Download Where Mathematics Come From: How The Embodied Mind Brings by George Lakoff PDF

By George Lakoff

This booklet is set mathematical rules, approximately what arithmetic means-and why. summary rules, for the main half, come up through conceptual metaphor-metaphorical rules projecting from the way in which we functionality within the daily actual global. the place arithmetic Comes From argues that conceptual metaphor performs a primary function in mathematical principles in the cognitive unconscious-from mathematics and algebra to units and common sense to infinity in all of its forms.

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Additional info for Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being

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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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