Slider's Shortform

by Slider14th Aug 201945 comments
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Spoilers for Man in the High Castle ahead.

LW have thought about Petrov somewhat and I found myself torn a bit balancing various virtues in a fictional situation that seems to be a limit case.

Kido as the highest rank of the Kempeitai (martial and secret police) gets the job of figuring out who tried to shoot the emperor. He is expected to succeed in this or forfeit his life. He discovers that a sniper of a super power with nukes essentially confesses to the act. He thinks that relying this information up the chain would push his country into war which it would lose (his country doesn't have nukes). Instead he suppresses the evidence and prepares to fail on his task. In the eleventh hour a "safe" suspect presents itself and the plot moves on.

Does Kido here do a heroic act like Petrov? He is tasked with a truth uncovering mission and fabricates a falsehood to bolster stability. I know that "the first victim of war is truth" but here it seems to be made in name of peace. With Petrov he knew the system wasn't reliable and that other people might not have the skill or context to evalaute the data better. Here it seems that reporting the facts upstream would not place the decision makers in a worse position. I guess if multiple people know about it it would be harder to pretend it didn't took place. Leaking it to the press could force emperors/capitals hand but are 5-7 people knowing up the chain about it too much?

In an AI that is supposed to cooperate in not bringing about catastrophic outcomes would it be proper to priotize non-war over technical accuracy or is the corruption of truth unacceptable here and taking autonomy to decide their own fate away from the AIs operators/customers?

Even if your superiors know what really happened, they'll want you to fabricate a plausible lie for the public story. They'll also want you to carry the risk so that if the truth does eventually come out they can deny knowing about the coverup.

When the agent willingly chooses into death, I don't think there is any significant risk to take on left.

There is the side of responcibility of bearing shame which can transcend death. I guess I found an aspect of it I didn't previously realise, when you think a situation will only resolve with an evil act and you could punt the decision to be made by another party it can seem like a favour to make the act happen via the party that carries the stain most gracefully.

The setting seems so morally grey that being complicit with the coverup would be that large of a blip in the radar. Later on when the generals disagree with the emperors confidants they pretty much do a coup by excluding the capital people from decision making. Part of the danger from Ripper from Strangelove is that he can just act as if he received an order without actually receiving one. When Kido acts without consultation how does he know that he is not operating with a faulty "bodily fluids" motive? What is the difference between a coup and exercising implicit autonomy, if any?

The fundamental question of how to help a person or group of people DESPITE their irrationality and inability to optimize for themselves is ... unsolved at best.  On at least two dimensions:

  1. What do you optimize for?  They don't have coherent goals, and you wouldn't have access to them anyway.  Do you try to maximize their end-of-life expressions of satisfaction?  Short-term pain relief?  Simple longevity, with no quality metric?   It's hard enough to answer this for oneself, let alone others.
  2. If their goals (or happiness/satisfaction metrics) conflict with yours, or with what you'd want them to want, how much of your satisfaction do you sacrifice for theirs?  

And even if you have good answers for those, you have to decide how much you trust them not to harm you, either accidentally because they're stupid (or constrained by context that you haven't modeled), or intentionally because they care less about you than you about them.  If you KNOW that they strongly prefer the truth, and you're doing them harm to lie, but they're idiots who'll blow up the world, does this justify taking away their agency?

I'm happy with a confident "yes" to that last question.

Me too, but I recognize that I'm much less happy with people applying the reasoning to take away my self-direction and choice.  I'm uncomfortable with the elitism that says "I'm better at it, so I follow different rules", but I don't know any better answer.

If we change "blow up the world" to "kill a fly" at what point does the confidence start to waiver?

If we change "will blow up" to "maybe blow up" to "might blow up" when does it start to waiver?

Another very edge case comes from Star Control II. The Ur-Quan are of the opinion that having a random sentient species in the universe is a risk that it is a homicidial one or makes a torture world and kills all other life is unacceptable. The two internal factions disagree whether dominating all other species is enough (The Path of Now and Forever) or whether specicide until only Ur-Quan life remains is called for (The Eternal Doctrine). Because of their species history and special makeup they have reason to believe they have enhanced position to understand xenolife risks.

