Testing the Diamond Hypothesis

Why did the Old World discover the New World and not vice-versa? Jared Diamond argued in Guns, Germs, and Steel that the ultimate cause of the asymmetry evident in the 1492 encounter was the orientation of the axes of the geological continents or worlds. Whereas Africa and the Americas are vertically aligned, the orientation of the Eurasian axis is horizontal. Because innovations (particularly innovations in food production) diffuse faster along longitude than latitude, this was a decisive conditioner. In particular, this meant that the most decisive advance in prehistory — the rise of sedentarism and food production — made a staggered appearance across the continents. Specifically, the arrival of the Neolithic transition was significantly later in the vertical worlds of Africa and the Americas than in the horizontal world of Eurasia.

Worlds.png

What explains this very broad, inter-continental pattern is indeed the axes of the continents. The Kruskal-Wallis test statistic for our Boolean variable (horizontal for Eurasia and vertical for Africa and the Americas) is highly significant (p<0.0001).

Orientation.png

But what does the pattern look like at finer scale? What is the geography of the Neolithic transition?

The next figure displays the time-depth of the transition across the globe. We see that the pattern is largely in line with that implied by the Diamond hypothesis. The Neolithic revolution in confined to the Levant until 9ka, from where it diffuses roughly along longitude, reaching the eastern and western extremities of Eurasia only by 4ka. We know that movement was attended by massive range expansions of Neolithic populations. The vertical continents on the other hand saw a delayed onset with many regions not transitioning until after the time of Christ.

Geometry.png

This geography conditioned not only the modes of subsistence of societies in the three worlds but also their fundamental political institutions. For state societies were impossible without massive grain production and storage — states could not survive for very long at all without easily controlled surplus. Even chiefdoms were impossible without sedentarism.

ethnographic_present 1.png

The time-depth of the Neolithic transition is in fact a function of geodesic distance from the Levant. (Geodesic distance is also called great-circle distance. It is the length of the shortest path between two points on the globe and can be obtained via the Haversine formula.) Note that Neolithic time-depth is an exponential function of distance from the Levant. This is as it should be since waiting times are exponentially distributed — exactly for Poisson processes and approximately otherwise.

Geometry.png

The fit for our single factor baseline is extraordinarily good, despite the fact the obvious diffusion hypothesis cannot be expected to work for the Americas which was robbed of all interaction with the Old World during most of the Holocene! We know that the first Americans walked into the New World accompanied by dogs and carrying bottle gourd seeds. So these mesolithic populations were already well on their way to the Neolithic. That’s why we see the pattern hold across the New World-Old World divide. What distance from the Levant is capturing is thus not simply the diffusion model of the spread of farming. Rather it captures the geometry of polarization in deep time. Put another way, the world was already polarized at the end of the Pleistocene. It was no coincidence that the Natufian culture emerged in the Levant. For the Levant was the center of the world-system on the cusp of the Neolithic Revolution.

singlefactormodel.png

The fixed-effect for continental axes does not vanish after we control for geodesic distance from the Levant. The next figure shows the residuals of  our baseline model. The difference between the residual means is 1750 years, which is highly significant (p<0.0001). The interquartile ranges (which contain the middling half of the observations in each category) do not overlap at all. Even the gap between the confidence intervals for the means is about 1100 years.

Unexplained.pngIn order to estimate the effect of the orientation of the axes, we fit three mixed effect models. In all three we admit random effects for world; meaning that we allow the volatility of the intercept to vary by world (Eurasia, Africa, Americas). Table 1 displays our estimates.

Geodesic distance from the Levant is by far the strongest correlate of Neolithic time-depth. We find that 56 percent of the variation in time-depth is explained by our single factor baseline. Turning to the two factor model, we find a statistically significant fixed-effect for the orientation of the continental axes. Our estimate says roughly that having a horizontal axis instead of a vertical one gave Eurasia a 2000 year head start over Africa and the Americas. These fixed-effects or slope coefficients only get more significant and larger once we control for absolute latitude. The fixed-effect for absolute latitude is extremely large and significant at the 1 percent level. We estimate that moving 28 degrees away from the equator (the interquartile range of absolute latitude in our sample) extends Neolithic time-depth by 600 years. But the effect our Heliocentric geometry is still dwarfed by the fixed-effect of distance from the Levant. We estimate that moving from the 25th to the 75th percentile of distance from the Levant extends Neolithic time-depth by 2200 years. Diamond was really onto something.

Table 1. Mixed-effect model estimates.
Single factor Two factor Three factor
Intercept 18,855 17,939 18,954
(tStat) 14.5 14.2 14.7
Log distance from the Levant -1,735 -1,705 -1,782
(tStat) -13.4 -13.2 -13.9
Axis 1,938 2,331
(tStat) 2.2 2.3
Absolute latitude -22
(tStat) -3.2
Random effect for world Yes Yes Yes
R^2 0.56 0.73 0.73
adj R^2 0.56 0.73 0.73
N 164 164 164
Source: Piketty (2015). Estimates in bold are significant at the 5 percent level.

