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Self-driving cars

tsutsifrutsi:

collapsedsquid:

tsutsifrutsi:

nostalgebraist:

phenoct:

nostalgebraist:

collapsedsquid:

I keep seeing people talk about how awesome self-driving cars will be, and how they’ll save lives because computer don’t make mistakes.  Whenever I see that, I’m wondering where the hell those people get their software from, cause the software I deal with is buggy shit.

And then, I heard that google wanted to sell their car without a steering wheel.  Seriously? What happens if the sensors get blocked, say, in the middle of a storm? What if it bugs out due to a road condition issue?  Do they really want a car that  can be bricked so easily and that at best could leave you stranded and make a road hazard? If this was a mature technology, then we’d know what the issues would be. It is not a mature technology.  I seriously doubt their competency in general for deciding not to include a manual steering system, and aggressively lobbying not to include one.

I mean, they seem to be doing OK, with their demos.  I’m concerned that their good record could be a result of the fact that they get to choose when and where to test.  I’m also concerned about what will happens to the cars as they age.  I just am weirded out by this constant optimism I seem to get from everywhere, even people I would have thought had a decent amount of technological pessimism through hard-earned experience.  Robotic technology has been overhyped shit since forever.

Yeah, I hadn’t really thought too hard about this but it seems like such an unpromising use of AI – the consequences for mistakes are gigantic and it’s basically impossible (?) to get a good sense of how well the algorithm will perform in practice without actually putting it into practice (dynamics will emerge from self-driving cars interacting, people changing their driving style in response to them, etc).

“Your life is now in the hands of this thing that did a little bit better than you on the training set” is a scary concept.

Software is buggy, humans are much buggier.

But they’re not buggy in the same ways.  When AI fails, it tends to fail in weird ways that a human never would, which may seem obviously catastrophic to a human – the sort of idea so bad you’d usually forget it was a possibility.  It’s certainly possible that performance would be better on the whole, but even then it is still scary because I’m risk averse and want to at least know what sorts of risks I’m facing.

To be concrete, I don’t want to be in a vehicle that could suddenly slam to a halt on the freeway because a programmer forgot about a rare-but-possible edge case somewhere.

(I don’t know much about self-driving cars and it would be nice to be wrong here.)

Robotics software doesn’t work like regular software. It’s not designed around a single blob of code that centrally controls a whole system of actuators, where a bug in that code will screw you over.

Instead, most of the way we design robots is an outgrowth of the subsumption architecture of Rodney Brooks (now better known as “the creator of the Roomba.”)

This architecture is used today in, for example, driverless subway systems. A subway system doesn’t have one “brain” that takes in all the facts about where all the cars are, what they see, etc., and then outputs acceleration commands to each car. Instead, each part of the subway system “sees” and “thinks” and “reacts” for itself—with the local parts being trusted to take local action, e.g. proximity sensors being directly capable of stopping the train; and with central parts mostly just giving strategic suggestions for the local processors to take-into-account. (Except, also, each layer’s suggestions to the layers below carry a weight-value, that can be boosted enough to dominate the lower layer’s calculation on how it should react. This is similar to a brain’s ability to override low-level modules like fight-or-flight response with reasoned responses like “be bigger than the bear.”)

Basically, when designing a subsumption system (or other hierarchical control system), there are safeguards engineered in at every level. But that’s the wrong way to think about it, because that still suggests centralization. What you’ve got is more like a military command structure: strategy comes down from the top, but individual soldiers, agents with their own preference-functions, are tasked with implementing that strategy. The safeguards are the “men on the ground”, the actual components getting things done. They’re agents in their own right, and the (maybe-buggy) high-level strategy has to go through them, and be considered right by them, to get run.

The vertebrate nervous system is subsumptive, in an important way. You, a brain, can decide to put your hand on a red-hot stove element. But your hand doesn’t like that idea very much, and will flinch away reflexively. The actual component implementing the strategy—the nerves in your hand—are capable of evaluating your strategy for themselves, and deciding against it. (You’re capable of overriding that decision with a forceful-enough command—if, say, you’re trying to reach through boiling water to rescue a friend—but you really have to force it; that much executive function isn’t available on a whim.)

Which is all to say: driverless cars work like that. They don’t stop dead on the road when there’s a bug in the brain, because “stopping dead on the freeway” is one of those dumb ideas that the individual components wouldn’t bother to implement. The correct strategy for a car is actually almost always “keep going at whatever speed and torque angle are required to optimize the distance between you, the cars in front of and behind you, and your lane markers.” Any central strategic calculation has to be better than that default strategy, or the “nervous system” of the car will just keep doing the default strategy, effectively “flinching away” from doing something so stupid as stopping on the freeway.

But I have heard that plane autopilots at least will just abort and handoff control to human operators in some cases.  In a driverless car without a steering wheel, that is not a possibility, so the only option would be to stop.

Your scenario assumes that the lane markers and nearby cars are identifiable, but if they are not, then what does the car do?  I pointed out sensor obstructions, there is also roadwork and other possible issues. There’s this basic problem of incoherent input that I don’t think this system solves. (or, in a worst case, could result in different systems in the car trying to do different things, which could be worse.)

[oops, essay-length]

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(via tsutsifrutsi)

Self-driving cars

thathopeyetlives:

nostalgebraist:

phenoct:

nostalgebraist:

collapsedsquid:

I keep seeing people talk about how awesome self-driving cars will be, and how they’ll save lives because computer don’t make mistakes.  Whenever I see that, I’m wondering where the hell those people get their software from, cause the software I deal with is buggy shit.

And then, I heard that google wanted to sell their car without a steering wheel.  Seriously? What happens if the sensors get blocked, say, in the middle of a storm? What if it bugs out due to a road condition issue?  Do they really want a car that  can be bricked so easily and that at best could leave you stranded and make a road hazard? If this was a mature technology, then we’d know what the issues would be. It is not a mature technology.  I seriously doubt their competency in general for deciding not to include a manual steering system, and aggressively lobbying not to include one.