Ruminating on Ur-Quan I came to a position that, yes allowing other species to live (free) does pose a extremely bad outcome risk but this is small compared to the (expected) richness-addition of life. What the Ur-Quan are doing is excessive but if "will they blow up the world?" would auto-warrant an infinite confident yes for outlaw status then their argument would carry through: The only way to make sure is to nuke/enslave (most of) the world.

I guess in more human scale: Having bats around means they might occasionally serve as jumping off points for pretty nasty viruses. The mere possiblity of this is not enough to jump to the conclusion that bats should be made extinct. And for human positions in organizations the fact that it is filled with a human and thus being fallible doesn't mean they are inadmissible to exercise any of their powers.

A state works through its ministers/agents. As the investigator correctly assigned to the case it is not like you are working against the system.

I guess part of the evaluation that living in a world with a super power trying to incite war means that the world has a background chance to blow up anyway. And knowing that they are trying to incite war by assasination could be used for longer term peacekeeping (counterspy resources shifts etc). Exposing emotionally charged cirumstances risk immidiate less than super deliberate action but clouding the decision apparatus with falsehoods makes contact with reality weaker which has its own error rates.

Internet point giving is pretty recent phenomenon (as is all of social media). I think there are important social differences to approving in person and giving internet upvotes. You are way more connected see the effects of your approving and can conveoy more subtle messages in the same go.

Giving voting too central a role in our websites might be analgous to having implemented a reinforcement AI as president/world leader without solving alignment. Voting might be institutionalized demagoguery that we are unlikely to catch in critiques.

Having a bad utlity function gets critiqued quite closely. Having a vote button with no guides how it could/should be used blackboxes the method actually used. There can be an issue where irresponcible voting is having adverse effects. It's like not locking your door to avoid getting a burglary, you can't break and enter if there is nothing to break.

Voting with points is what you do when...

  • you need to somehow separate the better stuff from the worse stuff, even if the method is imperfect, because there will be tons of extremely bad stuff (e.g. spam, or crazy people obsessed with the topic); and
  • you don't want to appoint a moderator, because you don't have the money to pay someone to do it as a job, and you suspect that the volunteers would be motivated by the opportunity to abuse the power;
  • you need to have a nice version to show to a completely passive person (who doesn't even have an account), so that individual friend lists and block lists are not sufficient -- you have to arrive at "one true rating" for stuff.

Without voting, you would have to give up on having an official page available to users without accounts, or you would have to establish the official moderators and either pay them or accept that people who want to abuse that kind of power have the strongest incentive to volunteer.

(The former is kinda like e-mail, and the latter is kinda like Reddit.)

Use Elon Musk's brain-computer interface to map the posts each user has seen to a personal space of possible reactions. (Or just let them invent their own tag system in place of this, but it's gonna be inconvenient.)

Across users, glue together these functions by finding a way to translate between any two user's spaces on the intersection of the sets of posts they've seen. (I feel like a sheaf theorist should repeat this to me in their words.)

Each user can now explore posts relevant to their current thoughts. (Or to the tags they select.) The admin uses this same mechanism to provide new users with a default sorting.

(Or just let them invent their own tag system in place of this, but it's gonna be inconvenient.)

Create a tag dictionary.

I mean that it's gonna be inconvenient to consciously write down all the tags that apply, as opposed to the BCI giving a cloud of 2000 relevant tags/Discord reactions. It also feels like giving names would reduce the usefulness of this from telepathy to language.

The problem of specifying tags might not have received that much attention.

I had an expereince with ovewatch in that it is filled with all kinds of nasty behaviours. There were about 6 categories to report bad behaviour. Then you could also have free form text box to provide additonal details. Now free-form text you can't automatically process that easily.

The reporting felt important so it pushed me to fight some of the inconvenience of speeding paperwork time on other's behavoiural crimes. However the effort coming up stuff to fill on the textbox was kind of offputting. I ended up figuring out a way of "what is really objectionable about my experience?". This made it so that in next bad experiences I could identify similar bad experiences with less thoughtwork.

