One Last Exchange of Letters in Significance with Nassim Nicholas Taleb

Significance Magazine is now hosting its final-exchange-of-letters on the future of war.  Once again, it is Steven Pinker and I dueling with Nassim Nicholas Taleb and Pasquale Cirillo.  You can judge for yourselves whether the four of us have hit a common groove.

If you feel sad because you have not followed all the twists and turns of this discussion then you should click through these links.


A New Graphical Manoeuvre (not Recommended)

Correction.  The first part of this post argues that an anomaly in a published graph is an error that has some substantive implications.  However, an alert reader, Ben Prytherch,  proposed a benign explanation for the anomaly.  I checked with the authors of the graph and it turned out that Ben is right.  So this is a formal correction.  I annotate this part of the post below and will write a follow up post about this as well.    [October 2, 2016]

Many of you know that for some months I’ve been involved in a discussion with Pasquale Cirillo and Nicholas Nassim Taleb.  Steven Pinker joined me in a recent exchange of letters with Cirillo and Taleb.

I won’t summarise the debate in this post but you can bone up by looking here, here and here. You will also rejoice to learn that there will be another exchange of letters soon.

For preparation I had another look at the Cirillo-Taleb paper and was taken aback by their  figure 14a:


The accompanying text says:

If …events…follow a homogeneous Poisson process…their inter-arrival times need to be exponentially distributed….Figure 14 shows that ….these characteristics are satisfactorily observable in our data set.  This is clearly visible in the QQ-plot of Subfigure 14a, where most inter-arrival times tend to cluster on the diagonal.

Please clear your head for the moment of the details (Poisson, QQ, etc.).  The key is that the points should line up along the diagonal, which they seem to do.  Great!

But wait.

The diagonal for this picture should be the 45 degree line whereas the line in the above picture is more like a 35 degree line.  Notice how the X axis goes out to 11 whereas the Y axis only goes up to 7.

[This is where I start to go wrong.  It turns out that the Y axis is scaled differently from the X axis.  If the scaling were the same then the points would line up on the 45 degree line. Personally, I think the exposition would be better if the scaling were the same on both axes but the way that Cirillo and Taleb have done this is not an error as I originally asserted.  October 2, 2016]

Here is the kind of plot we should see if the data really do follow an exponential distribution as Cirillo and Taleb claim their data do [and the pictures were done with the same scaling on both axes as I would have preferred, October 2, 2016]:


For this proper [replace “proper” with “clearer”, October 2, 2016] QQ graph both axes go to 5 and the diagonal is the 45 degree line.  (Ignore the fact that Cirillo and Taleb’s points are stacked above and below each other.  This is only because their data points are rounded to the nearest year)

Thus, Cirillo and Taleb’s figure 14a shows the opposite of what they claim; their data do not fit an exponential distribution.  When properly interpreted the Cirillo-Taleb graph suggests that the data do follow an exponential distribution.  October 2, 2016.

I have to say that I looked at figure 14a many times without noticing this problem.  Presumably they just made a mistake.  [My mistake, actually, October 2, 2016]

But what a slick manoeuvre this would be in the tradition exposed so well by Darrell Huff if done on purpose.  Your data need to be on a particular line.  You draw a line that goes through your data.  You declare success.  Busy people don’t notice you haven’t drawn the right line.  [Of course, Cirillo and Taleb did not engage in such trickery.  October 2, 2016]

By the way, Cirillo and Taleb’s figure 14b also [October 2, 2016] strikes me as out of tune with their accompanying text:



Moreover, no time dependence should be identified among inter-arrival times, for example when plotting an autocorrelogram (ACF).  Figure 14 shows that both of these characteristics [exponential distribution and no time dependence] are satisfactorily observable in our data set.

Again, without getting into the details, they are saying that the little bars are all near 0 (ignore the huge first bar).  I agree that the bars are, indeed, lowish.  But what about the ones near 0.2?  (These are correlations so they have to be between -1.0 and +1.0)  These larger bars do seem to be pretty much below the (unexplained) dotted blue line.  Maybe this is a statistical significance line?  If so then I’d agree to a formulation along the following lines:

We were unable to reject a hypothesis of 0 time dependence at the ??? level.  However, we only had a few hundred observations and with more data we might well reject such a hypothesis, at least for some time lags.  Still, it seems that any time dependence in the data is fairly weak.

I don’t see this as a massive smoking gun.  I believe that Cirillo and Taleb are in the right ball park with their interpretation of these correlations although they have overstated their case.  I do suspect, however, that if Nassim Taleb were standing in my shoes right now he would be shouting that I adamantly deny the overwhelming evidence of massive correlations.  [Well, maybe he wouldn’t.  He was pretty reasonable in our exchange about me correcting my error.  October 2, 2016]

In any case, despite what Cirillo and Taleb seem to think, neither of these pictures directly addresses the main issue that interests them: whether or not there is a trend toward fewer wars per unit of time

PS -I should mention that one of my colleagues, Alessio Sancetta, helped me think through this post.  Of course, all errors are mine and, as always, I’d love to hear from readers and will gladly fix any mistake I may have made.

