They then go on to develop a mathematical model which they claim produces predictions in good agreement with the empirical evidence of bank note dispersal, which was their intention, and furthermore in good agreement with two sets of data on long distance air travel.

And that, from there point of view, appears to be a step forward in creating models of human dispersal that are testable.

But if you believe that there are alternative distribution models you could put them forward for comparison.

(with “exit the money-tracking system for a long time, for instance in banks”, they are making the point that this does not happen, as you point out).

Thanks.

But seriously, this article talks in terms of “superdiffusion”, as opposed to “diffusion” which may deal with your central objection.

I found this page with a summary of the difference – http://chaos.ph.utexas.edu/research/annulus/rwalk.html

Funnily enough the term used is “Lévy flights”.

I enjoy a good piece of academic smack fu as much as the next guy, and the point of the post is very very VERY well taken. In fact, I sent the previous round of the debate to my students: we’re applied math types working in the life sciences, and I’m keenly aware of what we don’t know (which is why we work with experts in the field, and make sure we publish at least some of our work in actual specialty journals, to keep us honest). I keep warning my students about the dangers of falling into the math/physics/engineering arrogance trap.

But…

It would be nice to have another post one of these days on the conjugate outrage: the people in not-quite-yet mathematized fields that take whatever exotic thing they’ve just read about (“chaos theory”, 1/f noise, connectionism, Bell’s theorem, string theory, quantum computing, or the ever-popular “complexity”…) learn to repeat the jargon in knowing, quasi-mystical tones and and then mangle the living shit out of it in order to make a really harebrained, weakly supported model, or worse “theory”.

And then there’s the whole issue of disciplinary possessiveness and turf protection. I’m not saying that Daniel is motivated in this way, but the fact is that often people from the mathematical sciences do indeed have much to offer, but this capacity is viewed (by the paranoid) as a threat and their work dismissed, often using the very same style of argument presented above. The arrogance cuts both ways.

For a disease to come in internationally, I’d guess that the two major routes would be Ford workers/visitors (and the Ford people would be white collar), or international students coming to Ann Arbor. Now, the cash pattern would be different, because the Ford people would use a Ford credit card as much as possible, for ease of reimbursement. There might be a very low cash trace of their activies.

In a sense, this might be like the difference between diffusion in a system with a simple topology, and a system with a complex topology+major drivers. Perhaps like the difference between a lab glassware arrangement, and an organism.

A diffusion process usually considers sub-populations. One chemical will through another . But yes, overall, the population of molcules as a whole is not diffusing. Which is beside the point.

unlike molecules I suppose. All I can see here is a rather large chip on Daniel’s shoulder. There is no intelligent critique.

Some major German banks only use brand-new notes for ATMs and all notes are perfect. I know this to be true. But from one other major bank’s ATMs I received counterfeit DM banknotes (plural) before the DM was phased out. This was quite a shock.

Back in my own increasingly cashless society I watch the money that passes through my own hands. Well over 50% of the €uro banknotes I see does not come from this country.

But coinage does stick around. Before the €uro, we were told that all our coins would disperse through out Europe within a year, and we wouldn’t see them again. But this hasn’t happened. It’s quite rare that I see a foreign coin, and when I checked my coins last night, not a single one out of 24 was foreign.

We are pretty off topic here but actually they do. Banks don’t keep an “inventory” of notes at all; they keep as few as possible because they are non-interest bearing securities – you can actually make a fairly decent living doing behavioural scoring on patterns of ATM withdrawals so as to advise banks on how to minimise the amount of notes they have to float to keep the machines stocked.

Because of this, the notes that are in a bank are either a) ATM notes which are by definition held on a LIFO basis because that’s the way the machines are stacked or b) notes held at the counter, which have to be counted and moved back to the vault at close of business every day, a process which degrades them. Notes that have been held in a till (and shifted back and forth to the vault every day) for too long won’t be of sufficient quality to be put in an ATM after a while and this is a bad thing from the point of view of the bank as ATM-fresh notes are the kind they want to have.

Right, but if you want to track how a disease spread inside Los Angeles from a person who arrived by plane at the airport, diffusion might be an excellent way of doing so.

The methodology provides some insight which gets modified by other insights. This may or may not invalidate the starting model.

But even your mention of New York to LA doesn’t invalidate the diffusion analogy entirely. Fill a maze with water. Introduce a dye at one end of the maze. It will spread by diffusion, but be limited in its direct path by the maze walls. The method of spreading remains diffusion even if it has to go through distance 3X (because of the walls_to get to a location that is only 2X units from the initial starting point (if you measure without the walls).

Yes, simple diffusion can’t cover all the variables possible in a disease outbreak. But it has useful insights inside a local area. It tends not to fully explain the jumps from local area to local area.