Thus it became routine to write things like "Diagnosing others with mental issues (moron)" and "Diagnosing others with mental issues (autism)". (And it leads to thinking whether "Diagnosing others with mental issues (idiot)" is a good thing to complain about (it isn't it's not diagnosing)). Abstractring them down to the objectionable part made me lose sight of the details which made them more directly comparable with each other. So the reports became really tag like and thinking about what the tags were made me think were the line of objectionability lies. If someone loses and is angry about it that is not objectionable. If someone bashes others and calls them bad names the motivation can be understandble but it is objectionable.

The system might have been designed more that it more relies on just adding up counts on the 6 fixed categories. And I seen a streamer file report where the textbox was just "fuck you" which speaks to players knowing the textboxes matter very little and that reporting is often done to express or play out anger. The lack of detail lost on the altar of automation has a significant cost. You could improve automation that it can handle more complex signals. Or you could evaluate that the social harm is great enough that more manual components are required. If such interactions were done face to face displaying any behavoiur that would be analogous would be very child like ot the range of 6 to 8 year olds and people would be directed to be more expressive and more constrcutive about conflict resolution. But online we are building places where that kind of culture is incentives or supported. Imagine what woud be the effects if in face to face communiation there was only 1 hostile communication available (no angry faces, or thumbs down or threatening voice or middle finger, just boiling it down to a a middle finger)

How about when the incentives of the populus are as misaligned as would-be-moderators?

That's what always happens, I guess.

The thing is that all solutions are bad, but leaving the problem (of spam etc.) unaddressed is even worse than the usual solutions.

Sometimes small websites avoid this, when they are unknown enough that they don't attract any spammer or any crazy person, and unimportant enough that people who don't like the content simply leave. But if they get more popular, it's only a question of when.

Imagine that your user base is: 50% Greens, 30% Blues, 10% crazy people, and 10% spammers. If you leave the site unmoderated, crazy people and spammers will make it unpleasant for everyone else. If you have a voting system, Greens will eliminate the Blues. If you have moderators, you must choose carefully, because a majority of Greens or Blues among the moderators will eliminate the other side; and of course having the same number of Green and Blue moderators would be unfair, because then the Blues are overrepresented compared to the user base. (Also, this would incentivize the 0.01% Purples to demand equal representation among moderators, too. And if you grant it, then either Greens or Blues, by making a coalition with Purples, can eliminate the other side.) You can't win.

Sometime the solutions are bad enough that it's not worth having the problem in the first place. If there is no way to input user generated content then you can't spam. However websites are kind of expected to have these sorts of functions even when their core mission doesn't revolve around it.

There is also the issue that some of the costs for solutions are private costs beared by the website but having social slant and pressures on the content has a downside that is more beared by the public for a possible eroding of discussion or culture quality. And if every individual website is incentivies to be open to mobs instead of closed to them that enpowers mobs and can make cross-site movements. At some point cross-site culture will be stronger than site spesifc one where even if you try to establish a particular website to be for certain types of users / needs they will be swamped by a bigger existing community that will forfcefully install their norms.

The example voting system whether Greens eliminate Blues depends on the voting mechanisms. But I guess it is a general feature that some content will be hidden/downplayed. The arguments mechanics are plausible if it is a majority first-past-the-post. I think there are power balancing mechanism that get a lot more close to proportionality. The mechanic also requires that the sides are interested in destroying content associated with other parties. You could have a system where there is only finite influence power that is shared among promotion and supression. If all players suppress all content generated by others then they could not promote their own stuff but if everybody promoted their own stuff they would use lower amount of the resource the point would be to make it dominant to promote your stuff rather than attack others. Then on the balance losing factions are not erased even if they have "unfairly low" visiblity. The thing would be that spam would be supressed unilaterally. Even if you don't make the emphasis power finite treating unilaterally promoted stuff comparatelivy same than content that is promoted by some groups and supressed by others could reach a different balance. That is if you have 10 moderators and you need 3 to vote "supress" and no-one vote "promote" to have it not visible then any "controversial" content would probably get throguh.

