Comments on “The parable of the pebbles”
Comments are for the page: The parable of the pebbles
reference on crows; also about reproducibility in biology
The best place to start to see what’s been done on numerosity in crows is to look up Andreas Nieder, in Tubingen. The short version is that individual neurons in the relevant region of the brain are tuned for specific numbers of inputs. It does not seem that the crow “counts” the way your shepherd does so much as that it estimates a count, which can be either from a simultaneous viewing of objects or a sequential interaction (depending on the percept). Thus, larger numbers light up cells at a glance, as do small numbers; there is no extra delayfor “counting”. The “error function” in a comparison is therefore comes from the usual sort of analog synaptic interactions among neurons tuned to different values. There is a certain amount known about the neurophysiological details, but I’d have to look it up to remember them. The error metric is linear on a log scale (which I think is also true in human psychophysics, but don’t quote me). There are also cells tuned to zero, but this seems to act as a numerical value, not a categorical one - it is closer to “1”, further from “2”, etc on the same scaling as any other small number. Categorical evaluations can be made, however, for example for >, <, = and not = .
On a different point, I was reading through “the eggplant” and noticed your comment alluding to the reproducibility crisis in science. I don’t believe this actually exists. There are individual subjects, notably human psychology, where it is very real and has largely to do with the fact that the observations are so astronomically distant from underlying mechanism, connected only by uncountable layers of speculative philosophizing. But in basic biology, for example cell and molecular biology, where such a noise has been made about it, what people have taken to be a reproducibility crisis is really just a progressive denial of what you dub nebulosity. (Thanks for the word, by the way; it gives me a perfect way of talking about a concept that ought to be obvious to anyone who has ever done biology, but increasingly is disallowed.) It seems that the more our observations show us the inherent fuzziness of categories, and the chaotic (sensu stricto) connection between initial conditions and final observations in biology, the more that people try to pretend to a pseudo-Newtonian determinism that just doesn’t fit biological reality. One can come up with various sorts of sociological babel to account for this, but it comes back at us as a belief that science is getting less “rigorous”, when in fact, increasingly we are simply denying the intrinsic messiness of reality.
counting, rationality and Homo sapiens
From the perspective of the evolution of rationality, or perhaps its potential universality, it is interesting to note that recognizing numerical correspondence is not an exclusively human, or even primate, capability. Crows have demonstrated numerosity. They have the intrinsic capability to compare numerical quantities and recognize even rather abstract correspondences (eg., matching n sequential sounds to n visual objects). Whether the mechanisms used by crows and primates reflect evolutionary convergence or orthology is unclear at this point, to the best of my knowledge. In the experimental setting, ambiguities are generally minimized, this could easily be modulated. Either way, recordings from single neurons makes it clear that there is intrinsic nebulosity in the neural representation of numerical quantities - in crows and in primates - and that the neural circuitry employs error functions in making comparisons.