a broader sense will have to be on the proof-technology roadmap sooner or later, if correctness proofs are ever going to fulfill their promise outside selected examples. And when they do, there will not be a big difference between programming in C and programming in OCaml as far as proving correctness is concerned.
tl;dr: I don't think language safety is going to be more than a rounding error if you want to prove the correctness of a large piece of software down to the last bit, once all the techniques for doing that sort of thing at all are in place. The amount of program-specific logic in need of manual analysis is vastly greater than the amount of boilerplate a safe language can avoid.
The point is: if people understood how their bicycle worked, they’d be able to draw one even without having to literally have one in front of them as they drew it!
I don't think this is actually true. Turning a conceptual understanding into an accurate drawing is a nontrivial skill. It requires substantial spatial visualization ability, as well as quite a bit of drawing skill -- one who is not very skilled in drawing, like myself, might poorly draw one part of a bike, want to add two components to it, and then realize that there is no way to add a third component to the poor drawing without turning it into an illegible mess of ink. There is a reason technical drawing is an explicit course in engineering education.
I built a nontrivial construction yesterday, that I understand in great detail and personally designed in OpenSCAD beforehand, that I could not put on paper by hand in a way that is vaguely mechanically accurate, without a visual reference (be it the actual construction or the CAD model). At least, not in one try -- I might manage if it I threw away the first three sketches.
Even if such a person decides to do this, they will eventually get fed up and leave.
Will they, necessarily? The structure of the problem you describe sounds a lot like any sort of teaching, which involves a lot of finding out what a student misunderstands about a particular topic and then fixing that, even if you clear up that same misunderstanding for a different student every week. There are lots of people who do not get fed up with that. What makes this so different?
Pigeons have stable, transitive hierarchies of flight leadership, and they have stable pecking order hierarchies, and these hierarchies do not correlate.
one of the things you can do with the power to give instructions is to instruct others to give you more goodies.
It occurs to me that leading a flight is an unusual instruction-giving power, in that it comes with almost zero opportunities to divert resources in your own direction. Choosing where to fly and when to land affects food options, but it does not affect your food options relative to your flight-mates. Most leadership jobs give many more opportunities to turn the position into zero-sum personal benefits.
I suspect this is not a coincidence. Can anyone think of a case where the pecking order and the leadership hierarchy are uncorrelated in a situation where the leadership is exploitable for pecking opportunities?
General rationality question that should not be taken to reflect any particular opinion of mine on the topic at hand:
At what point should "we can't find any knowledgeable critics offering meaningful criticism against <position>" be interpreted as substantial evidence in favor of <position>, and prompt one to update accordingly?
Having lost this signaling tool, we are that much poorer.
Are we? Signaling value is both a blessing and a curse, and my impression is that it is generally zero-sum. Personally, I consider myself *richer* when a mundane activity or lifestyle choice loses its signaling association, for it means I am now less restricted in applying it.
At the time of writing, for the two spoilers in the main post, hovering over either will reveal both. Is that intentional? It does not seem desirable.
I think there is about a three orders of magnitude difference between the difficulties of "inventing calculus where there was none before" and "learning calculus from a textbook explanation carefully laid out in the optimal order, with each component polished over the centuries to the easiest possible explanation, with all the barriers to understanding carefully paved over to construct the smoothest explanatory trajectory possible".
(Yes, "three orders of magnitude" is an actual attempt to estimate something, insofar as that is at all meaningful for an unquantified gut instinct; it's not just something I said for rhetoric effect.)
I think it will be next to impossible to set up a community norm around this issue for all communities save those with a superhuman level of general honesty. For if there is a norm like this in place, Alice always has a strong incentive to pretend that she is punching based on some generally accepted theory, and that the only thing that needs arguing is the application of this theory to Bob (point 2). Even when there is in fact a new piece of theory ready to be factored out of Alice's argument, it is in Alice's interest to pass this off as being a straightforward application of some more general principle rather than anything new, and she will almost certainly be able to convincingly pass it off as such.
As soon as there is a community norm around building your new punching theories separately from any actual punches, anyone who can argue that their justification for punching Bob doesn't need any new theory, that is, that the justification follows trivially from accepted ideas, will have a that much stronger position. Thus, only the most scrupulous of punchers will ever actually implement step (1), and the norm will collapse.
Why oh way does this system make it so needlessly inconvenient to partake in these courses?
I just want to read the lecture material on the topics that interest me, and possibly do some of the exercises. Why do I need to create an account for that using a phony email, subscribe to courses, take tests with limited numbers of retries, and all of that? I am not aiming to get a formal diploma here, and I don't think you plan on awarding me any. So why can't I just... browse the lectures in a stateless web 1.0 fashion?
