Tuesday, November 29, 2011

Six Degrees of My Umbrella

I have inadvertently started a variant of Stanley Milgram's small-world problem with my attempt to get back the umbrella I accidentally left in Bath today.

First, I checked to confirm that I left it in Chris Budd's office rather than in a random place in Bath. The obvious possibility was to get it back to Oxford next Tuesday, as next week's seminar speaker is also from Oxford's Mathematical Institute. And then presumably I could get it back shortly thereafter.

But then Chris e-mailed me to point out that several of the complex systems people from Bath are attending a complex systems workshop in Oxford this Thursday. He called the conference 'cow' (which doesn't mean anything to me aside from synchronization issues, and cow sync isn't relevant here), but I think he means the Scaling in Social Networks workshop that is being held by CABDyN on Thursday. I can't go to this workshop, so either those people can go to Dartington House reception or the Somerville lodge, but it would be more convenient for them to just give this to somebody I know who is attending the same workshop. So once I confirm the identify of the workshop, my next step is to e-mail people who I think will be attending it to arrange for them to pick up the umbrella and then to give it to me.

As another variant, I still am in possession of copies of a pair of PhD theses that passed from Jaroslav Stark to Heather Harrington and then to me. These are copies of the theses written by one of my collaborators (Ricardo Carretero-González) and his wife, and the question is when is the next time and place I will see him---or whether I can get it back to them faster via an intermediary who will see him before I will but who I will see before he will.

So, essentially, the problem becomes not just to reach the target but to do it as fast as possible and consider temporal ordering as part of the whole process. There is perhaps some penalty to increasing the number of steps, but there is definitely a penalty for the amount of total time between the start of passing the 'message' (or the umbrella or the PhD theses) and the time it reaches the destination, and there can also be a penalty for 'inconvenience' from e.g. having to walk from the building where a workshop is being held to another building.

One could actually make a nice generalization of some message-passing problems by thinking about this in a tractable mathematical context. An appropriate abstract model with these kinds of effects would be a pretty neat mathematical problem, actually.

See, my research is practical!

Another comment: Sometimes its strange how inspiration is born.

Also: I know there has been some work on message-passing (and algorithms for it), but I believe that this leads to a different problem than what has been considered thus far.

And (hopefully) finally: It turns out that "COW" = "Camridge Oxford Warwick" and is an algebra and geometry meeting that moves around rather than the complex systems workshop. But my ideas still make sense. :)

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