youzicha:

nostalgebraist:

shlevy:

shlevy:

nostalgebraist replied to your post: Does Tumblr now allow links in asks, or did it…

i haven’t seen an ask from you, so apparently the latter, if i understand correctly?

Ha ha I love this website. Trying again.

Augh ok @nostalgebraist I was just asking if you’d read the functional decision theory paper from Yudkowsky and Soares, trying to decide if it’s worth reading and wondering if you had thoughts

I haven’t looked at it yet.

Do I understand correctly that FDT is the latest “TDT but it works this time” iteration?  If so, that’s neat if and only if it actually works this time, which has been frustratingly difficult to ascertain from the discussion I’ve seen so far (which all looks to me like people arguing over whether TDT is a good idea in the first place).

It doesn’t seem like this paper contains any technical improvements to TDT itself. Section 3 says

If a certain decision function outputs cooperate on a certain input, then it does so of logical necessity; there is no possible world in which it outputs defect on that input, any more than there are possible worlds where 6288 + 1048 6= 7336. The above notion of subjunctive dependence therefore requires FDT agents to evaluate counterpossibilities, in the sense of Cohen (1990), where the antecedents run counterto-logic. At first glance this may seem undesirable, given the lack of a satisfactory account of counterpossible reasoning. This lack is the main drawback of FDT relative to CDT at this time; we will discuss it further in section 5. […] 

Instead of despairing at the dependence of FDT on counterpossible reasoning, we note that the difficulty here is technical rather than philosophical. Human mathematicians are able to reason quite comfortably in the face of uncertainty about logical claims such as “the twin prime conjecture is false,” despite the fact that either this sentence or its negation is likely a contradiction, demonstrating that the task is not impossible. Furthermore, FDT agents do not need to evaluate counterpossibilities in full generality; they only need to reason about questions like “How would this predictor’s prediction of my action change if the FDT algorithm had a different output?” This task may be easier. Even if not, we again observe that human reasoners handle this problem fairly well: humans have some ability to notice when they are being predicted, and to think about the implications of their actions on other people’s predictions. While we do not yet have a satisfying account of how to perform counterpossible reasoning in practice, the human brain shows that reasonable heuristics exist.

which I guess can be paraphrased as “no, it doesn’t work yet”. Their formalization assumes that the agents are provided with a graph G which encodes “the logical, mathematical, computational, causal, etc. structure of the world more broadly”—I think this is exactly what Yudkowsky’s long TDT draft paper did also. (So I’m not sure why they renamed it from TDT to FDT?) 

Rather, the point of the paper is to give philosophical arguments for why this decision theory is preferable to CDT and EDT. The arguments are basically similar to what was posted on Overcoming Bias a decade ago, but worked out much more thoroughly.

The writing is really good now! The prose is succinct, the examples are both enlightening and clearly described, and it makes a point of comparing to related work from the academic philosophical literature. I feel it’s very convincing, but then again I was convinced already. I wonder what ogingat would say.

… huh.  If this is true, I guess I’m confused why this paper exists.  Are they just trying to get the attention of philosophy academia again, like the time they tried to hire a philosophy prof to write up TDT?

@the-grey-tribe

This is from 1999, and was written in the context of MacOS classic, BeOS, DOS, and Windows 95. KDE 1.0 had already been released.

Windows NT, OSX, BeOS, Amiga, had relatively similar GUIs but different underlying principles.

Symbolics, Plan9, Squeak/smalltalk-80, Oberon, and web bowsers have a completely different UI that reflects the difference in underlying concepts. All existed in the 90s, but they weren’t made for ordinary people. Ordinary people GUIs all followed the same pattern.

This continued until the iPhone arrived.

You have to differentiate the abstractions from the metaphors: A file is an abstraction. A floppy disk “save” icon is the metaphor. The picture of a file as a binder is a metaphor.

Stephenson was pointing out that the metaphor promises things it cannot deliver, while offering a familiar conceptual scaffold to users. The point is not just that files and directories are leaky abstractions, and that you don’t need to know how they work except when you do. The point is that the VISUAL metaphors are not explained.

When the visual metaphors are inaccurate, it’s in a way that is not exactly lying. The images are not even wrong: They don’t tell you anything explicitly.

Plain text is discrete and explicit in a way images and Word documents are not. You cannot hide things in an ASCII file. You can hide things in a .doc or .psd file. These files have metadata land layers and scripts and WYSIWYG is a deception. What you see might be what you get, but what you see is not all there is.

Thanks for the pushback on this.

I take your point about abstractions vs. metaphors.  A metaphor like “the desktop” has no precise specification, and there is no firm way to differentiate when lower levels are “leaking through.”  All you have is a system that looks like a literal desktop but doesn’t entirely behave like one.

Insofar as GUIs tend to involve a lot of “metaphors” in this sense, I suppose that graphics probably lend themselves to metaphors.  Nonetheless, I want to note that Stephenson seems equally concerned about the verbal side of GUI metaphors.  Long quote to representatively sample from his examples (the omitted paragraph is one I quoted in the OP):

At the upper (which is to say, closer to the user) levels, this is done through a set of conventions–menus, buttons, and so on. These work in the sense that analogies work: they help Eloi understand abstract or unfamiliar concepts by likening them to something known. But the loftier word “metaphor” is used.

The overarching concept of the MacOS was the “desktop metaphor” and it subsumed any number of lesser (and frequently conflicting, or at least mixed) metaphors. Under a GUI, a file (frequently called “document”) is metaphrased as a window on the screen (which is called a “desktop”). The window is almost always too small to contain the document and so you “move around,” or, more pretentiously, “navigate” in the document by “clicking and dragging” the “thumb” on the “scroll bar.” When you “type” (using a keyboard) or “draw” (using a “mouse”) into the “window” or use pull-down “menus” and “dialog boxes” to manipulate its contents, the results of your labors get stored (at least in theory) in a “file,” and later you can pull the same information back up into another “window.” When you don’t want it anymore, you “drag” it into the “trash.”

There is massively promiscuous metaphor-mixing going on here, and I could deconstruct it ‘til the cows come home, but I won’t. Consider only one word: “document.” When we document something in the real world, we make fixed, permanent, immutable records of it. But computer documents are volatile, ephemeral constellations of data. Sometimes (as when you’ve just opened or saved them) the document as portrayed in the window is identical to what is stored, under the same name, in a file on the disk, but other times (as when you have made changes without saving them) it is completely different. In any case, every time you hit “Save” you annihilate the previous version of the “document” and replace it with whatever happens to be in the window at the moment. So even the word “save” is being used in a sense that is grotesquely misleading—“destroy one version, save another” would be more accurate.

