4 ms·

I noticed years ago too that AI doomers and rationalist type were very prone to (infinity * 0 = infinity) types of traps, which is a fairly autistic way of thin

by novok 2y ago

I noticed years ago too that AI doomers and rationalist type were very prone to (infinity * 0 = infinity) types of traps, which is a fairly autistic way of thinking. Humanity long time ago decided that infinity * 0 = 0 for very good practical reasons.

shoo 2y ago
> Humanity long time ago decided that infinity * 0 = 0 I'm guessing you don't mean this in any formal mathematical sense, without context, infinity multiplied by zero isn't formally defined. There could be various formulations and contexts where you could define / calculate something like infinity * zero to evaluate to whatever you want. (e.g. define f(x) := C x and g(x) := 1/x, What does f(x) * g(x) evaluate to in the limit as x goes to infinity? C. And we can interpret f(x) as going to infinity while g(x) goes to zero, so we can use that to justify writing "infinity * 0 = C" for an arbitrary C... ) So, what do you mean by "infinity * 0 = infinity" informally? That humans regard the expected value of (arbitrarily large impact) * (arbitrarily small probability) as zero?
- incrudible 2y ago
  > That humans regard the expected value of (arbitrarily large impact) * (arbitrarily small probability) as zero? There are many arguments that go something like this: We don't know the probability of <extinction-level event>, but because it is considered a maximally bad outcome, any means to prevent it are justified. You will see these types of arguments made to justify radical measures against climate change or AI research, but also in favor space colonization. These types of arguments are "not even wrong", they can't be mathematically rigorous, because all terms in that equation are undefined, even if you move away from infinities. The nod to mathematics is purely for aesthetics.
- lupusreal 2y ago
  It's true in the informal sense. Normal people, when considering an "infinitely" bad thing happening (being killed, losing their home, etc) with a very low probability will round that probability to zero ("It won't happen to ME"), multiply the two and resultantly spend zero time worrying about it, planning for it, etc. For instance, a serial killer could kill me (infinitely bad outcome) but the chance of that happening is so tiny I treat it as zero, and so when I leave my house every day I don't look into the bushes for a psycho murderer waiting there for me, I don't wear body armor, I am unarmed, I don't even think about the chance of being killed by a serial killer. For all practical intents and purposes I treat that possibility as zero. Important to remember that different people gave different thresholds at which they round to zero. Some people run through dark parking garages and jump into their car because they don't round the risk of a killer under their car slashing their achilles tendons down to zero. Some people carry a gun everywhere they go, because they don't round the risk of encountering a mass shooter to zero. Some people invest their time and money pursuing spaceflight development because they don't round a dino-killing asteroid to zero. A lot of people don't round the chance of wrecking a motorcycle to zero, and therefore don't buy one even though they look like fun. The lesswrong/rationalist people have a tendency to have very low thresholds at which they'll start to round to zero, at least when the potential harm would be met out to a large portion of humanity. Their unusually low threshold leads them to very unusual conclusions. They take seriously possibilities which most people consider to be essentially zero, giving rise to the perception that rationalists don't think that infinity * 0 = 0.
  - dinkumthinkum 2y ago
    > It's true in the informal sense. Normal people, when considering an "infinitely" bad thing happening (being killed, losing their home, etc) with a very low probability will round that probability to zero ("It won't happen to ME"), multiply the two and resultantly spend zero time worrying about it, planning for it, etc. Is this the kind of thing that is part of the Less Wrong cult? I see this "multiply" word being used which I understand is part of the religious technology of LW. It all seems very sophomoric. I don't know what talking about "Infinity * 0" means in an informal sense means. What I can tell you is that "Normal people" are not multiplying "infinitely bad" with a "very low probability rounded to 0". For one, this is conflating multiple senses of infinite. I'm not sure anyone thinks likes bad outcomes are "infinitely bad", maybe in a schoolyard silly-talk kind of way, they just think it is bad. I think that's basically what Less Wrong is, a lot of fancy words and Internet memes and loose-talk about AI all strewn together in a "goth for adults" or some other kind of nerd social club.
    - lupusreal 2y ago
      > "I don't know what talking about "Infinity * 0" means in an informal sense means" I'm not a rationalist, I'm only using their language to make the mapping to their ideology simpler. A comet striking earth would be "infinitely bad". The chance of that happening is, as far as I'm concerned, zero (its not zero, but I round it down.) If you multiply the infinitely bad outcome by the zero percent chance of it happening, you result is that you shouldn't waste your time and emotional resources worrying about it. Normal people don't phrase this kind of reasoning with math terminology as rationalists do, but that terminology isn't where the rationalists go wrong. Where the rationalists go wrong isn't the multiplication, it's the failure to ignore very unlikely outcomes as normal people would. They think themselves too rational to ignore the possibility of unlikely things, but ironically it is normal people who don't spend their time dwelling on extremely unlikely bullshit have a more rational approach to life. The rationalists spend hours discussing scenarios like "What if a super AI manipulates people into engineering a super virus that wipes out humanity? Its technically possible; there's no law of physics which prevents this!", to which a normal person would respond by wondering if these people are on drugs, why would they spend so much time worrying about something which isn't going to happen?