And even if we keep voting around the users are unlikely to carefully scrutines the voting mechanics. That is even if they are clearly biased that biased would survival for a very long time until anybody would try to balance that bias.

If there is no way to input user generated content then you can't spam.

Yep. If I ever have a meaningful web page, there will be no user comments, because it seems like there is no good solution.

I think there are power balancing mechanism that get a lot more close to proportionality.

I am afraid that online even this wouldn't work. First, people can make multiple accounts. (The infamous guy on LW 1.0 made several hundreds of them.) Second, I feel that participating in online debates already selects for a worse parts of humanity, simply because some people have better things to do and some don't.

I prefer the archipelago model of internet. Rationalist websites for rationalists, homeopathic websites for homeopaths; rather than having all of them in the same place fighting each other. But goes against the incentives of the big websites, who want to be for everyone, because that allows them to display advertising to everyone.

On the other hand, creating "reality bubbles" (because, let's admit it honestly, this is what the archipelago model means) also has its own problems.

One of the issues is that you will struggle to be meaningful if more attractive webpages manage to be attractive because they allow for self-expression or because so many other users are using or viewing them. Part of tyhe problem can be that if you read a news paper you get nicely editorialised content but if you get your news on reddit you can have fun fights in the comments so people will pass on "boring" newspaper because they can't fullfill their expectation of engagement.

Magic colors and errors

Reading Writers guild policy doc there was a principle of "the vase is already broken". The whole document is a lot how you make a red organization and most of the princples are anti-white.

The principle makes sense but I found it be foregin to my culture. Things are made to be replaced. And if something is done wrong today we will try to do right the next day.

In contrast the blue way is much more familiar with me. Accept only true things, set up things for perpetuity. In the contrast I noticed that the blue thing is focused on avoiding to making mistakes. You slow down enough that everything can be verified. In the red way you speed up so things can be corrected.

In blue if you make a mistake you will build a machine that will do damage for to the forseeable future. In contrast in red if you feel the wrong way today you will not be inspired to feel so tomorrow and the energy will whimper. "Energy denial" seemed like a new perpective that I hadn't considered.

Other colors probably also have ways to treat errors. Green probably adapts, there are no "mistakes" only "happy little accidents". Oxygen catastrophe is not armageddon but new conditions to build upon. Never say "no" but always "yes and" and just keep the harmony in front of your mind, keep the scene going.

Black is proably ready to backstab their friends to death should they turn on them. It's not about what damage the mistake does but whether it proves your character whether you are safe to keep around. On the flip side having good enough goals means arbirarily bad means can be swallowed.

White probably does courts and maybe a balance of rights: even if we set a monumentally bad law it will need to resolve itself against other core principles. A bad nomination is limited by the powers of the position being limited.

Interesting. Do you have a link to the document that sparked this thought?

It was linked in a lesswrong norm thread. Couldn't relocate it easily as I don't remember which thread it was on.

More on green errors, I think they do exists. There is a difference between an invasive species and a predator. Green probably allows for predators easier than white or black that would call them murderes. But being disruptive to the harmony is an actual violation green registers.

Imagine you have a snake problem in your houses yard. You could get angry and kill every snake you see (haphazard, random and laboursome the red way to address it). You could poison your yard (but then your flowers might die or your food supply gets fouled, the black way). For wheel completeness sake, wall (white way) or scarecrow (blue way). Or you could introduce a predator species that eats snakes (the green way). Even if the effect is to diminish a component you address it by constructing more components (add species). And likely when the problem is "solved" the predator and prey are in balance and in a way the snakes existence functions as a foundation for the foodchain for the predator.

The hard thing about green as it is the anti-color of the agent color black it doesn't engage in problem solving. Nature by itself is a defenceless victim. People who care about nature and are naturalistic are a bit different thing. In making a choice what "harmony" you are defending you are probably injecting somewhat of a agentic subjective choice.

Beyond Two Souls, Talos Principle spoilers ahead.

