Steven Pinker -- How the Mind Works - Hampshire High Italian ...

Good Ideas 359mental categories like ownership, time, and will out of forms originallydesigned for intuitive physics. Other revisions take place as we live ourlives and grapple with new realms of knowledge.Even the most recondite scientific reasoning is an assembly of downhomemental metaphors. We pry our faculties loose from the domainsthey were designed to work in, and use their machinery to make sense ofnew domains that abstractly resemble the old ones. The metaphors wethink in are lifted not only from basic scenarios like moving and bumpingbut from entire ways of knowing. To do academic biology, we take ourway of understanding artifacts and apply it to organisms. To do chemistry,we treat the essence of a natural kind as a collection of tiny, bouncy,sticky objects. To do psychology, we treat the mind as a natural kind.Mathematical reasoning both takes from and gives to the other partsof the mind. Thanks to graphs, we primates grasp mathematics with oureyes and our mind's eye. Functions are shapes (linear, flat, steep, crossing,smooth), and operating is doodling in mental imagery (rotating,extrapolating, filling, tracing). In return, mathematical thinking offersnew ways to understand the world. Galileo wrote that "the book ofnature is written in the language of mathematics; without its help it isimpossible to comprehend a single word of it."Galileo's dictum applies not only to equation-filled blackboards in thephysics department but to elementary truths we take for granted. Thepsychologists Carol Smith and Susan Carey have found that childrenhave odd beliefs about matter. Children know that a heap of rice weighssomething but claim that a grain of rice weighs nothing. When asked toimagine cutting a piece of steel in half repeatedly, they say that one willfinally arrive at a piece so small that it no longer takes up space or hasany steel inside it. They are not of unsound mind. Every physical eventhas a threshold below which no person or device can detect it. Repeateddivision of an object results in objects too small to detect; a collection ofobjects each of which falls below the threshold may be detectable enmasse. Smith and Carey note that we find children's beliefs silly becausewe can construe matter using our concept of number. Only in the realmof mathematics does repeated division of a positive quantity always yielda positive quantity, and repeated addition of zero always yields zero. Ourunderstanding of the physical world is more sophisticated than children'sbecause we have merged our intuitions about objects with our intuitionsabout number.So vision was co-opted for mathematical thinking, which helps us see