I mean, they seem to be doing OK, with their demos.  I’m concerned that their good record could be a result of the fact that they get to choose when and where to test.  I’m also concerned about what will happens to the cars as they age.  I just am weirded out by this constant optimism I seem to get from everywhere, even people I would have thought had a decent amount of technological pessimism through hard-earned experience.  Robotic technology has been overhyped shit since forever.

Yeah, I hadn’t really thought too hard about this but it seems like such an unpromising use of AI – the consequences for mistakes are gigantic and it’s basically impossible (?) to get a good sense of how well the algorithm will perform in practice without actually putting it into practice (dynamics will emerge from self-driving cars interacting, people changing their driving style in response to them, etc).

“Your life is now in the hands of this thing that did a little bit better than you on the training set” is a scary concept.

Software is buggy, humans are much buggier.

But they’re not buggy in the same ways.  When AI fails, it tends to fail in weird ways that a human never would, which may seem obviously catastrophic to a human – the sort of idea so bad you’d usually forget it was a possibility.  It’s certainly possible that performance would be better on the whole, but even then it is still scary because I’m risk averse and want to at least know what sorts of risks I’m facing.

To be concrete, I don’t want to be in a vehicle that could suddenly slam to a halt on the freeway because a programmer forgot about a rare-but-possible edge case somewhere.

(I don’t know much about self-driving cars and it would be nice to be wrong here.)

The closest thing to compare that I can think of is probably cruise missile guidance systems pre-GPS. 


And that had the benefits of military grade hardware… (automotive grade is like the third best thing)… and also didn’t need to be perfect. (IIRC Turkey “praised” the USA for inventing a weapon that could miss by hundreds of miles). 


Even something really simple like a quadcopter with no real environment sensing equipment can respond in weird ways to sensor failure – in my experience, by suddenly rocketing high into the air, and getting back down under manual control (which you have to abruptly assume) is hard

Most significantly, I would expect self-driving cars to be barely usable around construction sites, “rural” roads, and road hazards of nearly any kind other than obstructions. 


Personally, I think that the way forward is 1. automated taxicabs, in dense cities where enviroment can be sorta controlled, and 2. incremental addition of advanced robotics to cars that are still mostly manually driven. 

(via thathopeyetlives)

Self-driving cars

phenoct:

nostalgebraist:

collapsedsquid:

I keep seeing people talk about how awesome self-driving cars will be, and how they’ll save lives because computer don’t make mistakes.  Whenever I see that, I’m wondering where the hell those people get their software from, cause the software I deal with is buggy shit.

And then, I heard that google wanted to sell their car without a steering wheel.  Seriously? What happens if the sensors get blocked, say, in the middle of a storm? What if it bugs out due to a road condition issue?  Do they really want a car that  can be bricked so easily and that at best could leave you stranded and make a road hazard? If this was a mature technology, then we’d know what the issues would be. It is not a mature technology.  I seriously doubt their competency in general for deciding not to include a manual steering system, and aggressively lobbying not to include one.

I mean, they seem to be doing OK, with their demos.  I’m concerned that their good record could be a result of the fact that they get to choose when and where to test.  I’m also concerned about what will happens to the cars as they age.  I just am weirded out by this constant optimism I seem to get from everywhere, even people I would have thought had a decent amount of technological pessimism through hard-earned experience.  Robotic technology has been overhyped shit since forever.

Yeah, I hadn’t really thought too hard about this but it seems like such an unpromising use of AI – the consequences for mistakes are gigantic and it’s basically impossible (?) to get a good sense of how well the algorithm will perform in practice without actually putting it into practice (dynamics will emerge from self-driving cars interacting, people changing their driving style in response to them, etc).

“Your life is now in the hands of this thing that did a little bit better than you on the training set” is a scary concept.

Software is buggy, humans are much buggier.

But they’re not buggy in the same ways.  When AI fails, it tends to fail in weird ways that a human never would, which may seem obviously catastrophic to a human – the sort of idea so bad you’d usually forget it was a possibility.  It’s certainly possible that performance would be better on the whole, but even then it is still scary because I’m risk averse and want to at least know what sorts of risks I’m facing.

To be concrete, I don’t want to be in a vehicle that could suddenly slam to a halt on the freeway because a programmer forgot about a rare-but-possible edge case somewhere.

(I don’t know much about self-driving cars and it would be nice to be wrong here.)

(via phenoct)

lovestwell:

jadagul:

nostalgebraist:

@jadagul (splitting off the infinite trolley thread which is getting long)

So there’s a lot to unpack there.

My post was assuming the usual real line, not the long line. In the regular real line, you just can’t get aleph-1 people into it without having aleph-1 people in some arbitrarily small interval. (Sketch of proof: choose an epsilon > 0. The line is a union of countably many intervals of length less than epsilon, and a countable union of countable sets is countable, so at least one interval must have uncountably many people in it).

On the long line things are different. We do have to back up and define things more carefully, because typically a “measure” only outputs a real (or complex) number or infinity, and so you can’t have a set with measure aleph-1. But it’s easy enough to route around that (as long as you can define the idea of adding infinite cardinals sensibly, which I think you can).

Then sure, you can take the long line and put one person in each [0,1) interval. There will be aleph-1 people on the track at “the same density” as the aleph-0 track.

But this is where we get back to my original complaint, which is that some (almost all!) people will never get hit by the train. Not only will they not get hit in finite time, they won’t get hit in countably infinite time. The train doesn’t have a way to get off the “usual” line onto the “long” part of the long line.

Basically, we say something is countable if for every element, you know how many elements you have to go through to get there. The set may be infinite but each individual element is only finitely far into the list. Which means you can ask questions like “when does the train hit this person?” Or “how many people will get hit before this person gets hit?” and have well-defined answers.

In uncountable sets, by definition, you can’t ask those questions. You can order an uncountable set (which means that for any two elements, you can ask which comes first). And if you believe in choice you can well-order an uncountable set (which means that for each element, there’s a “next” element–but not necessarily a “previous” element! There is, however, a “first” element). But none of that is enough to ask questions like “who is the fifth person to get hit?” or “How long will it take before John gets run over?”