Technical Appendix

I assumed a fair amount of knowledge above so here are a few more details for anyone out there who craves them.

The data underpinning the pictures is for large wars since 1500.  I don’t have it.  I believe that Cirillo and Taleb have not yet released their data yet but are planning to do so.

Figure 14a is about the distribution of time gaps between wars. Specifically, how often does the next war happen right away (0 time gap), how often do we wait 1 year, 2 years, etc.?

To do an exponential QQ plot you first fit an exponential distribution to the data. This fitted distribution then makes predictions on gaps between wars.  The predictions will be, for example, that 75% of the gaps will exceed 2 years or that 50% of the gaps will exceed 4 years, etc..  You then graphically compare the predictions with the actual gap distribution.  If all the predictions turn out to be exactly correct then the points will line up smack on the 45 degree line.  [In my opinion the above is how one should do a QQ plot that is easy to understand.  October 2, 2016]

How do we interpret the fact that, when done correctly, the points on the right in figure 14a lie well below the 45 degree line?  [What follows in the next paragraph would be true if the QQ plot had been drawn the way I describe but isn’t true of the actual Cirillo Taleb graph.]

This means that the actual gaps at the high end tend to be longer than would be predicted by the fitted exponential curve.  Loosely speaking, when the exponential is predicting a gap of 7 the actual gap turns out to be more like 10, etc..  In other words, the right-hand tail of the distribution of gaps between wars is stretched to the right compared to the exponential fit.

Figure 14b is checking for correlations between gaps at different time lags.  For example, the bar that reaches a height near 0.2 at a lag of 5 says that a longer gap 5 wars ago tends to be associated with a longer gap until the next war.  More generally, this shows that knowledge of past gaps appears to be (weakly) useful in predicting future gaps.




Forecasting World War III – An Exchange of Letters

I’m sure that this reminder of my article in Significance  will awaken warm memories in many of you.

In it, I used an article of Pasquale Cirrilo and Nassim Nicholas Taleb to help me make my case.  I think that the Cirillo-Taleb paper is quite interesting.  However, it is not in any way a shoot-down of Steven Pinker’s masterwork, The Better Angels of our Nature, as Cirillo and Taleb like to claim.   In fact, I argued in an earlier article that there isn’t even any great contradiction between Cirrilo-Taleb and Better Angels.

No matter.

I seem to have provoked Cirrilo and Taleb who wrote a protest letter to Significance about my piece.  To me, it feels like my main crime is that I didn’t dismiss Pinker as an incompetent writer of “popular science.”   Or perhaps the issue is that my short piece leaned more heavily on Better Angels than it did on Cirrilo-Taleb.  In any case, I don’t think that Cirrilo and Taleb help themselves very much with their letter.

Steven Pinker and I now have a joint reply to Cirrilo and Taleb in the current issue of Significance.

Please have a look.




Does the Deep Roots Theory of War Encourage Fatalism about War?

Something weird happened just when I stopped checking my favourite twiterati.

First there was an article by John Horgan.  Then suddenly there was this, this, this and probably much more, all saying that Horgan’s wrong about everything.


Maybe enough is enough.  Michael Shermer already has a good rebuttal to what Horgan wrote about war.   Still, I want to give my own take on the war discussion.

Horgan writes:

The biological theory that really drives me nuts is the deep-roots theory of war. According to the theory, lethal group violence is in our genes. Its roots reach back millions of years, all the way to our common ancestor with chimpanzees.

The deep-roots theory is promoted by scientific heavy hitters like Harvard’s Steven Pinker, Richard Wrangham and Edward Wilson. Skeptic Michael Shermer tirelessly touts the theory, and the media love it, because it involves lurid stories about bloodthirsty chimps and Stone Age humans.

I don’t know if all the people named above would say that war is “in our genes”.  However, it is obvious that very many humans are capable of great violence when they are placed in the wrong circumstances.  The Lucifer Effect by Phillip Zimbardo seems relevant here.  Social situations, such as a prison environment, can tap into a violent side of human nature which is invisible most of the time.  Of course, many humans can be violent on their own but group dynamics often seem to magnify the violence problem.  If this means that group violence is in our genes then I guess I think that group violence is in our genes.

Horgan continues:

I hate the deep-roots theory not only because it’s wrong, but also because it encourages fatalism toward war….Perhaps you believe the deep-roots theory. If war is ancient and innate, it must also be inevitable, right?

I really struggle here but I think I kind of get the point.  It seems to be that if war has been around for hundreds of thousands of year and is so deeply embedded in human nature that it has penetrated all the way down into our genes then what’s the point of struggling against war?  We might as well just accept it.

