Archive September 2010

Physicists aimee whitcroft Sep 16


Stunning timing!


xkcd’s newest strip is on the subject of physicists.    Why am I wittering about timing?  Well, given that I’ve just written a post about physicists explaining what’s going on, it’s pretty awesome synchronicity.

Oh yes, and we do laughing at them a little, as well :)

[HT: Jason for sending me the link, with the simple message 'apropos']

The mathematics of war aimee whitcroft Sep 13


War!  Hngh!

warWhat is it good for?  Well, the development of some interesting mathematics, if nothing else.  And raised eyebrows.  And scheming/strategising.

Last Monday morning (yes yes, I know – been busy, ‘k?!) I successfully managed to hie myself off to Dr Sean Gourley’s speech about, you guessed it, the mathematics of war.

Or, to be particular, the mathematics behind insurgencies’ ability to stave off defeat by much larger, more well-equipped forces.  Asymmetric warfare, in other words.

I am now going to attempt to share with you the (hopefully not too garbled) notes and learnings which I took therefrom.

Nash equilibria, open source intelligence, and oranges

Firstly, a brief explanation.  Up until relatively recently – the last coupla decades, really – warfare has been a more traditional affair.  Two sides, lined up against each other, having it out.  Clear knowledge of who one’s enemy is, where they are, and at least to some extent, what they’re up to.

And game theory (more specifically, Nash equilibria) was able to adequately help model how such conflicts might go.

Things are now different.  The concept of ‘your enemy’ has become far more complicated.  There are many conflicts all over the world at the moment, each featuring its own cast of insurgents/guerillas/terrorists/organised criminals and, um, often at least one ‘major’ force.

Gourley was interested in collecting data on these sorts of things (attack size, when, which conflict, deaths, injuries etc), but of course didn’t have official access to such data.  Because govts like to keep them to themselves.  So, how to get the data he wanted?  The answer: open source intelligence.

Yes, once again, ‘open source’ raises its beautiful shiny head above the parapet and grins charmingly at us.

Open source intelligence is, simply, the information that one can gather from citizen reporting, the news, NGO stats and so forth.  Yes, there’s a lot of noise, but there’s also some signal in there.  Data, in other words.    Even looking for second order effects can help one determine if something’s going on.  Perhaps the classic story about open source intelligence and second order effects is about the Alliance. Unable to be directly sure whether they had successfully bombed bridges in Germany, they looked at the price of oranges in cities, which had to be imported.  Spikes in the price of this acidic, vitamin C-containing fruit corresponded to bridges going down.

We haz data – now what?

So yes.  Gourley and co. collected a bunch of data for different conflicts around the world (Iraq, Colombia, etc), and then set about analysing it.  What they found was interesting – when deaths were plotted against cumulative frequency for a number of conflicts on a log-log graph, the resulting line looked an awful lot like something adhering to the power law, with an alpha (slope) hovering around 2.5.

Or, to put it more simply: the data suggested that insurgent conflicts (fought in different places, for different reasons) around the world might cluster around this value.

The next step was to try to explain this phenomenon.

war equation

Gosh, I hope I copied this down correctly :)

[Where P (the probability of an attack killing x no. people in a time window t) = a constant multiplied by x (the size of the attack), raised to the power of negative alpha (which is, roughly speaking, the slope of the line when plotted on a log-log graph)]

Lost yet?

For those of you not terribly comfortable with the equation, not to worry.  Of more interest is what it means.

Basically, it looks like the number of people killed in an attack is correlated with the strength of the attacking group.  And it’s worth being clear here – that’s strength, not size. A smaller group of people with oodles of moolah and weaponry is going to do more damage than a larger group with less moolah and weapons.  So one could look at alpha as the distribution of attack strengths, which leads us towards an organisational structure.


Well, ask yourself: how does one organise one’s forces to best fight the opposition? Now, bearing in mind that insurgencies aren’t centrally controlled but rather self-organising, how does the insurgency organise itself to take on a much stronger, conventional armed force?

There are a couple of possibilities – one might be taking the whole force, and dividing it up equally.  But the attacks that come out of that look more like a Gaussian distribution, not a power law distribution.  Which means that’s not how insurgencies are organising.

