Information Theoretic Measures and Their Applications

The concept of entropy, an ever-growing physical magnitude that measured the degree of decay of order in a physical system, was introduced by Rudolf Clausius in 1865 through an elegant formulation of the second law of thermodynamics [...]

The Temperature of the Brain

In 1881, Francis Ysidro Edgeworth attempted to provide a solid psychological basis for utility measurement. I will show that Edgeworth’s main struggle was to provide a possible measurement scale for a feeling—pleasure—using some kind of physical magnitude that would have allowed both intra and interpersonal comparisons, thus justifying the use of mathematical techniques to answer welfare issues. Edgeworth found inspiration in a similar quest, the invention of temperature, which had permitted the transformation of a feeling, “coldness,” into a physical quantity, temperature. Edgeworth faced two kinds of criticisms: concerning the use of psychological notions in economics and concerning the nature of utility itself. Both criticisms were also stated in terms of the thermodynamic metaphor, and the thermometer analogy played a major role in the exchanges. Following those criticisms and his own analysis, Edgeworth would move from a ratio to an ordinal understanding of utility, despite never abandoning the idea that economics should be psychologically grounded.

Lay evaluations of police and civilian use of force: Action severity scales

In modern societies, citizens cede the legitimate use of violence to law enforcement agents who act on their behalf.However, little is known about the extent to which lay evaluations of forceful actions align with or diverge from official use-of-force policies and heuristics that officers use to choose appropriate levels of responsive force.Moreover, it is impossible to accurately compare official policies and lay intuitions without first measuring the perceived severity of a set of representative actions.To map these psychometric scale values precisely, we presented participants with minimal vignettes describing officer and civilian actions that span the entire range of force options (from polite dialogue to lethal force), and asked them to rate physical magnitude and moral appropriateness.We used Bayesian methods to model the ratings as functions of simultaneously estimated scale values of the actions.Results indicated that the perceived severity of actions across all physical but non-lethal categories clustered tightly together, while actions at the extreme levels were relatively spread out.Moreover, less normative officer actions were perceived as especially morally severe.Broadly, our findings reveal divergence between lay perceptions of force severity and official law enforcement policies, and they imply that the groundwork for disagreement about the legitimacy of police and civilian actions may be partially rooted in the differential way that action severity is perceived by law enforcement relative to civilian observers.

Cognition-mediated evolution of low-quality floral nectars

Plants pollinated by hummingbirds or bats produce dilute nectars even though these animals prefer more concentrated sugar solutions. This mismatch is an unsolved evolutionary paradox. Here we show that lower quality, or more dilute, nectars evolve when the strength of preferring larger quantities or higher qualities of nectar diminishes as magnitudes of the physical stimuli increase. In a virtual evolution experiment conducted in the tropical rainforest, bats visited computer-automated flowers with simulated genomes that evolved relatively dilute nectars. Simulations replicated this evolution only when value functions, which relate the physical stimuli to subjective sensations, were nonlinear. Selection also depended on the supply/demand ratio; bats selected for more dilute nectar when competition for food was higher. We predict such a pattern to generally occur when decision-makers consider multiple value dimensions simultaneously, and increases of psychological value are not fully proportional to increases in physical magnitude.

The Development of Arabic Digit Knowledge in 4- to 7-Year-Old Children

Recent studies indicate that Arabic digit knowledge rather than non-symbolic number knowledge is a key foundation for arithmetic proficiency at the start of a child’s mathematical career. We document the developmental trajectory of 4- to 7-year-olds’ proficiency in accessing magnitude information from Arabic digits in five tasks differing in magnitude manipulation requirements. Results showed that children from 5 years onwards accessed magnitude information implicitly and explicitly, but that 5-year-olds failed to access magnitude information explicitly when numerical magnitude was contrasted with physical magnitude. Performance across tasks revealed a clear developmental trajectory: children traverse from first knowing the cardinal values of number words to recognizing Arabic digits to knowing their cardinal values and, concurrently, their ordinal position. Correlational analyses showed a strong within-child consistency, demonstrating that this pattern is not only reflected in group differences but also in individual performance.

Kinetics, Dynamics and Energy of Solid on the Example of a Tool Fixed Flexibly: Part 3 – Energy

This work is a continuation of the problems of kinetics and dynamics of solid on the example of a tool fixed flexibly under cutting. Present work is concerned on the development of work and energy. A special attention has been paid to the work description by underlying a distinctness and lack of connection with the energy notion. Polarization of these two magnitudes has been revealed. An adequate and extended definition of energy in general, with mechanical energy in particular, is formulated. There are three kinds of mechanical energy considered, located on the stable static potential field being one of the limits of the machining space-time. They are the following energies: repel, inertial, and gravitational. Proper measures/potentials have been assigned to these energies, treating the energy as a mental notion, having no physical meaning in contrast to the potential as the physical magnitude.

Fechner's Law: Where Does the Log Transform Come From?

This paper looks at Fechner's law in the light of 150 years of subsequent study. In combination with the normal, equal variance, signal-detection model, Fechner's law provides a numerically accurate account of discriminations between two separate stimuli, essentially because the logarithmic transform delivers a model for Weber's law. But it cannot be taken to be a measure of internal sensation because an equally accurate account is provided by a χ2 model in which stimuli are scaled by their physical magnitude. The logarithmic transform of Fechner's law arises because, for the number of degrees of freedom typically required in the χ2 model, the logarithm of a χ2 variable is, to a good approximation, normal. This argument is set within a general theory of sensory discrimination.