ABSTRACT: Different species of animals can discriminate numerosity, the countable number of objects in a set. The representations of countable numerosities have been deciphered down to the level of single neurons. However, despite its importance for human number theory, a special numerical quantity, the empty set (numerosity zero), has remained largely unexplored. We explored the behavioral and neuronal representation of the empty set in carrion crows. Crows were trained to discriminate small numerosities including the empty set. Performance data showed a numerical distance effect for the empty set in one crow, suggesting that the empty set and countable numerosities are represented along the crows’ “mental number line.” Single-cell recordings in the endbrain region nidopallium caudolaterale (NCL) showed a considerable proportion of NCL neurons tuned to the preferred numerosity zero. As evidenced by neuronal distance and size effects, NCL neurons integrated the empty set in the neural number line. A subsequent neuronal population analysis using a statistical classifier approach showed that the neuronal numerical representations were predictive of the crows’ success in the task. These behavioral and neuronal data suggests that the conception of the empty set as a cognitive precursor of a zero-like number concept is not an exclusive property of the cerebral cortex of primates. Zero as a quantitative category cannot only be implemented in the layered neocortex of primates, but also in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.
SIGNIFICANCE STATEMENT: The conception of “nothing” as number “zero” is celebrated as one of the greatest achievements in mathematics. To explore whether precursors of zero-like concepts can be found in vertebrates with a cerebrum that anatomically differs starkly from our primate brain, we investigated this in carrion crows. We show that crows can grasp the empty set as a null numerical quantity that is mentally represented next to number one. Moreover, we show that single neurons in an associative avian cerebral region specifically respond to the empty set and show the same physiological characteristics as for countable quantities. This suggests that zero as a quantitative category can also be implemented in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.
edit: The idea of zero is always one of those things that seemed like it didn’t need big brain mathematicians to develop, like the Pythagorean theorem being a common sense thing you naively get if you’ve ever walked somewhere with a diagonal shortcut. You have a practical need to understand the absence of something numerical if you are a social animal dealing with resource scarcity. If I forage 10 handfuls of berries and need to distribute that to my group of little monkey-ass things, I don’t eat unless I understand that I can give away 9 handfuls but not 10. Even if I knew nothing else about mathematics I’d know 10-10 equals some kind of total absence of berries, with those still existing as a category without a quantity.
The reason this corvid study is different from intuitively knowing that 10-10=no berries is where this 0/empty set is represented on the numberline.
Considering 0 as a number vs the empty set are two different concepts. It’s the difference between having a bank account with $0, vs having no bank account. They don’t close your account when you have $0, so it’s still an amount of money.
Crows considering 0 on the numberline, and differently from the empty set shows they have a more abstract concept of numbers than we thought.
Idk who authored this study, seems like a very specific kind of person who is both into number theory and neural pathways of birds to design.
Or Anthropology. Right now, we have realized that New Caledonian crows have entered an equivalent to the early stone age in humans. Therefore, we can gain a lot of insight both about the nature of technological progression and of the very nature of intelligence (and the differences between mammalian and avian intelligence) by doing these studies.
Isn’t the Pythagorean theorem less about the fact that a diagonal is shorter than taking a corner (which is indeed obvious) and more about calculating how much shorter it is?
https://www.livescience.com/crows-understand-concept-of-zero.html
https://www.jneurosci.org/content/41/22/4889
edit: The idea of zero is always one of those things that seemed like it didn’t need big brain mathematicians to develop, like the Pythagorean theorem being a common sense thing you naively get if you’ve ever walked somewhere with a diagonal shortcut. You have a practical need to understand the absence of something numerical if you are a social animal dealing with resource scarcity. If I forage 10 handfuls of berries and need to distribute that to my group of little monkey-ass things, I don’t eat unless I understand that I can give away 9 handfuls but not 10. Even if I knew nothing else about mathematics I’d know 10-10 equals some kind of total absence of berries, with those still existing as a category without a quantity.
The reason this corvid study is different from intuitively knowing that 10-10=no berries is where this 0/empty set is represented on the numberline.
Considering 0 as a number vs the empty set are two different concepts. It’s the difference between having a bank account with $0, vs having no bank account. They don’t close your account when you have $0, so it’s still an amount of money.
Crows considering 0 on the numberline, and differently from the empty set shows they have a more abstract concept of numbers than we thought.
Idk who authored this study, seems like a very specific kind of person who is both into number theory and neural pathways of birds to design.
Or Anthropology. Right now, we have realized that New Caledonian crows have entered an equivalent to the early stone age in humans. Therefore, we can gain a lot of insight both about the nature of technological progression and of the very nature of intelligence (and the differences between mammalian and avian intelligence) by doing these studies.
Isn’t the Pythagorean theorem less about the fact that a diagonal is shorter than taking a corner (which is indeed obvious) and more about calculating how much shorter it is?
This reminds me of Kropotkins mutual aid a factor of evolution.