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...

Aggregating the Right Moments

Should we prefer to give one person half a million minutes (i.e. one year) more life, or to give a million people one minute more each?  If iterated a million times over (once for each person in the million), the latter repeated choice is clearly better for all (by half a million minutes).  Moreover, as I suggested in comments to that post, if we assume that the million choices are independent of each other in value -- that is, the value of making one such choice does not depend on how the other choices are made -- then it quickly follows that it's better to give the million tiny benefits rather than the one big benefit, even in a one-off choice situation.

However, it's worth flagging that on one very natural (but philosophically distorting) way of imagining the situation, the independence assumption will not hold.