System Error: Morality Not Found
October 6th, 2007 –
It’s not often that I award someone the accolade of having caused a complete system crash in my mind. This year’s award goes to Philosophy Etc. for the following dilemma:
Imagine a universe containing infinitely many immortal people, partitioned into two “spheres”. (Every person is assigned a natural number N.) In one sphere, all the inhabitants live a blissful existence, whereas the members of the other sphere suffer unbearable agony. Now compare the following two variations:
1) Everyone starts off in the blissful sphere. But each day (N), one more person (N) gets permanently transferred across to the agony sphere, where they reside for the rest of eternity.2) Everyone starts off in the agony sphere. But each day (N), one more person (N) gets permanently transferred across to the blissful sphere, where they reside for the rest of eternity.
Which scenario is better? The answer, paradoxically, appears to be “both”. At any moment in time, there will be infinitely many people in the original sphere, and only a finite number who have been transferred across. So option 1 is better.
However, each particular person will spend only a finite amount of time in the first sphere, whereas they will spend an eternity in their post-transfer home. So option 2 is better.
Staring at this problem, I had the pleasant experience of a morality crash - my mind went completely blank. Of course, I did boot up again a few moments later, and remember the great excuse of being an infinite set atheist. Also I presently use Barbour’s timeless physics. So I only believe in finitely many minds of any given complexity bound, and don’t believe in any such thing as a “moment in time”.
But what if someone actually showed me an infinite set and a moment in time, forcing me to believe in them? Then I would be in trouble.
Everyone out there who thinks they’ve already finished solving the challenge of AI morality is cordially invited to explain what their AI would do, presented with such a dilemma.
On day N, the accrued number of person-days in the increasing sphere is
SUM(x*x for x from 0 to N). Since the numbers are large (infinite), I think it’s legal to call this a Riemann sum. So this is an integral of X from 0 to N, or
(N^2/2 - 0^2/2), or N^2/2
The number of person-days in the decreasing sphere is
(N*INF)-(N*N/2)
One person-day in hell is worth -1 util, while one day at Anime Central is 1 util. So:
First scenario at day N:
(N*INF) - (N^2/2) - (N^2/2) =
(N*INF) - (N*N)
Day INF:
(INF*INF) - (INF*INF) = 0
Second scenario at day N:
-(N*INF) + (N^2/2) + (N^2/2) =
-(N*INF) + (N*N)
Day INF:
-(INF*INF) + (INF*INF) = 0
I would actually be somewhat disturbed if that contains no mistakes. But according to this calculation, both scenarios have the same utility, namely zilch. Tossing a coin is a perfectly cromulent way to choose between them.
Of course I made a mistake. Hold the flamethrowers while I recalculate.
Tiiba, you can’t just add and subtract infinities as if they were natural numbers.
Eli: this reminds me of example 1 in section 15.3 of PT:LOS.
You can avoid this paradox by being an infinite set atheist, but that’s not the only way to avoid it. I think the problem here is trying to use a utility function which does not converge. We can’t treat all people and all time-slices as equally important; we need to use some sort of discounting.
I can see that this sounds inhumane. “Oh, sorry, you got discounted.” But decision theory consists of discounting the happiness of hypothetical people based on numbers which we call probabilities, and I think this situation is analogous.
“Tiiba, you can’t just add and subtract infinities as if they were natural numbers.”
Of course, of course. Infinities don’t behave like finite numbers. Is half the cardinality of the set of real numbers more or less than the length of the decimal expansion of pi?
But I’m assuming that the infinities I’m dealing with here are the same kind - the largest nonnegative integer. It seems like a reasonable assumption, since we’re counting people and days. So INF=INF, and INF*INF-INF*INF = 0.
Is half the cardinality of the set of real numbers more or less than the length of the decimal expansion of pi?
More.
the largest nonnegative integer
There’s no such thing.
Start here.
Disclaimer: I learned all my math by reading bathroom graffti.
It seems to me that your AI, as of your recent Summit lecture, would use the process that you use to figure out what should be done, which should work if you will ever figure out what should be done.
OTOH, it’s not clear to me how an AGI of the sorts that you have discussed could be a non-dogmatic infinite set atheist or theist, e.g. be capable of being shown an infinite set and coming to believe in the possibility of such things.
