### Wednesday, April 06, 2005

## Anjo Anjewierden: Comment on Getting Wet

In Anjo Anjewierden: Comment on Getting Wet Anjo describes a model of a blogging community as a network of pipes. We have been discussing this earlier and I originally proposed him an electrical model which is very similar physically, where links are modelled as resistors.

Actually I think the electrical network model is slightly richer. At first approximation you could make the "resistance" R of each link uniform say 1 Ohm. But on second thought there is also a characteristic time lag to be taken into account : the time in (days say) it typically takes for the reader to discover the link. In this electrical model the easiest way to model that (IMHO) is to to think of a blogger as a capicitor that is being charged. For a lag of a day with a 1 ohm resistor, the capacitance C would be 24*60*60 Farad. As is well known in electrical engineering, this makes the blog a frequency dependent purely imaginary node in the resistance network.

Z = 2pi sqrt(-1) f C

I find it sort of amusing that blogs turn up imaginary but as Robert Dijkgraaf pointed out in the NRC this weekend, nature is certainly complex. Every time a blog enters the network at time T that corresponds to an electrical (delta) pulse with spectrum exp( 2pi sqrt(-1) fT ) / 2pi.

Note that this gives the model two degrees of freedom : R and C.

This capitance model should give qualitatively different results from those of a pure resistor network with a more or less static current distribution. The reason is that the pulses contain lots of high frequency components and those HF components see little resistance in the capicitors. However at the edges of the network the pulses are smeared out and you effectively see a net avarage direct current component (this is how the rectifier in a computers powersupply works). That direct current component then trickles through slowly to other networks if they are connected.

What this models intuitively is that within a lively community the timescales for the spread of information can be quite different from that between the edges of two communities.

By the way we should only count links pointing _to_ a blog as they can be read by someone else and allow information to be passed on to someone else. In a related vein the model ignores the fact that information streams cannot be negative. We should just ignore this, unless we get large negative *average* flows.

Actually I think the electrical network model is slightly richer. At first approximation you could make the "resistance" R of each link uniform say 1 Ohm. But on second thought there is also a characteristic time lag to be taken into account : the time in (days say) it typically takes for the reader to discover the link. In this electrical model the easiest way to model that (IMHO) is to to think of a blogger as a capicitor that is being charged. For a lag of a day with a 1 ohm resistor, the capacitance C would be 24*60*60 Farad. As is well known in electrical engineering, this makes the blog a frequency dependent purely imaginary node in the resistance network.

Z = 2pi sqrt(-1) f C

I find it sort of amusing that blogs turn up imaginary but as Robert Dijkgraaf pointed out in the NRC this weekend, nature is certainly complex. Every time a blog enters the network at time T that corresponds to an electrical (delta) pulse with spectrum exp( 2pi sqrt(-1) fT ) / 2pi.

Note that this gives the model two degrees of freedom : R and C.

This capitance model should give qualitatively different results from those of a pure resistor network with a more or less static current distribution. The reason is that the pulses contain lots of high frequency components and those HF components see little resistance in the capicitors. However at the edges of the network the pulses are smeared out and you effectively see a net avarage direct current component (this is how the rectifier in a computers powersupply works). That direct current component then trickles through slowly to other networks if they are connected.

What this models intuitively is that within a lively community the timescales for the spread of information can be quite different from that between the edges of two communities.

By the way we should only count links pointing _to_ a blog as they can be read by someone else and allow information to be passed on to someone else. In a related vein the model ignores the fact that information streams cannot be negative. We should just ignore this, unless we get large negative *average* flows.

Comments:
Post a Comment

© Copyright 2004-2006 Rogier Brussee.These are my personal views and do not necessarily reflect those of my employer.