They're referring to this argument for where the distribution may come from (where the authors "model" the scientific community -- namely the contributors to the NIST database -- as a Boltzmann distribution in possibly the most hand-wavey argument I've seen in a paper):
> An entirely different yet equally fascinating possibility would be that, in an abstract sense, the scientific community itself can be interpreted as a thermodynamic ensemble. In this line of thinking, the individual members would be subject to a Boltzmann distribution in “curiosity” associated with a “temperature” determining how likely each researcher is to carry out research more or less closely tethered to a specific area of interest.
It's a cute idea, and maybe something I'd enjoy arguing over a drink. But the obvious problem with such a model is that there is no theoretical basis to argue it from -- if only because Boltzmann distributions (as with most thermodynamic effects) only start to apply when you have so many indistinguishable particles and thus so many microstates that multiplicative factors on the scale of Avogadro's number become trivial. Scientists are neither indistinguishable, nor are they this numerous.
To be fair, the effect described here is something that I wouldn't expect a-priori. I'm just disappointed the paper doesn't really offer much of a conclusion (or even hints at a decent argument).
> To be fair, the effect described here is something that I wouldn't expect a-priori.
True, but I'm not that convinced the Boltzmann really is the most natural distribution to claim fits. Especially on the blue side it looks like the residuals could be pretty atrocious. Why didn't they try to some other right-skewed distributions? You could try a log-normal for instance, that would have a much simpler interpretation.
I think this crazy thermodynamic idea is really the entire motivation for the paper, and explains why they didn't really spend any effort exploring it.
I guess my point is that I wouldn't necessarily expect there to be any clear trend to the set of all spectral lines. The Boltzmann fit looks fairly iffy to me as well -- it seems like they just picked an arbitrary distribution (which had a cute pseudo-explanation) that was unimodal with a log tail.
One possible explanation I thought of (which I'm surprised the paper doesn't consider) is whether this is just showing the distribution of wavelength ranges of spectrometers that researchers are using. I tried to find some examples online, but I guess you'd need to be involved in the field to know what exactly to search for.
> I wouldn't necessarily expect there to be any clear trend to the set of all spectral lines
Me neither, but admittedly mainly because I've never even considered the question.
Some reflection gives me the expectation that there should be fewer high frequency lines due to conservation of energy, and very many low frequency lines.
Then I imagine experimental limitations mean it's very hard to see all the low frequency transitions, but honestly I have no idea how the cross sections of the transitions go with energy so I should stop speculating.
> An entirely different yet equally fascinating possibility would be that, in an abstract sense, the scientific community itself can be interpreted as a thermodynamic ensemble. In this line of thinking, the individual members would be subject to a Boltzmann distribution in “curiosity” associated with a “temperature” determining how likely each researcher is to carry out research more or less closely tethered to a specific area of interest.
It's a cute idea, and maybe something I'd enjoy arguing over a drink. But the obvious problem with such a model is that there is no theoretical basis to argue it from -- if only because Boltzmann distributions (as with most thermodynamic effects) only start to apply when you have so many indistinguishable particles and thus so many microstates that multiplicative factors on the scale of Avogadro's number become trivial. Scientists are neither indistinguishable, nor are they this numerous.
To be fair, the effect described here is something that I wouldn't expect a-priori. I'm just disappointed the paper doesn't really offer much of a conclusion (or even hints at a decent argument).