What happens when we think about nothing? No, we don’t mean some zen “clear your mind” meditative exercise: we’re talking about math – and as it turns out, it takes a lot of brainpower to think about zero.
So. Zero is a weird number. Okay, not a weird number as in being abundant but not pseudoperfect – weird as in odd. Well, not odd as in indivisible by two – odd as in unusual. Wait! Not unusual as in its largest prime factor is larger than its square root – unusual as in strange. Yeah, let’s go with strange.
“Unlike other numbers such as one, two or three, which represent countable quantities, zero means the absence of something countable,” said Florian Mormann, a researcher in the Department of Epileptology at University Hospital Bonn (UKB) and the Transdisciplinary Research Area (TRA) “Life & Health” at the University of Bonn, in a statement.
But “at the same time [it] still has a numerical value,” he explained.
In other words, zero is both a number and not – which makes it a slightly more difficult concept to handle, psychologically speaking. Its discovery, at least two millennia ago, is often considered one of humanity’s most important achievements, and only a handful of non-human animals have ever been shown to even come close to our understanding.
And it’s not just in the development of humanity as a whole that zero turns up late – it’s also in humans individually. Typically, children only properly figure the concept out at around six years old, after a series of neurological hoops have been jumped. Crucially, the final two steps involve understanding that zero is less than one, and that it can be represented by a symbol.
It sounds obvious, but it’s not: “When you ask [a child] which number is smaller, zero or one, they often think of one as the smallest number,” Elizabeth Brannon, a neuroscientist at Duke University who was not involved in the new research, told Vox in 2018. “It’s hard to learn that zero is smaller than one.”
In fact, even adults can be tripped up when it comes to understanding zero – which sort of hints that something different is going on, neurologically speaking, when we think about it. But what?
“Despite its importance in mathematics, the neuronal foundation of zero in the human brain is unknown,” explain the researchers. “We conducted single-neuron recordings in neurosurgical patients while they made judgments involving nonsymbolic number representations (dot numerosity), including the empty set, and symbolic numbers (Arabic numerals), including numeral zero.”
By showing the patients, who had been fitted with microelectrodes inside their temporal lobes in preparation for surgery, various representations of zero, “we were able to measure the activity of individual nerve cells,” said first author Esther Kutter, a researcher in the Institute of Neurobiology at the University of Tübingen and the Department of Epileptology at UKB. “[We] actually found neurons that signaled zero.”
But it wasn’t quite as simple as just that: these neurons, the team discovered, “responded to either the Arabic numeral zero or the empty set,” Kutter explained, “but not to both.”
This, it seems, is not entirely surprising. Neurons are known to fire for both symbolic and nonsymbolic representations of positive integers – that the same should be true for zero just “extends […] previous findings” in that direction, the team write.
In fact, they even found evidence of a distance effect when the patients looked at zero as opposed to representations of integers – meaning that “at the neuronal level, the concept of zero is not encoded as a separate category ‘nothing’,” explained Andreas Nieder, a researcher at the University of Tübingen and one of the coauthors of the paper, “but as a numerical value integrated with other, countable numerical values at the lower end of the number line.”
In short, then, it seems we mostly think of zero similarly to how we do other integers. Crucially, though, it’s not identically – and it seems there’s one rather striking way in which our brains react differently to zero than they do natural numbers: they use a lot more neurons to do so.
Indeed, representations of zero triggered more neurons than any other single-digit number, the researchers found – and that might be part of why the number causes us such trouble.
“The empty set is encoded differently from other numbers at the neuronal population level, especially in the case of point sets,” explained Mormann. “This could explain why the recognition of the empty set also takes longer at the behavioral level than for other small numbers.”
The study is published in the journal Current Biology.
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