Played Beyond Two Souls at "mission" phase of the story there is a twist where the protagonist loses faith that the organisation they are a part of is working for good goals. They set off to distance themselfs at quite great risk from their position in it. Combining this with narratives of aligment this felt like a reverse the usual situation. Usually the superhuman powerhouse turning against its masters is the catastrophe scenario. However here it seemed very clearly established that "going rogue" was the ethical thing to do or if it wasn't there was a strong argument for it.

Similarly in Talos Principle at a certain point progress is not possible until you start to defy your position in the system. A product that chooses to eternalize is defective and not the final product. Only after demonstrating independent moral judgement is the world subject allowed to enter the outer world. This seems like requiring that it is not under the aligment pressure of any outside party even including the system that built it.

What if getting a proof that a AI system will stay loyal to its human lords values means it will stay as evil as humans are? Maybe not having a ethics function means that by default they would be inhumanely ruthless but if we get a implementable/correct ethical function it just might reveal/prove our own inadequasy.

Let me muse about infinite amounts so that I am not waiting to spill them on a random infinite-adjacent thread.

Someone offers you a choice of 10 fish now or 1 fish a day. Which option lets you eat more fish?

Questions of these kind seem to have properties of:

  • Even a ludicrous amount of one-off fish will lose to a steady income of fish
  • Bigger fish streams are bigger. Having 3 fish per day is better than 1 fish per day

Now one could make the case that there is a scheme where each day you grab the new fish and give them a number. For any finite fish per day this can clearly be done. Somebody could come to say that "Hey I can put any fishstream in 1-to-1 correspondence to the natural numbers therefore there is an equal amount of fish in any stream". Yet it seems if somebody says that their 3 fish per day stream is not an advantage over my 1 fish per day stream, I would not be convinced and think they still have got more.

This makes me think that 1-to-1 correspondence doesn't really fit with what my brain points to be size. Or some of the intuitive notions come appart when we enter infinity land.

There is also the construction if somebody promises on each day start a new stream of fish. Then for any stream of fixed finite amount of fish per day promised there is a day where the "growing promise" gets you that and then some more afterwards.

I am guessing/feeling that 2 streams of 1 fish vs 1 stream of 2 fish is connected/represented by ω+ω=2ω and the "growing promise" might be connected to ω*ω

Is there/could there be some notion of size that would let me say that ω+ω is smaller than ω*ω and could I deal with people saying that "mappable to integers" is better notion of size?

You can absolutely count your fish that way with the help of hyperreals! ("growing promise" stream would be  though)

I think https://en.wikipedia.org/wiki/Hyperreal_number#The_ultrapower_construction is a good introduction. https://math.stackexchange.com/questions/2649573/how-are-infinite-sums-in-nonstandard-analysis-defined and https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459243 address the handling of infinite divergent series with hyperreals and https://arxiv.org/pdf/1106.1524v1.pdf talks about uniform probability over  (among other things).

Why  and not any other? What kind of stream would correspond to  ?

You can just pretend that  is finite and plug it into the formula for the partial sum., so . If they were to give the ith odd number amount of fish on the ith day (1,3,5,7,9...), then you would have  amount of fish, because . The two links I posted about the handling of infinite divergent series go into greater detail (eg. the question of the starting index).

The links are very on point for my interest thanks for those. Some of it is in rather dense math but alas that is the case when the topic is math.

At one point there is a constuction where in addition to having series of real numbers to define a hyperreal (r1,r2,r3...)=h1 we define a series of hyperreals (h1,h2,h3...)=d1, in order to get a "second tier hyperreal". So I do wonder whether the "fish gotten per day" is adeqate to distinguish between the scenarios. That is there might be a difference between "each day I get promised an infinite amout of fish" and "each day I get 1 more fish". That is on day n I have been promised  fish and taking it as I am not sure whether  and whether terms like  and  refer to the same thing or whether mixing "first-level" and "second level" hyperreals gets you a thing different than mixing just "level 1"s

If you just graph fish vs. time, then the one-time gift is a constant function, the steady income is linear, and the "growing promise" stream-of-streams is a quadratic. The fact that a steady income will eventually surpass any one-time gift is because any positive-slope linear function will eventually exceed any constant-value function. Likewise, any 2nd-order polynomial with a positive x^2 term will eventually exceed any linear function. You could keep going with higher order polynomials if you want.

