Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.001.0001
- Subject:
- Psychology, Cognitive Neuroscience
‘Sensation’ is the subjective experience of a physical stimulus. This book traces the sources of two ideas how to measure sensation — Fechner's Law and Stevens' Power Law — and examines the evidence ...
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‘Sensation’ is the subjective experience of a physical stimulus. This book traces the sources of two ideas how to measure sensation — Fechner's Law and Stevens' Power Law — and examines the evidence and arguments in their support. Fechner's law is based on discriminations between separate stimulus magnitudes (Weber's Law), together with the additional premise that just noticeable differences are subjectively equal. But such discriminations can be modelled, with equal precision, using Gaussian noise of power density proportional to the stimulus magnitude. Moreover, Gaussian noise accommodates a wider range of phenomena and relates to the electrophysiology of sensory neurons. Stevens' Power Law describes the assignment of numbers to individual stimulus magnitudes. But there are empirical difficulties if one looks for a realization of the power law in elementary neural function, or uses it as a definitive measure of sensation, or merely as an operational characterization of how people use numbers. Each individual stimulus magnitude is judged relative to the stimulus presented on the preceding trial and the number assigned to it. The book finishes with a theory of sensory judgment, applicable to category judgment and absolute identification as well as magnitude estimation. The comparison of each stimulus in an experiment with its predecessor is little better than ordinal — ‘greater than’, ‘about the same as’, ‘less than’. This leads to great variability in estimates of stimulus magnitude. If the stimulus values lie in a geometric series and if participants judge ratios, the only meaningful relationship between stimulus and response is the linear regression of log numerical assignment on log stimulus magnitude, which equates to Stevens' Power Law. However, the ordinal nature of the comparison between one stimulus magnitude and another means that there is no metric for the measurement of sensation.Less
‘Sensation’ is the subjective experience of a physical stimulus. This book traces the sources of two ideas how to measure sensation — Fechner's Law and Stevens' Power Law — and examines the evidence and arguments in their support. Fechner's law is based on discriminations between separate stimulus magnitudes (Weber's Law), together with the additional premise that just noticeable differences are subjectively equal. But such discriminations can be modelled, with equal precision, using Gaussian noise of power density proportional to the stimulus magnitude. Moreover, Gaussian noise accommodates a wider range of phenomena and relates to the electrophysiology of sensory neurons. Stevens' Power Law describes the assignment of numbers to individual stimulus magnitudes. But there are empirical difficulties if one looks for a realization of the power law in elementary neural function, or uses it as a definitive measure of sensation, or merely as an operational characterization of how people use numbers. Each individual stimulus magnitude is judged relative to the stimulus presented on the preceding trial and the number assigned to it. The book finishes with a theory of sensory judgment, applicable to category judgment and absolute identification as well as magnitude estimation. The comparison of each stimulus in an experiment with its predecessor is little better than ordinal — ‘greater than’, ‘about the same as’, ‘less than’. This leads to great variability in estimates of stimulus magnitude. If the stimulus values lie in a geometric series and if participants judge ratios, the only meaningful relationship between stimulus and response is the linear regression of log numerical assignment on log stimulus magnitude, which equates to Stevens' Power Law. However, the ordinal nature of the comparison between one stimulus magnitude and another means that there is no metric for the measurement of sensation.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0008
- Subject:
- Psychology, Cognitive Neuroscience
Different stimulus continua have different Weber fractions. If Weber's Law holds, matching jnds across continua generates a power law relation. If numbers be regarded as an artificial continuum, ...