This. The phrasing "if you are on Vulcan, then you are on the mountain" *sounds* like it should be orthogonal to, and therefore gives no new information on and cannot affect the probability of, your being on Vulcan.
This is quite false, as can be shown easily by the statement "if you are on Vulcan, then false". But it is a line of reasoning I can see being tempting.
To me, this form of "epistemic should" doesn't feel like a responsibility-dodge at all. To me, it carries a very specific meaning of a particular warning: "my abstract understanding predicts that X will happen, but there are a thousand and one possible gotchas that could render that abstract understanding inapplicable, and I have no specific concrete experience with this particular case, so I attach low confidence to this prediction; caveat emptor". It is not a shoving off of responsibility, so much as a marker of low confidence, and a warning to everyone not to put their weight down on this prediction.
Of course, if you make such a claim and then proceed to DO put your weight down on the low-confidence prediction without a very explicit decision to gamble in this way, then you really are shoving responsibility under the carpet. But that is not how I have experienced this term being used, either by me or by those around me.
I agree that a distillation of a complex problem statement to a simple technical problem represents real understanding and progress, and is valuable thereby. But I don't think your summary of the first half of the AI safety problem is one of these.
The central difficulty that stops this from being a "mere" engineering problem is that we don't know what "safe" is to mean in practice; that is, we don't understand in detail *what properties we would desire a solution to satisfy*. From an engineering perspective, that marks the difference between a hard problem, and a confused (and, usually, confusing) problem.
When people were first trying to build an airplane, they could write down a simple property that would characterize a solution to the problem they were solving: (thing) is heavier than air yet manages to stay out of contact with the ground, for, let say at least minutes at a time. Of course this was never the be-all end-all of what they were trying to accomplish, but this was the central hard problem a solution of which they expected to be able to build on incrementally into the unknown direction of Progress.
I can say the same for, for example, the "intelligence" part of the AI safety problem. Using Eliezer Yudkowsky's optimization framework, I think I have a decent idea of what properties I would want a system to have when I say I want to build an "intelligence". That understanding may or may not be the final word on the topic for all time, but at least it is a distillation that can function as a "mere" engineering problem, a solution for which I can recognize as such and which we can then improve on.
But for the "safe" part of the problem, I don't have a good idea about what properties I want the system to achieve at all. I have a lot of complex intuitions on the problem, including simple-ish ideas that seem to be an important part of it and some insight of what is definitely *not* what I want, but I can't distill this down to a technical requirement that I could push towards. If you were to just hand me a candidate safe AI on a platter, I don't think I could recognize it for what it is; I could definitely reject *some* failed attempts, but I could not tell whether your candidate solution is actually correct or whether it has a flaw I did not see yet. Unless your solution comes with a mighty lecture series explaining exactly why your solution is what I actually want, it will not count as a "solution". Which makes the "safe" part of your summary, in my mind, neither really substantive understanding, nor a technical engineering problem yet.
I think what we are looking at here is Moloch eating all slack out of the system. I think that is a summary of about 75% of what Moloch does.
In these cases, I do not think such explanations are enough.
Eliezer gives the model of researchers looking for citations plus grant givers looking for prestige, as the explanation for why his SAD treatment wasn’t tested. I don’t buy it. Story doesn’t make sense.
On my model, the lack of exploitability is what allowed the failure to happen, whereas your theory on reasons why people do not try more dakka may be what caused the failure to happen.
If the problem were exploitable in the Eliezer-sense, the market would bulldoze straight through the roadblocks you describe. The fact that the problem is not exploitable allows your roadblocks to have the power they empirically have.
If more light worked, you’d get a lot of citations, for not much cost or effort. If you’re writing a grant, this costs little money and could help many people. It’s less prestigious to up the dosage than be original, but it’s still a big prestige win.
I don't think this is true, empirically. Being the first person to think of a new treatment with a proof of concept is prestigious. Working out all the details and engineering it into something practical is much less so.
My interpretation of this thesis immediately remind me of Eliezer's post on locality and compactness of specifications, among others.
Under this framework, my analysis is that triangle-ness has a specification that is both compact and local; whereas L-opening-ness has a specification that is compact and nonlocal ("opens L"), and a specification that is local but noncompact (a full specification of what shapes it is and is not allowed to have), but no specification that is both local and compact. In other words, there is a short specification which refers to something external (L) and a long lookup-table specification that talks only about the key.
I think this is the sensible way of caching out your notion of intrinsicness. (Intrinsicity? Intrinsicitude?)
In this interpretation, I don't think human morality should be judged as non-intrinsic. The shortest local specification of our values is not particularly compact; but neither can you resort to a nonlocal specification to find something more compact. "Whatever makes me happy" is not the sum of my morality, nor do I think you will find a simple specification along those lines that refers to the inner workings of humans. In other words, the specification of human morality is not something you can easily shorten by referring to humans.