The next figure displays these fixed-effects. Axis is a Boolean that equals 1 for Eurasia and 0 for Africa and the Americas. It’s interquartile range is set at 0.5. We display the product of the absolute values of our fixed-effects with their interquartile ranges. The error bars display the product of the standard errors of the fixed-effects with the interquartile ranges of the variates.

Fixed.png

Our revised estimate for the Eurasian advantage due to the orientation of the axis is 1300 years. For absolute latitude it is a more modest 380 years. We estimate that moving an interquartile range, from the 25th to the 75th quartile, in distance from the Levant reduces fitted time-depth by 1800 years. All three estimates are computed uniformly with the same formula: as the product of interquartile range and absolute value of the fixed effect. Diamond’s thesis now looks much more robust than before. The annoyingly large standard error has vanished. The effect is much more robust than previously reported here.

Finally, we should note than positing the existence of continental races is yet again actively misleading in answering this question. The patterns extends continuously across hypothetical continental races. In fact, had you started from the racialist prior, you’d miss the real geometry of polarization in prehistory. That was indeed how it went once Europeans started asking this question. A real break with scientific racialism is much more recent than we imagine. More on that soon.

continentalraces.png


Postscript.

We can also look the results of ANOVA. The first column displays the proportions of variation in time-depth explained by our three factors. So the share of distance from the Levant in explained variation is 57 percent and that of the Axis is 42 percent. Absolute latitude makes a minor contribution smaller than 2 percent, but interestingly it is more statistically significant than Axis. It is not clear why the standard error of the fixed-effect for Axis is so large. But Axis is definitely significant at the 5 percent level in the F-test. Diamond is in the clear.

 ANOVA for the three factor model
Share of explained variation (OLS) Fstat (MLE) pVal (Fstat)
Absolute latitude 0.015 10.1 0.0018
Axis 0.419 5.5 0.0207
log distance from Levant 0.566 193.3 0.0000

Post-postscript.

I trained as a geometer. Yet it took me hours to recall that the interquartile range of a Boolean random variable is 1/2. Anyway, useful trick of the trade for the future. I also solved the problem of the standard error of the Axis coefficient. Turns out, the introduction of random effects for worlds confounds the Axis signal. OLS performs better than GLM. I have updated my estimates above.

Finally, we reestimate the two factor model with OLS. We find that the model residuals are strongly polarized by axis. Rounding to the nearest hundreds, the difference in medians is 1500 years and highly significant in the Kruskal Wallis test (p<0.0001). The difference in means is 1300 years and also highly significant (tStat=5.92). The 95 percent confidence interval for the mean difference is (0.9, 1.8) in ka. The interquartile ranges of the two categories do overlap: vertical (-1.7, 0.5), horizontal (-0.4, 1.4). The sole outlier is China whose transition is dated to 9ka. Let’s just say radiometric dating in Chinese prehistory is problematic. At any rate, there is a systematic difference of more than 1000 years. Diamond really is in the clear.

OLSresidualsModel2.png


Post-post-postscript.

I really might be only person who cares about this. But looking at the outliers I found that Australia and New Zealand were folded into Eurasia and therefore assigned a horizontal axis. Both are of course vertical geographic isolates. But OLS responds badly to outliers. I recoded them to have a vertical axis and recomputed the models. Also, seeing the minor contribution of absolute latitude, I dropped it. So does the pattern hold after these adjustments?

Let’s begin with unadjusted time-depths. The difference remains striking and the outliers vanish.

PPPS1.png

The next table displays the means, confidence intervals for the means, medians and quartiles, as well as the p-value for the Kruskal-Wallis test for difference in median time-depth. The raw, unadjusted Eurasian advantage is about 3.5ka.

Unadjusted Neolithic time-depth.
Vertical Horizontal Difference
Mean 2.7 6.5 3.8
Lower 2.5 6.1 3.6
Upper 3.0 6.9 3.9
Q1 1.8 5.0 3.2
Median 3.0 6.5 3.5
Q3 3.5 7.5 4.0
KW: p < 0.0001. Values displayed in ka.

Just to visualize these differences, we display the means and the difference in means. The error bars are 95 percent confidence intervals.

PPPS2.png

PPPS3.png

We also displays the medians. The error bars are interquartile ranges.

PPPSmedian.png

We next adjust time-depths for distance from the Levant using OLS. The next table reports our estimates. Controlling for distance from the Levant, we estimate the Eurasian advantage at roughly 2ka.

Neolithic time-depth adjusted for distance from Levant.
Vertical Horizontal Difference
Mean -1.0 0.8 1.8
Lower -1.3 0.5 1.9
Upper -0.7 1.1 1.8
Q1 -2.0 0.2 2.2
Median -1.3 0.9 2.2
Q3 0.5 1.5 1.1
KW: p < 0.0001. Values displayed in ka. 

We display the difference in means. The error bar displays the confidence interval.

PPPS6.png

Finally, we display a boxplot for the residuals of our single factor model.

PPPS4.png

Diamond really is in the clear. Eurasia transitioned about 3.5ka before the vertical continents. After adjusting for distance from the Levant, Eurasia is estimated to have enjoyed a 2000 year head start.


Post-post-post-postscript.

PPPPS.png

 

 

 

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