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Different stimulus continua have different Weber fractions. If Weber's Law holds, matching jnds across continua generates a power law relation. If numbers be regarded as an artificial continuum, Stevens' Power Law results; so too does Ekman's Law (Weber's Law applied to sensation). This chapter looks at the relationship between the Weber fraction and the power law exponent, at the magnitude estimation of 1 kHz tones (a stimulus continuum that deviates from Weber's Law), and at the precision of magnitude estimates in relation to thresholds. The idea that the power law results from a matching of jnds across continua cannot be sustained.Less
Different stimulus continua have different Weber fractions. If Weber's Law holds, matching jnds across continua generates a power law relation. If numbers be regarded as an artificial continuum, Stevens' Power Law results; so too does Ekman's Law (Weber's Law applied to sensation). This chapter looks at the relationship between the Weber fraction and the power law exponent, at the magnitude estimation of 1 kHz tones (a stimulus continuum that deviates from Weber's Law), and at the precision of magnitude estimates in relation to thresholds. The idea that the power law results from a matching of jnds across continua cannot be sustained.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0011
- Subject:
- Psychology, Cognitive Neuroscience
This chapter explains why Stevens' Power Law is a power law, rather than some other kind of relation. If the stimulus values are chosen in a geometric series and participants are induced to judge ...
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This chapter explains why Stevens' Power Law is a power law, rather than some other kind of relation. If the stimulus values are chosen in a geometric series and participants are induced to judge ratios — that is, to distribute their responses on a logarithmic scale — the great variability of magnitude estimates means that linear regression of log numerical estimate on log stimulus magnitude is the only meaningful relationship to emerge from the experiment. The power law exponent is chiefly determined by the range of the physical variable in relation to the approximately uniform range of numbers used by Stevens' participants. The uniformity of that range is enhanced by instructions. The value of the exponent is, however, modified by prior expectations, which generate a small but systematic difference between the exponents estimated from magnitude estimation and production.Less
This chapter explains why Stevens' Power Law is a power law, rather than some other kind of relation. If the stimulus values are chosen in a geometric series and participants are induced to judge ratios — that is, to distribute their responses on a logarithmic scale — the great variability of magnitude estimates means that linear regression of log numerical estimate on log stimulus magnitude is the only meaningful relationship to emerge from the experiment. The power law exponent is chiefly determined by the range of the physical variable in relation to the approximately uniform range of numbers used by Stevens' participants. The uniformity of that range is enhanced by instructions. The value of the exponent is, however, modified by prior expectations, which generate a small but systematic difference between the exponents estimated from magnitude estimation and production.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0007
- Subject:
- Psychology, Cognitive Neuroscience
If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The ...
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If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The experimental evidence in this chapter says ‘Not so’. A variety of ideas have been proposed in attempts to save the role of magnitude estimates as measures of sensation. These include non-extensive ratio-scale measurement, attributing a subjective value to number itself, and a two-stage model for the judgment of the combined sensation of pairs of stimuli presented both simultaneously and successively (the resultant estimates are different). The idea of the power law as a definitive measure of sensation finally founders on certain situations, in the judgment of loudness and of brightness, in which an increase in total stimulus magnitude leads to a reduction in judged sensation.Less
If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The experimental evidence in this chapter says ‘Not so’. A variety of ideas have been proposed in attempts to save the role of magnitude estimates as measures of sensation. These include non-extensive ratio-scale measurement, attributing a subjective value to number itself, and a two-stage model for the judgment of the combined sensation of pairs of stimuli presented both simultaneously and successively (the resultant estimates are different). The idea of the power law as a definitive measure of sensation finally founders on certain situations, in the judgment of loudness and of brightness, in which an increase in total stimulus magnitude leads to a reduction in judged sensation.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0001
- Subject:
- Psychology, Cognitive Neuroscience
Since 1957, there has been a vigorous controversy about how to measure sensation — not the physical stimulus, but how that stimulus ‘feels’, subjectively, to the individual. The controversy has been ...
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Since 1957, there has been a vigorous controversy about how to measure sensation — not the physical stimulus, but how that stimulus ‘feels’, subjectively, to the individual. The controversy has been fought out between Fechner's Law, that sensation increases as the logarithm of stimulus magnitude, and Stevens' Power Law, that sensation increases as a power function. This chapter explains where those two proposals came from, and introduces some other ideas derived from dimensional analysis in the physical sciences that will be explored in subsequent chapters.Less
Since 1957, there has been a vigorous controversy about how to measure sensation — not the physical stimulus, but how that stimulus ‘feels’, subjectively, to the individual. The controversy has been fought out between Fechner's Law, that sensation increases as the logarithm of stimulus magnitude, and Stevens' Power Law, that sensation increases as a power function. This chapter explains where those two proposals came from, and introduces some other ideas derived from dimensional analysis in the physical sciences that will be explored in subsequent chapters.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0006
- Subject:
- Psychology, Cognitive Neuroscience
This chapter examines the hypothesis that the power law transform is realized in elementary neural function. It begins by examining studies that have looked for power law relationships between ...