Instead, the organisational structure which best fits what Gourley et al observed, was that each group would have a small number of groups which killed lots of people, lots of groups which killed very few people (per attack), and a bunch of groups in the middle.  Indeed, the maths suggests that it’s 316 times more difficult to kill ten people than it is one person, and 316 times more difficult again to kill 100 rather than 10 people.  And that multiplying exponent seems to stay as one looks at different conflicts.

Now, here’s where biology had some lessons for the mathematicians (hah!*).  Each group is subjected to forces of coalescence  and fragmentation.

With coalescence, there can be a formation bias towards the formation of large groups or towards the formation of small groups.  And the actions can be geographic (i.e. dominated by people one is near) in nature, or non-geographic. (hello mobile phones, internet etc).

Similarly, with fragmentation, groups can either split into two and factionalise, or they can split into many parts/shatter.

The interaction between these factors gives rise to different distributions – an understanding of how allowed Gourley et al to start looking at which structures best fit insurgencies.

How do insurgent organisational structures behave?

They found that the formation bias was towards large groups , with connections that aren’t geographical in nature.  Of course, the stronger they get, the more liable they’d be to find themselves on the radar of whichever the larger, conventional force is.  Who would then attack them.

Classic tall poppy syndrome stuff.

Said insurgent group would proceed to shatter (rather than factionalise).  However, it wouldn’t shatter randomly – instead, the next most successful group starts to accrete members.  So there’s this fluid system which allows a great deal of learning and innovation, as opposed to the conventional forces which have static, rigidly defined operating procedures.

All nicely explained in the picture below.

Figure 4 | Model framework for insurgency. The insurgent population comprises an overall strength N, distributed into groups with diverse strengths at each time-step t. This distribution changes over time as groups join and break up. Dark shadows indicate strength, and hence casualties that can be inflicted in an event involving that group. Figures 1 and 2 are derived from the number of events of size x aggregated over time. Figure 3 is derived from the number of events at a given time-step aggregated over size.

Model framework for insurgency. The insurgent population comprises an overall strength N, distributed into groups with diverse strengths at each time-step t. This distribution changes over time as groups join and break up. Dark shadows indicate strength, and hence casualties that can be inflicted in an event involving that group. Figures 1 and 2 are derived from the number of events of size x aggregated over time. Figure 3 is derived from the number of events at a given time-step aggregated over size. Credit: Nature, doi:10.1038/nature08631

Alpha – higher or lower?

So interesting patterns around alpha – 2.5 appears to be the value at which an insurgency is stably/sustainably fighting against the larger/stronger force.  That is, the conflict won’t end with an alpha of 2.5.  But what happens when alpha is higher or lower?

If one can drive alpha higher, then one drives the insurgency towards fragmented, fluid groups, and more groups (basically, more towards the guerilla feel).  These tend to peter out eventually.

If one can drive alpha lower, one has an insurgency made up of stronger, more robust groups, but fewer of them (more like a conventional war). There is the possibility of an actual win/defeat here.

How does one decide whether to drive alpha higher or lower?  Well, look at where alpha is currently, and  has been over time, and from there make a decision about what’s achievable.

Fascinatingly, the strategy that the maths suggests is counterintuitive – attack the weak groups, not the strong ones.


Now, what are the applications of this?  Well, it’s certainly got the US NSA and other such organisations interested, because of what it might be able to teach them about how to defeat the insurgencies with which they’re involved.

The model’s powerful – it can suggest how many insurgent groups are active, and how to deal with them.  Because insurgent wars which drag on kill an awful lot of people.

Which helps answer the question: why did Gourley start this research?  Well, he’s of the belief that the more we understand war, and how people die, the more we can stop it happening.  Hear hear :)

Oh yes, and there are other applications – the model can probably be drawn out to look more generally at how small groups successfully fight large groups.  As with companies (how small tech startups beat large tech giants), or even ,medicine (how drugs attack tumours in the body).

Brilliant stuff!

I’m hoping to be able to podcast Gourley’s talk (and the questions afterwards!), but while I wait for permission, here’s a brief TED talk he gave.

UPDATE: Sean’s given me permission to podcast his talk.  /celebrates

You can find it here**.


Oh yeah: and I highly recommend the BBC’s “The Story of Maths”, hosted by Oxford professor Marcus du Sautoy.

