Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,

In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann's later work on the subject have little merit. Most twentieth century innovations -- such as the identification of the state of a physical system with a probability distribution # on its phase space, of its thermodynamic entropy with the Gibbs entropy of #, and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics -- are thoroughly misguided.

Introduction Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe? It might seem, since it is widely agreed that the state of any quantum mechanical system is completely specified by its wave function, that quantum mechanics is fundamentally about the behavior of wave functions. Quite naturally, no physicist wanted this to be true more than did Erwin Schrodinger, the father of the wave function. Nonetheless, Schrodinger ultimately found this impossible to believe. His difficulty was not so much with the novelty of the wave function [2, page 156 of [3]]: "That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message." Rather, it was that

I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended while some recent views on irreversibility, due to Prigogine, are criticized.

physics/0110060

This paper, theoretically, examines concepts, propositions, and establishes the need for and develops an extension to Concept Maps (CMaps) called Cyclic Concept Maps (Cyclic CMaps). The Cyclic CMap is considered to be an appropriate tool for representing knowledge of functional or dynamic relationships between concepts. The Concept Map (CMap), on the other hand, is viewed as an appropriate tool for representing hierarchical or static knowledge. The two maps complement each other and collectively they capture a larger domain of knowledge, thus forming a more effective knowledge representation tool.

This work contains review of original quantum Hierarchic theory of condensed matter, general for liquids and solids and its numerous branches. Computer program (copyright, 1997, Kaivarainen), based on new theory, was used for comprehensive simulations of water and ice physical properties. Condensed matter is considered as gas of 3D standing waves (collective excitations) of different nature: thermal de Broglie waves (waves B), IR photons and thermal phonons. Quantitative interrelation between microscopic, mesoscopic (as intermediate) and macroscopic properties of condensed matter are demonstrated. New theories of total internal energy, including contributions of kinetic and potential energy, heat capacity, surface tension, vapor pressure, thermal conductivity, viscosity and self-diffusion are described. Hierarchic theory of osmotic pressure, based on new state equation, new theories of light refraction, Brillouin light scattering and Mössbauer effect are presented also in article and compared with available experimental data for water and ice. Lot of hidden parameters, inaccessible for experiment, describing the dynamic and spatial properties of 24 quantum collective excitations of matter, can be calculated also, as demonstrated on examples of water and ice. Total number of physical parameters of liquids and solids in wide T-interval, including that of phase transitions, to be possible to evaluate using CAMP computer program, is about 300. The agreement between theoretical and available experimental results is very good. The evidence of high-T mesoscopic molecular Bose condensation (BC) in water and ice in form of coherent clusters is obtained. The new mechanisms of the 1st and 2nd order phase transitions, related to such clusters formation/melting, their assembly/disassembly and symmetry change is proposed. Theory unifies dynamics and thermodynamics on microscopic, mesoscopic and macroscopic scales in terms of quantum physics. The idea of new optoacoustic device: Comprehensive Analyzer of Matter Properties (CAMP) with huge informational possibilities, based on computer program, elaborated and its multisided applications are described. This work may be considered as a

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Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian approach), all sources of uncertainty can be included in a logically consistent way. Practical formulae for the first moments of the probability distribution are derived up to second-order approximations. 1) Universit`a "La Sapienza" and Sezione INFN di Roma 1, Rome, Italy, and CERN, Geneva, Switzerland Email: giulio.dagostini@roma1.infn.it; URL: http://www-zeus.roma1.infn.it/ agostini 2) Sezione INFN di Roma 1, Rome, Italy (currently at Parco Scientifico e Tecnologico d'Abruzzo, L'Aquila, Italy) Email: mirko.raso@roma1.infn.it; URL: http://www-zeus.roma1.infn.it/ raso 1 Introduction The combination in quadrature of uncertainties due to systematic effects has become quite standard practice in physics. It is also common practice to add the...