[…]

So GUIs use metaphors to make computing easier, but they are bad metaphors. Learning to use them is essentially a word game, a process of learning new definitions of words like “window” and “document” and “save” that are different from, and in many cases almost diametrically opposed to, the old.

If I understand correctly, he is saying: even the verbal parts (like the names of options in menus) are “metaphors” as opposed to “abstractions.”  As Stephenson says, if you take the word “document” here too literally, you will be in for some nasty surprises – but this is not like a technical abstraction springing a leak, since the technical abstraction will have a spec (“you can pretend Precise Thing X is really Precise Thing Y”), while “document” is just a cloud of implicit associations.

Nonetheless!  I think Stephenson is going much too far when he talks about MS and Apple selling an “illusion” that one can usefully interact with the world through such metaphors.  After the passage above, he goes on to talk about how more and more devices are using GUIs, and how

by using GUIs all the time we have insensibly bought into a premise that few people would have accepted if it were presented to them bluntly: namely, that hard things can be made easy, and complicated things simple, by putting the right interface on them.

He’s going too far because no one, in my experience, actually trusts the metaphors for more than a few early moments.  His examples quoted above are good illustrations.  Yes, the word “save” is being used in a strange way, but people do not react to this by getting burned over and over again; people react by learning a new meaning for the word “save.”  More generally, people who interact with a “metaphorical” interface quickly develop a working facility with its actual behavior that obviates most of the dependence on the metaphors.

This is possible because the actual behavior is always largely predictable, even if the metaphors are bad.  By now, we all have a precise sense of what ought to happen when we choose “Save” (or “Open,” etc.) in a GUI menu, and would be rightfully indignant if something different were to happen.  For all I know, there really is some written spec about what these menu items should do on Windows or Mac OS, but even if there isn’t, there’s a de facto understanding which is just as good.  Some little open source gizmo I find on github might prefer to say it will “write a file to disk” instead, but this doesn’t really give me more information than “save” does.

(Indeed, while reading that passage, I had to stop for a moment to notice that I knew two meanings of the word “save” which did not agree.  I’m so used to the actual behavior of the GUI that it takes effort to remember what the metaphor was supposed to be.  Likewise, I can’t remember the last time I thought about the purported connection between GUI drag-and-drop and the act of moving papers around on a desk.  Can you?)

It’s possible that there is a young vs. old difference here – maybe older people who have trouble with computers are unable to make these leaps and have to keep relying on the bad metaphors?  And yes, the essay was written in 1999, and perhaps back then it was less clear how people would react to the ascension of GUIs.  (Still, they’d been around for over a decade.  Also, I first read this essay in 2005 or 2006, and it seemed overblown to me then.)  At best, I think we can say Stephenson raised a worry that may have been reasonable at the time, but which is no longer so.

ETA: to me it seems like Stephenson ignores the true ease and efficiency benefits GUIs can confer even to power users, and thus concludes that GUIs must be popular because of all this metaphor stuff.  Near the end, he says he likes BeOS because (paraphrasing) it has the power of Linux but isn’t as tedious to configure and maintain.  But he sums this up as “sometimes, in other words, I just want to go to Disneyland,” as if convenience requires illusions.  (But you can get a lot of convenience, without losing any power, through well-chosen default behavior.)

(via the-grey-tribe)

kitswulf:

invertedporcupine:

kitswulf:

invertedporcupine:

timtotal:

invertedporcupine:

@nostalgebraist  I don’t think these are analogous situations.  It would be nice if no one had to work all, and all labor is in some sense unfree in that one can’t really choose not to work at all if that leads to starvation.  Working for a wage that is less than one feels one deserves certainly feels coercive.  However, literal at-the-barrel-of-a-gun coercion is required to make people work for no pay.

You’re not working for no pay. If the wage cap is 10 million dollars, you’re working for 10 million dollars. I’m not convinced a wage cap is good policy, but to compare it to slavery is ridiculous.

People don’t work for the average dollar.  They work for the marginal dollar.  Let us suppose that that there is a wage cap of $10 million, and evil Bob the small business owner has already made $10 million dollars, but it’s only October.  

Bob is not going to do any work in November or December, because he will not receive any more money for doing so.  The marginal value to him of that work is zero.  The only way he is going to work is if you either put a gun to his head, or threaten to punish him through fines or imprisonment or some such.  At the point where someone is saying “work for zero more dollars than you already have, or I’m going to put you in prison”, a comparison to slavery is not ridiculous.

I say this as someone who thinks that libertarians claiming “taxation is theft” are being ridiculous in the more general case.  But  I roll to disbelieve on anyone making a utilitarian case for 100% marginal taxation at any level, because the counterfactual economic counterparties of the person being taxed into inactivity are also losing out in the process.  

As someone joining late; is this basically just Laffer Curves revisited?

Nobody had actually brought up the Laffer curve, but yes, there is a long-running problem where conservatives don’t understand that the United States has never been on the right side of the Laffer curve, whereas many (non-economist) liberals/leftists don’t understand that the Laffer curve is a mathematical identity and can’t possibly be false.

Yeah, this is actually one of my pet peeves, is people who knee-jerk go “The Laffer Curve is false” when like, empirically, if you get tax rates into the 70%+ range you can start to see it.

If the US ever applies a 70% marginal tax rate on anything please wake me up because I am having the New Deal-iest dream possible.

This situation is related to the Laffer curve in that both involve people avoiding an action when the after-tax reward for that action approaches zero.

But with the Laffer curve, the key point is that tax revenue goes to zero in that cases.  That’s a strong argument against a close-to-100% tax if the main point of the tax was to raise revenue.  But if we frame this as an “income cap” rather than a tax bracket, suddenly we can see that the policy might have some justification even if it were revenue-neutral.

For instance we don’t expect a minimum wage policy to raise “tax revenue,” but you could reframe the minimum wage as “100% income tax on people making under this wage” and it’d be symmetric with the case at hand.  (Floors/ceilings are not exactly the same as 100% tax brackets, and there may be differences in practice that I’m not appreciating.  But the difference between making something illegal and merely making it pointless seems economically unimportant.)

I also don’t understand the Bob example.  Bob owns his own business; if he wants to not go to work for two months, he can do that without government interference.  What he can’t do without government interference is give himself more than $10 million of what the company makes in a year, no matter what work he does or doesn’t do in that time.

Maybe under this setup the Bobs of the world would take more time off, or maybe fewer small businesses would be sustainable, but this would all flow naturally from decisions made under the new incentives.  No one is ever facing the barrel of a govt. gun in this process.  (The govt. guns would come in if Bob tried to evade paying his excess income in taxes, not if Bob stayed home from work.)

(via kitswulf)

@slatestarscratchpad

This is something a lot of people have complained about.

There are things that I get the impression happen all the time - for example, sophisticated people criticize New Atheism for not engaging with religion on the right level. Or people freak out because they got a bad score on an IQ test. Or people get called “autistic” as an insult. Or whatever. I know this happens from lived experience / seeing it again and again.

And I want to talk about that as an example of something, but I know from bitter experience that if I claim something happens, then people who find my point inconvenient will say it practically never happens and I’m making it up.

So then I link to ten examples of it happening, in relatively famous publications that seem like a good cross-section of the culture, and people tell me this is annoying, or weak-manning, or something.

What exactly am I supposed to do here? How do other people handle this?

I think it’s just a matter of connotation.  As a hypothetical, if you were to literally include a footnote to this exact text block of text every time you wrote a long chain of links, that would be … strange, and not a good idea, but it would completely clear up the problem.  The problem is that, on the page without such explanation, it looks more like you’re saying that the profusion of links should constitute strong, or even conclusive, evidence to the reader.  Rather than being weak evidence, but better than nothing.

If anything, using fewer links might help, or just prefacing with something like “here are a few more or less random examples,” where “a few” clarifies that the sheer quantity is not meant to have much convincing force, and “random” suggests that they are selected – like the proverbial colored balls from an urn – out of a much larger pool of your experiences, some of which happened IRL or are otherwise impossible to hyperlink.

(I’m not saying you never use that kind of phrasing, just that more would be welcome.)

(via slatestarscratchpad)

evolution-is-just-a-theorem:

nostalgebraist:

evolution-is-just-a-theorem:

nostalgebraist:

That said, I think we need a healthy skepticism towards image classification results, too.  State-of-the-art architectures like Inception seem to work by learning features that reliably discriminate each object from all others, but fall short of defining that object.

They are good at, say, recognizing a dog no matter what posture the dog is in – but they do this not through an understanding of body kinesiology (”a dog’s body can deform in this way and still be a dog, but not that one”), they do it by identifying the least deformable part of a dog and then looking just for that part.  This is why Deep Dream images were so full of dog heads, specifically.  (And of eyes in general.)

The characterizations they learn are like the “featherless biped” definition of a human – actually very good at discriminating humans from other things in almost every circumstance, yet clearly not capturing the fundamental concept, which means they produce false positives on things that are not even close to human (like Diogenes’ plucked chicken).

Auto-generating “plucked chicken” examples has become its own pursuit in neural net research, under the name of “adversarial examples.”  A recent paper (many thanks to whichever tumblr user put this on my dash) shows that you can get your robo-Diogenes to produce 3D objects that are basically always misclassified by some network, even when seen from different angles and under different lighting.

For example, they made this weird turtle, which the network reliably thinks is a rifle (seriously), in all three of these pics and many others:

It’s easy to come up with a plausible-sounding story for why this worked.  This turtle has a pattern on its back, but it’s not the very distinctive pattern we’re used to seeing on turtles.  And so of course the network learned to recognize turtles by looking for that pattern, because it’s a great way to reliably tell them apart from other roundish things with four feet and a head.  But this is a “featherless biped” type of definition, and can be defeated by a turtle that doesn’t have the pattern.

I think your attempt to figure out why this particular turtle is classified as a rifle is a mistake. Interpretability is hard, and it is very rare for the features a net learns to map cleanly to the features a human uses.

Is this true?  When you do gradient ascent to produce an image that is given high probability for some class, you get forms that that are quite recognizable to a human.  There were some pictures of this in the first part of Google’s “Inceptionism” post, but my favorite examples are from Audun M. Øygard’s implementation of the same idea:

“Screws”

“Pug”

There are many others behind the link; I wanted to reproduce more here, but because this is a “text post” tumblr refuses to put multiple images in a single row, and I don’t want the post to be too long.

In these examples, I note two things: (1) I can actually see the object, or at least what looks like part of it, and (2) it tends to spam copies of the most distinctive part of the object rather than the whole thing, which fits with my contention in the OP.

(Although one of the examples is “Loggerhead turtle” and it has a bunch of flippers and not very distinct shell patterns!  But there may be a difference between “Loggerhead turtle” and just “turtle” as classes, or it may reflect a difference in versions of the Inception architecture?  Would be possible in principle for me to test this myself, I guess)

Yes, it is in fact true. Obviously neural nets have to be picking up on some of the same features humans do, but determining which features “caused” a particular outcome is basically impossible (currently). Like, really, interpretability is hard. You can’t just look at some pictures and guess. You’re welcome to go peruse the literature on interpretability and see for yourself how difficult it is.

A more concrete argument: for 2D image classification, most adversarial examples are visually indistinguishable (to humans) from their source image. They’re not “this is a slightly weird looking turtle that’s been misclassified by the net and maybe the weirdness has something to do with it”. They’re “this image is a rifle and that image is a turtle, but if I want to find any differences between these images I’m going to need a magnifying glass”.

The manifold learned by neural nets is just… weird. You can move such a small distance that humans can’t tell the difference, and end up in a completely different category.

EDIT: Maybe this will help people understand the weirdness. We tend to break things down into obvious features. For the turtle we might have one for the shell pattern, one for the color, one for the size, whatever. A neural net will have completely bonkers features, like it looks for an edge on this side of the image and a corner on the opposite side and then a bit of color here and there. (Made up example, but possible). They don’t have to be anything remotely sane. And if they were, adversarial examples probably wouldn’t exist.

Ah, now I see what you’re saying.

I’m not proposing a theory that would rule out the 2D adversarial examples with near-invisible perturbations.  Rather, I think we need to take a fuller view of the types of adversarial examples that work, and also scrutinize what humans are actually capable of.

There was a paper that explained those 2D adversarial examples by saying that if you want to maximize the dot product of a weight vector and some perturbation, and the typical magnitude of the weight vector’s elements stay constant with increasing dimension, then the higher the dimension, the bigger you can make the dot product with a perturbation of fixed max norm.  This is an essentially linear phenomenon, and explains adversarial examples generated by small perturbations.

But not all adversarial examples are generated by small perturbations.  In that paper with the turtle and the baseball, they maximized an expected value over various translations, rotations, and lighting changes, and the perturbations they got (which I assume were as small as they could make them – they said they tried 4 values for the size parameter) were not imperceptible.  In the case of the baseball, you can really see high-level “espresso” features in the object, to the extent that a number of tumblr rebloggers said they might have thought some of the pictures were espressos (as would I).

Notably, these 3D translation-invariant examples are much closer to the real human visual task, where we get to constantly move our heads and object are also frequently moving.  The same people also did 2D physical examples that you can print on a piece of paper, and you can see things getting more perceptible as the range of transformations increases – see here, where a nearly imperceptible transformation can make a cat look like a computer under different zooms, but to get zooms + translations + rotations + mean shifts, you need to add some very perceptible, perhaps computer-y lines and angles to the cat pic.

brazenautomaton:

nostalgebraist:

brazenautomaton:

nostalgebraist:

I was talking last night about how I find the meta aspects of James Bond (actors, eras, books vs. films) fascinating even though I don’t like the books or movies themselves.  That led me to think about why I didn’t like the books or movies, which was not very interesting on the whole (there isn’t that much there to think about), but I did end up thinking there is something noteworthy about Bond’s “license to kill.”

As the audience of an action thriller, there is something strange about being told that the protagonist is licensed to kill.  In many action thrillers, the protagonists do kill other people at some point, but rarely (? I admit lack of familiarity w/ the genre) are we assured that they are legally allowed to do this.  When our hero is in a pulse-pounding life-or-death struggle with some aggressor, the questions foremost in our minds do not include “yes, but will he get away with it legally?” – not unless this is really a very different sort of story in disguise.

Ian Fleming is sometimes credited with creating the spy thriller genre, so maybe the license to kill is sort of an outdated artifact – something that seemed important to specify at first, but which turned out to be superfluous once the genre had been let loose on real audiences.  That’s the boring possibility.

What are the less boring possibilities?  Is this a fantasy about being able to commit murder with impunity?  Well, no, not straightforwardly.  Surveys show that lots of normal people have violent fantasies, and there are stories (like the movie God Bless America) about the fantasy of actually killing the people who inspire these fantasies.  But Bond doesn’t target people he viscerally hates, or even people who annoy him.  The Bond franchise puts little energy into making the audience actively loathe the villains, and many of the dead are henchmen who never even get personalities.

Another possibility: the license to kill is part of the core fantasy of the Bond character, which is (according to one theory) a combination of cruelty/sadism with social legitimacy.  A more familiar plot would grant moral legitimacy to cruelty/sadism: say, “we need to stop the terrorists whatever it takes, and in this case it takes hiring these crazy rebellious low-lifes with nothing to lose and tons of pent-up aggression; if they rack up a higher body count than necessary, well, the ends justify the means.”

In Bond, the ends are often pretty big (up to and including saving the world), but there is little focus on how Bond, or people like him, are necessary evils.  There’s little morality at all, even relative to the familiar sort of plot just mentioned, where even if it’s not at the forefront of conscious attention, there’s always the subtext (cf. the dicks/pussies/assholes speech from Team America) that society needs some guys like this.  No one, except the occasional conservative columnist, ever thinks about whether “society needs” guys like James Bond.

No, the Bond fantasy is about killing while being socially legitimate.  Being on top in man-on-man, life-or-death physical confrontations while also being on top of the social ladder – cool, rich, sexually irresistible, member of all the best clubs, studded with luxury goods and in perfect command of the vagaries of fashion.  The classic anti-Bond article is called “Sex, Snobbery and Sadism” and singles out the snobbery part as the key:

Moreover, both its hero and its author are unquestionably members of the Establishment. Bond is an ex-Royal Navy Commander and belongs to Blades, a sort-of super-White’s. Mr Fleming was educated at Eton and Sandhurst, and is married to a prominent society hostess, the ex-wife of Lord Rothermere. He is the foreign manager of that austere and respectable newspaper, the Sunday Times, owned by an elderly fuddy-duddy called Lord Kemsley, who once tried to sell a popular tabloid with her slogan (or rather his wife’s slogan) of ‘clean and clever’. Fleming belongs to the Turf and Boodle’s and lists among his hobbies the collection of first editions. He is also the owner of Goldeneye, a house made famous by Sir Anthony Eden’s Retreat from Suez. […]

Orwell, in fact, was wrong. Snobbery is no protection: on the contrary, the social appeal of the dual Bond-Fleming personality has added an additional flavour to his brew of sex and sadism. Fleming’s novels are not only successful, like No Orchids; they are also smart. The Daily Express, pursuing its task of bringing glamour and sophistication to the masses, has serialised the last three. Our curious post-war society, with its obsessive interest in debutantes, its cult of U and non-U, its working-class graduates educated into snobbery by the welfare state, is a soft market for Mr Fleming’s poison.

An apotheosis of the smug head boy, authorized by some mega-Umbridge to commit the ultimate act of naughtiness while the administration looks the other way.  When James Bond kills you, will it be moral? beautiful?  Who cares?  It’ll be legal, legitimate, all the best sorts of people will be for it.  The fucking prick.

“licensed to kill” is not about the legal justification per se. it’s not an assurance the killing is moral and justified.

it’s about “the things this guy is doing are so dangerous and the stakes are so high that the fact he’s going to kill a bunch of dudes is something they had to work out ahead of time. it’s an expected part of his job.”

the license to kill is an entry permit for the World Of Super-Spydom, where you just know assassins are going to try and kill you in every hotel room you ever stay in and you’ll turn their own garrotes against them because you’re so fucking competent and cool.

Ah!  That makes perfect sense.  Thanks.

to expand a bit: James Bond, (at least until the Daniel Craig films which were muddy in more than one way) is basically hypercompetence porn. Bond is the best at everything and he’s so the best that nothing fazes him. His license to kill is a sign that dangerous, thrilling life-or-death situations are an ordinary expected thing for him – John McClane is heroically going beyond the line of duty and pushing himself to the limit, James Bond is just doing his normal thing. That’s why we keep getting action shots of him in neat and still-pressed suits, because he’s just so goddamned cool and on top of things gunfights don’t even get him messy. That’s not even getting into his superscience gadgets that can get him out of any sticky situation.

The moral dissonance is created when you notice the intersection of “this super cool guy kills attackers in dangerous, thrilling situations with no problem at all” and “this guy is so super cool and competent, he’s never uncertain or anxious”. If he’s always certain and assured, he can’t be questioning himself. If he can’t be questioning himself, the movie cannot bring the morality of his actions into doubt, because the fact he never questions his morality would make him a villain. So the movie has to present everything like “well of course you shouldn’t even question the morality of things, look how dramatically evil and flamboyant the bad guy is!” That’s not going to work for everyone, especially given modern audiences’ deconstructionism, and the fact that after you make 26 movies in a series you are gonna fuck it up a few times.