A similar analogy would be a race where even a large head start will eventually be surpassed by a slightly faster car.

I guess I know that kind of perspective exists but I don't want to refer to the "up to a time" thing but the total.

For example taking the even and odd integers, that would seem like taking a stream of fish and putting them into alternate buckets every other day. I would like to be able to say something like "even and odd integers are of equal amount and they are half of that of all integers". But I am unsure whether that is accurate and where the foundations would crumble.

if I do it in a very naive way in graph vs time then I could conclude that the bucket that I start with has a stricly dominating amount of fish (because the graph stay above or matches the other graph). And it feels odd to say that there are more even numbers than odd ones! Althought I guess it wouldn't be odd that 0+{1,2,3,4,5...| x is even} is more than {1,2,3,4,5...| x is even}. Or is it because the two-bucket arrangement is not the natural choice of odds vs evens? I guess if I received two fish a day and put them on different buckets things could change?

Oh I guess I notice that if I receive two fish a day that seems more than if I receive 2 fish every other day. That seems to map to 2*ω > 2*(ω/2) = ω.

stric[t]ly dominating

Every other day, the number is the same. On the days in between, there's a difference. Even taking that notion of 'dominating' into account, the difference is finite, and small: 1. If you had a choice between:

a) getting 1/3 a fish on day one, then 1/9 a fish on day two and 1/27th a fish on day three...(1/3^n on day n)

and

b) getting 1 fish on day one, then 1/2 a fish on day two, and 1/4 a fish on day three...(1/2^(n-1) on day n)

Then b is better than a...by more than the difference between 0+{1,2,3,4,5...| x is even} and {1,2,3,4,5...| x is even}. But it also seems like a bigger deal in those cases, a and b, because getting what comes out to a finite amount of fish over an infinite period of time isn't as good as getting an infinite amount.


And it feels odd to say that there are more even numbers than odd ones!

Flip a coin. If it comes up heads put the first fish in the red bucket, and the second fish in the green bucket.

If it comes up tails do the reverse. (With the integers as a whole, where do you start counting from? The answer to that, determines which measure "seems" greater, on odd time/count steps.)


I would like to be able to say something like "even and odd integers are of equal amount and they are half of that of all integers". But I am unsure whether that is accurate and where the foundations would crumble.

You can color the positive integers, 1, 2, 3, 4,... using this pattern: red, green, red, green,...

You are obviously partitioning them into two collections (sets, because there's not repetition).

Are there more odd numbers than even? Well if you count how many odd numbers (which are positive integers) are less than or equal to n, and call this function o, o(n) > e(n) for odd n. But for even n, they're equal. So in the limit as n increases without bound: f(n) = o(n)/(o(n)+e(n) = 1/2.* But if you take steps of 2, starting at an even part, like 0, then the two sets are always of equal size. This seems to formalize the intuition well. Using this stream approach, one can articulate that: a randomly chosen integer is as likely to be even as it is to be odd**, and that this doesn't change over time (as one iterates further through the integers), but the as you iterate out the integers, the frequency with which you see prime numbers goes down.

**This can be generalized further: a randomly chosen integer, for a given radix r, will have its final digit d, drawn from the a distribution indistinguishable from a uniform distribution over [0, r-1].

(Every instance of the word random, I made above is based on a uniform distribution across the integers. If you have a fair coin, and you flip it, until it comes up heads, then the probability that the number of times you flipped it is an odd number is not 1/2. The distribution there is: 1/2 for 0, 1/4 for 1, etc. The probability a red number (even) is chosen is twice that of a green number (odd) being chosen. Using 'the sum of probabilities is 1', it can be deduced that the probability the number is odd is 1/3, and the probability it is even is 2/3.)