So yeah, if your set is “the set of points on the real line” then there’s a natural “total order”. (Although there isn’t really a natural well-order). So you could say “after time t=1 these (uncountably many people) have been run over.” But you couldn’t ask who gets hit first or anything.

My understanding is that “countable” is a description of a cardinality of a set, not of its order type, which is (confusingly) the aspect that is relevant for questions of counting one by one.

(This is just the point @bowtochris made about the original post, except until now I was too confused to understand it)

So, for instance, consider ω+1.  ω is just the order type of the natural numbers:

0 < 1 < 2 < 3 < … 

Then ω+1 corresponds to taking the natural numbers and adding on an extra element that’s greater than all of them:

0 < 1 < 2 < 3 < … < 0′

This thing has the same cardinality as the usual natural numbers, so it’s countable.  But with order type ω, for any number, we can define how many steps it takes to get there.  With order type ω+1, we can’t do this with 0′.  (And since the original picture just stated the cardinality, we can’t tell which of these we are dealing with.)

Of course, since these are both countable, we can put them in one-to-one correspondence, and thus rearrange the one with 0′ to the one where you can count to anything, including the numbers what 0′ gets mapped to.  So at worst this seems like an “ordering issue” rather than some issue with 0′ being “so far out” that it can’t be counted to.

But now consider the uncountable case.  Specifically, consider the first uncountable ordinary ω_1 (used to make the long line).  It orders all the countable ordinals, of which there are uncountably many.  So from one perspective, this contains all sorts of things you can “never count to.”  On the other hand, for any x∈ ω_1, the set of elements of ω_1 less than x is countable.  So wherever you are in ω_1, any inability to “count to that point” is again just an “ordering issue,” no worse than in the above case.

I guess this is just another way of stating your point that the train can’t ever get to “the ‘long’ part of the line.”  However, I don’t think this makes the original picture or problem somehow ill-defined.  There’s nothing wrong with depicting the uncountable people on the second track as a first one followed by a second one etc. – this implies that they are well-ordered, but ω_1 is well-ordered (even without the axiom of choice, I think?).

On either track, you can have various order types, implying various people who can’t be reached by counting – you can even have countably many of these on the first track.  But on the second track, no matter what the order is, you must have uncountably many people who can never be hit.  I’m not sure the “uncountably many” is the important part here – it also just seems important that you can have zero people who can never be hit on the first track, but can’t on the second.  But “people who can’t be hit” isn’t a concept that applies only to the second track – it’s just that on the first track you have somewhere between 0 and aleph_0 of them, while on the second you have aleph_1 of them.

Of course none of this is at all in the spirit of the original problem, since it gives you no way to hit “more people” on the second track.  Which is I guess what you’ve been saying.  But I don’t think this is because you can’t possibly answer “how long until John gets hit?” for the second track.  As on the first track, the answer will either be “[some finite time t]” or “never.”

(I should say, again, that I am a a complete newb at all of this and am basically just thinking through the process of learning basic stuff about infinite cardinals and ordinals.  So I apologize if this is tedious or irritating for that reason.)

(On another, uh, track entirely – it’s funny how utilitarianism breaks down with infinities.  You could add another person to one of these tracks without changing the cardinality, like in Hilbert’s hotel, but surely that’s bad and not neutral, right?))

So I think all of that is right.

But, as you observe, the original picture just gave us the cardinal, not the ordinal. For the cardinal aleph-0 you can choose an ordinal where every element is reachable. For the cardinal aleph-1 you can’t.

So a shorter but even more opaque version of my original criticism is that “the bottom picture is impossible because it implies an ordinal assignment where every person is reachable, but such an assignment is impossible.

Or, in other words, when you say

But I don’t think this is because you can’t possibly answer “how long until John gets hit?” for the second track. As on the first track, the answer will either be “[some finite time t]” or “never.”

the point is that we can choose an ordinal for the first track where the answer is never “never”, but you can’t do that for the second.

Miscellaneous notes: choice came in for well-ordering the reals. It’s utterly unambiguous that ω_1 is well-ordered, as is any ordinal; but you need choice to produce an actual bijection between the real line and some ordinal.

For the utilitarianism thing: I think this is why a number of dedicated utilitarians (including Yudkowsky) are finitists. This entire problem goes away if you do the (completely reasonable and physical) thing and just ask how long the train is going to be running and how many people it will kill in that time. Plausibly every real problem doesn’t actually involve infinity anything. But yes, all sorts of things break down when you throw in infinity.

I might have to link in my favorite application of choice now. It’s way better than Banach-Tarski.

Perhaps one possible next step, for the original picture to make interesting sense, is to generalize the meaning of an element always being “reachable” in such a way that, for the aleph-1 track, it’s more permissive than “reachable in a finite number of steps”, which isn’t achievable, but more strict than “being at the end of a proper initial segment of the ordering”, which is trivially satisfied by using the well-ordering of aleph-1 as an ordinal.

For that, we can look to first-order logic: if a track if our naive conception of N, let the formal track be any model of a suitably reach set of axioms for N (the Peano axioms for instance). The Lowenhelm-Skolem theorem then ensures that there exist track of any desired cardinality, such as aleph-1. We can take the top track to simply be N (although we don’t *have* to, it could also be a nonstandard countable model, but let’s maintain some levelheadedness), and the bottom track is a nonstandard model of Peano arithmetic. It remains true that any person on the bottom track can be reached in a number of steps that is a natural number, although for some people that natural number won’t be standard. 

The order on the bottom track will look like a copy of N followed by aleph-1 copies of Z arranged in some dense linear order without endpoints. I don’t know if much more is known about what this order could be for aleph-1. 

I think it still makes sense to speak of the trolley being twice faster on the top track, which means it’ll reach standard people on the top track twice faster than on the bottom track. It will reach nonstandard people on the bottom track in nonstandard time, and “eventually” will kill all aleph-1 of them.