It seems I did the person-day function wrong:
Accrued person-days in the increasing sphere:
pd(N) = 0 id N
WTF?
Let’s try this again.
It seems I did the person-day function wrong:
Accrued person-days in the increasing sphere:
pd(N) = 0 if N
Seems this blog has a number of bugs. First it screws up my link to a post on Yahoo 360, now it wrecks my post just because I included a less-than symbol. God help us all if this thing is entrusted with ethical decisions.
I think it’ll work if you use < instead.
Try 3.
It seems I did the person-day function wrong:
Accrued person-days in the increasing sphere:
pd(N) = 0 if N is less than 2
pd(N) = pd(N-1) + N-1 otherwise
I have no idea how to integrate that, though. Not even certain that I should.
Justification:
On day 0 we have an empty sphere. On day 1 there is 1 person in it with 0 days accrued. On day 2+ we receive another person with 0 days accrued, but the N-1 people already there accrue 1 day each.
The killer with this example is that for each individual person P, scenario 2 is better, but looking at the total accrued utility for all people over any bounded interval of time, scenario 1 is better.
If you try to calculate the total utility over the whole of time, you are trying to sum a divergent series, and then add it to infinity, so you will get yourself into a mess. (See Tiibba’s posts on how to do this.)
For me, this is not such a shocker, but that is probably because I am a mathematician and I am mentally prepared for the fact that infinite sets will totally screw up your intuition. This happens a lot! See, for example:
http://en.wikipedia.org/wiki/Peano_curve
http://en.wikipedia.org/wiki/Nowhere_differentiable
http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
As far as this particular scenario is concerned, the fact the there are infinitely many people and and that there is an infinite amount of time means that the moral theory which maximizes utility for each person does not maximize total utility.
I don’t think that this has any important implications for our understanding of morality as a whole, because it is a fact that there are only finitely many people in the world, and it is also the case that we cannot predict the effects of our actions infinitely far into the future, so realistic moral theories need only concern themselves with finite regions of spacetime inhabited by finitely many agents.
By the way, Tiiba, I think you should go and read up on a piece of mathematics called real analysis. We study it in the first year of university mathematics, and it is extremely interesting. See these wikipedia articles:
http://en.wikipedia.org/wiki/Divergent_series
http://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations
I think you should go and read up on a piece of mathematics called real analysis
I agree. Anyone having trouble following this discussion should consider learning some real analysis.
If option 2 is better for _each_ of participants, doesn’t it mean that it’s better for all of them together? There is no point in considering summed utility for all of them, since no one is interested in it.
The killer with this example is that for each individual person P, scenario 2 is better, but looking at the total accrued utility for all people over any bounded interval of time, scenario 1 is better.
If you try to calculate the total utility over the whole of time, you are trying to sum a divergent series, and then add it to infinity, so you will get yourself into a mess. (See Tiibba’s posts on how to do this.)
For me, this is not such a shocker, but that is probably because I am a mathematician and I am mentally prepared for the fact that infinite sets will totally screw up your intuition. This happens a lot! See, for example:
http://en.wikipedia.org/wiki/Peano_curve
http://en.wikipedia.org/wiki/Nowhere_differentiable
http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
As far as this particular scenario is concerned, the fact the there are infinitely many people and and that there is an infinite amount of time means that the moral theory which maximizes utility for each person does not maximize total utility.
I don’t think that this has any important implications for our understanding of morality as a whole, because it is a fact that there are only finitely many people in the world, and it is also the case that we cannot predict the effects of our actions infinitely far into the future, so realistic moral theories need only concern themselves with finite regions of spacetime inhabited by finitely many agents.
By the way, Tiiba, I think you should go and read up on a piece of mathematics called real analysis. We study it in the first year of university mathematics, and it is extremely interesting. See these wikipedia articles:
http://en.wikipedia.org/wiki/Divergent_series
http://en.wikipedia.org/wiki/Extended_real_
Eliezer Yudkowsky:
> However, each particular person will spend only a finite amount of time in the first sphere…
False. There are infinitely many people there, so always will some (infinitely many in fact) remain there.
Eternity? No way, paradox. You always have to take finite numbers into your calculations.
Please explain something to the mathematically challenged.
