Harmony theory

A more compatible model of schemas comes from harmony theory (Smolensky, 1986a, 1986b). Harmony theory is based on the premise that inferences are made through the activation of schemas. Figure 12.4 depicts the main components of the theory. One... 

Figure 12.4. The underlying structure of harmony theory (Adapted from Smokensky, 1986b, with permission of the MIT Press)...

Smolensky is more concerned with the mathematical development of harmony theory than with an elaboration of schema structure, although schemas play an essential role in harmony theory. He gives little attention to the nature of a schema, and his examples range from having a schema for a word to having a schema for a birthday party. By the definitions outlined here, only the latter qualifies as a schema. Thus, like Rumelhart et al.,... 

Harmony theory depends largely on probability theory, and one of its innovations is that it uses a probability distribution to represent the environment. Moreover, slots of a schema are filled by elements that have high probabilities. One interesting aspect of schemas in this theory is that they correspond to joint probability distributions and as such yield useful statistical measures. 

It is too early to determine the impact of harmony theory. It appears to provide a nice linkage between statistical or probabilistic aspects of modeling and more conventional representations. To date, it has not been widely used or validated empirically. 

Smolensky, P. (1986a). Formal modeling of subsymbolic processes an introduction to harmony theory. In N. E. Sharkey (Ed.), Advances in cognitive science, volume 1 (pp. 204-235). New York Halsted Press. 

Smolensky, P. (1986b). Information processing in dynamical systems Foundations of harmony theory. In D. Rumelhart, J. McClelland,... 

Horiuti s theory [14,15] is one of the harmonious theories for complex chemical reactions. The key concept of this theory is the idea of reaction pathways under steady-state conditions. This provides an opportunity to describe the steady-state behavior of the... 

The Seetion entitled The BasiC ToolS Of Quantum Mechanics treats the fundamental postulates of quantum meehanies and several applieations to exaetly soluble model problems. These problems inelude the eonventional partiele-in-a-box (in one and more dimensions), rigid-rotor, harmonie oseillator, and one-eleetron hydrogenie atomie orbitals. The eoneept of the Bom-Oppenheimer separation of eleetronie and vibration-rotation motions is introdueed here. Moreover, the vibrational and rotational energies, states, and wavefunetions of diatomie, linear polyatomie and non-linear polyatomie moleeules are diseussed here at an introduetory level. This seetion also introduees the variational method and perturbation theory as tools that are used to deal with problems that ean not be solved exaetly. 

It has been possible to develop axiomatic theories for complete and partial ignorance that, by studying the sets of acts and states, yield a better understanding of the choice of criteria, and are in harmony with logical formalization of intuitively acceptable notions. We have treated in a rudimentary fashion a subject that is deep, novel, and promising. 

Boltzmann (S) extended the theory to solids, and was led to a result which to a certain extent is in harmony with the law of Dulong and Petit. 

The idea that the growth of each metal was under the influence of one of the heavenly bodies (a theory in harmony with the alchemistic view of the unity of the Cosmos), was very generally held by the alchemists and in consequence thereof, the metals were often referred to by the names or astrological symbols of their peculiar planets. These particulars are shown in the following table —... 

Variation of the double-layer capacity with applied potential according to the Gouy-Chapman theory is shown in Figure 4.8. Equation (4.10) includes the approximation ifjyi = iIj(x = 0), which is in harmony with the basic assumption of this... 

Symmetry The word symmetry means the same measure, which denotes harmony and beauty of the parts. It also plays a very important role in molecular architecture and material properties. The study of molecular symmetry is through a branch of group theory, that is, the point groups of rotations that leave one point... 

The simplest explanation in harmony with the theory of Eotvos is furnished by the observation that bodies of this third class possess in all cases long chains of atoms so that the molecule must present a highly unsymmetrical appearance. The molecular surface will, if the molecules lie flat in the superficial layer, considerably exceed /M ... 

Accordingly, changes, mutations, and evolution are seen as the result of the maintenance of the internal structure of the autopoietic organism. Since the dynamic of the environment may be erratic, the result in terms of evolution is a natural drift, determined primarily by the inner coherence and autonomy of the living organism. In this sense, Maturana and Varela s view (Maturana and Varela, 1980 1986) is close to Kimura s (1983) theory of natural drift and to Jacob s (1982) notion of bricolage. Evolution does not pursue any particular aim - it simply drifts. The path it chooses is not, however, completely random, but is one of many that are in harmony with the inner structure of the autopoietic unit. 

This result, as well as the form of expressions (23) and (24), shows that the charge and current density relations (3), (4), and (8) of the present extended theory become consistent with and related to the Dirac theory. It also implies that this extended theory can be developed in harmony with the basis of quantum electrodynamics. 

This was not because their theories of matter were more advanced than the ideas of Democritus or of Empedocles. Indeed, in a very essential particular, their views were less in line with scientific advance than their predecessors. For Plato and Aristotle were not so much concerned with accounting for phenomena by the operation of properties inherent eternally in matter as they were in interpreting the phenomena of nature as the expression of design, harmony and beauty, as the expression of a directing will and intelligence. 

Aristotle, so that harmony, beauty, design, logical consistency came to be considered the criteria of the acceptability of theories rather than the data of observation or experiment. 

It is interesting that Weyl had a deep conviction that the harmony of nature could be expressed in mathematically beautiful laws and an outstanding characteristic of his work was his ability to unite previously unrelated subjects. He created a general theory of matrix representation of continuous groups and discovered that many of the regularities of quantum mechanics could be best understood by means of group theory. 

G. D. Birkhoff tried to give a mathematical theory of aesthetics by recognizing the complexity, C, and the order, O (i.e., its harmony and symmetry) that an object could be said to have. He then restated Hemsterhuis definition of the beautiful as that which gives us the greatest number of ideas in the shortest time as the relation aesthetic measure... 

The ammonium theory.—In the ammonium theory of H. Davy, A. M. Ampere, and J. J. Berzelius, it was assumed. that the ammonium compounds contain a metallic radicle, NH4 (4.31,38), which may replace potassium, sodium, etc., in different salts. When ammonia unites with hydrogen chloride, the NH4-radicle is formed which unites with chlorine to form ammonium chloride in the same way that potassium united with chlorine forms potassium chloride. The ammonium theory thus corresponds with the ethyl theory of J. J. Berzelius, and J. von Liebig. The nitrogen is assumed to be quinquevalent, and this is in harmony with the work of V. Meyer and M. T. Lecco, A. Ladenburg, and W. Lossen on the quaternary ammonium baseb, and with the isomorphism of the ammonium and the potassium salts. 

In harmony with the multiplet theory is the observed dependency on the nature of the catalyst, since the atoms of the latter are involved in the multiplet complex. 

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