OK, I have to admit this is a pretty eccentric idea . It occurred to me around New Year’s time. Please read this as entertainment, not science – or at best, entertaining science. I assume the esteemed reader to be familiar with Heisenberg’s uncertainty principle .
These days, even small-time lawyers are using the concept – as we were reminded by the Coen brothers in the magnificently quirky “The Man who wasn’t there” :
Forgetting the Coen twist, the uncertainty principle states that there is a fundamental limit to the accuracy with which you can jointly determine the position () and the momentum () of a particle in quantum world. Which one can write :
wherein is the root mean square operator and is the familiar Planck’s constant.
This has pretty deep philosophical implications because it means that we must abandon utopias of ever knowing those quantities simultaneously with arbitrary accuracy. Most sobering is that it is a direct consequence of the fundamental principles of quantum mechanics.
It occurred to me the other day while having a shower (which is a well-known fountain of ideas), that one could formalize a similar principle in climatology. Indeed, the basic curse of paleoclimatology is that the farther back in time you try to estimate temperatures, the more uncertain they become. We think we know last year’s globally average temperature pretty well (say within 0.05 C ). Last decade might have similar or even lower uncertainties because of the central limit theorem knocking down some measurement errors for you… but try going back 100 years and the measurement error and sampling bias become so large you’ll be lucky to have an accuracy of 0.5 C. And that is during a period broadly known in the field as “instrumental”, that is to say the one over which we have a reasonable number of physical measurements of temperature. As you can see on the following graph from Brohan et al, 2006, this uncertainty grows back in time rather quickly already.
Before about 1850 A.D., we no longer have enough direct measurements, so we have to rely instead on proxy indicators. All of them (corals, tree rings, ice cores, sediments, documentary evidence) have their pros and cons, but even if they can give a surprisingly coherent view of past climates, they are necessarily approximate. Hence, go back 1000 years and arguably, we don’t know this within 0.7 C, perhaps even 1 C (this is a very controversial number and I’d be surprised if no one picks up on it… With wacky ideas come rather loose numbers that one should not take too literally). Go back 10,000 years and a degree C or two might be all that you could hope for. And so on and so forth : the more time elapses and eons pass by, the more water flows under bridges, the more overprinted, worn and tired is the geologic record – and so grows the uncertainty in the estimated temperature.
Say you are trying to estimate said temperature, , over some period (or equivalently, the frequency ). The longer the period (i.e., the smaller the frequency), the more uncertain the estimate, so one could write something of the form :
Which is pretty naive and assumes an inverse relationship between the two variables, and is by no means a “universal” constant. More generally one could write :
where the subscript denotes a reference period (say, the last decade), and and are a positive constants, whose precise values are as yet undetermined. So one could play games with that and try to estimate them from a linear fit in log-log space… I’m not sure they would mean much, but who knows ? Perhaps one day we’ll have enough reliable data to be able to characterize this and it won’t seem so quirky. In any case, it’s now pretty far from Heisenberg, who must be shifting in his grave and the mere idea that I am using is august name for such silliness. Nevertheless, it is an uncertainty principle of sorts. And for no more fundamental reason that the degradation of geological records over time, which I guess one could view as a broad consequence of disequilibrium thermodynamics. But only loosely so, because bioturbation holds a large part of the blame, and darned if we have a consistent theory of living organisms that’s grounded in statistical mechanics. But I digresss.
In my defense, I would like to declare that this nonsense was scribbled on a piece of paper while leaning on a garbage can outside the Metropolitan Avenue subway station in Williamsburg, Brooklyn. Which we all know to be home to some pretty crazy stuff.
Now here’s the truly insane part of the story. The next day was my adoptive bigger sister’s birthday. ( If you happen to live far from home, I highly recommend you adopt, or get adopted by, a bigger sister. It’s loads of fun, especially when they have the same linguistic schizophrenia as yours). I was working from the Columbia University library that day, and decided to drop by to bring her a gift (she lives around the corner). I had no sooner entered her building and stepped into the elevator that a white-haired gentleman nimbly entering the lobby asked me to hold the doors. I happily obliged, and he promptly jumped into the cage a few seconds afterwards, with a mischievous smile on his face.
– “Piso cuatro, por favor “, he said with a distinguished Spanglish accent.
– “Si señor”, I replied, and pushed button 4.
He looked at me from top to bottom and asked in a spotless New England English (I must have looked really freaky) :
– “Are you a physicist ?”
– “Almost”, I replied, “I’m a geophysicist”.
– “Ah well, I am a physicist”, he went on. “And I recently had a very interesting epiphany about Heisenberg’s uncertainty principle.”
Before I could pick up my jaw from the floor, Mr Heisenberg Jr had disappeared into the depths of the 4th floor, only perceptible through the rustling of his raincoat as his walked down the corridor. And so it was decided that even though my Heisenberg idea might not pass into posterity past breakfast, it should at least be worthy of a little post.