It seems obvious to me that the second scenario would be much preferable for any individual. It is better to be in pain for a finite amount of time, no matter how long, than for an infinite amount of time.
Why doesn’t the math reflect this?
Mu. Aside from the paradox induced by the imposition of infinities, morality doesn’t work in terms of absolute happiness. Witness the documented paradoxes arising out of any variation on utilitarian moral theory.
Modelable morality can’t refer to a preferred state — to do would require that it be able to contain itself — but can refer to presently preferred direction, driving the system toward increasingly coherent agreement on principles promoting evolving subjective values over increasing scope of consequences.
Machine intelligence is crucial to this game of increasingly effective promotion of increasingly coherent values (supporting increasingly diverse expression), not to win, but to continue playing.
- Jef
This type of “paradox” is why I don’t trust mathematicians with my morality, but maybe I’m really missing something here as a non-math guy?
Immortality as “infinite time” seems like a relevant construct but I don’t see how “infinite people” is imaginable or even thoretically possible (ie assuming at the birth of the universe(s) there were 0 people and assuming a growth rate of any number, you still get a finite number of peeps at any future time). Certainly from a practical perspective we should assume finite peeps in the universe.
*
Thus the far simpler question is easy to answer when N=any number less than “infinity”. Option 2 yields an increasingly happy world. In fact, isn’t option 2,with finite people and much of the world in poverty, much like the kind of scenario many singularitarians are now advocating?
In fact, isn’t option 2,with finite people and much of the world in poverty, much like the kind of scenario many singularitarians are now advocating?
What? Which singularitarians are you referring to, and what are they advocating?
“So I only believe in finitely many minds of any given complexity bound, and don’t believe in any such thing as a “moment in time”.
But what if someone actually showed me an infinite set and a moment in time, forcing me to believe in them? Then I would be in trouble.”
Here’s my two cents. I can’t prove it mathematically, but in the subjective sense, I do believe in “moments of time”. Ask yourself, what does the Eliezer of five minutes ago currently experience? I presume nothing, but at least he doesn’t suffer in any way. If I *had* to make an ethical decision, I would choose Option 2, but you can be sure that I wouldn’t be happy about it. I’m glad this is a hypothetical and not necessary.
This is a somewhat well-known problem, though I don’t know where it originated (certainly not Philosophy Etc). It is a good one though.
The most obvious point to make is that if you draw the happy and unhappy people on a space-time diagram, you will find that they fill one quadrant and all those above the diagonal are happy, all those below are unhappy (if time goes up the page). Example two reverses which is which. Integrating across the time dimension gives one answer, integrating across the space dimension gives the other. Integrating based on increasing rectangles of N days/people says that they are both the same.
For those tempted by the beauty of this third possibility, note that you get a different answer if the bubble expands at a different rate and what is so special about keeping persons and days matched up? Why not rectangles of a person and a second, or a person and a year (they each give different results).
I believe that Nick Bostrom has thought more about this kind of thing than anyone else. Indeed he has an excellent paper on it at
http://www.nickbostrom.com/ethics/infinite.pdf
This is a serious paper and was only rejected by the top ethics journal due to it being too long to publish (it made it all the way to the editorial board).
An example of a good infinite ethics dilemma: Is it better to have an infinite line of people where 99 of every hundred are happy and the other in agony than the other way around. If not, then that is rather strange. If so, then we can improve the world purely by shifting people around even though this doesn’t make anyone happier. I honestly don’t know what to say about this type of case.
For those who think this is complete whimsy or that you cannot have infinitely many people, do check Nick’s article. He points out that according to a widely held viewpoint among cosmologists the universe does indeed have infinitely many happy and unhappy people. I don’t think that Eliezer can be at all certain that there are only finitely many persons (I would like to see him try to ascribe a probability greater than 90% to this statement). Nick’s paper on brain duplication and experience is highly relevant here.
Toby.
Peter: I don’t think discounting is a good way to solve this. It is temporal discounting and not very similar to probabilistic discounting. For any discount rate, you are setting a time in the future at which people then count less than a googleplexth of what us people now count, simply in virtue of having different space-time coordinates. This hardly seems to be a the type of thing one which to discriminate.
Also, for any two discount rates, we can construct dilemmas for which they disagree on what is right. So you would need to find a non arbitrary discount rate and I have no idea what this could be. Even then, I think it is morally preposterous.