I don’t understand this, but it sounds cool and I want to, so I’m reblogging for future reference (and for other people less ignorant than me).

(The question “what would the uncountable track look like?” has made me suddenly motivated to learn more about transfinite stuff, so I wonder if it could be used – outside of the ethical dilemma context – as a motivating example at the start of a class/textbook or something?  Maybe it already has been)

(via lovestwell)

shlevy:

nostalgebraist:

@jadagul (splitting off the infinite trolley thread which is getting long)

So there’s a lot to unpack there.

My post was assuming the usual real line, not the long line. In the regular real line, you just can’t get aleph-1 people into it without having aleph-1 people in some arbitrarily small interval. (Sketch of proof: choose an epsilon > 0. The line is a union of countably many intervals of length less than epsilon, and a countable union of countable sets is countable, so at least one interval must have uncountably many people in it).

On the long line things are different. We do have to back up and define things more carefully, because typically a “measure” only outputs a real (or complex) number or infinity, and so you can’t have a set with measure aleph-1. But it’s easy enough to route around that (as long as you can define the idea of adding infinite cardinals sensibly, which I think you can).

Then sure, you can take the long line and put one person in each [0,1) interval. There will be aleph-1 people on the track at “the same density” as the aleph-0 track.

But this is where we get back to my original complaint, which is that some (almost all!) people will never get hit by the train. Not only will they not get hit in finite time, they won’t get hit in countably infinite time. The train doesn’t have a way to get off the “usual” line onto the “long” part of the long line.

Basically, we say something is countable if for every element, you know how many elements you have to go through to get there. The set may be infinite but each individual element is only finitely far into the list. Which means you can ask questions like “when does the train hit this person?” Or “how many people will get hit before this person gets hit?” and have well-defined answers.

In uncountable sets, by definition, you can’t ask those questions. You can order an uncountable set (which means that for any two elements, you can ask which comes first). And if you believe in choice you can well-order an uncountable set (which means that for each element, there’s a “next” element–but not necessarily a “previous” element! There is, however, a “first” element). But none of that is enough to ask questions like “who is the fifth person to get hit?” or “How long will it take before John gets run over?”

So yeah, if your set is “the set of points on the real line” then there’s a natural “total order”. (Although there isn’t really a natural well-order). So you could say “after time t=1 these (uncountably many people) have been run over.” But you couldn’t ask who gets hit first or anything.

My understanding is that “countable” is a description of a cardinality of a set, not of its order type, which is (confusingly) the aspect that is relevant for questions of counting one by one.

(This is just the point @bowtochris made about the original post, except until now I was too confused to understand it)

So, for instance, consider ω+1.  ω is just the order type of the natural numbers:

0 < 1 < 2 < 3 < … 

Then ω+1 corresponds to taking the natural numbers and adding on an extra element that’s greater than all of them:

0 < 1 < 2 < 3 < … < 0′

This thing has the same cardinality as the usual natural numbers, so it’s countable.  But with order type ω, for any number, we can define how many steps it takes to get there.  With order type ω+1, we can’t do this with 0′.  (And since the original picture just stated the cardinality, we can’t tell which of these we are dealing with.)

Of course, since these are both countable, we can put them in one-to-one correspondence, and thus rearrange the one with 0′ to the one where you can count to anything, including the numbers what 0′ gets mapped to.  So at worst this seems like an “ordering issue” rather than some issue with 0′ being “so far out” that it can’t be counted to.

But now consider the uncountable case.  Specifically, consider the first uncountable ordinary ω_1 (used to make the long line).  It orders all the countable ordinals, of which there are uncountably many.  So from one perspective, this contains all sorts of things you can “never count to.”  On the other hand, for any x∈ ω_1, the set of elements of ω_1 less than x is countable.  So wherever you are in ω_1, any inability to “count to that point” is again just an “ordering issue,” no worse than in the above case.

I guess this is just another way of stating your point that the train can’t ever get to “the ‘long’ part of the line.”  However, I don’t think this makes the original picture or problem somehow ill-defined.  There’s nothing wrong with depicting the uncountable people on the second track as a first one followed by a second one etc. – this implies that they are well-ordered, but ω_1 is well-ordered (even without the axiom of choice, I think?).

On either track, you can have various order types, implying various people who can’t be reached by counting – you can even have countably many of these on the first track.  But on the second track, no matter what the order is, you must have uncountably many people who can never be hit.  I’m not sure the “uncountably many” is the important part here – it also just seems important that you can have zero people who can never be hit on the first track, but can’t on the second.  But “people who can’t be hit” isn’t a concept that applies only to the second track – it’s just that on the first track you have somewhere between 0 and aleph_0 of them, while on the second you have aleph_1 of them.

Of course none of this is at all in the spirit of the original problem, since it gives you no way to hit “more people” on the second track.  Which is I guess what you’ve been saying.  But I don’t think this is because you can’t possibly answer “how long until John gets hit?” for the second track.  As on the first track, the answer will either be “[some finite time t]” or “never.”

(I should say, again, that I am a a complete newb at all of this and am basically just thinking through the process of learning basic stuff about infinite cardinals and ordinals.  So I apologize if this is tedious or irritating for that reason.)

(On another, uh, track entirely – it’s funny how utilitarianism breaks down with infinities.  You could add another person to one of these tracks without changing the cardinality, like in Hilbert’s hotel, but surely that’s bad and not neutral, right?))

But on the second track, no matter what the order is, you must have uncountably many people who can never be hit.

Assuming the “second track” here is the one with aleph 1 cardinality, why is this the case? Say the track is the real line, then for any person on it we can find a time (in terms of X) after which that person is hit, no? Or say even that just the first meter of the track is the real interval (0,1], then everyone on it is hit in finite time!

Here we were talking over whether there can be aleph_1 people on a track (and what that means) in the way it’s depicted in the picture, where they’re lined up one by one, and it takes some finite amount of time to hit each one.

(In other words, the question is what happens when we have a well-order on the people.  The Axiom of Choice implies that there is a well-order on the real numbers, but it’s not the usual order and we have no idea what it looks like.  My statement isn’t true for the reals with the usual order, but that’s because it isn’t a well-order.)

