Computational Irreducibility and Computational Analogy

In a previous paper [1], we provided a formal definition for the concept of computational irreducibility (CIR), that is, the fact that for a function f from N to N it is impossible to compute f (n) without following approximately the same path as computing successively all the values f (i) from i = 1 to n. Our definition is based on the concept of enumerating Turing machines (E-Turing machines) and on the concept of approximation of E-Turing machines, for which we also gave a formal definition. Here, we make these definitions more precise through some modifications intended to improve the robustness of the concept. We then introduce a new concept: the computational analogy, and prove some properties of the functions used. Computational analogy is an equivalence relation that allows partitioning the set of computable functions in classes whose members have the same properties regarding their CIR and their computational complexity. Introduction 1

Understanding analogical reasoning : viewpoints from psychology and related disciplines

Analogy and metaphor have a long history of study in linguistics, education, philosophy and psychology. Consensus over what analogy is or how analogy functions in language and thought, however, has been elusive. This paper, the first in a two part series, examines these various research traditions, attempting to bring out major lines of agreement over the role of analogy in individual human experience. As well as being a general literature review which may be helpful for newcomers to the study of analogy, this paper attempts to extract from these literatures existing theories, models and concepts which may be interesting or useful for computational studies of analogical reasoning

Automated Generation of Cross-Domain Analogies via Evolutionary Computation

Analogy plays an important role in creativity, and is extensively used in science as well as art. In this paper we introduce a technique for the automated generation of cross-domain analogies based on a novel evolutionary algorithm (EA). Unlike existing work in computational analogy-making restricted to creating analogies between two given cases, our approach, for a given case, is capable of creating an analogy along with the novel analogous case itself. Our algorithm is based on the concept of "memes", which are units of culture, or knowledge, undergoing variation and selection under a fitness measure, and represents evolving pieces of knowledge as semantic networks. Using a fitness function based on Gentner's structure mapping theory of analogies, we demonstrate the feasibility of spontaneously generating semantic networks that are analogous to a given base network.Comment: Conference submission, International Conference on Computational Creativity 2012 (8 pages, 6 figures

Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics

In this philosophical paper, we explore computational and biological analogies to address the fine-tuning problem in cosmology. We first clarify what it means for physical constants or initial conditions to be fine-tuned. We review important distinctions such as the dimensionless and dimensional physical constants, and the classification of constants proposed by Levy-Leblond. Then we explore how two great analogies, computational and biological, can give new insights into our problem. This paper includes a preliminary study to examine the two analogies. Importantly, analogies are both useful and fundamental cognitive tools, but can also be misused or misinterpreted. The idea that our universe might be modelled as a computational entity is analysed, and we discuss the distinction between physical laws and initial conditions using algorithmic information theory. Smolin introduced the theory of "Cosmological Natural Selection" with a biological analogy in mind. We examine an extension of this analogy involving intelligent life. We discuss if and how this extension could be legitimated. Keywords: origin of the universe, fine-tuning, physical constants, initial conditions, computational universe, biological universe, role of intelligent life, cosmological natural selection, cosmological artificial selection, artificial cosmogenesis.Comment: 25 pages, Foundations of Science, in pres

Report on the final panel discussion on computational aeroacoustics

Some important conclusions about future prospects for aeroacoustics in general, and for computational aeroacoustics in particular, that were reached in the course of the Final Panel Discussion of the Workshop on Computational Aeroacoustics held from 6 to 9 April 1992 by ICASE and NASA Langley Research Center are summarized by the panel chairman. Aeroacoustics must now be involved in interactions with computational fluid dynamics (as applied not only to deterministic flows but also to the statistical characteristics of turbulence), while additionally incorporating rigorous comparisons with experiment. The new Computational Aeroacoustics will press forward in two parallel ways. In one of them, CFD will be used to determine aeroacoustic source strengths, the associated radiation being derived by the Acoustic Analogy approach in one of its forms. In the other, a direct Computational Aeroacoustics will apply CFD techniques over a region extending beyond the flow field so as to include at least the beginnings of the acoustic far field. There are some particularly important areas of study, including rotor noise, boundary-layer noise, and the noise of supersonic jets, where it is strongly recommended that use of both methods is continued. On the other hand, important problems of the diffraction of radiation from aeroacoustic sources around complicated aircraft shapes will require the use of comprehensively Computational Aeroacoustics, while Acoustic Analogy methods seem better suited to estimating subsonic jet noise. The study of model problems to allow comparisons with experiment will be valuable in both lines of attack