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Paintbrush is Pump: Image Based Thought

coberst

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Paintbrush is Pump: Image Based Thought

Einstein said that his creative talents were a result not of mathematical skills but the result of his ability to visualize. He indicated that he did the tedious task of converting muscular movements and visualized images to words and equations only after he had completed his creative task. For example his first insight into “relativity” happened when he imagined riding on a beam of light.

What are the roles for images in human thought?

Einstein’s images might best be thought of as metaphors without words. To be more specific they are image-based metaphors wherein the source domain is a visualized scene whose inference structure can be mapped into the target domain, i.e. in this case the scientific domain.


Donald Schon, a researcher in the cognitive sciences, tells us of a group working on a difficult task of designing a satisfactory paintbrush made of synthetic bristles. In the middle of a discussion among the technicians designing the brush one of the group had that eureka moment and shouted “You know, a paintbrush is a kind of pump”. This insight Schon explains caused the designers “to notice new features of the brush and of the painting process”.

In this example and in the Einstein example the source domain, information rich with concrete experiences, has an inference structure which is immediately mapped into the target domain structure. Only later are the results, the images, accumulated into words and equations. As Oliver Wendell Holmes concluded “We need to think of things instead of words”.


 

MoonlessNight

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I completely agree with the sentiment, I just want to note that your original post makes it seem like visualization and abstract understanding are at odds with mathematics. That couldn't be less true. Mathematics is all about finding the meanings between various systems and objects, and the breakthroughs often come from the right visualizations. At least that's what gets me through it.

Well I guess technically you can't get exact visualizations for everything, for instance I can't see in my head what objects in four or higher dimensions look like. But nevertheless picking away at those types of problems still does usually come down to stumbling across the right picture.
 
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