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This chapter examines the hypothesis that the power law transform is realized in elementary neural function. It begins by examining studies that have looked for power law relationships between stimulus magnitude and the frequency of discharge in primary neural response. Physiological responses do not correlate well with magnitude estimates, and the electrophysiological data tell us nothing. The idea that sensation is related in some simple manner to physiological function meets further difficulty in the variability of independent estimates of the power law exponent, chiefly for 1000 Hz tones; and there are some participants who do not give power law estimates, but veridical estimates instead. Finally, there are sensory illusions that are intelligible only on the basis that perception is differentially coupled to the stimulus. Differential coupling precludes any direct relationship with sensation.Less
This chapter examines the hypothesis that the power law transform is realized in elementary neural function. It begins by examining studies that have looked for power law relationships between stimulus magnitude and the frequency of discharge in primary neural response. Physiological responses do not correlate well with magnitude estimates, and the electrophysiological data tell us nothing. The idea that sensation is related in some simple manner to physiological function meets further difficulty in the variability of independent estimates of the power law exponent, chiefly for 1000 Hz tones; and there are some participants who do not give power law estimates, but veridical estimates instead. Finally, there are sensory illusions that are intelligible only on the basis that perception is differentially coupled to the stimulus. Differential coupling precludes any direct relationship with sensation.
Craig P. Speelman and Kim Kirsner
- Published in print:
- 2005
- Published Online:
- January 2008
- ISBN:
- 9780198570417
- eISBN:
- 9780191708657
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570417.003.0002
- Subject:
- Psychology, Cognitive Psychology
This chapter presents the history of research into skill acquisition, and reviews the key questions and theories that have framed this research. Issues include the existence of plateaus in learning ...
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This chapter presents the history of research into skill acquisition, and reviews the key questions and theories that have framed this research. Issues include the existence of plateaus in learning curves, the effects of part versus whole task training and massed versus distributed practice, knowledge of results, the form of learning curves and their mathematical description, the power law of practice, transfer of training, and phases of skill acquisition. Theories reviewed are divided up into those that propose that skill acquisition proceeds through a process of strategy refinement (e.g., the theories of Crossman, Anderson (ACT-R), Newell et al. (SOAR), and MacKay, as well as some connectionist theories) as opposed to those that propose that skilled performance results from improved memory retrieval (e.g., the theories of Logan (Instance theory) and Palmeri (EBRW)). The theories are evaluated in terms of their ability to provide accounts versus explanations of the power law of practice.Less
This chapter presents the history of research into skill acquisition, and reviews the key questions and theories that have framed this research. Issues include the existence of plateaus in learning curves, the effects of part versus whole task training and massed versus distributed practice, knowledge of results, the form of learning curves and their mathematical description, the power law of practice, transfer of training, and phases of skill acquisition. Theories reviewed are divided up into those that propose that skill acquisition proceeds through a process of strategy refinement (e.g., the theories of Crossman, Anderson (ACT-R), Newell et al. (SOAR), and MacKay, as well as some connectionist theories) as opposed to those that propose that skilled performance results from improved memory retrieval (e.g., the theories of Logan (Instance theory) and Palmeri (EBRW)). The theories are evaluated in terms of their ability to provide accounts versus explanations of the power law of practice.
Stephen Handel
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195169645
- eISBN:
- 9780199786732
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195169645.003.0003
- Subject:
- Psychology, Cognitive Psychology
If the goal of sensory systems is to maximize information transmission, there should be a match between the functioning of the sensory systems and the statistical properties of the objects in the ...