* You see?  Biology’s not just, ahem, “stamp collecting”…

** Full props to the Internet Archive for letting people upload files, for free :)



Bohorquez, J., Gourley, S., Dixon, A., Spagat, M., & Johnson, N. (2009). Common ecology quantifies human insurgency Nature, 462 (7275), 911-914 DOI: 10.1038/nature08631

Interesting bitties: different alphas, plastic to oil, drunk voles and a fry aimee whitcroft Sep 10

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Whilst in the process of writing other, more long-form posts, I thought I’d throw you all the proverbial bone.

A bone

A bone

Or, to be more precise, smattering of things wot I has found interesting today, and which you might find interesting too.

First up!

Akinori Ito goes down as favourite human being of the day.  It would appear that he has come up with a way of making the previously one-way process of oil –> plastic into a two-way process.  Turning plastic back into oil, in other words.

And it’s apparently “safe, eco-friendly and efficient”.

It has not yet, however, dented my aversion for buying bottled water.


Oh dear.  The idea of a ‘universal constant’ may, just may, be in jeopardy. Scientists have long pondered whether the constants which govern the interactions of, um, _stuff_ in our little corner of the galaxy, can be extrapolated as being the same elsewhere in the universe.

Now, it looks like at least one of the constants, called alpha, may not be universal after all. Alpha tells us the strength of electromagnetism, and scientists using the pragmatically named Very Large Telescope (VLT) in Chile (and measurements from other telescopes, too) appaers to vary “continuously along a preferred axis through the universe”.

If it’s actually the case, it would we’d have to have a seriously close look at our physics theories, and come up with something better and ‘deeper’.   It also means the chances of, say, life occurring could differ in different parts of the universe.  Hmmm.


For the Friday ‘aaaaah‘ factor, I present to you a baby seahorse.  Apparently, the official name for such a creature is a ‘fry’.

And it’s a really rare thing to be able to find and photograph one of these, so there  is also much excited rejoicing going on in science circles.

For the Friday ‘hehehehe, how appropriate’ factor, a study showing that prairie voles are a valid model for studying the effects of social influence on excessive drinking.

Not sure whether I feel happy or sorry for them, frankly.


And then there’s this.  Not because it’s sciencey, but because it’s topical, made me giggle, and gently pokes fun at the famously unintelligible Kiwi accent.

Interesting bits: starving to stay awake, and an LCA on Li-Ion aimee whitcroft Sep 03

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I have seen many interesting sciencey things this week.  Which makes sense, given that a large part of my job is to track new research.  Sadly, and for the sake of brevity, I’ve had to pick but two for this post.

Aaaah, isn't he/she/it cute?

Aaaah, isn't he/she/it cute?

Starving to stay awake?

Another interesting factoid related to, well, taking in less calories than one might need.  It’s already been shown that calorie restriction lengthens lives.  Admittedly, this has yet to be proven in humans, but I can’t help thinking of all those Asian centenarians who have lived on a simple diet of rice and whatnot for, well, over a century.  Now, something new!

We all know that being tired results in, well, cognitive impairment.  A failure to, shall we say, be operating on all six cylinders, including learning impairment. However, scientists playing with fruit flies (as they are wont to do) have discovered something interesting: flies who were starved remained awake but didn’t appear to suffer the negative consequences of this wakefulness. Looking at two different lines of flies, they found that those who have genes meaning they have excess fat were resistant to starvation (and hence this effect), whereas those who were naturally lean, weren’t (and hence got the benefits).

What this shows?  That lipid (fats) metabolism, sleep and starvation seem to be intricately intertwined, and further, that lipid metabolism may play an important part in the ability to recover from sleep deprivation, as well as protecting against some of the impairments which can result.  Which could help explain why people who suffer routine sleep deprivation tend to be, um larger (also, men: beware!  sleep deprivation could kill ya).

What might be a reason?  Well, we’re not sure, but it could be that the body reckons that finding food is more important than sleeping.  Which makes sense, I guess :)

One question, though – do flies get hyperglycaemic?  ‘Cause I know I get shaky, and then ok, and then completely homicidal* when it happens.

electric carLi-ion LCA

In other news, those clever white-jacketed** peeps we call scientists have done the first lifecycle analysis (LCA) on a lithium-ion (Li-ion) battery such as one would use in an electric car.  Li-ion batteries are great – they’re basically maintenance-free, lighter, and can store more energy than other batteries (including NiMH batteries).  Also, they don’t lose capacity if you keep recharging them from a less-than-full state (unlike, sigh, many other batteries), live for ages, and don’t self-discharge much.  So we likes em.