saagarjha 2y ago
No, humanity decided that infinity doesn't exist and anyone trying to tell you about it is selling you religion.
- harrison_clarke 2y ago
  not exactly a rationalist thing, but a lot of bay-area people will tell you that exponential growth exists, and it's everywhere i can't think of any case where exponential growth actually happens, though. exponential decay and logistic curves are common enough, but not exponential growth
  - alain94040 2y ago
    Viruses until they reach their plateau of course.
    - scotteric 2y ago
      That would be the logistic curve then
  - bee_rider 2y ago
    Well yeah their whole business model is convincing investors that logistic functions and exponentials are the same thing, actually.
  - ben_w 2y ago
    The rats I hang out with know the difference between exponential and logistic just fine. Hmm. Not sure if it matters, but I'd note logistic curves can be hard to distinguish from an exponential for long enough that the difference isn't always very consequential — a nuke exploding doesn't keep doubling in power every few microseconds forever, but for enough doubling periods that cities still get flattened.
yellowapple 2y ago
> Humanity long time ago decided that infinity * 0 = 0 for very good practical reasons. Among them being that ∞ × 0 = ∞ makes no mathematical sense. Multiplying literally any other number by zero results in zero. I see no reason to believe that infinity (positive or negative) would be some exception; infinity instances of nothing is still nothing.
- ryandv 2y ago
  The problem is that infinity is neither a real nor a complex number, nor an element of any algebraic field, and the proposition that "x * 0 = 0" only holds if x is an element of some algebraic field. It is a theorem that depends on the field axioms. The real numbers can be extended to include two special elements ∞ and -∞, but this extension does not constitute a field, and the range of expressions in which these symbols make sense is very strictly and narrowly defined (see Rudin's PMA, Definition 1.23): (a) If x is real then x + ∞ = +∞, x - ∞ = -∞, x / +∞ = x / -∞ = 0. (b) If x > 0 then x * (+∞) = +∞, x * (-∞) = -∞. (c) If x < 0 then x * (+∞) = -∞, x * (-∞) = +∞. The extended real number system is most commonly used when dealing with limits of sequences, where you may also see such symbols appear: 3.15 Definition Let {sₙ} be a sequence of real numbers with the following property: For every real M there is an integer N such that n ≥ N implies sₙ ≥ M. We then write sₙ ⟶ +∞. In no other contexts do the symbols ∞ and -∞ make any sense. They only make sense according to the definitions given. It's usually the case that when you see people discussing infinity that they are actually talking about sequences of numbers that are unbounded above (or below). The expression "sₙ ⟶ +∞" is meant to denote such a sequence, and the definitions that extend the real number line (as in Definition 1.23 above) are used to do some higher-level algebra on limits of sums and products of sequences (e.g. the limit of sₙ + tₙ as n becomes "very large" for two sequences {sₙ}, {tₙ}) to shortcut around the lower-level formalisms of epsilons and neighborhoods of limit points in some metric space, which is how the limits of sequences are rigorously defined. In no case do the symbols ∞ and -∞ refer to actual numbers. They are used in expressions that refer to properties of certain sequences once you look far enough down the sequence, past its first, second, hundredth, umpteenth, "Nth" terms, and so on. Thus when you see people informally and loosely use expressions such as "infinity times zero" they're not actually multiplying two numbers together, but rather talking about the behavior of the product of two sequences as you evaluate terms further down both sequences; one of which is unbounded, while the other can be brought arbitrarily close to (but not necessarily equal to) zero. You will notice that no conclusions can be drawn regarding the behavior of such a product in general, whether referencing the definitions comprising the extended real number system or the lower-level definitions in terms of epsilons and neighborhoods of limit points. So much confusion today comes down to people confidently using words, symbols, and signs they don't understand the definitions nor meanings of. Sometimes I wonder if this is the real esoteric meaning of the ancient Tower of Babel mythos.
coldtea 2y ago
>which is a fairly autistic way of thinking. Any prominent ones of them I've read or met either openly shares their diagnosis, or 100% fits the profile.
bowsamic 2y ago
They actively look for ways for infinity to happen. Look at Eli's irate response to Roko's basilisk. To him even being able to imagine that there is a trap means that it will necessarily be realised. I've seen "rationalist" AI doomers who say things like "given enough time technology will be invented to teleport you into the future where you'll be horifically tortured forever". It's just extrapolation, taken to the extreme, and believed in totally religiously.
meroes 2y ago
Reminds me of the https://en.wikipedia.org/wiki/Measure_problem_(cosmology) https://en.wikipedia.org/wiki/Measure_problem_(cosmology).
whimsicalism 2y ago
i think you are putting too many people in one bucket

