Natural Variability and Climate Sensitivity

Now, the unfortunate thing is that the mice are too light and come along too infrequently for you to get a good estimate of the stiffness of the spring by just watching the response of the platform to mice jumping on it. However, from looking through other dusty records elsewhere in the basement of the British Museum, you discover some notes from an earlier curator, who had also observed the box. He notes that there used to be big, heavy rats in the Museum basement, and has written down some things about what happens when the rats jump on the platform. From indirect evidence, like footprints in the dust, size of rat droppings, shed fur, plus some incomplete notes left behind by the rat catcher, you infer that the typical rat weighed a quarter kilogram. Now, the curator has left behind some notes about how much the platform drops when a rat jumps onto it from the shelf just above the platform. Unfortunately, the curator was a scholar of Old Uighur, and left behind his notations in the Old Uighur numeration system so his rivals couldn’t read it. Also unfortunately, the curator died before publishing his explanation of the Old Uighur numeration system, and that has been lost to time. Using the same Uighur wheat production records available to the curator, you estimate that his notes mean that the typical displacement is 10 centimeters per rat. From this you estimate that the stiffness of the spring is such that a 1 kilogram brick would cause a 40 centimeter displacement of the platform. Things are looking good. You get paid a handsome sum. Then, one day, to your horror, you open a journal of Uighur studies and find a lead article proving that everybody has been interpreting Uighur wheat production records wrong, and that all previous estimates of what the Uighur numbers mean were off by a factor of two. That means that while you thought the typical displacement of the platform was 10 centimeters per rat, the "natural variability" caused by rats jumping on the platform is much greater than you thought. It was actually 20 centimeters, using the new interpretation of the Uighur numbering system. Does that mean you ring up the Museum and say, "I was all wrong — the natural variability was twice what we thought, so it is unlikely that adding a new brick to the platform will cause as much effect as I told you last year!" No, of course you don’t. Since you have no new information about the weight of the rats, the correct inference is that the spring in the box is softer than you thought, so that the predicted effect of adding a brick will be precisely twice what you used to think, and more likely to break something. However, being a cautious chap, you also entertain the notion that maybe the displacement of the platform was more than you thought because the rats were actually fatter than you thought; that would imply less revision in your estimate of the stiffness of the spring, but until you get more data on rat fatness, you can’t really say. If you think all this is obvious, please hold the thought in mind, and bring it back when, towards the end of this commentary, I tell you what Esper et al. wrote in an opinion piece regarding the implications of natural variability observed over the past millennium.

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