There is an important sense in which goodness is more like being ∆-shaped than it is like being L-opening. Namely, goodness of a state of affairs is something that I can assess myself from outside a simulation of that state. That is of course only true because human brains have complex brainware for judging morality, and do not have complex brainware for judging L-opening. For that reason, I don't think "can humans simulate this in a local way" is a measure that is particularly relevant.
Consensus tends to be dominated by those who will not shift their purported beliefs in the face of evidence and rational argument.
I have tried exactly this with basic topology, and it took me bloody ages to get anywhere despite considerable experience with coq. It was a fun and interesting exercise in both the foundations of the topic I was studying and coq, but it was by no means the most efficient way to learn the subject matter.
My take on it:
You judge an odds ratio of 15:85 for the money having been yours versus it having been Nick's, which presumably decomposes into a maximum entropy prior (1:1) multiplied by whatever evidence you have for believing it's not yours (15:85). Similarly, Nick has a 80:20 odds ratio that decomposes into the same 1:1 prior plus 80:20 evidence.
In that case, the combined estimate would be the combination of both odds ratios applied to the shared prior, yielding a 1:1 * 15:85 * 80:20 = 12:17 ratio for the money being yours versus it being Nicks. Thus, you deserve 12/29 of it, and Nick deserves the remaining 17/29.
So it's nonstandard clever wordplay. Voldemort will still anticipate a nontrivial probability of Harry managing undetected clever wordplay. Which means it only has a real chance of working when threatening something that Voldemort can't test immediately.
I don't think this is likely, if only because of the unsatisfyingness. However:
And the messages would come out in riddles, and only someone who heard the prophecy in the seer's original voice would hear all the meaning that was in the riddle. There was no possible way that Millicent could just give out a prophecy any time she wanted, about school bullies, and then remember it, and if she had it would've come out as 'the skeleton is the key' and not 'Susan Bones has to be there'. (Ch.77)
Some foreshadowing on the idea of ominous-sounding prophecy terms actually referring to people's names.
Beneath the moonlight glints a tiny fragment of silver, a fraction of a line... (black robes, falling) ...blood spills out in litres, and someone screams a word.
"blood spills out in litres" meshes well with "TEAR APART".
MIRI Mission/MIRI Effectiveness .395 (1331)
This result sets off my halo effect alarm.
I took the survey. No scanner available, alas.
Seconded. P versus NP is the most important piece of the basic math of computer science, and a basic notion of algorithms is a bonus. The related broader theory which nonetheless still counts as basic math is algorithmic complexity and the notion of computability.
I've always modeled it as a physiological "mana capacity" aspect akin to muscle mass -- something that grows both naturally as a developing body matures, and as a result of exercise.
Certainly, though I should note that there is no original work in the following; I'm just rephrasing standard stuff. I particularly like Eliezer's explanation about it.
Assume that there is a set of things-that-could-happen, "outcomes", say "you win $10" and "you win $100". Assume that you have a preference over those outcomes; say, you prefer winning $100 over winning $10. What's more, assume that you have a preference over probability distributions over outcomes: say, you prefer a 90% chance of winning $100 and a 10% chance of winning $10 over a 80% chance of winning $100 and a 20% change of winning $10, which in turn you prefer over 70%/30% chances, etc.
A utility function is a function f from outcomes to the real numbers; for an outcome O, f(O) is called the utility of O. A utility function induces a preference ordering in which probability-distribution-over-outcomes A is preferred over B if and only if the sum of the utilities of the outcomes in A, scaled by their respective probabilities, is larger than the same for B.
Now assume that you have a preference ordering over probability distributions over outcomes that is "consistent", that is, such that it satisfies a collection of axioms that we generally like reasonable such orderings to have, such as transitivity (details here). Then the von Neumann-Morgenstern theorem says that there exists a utility function f such that the induced preference ordering of f equals your preference ordering.
Thus, if some agent has a set of preferences that is consistent -- which, basically, means the preferences scale with probability in the way one would expect -- we know that those preferences must be induced by some utility function. And that is a strong claim, because a priori, preference orderings over probability distributions over outcomes have a great many more degrees of freedom than utility functions do. The fact that a given preference ordering is induced by a utility function disallows a great many possible forms that ordering might have, allowing you to infer particular preferences from other preferences in a way that would not be possible with preference orderings in general. (Compare this LW article for another example of the degrees-of-freedom thing.) This is the mathematical structure I referred to above.
