Physicists in action, latest in an occasional series

by Daniel on January 27, 2006

Here we go again … this story has been making the news recently, about some types at the Max Planck Institute for Dynamics and Self-Organization. They have got some data from a site that tracks dollar bills and used it to make a statistical model of human travel, which will apparently save us all from bird flu.

I saw the news story in the Guardian and thought “I wonder if they will discover that the phenomenon they are studying is described by a power law?” … and the answer is yes they do.

I then thought “I wonder if they will more or less entirely ignore the existing literature on epidemics?” … and as far as I can see the answer is yes they do.

And finally I thought “It would be presumably too much to hope that there is a serious attempt made to test the power law model against alternative distributional assumptions” … and the answer is yes, it would be too much to hope.

They’re also quite naive about banknotes. At one point in the paper, they seem to believe that bank notes “exit the money-tracking system for a long time, for instance in banks”. Of course, banks don’t contain large piles of banknotes sitting around for months on end; the only bank notes you will find in a bank are the ones being stored in the ATMs and the tills, and these obviously turn over pretty rapidly. Furthermore, I would guess that the average human being makes fewer journeys to a banknote sorting centre than the average banknote (I suspect that several of the odd statistical properties that they found relate to the locations of sorting centres in the US). Humph.

People have been laughing at physicists for this sort of thing for quite a while now but with no noticeable effect. It’s all very laudable that they’re taking a bit of interest, but we still clearly haven’t conquered the hard-science arrogance problem yet …

Edit: Actually thinking about it, this is not an entirely worthless paper. If they are correct to claim that epidemic models use a diffusion process to model travelling humans (and there is nothing in the paper to make me think they have done an exhaustive literature search) then epidemic models are being silly and should stop. Human beings don’t diffuse – they go from one specific place to another. Otoh I seem to remember a lot of quite detailed modelling of SARS which certainly did take airline routes into account so I suspect that the diffusion assumption is really only found in toy models in basic-level textbooks.

{ 42 comments }

1

foo 01.27.06 at 11:01 am

Not arguing, just asking (two questions):

If someone was going to quote the existing literature on epidemics, where would you suggest they start? (My untrained eye sees five references, out of twenty-three, to work on epidemics. Are these the wrong references? Or incomplete? Are there major papers missing?)

Also, if “several of the odd statistical properties that they found relate to the locations of sorting centres in the US,” where does the correlation with the BTS and airline data come in? Is that spurious, or…?

I’m (really) not trying to be argumentative. Just curious. Thank you for writing this post…

2

Dan Simon 01.27.06 at 11:55 am

we still clearly haven’t conquered the hard-science arrogance problem yet …

You mean the physics arrogance problem, right? As a computer scientist who has occasionally had to deal with physicists, I can assure you that (1) not every “hard science” (if CS can be said to be one) treats other fields as if they don’t exist, and (2) physicists treat us with every bit as much ignorant contempt as they treat you.

3

Dan K 01.27.06 at 12:02 pm

What, you mean that ‘real’ scientists are dilettante social scientists? Imagine that.

4

Nabakov 01.27.06 at 12:34 pm

I got a nosebleed reading that linked piece so I couldn’t work if they attempted to distingush amongst denominations. And if so, what demominations would be most likely handled by frequent flyers?

5

kw 01.27.06 at 12:50 pm

“And if so, what demominations would be most likely handled by frequent flyers?”

20s or 5s: the former because of ATMs, the latter because of drinks.

6

Bill Tozier 01.27.06 at 1:06 pm

I have just overheard–for the fourth time–a respected faculty member in my new department opining that, “What those people on eBay need is a good stochastic-calculus-based insurance scheme to manage the risk that an unscrupulous seller will not send them the thing they bought. See this simple formula, derived from first principles, that captures all the uncertainty about the transaction in this two-variable function of the seller’s feedback rating? There you have it!”

In other words: It ain’t just physicists.

I am preparing a followup paper, building on my work with Dr. Shalizi, with the working title of “A Simple Model of Simple Models: Proof that the upper bound of model utility inversely relates to the spontaneous reinvention rate.”

I have it down to one variable, don’t you see. I am collecting my strength for the last push to reduce the model to zero variables. But I see the light at the end of the tunnel….

