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Unnatural Numb3r

by: Thomas Sprague

the modern neuroscience of an ancient cognitive capacity

In 2551 BC, one of the most profound engineering accomplishments of the ancient world was made. 2.3 million stones, each weighing over 100,000 pounds, were carefully extracted, smoothed, and hauled up a complex system of ramps to create a lasting monument for the pharaoh Khufu: the Great Pyramid at Giza. For thousands of years, the 450 foot-tall structure stood as the tallest man-made monument in the world. Even now, its construction remains so precise that you cannot slide a postcard between two stones. All of this was accomplished without any modern engineering equipment—no calculators, computers, or advanced geographic surveying technology. Our unique advanced cognitive abilities – those that enable engineers and architects to undertake such endeavors – go back thousands of years. But where do these faculties come from?

When we consider those things that separate humans from nonhuman primates, it is easy to focus on human-specific capacities like language and music. These profound behavioral adaptations are certainly the result of immense evolutionary progress. But, as we all learned in high school biology, we share about 96% of our genetic material with our closest living relative, the chimpanzee. If all of our species’ new cognitive proficiencies are in fact brand new developments in the human genome, then that miniscule genetic change would have needed to go quite a long way. But mother nature is smarter than this – modern neuroscience is unveiling how the story of our escape from the jungle into the vast networked civilization we know today could be told in terms of adaptation rather than innovation: why reinvent the wheel when instead you could add tires and use a new alloy?

In the past twenty years, neuroscientists around the world have begun to examine where our understanding of and ability to work with complex symbolic numerical and mathematical concepts originated. To what extent can our numerical skills be called “unique” from the rest of the animal kingdom? What was it that changed – possibly within that 4% of genetic code – that adorned our brains with the capacity to count and comprehend precise numerical quantities?

First, let’s look more deeply into where our numerical knowledge originated from an evolutionary perspective. To do so, we can examine approximate numerical cognition in humans compared with other animals. Consider a small group of chimpanzees exploring a treacherous part of the jungle inhabited by a different hostile group. How does this group of explorers make a decision whether or not to engage in conflict with the hostiles? A basic numerical competence is required on the part of the animals to make such a judgment – the invaders must compare the number of members among their group to the number of enemies they may need to fight. In experimental settings, a group of chimpanzees does not approach a simulated intruder (signaled by a fake call played from a speaker) unless the group numbers three or more.1 Again, mother nature is efficient: three appears to be the number of adult male chimpanzees needed to kill another chimpanzee.2

But it’s not only monkeys which show this kind of numerical understanding – fish, bees, cats, dogs, and human infants show similar preferences for “more”, especially when detecting novelty or making decisions.3-6 These findings appear to be rather simple and self-explanatory – of course animals can distinguish more from less – but they tell us something quite deep. Understanding number, at least in an approximate sense, is not something that makes humans special.

Numerical ability, then, is clearly present throughout the animal kingdom. So what is different about the numerical cognition of humans compared to that of other animals? As mentioned above, human infants and many animal species can be remarkably good at making greater/fewer judgments about relevant objects in the world. But monkeys, unlike people, do not approximate pi or build enormous monuments to dying leaders. It instead appears to be an extension of this evolutionarily-conserved approximate-numerical system that results in the mathematical knowledge of number found across much of human civilization.

What evidence exists to suggest number is something the brain treats in a special way? Those who have taken a cognitive psychology class are likely familiar with the general (though not universal) understanding that the fusiform gyrus, a strip of cortex across the rear underside of the brain is responsive to images that require fine visual expertise to discriminate. This part of the brain responds especially strongly when viewing an upright image of a face, but also when someone with expertise for identifying objects, such as classic cars or species of birds, views images of cars or birds, respectively. The brain is smart – why waste precious space and energy building a smattering of parts and pieces that all accomplish the same function on different kinds of inputs? Instead, mother nature appears to have found a way to allocate resources such that a single chunk takes care of the critical operation, and performs this task on different kinds of information received – in the previous example, discrimination of fine details of visual images, whether faces, birds, or cars.

Numerical cognition appears to work the same way. Early neuroimaging experiments, mostly using functional magnetic resonance imaging (fMRI), a technique whereby researchers can peek inside the skull and see where blood is flowing as a subject performs a task, found that a small area on both sides of the brain called the intraparietal sulcus (IPS) responded especially strongly when subjects performed tasks related to numbers. Whether the numbers were presented as dot patches, spoken or written words, or arabic numerals, the same part of the brain about 4 inches diagonally above and behind each ear responded robustly.7-9,5 This piece of cortex was responsive to number, regardless of how the subject received this information.

