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It’s always been intuitively obvious that we handle small numbers more easily than large ones. But the discovery that the brain has different systems for representing small and large numbers provokes new questions about memory, attention, and mathematics…

More than 150 years ago, the economist and philosopher William Stanley Jevons discovered something curious about the number 4. While musing about how the mind conceives of numbers, he tossed a handful of black beans into a cardboard box. Then, after a fleeting glance, he guessed how many there were, before counting them to record the true value. After more than 1,000 trials, he saw a clear pattern. When there were four or fewer beans in the box, he always guessed the right number. But for five beans or more, his quick estimations were often incorrect.

Jevons’ description of his self-experiment, published in Nature in 1871, set the “foundation of how we think about numbers,” said Steven Piantadosi, a professor of psychology and neuroscience at the University of California, Berkeley. It sparked a long-lasting and ongoing debate about why there seems to be a limit on the number of items we can accurately judge to be present in a set.

Now, a new study in Nature Human Behaviour has edged closer to an answer by taking an unprecedented look at how human brain cells fire when presented with certain quantities. Its findings suggest that the brain uses a combination of two mechanisms to judge how many objects it sees. One estimates quantities. The second sharpens the accuracy of those estimates — but only for small numbers…

Although the new study does not end the debate, the findings start to untangle the biological basis for how the brain judges quantities, which could inform bigger questions about memory, attention and even mathematics…

One, two, three, four… and more: “Why the Human Brain Perceives Small Numbers Better,” from @QuantaMagazine.

* Sun Tzu

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As we stew over scale, we might spare a thought for a man untroubled by larger (and more complicated) numbers, Émile Picard; he died on this date in 1941. A mathematician whose theories did much to advance research into analysis, algebraic geometry, and mechanics, he made his most important contributions in the field of analysis and analytic geometry. He used methods of successive approximation to show the existence of solutions of ordinary differential equations. Picard also applied analysis to the study of elasticity, heat, and electricity. He and  Henri Poincaré have been described as the most distinguished French mathematicians in their time.

Indeed, Picard was elected the fifteenth member to occupy seat 1 of the Académie française in 1924.

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