on optionality, icarus & the point of having wings

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i’ve been trying to get back into drawing and painting lately, and unrelatedly one of my favorite piano pieces is called icarus (click play on the bottom of your screen for those who want the full auditory experience lol), which happened to be playing when this occurred to me. naturally, as an associative thinker, i immediately decided my first object of creation would be a drawing of icarus. so i started looking up the ways other ppl had drawn him for inspo beforehand (the actual sketch came out kind of subpar, but maybe the next time i look back at this i’ll be confident enough to attach it here). on google images i kept getting images of a very anguished man plunging into the ocean. which, fair enough, i would probably also look pretty anguished if my wings melted in midair, but that wasn't the version i wanted.

a movie character exclaiming i give you icarus!

maybe in part it was for the aesthetics, but i had this whole vision of icarus just before the fall, with hope and a little delusion on his face. having flown high enough to see the world from above, looking toward the sun, i wanted him to be choosing to fly closer, fully aware that he wasn’t invincible and that his wings would melt, but wanting to anyway. i think there's something incredibly beautiful about that interpretation. common sense says, surely the experience of being a little closer to the sun cannot be worth the entire remainder of his life? ah but the romantics! instinctively i want to say my heart lies with them, and my aesthetic tastes too.

i feel like the most common interpretations of icarus nowadays are about hubris or entrepreneurship, something along the lines of chasing a dream despite the possibility of failure. but i’m trying to take this a different way, and make it about choosing an experience without requiring that anything come of it. which sounds inspiring until you think about it for more than 10 secs, so i've been trying to figure out whether there's actually a defensible philosophy here, or if i'm just romanticizing a very bad decision.

what the myth actually says

first, a clarification that this isn't really what happens in the original myth. in ovid's metamorphoses, book viii, daedalus fashions wings out of feathers and wax to escape crete with his son. he warns icarus to take the middle path, because flying too low will weigh down his wings with moisture and flying too high will melt the wax. icarus becomes delighted by flying, abandons his father's guidance, and ascends toward the heavens. the sun melts his wings, he cries out for his father, and he drowns. there is zero indication that he knew the fall was inevitable and deliberately accepted it. he's also a boy, and daedalus is absolutely devastated, which complicates the idea that this was some beautiful, autonomous decision with consequences borne by icarus alone. the familiar reading is therefore one of youthful recklessness, excess, or hubris. although it's worth noticing what ovid actually gives as the motive: icarus leaves his father caelique cupidine tractus, drawn by longing for the sky. nothing in there about defeating the sun or proving his superiority. he wanted to be up there, which is honestly closer to my version than i expected.

modern writers have taken the story in a more sympathetic direction. my favorite is jack gilbert's failing and flying, which begins with “everyone forgets that icarus also flew.”

gilbert is writing about love, and how we retrospectively classify relationships that end as failures, as though the ending somehow invalidates everything that came before it. the poem argues that something can come to an end without having been a mistake. i love this, and so i think there are actually 3 possible interpretations that are making us romanticize icarus.

  • the flight had value even though it ended in a fall
  • choosing to fly may have been reasonable even if there was a risk of falling
  • choosing to fly would have been reasonable even if he knew with certainty that he would fall.

these are not the same! the first is about how we evaluate an experience after the fact, the second is about decisions under uncertainty, and the third is about knowingly accepting a fixed sacrifice. you can believe the first without believing the second, and the second without believing the third. people blur the first two constantly, enough that behavioral research has a name for it, outcome bias: we judge a decision more favorably once we learn it turned out well, even when the person deciding knew exactly the same things either way. a good decision can end badly, and a bad decision can produce something wonderful. and gilbert gives us no obvious reason to think that icarus would have been right to sacrifice the rest of his life for one more moment in the sky. so that third claim is the one i'm interested in testing, even if it turns out to be too strong.

on keeping your options open

i think part of why i was drawn to this version of icarus is that i've always liked having options. i love the feeling of being able to do a hundred different things, have different research areas, different careers, different places to live, different possible versions of my life. there's a kind of pleasure in not having chosen yet, because every possibility remains available in theory (this framing also comes from this quote of kierkegaard’s who i’ll later bring up anyway lol. he is the goat.)