by novok 2y ago

shoo 2y ago

> Humanity long time ago decided that infinity * 0 = 0 I'm guessing you don't mean this in any formal mathematical sense, without context, infinity multiplied by zero isn't formally defined. There could be various formulations and contexts where you could define / calculate something like infinity * zero to evaluate to whatever you want. (e.g. define f(x) := C x and g(x) := 1/x, What does f(x) * g(x) evaluate to in the limit as x goes to infinity? C. And we can interpret f(x) as going to infinity while g(x) goes to zero, so we can use that to justify writing "infinity * 0 = C" for an arbitrary C... ) So, what do you mean by "infinity * 0 = infinity" informally? That humans regard the expected value of (arbitrarily large impact) * (arbitrarily small probability) as zero?

incrudible 2y ago
> That humans regard the expected value of (arbitrarily large impact) * (arbitrarily small probability) as zero? There are many arguments that go something like this: We don't know the probability of <extinction-level event>, but because it is considered a maximally bad outcome, any means to prevent it are justified. You will see these types of arguments made to justify radical measures against climate change or AI research, but also in favor space colonization. These types of arguments are "not even wrong", they can't be mathematically rigorous, because all terms in that equation are undefined, even if you move away from infinities. The nod to mathematics is purely for aesthetics.
lupusreal 2y ago
It's true in the informal sense. Normal people, when considering an "infinitely" bad thing happening (being killed, losing their home, etc) with a very low probability will round that probability to zero ("It won't happen to ME"), multiply the two and resultantly spend zero time worrying about it, planning for it, etc. For instance, a serial killer could kill me (infinitely bad outcome) but the chance of that happening is so tiny I treat it as zero, and so when I leave my house every day I don't look into the bushes for a psycho murderer waiting there for me, I don't wear body armor, I am unarmed, I don't even think about the chance of being killed by a serial killer. For all practical intents and purposes I treat that possibility as zero. Important to remember that different people gave different thresholds at which they round to zero. Some people run through dark parking garages and jump into their car because they don't round the risk of a killer under their car slashing their achilles tendons down to zero. Some people carry a gun everywhere they go, because they don't round the risk of encountering a mass shooter to zero. Some people invest their time and money pursuing spaceflight development because they don't round a dino-killing asteroid to zero. A lot of people don't round the chance of wrecking a motorcycle to zero, and therefore don't buy one even though they look like fun. The lesswrong/rationalist people have a tendency to have very low thresholds at which they'll start to round to zero, at least when the potential harm would be met out to a large portion of humanity. Their unusually low threshold leads them to very unusual conclusions. They take seriously possibilities which most people consider to be essentially zero, giving rise to the perception that rationalists don't think that infinity * 0 = 0.
- dinkumthinkum 2y ago
  > It's true in the informal sense. Normal people, when considering an "infinitely" bad thing happening (being killed, losing their home, etc) with a very low probability will round that probability to zero ("It won't happen to ME"), multiply the two and resultantly spend zero time worrying about it, planning for it, etc. Is this the kind of thing that is part of the Less Wrong cult? I see this "multiply" word being used which I understand is part of the religious technology of LW. It all seems very sophomoric. I don't know what talking about "Infinity * 0" means in an informal sense means. What I can tell you is that "Normal people" are not multiplying "infinitely bad" with a "very low probability rounded to 0". For one, this is conflating multiple senses of infinite. I'm not sure anyone thinks likes bad outcomes are "infinitely bad", maybe in a schoolyard silly-talk kind of way, they just think it is bad. I think that's basically what Less Wrong is, a lot of fancy words and Internet memes and loose-talk about AI all strewn together in a "goth for adults" or some other kind of nerd social club.
  - lupusreal 2y ago
    > "I don't know what talking about "Infinity * 0" means in an informal sense means" I'm not a rationalist, I'm only using their language to make the mapping to their ideology simpler. A comet striking earth would be "infinitely bad". The chance of that happening is, as far as I'm concerned, zero (its not zero, but I round it down.) If you multiply the infinitely bad outcome by the zero percent chance of it happening, you result is that you shouldn't waste your time and emotional resources worrying about it. Normal people don't phrase this kind of reasoning with math terminology as rationalists do, but that terminology isn't where the rationalists go wrong. Where the rationalists go wrong isn't the multiplication, it's the failure to ignore very unlikely outcomes as normal people would. They think themselves too rational to ignore the possibility of unlikely things, but ironically it is normal people who don't spend their time dwelling on extremely unlikely bullshit have a more rational approach to life. The rationalists spend hours discussing scenarios like "What if a super AI manipulates people into engineering a super virus that wipes out humanity? Its technically possible; there's no law of physics which prevents this!", to which a normal person would respond by wondering if these people are on drugs, why would they spend so much time worrying about something which isn't going to happen?

