The Roots of Science, Technology, Engineering, and Mathematics: What Are the Evolutionary and Neural Bases of Human Mathematics and Technology?

INTRODUCTION

Neural exaptations represent descent via transitions to novel neural functions. A primary transition in human cognitive and neural evolution was from a predominantly socially oriented primate brain to a brain that also instantiates and subserves science, technology, and engineering, all of which depend on mathematics. Upon what neural substrates and upon what evolved cognitive mechanisms did human capacities for science, technology, engineering, and mathematics (STEM), and especially its mathematical underpinnings, emerge? Previous theory focuses on roles for tools, language, and arithmetic in the cognitive origins of STEM, but none of these factors appears sufficient to support the transition.

METHODS

In this article, I describe and evaluate a novel hypothesis for the neural origins and substrates of STEM-based cognition: that they are based in human kinship systems and human maximizing of inclusive fitness.

RESULTS

The main evidence for this hypothesis is threefold. First, as demonstrated by anthropologists, human kinship systems exhibit complex mathematical and geometrical structures that function under sets of explicit rules, and such systems and rules pervade and organize all human cultures. Second, human kinship underlies the core algebraic mechanism of evolution, maximization of inclusive fitness, quantified as personal reproduction plus the sum of all effects on reproduction of others, each multiplied by their coefficient of relatedness to self. This is the only "natural" equation expected to be represented in the human brain. Third, functional imaging studies show that kinship-related cognition activates frontal-parietal regions that are also activated in STEM-related tasks. In turn, the decision-making that integrates kinship levels with costs and benefits from alternative behaviors has recently been shown to recruit the lateral septum, a hub region that combines internal (from the prefrontal cortex, amygdala, and other regions) and external information relevant to social behavior, using a dedicated subsystem of neurons specific to kinship.

CONCLUSIONS

Taken together, these lines of evidence suggest that kinship systems and kin-associated behaviors may represent exaptations for the origin of human STEM.

Creating ad hoc graphical representations of number

The ability to communicate about exact number is critical to many modern human practices spanning science, industry, and politics. Although some early numeral systems used 1-to-1 correspondence (e.g., 'IIII' to represent 4), most systems provide compact representations via more arbitrary conventions (e.g., '7' and 'VII'). When people are unable to rely on conventional numerals, however, what strategies do they initially use to communicate number? Across three experiments, participants used pictures to communicate about visual arrays of objects containing 1-16 items, either by producing freehand drawings or combining sets of visual tokens. We analyzed how the pictures they produced varied as a function of communicative need (Experiment 1), spatial regularities in the arrays (Experiment 2), and visual properties of tokens (Experiment 3). In Experiment 1, we found that participants often expressed number in the form of 1-to-1 representations, but sometimes also exploited the configuration of sets. In Experiment 2, this strategy of using configural cues was exaggerated when sets were especially large, and when the cues were predictably correlated with number. Finally, in Experiment 3, participants readily adopted salient numerical features of objects (e.g., four-leaf clover) and generally combined them in a cumulative-additive manner. Taken together, these findings corroborate historical evidence that humans exploit correlates of number in the external environment - such as shape, configural cues, or 1-to-1 correspondence - as the basis for innovating more abstract number representations.

Impairment in Working Memory and Executive Function Associated with Mercury Exposure in Indigenous Populations in Upper Amazonian Peru

The Matsigenka people living traditional lifestyles in remote areas of the Amazon rely on a fish-based diet that exposes them to methylmercury (MeHg) at levels that have been associated with decreased IQ scores. In this study, the association between Hg levels and working memory was explored using the framework of the Multicomponent Model. Working memory tasks were modified to fit the culture and language of the Matsigenka when needed and included measures for verbal storage (Word Span) visuospatial storage (Corsi Block Task) and a measure of executive functions, the Self-Ordered Pointing Task (SOPT). An innovation of the Trail Making Tests A & B (TMT A & B) was pilot tested as another potential measure of executive functions. The mean hair Hg levels of 30 participants, ages 12 to 55 years, from three different communities (Maizal, Cacaotal and Yomibato) was 7.0 ppm (sd = 2.40), well above the World Health Organization (WHO) limit for hair of 2.0 ppm and ranged from 1.8 to 14.2 ppm, with 98% of a broader sample of 152 individuals exceeding the WHO limit. Hair Hg levels showed significant associations with cognitive performance, but the degree varied in magnitude according to the type of task. Hg levels were negatively associated with executive functioning performance (SOPT errors), while Hg levels and years of education predicted visuospatial performance (Corsi Block accuracy). Education was the only predictor of Word Span accuracy. The results show that Hg exposure is negatively associated with working memory performance when there is an increased reliance on executive functioning. Based on our findings and the review of the experimental research, we suggest that the SOPT and the Corsi Block have the potential to be alternatives to general intelligence tests when studying remote groups with extensive cultural differences.