and to be fair, optionality is genuinely valuable. when you're uncertain about the future, keeping your options open lets you respond to new information. economists have formalized something similar through real options, meaning when a decision is irreversible and its returns are uncertain, waiting can have value because it preserves the ability to decide later, potentially with better information. but. the purpose of an option is that you might eventually exercise it. suppose you have the opportunity to move to a new country for a year. you could go, learn the language, make friends, have a completely unfamiliar life, or you could stay where you are, because leaving would mean giving up other opportunities and potentially falling behind on whatever career path you're already on. staying preserves certain possibilities, while leaving realizes a particular one, and neither is inherently better than the other, but notice that if you keep choosing the option that preserves the most possibilities, you can end up with a life that consists almost entirely of preparation for other lives.

and real-life options are harsher than financial ones, because what you lose by waiting is experiences rather than money, and the opportunity might disappear simply because time passes. this is roughly where kierkegaard enters the picture. in the sickness unto death, he describes a kind of despair associated with possibility, where a person becomes lost in imagined futures and fails to turn any of them into actuality. he’s not even making a modern economic argument about optionality, and his account of despair has a much broader religious context, but the connection is hard to miss, in that possibility without actuality is not necessarily freedom. it can become a way of never having to choose. also, the quote i linked up top isn't even kierkegaard speaking as himself. it's from either/or, said by the aesthete, a guy who lives for possibility, and the entire second half of the book is a judge writing him very long letters about why he should commit to something. so the line i liked best was written as the position you're supposed to grow out of lol.

what's funny is that in my earlier hyperion post, i argued for something that seems almost opposite to this. i was worried about preference transformations that lock someone into a particular future self, destroying their ability to reconsider what they want. i proposed preserving future preference option value as a potential part of autonomy. i still believe that! but i think i was implicitly treating two different things as similar. preserving the capacity to reconsider a choice is not the same as preserving every possible choice. the first protects your agency. the second, taken to its extreme, can prevent you from using it, and also there's a further complication in that some experiences don't become available until after you've made a substantial commitment. you can't experience what it's like to become genuinely good at piano by taking a beginner lesson in thirty different instruments. you can't experience the later stages of a research project if you abandon every idea once another interesting one appears. michael bratman's work on planning agency is relevant here. intentions help us organize action over time, avoiding the need to reconsider every decision at every moment, and a project can require a degree of stability that makes it possible to do things we couldn't accomplish through a series of isolated choices.

i've had a bit of a "bias toward action" ever since i first heard the phrase at openai, and i think there's a pretty defensible decision-theoretic case for it - the main idea being that when an action is relatively reversible, and trying something gives you information that thinking about it wouldn't, acting can actually increase your future optionality. instead of spending forever trying to predict which path is best, you can try one, learn something, and adjust. that's not a blanket excuse to act, though. the test is whether the expected value of the information you'll gain exceeds the cost of obtaining it, and trying something is especially useful when the evidence is hard to acquire any other way, and when you'll actually have opportunities to act on what you've learned.

exploration without an eventual payoff

there's another distinction i find interesting here, which comes from the way we normally think about exploration. in reinforcement learning, consider a very simple exploration-exploitation problem. you have several possible actions with uncertain rewards, you can exploit the one you already think is best, or explore an unfamiliar one to learn whether it might be better.

exploration is valuable partly because the information you gain can improve your future decisions. but now suppose you're on the very last round, and there are no future decisions to improve, so learning which action has the highest reward after taking your final action is instrumentally useless. in the simplest version of the problem, you should just choose the action with the highest expected immediate reward. unless, of course, exploration itself has value to you. if you genuinely enjoy discovering what the unfamiliar action produces, then exploration isn't just an investment in future exploitation - it's actually part of the reward. (this is basically what i was poking at in my inglorious basterds post. i put an ai agent in what was pretty much its last round, and not one response treated the experience it had left as worth anything on its own. it just kept looking for another round.)

