By George Lakoff
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Additional info for Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being
Here is one of the now-classic experimental procedures (Starkey 8k Cooper, 1980): Slides were projected on a screen in front of babies sitting on their mother's lap. The time a baby spent looking at each slide before turning away was carefully monitored. When the baby started looking elsewhere, a new slide appeared on the screen. At first, the slides contained two large black dots. During the trials, the baby was shown the same numbers of dots, though separated horizontally by different distances.
Landing completes the process of jumping. The com pletion, landing, is conceptualized as part of the jumping, as internal to what "jump" means. There is a minimally contrasting case that exemplifies case 2: fly ing. In the everyday concept of flying, as with birds and planes, landing is part of the conceptual frame. Landing follows flying and is a completion of flying. But landing is not conceptualized as part of flying. Landing is a completion of flying but it is external to flying. The distinction between an internal completion, as in jump, and an external completion, as in fly, is crucial in aspect.
Finally, to show that this result had to do with abstract number and not par ticular objects, other experimenters had the puppets change to balls behind the screen. When two balls appeared instead of two puppets, four- and five-montholds (unlike older infants) manifested no surprise, no additional staring at the stage. But when one ball or three balls appeared where two were expected, the babies did stare longer, indicating surprise (Simon, Hespos, fin Rochat, 1995). The conclusion was that only number, not object identity, mattered.
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