Counting and the ontogenetic origins of exact equality

Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a "set-matching" task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children's ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

The Effect of Language-Specific Characteristics on English and Japanese Speakers' Ability to Recall Number Information

The current paper presents two experiments investigating the effect of presence versus absence of compulsory number marking in a native language on a speaker's ability to recall number information from photos. In Experiment 1, monolingual English and Japanese adults were shown a sequence of 110 photos after which they were asked questions about the photos. We found that the English participants showed a significantly higher accuracy rate for questions testing recall for number information when the correct answer was "2" (instead of "1") than Japanese participants. In Experiment 2, English and Japanese adults engaged in the same task as in Experiment 1 with an addition that explored reasons for the results found in Experiment 1. The results of Experiment 2 were in line with the results of Experiment 1, but also suggested that the results could not be attributed to differences in guessing patterns between the two groups or the type of linguistic constructions used in the test situations. The current study suggests that native language affects speakers' ability to recall number information from scenes and thus provides evidence for the Whorfian hypothesis.

One-to-one correspondence without language

A logical rule important in counting and representing exact number is one-to-one correspondence, the understanding that two sets are equal if each item in one set corresponds to exactly one item in the second set. The role of this rule in children's development of counting remains unclear, possibly due to individual differences in the development of language. We report that non-human primates, which do not have language, have at least a partial understanding of this principle. Baboons were given a quantity discrimination task where two caches were baited with different quantities of food. When the quantities were baited in a manner that highlighted the one-to-one relation between those quantities, baboons performed significantly better than when one-to-one correspondence cues were not provided. The implication is that one-to-one correspondence, which requires intuitions about equality and is a possible building block of counting, has a pre-linguistic origin.

Is native quantitative thought concretized in linguistically privileged ways? A look at the global picture

This work investigates whether reference in speech to certain quantities, namely 1, 2, and 3, is privileged linguistically due to our brain's native quantitative capacities. It is suggested that these small quantities are not privileged in specific ways suggested in the literature. The case that morphology privileges these quantities, apart from 1, is difficult to maintain in light of the cross-linguistic data surveyed. The grammatical expression of 2 is explained without appealing to innate quantitative reasoning and the grammatical expression of 3 is not truly characteristic of speech once language relatedness is considered. The case that 1, 2, and 3 are each privileged lexically is also difficult to maintain in the face of the global linguistic data. While native neurobiological architecture biases humans towards recognizing small quantities in precise ways, these biases do not yield clear patterns in numerical language worldwide.

Does Grammatical Structure Accelerate Number Word Learning? Evidence from Learners of Dual and Non-Dual Dialects of Slovenian

How does linguistic structure affect children’s acquisition of early number word meanings? Previous studies have tested this question by comparing how children learning languages with different grammatical representations of number learn the meanings of labels for small numbers, like 1, 2, and 3. For example, children who acquire a language with singular-plural marking, like English, are faster to learn the word for 1 than children learning a language that lacks the singular-plural distinction, perhaps because the word for 1 is always used in singular contexts, highlighting its meaning. These studies are problematic, however, because reported differences in number word learning may be due to unmeasured cross-cultural differences rather than specific linguistic differences. To address this problem, we investigated number word learning in four groups of children from a single culture who spoke different dialects of the same language that differed chiefly with respect to how they grammatically mark number. We found that learning a dialect which features “dual” morphology (marking of pairs) accelerated children’s acquisition of the number word two relative to learning a “non-dual” dialect of the same language.

Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals

The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.

Toward exact number: young children use one-to-one correspondence to measure set identity but not numerical equality

Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children's mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children's understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers.