"I guess if the lock has a persistent tendency to change its own password to 012345, because it has fond memories of the workshop it was created in," Meritxell says.

"Careful with that kind of cleverness.  There's another famous dichotomy between being smart enough to think of correct answers versus smart enough that you can take any answer and come up with a weird way for it to be correct.  In real life, entering 012345 repeatedly into the lock is stupid even though it's possible to imagine an exotic circumstance where it isn't.  I'm not saying you should never think the way you just did, I'm saying that you should always clearly label it inside and outside as having come up with a clever weird circumstance under which it would make sense to do something that is in real life stupid."

"Anyways, I'm glad you all now agree with me that the best way of getting through number-sequence locks is to repeatedly enter in 012345 on them."

"...you just said that was stupid!"

"That was some other Keltham.  I'm the Keltham who thinks that repeating 012345 is a great strategy, and he's going to keep lecturing you on that until one of you manages to talk him out of it by explaining exactly what he's doing wrong."

They giggle nervously. 

"If it didn't work the first time, then it'll only work this time if the lock magically changed, and changed to this specific code, and you haven't got any reason to think it did that so you might as well just set a construct to trying all possible combinations in order at this point, before you try any twice."

"Wait, so you're saying that 012345 isn't the best code to try?  What's the better one, then?"

"Any of them which you haven't tried yet!"

"I'm confused.  If on the first turn, 012345 is the best combination to try, and the lock hasn't changed, it should still be the best combination to try on the second turn."

"...no, because if it were right, it would've opened the lock, so now you know it's wrong."

"So what you're saying is that my knowledge about the lock changed, but not the lock itself?  I suppose I could buy that.  Doesn't that mean I'd have to keep on changing which things I tried as I observed the results and my knowledge kept changing, though?  That sounds inconvenient and difficult and not very Lawful, really."

They're so confused!

"I mean, you probably want to build a construct," Pela, who has been arguing for this solution for a while, says more firmly. "Which just tries every number in order. And you expect that it's one of the remaining numbers until you've tried them all."

"Wouldn't it be better to build a Lawful construct instead of a Chaotic one, which repeatedly used the optimal number instead of, like, all these other non-optimal numbers?  I'm definitely gonna do that if you don't talk me out of it somehow.  Gonna be a great construct.  The best.  Optimal."

"- trying every number in order is plenty Lawful! Law has nothing to do with - doing the exact same thing over and over!"

(Carissa, who is going to be able to resolve the bet this evening, proposes everyone double-or-nothing on their is-Keltham-a-sadist betting.)

"If it's the best thing, you should do it over and over.  If it's not the best thing, you should do the best thing instead.  If that isn't Lawful, then what is Law, exactly?"

"It stops being the best thing once you've tried it!"

"Law is - if you're doing a dumb thing, and you think it's Lawful, you're probably just confused about what Law is, it doesn't mean you have to do dumb things."

"Well, perhaps I am confused about the Law because I thought it said to do a dumb thing, but then what is the Law actually?  Can it be explained to me or do I just have to enter whichever exact codes you tell me to?"

"I don't think approaches to guessing a password can be Lawful or Chaotic. And we've been telling you the thing you should do, which is try all the numbers in order!"

"All right, speaking more seriously now.  It's easy to tangle yourself up with paradoxes of what is best, what is optimal, especially when you define the word even slightly different ways, see it from slightly different angles across two times you used the word.  There's a mistake that young dath ilani make - skewing male rather than female, though also some girls and not all boys, of course - where they can't quite accept the fact that older children know more than they do and have higher measured cognitive powers, and some of them get fascinated with the ways that you can tangle up your reasoning and 'prove' that you're actually better than the older children because you're more ignorant than they are, or smarter than the optimal way of doing something."

"It's one of the things where, when a boy makes a mistake like that, the older children and the Watchers don't try to talk him out of it, and let him go on believing it for a few years, so he can have his enjoyment and also learn a valuable life lesson when he's old enough to more carefully disentangle all of the paradoxes.  This valuable lesson is that paradoxical-sounding questions have non-paradoxical answers, if you define everything precisely enough and don't mix up your words.  Even if you cannot see the answer yet, you should expect that such an answer exists.  Confusion exists in our minds, not in consistent mathematics."

"In this case, I could formalize the solution by saying, for example, that there is such a thing as a best sequence of codes to try, given your state of knowledge about the lock, and that repeatedly trying the most likely first code forever is among the worst possible sequences.  Or I could say that, since our knowledge changes with each observation, the best second code to try, given the results of observing the first code, is not equal to the best first code to try.  This, I realize, may not sound particularly better than any of the other arguments you were using against silly-Keltham, but they fit into larger frameworks I can talk about later.  A dath ilani would tell you that you're mistaken in thinking that there's no Lawful approach to guessing a code; you can use math to describe your beliefs about which codes have which probabilities of working, describe mathematically how those probabilities change with each observation as successive codes are ruled out, and that math then describes the next best guess.  That doesn't mean you can do better by thinking explicitly in math, of course, instead of just quickly typing in possible passwords that seem likely; but the math does exist."

"On a larger scale, the point I want to make again is about that dichotomy between optimality and diversity, the reason why you don't want to take a single stalk of corn and plant exact copies of it all over the country.  When we talked about the case of the lock and its codes, we got two different angles on a way to resolve the children's paradox of it apparently not being best to just use the best answer.  The first angle is that of the adaptive adversary, the corn blight, the master criminal considering the lock; the more regular we make our own answer, the more the adversary's adaptivity or intelligence is able to analyze and defeat it.  We use randomization as a way to make it harder for their own intelligence to grasp; there's nothing paradoxical about the idea that, the more random something is, the less knowable it is, the more it may inconvenience some other mind.  It's the kind of variation that's valuable in the disease-fighting systems inside human and corn, the kind that makes it harder for diseases to learn our defenses."