saagarjha 2y ago

No, humanity decided that infinity doesn't exist and anyone trying to tell you about it is selling you religion.

harrison_clarke 2y ago
not exactly a rationalist thing, but a lot of bay-area people will tell you that exponential growth exists, and it's everywhere i can't think of any case where exponential growth actually happens, though. exponential decay and logistic curves are common enough, but not exponential growth
- alain94040 2y ago
  Viruses until they reach their plateau of course.
  - scotteric 2y ago
    That would be the logistic curve then
- bee_rider 2y ago
  Well yeah their whole business model is convincing investors that logistic functions and exponentials are the same thing, actually.
- ben_w 2y ago
  The rats I hang out with know the difference between exponential and logistic just fine. Hmm. Not sure if it matters, but I'd note logistic curves can be hard to distinguish from an exponential for long enough that the difference isn't always very consequential — a nuke exploding doesn't keep doubling in power every few microseconds forever, but for enough doubling periods that cities still get flattened.

yellowapple 2y ago

> Humanity long time ago decided that infinity * 0 = 0 for very good practical reasons. Among them being that ∞ × 0 = ∞ makes no mathematical sense. Multiplying literally any other number by zero results in zero. I see no reason to believe that infinity (positive or negative) would be some exception; infinity instances of nothing is still nothing.

ryandv 2y ago
The problem is that infinity is neither a real nor a complex number, nor an element of any algebraic field, and the proposition that "x * 0 = 0" only holds if x is an element of some algebraic field. It is a theorem that depends on the field axioms. The real numbers can be extended to include two special elements ∞ and -∞, but this extension does not constitute a field, and the range of expressions in which these symbols make sense is very strictly and narrowly defined (see Rudin's PMA, Definition 1.23): (a) If x is real then x + ∞ = +∞, x - ∞ = -∞, x / +∞ = x / -∞ = 0. (b) If x > 0 then x * (+∞) = +∞, x * (-∞) = -∞. (c) If x < 0 then x * (+∞) = -∞, x * (-∞) = +∞. The extended real number system is most commonly used when dealing with limits of sequences, where you may also see such symbols appear: 3.15 Definition Let {sₙ} be a sequence of real numbers with the following property: For every real M there is an integer N such that n ≥ N implies sₙ ≥ M. We then write sₙ ⟶ +∞. In no other contexts do the symbols ∞ and -∞ make any sense. They only make sense according to the definitions given. It's usually the case that when you see people discussing infinity that they are actually talking about sequences of numbers that are unbounded above (or below). The expression "sₙ ⟶ +∞" is meant to denote such a sequence, and the definitions that extend the real number line (as in Definition 1.23 above) are used to do some higher-level algebra on limits of sums and products of sequences (e.g. the limit of sₙ + tₙ as n becomes "very large" for two sequences {sₙ}, {tₙ}) to shortcut around the lower-level formalisms of epsilons and neighborhoods of limit points in some metric space, which is how the limits of sequences are rigorously defined. In no case do the symbols ∞ and -∞ refer to actual numbers. They are used in expressions that refer to properties of certain sequences once you look far enough down the sequence, past its first, second, hundredth, umpteenth, "Nth" terms, and so on. Thus when you see people informally and loosely use expressions such as "infinity times zero" they're not actually multiplying two numbers together, but rather talking about the behavior of the product of two sequences as you evaluate terms further down both sequences; one of which is unbounded, while the other can be brought arbitrarily close to (but not necessarily equal to) zero. You will notice that no conclusions can be drawn regarding the behavior of such a product in general, whether referencing the definitions comprising the extended real number system or the lower-level definitions in terms of epsilons and neighborhoods of limit points. So much confusion today comes down to people confidently using words, symbols, and signs they don't understand the definitions nor meanings of. Sometimes I wonder if this is the real esoteric meaning of the ancient Tower of Babel mythos.

coldtea 2y ago

>which is a fairly autistic way of thinking. Any prominent ones of them I've read or met either openly shares their diagnosis, or 100% fits the profile.

bowsamic 2y ago

They actively look for ways for infinity to happen. Look at Eli's irate response to Roko's basilisk. To him even being able to imagine that there is a trap means that it will necessarily be realised. I've seen "rationalist" AI doomers who say things like "given enough time technology will be invented to teleport you into the future where you'll be horifically tortured forever". It's just extrapolation, taken to the extreme, and believed in totally religiously.

meroes 2y ago

Reminds me of the https://en.wikipedia.org/wiki/Measure_problem_(cosmology) https://en.wikipedia.org/wiki/Measure_problem_(cosmology).

whimsicalism 2y ago

i think you are putting too many people in one bucket