At 14:04 13/08/07 +0100, Ted Harding wrote (in small part):
>I've not managed to read the News Sceintist on-line (the site crashes
>all my browsers), so will comment without knowing what the NS said.
You haven't missed all that much. The site doesn't crash my browser but,
without a subscription, one only gets 2.5 paragraphs. Furthermore, it
appears that the 'news' item (not really an 'article') only amounts to 477
words in total, so I suspect one would have to go bavk to the source
publication, rather than NS, to learn much more than Paul has told us.
Whilst some of the potential applications mentioned in the NS piece (e.g.
at what point does traffic suddently 'grind to a halt') are seemingly more
complex and interesting (but perhaps better considered in relation to chaos
theory?) it does at first sight seem that (and as Ted also seems to imply)
the model they have studied (seemingly liquid to solid phase transition) is
somewhat over-simplistic, leaving us rather intrigued to discover the full
details of what is being said.
However, on reflection, I wonder if that 'first sight' (at least mine) is,
in fact, itself too naive and over-simplified - and maybe what is being
suggested is much more subtle (and 'molecular') than that - again, maybe
closer to something best dealt with using considerations of chaos
theory. As Ted says, we are used to the concept that temperature of a
collection of 'well stirred' matter is essentially a measure of the mean
kinetic energy of its molecules - i.e. a reflection of the molecules' mean
squared velocity. On that basis, we expect a phase change to occur when
that 'temperature' reaches a particular value, which is 'precisely known'
for a given type of matter at (where appropriate) a given pressure.
However, that normal view is all based on 'averages'. Even when, say, a
liquid is 'perfectly stirred', I can but presume that individual molecules
show a scatter of energies/velocities around the mean for the whole
collection of matter. If that is the case, then the precise moment at
which phase transition occurs might be dependent upon more than 'the
average' - since the greater the scatter of individual molecule, the more
individual molecules would be expected to have energies on the wrong side
of the critical value for phase change, even when the average for the whole
collection of matter was at, or even beyond, that critical value. It
could, for example be that phase transition requires a certain average
'temperature' AND and an instantaneous situation in which more than a
certain proportion of individual molecules are at/below the 'critical level'.
If any of my speculation above is true, then there would presumably be
scope for study of a small number of molecules/elements to provide an
estimate on variability of molecular energy which could assist in
predicting (necessarily probabilistically) exactly when a phase transition
would occur.
... just my wild thoughts on the subject!
>To come back to Gallup and the Holy Grail: Perhaps the outcome
>of an election could be predicted from a few voters, if the
>voters as a whole were sufficiently stirred?
Indeed! Of course, George Gallup was right in saying that (already, not
eventually) it is possible to 'predict' the outcome of an election from a
tiny handful of voters (indeed, even one!) - the question, of course, is
how good that prediction would be! In any event, as George knows only too
well, the problem is not so much a statistical one as a matter of human
behaviour. The problem with political opinion polls is not so much one of
sample selection and sampling error (which can be quantified), but the
fact that the responses given by participants in the polls so often differ
from the truth about how they eventually vote (if, indeed, they do vote)!
Kind Regards,
John
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