Why an LCA??  First, a word on what an LCA is. Basically, it’s the assessment of any given product from the moment it becomes a glint in a manufacturer’s eye, to the moment it ends up being dumped/recycled. The purpose is measure exactly how much energy and resources go into making said product, and include not only the making of the product itself, but also the energy/resource costs of all its components, and also its eventual dumping/destruction/recycling.

The worry with electric cars is that the environmental impact of actually _producing_ Li-ion batteries might outweigh any environmental benefits conferred by using electric rather than petroleum-engined cars.  This, it turns out, is not the case.  Indeed, such a battery accounts for at most 15% of the total environmental burden of an electric car, of which a little over half comes from the refinement and processing of its raw materials.

What _does_ matter, however, is the source of the electricity which powers our little electric environment-saver.  Assuming that the electricity comes from the mix of coal, nuclear and hydroelectric power sources which is usual in Europe***, an electric car beats a conventional one only if said conventional car is less efficient than 3-4 litres per 100km (70mpg).   The electric car’s goodness worsens by another 13% if only coal-powered electricity, but (and this is awesome for NZ), the figures improves by 40% if only hydroelectric (or, one can assume, another sustainable energy) is used.  Hooray!

In short, basically, electric cars are only as good as their electricity source.  Of course.

In electric cars, environmental impact depends on fuel source – For the first time, researchers have conducted a life cycle analysis on an electric car being run by a lithium-ion battery, and found that it isn’t the battery itself which forms the major environmental burden.  Rather, it’s the source from which the electricity generated came.  In order for any petrol car to be as environmentally friendly as an electric car (with an Li-Ion battery and powered by a typical European electricity mix), it can must consume 3-4 litres per 100 km.  Published in Environmental Science and Technology.


* Apparently, precipitous blood sugar level drop is particularly prevalent in females.  With attendant homicidal leanings (seriously, I’ve scared sandwich people badly).  So lads, feed yer hungry ladies!

** Yes, I know that’s  generally not the case anymore.  Nor are they generally strait-jacketed, either :)

*** This mix of fuel sources makes three times as much pollution as the battery’s entire lifecycle



One of the many articles on links between sleep deprivation and obesity

How sleep deprivation can kill ya (boys)

Calorie restriction benefits


Li-ion battery


Matthew S. Thimgan, Yasuko Suzuki, Laurent Seugnet, Laura Gottschalk, Paul J. Shaw (2010). The Perilipin Homologue, Lipid Storage Droplet 2, Regulates Sleep Homeostasis and Prevents Learning Impairments Following Sleep Loss PLoS Biology : 10.1371/journal.pbio.1000466

Notter DA, Gauch M, Widmer R, Wäger P, Stamp A, Zah R, & Althaus HJ (2010). Contribution of li-ion batteries to the environmental impact of electric vehicles. Environmental science & technology, 44 (17), 6550-6 PMID: 20695466

Introducing a new blogger: seeing data aimee whitcroft Sep 03

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Haha!  We are pleased as punch to introduce the third in our blitz of blogs this week.


Chris McDowell will be the force behind seeing data (first post up shortly), a blog all about data visualisation.  For those of who aren’t familiar with the subject, data vis (viz)* is the artform behind taking numbers, and making of them graphics at which people can point their eyes.  One such subsection of this is, of course, infographics.  Which are everywhere.

So, welcome to Chris! We look forward to seeing what you show us :)


* I had to physically restrain myself from making a pun there

Introducing a new blogger: Shaken Not Stirred aimee whitcroft Sep 02

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Man, what a week!

We are most proud and yayfull to be introducing our second new blog this wee: Shaken Not Stirred (first post up in about 15 minutes).

To be penned by Jesse Dykstra, who’s down south at Canterbury University, it’ll be focusing on natural hazards.  Of which New Zealand is full.  And also disaster management, of which, happily, NZ is less in need. Whew.

Of course, it won’t just be focussed on NZ, but also on global issues (the first post will demonstrate that).

Welcome, Jesse, to the stable!  We’re very happy to have you :)


Exciting postscript: look out for our third new blogger to swell the ranks in the very near future.

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