NUDGE: IMPROVING DECISIONS ABOUT HEALTH, WEALTH, AND HAPPINESS by Richard H. Thaler and Cass R. Sunstein Penguin Books, 2009, 312 pp, ISBN 978-0-14-311526-7This book is best described formally as a general explanation of and advocacy for libertarian paternalism, a term coined by the authors in earlier publications. Informally, it is about how leaders, systems, organizations, and governments can nudge people to do the things the nudgers want and need done for the betterment of the nudgees, or of society. It is paternalism in the sense that "it is legitimate for choice architects to try to influence people's behavior in order to make their lives longer, healthier, and better", (p. 5) It is libertarian in that "people should be free to do what they like - and to opt out of undesirable arrangements if they want to do so", (p. 5) The built-in possibility of opting out or making a different choice preserves freedom of choice even though people's behavior has been influenced by the nature of the presentation of the information or by the structure of the decisionmaking system. I had never heard of libertarian paternalism before reading this book, and I now find it fascinating.Written for a general audience, this book contains mostly social and behavioral science theory and models, but there is considerable discussion of structure and process that has roots in mathematical and quantitative modeling. One of the main applications of this social system is economic choice in investing, selecting and purchasing products and services, systems of taxes, banking (mortgages, borrowing, savings), and retirement systems. Other quantitative social choice systems discussed include environmental effects, health care plans, gambling, and organ donations. Softer issues that are also subject to a nudge-based approach are marriage, education, eating, drinking, smoking, influence, spread of information, and politics. There is something in this book for everyone.The basis for this libertarian paternalism concept is in the social theory called "science of choice", the study of the design and implementation of influence systems on various kinds of people. The terms Econs and Humans, are used to refer to people with either considerable or little rational decision-making talent, respectively. The various libertarian paternalism concepts and systems presented are tested and compared in light of these two types of people. Two foundational issues that this book has in common with another book, Network of Echoes: Imitation, Innovation and Invisible Leaders, that was also reviewed for this issue of the Journal are that 1 ) there are two modes of thinking (or components of the brain) - an automatic (intuitive) process and a reflective (rational) process and 2) the need for conformity and the desire for imitation are powerful forces in human behavior. …

Nudge: Improving Decisions about Health, Wealth, and Happiness

http://semantics.uchicago.edu/kennedy/classes/s09/experimentalsemantics/feigenson-etal04.pdf

Core systems of number

Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal 'number sense' than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.

Individual differences in non-verbal number acuity correlate with maths achievement

There is considerable interest in the structural and functional properties of the angular gyrus (AG). Located in the posterior part of the inferior parietal lobule, the AG has been shown in numerous meta-analysis reviews to be consistently activated in a variety of tasks. This review discusses the involvement of the AG in semantic processing, word reading and comprehension, number processing, default mode network, memory retrieval, attention and spatial cognition, reasoning, and social cognition. This large functional neuroimaging literature depicts a major role for the AG in processing concepts rather than percepts when interfacing perception-to-recognition-to-action. More specifically, the AG emerges as a cross-modal hub where converging multisensory information is combined and integrated to comprehend and give sense to events, manipulate mental representations, solve familiar problems, and reorient attention to relevant information. In addition, this review discusses recent findings that point to the existence of multiple subdivisions in the AG. This spatial parcellation can serve as a framework for reporting AG activations with greater definition. This review also acknowledges that the role of the AG cannot comprehensibly be identified in isolation but needs to be understood in parallel with the influence from other regions. Several interesting questions that warrant further investigations are finally emphasized.

/pdf/the-angular-gyrus-multiple-functions-and-multiple-4206xtv5tl.pdf

The Angular Gyrus: Multiple Functions and Multiple Subdivisions

Is calculation possible without language ? Or is the human ability for arithmetic dependent on the language faculty ? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of munduruku, an Amazonian language with a very small lexicon of numbers words. Our results imply a distinction between a non-verbal system of number approximation and a language-based counting system for exact number and arithmetic.

/pdf/exact-and-approximate-arithmetic-in-an-amazonian-indigene-1mh96jcq05.pdf

Exact and Approximate Arithmetic in an Amazonian Indigene Group

The construction of large number representations in adults

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations. Here we present a new theoretically motivated and empirically supported account of the development of numerical estimation, based on the idea that number-line estimation tasks entail judgments of proportion. We extend existing models of perceptual proportion judgment to the case of abstract numerical magnitude. Two experiments provide support for these models; three likely sources of developmental change in children’s estimation performance are identified and discussed. This work demonstrates that proportion-judgment models provide a unified account of estimation patterns that have previously been explained in terms of a developmental shift from logarithmic to linear representations of number.

The development of numerical estimation: evidence against a representational shift

Educated humans use language to express abstract number, applying the same number words to seven apples, whistles, or sins. Is language or education the source of numerical abstraction? Claims to the contrary must present evidence for numerical knowledge that applies to disparate entities, in people who have received no formal mathematics instruction and cannot express such knowledge in words. Here we show that preschool children can compare and add large sets of elements without counting, both within a single visual-spatial modality (arrays of dots) and across two modalities and formats (dot arrays and tone sequences). In two experiments, children viewed animations and either compared one visible array of dots to a second array or added two successive dot arrays and compared the sum to a third array. In further experiments, a dot array was replaced by a sequence of sounds, so that participants had to integrate quantity information presented aurally and visually. Children performed all tasks successfully, without resorting to guessing strategies or responding to continuous variables. Their accuracy varied with the ratio of the two quantities: a signature of large, approximate number representations in adult humans and animals. Addition was as accurate as comparison, even though children showed no relevant knowledge when presented with symbolic versions of the addition tasks. Abstract knowledge of number and addition therefore precedes, and may guide, language-based instruction in mathematics.

https://www.pnas.org/content/pnas/102/39/14116.full.pdf

Abstract number and arithmetic in preschool children

http://web.mit.edu/bcs/nklab/media/pdfs/2006Barth.pdf

Non-symbolic arithmetic in adults and young children.

Mental representations of numerical magnitude are commonly thought to undergo discontinuous change over development in the form of a “representational shift.” This idea stems from an apparent categorical shift from logarithmic to linear patterns of numerical estimation on tasks that involve translating between numerical magnitudes and spatial positions (such as number-line estimation). However, the observed patterns of performance are broadly consistent with a fundamentally different view, based on psychophysical modeling of proportion estimation, that explains the data without appealing to discontinuous change in mental representations of numerical magnitude. The present study assessed these 2 theories’ abilities to account for the development of numerical estimation in 5- through 10-year-olds. The proportional account explained estimation patterns better than the logarithmic-to-linear-shift account for all age groups, at both group and individual levels. These findings contribute to our understanding of the nature and development of the mental representation of number and have more general implications for theories of cognitive developmental change.

/pdf/developmental-change-in-numerical-estimation-262i8iiild.pdf

Hilary Barth

Papers

The construction of large number representations in adults

The development of numerical estimation: evidence against a representational shift

Abstract number and arithmetic in preschool children

Non-symbolic arithmetic in adults and young children.

Developmental change in numerical estimation.