To Bee or not to Bee, this is the Question … The Inborn Numerical Competence of Humans and Honeybees

Abstract

Human inborn numerical competence means our ability to recognize object numbers precisely under circumstances which do not allow sequential counting. This archaic process has been called “subitizing”, from the Latin “subito” = suddenly, immediately, indicating that the objects in question are presented to test persons only for a fraction of a second in order to prevent counting. In contrast, however, sequential counting, an outstanding cultural achievement of mankind, means to count “1, 2, 3, 4, 5, 6, 7, 8 …” without a limit. The following essay will explain how the limit of numerical competence, i.e., the recognition of object numbers without counting, has been determined for humans and how this has been achieved for the first time in case of an invertebrate, the honeybee. Finally, a hypothesis explaining the influence of our limited, inborn numerical competence on counting in our times, e.g., in the Russian language, will be presented. Subitizing versus counting by young Down syndrome infants and autistics and the Savant syndrome will be discussed.

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Acknowledgments

This esssay is dedicated to Academician Professor Dmitri G. Knorre, former Director of the Novosibirsk Institute of Bioorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation, on the occasion of his 85^th birthday on July 28, 2011. I thank Dr. E. Weichselgartner (University of Trier), Profs. H. Hoehn and M. Erler (University of Würzburg) for valuable advice; Prof. Ilse Kunert (Munich) for explaining how Russians count any objects and Profs. H. Beier and J. Tautz (University of Würzburg) for critical reading of the manuscript. I am especially grateful to Klara Azzami for remodelling Table 1 and for help with Figure 1, and Mario Pahl for Figure 2 and for helpful comments.

Figures and Tables

Figure 1 The “magical number four”: Presentation of honeybees in ancient Egypt. (A) 4^th dynasty (∼2613–2404 B.C.), Roemer-Pelizaeus-Museum, Hildesheim, Germany; (B and C) 5^th dynasty (∼2500–2350 B.C.) and (D) 19^th dynasty (∼1292–1186 B.C.), Egyptian Museum in Berlin-Charlottenburg, Germany, reproduced with permission.

Figure 2 (adapted from Pahl et al.13). Delayed match-to-sample (DMTS) setup in a Y-maze. The bee has to memorize the sample stimulus A (two blue dots) and to recall it when deciding for one of the two matching stimuli A' or B' inside the maze. The exit A' leads to a reward (a sugar solution) in this example. The location of the reward was randomized irregularly among A' and B', respectively. During testing, the arrangement of dots differed between the entrance A and the correct exit A'. In order to make the task much more difficult, the dots were arranged in randomized orientations between stimulus A and A'. Finally the dots were replaced by novel objects some of which the bees had never seen before: yellow lemons, green leaves, yellow stars or blue dots in random orientations.6 Baffles behind the exits A' and B' prevent the bees from seeing the reward. In this context it is relevant to remember that the duration of the visual working (short term) memory of the honeybee is less than 10 seconds.14.

Table 1 A summary of 1,027 trials to determine the precision of numerical discrimination when sequential counting is prevented (modified from Jevons2)

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Notes

† The works of Aristotle: 490a32-b7=Book I. 5: .”.. Creatures that have two winglets or fins, or that have none at all like serpents, move all the same with no less than four points of motion; for there are four bends in their bodies as they move, or two bends together with their fins. Bloodless and many-footed animals, whether furnished with wings or feet, move with more than four points of motion; as, for instance, the dayfly moves with four feet and four wings: and, I may observe in passing, this creature is exceptional not only in regard to the duration of its existence, whence it receives its name, but also because though a quadruped it has wings also. All animals move alike, four-footed and many-footed; in other words, they all move cross-corner-wise. And animals in general have two feet in advance; the crab alone has four…” 552b17-23=Book V. 19: “…On the river Hypanis in the Cimmerian Bosphorus, about the time of the summer solstice, there are brought down towards the sea by the stream what look like little sacks rather bigger than grapes, out of which at their bursting issues a winged quadruped. The insect lives and flies about until the evening, but as the sun goes down it pines away, and dies in at sunset having lived just one day, from which circumstance it is called the ephemeron…”

‡ Cicero: De Officiis, Liber Secundus, § 11: “… Expertes rationis equi, boves, reliquae pecudes, apes, quarum opera efficitur aliquid ad usum hominum atque vitam. […Without intelligence are horses, cattle, other (domestic) animals (and) bees, by the activities of which something is achieved for humans and their livelihood.]” Translation by the author.