Also note that on temporal discounting, people in the past matter a lot more than we do.
It is temporal discounting and not very similar to probabilistic discounting.
I think it’s similar. If you’re using some sort of algorithmic probability distribution, then you’re assigning probabilities (ie. weights applied to your utility function) to hypothetical selves based on their location in the set of computations, and this tells you not to buy lottery tickets. Your within-universe space-time coordinates are part of your location in the set of computations.
I don’t think that is right. Probability discounting is like counting a group less because they are fewer. If I ‘discount’ the 1% chance of a hiking accident relative to the 99% chance of a great trip, that is because 99 times as much probability mass of me has that experience. This is similar to giving a benefit to 99 people rather than to 1.
Temporal discounting is similar to valuing nearby persons more than further away persons.
It is true that in both cases we are scaling the value by a factor, but that is the only analogy. In one case it is clearly legitimate, in the other many people (including myself) think that it is not. Temporal discounting is only like probabilistic ‘discounting’ in the way that racial ‘discounting’ is also similar. In economics and moral philosophy, the word “discounting” only refers to the temporal kind.
Do you object to weighting utilities by location in the space of computations, or do you disagree that your within-universe space-time coordinates are part of your location in the space of computations?
I’m unsure what you mean by ’space of computations’ here.
I’m referring to algorithmic probability distirbutions.
OK. I’m not stranger to such things (having published on the topic), but I don’t see how it gives a convincing analogy here. I think there are a large number of things that your 10:22am comment could mean depending on exactly how we interpret the space of computations as probability (objective vs subjective etc). Regardless of how time manifests in your space of computations model of the universe (or is it just modelling an individual agent’s model of the universe?), I don’t think it is going to come out as the type of thing for which discounting is sensible, any more than discounting for location or velocity or whatever.
That said, I’d be interested to talk to you about such things if we are ever in the same city.
Are you saying that you need to figure this out to solve AI morality, or that a solution to AI morality will immediately answer the question? It seems to me more like this is the sort of question you would build an AI to answer.
“Are you saying that you need to figure this out to solve AI morality” (?)…
Fortunately, no. It’s only a special case hypothetical.
…”or that a solution to AI morality will immediately answer the question?”
Probably. It depends on your definition of “morality” (which has no objective counterpart). The Friendly AI will either derive its “morality” from humans (eg. CEV) or it will use whatever sort of innate “morality” that it is programmed with (intentionally or not).
If you assume that the infinities in question are countable, then each person can be assigned a whole number X representing the day on which he or she will switch from pleasure to agony or vice versa.
Under those circumstances, for any given person, scenario 2 would seem to be better.
True enough, but the problem that caused Eliezer’s ‘crash’ is that at every given time, scenario 1 is better.
What we are looking for is a statement of the form ’scenario X is better’ without the qualifying phrase ‘for every given Y’. In finite cases, we can simply move from the qualified claim to the unqualified one, but in this infinite case this would lead to a contradiction.
Assuming a limited amount of suffering/pleasure per person per unit time:
In scenario 1 we have, for any value of time t, the total amount of suffering is negligible compared to the amount of pleasure.
In scenario 2 we have, for any value of time t, the total amount of pleasure is negligible compared to the amount of suffering.
So scenario 1
In scenario 1, for any given person, the total amount of that person’s pleasure is negligible compared to the amount of their suffering.
In scenario 2, for any given person, the total amount of their suffering is negligible compared to their pleasure.
So scenario 2.
Man, am I glad I expect never to see an infinite set.
Firstly, the above analysis covers the total of suffering/pleasure of all the persons, which is what you want to use to decide.
Secondly, the analysis you suggest is wrong. If you want to analyse per person, here’s the result:
In scenario 1, for any value of t, the probability that any person N has suffered until then is negligible.
In scenario 2, for any value of t, the probability that any person N has felt any pleasure until then is negligible.
So even if you make the analysis based on individual persons, scenario 1 still is superior _for any value of t_
Ignore the previous comment, theres trouble selecting randomly from an infinite set
You know, that’s an interesting point. Does the Axiom of Choice matter to this question?
(Sorry if that’s stupid, most of my math is from bathroom graffiti too.)
Does the Axiom of Choice matter to this question?
