Number sense exists for rational numbers, say York researchers

Close-up of a blue human eye

Running past the kitchen counter, you catch a glimpse of a plate of raspberries. Although you don’t stop to count them, you’re left with a rough idea of how many there were. Rushing back past the counter again, you now see a plate of blueberries. You can tell just by looking that there were more raspberries than blueberries.

Cognitive scientists call this capacity for estimating numbers ‘the number sense.’ Studies have found evidence for it in a wide range of animals, including fish, birds and mammals. Even human infants seem to have it since, if you show a six-month-old displays of 12 dots until they get bored and look away, they’ll recover interest and look intently if you switch to a display with six or 24 dots.

But does the number sense really represent ‘numbers?’ Could all of these organisms really be innate mathematicians? Or might the ‘number’ sense instead represent something simpler, such as how much surface area is covered with red stuff, or how densely the raspberries are packed together?

Jacob Beck
Jacob Beck
Sam Clarke
Sam Clarke

In a new target article in Behavioral and Brains Sciences, York Research Chair in the Philosophy of Visual Perception Jacob Beck and VISTA Postdoctoral Fellow Sam Clarke (now a MindCore Fellow at the University of Pennsylvania) argue that number sense does represent numbers.

“We both noticed that cognitive scientists have been locked in a debate about whether the number sense represents numbers,” said Clarke.

“And as philosophers, we noticed that there were conceptual issues that kept tripping people up,” added Beck. “So we decided to dive deep into the empirical literature and try to figure out what was really going on.”

Beck and Clarke concluded the number sense not only represents positive whole numbers such as one, two and three, but also rational numbers more generally, such as one-half and two-and-a-half. “But not irrational numbers, such as 𝜋 or √2,” said Clarke. “We drew the line there.”

Their target article has been published alongside 26 commentaries by 62 researchers and their reply. The commentators hail from a variety of disciplines, including vision science, philosophy, neuroscience, developmental psychology and education.

“It was a tremendous honour,” said Clarke, “if also a bit intimidating, to have so much attention lavished on our arguments. We learned so much. The whole process was amazing.”

Read the exchange here.