(via shlevy)

jadagul:
“youzicha:
“nostalgebraist:
“cromulentenough:
“nostalgebraist:
“shlevy:
“shlevy:
“via trolley problem memes
”
i… guess not?, it’s not like it’ll run out in either case,and according to the figure the person density is the same on both tracks...

jadagul:

youzicha:

nostalgebraist:

cromulentenough:

nostalgebraist:

shlevy:

shlevy:

via trolley problem memes

i… guess not?, it’s not like it’ll run out in either case,and according to the figure the person density is the same on both tracks (tags via @itsbenedict​)

That can’t actually be right though, because then both tracks would be countable. The density of the lower track can’t be constant, my gut feeling is that it can’t even have a well defined density everywhere in the sense of “finite number of people per finite amount of track” but I’m not sure of that one.

I’m really tired so this may be nonsense, but you may be able to do it by putting a measure on the long line?

2* aleph-null is still aleph null though right? aleph one is so much bigger than aleph null that it should definitely be you send it down the aleph-null track.

At any finite time, though, the offshoot would have hit twice as many people as the original.  You’ll never see the difference between the two infinities reflected in reality.  (Say, if you didn’t know whether the length of a given track was aleph_0 or aleph_1, you’d never be able to tell by just looking at what had happened so far.)

I guess one might care about the different infinities if one though that what mattered was not who had been hit at any given time, but how many people, in total, were in the state of “will be hit eventually.”  Even then, though, you’d have to come up with some sort of utilitarian aggregation rule that behaves well over infinite cardinals (and doesn’t treat them all as the same).

This is obviously not a problem with any kind of practical importance, but it’s pretty fun to think about

I think it may be hard to find a definition of “will be hit eventually” which makes that dilemma work.

Suppose we have some monotonically increasing function f : ℝ → (Sets of people), such that f(t) is the set of people that have been hit at time t. Then it seems the set of people that will eventually be hit is ⋃{f(t) | t∈ℝ}. By monotonicity, this is the same as ⋃{f(t) | t∈ℕ}.

But now, if at any finite time the function f for the lower track is smaller than the the function for the upper track, then f(t) is always countable, so the “eventual” set is a countable union of countable sets.

Conversly, if you really want to fit ℵ₁ people on the lower track, then it seems you need to pack them really densely (like, one on every point of the continuum), so at some point the number of victims of the lower train will overtake the upper one…

Since people apparently had an actual discussion about this…I guess I’ll expand on the earlier shitpost.

Youzicha’s post is basically it. The picture makes it look like people are tied to the aleph-1 track one by one, in order. Which means that for each person you can ask “where is he in the line of people on the track?” and get an actual answer out. And that’s exactly what being countable, i.e. aleph-0 in cardinality, i.e. not aleph-1.

In contrast, suppose you have aleph-1 people tied to the line. If the density of people is constant, then any non-empty interval of the line contains aleph-1 people (because the line is the union of countably many such intervals) and thus the train kills aleph-1 people as soon as it starts moving.

If the density isn’t constant I’m not even sure how you can write down these definitions (I’m not convinced “density” in the previous paragraph is well-defined). But all that “the track contains aleph-1 people” would mean is that some interval contains aleph-1 people. If the train is going to hit such an interval, it obviously kills “more” in the aleph-1 track. If it doesn’t hit such an interval, the fact that the track “contains aleph-1 people” is not relevant to anything.

Yeah – tbh I feel kinda stupid now for babbling about this without noticing how weird it is that people are lined up on the aleph_1 track.

I had been thinking about whether you could put a “person density” on the track that’s finite-valued (i.e. no Dirac deltas) and gives you the number of people on an interval when integrated.  Of course this isn’t the same thing as the problem as pictured, but I think you may be able to set this up in a way that preserves the spirit of the problem as written?  You put a measure on the topological long line, so that locally everything is the same as on the other track, but the order types are different and there’s some sense in which the track “contains aleph_1 people.”  (This seems like a counterexample to your third paragraph?)

I have a very amateur hazy bullshit understanding of all of this, so this may not work, but in either case I am curious because I’d like to understand this stuff better.  For instance I don’t really understand the relationship between countability, concepts like total order and well-order, and “people are lined up on the track one by one.”  Clearly there are well-ordered sets that aren’t countable (and thus can’t be “counted” in the one-by-one sense), but I have a hard time visualizing this or imagining what an “admissible” picture of it might look like in the trolley picture (if any exists).

(via jadagul)

lovestwell:

nostalgebraist:

The most common complaint about my stories is that I promise too much and don’t deliver.  Some of this is just poor planning that I can get better at.

But I worry that the majority of it is inescapable, because it’s hard for me to write without adopting a bias toward “saying yes to new shit” – being willing to put in anything that seems fun to me, and hoping it’ll fall into place in the bigger picture eventually.

It would be one thing if I could just stop doing this and retain a core of essential material without extraneous loose ends.  But without the devil-may-care attitude that produces the loose ends, I can’t even produce the essential material.

Presumably (a lot of) Real Authors deal with this by revising and reworking over a long period of time, but that feels very weird to me.  I like writing serial fiction because it’s almost like roleplaying as the characters.  Being able to “undo” some character’s action in order to improve the plot still feels wrong.

I’m beginning to think that many readers (including myself) implicitly grade authors on how well they perform under the constraints that they, or they story’s logic, or the story’s world, impose. What I’m trying to say is that maybe instead of looking at it in terms of “promise and not deliver”, look at it in terms of “set up a tightrope walk, CHEATED while tightrope walking”. The “cheated” thing is an instinctive reaction to the feeling that the author is exercising too much freedom in throwing shit around. We don’t like it, because… I’m not sure? Maybe because we feel that universe and our lives are relatively tightly constrained, and so our stories should be too? Not as tight as to forbid all magic, SF, miracles, whatever (although now that I think about it, maybe some people who don’t like SF/fantasy don’t like it because of that). But we feel the magic aspects should be world-building, not author’s-ass-saving. 