On a certain level, saying James Bond should feel bad about all the dudes he kills and that he’s a bad guy for all of the super-spying he gets up to, is like saying Batman shouldn’t dress up in a bat suit and should spend all that money on soup kitchens. A few steps removed from “musicals are unrealistic, people don’t sing that much”. It’s objecting to a baseline assumption the story has to have in order to fulfill its function. 

But on the other hand, it’s totally fair to say “I don’t like stories that are based on that assumption, and I don’t wanna read them”. It’s not like there’s anything wrong with that, and I’m not trying to argue you out of your stance or anything.

The modern Daniel Craig Bond films tried to make the character “darker” and “more realistic” on this axis among others. I’d love to be able to say that abandoning the thing that made the character work was the only thing that ruined the films, but Casino Royale was actually a very good movie on its own, and the next three had problems with leaden pacing and bloated runtimes and limp plots and utterly failed attempts at establishing personal stakes (The bad guy in Spectre claims to be responsible for every bad thing that happened in Bond’s life, and I wanted to scream “NO! YOU DIDN’T EARN THAT! YOU DIDN’T EARN A GOD DAMN THING!” but I was in a theater)

Again, this makes sense, although I’d argue that the hypercompetence and the “social legitimacy” are supposed to bleed into one another.  There are hypercompetent outsider characters (many supervillains fall into that category, at least until the moment they’re defeated), but Bond isn’t an outsider, he’s the ultimate insider (while the bad guys tend to be conspicuously weird, to contrast with him).  I don’t think I’m really disagreeing with you there, though.

Anyway, the reason I dislike the character is not really moral, but emotional.  I don’t relate to Bond or want to be him – instinctively, I want to hate him, in the way I expressed in the last paragraph of the OP.  When I see a character who is so unfazeable – not only does he dispatch the assassin, he does so without ruffling his suit, and has a perfect one-liner ready for the occasion – I want to see him taken down a peg.  But that isn’t what these stories are about (although Casino Royale had a bit of it, haven’t seen the other Daniel Craig movies).  So according to usual movie emotional logic, I should be eagerly awaiting this guy’s comeuppance, but instead he’s just the hero and I’m supposed to happily watch him do his thing without a hitch.

(via brazenautomaton)

kontextmaschine:

nostalgebraist:

brazenautomaton:

nostalgebraist:

One thing I thought about while reading that series was how long it took for the creators to start thinking clearly about design, even on a very basic level.

There’s a clear pattern across many of the early sets where it looks like the designers only thought about a card in some hypothetical context they had in mind for it, and ignored how likely that context was.  An ability that only functions in a rare situation is, obviously (I would think?), much less valuable than the same ability without the restriction.  But the designers didn’t seem to realize this, and would print cards that did mediocre things in rare situations while appearing to believe they were printing mediocre cards, not bad ones.

The post on Ice Age block begins with a discussion of the card Balduvian Shaman, which I actually assumed was a parody until I read the accompanying blog text.  Balduvian Shaman is a blue 1/1 for U with the following rules text:

Permanently change the text of target white enchantment you control that does not have cumulative upkeep by replacing all instances of one color word with another. For example, you may change “Counters black spells” to “Counters blue spells.” Balduvian Shaman cannot change mana symbols. That enchantment now has Cumulative Upkeep: (1).

“Wasn’t Magic founded by a bunch of math Ph.Ds?” I thought.  “How could they have not thought about probability?“  Which made it especially strange to read, in the very next paragraph:

What sort of designer would think that such fiddly, bean-counting cards would be fun? If you guessed college guys studying math and physics, you’d be right! Skaff Elias’s feature article is pretty essential background material here, so go read that instead if you were looking for actual history.

Some versions of this problem was around at least as late as Weatherlight, which was supposed to be a graveyard-seemed set, but which didn’t appreciate that players would only treat their graveyards differently if the graveyard-related abilities were sufficiently powerful (creating an incentive to shift other behavior to accommodate them).

Balduvian Shaman is better than it sounds because of white’s ten-ubiquitous Circle of Protection : [color] enchantments, you can maindeck Circles of Protection and then change them to the colors your opponent has

I mean it isn’t GOOD, but it’s not quite as much an edge case as you think

Oh!  That’s cool, the card makes some sense to me now

Even as I was writing, I realized Balduvian Shaman wasn’t an ideal example of the phenomenon I meant, because the necessary conditions are all things you can control.  The really bad cases are ones that only work if your opponent does something, especially something easily avoidable.

The clearest cases are where they introduced a mechanic on a few not-great cards and then added hosers for that mechanic (bands with other, snow-covered lands).  The mechanic never takes off because cards with the mechanic are always “maybes” for inclusion and the hosers mean they’re slightly worse than the alternative “maybes,” and then since no one uses the mechanic cards, the hosers become totally useless, so no one uses them either.

and the Ward enchantments, a cycle of one white mana “protection from X” creature enchants

I think I might have been at this even earlier than you guys, I remember the changes when the ideas of “card advantage” and “the mana curve” were first popularized

It also occurs to me that these designs may have made sense under the assumption that players wouldn’t buy many cards, and so their decks would be closer to random samples from the set

In that case, people would play the new mechanic cards because they didn’t have a choice, and so the mechanic and its hosers would sometimes come up, and no one would care about whether “snow-covered” was a good thing, it’d just be a source of occasional mechanical grace notes

(via drethelin)

ark-shifter:

nostalgebraist:

waystatus:

nostalgebraist:

I was just looking over the various people who’ve translated FFVI into English, and it was fun seeing what people did with the opening narration.

Classic 1994 Woolsey:

Long ago, the War of the Magi reduced the world to a scorched wasteland, and Magic simply ceased to exist.

1000 years have passed… Iron, gunpowder and steam engines have been rediscovered, and high technology reigns.

But there are those who would enslave the world by reviving the dread destructive force known as “Magic”.

Can it be that those in power are on the verge of repeating a senseless and deadly mistake?

Tom Slattery’s translation for the GBA version, supposed to be more accurate on the whole:

The ancient War of the Magi… When its flames at last receded, only the charred husk of a world remained. Even the power of magic was lost…

In the thousand years that followed, iron, gunpowder, and steam engines took the place of magic and life slowly returned to the barren land.

Yet there now stands one who would reawaken the magic of ages past and use its dreaded power as a means by which to conquer all the world.

Could anyone truly be foolish enough to repeat that mistake?

Unofficial translation by Sky Render, which is widely viewed as awkward although more literally “faithful” than Woolsey (not least by the translator themselves, cf. their later LP of it):

Long ago, humans battled one another, and the world became a scorched wasteland. The power of “magic” simply vanished.

1000 years have passed… Iron, gunpowder, and steam engines have been developed. Machinery has been revived to replace magic.