I can grant that this idea is not crazy.  Still, upon reflection it just doesn’t make sense.

The drive to have sex must be “in the genes” and go really far back in time.  Yet human populations are able to control their growth even though the sex drive is strong and innate.

More to the point, I have never heard anyone say that there is no point in trying to contain our sexual desires and that females will be perennially pregnant because the sex drive is “in the genes”. If anything the opposite is true.  The widely acknowledged strength of the sex drive has led to technological and cultural innovations aimed at avoiding excessive pregnancies.  Perhaps the main reason we take the sex drive so seriously is that we know it is inate and strong so we need to work hard overcome it.

The main point in Steven Pinker’s book “The Better Angels of our Nature” is that we humans have gradually been overcoming our in-built tendencies toward violence. Yet Horgan still cites Pinker as encouraging a fatalistic attitude that humans aren’t capable of winning the war against war.  This accusation is truly puzzling. Surely our long history of success in gradually overcoming violence should encourage us to believe that it is very much possible to continue further along this path toward peace.

Indeed. the link Horgan gives to unpack his claim that the “deep-roots” theory encourages fatalism about war goes to a story about Horgan meeting an ex military guy at a conference who thinks that war will be with us for the forseable future so we had better prepare for it rather than hoping it will go away.  The guy cites experience since Napolean and doesn’t mention anything about ancient, let alone pre-historic wars.  This story strikes me as a nonsequiter to the deep-roots-leads-to-fatalism claim.

What about the substative dispute about the roots of war?

As I understand it Horgan’s vision runs along the following lines.  A long time ago humans were peaceful.  Then some anomalous humans injected twisted ideas about warfare into our culture.  These carried us out of our natural, peaceful state to which our genes predispose us.

A central problem with Horgan’s vision, at least as I understand it, is that when the war idea comes it spreads and entrenches itself.  So the vision itself still seems to accept the premise that humans have the potential for group violence within them, ready to be tapped by entrepreneurs of violence.  That is, if the group violence idea is so alien to the human character why has it proved so attractive and resilient to humans?  Shouldn’t such an unnatural cultural implant be relatively easy to eradicate?


Maybe there is a good answer to these questions.  But for now I will continue believing that humans have inate tendencies toward group violence which can be overcome with enough effort.  We have had much success in violence reduction over the centuries and we should continue to work hard to do better in the future.  .

A Peaceful Start to the New Year?

Joshua Goldstein and Steven Pinker, both authors of important and timely books on the decline of violence, have an interesting joint article suggesting that we’re back on track after a bit of a reversal over the last few years.

What they say makes sense to me in light of recent developments.  The war in Syria, spilling over into Iraq, is surely the main reason for the recent spike in violence.  But now Syria, as well as Ukraine and Yemen, are  experiencing imperfect ceasefires that do seem to be reducing violence in these places.  Goldstein and Pinker point to some other positive developments around the globe as well.

Of course, it isn’t hard for an avid news reader to find some negative developments.  But it seems right to me that Syria is the real driver of global violence trends and that Syria has become less violent over the last month plus.

Still, I’d be much happier if Goldstein and Pinker just deleted this bit:

According to the Syrian Observatory for Human Rights, the rate of killing has dropped by nearly half since the cease-fire began. That means that around 2,000 lives were spared in the first month. Since Syria is by far the world’s largest war, this reduction takes a big bite out of the global rate of war deaths as well.

Go to the web site of the Syrian Observatory for Human Rights (SOHR) to find the SOHR dataset you’ll see why.  In fact, there is nothing there that can be construed as a dataset.  You can fish out reports saying that SOHR has “documented” X number of deaths in month Y.  But the SOHR seems to use the word “document” the way that most people use the word “assert”.

Certainly the SOHR does document many incidents in a more conventional sense and I was told by a Syria expert that these normally check out and are timely.  But do the numbers of people killed in documented incidents add up to the monthly totals publicized by the SOHR?  I don’t know but I kind of doubt it.

I would like to see documentary proof of the deaths the SOHR says it has documented.


Forecasting World War III

Hello again.

I apologize for going silent for so long.  I felt overwhelmed at the end of our teaching term, transitioned into family fun and obligations and then have been unconscionably slow getting out of the starting blocks since the new year began.   I’ll now become active again, although I’ll warm up by drawing attention to a few things already in the public domain.

Please have a look at this short article I wrote for Significance Magazine.  It is an outgrowth of an earlier article I wrote on an ongoing discussion/argument between Steven Pinker and Nicholas Nassim Taleb. (By the way, here is a nice recent article on Pinker-Taleb, taking a very pro-Pinker stance.)

PS – I’m an economist, not a statistician, but Significance still wanted me to write for their “Ask a Statistician” column.