Sunday, May 21, 2017

Nanoseconds that Matter

Take an arbitrarily short duration -- I'll speak of 'nanoseconds' for familiarity and convenience, but you could use an even smaller measure of time.  Could removing a mere (arbitrary) nanosecond from your life plausibly make your life any worse on the whole?  You might think not, on the basis that "surely nothing of any significance could occur during such a short time."  On the other hand, if you remove all the nanoseconds then we have no life left at all, which is certainly a significant difference.  Is it coherent to think that many individually worthless moments might collectively have value?

I have my doubts, and have previously suggested that such putatively vague goods (as a "sufficient duration to matter") are better understood as graded and/or involving threshold effects.  A friend suggested minuscule scales of time as a challenge to this view, but I think my approach still makes good sense of this case.  Here's how...


Some goods are extended in duration and plausibly independent / proportioned in value such that 1/n of the duration has 1/n of the value of the whole.  Hedonic pleasure is perhaps the paradigm example of this.  A tiny (but non-zero) period of pleasure can thus be expected to have a correspondingly tiny (but non-zero) value.

Is that enough to refute the claim that no nanoseconds matter?  Well, one might push back against my counterexample by insisting that a mere nanosecond (or picosecond, or whatever) can make no difference to the actual amount of pleasure felt.  This claim might be defended in either of two ways:

(1) appeal to some kind of 'discernibility' criterion, such that if you cannot discriminate between an experience lasting an extra nanosecond and one without, then there is no difference in the felt, subjective experience. But this fails, because we know that indiscriminability is insufficient for phenomenal identity (since the former relation is intransitive and identity isn't).

(2) the critic might claim that during a sufficiently short period of time no physical processing in the brain sufficient to give rise to (continued) experience will have occurred.  But in that case, we have simply transformed this into a chunking case: The minimum phenomenal duration must, we're assuming, extend for longer (let's say it is 100 nanoseconds), in which case there must be some extension of brain processing in physical time sufficient to give rise to 100 nanoseconds more phenomenal experience.  Assuming that this happens, on average, once every 100 nanoseconds of physical time, it would seem that an arbitrary 1 ns extention of physical processing gives you a 1/100 chance of getting a bonus 100 ns of experience.  Even though 99% of nanoseconds have now been rendered worthless, the remaining 1% have their value boosted one hundredfold, returning the expected value of the nanosecond to our (slight but non-zero) starting point.

So: some nanoseconds (or picoseconds, etc.) matter.  Further, a similar story may be told about various non-hedonic goods.  These will likewise tend to be graded, building up in value over time, perhaps with elements of 'chunking' or threshold effects here or there.  Consider having an idea, or writing a book.  It might at first seem inconceivable that a mere nanosecond could ever make a difference to such projects.  But there will be some crucial period during which the idea becomes more fully-formed and clear in your mind, and its value may increase with its clarity and completeness, and some nanoseconds simply must make a difference to these dimensions (since they involve precise physical mechanisms such as firing neurons).  Similarly when writing a book, there will be some nanosecond that makes the difference between your successfully pressing a key on your keyboard vs failing to do so.  Obviously the vast majority of nanoseconds are not going to be of great value, but that is not needed. All we need is value proportional to their duration, which is very small indeed.  Can you really see any grounds to deny even that?

1 comment:

  1. I've been thinking about this a bit more -- and apologies if you've already deatl with this somewhere. By this point you've spent so much time thinking about this family of topics that there are a lot of parts of it spread across several posts! I always worry that I'm fatally ignoring something that you dealt with explicitly in a paragraph in a linked post that I read a little too quickly. And it's particularly an issue here, since I'm rusty on matters of expected value, which increases my chance of missing some key qualification.

    I'm not sure (1) is completely handled by the intransitivity argument. The argument linked to in the post only considers phenomenal experience; but as I noted in the previous, we actually need to be considering some mix of phenomenal experience and deliberate action. Action is the more obvious problem here: what kind of action-difference does a nanosecond allow? And for an action-difference the time difference needs to be (1) at least indirectly discernible, otherwise it can't be taken into account and (2) such that there is room for at least partial control with respect to that difference in duration. Both of these start running into problems below a certain threshold of duration. Thus it is difficult to see how a nanosecond (much less a picosecond) could, under any circumstances at all, lead to greater richness, complexity, or value-conduciveness of action. There is a cumulative character to action, so in those terms, we do seem to have reason to think that the whole is greater than the sum of its parts. Even if a nanosecond's difference does make difference, if you give two nanoseconds it seems plausible that the second nanosecond, allowing one to build on the first, is massively more valuable than the first. This raises the possibility that a half a million minutes for one person may involve far greater action-value than single minutes distributed among half a million people, all other things being equal. I think this is a better way of looking at the worry about chunking that I mentioned in the comment on the previous post, and it does a better job of taking into account the points you make in this post that are relevant.

    (It occurs to me that this is one way of thinking about the point you raised in the previous post, the difference between a minute on one's death-bed and a minute in the midst of your life: if there is a cumulative effect, then the more time follows it, the greater the value due to later minutes allowing one to build on prior ones, even without counting anything else. But this significantly complicates any attempt to compare a lot of little gifts of time with a few big gifts of time.)

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