 |
 |
A point worth making is that in the ideal gas laws as derived in classical statistical mechanics it’s assumed, among other things, that the particles don’t have any relevant macroscopic properties such as size or weight.
This assumption is obviously rather debatable in some of the proposed applications (e.g. traffic jams). However, there is work in progress on so-called granular gases (both theoretical and experimental – some people have fun with agitating frames containing a layer of ball-bearings (i.e. 2-D gas) …
The following link (found by Googling "granular gases" + "stable distribution") looks like a good starting point for beginners
http://theses.ulb.ac.be/ETD-db/collection/available/ULBetd-10172005-120819/unrestricted/thesis.pdf
An inexpert skim of some of this suggests that power-law tails and distributions from the stable family characterise these far-from-equilibrium systems (the equilibrium position of a “gas” of heavy ball-bearings is clearly a heap, not a cloud).
Best wishes,
Julian
From: email list for Radical Statistics [mailto:[log in to unmask]] On Behalf Of BYRNE D.S.
Sent: 16 August 2007 15:05
To: [log in to unmask]
Subject: Re: [RADSTATS] The holy grail?
This is all about simple complexity and may or may not be correct in relation to such simple complex systems. By a simple complex system I mean a system where emergence occurs solely as a result of interaction among the elements of the system. So for example if we look at a flock of starlings changes in flight pattern result from each bird observing very simple rules in relation to its neighbours but the whole flock generally makes quite complex changes of direction as one, although even here groups may split off. Another example is traffic jams, and Gawd help us all, perhaps financial markets.
The key issue would be identifying when a phase shift is about to occur. If there is a constant monitoring of information, or of course in reality a lot of repeated observations, across large numbers of cases, then we might see that point BUT that would seem to destroy the object of the whole exercise since we have to look at lots of cases to know when we can derive information from a few cases. Financial markets might be an example because aggregate data is generated and can be tracked so monitoring some cases might be enough BUT since the cases would be human subjects as market makers the monitoring might change their behaviour.
Crowds are another matter and again how would you monitor - CCTV I suppose. So expect to have the polises charge you on a demonstration because five people are moving so as to trigger a response - recipe for revolution perhaps?
David Byrne
From: email list for Radical Statistics on behalf of Paul Spicker
Sent: Mon 8/13/2007 1:12 PM
To: [log in to unmask]
Subject: The holy grail?
There is a remarkable claim in the "news" section of New Scientist this week, in a piece entitled "Predicting change, not a moment too soon". A piece in Physical Review E (which I don't have access to: ref DOI: 10.1103/PhysRevE.75.051125) claims that changes in the behaviour of swarms, crowds, traffic jams or similar systems can be predicted by monitoring a very small number of particles. "Using a mathematical model of a phase transition, they attempted to detect an oncoming change by monitoring only a small fraction of the elements in the system. They found that they could do so by focusing on the 'mutual information' shared by those elements. ...In a disordered state, looking at a particle gives no information about what others are doing. As the system approaches a phase transformation, the mutual information betwen particles increases, so that one particle's behaviour does provide information about the speed and trajectory of other particles. ... The researcher's simulations suggest that in a crowd of, say, 1000 people, observations on as few as five people might be sufficient."
I think it was George Gallup who suggested that it might be ultimately be possible to predict election results using five people. I'm not, sure, though, that I believe it. If anyone's in a position to appraise the technique it would be fascinating to know about it.
Paul Spicker
******************************************************
Please note that if you press the 'Reply' button your
message will go only to the sender of this message.
If you want to reply to the whole list, use your mailer's
'Reply-to-All' button to send your message automatically
to [log in to unmask]
Disclaimer: The messages sent to this list are the views of the sender and cannot be assumed to be representative of the range of views held by subscribers to the Radical Statistics Group. To find out more about Radical Statistics and its aims and activities and read current and past issues of our newsletter you are invited to visit our web site www.radstats.org.uk.
*******************************************************
This email has been scanned for all viruses by the MessageLabs Email
Security System.