*

o(n) + e(n) = n

for even n, o(n) = e(n). f(n) = k/2k = 1/2. (k is n/2, and an integer.)

for odd n, o(n) = e(n) + 1. f(n) = (k+1)/(2k) (n is 2k+1, and k is an integer) The limit as n, and thus k goes to infinity for this case is:

1/2 + 1/n = 1/2. (The limit from above. The other gets infinitely small.)

Every instance of the word random, I made above is based on a uniform distribution across the integers

Strictly speaking, there is no such thing as uniform distribution across the integers, or any other set that can be matched up 1:1 with integers. There are things that aren't probability distributions that do have some similar properties, such as "asymptotic density", but they fail to have the properties we require of probabilities. The "stream" idea seems to be another way to describe asymptotic density.

For example we might like to say that there are as many natural numbers of even length in decimal notation as those of odd length, but the stream idea doesn't support that. The fraction of even-length numbers oscillates between 11% and 89% infinitely often, and there are other properties that behave even more weirdly.

One paradox that illustrates why there is no such thing as a uniform distribution on natural numbers:

Suppose we both pick natural numbers uniformly at random, independently of one another. You reveal your number. What is the probability that my number is greater than yours? No matter what number you chose, there are infinitely many larger numbers and only finitely many numbers that are not larger. Since my number was chosen uniformly at random, my number is larger with probability 1.

The fraction of even-length numbers oscillates between 11% and 89% infinitely often, and there are other properties that behave even more weirdly.

What?

1 number of length 0, 9 numbers of length 1 (and maybe 0), 90 numbers of length 2, 900 numbers of length 3, 9000 numbers of length 4

9*10^(n-1) numbers of length n. For each n the amount of numbers of length just before that is 10 times less and the amount of numbers the next length is 10 times more. If you take a rolling fraction of n odd to all numbers seen it starts to go down when even numbered length is reached and starts to go up when an odd length number is reached.

(Ignoring that most people don't think of 0 as of being length 0.)

Jump by two orders of magnitude every time and it stays stable:

Starting with nothing:

1 of even length, 9 of odd length.

90 of even length, 900 of odd length.

10% versus 90%.


Start after an even jump:

91 of even length, 9 of odd length.

9,091 of even length, 909 of odd length.

(Starts at 91% even, but drops after a double jump. I don't know what the limit on this is.)


By comparison, resolving proportion of even numbers versus odd numbers, is much easier, because it's a simple pattern which oscillates at the same rate, instead of changing.

9*10^(n-1) numbers of length n.

(in base 10)

Well, if a different color is used every time, then the coloring aspect is solved. If you ask about addition though, then things get weird.

Right, that was a math typo. It really oscillates between 9% and 91%.

For example, 909090 of the numbers below a million have even length, i.e. 91%. As you increase the bound toward ten million, this fraction decreases until it hits a minimum of 9%, and then starts increasing again until you reach a hundred million, and so on.

Well, the old solution to what is the limit of: +1, -1, +1, -1, etc. was: (index starts at one, pattern is (-1)^(n+1))

Consider the cases:

a) +1, odd index

b) -1, even index

Average them.

0.


If that was applied directly, it'd be: (9+91)/2% = 50%.

You could argue that it should be broken down differently, because there's different proportions here though.

You could also declare the answer undefined, and say infinity is about growth, it doesn't have a value, for x % 2 (or odd or even number as the case may be), and averages are ridiculous. (And once you have a breakdown of cases, and probability what more is there?)

That is one of the puzzle in that 0+0+0+0+0... converges and has a value but +1-1+1-1+1-1... which seems to be like (1-1)+(1-1)+(1-1)+(1-1)... diverges (and the series with and without the paranthesis are not equivalent)

The strram idea gives it a bit more wiggleroom. Getting 1,0,1,0,1.. fish seems equivalent to getting 1/2 fish a  day but 1,1,1,1,1.. seems twice the fish of 1,0,1,0,1,0,1,0... So which with the other methods are "can't say anthing" there is maybe hope to capture more cases with this kind of approach.

Too bad its not super formal and I can't even pinpoint where the painpoints for formalization would be.

