How do animals ‘do’ geometry?

How do they, indeed? A reply to Biegler et al.

“…And which groups learn faster may provide important information about the use of geometric principles by animals. We are in basic agreement with Biegler et al (1999) that further studies are needed before we can answer the question 'How do animals ''do'' geometry? '…”

“…We reached two conclusions based on this rather precise transfer: (1) the birds used the relationship between the landmarks (rather than goal-landmark relationships) to solve the problem; and (2) the birds had learned a general principle which they could then apply to new interlandmark distances. Biegler et al (1999) propose a model that agrees with our first conclusion but suggests that we were premature in the second. According to their model the nutcrackers learned specific vectors for each interlandmark distance used during training.…”

“…Biegler et al (1999) suggest two tests. One would be to test nutcrackers with distances outside the range of interlandmark distances with which they were trained, especially at shorter distances.…”

“…As part of a larger study exploring geometric rule learning, we have collected data on this point and preliminary (unpublished) analyses do not support the prediction. Biegler et al (1999) also suggest that we test the birds with rotated landmarks, varying the distance between the landmarks during the tests. While the results of such a test would be of interest, they might well be inconclusive.…”

The use of relative and absolute bearings by Clark’s nutcrackers,Nucifraga columbiana

“…nutcrackers readily learned the task. When the landmarks were presented at novel interlandmark distances within the range with which they had been trained, birds continued to search halfway between the landmarks, demonstrating they had probably learned something about the geometric relationship between the goal and landmarks rather than memorizing the training configurations (but see Biegler, McGregor, & Healy, 1999, and the reply by Kamil & Jones, 1999).…”