Neat. The minimal example would be if each risk had 50% chance of happening: then the observable correlation coefficient would be -0.5 (not -1, since there is 1/3 chance to get neither risk). If the chance of no disaster happening is N/(N+2), then the correlation will be -1/(N+1).
It is interesting to note that many insurance copula methods are used to make size-dependent correlations, but these are nearly always of the type of stronger positive correlations in the tail. This suggests - unsurprisingly - that insurance does not encounter much anthropic risk.
It is pretty cute. I did a few Matlab runs with power-law distributed hazards, and the effect holds up well: http://aleph.se/andart2/uncategorized/anthropic-negatives/
The effect is even clearer if we have a probabilistic relation between pandemics, recessions and extinction (something like: extinction risk proportional to product of recession size times pandemic size). Then we would see an anti-correlation rising smoothly with intensity.
So something like the plot of asteroid impact sizes vs time in "The Anthropic Shadow" where the upper-right corner is empty?
This is incidentally another way of explaining the effect. Consider the standard diagram of the joint probability density and how it relates to correlation. Now take a bite out of the upper right corner of big X and big Y events: unless the joint density started in a really strange shape this will tend to make the correlation negative.
This is known as Berkson's paradox and it is ubiquitous. A lot of people have written about it and its implications, e.g. Yvain (underlying reasons why anti-correlations arise are very similar).
Interesting. Something's a bit odd, though. If the events are rare, then it's hard to know what the correlations are with any precision. If the events are common, then, yes, we should be able to see the anti-correlation, but this would be a really bad sign -- there'd be no reason to think that the disastrous event where both co-occur isn't right around the corner.
ETA: I exaggerate a bit. There'd be no reason if the independence model was true. If, in reality, there was some circumstance specially protecting us somehow the situation wouldn't have to be dire.
In the biz we call this selection bias. The most fun example of this is the tale of Abraham Wald and the Surviving Bombers.
While maybe not essential, the "anti-" aspect of the correlations induced by anthropic selection bias at least seems important. Obviously, the appropriate changes of variables can make any particular correlation go either positive or negative. But when the events all measure the same sort of thing (e.g., flooding in 2014, flooding in 2015, etc.), the selection bias seems like it would manifest as anti-correlation. Stretching an analogy beyond its breaking point, I can imagine these strange anti-correlations inducing something like anti-ferromagnetism.
There is a strange correlation between paradox of young Sun (it had lower luminosity) and stable Earth temperature which was provided by higher greenhouse effect. As sun goes brighter, CO2 declined. It was even analyses as evidence of anthropic effects.
In his article "The Anthropic Principle in Cosmology and Geology" [Shcherbitsky, 1999], A. S. Shcherbakov thoroughly examines the anthropic principle's effect using the historical dynamics of Earth's atmosphere as an example. He writes: "It is known that geological evolution proceeds within an oscillatory regime. Its extreme points correspond to two states, known as the 'hot planet' and 'white planet'... The 'hot planet' situation occurs when large volumes of gaseous components, primarily carbon dioxide, are released from Earth's mantle...
As calculations show, the gradual evaporation of ocean water just 10 meters deep can create such greenhouse conditions that water begins to boil. This process continues without additional heat input. The endpoint of this process is the boiling away of the oceans, with near-surface temperatures and pressures rising to hundreds of atmospheres and degrees... Geological evidence indicates that Earth has four times come very close to total glaciation. An equal number of times, it has stopped short of ocean evaporation. Why did neither occur? There seems to be no common and unified saving cause. Instead, each time reveals a single and always unique circumstance. It is precisely when attempting to explain these that geological texts begin to show familiar phrases like '...extremely low probability,' 'if this geological factor had varied by a small fraction,' etc...
In the fundamental monograph 'History of the Atmosphere' [Budyko, 1985], there is discussion of an inexplicable correlation between three phenomena: solar activity rhythms, mantle degassing stages, and the evolution of life. 'The correspondence between atmospheric physicochemical regime fluctuations and biosphere development needs can only be explained by random coordination of direction and speed of unrelated processes - solar evolution and Earth's evolution. Since the probability of such coordination is exceptionally small, this leads to the conclusion about the exceptional rarity of life (especially its higher forms) in the Universe.'"
You should probably include war as another resource-depleting event which amplifies the effects of an epidemic.
War also has a way of throwing lots of stressed people together under unsanitary conditions. Soldiers, refugees, people in bomb shelters, etc.
The canonical example of a war coinciding with a pandemic is probably the 1918 Spanish Flu, which killed more people than WWI did.
This is nice in principle, although I'm not sure if there's much chance of finding enough events to observe a real effect.
It might be easier to detect a positive correlation on small events that goes missing on larger ones?
Should the first blurb begin "Imagine that civilization would definitely be destroyed by" instead of "Imagine that the only way that civilization could be destroyed was by"? That's what it seems like to me based on the second blurb.
It's easier to reason with a single cause of destruction: see http://lesswrong.com/lw/hw8/caught_in_the_glare_of_two_anthropic_shadows/
Then maybe "Imagine that civilization would definitely be destroyed iff there was a..."?
The rest of the post still reads to me as if pandemic + recession is sufficient, not just necessary, for implying extinction. To be explicit, it sounds like you have ruled out the possibility of observing pandemic + recession + non-extinction, I would have thought you'd want to say that pandemic + recession = extinction, rather than the weaker statement that extinction requires pandemic + recession.
The pandemic/recession example is almost certainly wrong; it was just an illustration of the concept.
Yes, resources let you have an organized, strong state, which is vital to enforce quarantines. Milan and Venice managed almost completely to shield themselves from the Black Death through stringent isolation of the sick.
Sure. You can supply food and water and other forms of palliative care (if you don't have food and water, Ebola might kill you but thirst & starvation definitely will kill you), and resources can be used to enforce quarantines like posting watchmen to sealed-up houses or soldiers to bottlenecks.
Imagine that the only way that civilization could be destroyed was by a large pandemic that occurred at the same time as a large recession, so that governments and other organisations were too weakened to address the pandemic properly.
Then if we looked at the past, as observers in a non-destroyed civilization, what would we expect to see? We could see years with no pandemics or no recessions; we could see mild pandemics, mild recessions, or combinations of the two; we could see large pandemics with no or mild recessions; or we could see large recessions with no or mild pandemics. We wouldn't see large pandemics combined with large recessions, as that would have caused us to never come into existence. These are the only things ruled out by anthropic effects.
Assume that pandemics and recessions are independent (at least, in any given year) in terms of "objective" (non-anthropic) probabilities. Then what would we see? We would see that pandemics and recessions appear to be independent when either of them are of small intensity. But as the intensity rose, they would start to become anti-correlated, with a large version of one completely precluding a large version of the other.
The effect is even clearer if we have a probabilistic relation between pandemics, recessions and extinction (something like: extinction risk proportional to product of recession size times pandemic size). Then we would see an anti-correlation rising smoothly with intensity.
Thus one way of looking for anthropic effects in humanity's past is to look for different classes of incidents that are uncorrelated at small magnitude, and anti-correlated at large magnitudes. More generally, to look for different classes of incidents where the correlation changes at different magnitudes - without any obvious reasons. Than might be the signature of an anthropic disaster we missed - or rather, that missed us.