Even scientists are fond of thinking of the human brain as a computer,
> following sets of rules to communicate, make decisions and find a meal.
> Almost all adults understand that it's the last digit—and only the last
> digit —that determines whether a number is even, including participants in
> Lupyan's study. But that didn't keep them from mistaking a number like 798
> for odd.
> A significant minority of people, regardless of their formal education,
> believe 400 is a better even number than 798, according to Lupyan, and also
> systematically mistake numbers like 798 for odd. After all, it is mostly
> odd, right?
> "Most of us would attribute an error like that to carelessness, or not
> paying attention," says Lupyan, whose work was published recently in the
> journal Cognition. "But some errors may appear more often because our
> brains are not as well equipped to solve purely rule-based problems."
> Asked in experiments to sort numbers, shapes, and people into simple
> categories like evens, triangles, and grandmothers, study subjects often
> broke simple rules in favor of context.
> For example, when asked to consider a contest open only to grandmothers
> and in which every eligible contestant had an equal chance of victory,
> people tended to think that a 68-year old woman with 6 grandchildren was
> more likely to win than a 39-year old woman with a newborn grandkid.
> "Even though people can articulate the rules, they can't help but be
> influenced by perceptual details," Lupyan says. "Thinking of triangles
> tends to involve thinking of typical, equilateral sorts of triangles. It is
> difficult to focus on just the rules that make a shape a triangle,
> regardless of what it looks like exactly."
> In many cases, eschewing rules is no big deal. In fact, it can be an
> advantage in assessing the unfamiliar.
> "This serves us quite well," Lupyan says. "If something looks and walks
> like a duck, chances are it's a duck."
> Unless it's a math test, where rules are absolutely necessary for success.
> Thankfully, humans have learned to transcend their reliance on similarity.
> "After all, although some people may mistakenly think that 798 is an odd
> number, not only can people follow such rules—though not always
> perfectly—we are capable of building computers that can execute such rules
> perfectly," Lupyan says. "That itself required very precise, mathematical
> cognition. A big question is where this ability comes from and why some
> people are better at formal rules than other people."
> That question may be important to educators, who spend a great deal of
> time teaching rules-based systems of math and science.
> "Students approach learning with biases shaped both by evolution and
> day-to-day experience," Lupyan says. "Rather than treating errors as
> reflecting lack of knowledge or as inattention, trying to understand their
> source may lead to new ways of teaching rule-based systems while making use
> of the flexibility and creative problem solving at which humans excel."
The difficulties of executing simple algorithms: why brains make mistakes
It is shown that educated adults routinely make errors in placing stimuli
into familiar, well-defined categories such as triangle and odd number.
Scalene triangles are often rejected as instances of triangles and 798 is
categorized by some as an odd number. These patterns are observed both in
timed and untimed tasks, hold for people who can fully express the
necessary and sufficient conditions for category membership, and for
individuals with varying levels of education. A sizeable minority of people
believe that 400 is more even than 798 and that an equilateral triangle is
the most "trianglest" of triangles. Such beliefs predict how people
instantiate other categories with necessary and sufficient conditions,
e.g., grandmother. I argue that the distributed and graded nature of mental
representations means that human algorithms, unlike conventional computer
algorithms, only approximate rule-based classification and never fully
abstract from the specifics of the input. This input-sensitivity is
critical to obtaining the kind of cognitive flexibility at which humans
excel, but comes at the cost of generally poor abilities to perform
context-free computations. If human algorithms cannot be trusted to produce
unfuzzy representations of odd numbers, triangles, and grandmothers, the
idea that they can be trusted to do the heavy lifting of moment-to-moment
cognition that is inherent in the metaphor of mind as digital computer
still common in cognitive science, needs to be seriously reconsidered.
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