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If the goal of sensory systems is to maximize information transmission, there should be a match between the functioning of the sensory systems and the statistical properties of the objects in the environment. Analyses of the distribution of acoustical and visual energies indicate that they follow a power law, 1/f, so that there is a constant relationship between frequency and amplitude, namely equal power in all octave regions. To encode this distribution, the auditory and visual systems use cells that resemble Gabor functions that decorrelate local sensory energy to detect the redundancies such as continuous boundaries that signify objects. There is sparse coding so that only a small number of cells fire for any input and those cells minimize the uncertainty problem by trading frequency resolution with orientation or time resolution. The perceptual outcomes are combined with Bayesian prior probabilities to identify the most likely object.Less
If the goal of sensory systems is to maximize information transmission, there should be a match between the functioning of the sensory systems and the statistical properties of the objects in the environment. Analyses of the distribution of acoustical and visual energies indicate that they follow a power law, 1/f, so that there is a constant relationship between frequency and amplitude, namely equal power in all octave regions. To encode this distribution, the auditory and visual systems use cells that resemble Gabor functions that decorrelate local sensory energy to detect the redundancies such as continuous boundaries that signify objects. There is sparse coding so that only a small number of cells fire for any input and those cells minimize the uncertainty problem by trading frequency resolution with orientation or time resolution. The perceptual outcomes are combined with Bayesian prior probabilities to identify the most likely object.
Wolfgang Götze
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199235346
- eISBN:
- 9780191715600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199235346.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials
In order to identify the essential items of the mode-coupling-theory scenarios, this chapter describes asymptotic expansions of the correlation functions for small frequencies and small separations ...
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In order to identify the essential items of the mode-coupling-theory scenarios, this chapter describes asymptotic expansions of the correlation functions for small frequencies and small separations of the coupling constants from their critical values. For generic glass transitions the leading-order asymptotic contributions are specified by two scaling laws. The slowing down of the dynamics is governed by two time scales, which exhibit power-law dependencies on the separation coordinates. Stretching is caused by the interplay of a critical power-law relaxation and a von-Schweidler-power-law decay. Logarithmic relaxation is the leading-order behaviour near higher-order singularities. The leading-order asymptotic corrections determine the range of validity of the leading-order formulas. Strong-coupling effects are shown to cause Cole–Cole relaxation processes for the critical decay near generic transitions and sublinear power-law variations of the mean-squared displacements near higher-order ones.Less
In order to identify the essential items of the mode-coupling-theory scenarios, this chapter describes asymptotic expansions of the correlation functions for small frequencies and small separations of the coupling constants from their critical values. For generic glass transitions the leading-order asymptotic contributions are specified by two scaling laws. The slowing down of the dynamics is governed by two time scales, which exhibit power-law dependencies on the separation coordinates. Stretching is caused by the interplay of a critical power-law relaxation and a von-Schweidler-power-law decay. Logarithmic relaxation is the leading-order behaviour near higher-order singularities. The leading-order asymptotic corrections determine the range of validity of the leading-order formulas. Strong-coupling effects are shown to cause Cole–Cole relaxation processes for the critical decay near generic transitions and sublinear power-law variations of the mean-squared displacements near higher-order ones.
M. E. J. Newman
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199206650
- eISBN:
- 9780191594175
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206650.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Generative network models model the mechanisms by which networks are created. The idea behind models such as these is to explore hypothesized generative mechanisms to see what structures they ...
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Generative network models model the mechanisms by which networks are created. The idea behind models such as these is to explore hypothesized generative mechanisms to see what structures they produce. If the structures are similar to those of networks observed in the real world, this suggests — though does not prove — that similar generative mechanisms may be at work in the real networks. This chapter examines the best-known example of a generative network model: the ‘preferential attachment’ model for the growth of networks with power-law degree distributions. Exercises are provided at the end of the chapter.Less
Generative network models model the mechanisms by which networks are created. The idea behind models such as these is to explore hypothesized generative mechanisms to see what structures they produce. If the structures are similar to those of networks observed in the real world, this suggests — though does not prove — that similar generative mechanisms may be at work in the real networks. This chapter examines the best-known example of a generative network model: the ‘preferential attachment’ model for the growth of networks with power-law degree distributions. Exercises are provided at the end of the chapter.
M. E. J. Newman
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199206650
- eISBN:
- 9780191594175
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206650.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The previous chapters looked at different types of natural and man-made networks and techniques for determining their structure, the mathematics used to represent networks formally, and the measures ...