Nope.
Forget maths, forget statistics, I believe the key to this question is based in if each of these people know what the future holds for them.
If they do, solution 2 seems the more “moral” of the options - every person has something to look forward to eventually.
If not, solution 1 one seems the most moral - each person will enjoy the pleasure of being in the “happy” circle, with no worries of any kind.
We don’t decide on our moral positions using calculators, so why should AI?
Because it IS a calculator?
If it *is* a calculator (and I know we aren’t talking pocket calculators here), then surely it isn’t AI. Intelligence is more than just crunching numbers, and my original point was that a mathmatical approach cannot be applied to this moral situation.
Let one person for one day in heaven be worth 1, and one person for one day in hell be worth -1.
Now imagine the top left hand corner of an infinite dimensional matrix with time going down and people going across. In the first case everybody starts off in heaven, so fill in this row with all 1s. In the next row down the first entry is a -1, and then all 1s. Then two -1s followed by all 1s. And so on…
If you draw this and think about it for a moment, it’s not hard to see that every 1 can be paired with a -1, thus canceling each other out. By every, I mean on the whole infinite matrix. In math speak, the two sets are equipotent. In some sense the “good” and the “bad” are of equal size.
Repeating the same procedure for the second case yields the same result. Thus the answer is indeed “both”.
But have I really failed as an AI moralist if my AI can’t solve an unsolvable dilemma?
I’d classify both options as “unacceptable” and go with option 3: “keep thinking, maybe there’s some way to avoid infinitely many people suffering unbearable agony”. Is that cheating? Maybe, but it would be my answer in reality. It seems like it would be OK to design a system that would crash in this case (or hang).
By the way, who is this “someone” who “actually” showed you this universe? That would be very useful to know.
“Everyone out there who thinks they’ve already finished solving the challenge of AI morality is cordially invited to explain what their AI would do, presented with such a dilemma.”
I have not solved the AI morality problem, but I think I can handle this one: Infinity screws up the human intuition. Your reasoning, if I understand correctly, goes like:
1). From the perspective of any given person, they will only spend a finite amount of time in agony, followed by an infinite amount of time in paradise. Therefore, agony -> paradise is better.
The human intuition here is that if you pick a person, ve will surely have some number N, and so after N time periods his suffering will end; therefore his suffering is finite. This logic breaks down when you deal with infinities, because you *cannot* just pick a person with a number N; for any number N, there are more numbers above it than below it, and so no matter how high N is you are not taking all the people above N into account.
A simpler way to look at it is just to do the utility integrals. The integral of pleasure -> agony dt is infinity - c(n^2) = infinity; the integral of agony -> pleasure is c(n^2) - infinity = - infinity, no matter how large c or n become.
Tom, you’re begging the question by first summing across people and then integrating over time. You could also integrate over time and then sum across people, and the result would be different.
“You could also integrate over time and then sum across people, and the result would be different.”
You would have to do the integral from now until the bubble switch (0 -> + infinity), and then the integral from the bubble switch into eternity (+infinity -> +infinity). You can’t integrate from positive infinity to positive infinity; it doesn’t make any sense.
The bubble switch occurs at time N, not time +infinity.
“The bubble switch occurs at time N, not time +infinity.”
See, this is the reasoning barf I described above. For any given person you select, there will be a specific time N when the function flips. But you can’t use a variable N, because no matter how high N is, there are still far more people above it than there are below it. Imagine the bubble as a FIFO stack- if you select a particular person at index N, you aren’t fairly calculating the utility for the entire stack, because there are far more people above N than below it.
\sum_{N=0}^{\infty} (\int_{t=0}^{\infty} U(N, t) dt)
vs.
\int_{t=0}^{\infty} (\sum_{N=0}^{\infty} U(N, t)) dt
OK, I should clarify that.
If you render the above expressions in LaTeX, they should look nice unless I made a mistake.
In the first case, we are evaluating an integral for each person. Each person has their very own unique individualized integral, so we are allowed to talk about the integral from 0 to N and the integral from N to infinity! Then we sum all of the integrals.
In the second case, we are evaluating a sum for each moment in time. Each time has its own unique individualized sum, so we can break it up into the sum from 0 to N and the sum from N+1 to infinity! Then we integrate all of the sums.
