#spatial reasoning

Arithmetic as a Spatial Problem

solution to the puzzle from earlier

Tversky devotes a lengthy section to gesture, and for good reason: We do it incessantly. We do it naturally when we talk. But Tversky argues that gesturing is more than just a by-product of speech: it literally helps us think. She invites us to try this experiment: “Sit on your hands. Then explain out loud how to get from your house to the supermarket, train station, your office or school.” Turns out, it’s hard. When we can’t gesture, we have trouble speaking; we simply “can’t find the words,” she writes. (She notes that this isn’t just a thought experiment; it’s been confirmed in the lab.) Even people who have been blind from birth seem to rely on gesturing, she says.  Tversky argues that our ability to imagine the layout of objects in space is at the root of a more general — and more essential — skill. This ability, she believes, is the key to abstract thought. “Spatial thinking enables abstract thinking,” she writes. The mind imagines the world, but the objects of the mind are not physical objects. What are they? We might call them ideas; psychologists often call them representations. The important thing is their astounding versatility: we can manipulate them, change them, play with them. They can become “symbols in mathematics, words in poetry, particles in physics, molecules in chemistry, buildings in a neighborhood, dancers on a stage,” she writes. [...] What seems to be universal is the way we imagine time in a linear fashion. Tversky intuits that her readers may be wondering about cyclical conceptions of time (think of all the things that recur every day, like our various meals, or every year, like the seasons). And what about Eastern cultures, which we’re often told have a more cyclical perspective? But Tversky has collected data from China, and it matches the Western form: “Chinese participants responded the same as Americans, overwhelmingly creating linear representations of cyclical events,” she writes. (And then there’s what Tversky calls the “Famous Ambiguous Question”: What does it mean when we receive a memo that says that Wednesday’s meeting “has been moved forward two days”? Apparently half of us take it to mean the meeting has been moved to Monday, half of us presume it means Friday.)

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