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The previous chapters looked at different types of natural and man-made networks and techniques for determining their structure, the mathematics used to represent networks formally, and the measures and metrics used to quantify network structure. This chapter combines what have been learned so far, applying theoretical ideas and measures to empirical network data to get a picture of what networks look like in the real world. It shows that there are a number of common recurring patterns seen in network structures, patterns that can have a profound effect on the way networked systems work. Among other things, the chapter discusses component sizes, path lengths and the small-world effect, degree distributions and power laws, and clustering coefficients. Exercises are provided at the end of the chapter.Less
The previous chapters looked at different types of natural and man-made networks and techniques for determining their structure, the mathematics used to represent networks formally, and the measures and metrics used to quantify network structure. This chapter combines what have been learned so far, applying theoretical ideas and measures to empirical network data to get a picture of what networks look like in the real world. It shows that there are a number of common recurring patterns seen in network structures, patterns that can have a profound effect on the way networked systems work. Among other things, the chapter discusses component sizes, path lengths and the small-world effect, degree distributions and power laws, and clustering coefficients. Exercises are provided at the end of the chapter.
Anat Ninio
- Published in print:
- 2006
- Published Online:
- April 2010
- ISBN:
- 9780199299829
- eISBN:
- 9780191584985
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199299829.003.0003
- Subject:
- Psychology, Cognitive Models and Architectures
This chapter presents arguments in favour of considering syntactic development as a kind of cognitive skill learning, with transfer, generalization, and other practice effects demonstrating the ...
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This chapter presents arguments in favour of considering syntactic development as a kind of cognitive skill learning, with transfer, generalization, and other practice effects demonstrating the interconnectedness of even the earliest lexical-specific syntactic formulae. It presents the literature on the Power Law of Practice that states: ‘The speed of performance of a task increases as a power-law function of the number of times the task is performed’. The implications of the power-function speed-up for first language acquisition are that if syntactic acquisition is indeed like skill learning, syntax should transfer right away, the very first items learned facilitating the acquisition of all further ones. Developmental evidence regarding learning curves and generalizations in early syntax shows that syntactic development is like skill-learning, with early transfer, facilitation, and generalization demonstrating that children's lexical-specific combinatory rules are interconnected as the skill-learning approach predicts.Less
This chapter presents arguments in favour of considering syntactic development as a kind of cognitive skill learning, with transfer, generalization, and other practice effects demonstrating the interconnectedness of even the earliest lexical-specific syntactic formulae. It presents the literature on the Power Law of Practice that states: ‘The speed of performance of a task increases as a power-law function of the number of times the task is performed’. The implications of the power-function speed-up for first language acquisition are that if syntactic acquisition is indeed like skill learning, syntax should transfer right away, the very first items learned facilitating the acquisition of all further ones. Developmental evidence regarding learning curves and generalizations in early syntax shows that syntactic development is like skill-learning, with early transfer, facilitation, and generalization demonstrating that children's lexical-specific combinatory rules are interconnected as the skill-learning approach predicts.
Marc-Olivier Coppens
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0016
- Subject:
- Mathematics, Applied Mathematics
Symmetry is key in solving many scientific and engineering problems. Drawing on examples from chemical engineering, this chapter illustrates how recognizing fractal scaling and other invariant ...
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Symmetry is key in solving many scientific and engineering problems. Drawing on examples from chemical engineering, this chapter illustrates how recognizing fractal scaling and other invariant patterns that envelop multiple scales is an excellent way to bridge multi-scale gaps. Such invariants are frequently observed in biological systems, which are only able to function thanks to the conservation of microscopic properties up to macroscopic scales in a scale-free way. Similarly, by imposing such invariant distributions in engineering designs, the advantages of microscopic (micro- or nanoscale) designs are preserved for macro-scale applications, while considerably reducing complexity and increasing efficiency. This holistic view helps to simplify multi-scale problems, and is proposed as a useful supplement to atomistic, bottom-up approaches.Less
Symmetry is key in solving many scientific and engineering problems. Drawing on examples from chemical engineering, this chapter illustrates how recognizing fractal scaling and other invariant patterns that envelop multiple scales is an excellent way to bridge multi-scale gaps. Such invariants are frequently observed in biological systems, which are only able to function thanks to the conservation of microscopic properties up to macroscopic scales in a scale-free way. Similarly, by imposing such invariant distributions in engineering designs, the advantages of microscopic (micro- or nanoscale) designs are preserved for macro-scale applications, while considerably reducing complexity and increasing efficiency. This holistic view helps to simplify multi-scale problems, and is proposed as a useful supplement to atomistic, bottom-up approaches.