In HPMOR, some people were turned off by how Harry was not being emotionally his age at all, it worked well with the plot but was not believable in terms of character. And then later EY said “of course but this is how I planned it all along, because Harry is a shard of Voldemort and his extreme emotional coldness is yada yada yada”. And that didn’t satisfy ANYONE (I’m exaggerating) because that feeling of “this is under-constrained. EY is puppeteering Harry in ways that are too easy for him. Real-life Harry would not be so convenient to EY’s plotting” is local, it’s generated while reading the text, and is not placated by a later global retrofit, even if for the author it was not a retrofit.

A while ago I wrote why I liked FN less than TNC and I think I wrote smth like FN feeling much less “tight”, and I’m thinking now this may be more usefully expanded into thinking in terms of constraints. FN felt like something that didn’t respect enough its own/its author’s previously imposed constraints, and that was a turn-off. I’ve just read the earlier exchange with a critic of FN you just posted, and I’m inclined to interpret their criticism in the same vein. LUDWIG feels like a huge cheaty character because once the reader realizes that this mind-out-of-thin-air controls the entire sphere it feels like the author is WAY under-constrained, and is just throwing stuff around w/o trying to internally motivate it. And just as with EY, it doesn’t help to say “but this is globally explained by Martin etc.” It doesn’t help with the local feeling of – uhm-this-is-falling-apart–

So yeah, I don’t know how to square that with “saying yes to new shit“, but certainly part of the answer might be careful editing later. I think lots of writers put in substantial work while editing to bury their leads, to reshape the flow of information, and precisely to manage the readers’ feelings of constraint-strength. “I know this tightrope is legit, but this colorful vest that I’m wearing - the audience are definitely going to think it’s a safety harness. I need to come up with more decisive ways to let them know IN ADVANCE it’s not. Taking it off and letting them see it up close when the walk is over? - not good enough”.

(I don’t know if that makes much sense, and I’ve no time to write this shorter and more thought-out, sorry)

Hmmm.  Part of what going on here is that (IMO) there are certain kinds of stories that are inherently hard to make tightly constrained, particularly those where “the (partial) incomprehensibility of the rules” is a core, non-removable feature.  This includes stories where the incomprehensibility has aesthetic appeal – say in many stories that get categorized as surrealist fiction, weird fiction, magical realism, slipstream, etc. – as well as stories about encounters with entities far more powerful and/or intelligent than human beings.

If you’re writing this kind of story, you can either completely eschew “making sense,” or you can strive for making a kind of partial sense, with the knowledge that this will have to be fundamentally unsatisfactory in a certain way – there is usually going to be a big hole somewhere that could potentially explain or do anything, like the way a single logical contradiction in a system makes every statement true.

I’ve just made the latter category sound bad, but I actually really like it and I’m always happy when I see another instance of it.  I can easily get frustrated with surrealist, magical realist, etc. fiction because the fantasy elements feel weightless and artificial because they seem to have no rules, not even alien ones.  (I feel this way about Haruki Murakami, for instance.)  “Being extremely and continually weird while still using cause-and-effect explanations and partially defined rules” is a sweet spot for me, since it’s how I intuitively feel these kinds of stories would play out if they were “really happening” – there’d at least be patches of explicability here and there, because we’d build little local models in our heads that would at least sometimes capture the local characteristics of the alien-rules.

But like I said in that other post, for me this is the best of both worlds, but I can easily see how someone would experience it as the worst of both worlds – inviting all the head-scratching of a real rule-bound story without rewarding it.  I think this difference says a lot about the very divergent reactions to Floornight.

In particular, people who liked the story tended to see it as “climbing up from surrealism” (which is how I saw it) rather than “climbing down from hard SF.”  All the science-y terms made the story look like an attempt at rule-bound SF to many people, which then led to disappointment when their efforts at figuring it out were wasted.  For me, and some other readers, the mere appearance of some rule-boundedness was a “bonus” layered onto a story whose main appeal was surreal weirdness.

From the “climbing up from surrealism” viewpoint, it’s simply in the nature of the genre to introduce bizarre unmotivated elements like LUDWIG, and the fun (for author and, hopefully, reader) is to see how much this chaos can be made to seem orderly.  It won’t be as orderly as something intended to be orderly in the first place, but that’s not the game we’re playing.  (Incidentally, I felt much more satisfied with my plotting in Floornight than in TNC precisely because with the former the task was so much closer to being impossible; with Floornight I thought “if this makes any sense, I’m a genius” and with TNC I thought “if this isn’t airtight, I’m shameful.”)

(via lovestwell)

reddragdiva:

nostalgebraist:

nostalgebraist:

Does anyone have any good resources about “why Wikipedia worked?”

What I mean is – there was this time early on when almost everyone, including me, treated Wikipedia as both (1) completely untrustworthy and (2) not at all comprehensive.  This made sense, since it was just a collection of words put together by god-knows-who, covering only the topics that god-knows-who felt like writing about for god-knows-what-reason.  But these days, it’s treated as a useful first place to look for information about almost anything.

I’m not so confused about how (1) changed, because Wikipedia has various ways of resisting vandalism and of getting dedicated teams to creating articles deliberately.  It’s not actually just like reading bathroom graffiti, which is how we used to think about it back in the day.

But (2) still baffles me.  How did Wikipedia get to be a real encyclopedia, indeed possibly the most encyclopedic encyclopedia ever created?  Everyone knows about “fancruft,” and I’ve seen complaints that the overall content is skewed toward the interests of techies with lots of free time.  But that skew is far, far less pronounced than I ever would have imagined at the outset.  Even if Wikipedia doesn’t literally cover everything, it feels like it does.  You can look up things too boring, too esoteric, too wonkish, too trivial, too down-to-earth, too “academic specialists only” – too anything – for any other encyclopedic effort to cover, and there it is, on Wikipedia, presented in a careful formal voice, as if you’d just dispatched a personal research assistant to report on it for you.

