Otto Koehler

Numerical Competence in Animals

The German zoologist Otto Koehler (1889-1974) was the first scientist to convincingly demonstrate numerical competence in animals.

The first part of this post is based upon a panel from Counting on neurons: the neurobiology of numerical competence” (Nieder 2005)

Koehler established a number of experimental paradigms, including simultaneous or successive stimulus presentation and matching to sample and oddity matching procedures. (Koehler 1956)

He thought that animals had two numerical capabilities; a visuo-spatial one when the items to be counted were displayed all at once or simultaneously, and a temporal one when the items were displayed successively, one after the other.

He called the first capability “simultaneously seeing the number of items”, what might now be called subitising, and the second “successively acting upon the number of items”.

He tested the simultaneous capability using his match to sample experimental paradigm. A sample numerosity is indicated by ink blots, pebbles or lumps of plasticine. The task of the animal subject is to find one of two box lids that match the sample number, lift the lid off the box and find a food reward inside.

KoehlerCrowOne of Koehler’s animal subjects attempting a match to sample test

One way Koehler tested the second, sequential capability was by training birds to peck a certain number of grains from two piles of grain. For example, a bird trained on ‘five’ could eat all three grains from a small pile and two additional grains from a second, larger pile, before flying off, leaving the rest of the grains untouched. The animals also learned to combine both the simultaneous and the sequential task.

Clever Hans Effect

Clever Hans was a horse who could apparently do quite difficult arithmetic but who was shown in 1907 to be getting unintentional cues from his owner or other people watching him.

Koehler was aware of potential non-numerical cues that the birds might have relied on to solve the tasks, so he eliminated figural, positional and temporal cues to the subjects. To avoid giving the animals unconscious cues, the experimenter was out of sight of each animal throughout the sessions. An automatic spring-loaded device shooed the birds if they made errors. The experimental sessions were filmed and thoroughly analysed off-line. Most notably, Koehler introduced transfer tests in which the punishment contingency was removed. During such transfer tests, the birds successfully applied the learned numerosity discriminations to novel situations without feedback on their behaviour.

Over the years, Koehler and his students tested eight animal species in the numerical competence project and derived upper numerosity discrimination limits for each. 5 for pigeons, 6 for budgerigars and jackdaws, and 7 for ravens, african grey parrots, amazones, magpies, squirrels and humans. His work, which was published in many scientific articles, served as the basis for all the following investigations into non-verbal numerical competence and its neural foundation.

Thinking Without Words

Koehler thought that the numerical competence displayed by animals showed the non-verbal ancestral nature of some human and animal thought.

“When I want to nail and have no hammer, I go round and seek. I do not think in words, this newspaper, that glass would not do; I should better say I do not see them. But casually seeing my foot, I know at once that my shoe will be an excellent hammer. I already have its tip in my hand and strike the nail with its heel, before finding words, such as tool-character, Ersatz and the like. Most brainwaves, even in Man, may be wordless in the beginning. One has enjoyed already the invention, before one seeks the first word to describe it.”

“We owe our deepest thanks to language which, from animals, made us humans and opened the new plane of the mind, developing itself in continuous interaction, between thinking with words and without words. We should be extremely ungrateful, if we did not appreciate our thinking without words which we owe to our animal ancestors. It links the mind to the earth on which we stand. It is in all earthly matters, the touchstone on which to test words as to their validity.”


If one maps emotional and irrational to non-verbal, and intellectual and rational to verbal, this seems to be getting very close to the ideas about problem solving espoused in Design Methods. In particular the hypotheses of Synectics described there.

i) creative efficiency in people can be markedly increased if they understand the psychological processes by which they operate;

 ii) in creative process the emotional component is more important than the intellectual, the irrational more important than the rational;

iii) it is these emotional, irrational elements which can and must be understood in order to increase the probability of success in a problem-solving situation

Donald Schön is credited with developing with Gordon the importance of the hedonic response in the creative process, which they say can take two forms:

1. It is a pleasurable feeling, developed toward the successful conclusion of a period of problem solving concentration, that signals the conceptual presence of a major new viewpoint which promises to lead to a useful solution.

2. It is a pleasurable feeling which occurs in a minor way acting as a moment-to-moment evaluation of the course of the creative process itself.

Gordon goes on to state:

The PROCESS of producing either aesthetic or technical objects is accompanied by certain useful emotional responses, and that these responses must not be rejected as irrelevant, but must be schooled and liberated.


Gordon W.J.J. (1961) Synectics. Harper & Row. New York, Evanston and London

Koehler, O. (1957) Thinking Without Words. Proceedings of the14th International Congress of Zoology. Copenhagen

Niedler, A. (2005)  Counting on neurons: the neurobiology of numerical competence. Nature Reviews Neuroscience 6, 177-190 (March 2005) | doi:10.1038/nrn1626

About Graham Shawcross

Architect PhD student at Edinburgh University Interested in order, rhythm and pattern in Architectural Design
This entry was posted in Architecture, Brain Physiology, Design Methods, Enumeration, Logic and tagged , , , , . Bookmark the permalink.

One Response to Otto Koehler

  1. Noureddine says:

    wow , thank you sir please continue the good work ❤


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