Lee Cronk and Beth L. Leech
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691154954
- eISBN:
- 9781400845484
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691154954.003.0007
- Subject:
- Sociology, Comparative and Historical Sociology
This chapter explores the concept of emergence in relation to cooperation, and more specifically how social interactions can lead to the spontaneous emergence of norms, conventions, and other social ...
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This chapter explores the concept of emergence in relation to cooperation, and more specifically how social interactions can lead to the spontaneous emergence of norms, conventions, and other social institutions that help coordinate social behavior. People can coordinate their social behaviors if they have common knowledge both about how to do so and about the fact that everyone else also knows how to do so. Such common knowledge is often enshrined in norms about social behavior, for example, which side of the road to drive on. The chapter first provides a brief historical background on the importance of emergence in the social sciences before discussing instances in which emergent phenomena help people cooperate. It also considers how mathematics helps shape cooperation and the ways that power law curves, criticality, and assurance games contribute to the study of cooperation.Less
This chapter explores the concept of emergence in relation to cooperation, and more specifically how social interactions can lead to the spontaneous emergence of norms, conventions, and other social institutions that help coordinate social behavior. People can coordinate their social behaviors if they have common knowledge both about how to do so and about the fact that everyone else also knows how to do so. Such common knowledge is often enshrined in norms about social behavior, for example, which side of the road to drive on. The chapter first provides a brief historical background on the importance of emergence in the social sciences before discussing instances in which emergent phenomena help people cooperate. It also considers how mathematics helps shape cooperation and the ways that power law curves, criticality, and assurance games contribute to the study of cooperation.
Bruce Rogers
- Published in print:
- 2018
- Published Online:
- May 2019
- ISBN:
- 9780691159263
- eISBN:
- 9780691184074
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159263.003.0005
- Subject:
- Political Science, Political Economy
This chapter aims to build better models of web traffic. It shows how web traffic is roughly power law distributed, in which a highly concentrated “head” of the Web is coupled with a long, diffuse ...
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This chapter aims to build better models of web traffic. It shows how web traffic is roughly power law distributed, in which a highly concentrated “head” of the Web is coupled with a long, diffuse “tail” of tiny sites. These power law-like patterns have provoked vigorous debate about whether the Web is dominated by new or old elites. To address these issues, this chapter builds new models that scale seamlessly from the largest websites down to hundreds of smaller ones. It builds and tests these models with a rich dataset from Hitwise, a web measurement firm. As this chapter shows, digital audience growth follows predictable patterns. These patterns look much like the growth of cities over time, or the fluctuations of stocks on an equity market (more on that shortly), or even the growth and decline of biological species. This chapter borrows mathematical models and techniques from other disciplines to demonstrate these patterns, focus with a focus on understanding the principles and intuition behind the models.Less
This chapter aims to build better models of web traffic. It shows how web traffic is roughly power law distributed, in which a highly concentrated “head” of the Web is coupled with a long, diffuse “tail” of tiny sites. These power law-like patterns have provoked vigorous debate about whether the Web is dominated by new or old elites. To address these issues, this chapter builds new models that scale seamlessly from the largest websites down to hundreds of smaller ones. It builds and tests these models with a rich dataset from Hitwise, a web measurement firm. As this chapter shows, digital audience growth follows predictable patterns. These patterns look much like the growth of cities over time, or the fluctuations of stocks on an equity market (more on that shortly), or even the growth and decline of biological species. This chapter borrows mathematical models and techniques from other disciplines to demonstrate these patterns, focus with a focus on understanding the principles and intuition behind the models.