What confuses me is why volunteers created this thing.  I can see people wanting to work on Wikipedia articles about personal areas of interest.  But if that were the only motivation, I can’t imagine it being nearly as comprehensive as it is, particularly about things few people care about.  What motivated people to make it so comprehensive, and why did they succeed?  Is there any way we could have predicted this in the early days?  Can we recreate this success with other projects?

I’m willing to believe this, but it still seems startling to me that all these people would also end up specifically wanting to contribute to Wikipedia, in such a way that so many obscure things end up on WIkipedia in such a complete, homogeneous way

i guess I am generalizing from my own experience here, which is that even when I’ve been obsessed with something or though the Wikipedia article on something was wrong or insufficient, I’ve just never felt inclined to actually edit Wikipedia.  It just has no appeal to me, for some reason.  And if I am like this, I imagine various other people are too

ACTUAL ANSWER, FROM THE TRENCHES OF WIKIPEDIA:

nobody knows. we don’t know either.

everyone has surmises. coming up with just-so stories about wtf we’re doing here goes back just about as far as wikipedia itself.

my closest guess is a successful attempt to harness “someone is WRONG on the internet.” from this i think most else about wikipedia follows.

it’s also important to remember that wikipedia’s success - its progress from niche to interesting to popular to mainstream to part of the infrastructure of society - was a complete surprise to everyone involved.

(although i did predict in 2005 that in ten years, the only encyclopedia would be wikipedia or a fork descended from wikipedia. i still thought a fork of wikipedia was a viable option.)

the way it moved to acceptance as the place to look stuff up was convenience. this is the first encyclopedia that ~everyone reads ~daily, that isn’t just remembered tomes on the shelf of a high school library (if your high school was that lucky). britannica may or may not be better (spoiler: it isn’t in 2016) but wikipedia was highly available in a way it could only play catchup with.

there are endless things wrong with wikipedia of course. quite literally: every possible obvious problem you can think of, happens every day and has done for years. no really, you won’t be able to think of one that isn’t well-known to everyone involved. snafu.

Thanks for the inside perspective.  (Incidentally, the second post in the above chain was a response to this, but tumblr has for some reason removed that post and made it look like I’m replying nonsensically to myself.  What will this wacky, eccentric website do next???)

(via reddragdiva)

 ozymandias271:

nostalgebraist:

Does anyone have any good resources about “why Wikipedia worked?”

What I mean is – there was this time early on when almost everyone, including me, treated Wikipedia as both (1) completely untrustworthy and (2) not at all comprehensive.  This made sense, since it was just a collection of words put together by god-knows-who, covering only the topics that god-knows-who felt like writing about for god-knows-what-reason.  But these days, it’s treated as a useful first place to look for information about almost anything.

I’m not so confused about how (1) changed, because Wikipedia has various ways of resisting vandalism and of getting dedicated teams to creating articles deliberately.  It’s not actually just like reading bathroom graffiti, which is how we used to think about it back in the day.

But (2) still baffles me.  How did Wikipedia get to be a real encyclopedia, indeed possibly the most encyclopedic encyclopedia ever created?  Everyone knows about “fancruft,” and I’ve seen complaints that the overall content is skewed toward the interests of techies with lots of free time.  But that skew is far, far less pronounced than I ever would have imagined at the outset.  Even if Wikipedia doesn’t literally cover everything, it feels like it does.  You can look up things too boring, too esoteric, too wonkish, too trivial, too down-to-earth, too “academic specialists only” – too anything – for any other encyclopedic effort to cover, and there it is, on Wikipedia, presented in a careful formal voice, as if you’d just dispatched a personal research assistant to report on it for you.

What confuses me is why volunteers created this thing.  I can see people wanting to work on Wikipedia articles about personal areas of interest.  But if that were the only motivation, I can’t imagine it being nearly as comprehensive as it is, particularly about things few people care about.  What motivated people to make it so comprehensive, and why did they succeed?  Is there any way we could have predicted this in the early days?  Can we recreate this success with other projects?

I suspect (part of) the answer is that people have way, way, way more passionate personal areas of interest than we naively expect.

somewhere out there there is someone who really, genuinely cares about the county municipalities of Norway, or nineteenth-century German genre painters, or the economic history of the Vatican, and by god they are going to tell everyone the shit they know about it

I’m willing to believe this, but it still seems startling to me that all these people would also end up specifically wanting to contribute to Wikipedia, in such a way that so many obscure things end up on WIkipedia in such a complete, homogeneous way

i guess I am generalizing from my own experience here, which is that even when I’ve been obsessed with something or though the Wikipedia article on something was wrong or insufficient, I’ve just never felt inclined to actually edit Wikipedia.  It just has no appeal to me, for some reason.  And if I am like this, I imagine various other people are too

(via bpd-dylan-hall-deactivated20190)

waystatus:

nostalgebraist:

nostalgebraist:

A thing I really need to get myself to do less is “treating people’s stances on controversial fiction or other art as reflective of deep psychological or even ‘spiritual’ traits which make them deeply similar to me or deeply different from me”

I don’t actually believe that the world works this way, but it’s so easy for me to slip into thinking like this without realizing that I’m doing this

(It’s probably obvious that I was thinking about this because of the particular case “people who like Homestuck but dislike Act 6 are My People,” but there are various other examples, many of them even less well-founded than that.  For instance, despite not having watched enough Doctor Who to judge, I’ve picked up “people who like Moffat’s run on Doctor Who despite its flaws are My People” simply because of Esther and Andrew Rilstone)

Another example, which has some basis in fact, is James Joyce vs. Virginia Woolf

James Joyce was (on a material level) a regular bloke who struggled with money and drank too much and got into fights, and worked for several stretches as a clerk (the literary intelligentsia at the time looked down their noses at clerks), and he wrote about regular blokes who did these things, and scandalized a lot of people by making his characters talk like the regular blokes they were, crude dirty jokes and all.  His sympathetic everyman character in Ulysses was Jewish in a time when that was a big deal.   OTOH he was pretty awful at writing women and the main female character in Ulysses is like this ~eternal feminine~ ur-woman who only thinks Woman Thoughts (with no punctuation, naturally, because they just flow, you see).

