In my previous post
I took issue with Lovejoy's claim to show, by statistical analysis of global temperature data since 1500, that the probability that natural processes would produce the amount of warming observed in the period 1880 to 2008 was less, probably much less, than one in a hundred. My complaint was not with his conclusion, which might well be true, but with his argument.
In order to calculate the probability that what happened would happen as a result of natural causes of temperature change, Lovejoy needed a probability distribution showing what the probability was of a natural cause producing any given temperature change. He could estimate that distribution by looking at changes over the period from 1500 to 1880 on the (plausible) assumption that humans had little effect on global temperature over that period. But that data could not tell him the probability distribution for events rare enough to be unlikely to show up in his data, for instance some cause of warming that occurred with an annual probability of only .001.
His solution to that problem was to assume a probability distribution, more precisely a range of possible distributions, fit it with the data he had and deduce from it the probability of the rare large events that might have provided a natural cause for 20th century warming. That makes sense if those events are a result of the same processes as the more frequent events, just less likely versions of them—just as flipping a coin and getting eight heads in a row is a result of the same processes that give you four, five, or six heads in a row. But it makes no sense if there are rare large events that are produced by some entirely different process, one whose probability the observed events tell us nothing about—if, for instance, you got four heads in a row by sheer luck, forty heads in a row because someone had slipped you a two headed coin. The forty heads, or the hypothetical rare cause of large warming, would be a black swan, an event sufficiently rare that it had not been observed and so was left out of the calculation.
It occurred to me, after considering a response by Lovejoy and a comment on the Google+ version of my post, that not only was such a black swan event possible in the context of climate, one had occurred. AGW itself is a black swan, a cause of rapid warming whose probability cannot be deduced by looking at the distribution of climate change from the period 1500 to 1880.
If the point is not clear, imagine that Lovejoy wrote his article in 1880. Since warming due to human activity had not yet occurred, there would be no reason for him to distinguish between causes of warming and natural causes of warming. He would interpret the results of his calculations as showing that the probability of warming by a degree C over the next 128 years was less, probably much less, than .01. He would be assuming away the possibility of some cause of substantial warming independent of the causes of past warming, one whose probability could not be predicted from their probability distribution.
That cause being, of course, greenhouse gases produced by human action.