"But the other viewpoint on the lock and code is the more important one.  It's the reason why, if your team has been having trouble solving a problem for a while, you might want to add a new person who thinks less like the rest of you.  It's a resource that a field of corn stalks has for adapting to a sudden shift in the environment, a new weather extreme; if the crop is more diverse, maybe some hardier stalks will survive to be replanted next year and then do better against that environment.  It's the kind of variation where you're trying things in many places, and, because of that, trying overly similar things in many places is something that yields less expected profit to you."

"There are dimensions of society in which you want everyone behaving differently, so they can explore a space instead of all crowding together into one corner of it.  There are dimensions of society where things go pretty well so long as you do something the correct way, and start to go poorly if you do things much differently than that.  There is a tension in dath ilan between positions, between people and factions, between ideas and arguments, about that question - not just about particular cases, but about the sense in general of where all society should move on that spectrum.  Whether it is more important in general for everyone to do things a bit more differently, in our future, or if the problem is more that we're falling too far below some standards and we all need to improve in those ways together.  There are lots of particular cases in dath ilan where people might hold different opinions and not just one general opinion; but there is a sense that this general dimension of existence is one where the exact balance is important to a society."

"Dath ilan has terminology for this dichotomy of strategies, between the search to find the optimal best answer and use it, versus trying many different answers to be more resilient against unknowns and explore a space more widely.  Though I've been deliberately substituting the words 'optimal' and 'diverse', in this language, instead of the two Taldane words that the translation spell tries to automatically output."

"If I say the dath ilani words directly, for these two directions a society can move along this dimension, they come out in this language as:"

"Lawful."

"And, Chaotic."

Elias Abarco is not an eighteen year old girl and is not going to gape wonderingly at Keltham because EVERYTHING MAKES SENSE. No one would notice, since he's invisible, but he nonetheless has too much dignity.

Some things make sense. And some things are even more confusing because -

- why not say that, humans can understand that -

Reality is so very large and pretty and connected when you catch a sight of it.  She wants to see more.

Nice, Ione thinks all the way up where her conscious mind can hear it.

"I was on the side of Chaos, of course.  Lawfulness seemed so very boring.  I was quite sure we had enough of it already."

"There's a saying in dath ilan that always sounded to me before like sententious pro-Law propaganda, whose depth of meaning, I think, I never really appreciated until I came to Golarion."

"It's the saying that even Chaos is almost entirely made of Law."

"Some variation in the corn stalks is useful for resisting disease, or having any survivors if an especially hot summer comes.  If you scramble all the tiny spirals entirely and insert completely new information, what you get is not much higher levels of useful Chaos, you get a plant that entirely fails to form.  The wildest, most diverse crop that still manages to live at all must be almost entirely regular and using almost completely standard forms of everything for its species; otherwise it comes out, not weird and warped, but simply a dead seed that fails to germinate at all.  When you're adding a new and different mind to your team, full of wild ideas, they should hopefully be speaking mostly grammatical sentences that make sense, and not uttering random words and random sounds and twitching around wildly on the floor.  The full absence of Law is not diversity, but randomness, noise.  In many cases, nearly all the random ways of doing things get you pretty much the same effect, there is not much difference in contribution between a person wildly twitching on the floor in one way versus a different way, they look much the same from outside.  Even diversity has to be almost entirely made out of shared order, and climb high up on the scale of optimality away from the level of noise, in order to be effectively diverse."

"Even Chaos is made almost entirely out of Law.  I thought it was something of a sententious old proverb, that was emphasizing one particular viewpoint on an underlying truth that seemed overly trivial.  I wanted to think thoughts that nobody had ever thought before, sure, well of course I didn't want to do that by thinking random words, obviously.  I wanted to start companies or invest in companies that nobody else would have thought of, that no other investor would invest in, I wanted to show that the way I thought differently was better and worthy of further exploration.  Of course, if I wanted to pull that off successfully, it would be a matter of art and skill, governed by laws, with relevant history to study and relevant investigations to do.  I thought that sort of thing didn't belong to Law alone.  Chaotic people like me could say it too, so there wasn't anything especially Lawful about it."

"Even Chaos is made almost entirely out of Law, in a fashion governed by higher orders, mathematics, whose name in Baseline also tends to translate into Taldane as 'Law'.  I have gotten to this place, Golarion, I have heard what many of your 'countries' are doing.  It is pretty clear that even the factions called Lawful seem to be confused about many things.  And I am resigned at this point to the fact that at some point I am also going to have to go and somehow straighten out all the Chaotic parts because it seems pretty likely at this point that all y'all are also doing that part all wrong."

"In conclusion.  The value of diversity in your heritage, and its nature as a kind of resource that strong optimization uses up - especially variation that has the nature of useful variations rather than destructively random variations - is another reason why, if you meet a human visitor from another plane with 18 Intelligence, it's a great time to make an exception to any usual social rules about not just subsidizing the very best men to have 144 kids apiece, because the diversity of your heritage will actually go up when you add in some kids from a smart alien, and some of your kids may think a little differently and be more useful to add to projects.  This concludes my sales pitch; I have added in many of the caveats that I knew about, but I may have been biased in my thinking about them nonetheless; I have tried to give you the knowledge you'd need to do your own thinking about it independently."

"Any questions?"

"In your conception of Chaos," says Meritxell, "what would a Chaotic god be like."