The great magic war faded into a legend. But the power of “magic” has been revived secretly, by the powerful military empire, run by a man who wants to rule the world.

Would this man be willing to destroy the world again for his own greed…?

(Unfortunately, Lina Darkstar never translated this part.)

---

I can’t tell how much of this is nostalgia, but the Woolsey version seems best to me here.  For one thing, “dread destructive force” is a good phrase (though so is Slattery’s “charred husk of a world”), and I like “high technology reins.”

Just as importantly, the Woolsey translation avoids the blunt moralizing of the other two (which I figure must have been in the original script, since it’s in two out of three translations).  The other two mention an individual villain, and finish on a note of “fuck that guy,” which fees like putting the cart before the horse – it’s like a movie that starts by telling you “there will be a bad guy in this movie, and you should hate him, because he’s evil.”

Woolsey generalizes it to an unnamed plural group, and his last sentence lacks the exasperation of the other two.  It’s not “how could this one guy possibly be so evil?”, it’s “have today’s rulers failed to learn the lessons of history?”, which is a much more interesting question.  “Can it be that those in power are on the verge of repeating a senseless and deadly mistake?” sounds like something you could easily hear in real-life political discussion; the others sound like we’re reading someone’s story outline.

I also played FFVI (with the original translation, I think?) and I like the Slattery version best.

My problem with the Woolsey version is that it’s actually kind of awkward. The capital-M in Magic and the “re”discovery of technology that doesn’t seem to have previously existed both sound very odd to my ear. There’s also something that I can’t place about the overall structure of that paragraph which sounds off to me. It sounds like a lot of old game translations do to me, which is to say it sounds like they didn’t quite have the budget to hire a really good translator, so they settled for a mediocre one.

I’m okay with the moralizing based mostly what I remember from the plot. “Those in power” are literally Gehstal and maybe Kefka. There’s no other force that wants what Gehstal wants; there’s no other force that could do it if they wanted. The most important thing about a translation is that it not be misleading, and I feel that a translation that led me to think that FFVI was about anything approaching real life politics, particularly when it comes to Gehstal himself, would just not be true.

Yeah, that’s true, it’s not like the rest of the story is especially subtle.

I agree about the slight awkwardness of the Woolsey version, although I think the Slattery version is still awkward by the non-video game standards.  “The ancient War of the Magi… When its flames at last receded” is an odd way of introducing a subject.  (Compare: “The Second World War … when it finally ended […]”).

It is indeed odd that Woolsey has “rediscovered,” especially since he was trying to economize on character count (he kept editing his script down and still getting told it was too big).

Re: the last part, I agree that the passage is talking about Gehstal – the relevant text even plays over a shot of him addressing imperial officers.  But then, Gehstal himself isn’t all that big a focus in FFVI.  On the third hand, Kefka is more of a focus, and it makes sense to emphasize G over K at this point because the game is doing the usual villain fake-out thing, like with President Shinra in FFVII.

On the fourth hand, though, the sheer destructiveness of magic seems even more important than these particular villains.  It’s hard for me to look at FFVI and not think of nuclear weapons and the Cold War; the later parts of the game feel much like a post-nuclear-war scenario, with the strange new monsters (mutants?) running around, and the way it all happens in one catastrophic blast that affects the whole globe.  And the scary thing about nukes isn’t that they might get used by an exceptionally awful ruler, it’s that they’re dangerous in the hand of the merely normally awful rulers who we take for granted on the global stage.  There have been a lot of Kefkas in the past (IRL and presumably in the FFVI world too), it’s just that this one got his hands on the nuclear codes.

So “this guy is so bad, we can’t trust him with magic” seems like the wrong emphasis.  Everyone is untrustworthy with nukes until proven otherwise.

Oh, hi! My ears were burning. In retrospect I really wish I’d had the sticking power to go back and translate the stuff I skipped over at the beginning, but… life happened.

Anyway here’s my thoughts, a good thirteen years later. Gosh, it’s so much easier now that I can just look up the original on flipping Youtube.

For the penultimate line, I favor “There are those who would reawaken the legendary power of magic, and with that dread destructive force, enslave the world.”

So, Woolsey’s plural indeterminate, with a dash of Slattery’s grammatical structure. 

For the final line, I’d go even more general than Woolsey: “Could mankind really be on the verge of repeating such a mistake…?” I would say it’s not just ‘have today’s rulers failed to learn from history’, but ‘have today’s people failed to do so’. 

I really like it for how that spreads the blame around to all the progress and industrialization of the FF6 world at the time. There’s an implicit question of whether Kefka and Geshtal are just the worst products of the entire industrial revolution. And I think that question is carried through a lot of the later game; Cid’s regret that he developed Magitek, say. Even Narshe wouldn’t have uncovered that Esper if they hadn’t been mining so deep.

(via ark-shifter)

waystatus:

nostalgebraist:

I was just looking over the various people who’ve translated FFVI into English, and it was fun seeing what people did with the opening narration.

Classic 1994 Woolsey:

Long ago, the War of the Magi reduced the world to a scorched wasteland, and Magic simply ceased to exist.

1000 years have passed… Iron, gunpowder and steam engines have been rediscovered, and high technology reigns.

But there are those who would enslave the world by reviving the dread destructive force known as “Magic”.

Can it be that those in power are on the verge of repeating a senseless and deadly mistake?

Tom Slattery’s translation for the GBA version, supposed to be more accurate on the whole:

The ancient War of the Magi… When its flames at last receded, only the charred husk of a world remained. Even the power of magic was lost…

In the thousand years that followed, iron, gunpowder, and steam engines took the place of magic and life slowly returned to the barren land.

Yet there now stands one who would reawaken the magic of ages past and use its dreaded power as a means by which to conquer all the world.

Could anyone truly be foolish enough to repeat that mistake?

Unofficial translation by Sky Render, which is widely viewed as awkward although more literally “faithful” than Woolsey (not least by the translator themselves, cf. their later LP of it):

Long ago, humans battled one another, and the world became a scorched wasteland. The power of “magic” simply vanished.

1000 years have passed… Iron, gunpowder, and steam engines have been developed. Machinery has been revived to replace magic.

The great magic war faded into a legend. But the power of “magic” has been revived secretly, by the powerful military empire, run by a man who wants to rule the world.

Would this man be willing to destroy the world again for his own greed…?

(Unfortunately, Lina Darkstar never translated this part.)

---

I can’t tell how much of this is nostalgia, but the Woolsey version seems best to me here.  For one thing, “dread destructive force” is a good phrase (though so is Slattery’s “charred husk of a world”), and I like “high technology reins.”