this is the thing when it comes to icarus - most conventional interpretations of ambition still treat extraordinary experiences as instrumental! fly higher to accomplish something, discover something useful, prove yourself, become someone important, even romanticized failure narratives tend to preserve that structure. the person attempted something great, and the attempt deserves recognition despite its outcome. but what if icarus wasn't trying to accomplish anything? what if he didn't want to conquer the sun, become famous, or bring some great discovery back to earth? what if he just wanted to know what it was like to be up there? this is a claim about non-instrumental value, or that an experience can be worth having for its own sake, rather than for what it enables afterward. and to be clear, the value doesn't have to be mere pleasure. someone can value having genuinely done something, encountering something cool, or participating in an activity, even if the experience isn't especially enjoyable and produces no lasting achievement. this makes the argument applicable to a surprisingly large fraction of ordinary life. sometimes i follow a research question because it's interesting, even when i have no reason to believe it will produce a paper. there are hobbies i want to learn knowing i probably won't become particularly good at them, nor will they be useful for anything, and also often i want to go places simply because i've never been there. we're so used to defending those choices by imagining eventual benefits that it's easy to overlook the simpler possibility that the activity itself is valuable. (but this still doesn't establish that any price is worth paying for it.)

the math

suppose you have two options: fly safely at a moderate altitude, or ascend toward the sun. let G(a) represent the value you get from undertaking action a itself. this includes things like wonder, discovery, effort, and the experience of flying. let F(a) represent the value of the future that remains available afterward. then, in a deliberately simplified model:

V(a)=E[G(a)+F(a)]V(a) = E[G(a) + F(a)]

G(a) is allowed to be valuable without contributing anything to F(a). we don't have to pretend every interesting experience is an investment in future success. but we also can't just ignore F(a) because we like the immediate experience. to make the tradeoff explicit, suppose flying higher gives icarus some additional experiential value, which we'll call ΔG, but also increases his probability of dying by Δp. call the expected value of the future he'd otherwise have F(safe), and say there are additional opportunity costs ΔC. under simplifying assumptions that those quantities can be compared, and that the future conditional on survival is otherwise the same, we get:

ΔV=ΔG−Δp×F(safe)−ΔC\Delta V = \Delta G - \Delta p \times F(\text{safe}) - \Delta C

flying higher is justified by this model only if the additional experience outweighs the additional expected loss. obviously i don't believe anyone can actually assign reliable numerical utilities to being near the sun, and this formulation ignores an enormous amount of moral and psychological complexity (daedalus, for one, appears nowhere in it, even though the cost of the fall was never only icarus's). some values may not even be meaningfully commensurable. but it identifies the logical burden on the romantic interpretation. the fact that an experience has intrinsic value doesn't imply its value is infinite, and the fact that a sacrifice is chosen doesn't imply it's justified. if icarus knows with certainty that ascending will kill him, he isn't merely trading some possibilities for others. he's trading essentially every future experience for the one he's having now. that's an extraordinary claim about relative value, and a desire to see the sun doesn't settle it. in ordinary life, though, the tradeoffs are usually less extreme. spending every weekend of a season on the water instead of recruiting might cost you some more predictable professional opportunities, but it doesn't eliminate the rest of your life. choosing a less prestigious job or taking a year to learn something completely unrelated to your career can close doors without ending your ability to choose again. so there's a perfectly defensible weaker stance here, or that some possibilities are worth realizing even when doing so destroys other valuable possibilities! we don't need to defend the literal fatal flight to defend that.

but how do you know whether the experience is worth it?

even if we agree that certain experiences have intrinsic value, how are we supposed to know their value before having them? a substantial part of what i was trying to articulate already exists in philosophy. l. a. paul's transformative experience explores choices that change not only what we know but potentially what we care about (i went through her parenthood example in my hyperion post, so i'll spare you the repeat). paul proposes that one way of approaching transformative choices is through their revelatory value: the value of discovering what an experience is like and who you become through it. this is extremely close to what i was trying to say about icarus.

but there are important objections to treating revelation as the basis of a decision. other philosophers have argued that uncertainty about what an experience feels like doesn't make ordinary evidence irrelevant. you can still know that a particular life change is expensive, dangerous, or likely to make you miserable, even if you can't fully anticipate its subjective character. my favorite version of this is the shark problem. paul herself grants that you don't need to know what being eaten alive by sharks is like to know you should stay out of the water, and campbell and mosquera argue that concession is hard to square with the rest of her view. flying into the sun is about as sharky as an outcome gets. and wanting to discover who you'll become doesn't automatically justify choices with major foreseeable costs to yourself or others. that seems right.