7

joe o 01.27.06 at 1:18 pm

I just found one of those marked up bills in my pocket this morning. According to the website, it hasn’t gone very far.

8

tim 01.27.06 at 1:19 pm

…not every “hard science” (if CS can be said to be one)…

It can’t. In fact, it can’t even be called a science. The tip off is when a field finds it necessary to make “science” part of its name because it wouldn’t otherwise be apparent.

Compare:

Physics, Chemistry , Biology – real science

Political Science, Social Science, Library Science, Computer Science – not real science

Not that there’s anything wrong with that. Some of my best friends are computer scientists.

9

A. Random Physicist 01.27.06 at 1:22 pm

It’s also not just the social sciences. The physics literature contains lots of papers on (for example) protein folding whose abstracts are essentially: “Hey, I know about phenomenon X from my work on [solitons, nonlinear lattices, mean field theory, etc]. Here’s a toy model of a protein (that just happens to be very similar to the model I’ve already studied). Phenomenon X occurs in this model! Maybe phenomenon X is the key to understanding protein folding!”

I can understand how that stuff appears in the physics literature (publish or perish, after all), but with that said, aren’t the editors and referees at Nature the real villians in this particular story? Don’t they know any appropriate reviewers for papers like these?

10

Kieran Healy 01.27.06 at 1:33 pm

The tip off is when a field finds it necessary to make “science” part of its name

Sociology is coming out well ahead of materials science then. Good news for me, bad news for the buildings I inhabit, I guess.

11

pedro 01.27.06 at 1:37 pm

I sympathize with D^2, but I also agree with a. random physicist. Isn’t it a bit too much to attribute arrogance to these particular physicists? Negligence is one thing, but there’s no reason to believe–a priori–that they espouse the arrogant attitude with which *some* practitioners of the former queen of sciences approach other subjects.

12

Todd 01.27.06 at 1:55 pm

Sociology is coming out well ahead of materials science then. Good news for me, bad news for the buildings I inhabit, I guess.

You forgot Neuroscience. Bad news for the ol’ noggin’, too.

13

Sebastian Holsclaw 01.27.06 at 2:18 pm

RE: “Human beings don’t diffuse – they go from one specific place to another. Otoh I seem to remember a lot of quite detailed modelling of SARS which certainly did take airline routes into account so I suspect that the diffusion assumption is really only found in toy models in basic-level textbooks.”

I’m a complete layman in this area, so take it for the very little its worth.

The “humans go from one specific place to another” objection isn’t really much of an objection. Individual humans do, but in describing groups diffusion might be a perfectly servicable model for locales. You have to talk about planes or other long-distance vehicles to deal with transmission from one local area to another, but diffusion might be fine in describing transmission in a local area.

Now it may be a perfectly horrible model on further examination. I’m just suggesting that the idea shouldn’t be dismissed just because individuals don’t difuse.

14

promo 01.27.06 at 2:40 pm

“Human beings don’t diffuse – they go from one specific place to another. Otoh I seem to remember a lot of quite detailed modelling of SARS which certainly did take airline routes into account so I suspect that the diffusion assumption is really only found in toy models in basic-level textbooks.”

The statement about human beings diffusing is naive-diffusion is a statistical concept. Even specific particles undergoing brownian motion go from one place to another. Also, if this model is so naive and basic so as to be found in basic textbooks, isn’t it a bit surprising that it is not well known to the social scientists here.

Physicists would not be doing this sort of stuff if there were already any social scientists using these approaches in a significant manner.

15

Steve LaBonne 01.27.06 at 2:49 pm

Indeed, Sebastian, since one could also use Daniel’s objection to “invalidate” statistical mechanics- individual molecules don’t “diffuse” either!

16

nik 01.27.06 at 2:59 pm

“If someone was going to quote the existing literature on epidemics, where would you suggest they start?”

The standard text is “Infectious Diseases of Humans: Transmission and Control” co-authored by Robert May, a Theoretical Physicist, the arrogant bastard.

For what it’s worth the paper doesn’t ignore ecology. It starts off by identifying a technique in ecology (the dispersal curve) identifies a problem with a sub-set of curves (the absence of a typical scale length, which means diffusion approximations fail) and adapts an idea from physics to solve it. I’m not sure this isn’t the good kind of cross-disciplinary work.