Just as importantly, the Woolsey translation avoids the blunt moralizing of the other two (which I figure must have been in the original script, since it’s in two out of three translations).  The other two mention an individual villain, and finish on a note of “fuck that guy,” which fees like putting the cart before the horse – it’s like a movie that starts by telling you “there will be a bad guy in this movie, and you should hate him, because he’s evil.”

Woolsey generalizes it to an unnamed plural group, and his last sentence lacks the exasperation of the other two.  It’s not “how could this one guy possibly be so evil?”, it’s “have today’s rulers failed to learn the lessons of history?”, which is a much more interesting question.  “Can it be that those in power are on the verge of repeating a senseless and deadly mistake?” sounds like something you could easily hear in real-life political discussion; the others sound like we’re reading someone’s story outline.

I also played FFVI (with the original translation, I think?) and I like the Slattery version best.

My problem with the Woolsey version is that it’s actually kind of awkward. The capital-M in Magic and the “re”discovery of technology that doesn’t seem to have previously existed both sound very odd to my ear. There’s also something that I can’t place about the overall structure of that paragraph which sounds off to me. It sounds like a lot of old game translations do to me, which is to say it sounds like they didn’t quite have the budget to hire a really good translator, so they settled for a mediocre one.

I’m okay with the moralizing based mostly what I remember from the plot. “Those in power” are literally Gehstal and maybe Kefka. There’s no other force that wants what Gehstal wants; there’s no other force that could do it if they wanted. The most important thing about a translation is that it not be misleading, and I feel that a translation that led me to think that FFVI was about anything approaching real life politics, particularly when it comes to Gehstal himself, would just not be true.

Yeah, that’s true, it’s not like the rest of the story is especially subtle.

I agree about the slight awkwardness of the Woolsey version, although I think the Slattery version is still awkward by the non-video game standards.  “The ancient War of the Magi… When its flames at last receded” is an odd way of introducing a subject.  (Compare: “The Second World War … when it finally ended […]”).

It is indeed odd that Woolsey has “rediscovered,” especially since he was trying to economize on character count (he kept editing his script down and still getting told it was too big).

Re: the last part, I agree that the passage is talking about Gehstal – the relevant text even plays over a shot of him addressing imperial officers.  But then, Gehstal himself isn’t all that big a focus in FFVI.  On the third hand, Kefka is more of a focus, and it makes sense to emphasize G over K at this point because the game is doing the usual villain fake-out thing, like with President Shinra in FFVII.

On the fourth hand, though, the sheer destructiveness of magic seems even more important than these particular villains.  It’s hard for me to look at FFVI and not think of nuclear weapons and the Cold War; the later parts of the game feel much like a post-nuclear-war scenario, with the strange new monsters (mutants?) running around, and the way it all happens in one catastrophic blast that affects the whole globe.  And the scary thing about nukes isn’t that they might get used by an exceptionally awful ruler, it’s that they’re dangerous in the hand of the merely normally awful rulers who we take for granted on the global stage.  There have been a lot of Kefkas in the past (IRL and presumably in the FFVI world too), it’s just that this one got his hands on the nuclear codes.

So “this guy is so bad, we can’t trust him with magic” seems like the wrong emphasis.  Everyone is untrustworthy with nukes until proven otherwise.

(via waystatus)

bayes: a kinda-sorta masterpost

raginrayguns:

@nostalgebraist:

5. Why is the Bayesian machinery supposed to be so great?

This still confuses me a little, years after I wrote that other post.  A funny thing about the Bayesian machinery is that it doesn’t get justified in concrete guarantees like “can unscrew these screws, can tolerate this much torque, won’t melt below this temperature.”  Instead, one hears two kinds of justifications:

(a) Formal arguments that if one has some of the machinery in place, one will be suboptimal unless one has the other parts too

(b) Demonstrations that on particular problems, the machinery does a slick job (easy to use, self-consistent, free of oddities, etc.) while the classical tools all fail somehow

E. T. Jaynes’ big book is full of type (b) stuff, mostly on physics and statistics problems that are well-defined and textbook-ish enough that one can straightforwardly “plug and chug” with the Bayesian machinery.  The problem with these demos, as arguments, is that they only show that the tool has some applications, not that it is the only tool you’ll ever need.

Examples of type (a) are Cox’s Theorem and Dutch Book arguments.  These all start with the hypotheses and logical relations already set up, and try to convince you (say) if you have degrees of belief, they ought to conform to the logical relations.  This is something of a straw man argument, in that no one actually advocates using the rest of the setup but not imposing these relations.  (Although there are interesting ideas surprisingly close to that territory.)

The real competitors to Bayes (e.g. the classical toolbox) do not have the “hypothesis space + degrees of belief” setup at all, so these arguments cannot touch them.

Yeah, Jaynes starts with Cox’s theorem, which I think of as a sort of filter, which you can drop a system through and see where it gets stuck, and if it doesn’t get stuck and makes it all the way through, it’s probability theory. But he doesn’t really present any other systems that you can drop through the filter. He mostly criticizes orthodox statistics which you can’t really drop through it.

When I first read read Jaynes, the example I dropped through Cox’s theorem is fuzzy logic, defining Belief(A and B) = min(Belief(A), Belief(B)), and disjunction as maximum. This gets stuck because you can hold Belief(A) constant and increase Belief(B) without necessarily increasing Belief(A and B). That’s not allowed. I was very impressed with Cox’s theorem for excluding this, since I had not even noticed this property, and when brought to my attention it was in fact unreasonable.

It makes me wonder, if I would have been less impressed if I had started by using Dempster-Shafer theory as an example. Dempster-Shafer theory is the “interesting idea” that nostalgebraist linked to above. I’m writing this post to discuss it more thoroughly. tl;dr summary: Dempster-Schafer theory can be thought of as breaking the rule that there’s a “negation function” mapping Belief(~A) to Belief(A), and makes you wonder why we really need such a function.

So, as everyone in the internet Bayesianism discourse knows, Dempster-Schafer theory gives every proposition two numbers. These are the belief, Bel(A), and the plausibility, Plaus(A). Belief is how much it’s supported by the evidence, and plausibility is the degree to which it’s allowed by the evidence. Plausibility is higher.

As few discoursers seem to realize, Plaus(A) is just 1-Bel(~A), so in a sense Bel is all you need. It’s interesting, then, to drop Bel through Cox’s theorem, and see where it gets stuck.

And the first place I notice is at the following desideratum in Cox’s theorem:

There exists a function S such that, for all A, Bel(~A) = S(Bel(A)).

Bel(A) breaks this rule, supposedly ruling it out as a quantification of confidence. But how bad is it, really?

