The Animals That Weigh Numbers Without Counting Them

AFew claims in animal cognition travel as far on as little evidence as the claim that an animal can count. A honeybee that flies past three landmarks and settles at the fourth, a lioness that advances only when the roars ahead of her are outnumbered by the roars behind — such findings are reported, almost by reflex, in the vocabulary of arithmetic. The borrowing is not innocent. Counting, as the word is used of a child, means running through an ordered list of symbols, attaching one symbol to each item in turn, and treating the last symbol reached as a property of the whole set; nothing in that definition is delivered by a bee settling at the fourth landmark. What the laboratories in fact measure is discrimination between quantities, and whether an ability of that kind has earned the older word is the argument the field has never settled.

BRenata Kolbe, a comparative psychologist at the Halvorsen Institute of Cognitive Biology, argues that these performances are the output of a single estimator crude enough to need no symbols at all. On her account an animal compares two collections by their ratio, so that the difficulty of a choice depends on how the two quantities stand to each other and not on how large either of them happens to be; a bird that separates two items from five will separate twenty from fifty just as readily. Between 2014 and 2021 her group ran 38,000 trials with 96 animals drawn from seven species, and recorded that a choice is made, on average, about 1.6 seconds after both arrays are exposed. Fed nothing but the ratio of the two quantities, her model reproduced 84 per cent of the choices her animals actually made. Nothing in the account keeps a number: a quantity is discarded as soon as the comparison it was needed for is over, and what survives is only a record of which side was the greater.

CAn explanation of that shape makes a prediction, and Kolbe has tested it. If a choice is nothing but two magnitudes weighed against each other as they arrive, the animal should be beaten wherever two large collections differ by a single item, and beaten too wherever the winning collection must be identified after it has passed out of sight. In her matched-ratio sessions, animals asked to separate four items from five succeeded on 58 per cent of trials, against 93 per cent when the same animals separated two items from five. Accuracy above chance on the large-set trials was confined to sessions in which the two collections were exposed side by side rather than one after the other. The contrast is instructive, since a nutcracker storing seed handles the delayed version comfortably and the simultaneous one poorly. Kolbe insists that the figures be read as a fence around one explanation rather than a verdict on the animals themselves.

DYusuf Adeyemi, a behavioural ecologist at the Tarnholm Field Station, replies that an animal choosing between arrays of dots on a screen for a food reward is working in conditions its species never meets, and that a failure recorded there describes the apparatus at least as much as its occupant. His own birds are wild carrion crows, tested at caches of real food along a single valley, an arrangement now widely copied but thought impractical when he began it in 2019. Under that regime, 68 per cent of his crows returned to the larger of two caches after a delay of ten minutes, even where the caches held seven items and eight. Adeyemi grants two weaknesses. His nineteen birds all came from one valley population, and the running total he calls sequential updating was inferred from the order of the visits and their timing alone, because nothing yet allows it to be measured in a free-living bird.

EThe argument has carried well beyond the aviary. Survey teams have taken up the ratio rule as an engineering principle: a 2020 study turned it into an automatic count of nesting seabirds from photographs that cut error by 27 per cent, although the gain disappeared wherever the birds overlapped in the frame. Agencies in three countries have commissioned similar tools, and one was criticised for advertising its output as counting learned from crows. Kolbe points out, uncomfortably for her own position, that the rule was fitted entirely on arrays of identical black dots and predicts nothing about a moving flock. Adeyemi, for his part, holds that the two accounts answer different questions rather than the same one, and that funding bodies read a report of skill as evidence that an animal has been explained. Both regret the habit of publishing the one bird that succeeded rather than the spread of the untidy ones.

FA settlement of sorts is forming in which the two accounts are given different work rather than ranked against each other. Where both collections are in view at once, choice behaves as the ratio rule says it should, with no quantity kept from one moment to the next, which would explain both the speed of the response and the animals' indifference to how many items they saw on the previous trial. Where a choice must survive a gap in time, attention has turned instead to sequential updating, a total revised at each visit rather than a number held whole. What remains open is whether such a total is maintained in the wild, where foraging is broken off by predators and rivals and no visit is ever completed undisturbed, and no field method now available can decide the matter. What both researchers reject is the assumption behind the older vocabulary: that an animal without symbols must be either a failed arithmetician or nothing at all.