Buzsáki György
- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195301069
- eISBN:
- 9780199863716
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195301069.003.0002
- Subject:
- Neuroscience, Neuroendocrine and Autonomic, Techniques
The neocortex is built from five principal-cell types and numerous classes of interneurons. Early formulation of cortical structure emphasized the modularity of the neocortex. Its robust local ...
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The neocortex is built from five principal-cell types and numerous classes of interneurons. Early formulation of cortical structure emphasized the modularity of the neocortex. Its robust local tensegrity organization has allowed for continuous growth. Medium- and long-range connections that compose the white matter and interconnect nonadjacent cortical neuronal circuits are relatively sparse but sufficient to keep the synaptic path lengths constant in brains of different sizes. Such interconnectedness is a prerequisite for global operations in finite temporal windows. The small-world-like, scale-free organization of cortical architecture may provide some quantitative rules for the growth of both cell numbers and associated axonal connections while minimizing the cost of connectivity, though available anatomical data indicate that cortical areas processing similar kinds of information are more strongly connected than required. Limiting excitatory spread and segregation of computation are solved by balanced interactions between the excitatory principal cells and inhibitory interneurons.Less
The neocortex is built from five principal-cell types and numerous classes of interneurons. Early formulation of cortical structure emphasized the modularity of the neocortex. Its robust local tensegrity organization has allowed for continuous growth. Medium- and long-range connections that compose the white matter and interconnect nonadjacent cortical neuronal circuits are relatively sparse but sufficient to keep the synaptic path lengths constant in brains of different sizes. Such interconnectedness is a prerequisite for global operations in finite temporal windows. The small-world-like, scale-free organization of cortical architecture may provide some quantitative rules for the growth of both cell numbers and associated axonal connections while minimizing the cost of connectivity, though available anatomical data indicate that cortical areas processing similar kinds of information are more strongly connected than required. Limiting excitatory spread and segregation of computation are solved by balanced interactions between the excitatory principal cells and inhibitory interneurons.
Ralph Hertwig, Ulrich Hoffrage, and Rüdiger Sparr
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780195315448
- eISBN:
- 9780199932429
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195315448.003.0116
- Subject:
- Psychology, Cognitive Psychology, Human-Technology Interaction
This chapter analyzes how valuable the assumption of systematic environment imbalance is for performing rough-and-ready intuitive estimates, which people regularly do when inferring the quantitative ...
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This chapter analyzes how valuable the assumption of systematic environment imbalance is for performing rough-and-ready intuitive estimates, which people regularly do when inferring the quantitative value of an object (e.g., its frequency, size, value, or quality). The chapter outlines how systematic environment imbalance can be quantified using the framework of power laws. It investigates to what extent power-law characteristics and other statistical properties of real-world environments can be allies of two simple estimation heuristics, QuickEst and the mapping heuristic. The analyses, which involve comparing the estimation performances of the heuristics relative to more complex strategies, demonstrate that QuickEst could be particularly suited for deriving rough-and-ready estimates in skewed distributions with highly dispersed cue validities, whereas the mapping heuristic might be most suited when the cues have similar validities.Less
This chapter analyzes how valuable the assumption of systematic environment imbalance is for performing rough-and-ready intuitive estimates, which people regularly do when inferring the quantitative value of an object (e.g., its frequency, size, value, or quality). The chapter outlines how systematic environment imbalance can be quantified using the framework of power laws. It investigates to what extent power-law characteristics and other statistical properties of real-world environments can be allies of two simple estimation heuristics, QuickEst and the mapping heuristic. The analyses, which involve comparing the estimation performances of the heuristics relative to more complex strategies, demonstrate that QuickEst could be particularly suited for deriving rough-and-ready estimates in skewed distributions with highly dispersed cue validities, whereas the mapping heuristic might be most suited when the cues have similar validities.
Wolfgang Götze
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199235346
- eISBN:
- 9780191715600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199235346.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter presents an elementary discussion of some glassy-dynamics features, which are exhibited by experimental data and by molecular-dynamics-simulation results. The outstanding property of ...