Suppose I’m happily using Dempster-Shafer theory for, I don’t know, assessment of fraud risk, when strawman!Cox bursts into my office, and declares “I’ve come to save you from your irrational degrees of belief!”

As the perfectly reasonable foil to this hysterical and unreasonable strawman, I reply in a tone of pure, innocent curiosity: “What do you mean? I’d love any opportunity to improve my fraud detection.”

“Well,” Cox begins, filliping a coin and covering it, “your Bel(Heads)=0.5, and your Bel(~Heads)=0.5, right?”

“Certainly,” I reply.

“And this case you’re reviewing, Bel(Fraud) = 0.5, correct?”

“Absolutely.”

“And your Bel(~Fraud)?”

“0.2.”

“That’s irrational!” he shrieks, throwing his hands in the air and revealing that the coin was a heads. “Let S be the function that maps from Bel(A) to Bel(~A). What’s S(0.5)? Is it 0.5, or 0.2?” He puts his hands on my desk, leans forward, and demands, “Which is it?”

“There is no such function,” I reply. “Why should there be?”

So, what can Cox do to convince me my assignments are irrational? Or that my fraud detection would be more efficient if there existed this negation function S?

So, that’s where I end up when I drop Dempster-Shafer Bel through Cox’s theorem, and this time I don’t feel I’ve revealed any flaw in the system.

Shafer himself says the same thing, actually:

Glenn Shafer:

Most of my own scholarly work has been devoted to representations of uncertainty that depart from the standard probability calculus, beginning with my work on belief functions in the 1970s and 1980s and continuing with my work on causality in the 1990s [18] and my current work with Vladimir Vovk on game-theoretic probability ([19], www.probabilityandfinance.com). I undertook all of this work after a careful reading, as a graduate student in the early 1970s, of Cox’s paper and book. His axioms did not dissuade me. As Van Horn notes, with a quote from my 1976 book [17], I am not on board even with Cox’s implicit assumption that reasonable expectation can normally be expressed as a single number. I should add that I am also unpersuaded by Cox’s two explicit axioms. Here they are in Cox’s own notation:

1. The likelihood ∼ b|a is determined in some way by the likelihood b|a: ∼ b|a = S(b|a). where S is some function of one variable.

2. The likelihood c ·b|a is determined in some way by the two likelihoods b|a and c|b · a: c · b|a = F(c|b · a, b|a), where F is some function of two variables.

I have never been able to appreciate the normative claims made for these axioms. They are abstractions from the usual rules of the probability calculus, which I do understand. But when I try to isolate them from that calculus and persuade myself that they are self-evident in their own terms, I draw a blank. They are too abstract—too distant from specific problems or procedures—to be self-evident to my mind.

Shafer goes on to quote and respond to Cox’s argument that there should exist F, but since I’m talking about S, I’m gonna look up how Jaynes argued for it.

ET Jaynes:

Since the propositions now being considered are of the Aristotelian logical type which must always be either true or false, the logical product AA̅ is always false, the logical sum A+A̅ always true. The plausibility that A is false must depend in some way on the plausibility that it is true. If we define u ≣ w(A|B), v ≣ w(A̅|B), there must exist some functional relation

v = S(u)

And that’s it. To explain notation w is the function that is eventually shown to have a correspondence with a probability mass function, overbar means “not”, and logical “sums” and “products” are conjunctions and disjunctions.

So, why must there exist this functional relation? Perhaps instead, the belief in A could change without altering the belief in ~A? That can happen in Dempster-Shafer I think, and it does seem kind of crazy. But even disallowing that, and allowing that there must be a function between belief in A and ~A, is it really the same function for every A? Why should it be?

Anyway, yeah. So, idk if I’d say, like nostalgebraist does, that Dempster-Shafer theory is surprisingly close to having the hypothesis space + beliefs setup but without the same constraints. I’d say instead that it’s exactly that. But I’m not totally sure since I’ve only read the basics and maybe things change in more complex applications.

Good stuff!!

To be completely honest, when I was writing that part you quoted, I was like “oh shit wait, D-S does have the same setup, so how does it get around the Cox and Dutch Book type stuff, or maybe it doesn’t? um….” and then in the interests of getting on with the rest of the post, I just hedged by being vague (“surprisingly close to that territory”)

So thanks for answering the question I was curious about but had to ignore.

I started wondering about the equivalent of the above in the measure-theoretic picture (i.e. why K-S doesn’t define a probability measure).  If you translate “logical negation” to “set complement” like usual, then it violates additivity: A and ~A are disjoint, and together they make the whole space, so area(A) = area(whole space) - area(~A).  This seems easier to understand than the Cox S thing, which fits with what Shafer said.

(Apparently, instead of a measure, it’s a “fuzzy measure.”  Instead of additivity, a fuzzy measure just needs to get the correct order on what I was calling “obviously-nested” sets earlier)

I can see the strong intuition behind the Cox S desideratum.  You should be able to take the negation of everything without changing any of the content.  Like, when we talk about A and ~A, neither has the intrinsic property of “being the one with the tilde.”  (Likewise with sets A, A^c.)  You can see the desideratum as a relatively weak way of trying to make things symmetric under negation – everything goes through the same function, so hopefully every property of b|a will have an equivalent for S(b|a).

So, if there’s an asymmetry between one side and the other, what broke the initial symmetry?  How do you decide which side is which?  (That’s what I imagine the strawman!Cox figure saying)

But then, A and ~A are always distinct, even if not because “one has the tilde.”  So for the D-S-using fraud protection worker, it is easy to break the symmetry because “Fraud” and “not Fraud” are different things.  (Thus if they’d flipped all their tildes at the start, the symmetry would have broken the same way, “not Fraud” getting 0.2 and “Fraud” getting 0.5.)

Still, if we are understanding the “not” here either as logical negation or as set complement, this is still nonsensical.  Because in both those frameworks, the negation doesn’t contain any information not contained in the original.  Except …

If I think of “the information” used to specify sets S or S^c as a boundary, then S is “everything inside here” and S^c is “everything outside of here.”  Of course this visual picture is depending on topological notions not present in the sets alone, but it suggests something true about spaces of ideas/hypotheses: we can draw a boundary around some ideas we know about, and the “inside here” set is all stuff we know about, but the “outside of here” set includes all other ideas, including ones we haven’t thought of.  So this is a very natural distinction in practice.

How would you formalize that?  I guess you’d have set theory in a universe (=“outcome space”) that wasn’t fully known, so you could say stuff like “I know 1 and 2 are in the universe, and I can make the set {1, 2}, but I don’t know if 3 is in the universe.”  This probably exists but I don’t know what it’s called.

(via raginrayguns)