Bill Todd <billtodd at foo.mv.com> wrote in message
news:81ql8p$dn9$1 at pyrite.mv.net...
> Are you really stating that, at least in mathematics and physics, 'random'
> and 'not completely deterministic' are exact synonyms? If so, I don't
> believe that this captures the entire sense of the English definition
Since I'm obviously not communicating my reservations very well, I'll give
an example, then try to shut up:
I don't believe that the result of the toss of a two-headed coin is properly
characterized as 'random' simply because there is a small but finite
probability that the coin will wind up on its edge. It's not clear to me
that there is any qualitative difference (though there is plenty of
quantitative difference) between that situation and any other non-uniform
distribution of results (at least where 'non-uniform' is defined as
'possessing some apparent, though not necessarily perfect, structure').
Going beyond that, it's hard not to think that the complete *absence* of a
discernible pattern is not itself significant (I'm less confident of this,
but perhaps it's because nature generally seems to abhor such an absence and
that therefore one has to suspect some artificial cause), at least for a
sufficiently large set of instances - but a *single* such instance, in
isolation, could appear to have a random value.
That definition of 'random' is thus relative to the observer's perceptive
ability, and seems to fit the intent of the original post. I think it
(possibly absent the uniform case) is also consistent with the English
language definition (though as usual with only one of several options): for
example, a quick look at the on-line WWWebster Dictionary yields
1 a : lacking a definite plan, purpose, or pattern b : made, done, or chosen
at random <read random passages from the book>
2 a : relating to, having, or being elements or events with definite
probability of occurrence <random processes> b : being or relating to a set
or to an element of a set each of whose elements has equal probability of
occurrence <a random sample>; also : characterized by procedures designed to
obtain such sets or elements <random sampling>
The first definition (1a) is pretty much the one I've been suggesting. 2a
seems to be the one others have been suggesting. 2b is the one I first
suggested, without thinking about it in sufficient depth.