Towards quantifying the good of success

Yesterday, I argued that the good of success contributes to one’s well-being at the time of one’s striving for success rather than at the time of the success itself.

It seems, then, that the longer you are striving, the longer the amount of time that you are having the good of success. Is that right?

We do think that way. You work on a book for five years. Success is sweeter than if you work on a book for one year.

But only other things being equal. It’s not really the length of time by itself. It’s something like your total personal investment in the project, to which time is only one contribution. Gently churning butter for an hour while multitasking other things (using a pedal-powered churn, for instance) does not get you more good of success than churning butter with maximum effort for fifteen minutes, if the outputs are the same.

We might imagine—I am not sure this is right—that the good of success is variably spread out over the time of striving in proportion to the degree of striving at any given time.

What else goes into the value of success besides total personal investment? Another ingredient is the actual value of the product. If you’ve decided to count the hairs on your toes, success is worth very little. Furthermore, the actual value of the product needs to be reduced in proportion to the degree to which you contributed.

Thus, if Alice and Bob both churned butter and produced n pounds, the value of the output is something like bn, where b is the value of butter per pound. If the investments put in by Alice and Bob are I_A and I_B, then Alice’s share of the value is bnI_A/(I_A+I_B). But since the value of success is proportional also to the absolute investment, I think that the considerations given thus far yield a formula for the value of success for Alice proportional to:

• bnI_A²/(I_A+I_B).

Next note that one way to think about the degree to which you contributed is to think as above—what fraction of the total investment is yours. However, even if you are the only person working on the project, the degree of your contribution may be low. Let’s say that you have moved into a house with a mint bush. Mint bushes are aggressive. They grow well with little care (or so we’ve found). But you do water it. The mint bush added half a pound to its weight at the end of the season. You don’t, however, get credit for all of that pound, since even if you hadn’t watered it, it would likely have grown, just not as much. So you only get credit for the portion of the output that is “yours”. Moreover, sometimes things work probabilistically. If the success is mostly a matter of chance given your investment, I think you only get good-of-success credit in proportion to the chance of success—but I am not completely sure of this.

But here is something that makes me a little uncertain of the above reasoning. Suppose that you have some process where the output is linearly dependent on the investment of effort. You invest I, and you get something of value cI for some proportionality constant c. By the above account, to get the value of success, you should multiply this by I again, since the value of success is proportional to both the value of the output and the effort put in. Thus, you get cI². But is it really the case that when you double the effort you quadruple the value of the success? Maybe. That would be interesting! Or are we double-counting I?

Another question. When we talk about the value of the output, is that the objective value, or the value you put on it, or some combination of the two? Counting the hairs on your toes has little objective value, but what if you think it has significant value? Doesn’t success then have significant value? I suspect not.

But what about activities where the value comes only from your pursuit, such as when you try to win at solitaire or run a mile as fast as you can? In those cases it’s harder to separate the value of the output from the value you put on it. My guess is that in those cases there is still an objective value of the output, but this objective value is imposed by your exercise of normative power—by pursuing certain kinds of goals we can make the goal have value.

Let’s come back to counting hairs on toes. If you’re doing it solely for the sake of the value of knowledge, this has (in typical circumstances) little objective value. But if your hobby is counting difficult to count things, then maybe there is additional value, beyond that of trivial knowledge, in the result.

I suspect there are further complications. Human normativity is messy.

And don’t ask me how this applies to God. On the one hand, it takes no effort for God to produce any effect. On the other hand, by divine simplicity God is perfectly invested in everything he does. But since my metaethics is kind-relative, I am happy with the idea that this will go very differently for God than for us.

"Commitment": Phenomenology at the rock wall

If you watch people rock climbing enough (in my case, only in the gym, as I have seen disturbing outdoor climbing safety numbers, while gym climbing safety numbers are excellent), you will hear a climber get advised to “commit” more. The context is usually a dynamic move for a hold, one where the climber’s momentum is essential to getting into position to secure the hold, with the paradigm example being a literal jump. The main physiological brunt of the advice to “commit” is to put greater focused effort into jumping higher, reaching further, grabbing more strongly, etc. But the phenomenological brunt of the advice is to will more strongly, with greater, well, commitment. And sometimes when one misses a move, one feels the miss as due to a lack of commitment, a failure to will strongly enough.

While once I heard someone at the gym say “Commit like you’re married to it”, the notion of commitment here seems quite different from the ordinary notion tied to relationships and long-term projects. The most obvious difference is that of time. In the ordinary case, a central component of commitment is a willingness to stick to something for an extended period of time. The climber’s “commitment” lasts at most a second or two. This results in what seems to be a qualitatively different phenomenology, but it could still be that the difference is quantitative, much as living through a week and living through a second only feels qualitatively different.

