“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.”
and
“For example, some neurons are tuned to the number 3. When they’re presented with three objects, they fire more. Other neurons are tuned to the number 5 and fire when presented with five objects, and so on. These neurons aren’t exclusively committed to their favorites: They also fire for numbers adjacent to it. (So the neuron tuned to 5 also fires for four and six objects.) But they don’t do it as often, and as the presented number gets farther away from the preferred number, the neurons’ firing rate decreases”
So, the experiment was about integers, not numbers in general, and the neurons don’t necessarily encode integers, but also could encode reals with noise/uncertainty.
I think the latter decently describes the experimental data if the noise/uncertainty is around 20% of the value. Rounding such a signal to integers will be faultless for n < 4, and get increasingly worse the larger n is.
In pseudocode:
Round(n * (1 + gaussianRandom())) == n
To support a claim that we’re better at smaller integers, I think you’d have to show that the standard deviation for larger n goes up superlinearly.
(An alternative way to phrase this is by claiming that these cells encode logarithms of numbers)