Even more interesting is a follow-up experiment in which a team of researchers posed several cognitively-relevant questions regarding an image which consisted of 2 different Arabic numeralswith different sizes, brightness, and numerical values. Each subject was asked to determine which numeral was bigger in size, brighter in color, and larger in value. Even though the questions were quite varied, the subjects’ brains responded the same way to all these kinds of judgments.10

But what do judgments of size, brightness and number have in common? It turns out that the brain may have found a way to represent and compare specifically the magnitude of a stimulus in an abstract fashion, without regard to which kind of magnitude is being compared. 9 The IPS, like the entire brain, sits inside the pitch-black attic of the skull, with its only source of information being the thousands and thousands of cellular wires carrying signals from other parts of the brain and the sensory organs. It has no idea whether the signals it receives are coming from the ears or the eyes, or whether the information encoded is about brightness, size, or number. In a sense, where the information is coming from doesn’t really matter – the same neural algorithm can discriminate any of these different examples of magnitude information.

Given that our sense of number may just be a particular implementation of a more abstract sense of “how big” in general, it could plausibly follow that individuals that have a more keenly-attuned magnitude comparison system, that is, subjects who are better at comparing the number of objects presented during a quick display, are more likely to succeed at grasping more advanced mathematical concepts. This indeed turns out to be the case – in a study of 64 high school students, those students who had performed better in math courses early in school performed better when asked to determine which of two dot fields contained more dots, a common test of the abstract number system.11 Though it is not clear whether these students had better abstract numerical abilities because they had better symbolic math training or if they instead were better at symbolic math as a function of their better abstract numerical abilities, this does tell us that symbolic math skill and abstract numerical abilities are correlated. Symbolic math is not a separable skill, but rather sits on top of the ancient numerical abilities present across the animal kingdom.

How, then, do we learn our more precise concept of mathematical number? Though children of very young ages can reliably discriminate between 2 numbers of the proportion 2:1, it takes longer before they are able to make more finegrained distinctions. Abstract numerical ability is early and innate – but an understanding of numerical quantities, such as “5,” “13,” and “42” rather than qualities such as “a few,” “some more,” and “a lot” takes time. In the Presidential Lecture at the 2009 Society for Neuroscience annual meeting in Chicago, IL, Elizabeth Spelke of Harvard University argued that explicit verbal counting, which requires persistent practice and which animals never acquire, is the “missing link” between the abstract numerical abilities of the animal kingdom and the precise mathematical skills found exclusively in humans. At first, Spelke says, human infants can only indirectly represent quantity – for example, an infant would have an idea that two balls were more than one ball, but would not know that two balls were two balls (they would be understood as “ball and ball”, not “two balls”). It is not until the operation of counting is learned, typically verbally, that the concept of natural number emerges. Once the understanding is in place that each succeeding number, with its own linguistic label, is one more than the previous number, the entire realm of natural numbers becomes available to the child. They have gained access to a secret known only to humans which allows for equally-precise representation of any quantity – from 4 marbles to 133 blocks.

Some cultures never acquire such understanding of countable natural number, much less more advanced symbolic mathematical concepts. Thus, they should only be able to make numerical decisions through the abstract number system. Stanislas Dehaene from INSERM in Paris, France set out to understand the way Amazonian tribes, who do not have words for numbers greater than 5, represent and make decisions about number. Each subject was asked to indicate where a number, as indicated by a quantity of physical objects presented to the subject, should fall on a number line. Performance suggested that number was represented in a logarithmic fashion, rather than the linear representation afforded by precise natural numbers.8,12 Performance of infants and animals trained to make numerical discriminations, along with recordings of single neurons in behaving monkeys and fMRI measurements in humans, also hint at a logarithmic representation of abstract number.5,13,14 Even without explicit numerical understanding, the brain can still make roughly accurate judgments of relative quantity, which are sufficient in most situations.

It thus appears that a relatively small adaptation allowed humans to implement an old but powerful quantity-evaluation system in a new important way, giving rise to feats like the pyramids of Giza. But the ancient Egyptians built the pyramids with none of the advanced technologies we know and cherish today; similarly, species around the world live and thrive without erecting edifices or calculating interest rates. Nevertheless, the primitive magnitude-estimation system is more than enough for survival among nonhuman species, and the ancient Egyptian construction techniques were more than suitable for building massive monuments. The numerical abilities we have now, despite their apparent uniqueness, may just be icing on the evolutionary cake.


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