Thursday, October 02, 2008

A refined theory of wind in cambridge

in this continuing series on the problem of wind in Cambridge, and the fact that whatever direction you cycle in, it is against you, we apply the theory of complex dynamical systems, and topological manifolds to prove that, unless Cambridge is converted into a toroidal vertex, the problem is insurmountable, just like some of the bikes.

Essentially there is a set of subjects with a power law distrbution of popularity, and hence there is a distribution of people and rooms that have to be fit together across a set of spaces over time - aside from the known computationally harsh (technical term) problem of scheduling the rooms at all, there is a packing problem - now this means that there are always different numbers of people going in each direction from A->B, and then after a lecture from B->A. Consider then the time of events. One arranges for lectures to be in fixed length slots (for no other reason than otherwise the schedule would be temporally as well as spatially intractable) and yet this creates a set of waves of air across cambridge with fractal vorticies. Now consider the preferred size slot. Clearly there is a tendancy for people to arrive just in time (or just too late) for a lecture. This has a knock on (off) effect which re-enforces the pessimal slot length choice.

If it was an ecosystem (and we used some natural selection - e.g. based on energy left mapping to chances of passing) then we could fail more people, and find a more linear relationship between class size, room size and slot size and then easily solve the packing problem, but the system is essentially sufficiently large that the chances of this are zero.

In the next piece, I will look at whether combined oxygen and cash would be a solution to the market turmoils created by subprime loans.

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