Guys I think this is a becoming an irrelevant distraction. I think people are wasting time messing around with this problem because it is amusing rather than because it will actually lead to any progress on the front of defining ethical systems for real-world AIs.
Yes, infinity will screw with your intuition, but for real world morality we can confine our attention to finite spacetime regions containing finitely many agents. Enough said.
When you find yourself confused about something, it may be a good idea to try to resolve your confusion even if the target of that confusion doesn’t seem important. Your confusion may be the symptom of a problem with your reasoning methods, and it’s a good idea to fix those problems.
In general, this can be a good heuristic. In this case, I think there is a specific reason why working on “infinite morality” problems will not help us with the real-world “finite morality” problems.
My reasoning is as follows: infinite morality and real world finite morality are both generalizations of the principal of maximal utility over a finite set of agents with some simple utility function (e.g. number of people alive); however they are generalizations in two different directions.
Real world morality is hard because when we try to map states of the real world W onto the reals R (via a utility function), the domain space W is essentially impossible to define in precise terms. This is because we do not have a system of “artificial ontology”. Until we have a such a system, we will not be able to do real-world utility maximization.
Infinite morality (of the kind Eliezer was talking about) uses a very very simple characterization of the world - in the case you have all been considering, the world is defined to be a function from the natural numbers (time) to a countable infinity of copies of the set {0,1}, where 0 = hell and 1 = paradise. The difficulty in these infinite scenarios is all in the fact that there are infinitely many agents over infinite time.
Therefore when you study “infinite morality”, you are avoiding the real problem - which is how to characterize the real world in all it’s complexity and how to define sensible utility functions on it. It is an amusing distraction.
No one can ever show you an infinite set, as it would take them an infinitely long time to do so.
Zing!
This reasoning is unsound: Suppose I show you one element of my set in the next second, then one element in the 1/2 of a second after that, and then one element in the 1/4 second after that, and then one element in the 1/8th of a second after that, etc etc.
After 2 seconds, I have shown you infinitely many elements, yet I showed you each element in a finite amount of time.
But I really shouldn’t have said that because I’m failing to follow my own advice about not talking about infinity! Darn… I hate it when I do that….
What? Which singularitarians are you referring to, and what are they advocating?
I’m thinking Kurzweil’s notion that with the advent of pre to post singularity computing we’ll be able to solve all human problems, moving people from poverty to affluence to immortality.
But I also think one needs infinite patience to even contemplate using infinity constructs in this fashion. This leaves me out!
I do think this is starting to look a bit over-thought. The whole thing can be rendered useless if you bear in mind that in either scenario, there will always be not just an infinite number of people in one scenario, but infinitely *more* people than in the other, whichever way you decide to think about it. By this rationale, Scenario 1 is ‘better’.
[I’m about to do some things with infinity that you probably won’t enjoy. Dsclaimer over!]
However, the notion of ‘residing for eternity’ suggests that an infinite amount of time passes, which means that an infinite number of people will have passed into the second sphere. Now you have to ask yourself which of the following is the bigger number: an infinite number of people in the first sphere (highest possibly integer, presumably), or an infinite number of days (to measure how many people have ‘flipped’ to the second sphere.) Getting extremely tenuous, you could probably argue that if the infinite number of people is ‘fixed’, but the number of days will continue to increase…infinitely. Correct me if I’m wrong, but doesn’t this suggest that the INF(days) is a higher aleph than than the INF(people in first sphere)? Maybe not, I’m not a mathematician.
But all this aside, I’d say the second option is the better from a holistic, but purely experiential point of view as well. In Scenario 1, there is a non-zero probability that you will, at some point, be transferred to a hell-hole. In Scenario 2, there is no doubt that you will spend an infinite amount of time in heaven. Granted, you may have to wait an infinite amount of time to get there, but if we’re dealing in infinites, I imagine that’s just an inconvenience.
Here’s an interesting closer for you, from a purely selfish, individualistic point of view (and yes, I know that’s not the aim of the exercise). Put me in Scenario 1 please. Since I’m in there sharing heaven with an infinite number of people, I don’t mind the odds of suddenly getting picked out. I have an *infinitely* better chance of winning the lottery tonight. If that happens, I’ll post on here and let you know I was wrong. Apologies for length, I’m at work and extraordinarily bored.