But there seems to be a more obviously qualitative difference. The rock-climbing sense of “commit” is essentially occurrent: there is an actual expending of effort. But the ordinary sense is largely dispositional: one would expend the effort if it were called for. Moreover, the rock-climbing sense of the word is typically tied to near-maximal effort, while in the ordinary sense one counts as committed to a project as long as one is willing to expend a reasonable amount of effort. In other words, when it would be unreasonable to expend a certain degree of effort, in the ordinary sense of the word one is not falling short of commitment: the employee unwilling to sacrifice a marriage to the job is not short on commitment to the job. The rock-climbing sense of commitment is not tied to reasonableness: a climber who holds back on a move out of a reasonable judgment that near-maximal effort would be too likely to result in an injury is failing to commit on the move—and typically is doing the right thing under the circumstances (of course in both sense of the word “commit”, there are times when failure to commit is the right thing to do).

Finally, the ordinary sense of divides into normative and non-normative commitment. Normative commitment is a kind of promise—implicit perhaps—while non-normative commitment is an actual dispositional state. Each can exist without the other (though it is typically vicious when the normative exists without the dispositional). In the climbing case, normally the normative component is missing: one hasn’t done anything promise-like.

Here is a puzzle. Bracket the cases where one holds back to avoid an over-use or impact injury (I would guess, without actually looking up the medical data, that when one is expanding more effort, one is more tense and injury is likely to be worse). One also understands why someone might fail to commit to a job or a relationship, in either the normative or the non-normative sense: a better thing might come one’s way. But when one is in the middle of a strenous climbing move, one typically isn’t thinking that one might have something better one could do with this second of one’s time. So: Why would someone fail to commit?

My phenomenology answers in two ways. First and foremost, fear of failure. This is rationally puzzling. One knows that a failure to commit to a climbing move increases the probability of failure. So at first sight, it seems like someone who goes to a dog show out of a fear of dogs (which is different from the understandable case of someone who goes to a dog show because of a fear of dogs, e.g., in order to fight the fear or in order to have a scary experience). But I think there is actually something potentially rational here. There are two senses of failure. One sense is external: one is failing to meet some outside standard. The second sense is internal to action: one is failing to do what one is trying to do. The two can be at cross-purposes: if I have decided to throw a table tennis match, my gaining a point can be a failure in the action-internal sense but is a success in the external sense.

In climbing, outside of competitive settings, it is the action-internal sense that tends to be more salient: we set our own goals, and what constitutes them as our goals is our willing of them. Is my goal to climb this route, to see how hard it is, or just to get some exercise? It’s all in what I am trying to do.

But in the action-internal sense, generally the badness of a failure increases with the degree to which one is trying. If I am not trying very hard, my failure is not very bad in the action-internal sense. (Of course, in some cases, my failure to try very hard might bad in some external sense, even a moral one—but it might not be.) So by trying less hard, one is minimizing the badness of a failure. There is a complex rational calculus here, whether or not one takes into account risk averseness. It is easy to see how one might decide, correctly or not, that giving significantly less than one’s greatest effort is the best option (and this is true even without risk averseness).

The secondary, but also interesting, reason that my phenomenology gives for a refusal to commit is that effort can be hard and unpleasant.

Effortlessness and omnipotence

All of the extant definitions of omnipotence are missing what seems to me to be an important ingredient. A typical definition says something like: "God can do anything that's logically possible." But that's not quite enough. One needs to specify that God can do everything effortlessly. This is an easy emendation, of course, but an important one.

Effort

A concept that I haven't seen much contemporary discussion of is effort. A jstor title search finds 18 entries, most notably an 1897 piece by Dewey. But there is very little recent material: There are a few interesting-looking pieces from the 70s (one on effort and desert, and two on effort and freedom of the will), and there is 2009 Business ethics piece on withholding job effort. The subject seems to have been largely neglected in recent times, though it was an active area of interest at the end of the 19th century (in addition to the Dewey piece, there is William James' 1880 Feeling of Effort.

So, if some graduate student needs a project in moral psychology or metaphysics, effort might be worth some attention. A dollop of history—thinking about conatus, say—wouldn't be amiss.

What made me think of the topic was struggling with wind in a canoe, and being struck by the idea that the feeling of effort or struggle, while unpleasant, does not seem to be classifiable as even prima facie evil.

Ability comes in degrees. I can easily lift a pound. With a moderate effort I can lift forty. And over that, effort significantly increases and ability peters out. There is some kind of a connection between ability and effort. Where ability is limited, at the edge of ability there seems to be a need for effort. So it may be that thinking about effort would help advance some of our understanding of ability, and hence of freedom of the will. But that's speculation. (On a connection with freedom, also see this and the responses in the above-mentioned jstor search.)

Here's an argument that has just occurred to me. The more effort of will, mind or muscle it would take for x to A, the less we blame x for failing to A. But the limiting case of increased need for effort is impossibility. So if Aing is impossible to x, for reasons of will, mind or muscle, then we will least, if at all, blame x for failing to A. This is a kind of principle of alternate possibilities. I am not that impressed with this argument. While the limiting case of increased need for effort is an impossibility of some sort, there may be sorts of impossibility that are not limiting cases of increased need for effort.