It's full of hidden assumptions that are constantly violated in practice, e.g. that an agent can know probabilities to arbitrary precision, can know utilities to arbitrary precision, can compute utilities in time to make decisions, makes a single plan at the beginning of time about how they'll behave for eternity (or else you need to take into account factors like how the agent should behave in order to acquire more information in the future and that just isn't modeled by the setup of vNM at all), etc.
Those are not assumptions of the von Neumann-Morgenstern theorem, nor of the concept of utility functions itself. Those are assumptions of an intelligent agent implemented by measuring its potential actions against an explicitly constructed representation of its utility function.
I get the impression that you're conflating the mathematical structure that is a utility function on the one hand, and representations thereof as a technique for ethical reasoning on the other hand. The former can be valid even if the latter is misleading.
It's more than a metaphor; a utility function is the structure any consistent preference ordering that respects probability must have. It may or may not be a useful conceptual tool for practical human ethical reasoning, but "just a metaphor" is too strong a judgment.
A more involved post about those Bad Confused Thoughts and the deep Bayesian issue underlying it would be really interesting, when and if you ever have time for it.
Upvoted for the simple reason that this is probably the first article I've EVER seen with a title of the form 'discussion about ' which is in fact about the quoted term, rather than the concept it refers to.
As a point of interest, I want to note that behaving like an illiterate immature moron is a common tactic for (usually banned) video game automation bots when faced with a moderator who is onto you, for exactly the same reason used here -- if you act like someone who just can't communicate effectively, it's really hard for others to reliably distinguish between you and a genuine foreign 13-year-old who barely speaks English.
"Worst case analysis" is a standard term of art in computer science, that shows up as early as second-semester programming, and Eliezer will be better understood if he uses the standard term in the standard way.
Actually, in the context of randomized algorithms, I've always seen the term "worst case running time" refer to Oscar's case 6, and "worst-case expected running time" -- often somewhat misleadingly simplified to "expected running time" -- refer to Oscar's case 2.
A computer scientist would not describe the "omega" case as random -- if the input is correlated with the random number source in a way that is detectable by the algorithm, they're by definition not random.
A system that reliably behaves like the omega case is clearly not random. However, a random system such as case 2 may still occasionally behave like omega, with probability epsilon, and it is not at all unreasonable or uncommon to require your algorithm to work efficiently even in those rare cases. Thus, one might optimize a random system by modelling it as an omega system, and demanding that it works well enough even in that context.
Group selectionism alert. The "we are optimized for effectively playing the iterated prisoner's dilemma" argument, AKA "people will remember you being a jackass", sounds much more plausible.
Even with measurements in hand, old habits are hard to shake. It’s easy to fall in love with numbers that seem to agree with you. It’s just as easy to grope for reasons to write off numbers that violate your expectations. Those are both bad, common biases. Don’t just look for evidence to confirm your theory. Test for things your theory predicts should never happen. If the theory is correct, it should easily survive the evidential crossfire of positive and negative tests. If it’s not you’ll find out that much quicker. Being wrong efficiently is what science is all about.
-- Carlos Bueno, Mature Optimization, pg. 14. Emphasis mine.
I already knew it, but this post made me understand it.
Passphrase: eponymous haha_nice_try_CHEATER
Well played :)
Trust -- the quintessential element of your so-called "tell culture" -- and vulnerability are two sides of the same coin.
That's true in general. In network security circles, a trusted party is one with the explicit ability to compromise you, and that's really the operational meaning of the term in any context.
My own definition - proto-science is something put forward by someone who knows the scientific orthodoxy in the field, suggesting that some idea might be true. Pseudo-science is something put forward by someone who doesn't know the scientific orthodoxy, asserting that something is true.
This seems like an excellent heuristic to me (and probably one of the key heuristics people actually use for making the distinction), not not valid as an actual definition. For example, Sir Roger Penrose's quantum consciousness is something I would classify as pseudoscience without a second thought, despite the fact that Penrose as a physicist should know and understand the orthodoxy of physics perfectly well.
Taking the survey IS posting something insightful.
Taken to completion.
The Cryonics Status question really needs an "other" answer. There are more possible statuses one can be in than the ones given; in particular there are more possible "I'd want to, but..." answers.
To figure out a strange plot, look at what happens, then ask who benefits. Except that Dumbledore didn't plan on you trying to save Granger at her trial, he tried to stop you from doing that. What would've happened if Granger had gone to Azkaban? House Malfoy and House Potter would've hated each other forever. Of all the suspects, the only one who wants that is Dumbledore. So it fits. It all fits. The one who really committed the murder is - Albus Dumbledore!
I think if you use this line of reasoning and then allow yourself to dismiss arbitrary parts of it as "not part of the plan", you can make a convincing argument for almost anything. For that reason, I consider the entire theory suspect.