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This chapter presents an elementary discussion of some glassy-dynamics features, which are exhibited by experimental data and by molecular-dynamics-simulation results. The outstanding property of this slow dynamics is the stretching of the relaxation functions on time intervals covering several orders of magnitude. The evolution of the complex relaxation patterns upon compressing or cooling the liquid appear as precursors of hidden liquid–glass transitions, which are characterized by certain crossover values for the density or temperature, respectively. The repulsion-induced cage effect in the systems causes relaxation plateaus and the interplay of two power-law decay processes. If the repulsive interaction is complemented by a strong short-range attraction, the plateaus can disappear and the correlations exhibit logarithmic decay.Less
This chapter presents an elementary discussion of some glassy-dynamics features, which are exhibited by experimental data and by molecular-dynamics-simulation results. The outstanding property of this slow dynamics is the stretching of the relaxation functions on time intervals covering several orders of magnitude. The evolution of the complex relaxation patterns upon compressing or cooling the liquid appear as precursors of hidden liquid–glass transitions, which are characterized by certain crossover values for the density or temperature, respectively. The repulsion-induced cage effect in the systems causes relaxation plateaus and the interplay of two power-law decay processes. If the repulsive interaction is complemented by a strong short-range attraction, the plateaus can disappear and the correlations exhibit logarithmic decay.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0012
- Subject:
- Psychology, Cognitive Neuroscience
Exponents estimated for different stimulus continua are approximately inversely related to the log stimulus range; but that ceases to be true when comparisons are made between different ranges on the ...
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Exponents estimated for different stimulus continua are approximately inversely related to the log stimulus range; but that ceases to be true when comparisons are made between different ranges on the same continuum. This chapter looks at some problems arising from comparisons between different ranges within a common continuum, and from very first judgments in an experiment (for which stimulus range is undefined). But participants still have prior expectations about the task they have agreed to perform, and the chapter endeavours to relate the different results to those expectations.Less
Exponents estimated for different stimulus continua are approximately inversely related to the log stimulus range; but that ceases to be true when comparisons are made between different ranges on the same continuum. This chapter looks at some problems arising from comparisons between different ranges within a common continuum, and from very first judgments in an experiment (for which stimulus range is undefined). But participants still have prior expectations about the task they have agreed to perform, and the chapter endeavours to relate the different results to those expectations.
Mia de Kuijper
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780195171631
- eISBN:
- 9780199871353
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195171631.003.0006
- Subject:
- Economics and Finance, Macro- and Monetary Economics
In Chapter 5 the new economic paradigm for the 21st century—a paradigm that is consistent with the emergence of perfect information—is introduced. This chapter demonstrates that due to the second ...
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In Chapter 5 the new economic paradigm for the 21st century—a paradigm that is consistent with the emergence of perfect information—is introduced. This chapter demonstrates that due to the second inevitable trend, in transparency several aspects of mainstream economics need to be revisited. For instance, in transparency the two conditions for a general equilibrium cannot coexist, hence a general equilibrium is not possible. Also, the often-used simplifying assumption of normal distributions is not valid. Extraordinary profits and profit power, in contrast, are being proven to be valid economic concepts. In transparency, interdependence of decision making will turn a group into a network. For instance, an economic aggregate, such as “buyers,” becomes a network. The question is what kind of network. Powerlaw distributions—and powerlaw networks—can provide a new paradigm under certain conditions. These four conditions for powerlaw network dynamics in economic aggregates are derived in this chapter. This is the basis for the economics of perfect information, powerlaw economics.Less
In Chapter 5 the new economic paradigm for the 21st century—a paradigm that is consistent with the emergence of perfect information—is introduced. This chapter demonstrates that due to the second inevitable trend, in transparency several aspects of mainstream economics need to be revisited. For instance, in transparency the two conditions for a general equilibrium cannot coexist, hence a general equilibrium is not possible. Also, the often-used simplifying assumption of normal distributions is not valid. Extraordinary profits and profit power, in contrast, are being proven to be valid economic concepts. In transparency, interdependence of decision making will turn a group into a network. For instance, an economic aggregate, such as “buyers,” becomes a network. The question is what kind of network. Powerlaw distributions—and powerlaw networks—can provide a new paradigm under certain conditions. These four conditions for powerlaw network dynamics in economic aggregates are derived in this chapter. This is the basis for the economics of perfect information, powerlaw economics.