17

Ken C. 01.27.06 at 3:04 pm

“As a computer scientist who has occasionally had to deal with physicists”

Computer scientist? That’s like, a really good programmer, right? Here, would you code this up for me? Such a nice, nice code monkey!

Don’t worry, if you ignore the crappy model I pulled out of my ass, and use a better one, I’ll pretend to my physics friends that it was all my idea. Faking stuff is bad: I know that now. But since non-physicists don’t really exist, they can’t be stolen from, can they?

You have a “mathematical proof” of something? What’s that? …oh. But I like better this argument that I jotted on the back of an envelope with a crayon. Besides, since the claim is true for n=1 and n=2, we know it works for all complex n, so why bother?

18

Daniel 01.27.06 at 3:16 pm

Sebastian and Steve: directed transport isn’t going to be a diffusion phenomenon. More people go from New York to Los Angeles than go from New York to Oklahoma City, which they wouldn’t if the population is diffusing.

19

Glenn Bridgman 01.27.06 at 3:18 pm

I’m glad to see everyone has had their pre-existing prejudices confirmed.

20

Daniel 01.27.06 at 3:19 pm

Nik: But if they’d looked even a little bit into the ecological literature, they’d have found that the models which are actually used don’t depend on the assumption of a simple diffusion process. The other clue that they are dilettantes is this hokey wheresgeorge.com stuff. This has the absolute stink of a dataset in search of a problem.

21

Steve LaBonne 01.27.06 at 3:23 pm

Re #17: Now that’s a valid point, unlike the one that individual people follow specific paths. So do molecules, in (classical) stat. mech.

22

j random hacker 01.27.06 at 3:52 pm

They’re also quite naive about banknotes. At one point in the paper, they seem to believe that bank notes “exit the money-tracking system for a long time, for instance in banks”. Of course, banks don’t contain large piles of banknotes sitting around for months on end; the only bank notes you will find in a bank are the ones being stored in the ATMs and the tills, and these obviously turn over pretty rapidly.

They don’t appear to assert that notes exit the system–rather, it seems like they’re just considering this as an explanation. I don’t see any reason to believe that many notes don’t sit around in banks for long periods. Notes don’t “spoil”, so banks might just as well use a first-in-first-out inventory, which would result in some notes hanging around for long periods. And god only knows what the Federal Reserve Banks do with theirs (i.e., the ones they don’t destroy).

Furthermore, I would guess that the average human being makes fewer journeys to a banknote sorting centre than the average banknote (I suspect that several of the odd statistical properties that they found relate to the locations of sorting centres in the US).

Probably so, but isn’t this irrelevant? What matters is where the notes appear and where they disappear. Presumably these both happen at local banks (assuming that bank employees are not adding entries to wheresgeorge), and those are presumably distributed more-or-less according to population density.

As for inter-disciplinary respect, it’d be very interesting to see a graph showing what each generally thinks of the other. As a computer science/programmer type, it usually feels like we’re at the very bottom of the heap (perhaps excluding K-12 educators).

23

Bro. Bartleby 01.27.06 at 4:41 pm

Hmm, this all may explain Bro. Juniper’s recent want to fiddle with the monastery name, suggesting we rename the Zoon Blauw Monastery to Quarks of Hadron. He explained that we would address one another with the title ‘Quark’ as in Quark Juniper, and that we the many quarks would be held together within the Hadron (monastery) by strong interactions (our faith). He is currently working on a proposal to present to Abbot Eastley, who in his former life was a particle physicist (an unpublished one, I might add, who toiled in the obscurity of the trenches of application).

24

theorajones 01.27.06 at 4:47 pm

Gack, I remember thinking that the most obvious and irrefutable sign of dilletantism was the obvious selection bias in the data set. Can’t imagine people who self-select to participate in this odd endeavor are at all a microcosm of the pool of susceptibles.

I bow to dsquared’s superior dilletantism-radar.

Although I am partial to the inverse square law–I’ve found that it’s a red flag that someone is being clever and not rigorous.

25

abb1 01.27.06 at 5:16 pm

Dilettantism, huh. Big deal, what’s the harm? Uncounted petabytes of useless new data are created every day, what’s so special about this 10K piece?

