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?