the interesting thing is that exploration can have value without becoming an all-purpose justification for taking risks. wanting to find out what it's like to live somewhere else is one reason to move, it doesn't mean you should move to literally any place under literally any circumstances, and the fact that you might become someone who values the decision afterward isn't conclusive either. otherwise we could justify almost any transformative experience by pointing out that future-you might approve of it. so we have a difficult asymmetry, in that we may have to experience something before we fully understand its value, but experiencing it may require giving up things whose value we already understand. i don't think there's a universal decision procedure that resolves this, because we can use evidence, compare opportunity costs, consider our existing commitments, and seek more reversible ways of learning, but eventually some choices involve accepting that we can't know precisely what we're choosing. the fact that the choice is uncertain doesn't make it irrational, only less “obviously correct.”

why not just come back?

suppose icarus could get just as close to the sun, see everything he wanted to see, and return safely. would he take that option? if yes, then the fall was never what made the experience valuable. it was an unfortunate cost he was willing to accept. if no, we need a different explanation. perhaps the danger itself is part of what he wants to experience, or perhaps he finds something meaningful about sacrifice. but then we have to defend that preference separately, rather than just assuming that greater sacrifice makes an experience more profound. people sometimes confuse being willing to pay a cost with valuing the cost itself.

if i leave a comfortable job to experience a radically different life, i might rationally accept the loss of security, but i wouldn't value the new life any less if someone offered me the same experience without the financial sacrifice. i think this is the point at which some versions of romantic icarus become a little self-indulgent. there's an aesthetic appeal to the image of someone who burns for what they love, but the beauty of the image isn't an argument for the rationality of the decision. to push it further, what if icarus had already spent an hour near the sun? would another minute be worth the rest of his life? what about another ten seconds? if the closer he gets, the less additional wonder there is to experience, but the danger continues increasing, then surely there's some point at which going higher stops making sense. the fact that he has come a long way doesn't establish that he should continue, and neither does the fact that the thing he's pursuing is beautiful. gilbert can be completely right about the flight and still not tell us whether those last ten seconds were worth choosing.

so… takeaways from icarus?

in the beginning i listed

  • the flight had value even though it ended in a fall
  • choosing to fly may have been reasonable even if there was a risk of falling
  • choosing to fly would have been reasonable even if he knew with certainty that he would fall.

going back to these 3 interpretations of mine, i think we can conclude the first holds up completely, the second like more or less depending on the numbers (which in real life are way less dramatic than death by sun), and the third, the one i actually wanted, i have by no means been able to prove :( i can't defend the idea that consciously choosing death for an extraordinary experience is automatically admirable, or that a more intense experience necessarily outweighs the entire future it forecloses, but with that said, this doesn’t reduce the story to just a silly warning about flying too high. the middle position is, an experience doesn't need to produce a future benefit to justify choosing it, but its intrinsic value doesn't exempt it from having to justify its costs.

this sounds boringly reasonable when written out like that, but actually i think we routinely violate the first half. we evaluate research through publications, hobbies through skill acquisition, education through employability, relationships through whether they last. even our leisure time somehow has to make us more productive or well-rounded. and there's nothing inherently wrong with caring about those things. i take issue with when every experience has to justify itself by pointing at something that happens afterwards.

at the same time, this gives me something of a correction to my own love of breadth. the romantic icarus could just be someone who commits to one extraordinarily difficult thing, knowing that doing so means giving up a hundred others. we need options because we don't know what we'll want, because circumstances change, because autonomy matters. but those are reasons for keeping possibilities available when their availability serves something we value. and this is the question i want to ask myself more often, am i preserving this option because i have a good reason to believe i'll want it later, or because choosing something else would force me to acknowledge all the lives i won't get to live? it could very well be fear and not caution sending me there.

back to the sketch - i had wanted to capture someone who understood that his wings would melt and decided the sun was worth dying for anyway, but now i think the more interesting moment is slightly earlier, when he can still choose, when he has seen enough to know what he'd be leaving behind, and is trying to decide what he values enough to go toward. ps if he could have seen the sun and returned safely, i hope he would have, bc the sun was the point.

references / things this draws on