26

Maynard Handley 01.27.06 at 5:24 pm

Might I suggest that at least part of the reason is the shocking lack of interest on the part of social scientists in telling the world of what they know?
The world is full of pop physics books, pop astronomy, pop biology, geology, chemistry. These books may not be perfect, but they do at least allow interested outsiders to have some feel for what is known and unknown in the field.

But when it comes to pop sociology and related fields, the cupboard gets bare pretty damn quickly. I can think of Malcolm Gladwell’s Blink and The Tipping Point, at a stretch maybe Freakanomics, and that’s it. This is quite ridiculous.
Sociologists produce plenty of earnest tomes for the public about the plight of some small group of people in some area of the country, but they seem to produce nothing in the way of survey books that are both engaging and that give the public an overview of what is known to be true and known to be false in the field.

27

will u. 01.27.06 at 6:16 pm

“More people go from New York to Los Angeles than go from New York to Oklahoma City, which they wouldn’t if the population is diffusing.”

Introduce a chemical potential!

28

Sebastian Holsclaw 01.27.06 at 6:39 pm

“Sebastian and Steve: directed transport isn’t going to be a diffusion phenomenon. More people go from New York to Los Angeles than go from New York to Oklahoma City, which they wouldn’t if the population is diffusing.”

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.

29

Daniel 01.27.06 at 7:00 pm

Notes don’t “spoil”

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.

30

hirvi 01.28.06 at 3:14 am

Daniel, banks differ.

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.

31

neil 01.28.06 at 5:09 am

“Human beings don’t diffuse – they go from one specific place to another.”

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

32

neil 01.28.06 at 5:15 am

“More people go from New York to Los Angeles than go from New York to Oklahoma City, which they wouldn’t if the population is diffusing.”

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.

33

Barry 01.28.06 at 10:06 am

(replying to 31 and 32) Not actually – the socio-geography of individual regions will matter a lot. For example, I live in Ann Arbor, a university community 30 miles west of Detroit. The highway leading to the west, I-94, will be noticeably quieter during two weeks of July, and the week between Christmas and New Year’s Day. That’s because of Ford Motor Company’s operating pattern.

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.

34

Dan K 01.28.06 at 10:55 am

Uh, Maynard Handley, you’re kiddin´, right? Take a look at the shelves at the airport next time you travel, and there you have all the pop psychology and pop sociology you can stomach. It’s all about becoming a better person or manager . Most of it is shite, but I gather that most professional physicist feel the same about pop physics books.

35

Daniel 01.28.06 at 11:18 am

Neil, your attempt at intellectually patronising me didn’t work. The phrase “specific places” was there for a reason; see comment number 18 above where I point this out again. Since literally nobody appears to think that human travel is correctly measured by a diffusion process in physical space, you are on a sticky wicket trying to claim it is.

36

mondo dentro 01.28.06 at 5:54 pm

All right.

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.

37

agm 01.29.06 at 1:57 am

Oh, cmon, lay off the pwer laws. How else are we supposed to reduce everything to a 1-D system and ignore any other subtleties?

38

Daniel 01.29.06 at 4:35 pm

Mondo; if you want to write such a piece, I’ll publish it as a guest editorial.

39

neil 01.29.06 at 6:05 pm

Daniel, apologies for the weak attempt at condescension, I’ll try harder next time.

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”.

40

Daniel 01.31.06 at 4:24 am

No, that won’t do either, or at least not until American Airlines starts scheduling flights to randomly selected empty fields in the MidWest. This just isn’t a diffusion process and no amount of extension of the diffusion equation is going to make it into one. What with being a financial analyst and all I do know the odd thing about jump-diffusions you know, they do come up from time to time in the option pricing literature.

41

abb1 01.31.06 at 12:37 pm

I don’t know shit about diffusion, much less about super-diffusion, but to avoid the “randomly selected empty fields in the MidWest” problem can’t we transform the map into population-density-adjusted cartogram, the way they do here?

Thanks.

42

neil 01.31.06 at 5:34 pm

Daniel, reading the paper I don’t think they are arguing for the sort of naive “humans diffuse” model you deplore. My reading of the introductory paragraph is that they are critical of the current situation whereby “the assumption that humans disperse diffusively still prevails in models” despite the lack of quantitative assessment i.e. lack of evidence – something I think you would agree with.

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).

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