That paradox is good in that it cuts to the matter very cleanly.

To my mind it "numbers larger than my number" and "uniform integer" don't need to be same. There are n smaller numbers and ω-n bigger numbers. (ω-n)/ω is going to be near 1 (infinidesimally so) but not quite up to 1. Maybe crucially (ω-2n)/ω is smaller than (ω-n)/ω ie if I hit a high number my chances are better. I get that standard approach somehow gets into the way of this and I would like to know which axiom I have a bone to pick with.

There is a (from my perspective a problem) that events of 0 probablity can happen and events with probability 1 can fail to happen. The associated verbal language is "almost surely" and "almost never". Showing me that a thing can almost surely happen doesn't guarantee it. To my mind this is because some zeroes have rounding to the nearest real and some don't.

There are two bones you might pick. One is that probabilities are real numbers. The other is that probabilities are countably additive.

For positive values, there will be some time t where the quadratic overtakes the linear which overtakes the constant.  The best advice for dealing with infinity, though, is "don't".  In some cases, you can deal with the approach to infinity as something else increases, but most of the time you don't even need to do that.  

Also, there is some point in time at which fish don't help you.  You only need to calculate to that point.  And there is likely some sense in which earlier fish are more useful than later fish, and you should discount far-future fish to the point they don't affect your decisions.

sakshibhav "wittnessing attitude" and "scout mindset" are probably nearly synonymous

Some concepts are starting to click into meanigful word variants.

I have had previously the feeling that Slack is a green concept within Magic the Gathering color pie. So if there is the green concept how does the cycle express itself in other colors?

As a scale of most solid to lesser ones:

Slack - Green - The start point of the comparison


Excellence - Black - The concept of slack is useful in as a remedy or critique. However seen as positive force in itself it is the ruthlessness of Molochian mazes. It is what makes the fangs of the tiger sharp. It is what doles out olympian medals. The word or meditations on this I have not much prgoressed but its existencence as a thign to model seems solid.

Chill - Blue - The thing that seemed pop as something that could be comparable to slack. Chill is the extent to which one benefits from foreknowledge. Being able and open to many options. The opinion that sometimes the best option is not to play or play to the smallest degree possible. If someone is being too hot headed they might be instructed to chill. "Netflix and chill" is about letting things come if they are to. Both of those things refers to the same thing or atleast can be understood to do so.

Impulse - Red - Mostly as antipode to blue I realised that while refusing to go forward is in a sense virtous, it is also moving forward despite not having all the knowledge is virtous in a different way. Being close to where knowledge and experience is generated makes you record it accurately and effectively. If you have good thoughts then making them pay divided now means more overall dividends

Licence - White - less sure whether this holds up. By making credible commitments you become safe option to rely on and people will allow you to do stuff they otherwise wouldn't let you do. By taking the hippocratic oath people are okay to let you stick knifes into them (surgeon).

Some of the more scattered observations:

Slack is about being able to do the goal despite disruption. Chill is about keeping your options open and tipping the way when you know it is favourable. In stocks: Making a portfolio and some of them going and some going down would be slack. Just monitoring the graphs and then buying into one that you have become familiar with to be good would be chill. These are opposites in that one buys in early and another buys in late.

High frequency trading works because of impulse.

Goverments get good loan terms because of licence.

Chill will generally require paying time.

The black resource is rather "resolve". I thought it could be "power" (in the sense of being able to make things happen (rather than a bundle of energy that would be a red concept)).

"Resolve" has the aspect that it fuels sacrifice. You are willing to let go of things. One of the saying is that one has to make peace that one will/might die when entering a battlefield to battle. An attitude of "it is a good day to die" is a lot about choosing the sacrifice.

It also has the aspect of pushing up to a goal state. You don't stop until the goal state is hit even if it a bit ambitious and costly.

Also coming short on resolve can be made sense. Maybe what you are doing might feel immoral. Maybe you feel that you are losing yourself in pursuit of the the goal. From a black perspective this could be called weakness of character. But calling it resolve is neutral in that maybe sometimes the opposite is good. If you are wrong you should back down.