Virginia Woolf grew up in a rich snooty literary family where people like Henry James would just come over for tea sometimes, her dad was a notable historian and literary critic, her mom was a model for the Pre-Raphaelite painters, and their house had a giant library from which she learned the classics.  She wrote about similarly high-society characters.  But she was a feminist, who wrote a now-classic book (A Room of One’s Own) about the material factors that suppress women’s writing and how well women could write if they were freed from these factors, and how women in literature are so often idealized muses or ~eternal feminine~ archetypes rather than 3D POV characters, etc.  Nonetheless, some women saw Woolf as out of touch with the condition of women outside of the high-society bubble she lived in.  Woolf was put off by Ulysses, because it seemed like “the book of a self-taught working man, & we all know how distressing they are.”

I feel so much more positively about Joyce, who injected a giant fuck-you dose of “how regular blokes live and talk” into literary a tradition about rich people with servants, than about Woolf, who was a feminist within her tiny coterie world cloistered apart from the vast, vast majority of women.


But that’s all a slanted, superficial, fairly ignorant history as recounted by my brain which is convinced, largely on personal experience unrelated to any of the above, that Joyce>Woolf people are My People and Woolf>Joyce people are Not My People

And I need to remind myself that all class-and-gender whatever aside, these are very different authors (on the page, in their work) and that preferring one to the other does not usually mean anything of any significance.  You read a page of Joyce and then a page of Woolf and you don’t see any of the above; you just see that they were very different writers.

FWIW, the trait I associate with Joyce the most is less working-classness and more being incomprehensible. (I associate him more with Finnegan’s Wake than with Ulysses, though I admit this is at least as unfair as your characterization of him.) But the idea to me that Joyce was introducing a dose of “how regular blokes live and talk” into literature seems absurd to me when he wrote a book that has thousand-letter-long onomatopoeia and sentences that that mean things in English but also different things in some other language.

I was unclear there.  It’s true that Ulysses (and FW even more) are very difficult to read and include many elements comprehensible only if (and not iff!) you have various kinds of obscure knowledge.  (This has led to a common, and probably fair, charge of hypocrisy against Joyce, that he wrote a book about everymen than no ordinary person could read.)

But this wasn’t that only thing that struck people about Joyce’s work at the time.  Note that the Woolf quote I linked didn’t criticize Ulysses for being opaque, although it was remarkably opaque, but for seeming low-class.  It was also the subject of two obscenity trials because of its explicit sexual content.  The first concluded a specific part of the book was obscene, and precluded the book from being published in the U.S. for a number of years.

The second ruled that the full book was not obscene.  To come to this determination, the judge read the book, thought over it, and in his decision, wrote that the “obscene” elements were necessary to portray the thoughts of Joyce’s “regular bloke” characters in the honest detail which he was committed to:

In writing “Ulysses”, Joyce sought to make a serious experiment in a new, if not wholly novel, literary genre. He takes persons of the lower middle class living in Dublin in 1904 and seeks not only to describe what they did on a certain day early in June of that year as they went about the City bent on their usual occupations, but also to tell what many of them thought about the while.

Joyce has attempted — it seems to me, with astonishing success — to show how the screen of consciousness with its ever-shifting kaleidoscopic impressions carries, as it were on a plastic palimpsest, not only what is in the focus of each man’s observation of the actual things about him, but also in a penumbral zone residua of past impressions, some recent and some drawn up by association from the domain of the subconscious. He shows how each of these impressions affects the life and behavior of the character which he is describing.

[…]

To convey by words an effect which obviously lends itself more appropriately to a graphic technique, accounts, it seems to me, for much of the obscurity which meets a reader of “Ulysses”. And it also explains another aspect of the book, which I have further to consider, namely, Joyce’s sincerity and his honest effort to show exactly how the minds of his characters operate.

If Joyce did not attempt to be honest in developing the technique which he has adopted in “Ulysses” the result would be psychologically misleading and thus unfaithful to his chosen technique. Such an attitude would be artistically inexcusable.

It is because Joyce has been loyal to his technique and has not funked its necessary implications, but has honestly attempted to tell fully what his characters think about, that he has been the subject of so many attacks and that his purpose has been so often misunderstood and misrepresented. For his attempt sincerely and honestly to realize his objective has required him incidentally to use certain words which are generally considered dirty words and has led at times to what many think is a too poignant preoccupation with sex in the thoughts of his characters.

The words which are criticized as dirty are old Saxon words known to almost all men and, I venture, to many women, and are such words as would be naturally and habitually used, I believe by the types of folk whose life, physical and mental, Joyce is seeking to describe.

[…]

As I have stated, “Ulysses” is not an easy book to read. It is brilliant and dull, intelligible and obscure by turns. In many places it seems to me to be disgusting, but although it contains, as I have mentioned above, many words usually considered dirty, I have not found anything that I consider to be dirt for dirt’s sake. Each word of the book contributes like a bit of mosaic to the detail of the picture which Joyce is seeking to construct for his readers.

If one does not wish to associate with such folk as Joyce describes, that is one’s own choice. In order to avoid indirect contact with them one may not wish to read “Ulysses”; that is quite understandable. But when such a real artist in words, as Joyce undoubtedly is, seeks to draw a true picture of the lower middle class in a European city, ought it to be impossible for the American public legally to see that picture?

In Judge Woolsey’s opinion, the book’s incomprehensibility and its dedication to “how regular blokes live and talk” were connected rather than opposed: Joyce wanted to depict every thought and impressions of his characters honestly, and this involved using explicit sexual content, dirty words, etc.

I personally think this is overly simplistic – much of the difficulty (in the latter half of the book) comes from literary parodies and imitations which the characters themselves would not recognize, for instance.  But I hope I am building some sort of case that the depiction of “how regular blokes live and talk” was part of what struck people, at the time, as remarkable about Ulysses.

(via waystatus)