Reductionism and the Universal Calculus

In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to model its behavior with the symbolic language of mathematics. In this essay, I examine an ambitious 16th and 17th-century intellectual agenda from the perspective of Wigner's question, namely, what historian Paolo Rossi calls "the quest to create a universal language." While many elite thinkers pursued related ideas, the most inspiring and forceful was Gottfried Leibniz's effort to create a "universal calculus," a pictorial language which would transparently represent the entirety of human knowledge, as well as an associated symbolic calculus with which to model the behavior of physical systems and derive new truths. I suggest that a deeper understanding of why the efforts of Leibniz and others failed could shed light on Wigner's original question. I argue that the notion of reductionism is crucial to characterizing the failure of Leibniz's agenda, but that a decisive argument for the why the promises of this effort did not materialize is still lacking.Comment: 11 pages, 1 figur

Integrative biological simulation praxis: Considerations from physics, philosophy, and data/model curation practices

Integrative biological simulations have a varied and controversial history in the biological sciences. From computational models of organelles, cells, and simple organisms, to physiological models of tissues, organ systems, and ecosystems, a diverse array of biological systems have been the target of large-scale computational modeling efforts. Nonetheless, these research agendas have yet to prove decisively their value among the broader community of theoretical and experimental biologists. In this commentary, we examine a range of philosophical and practical issues relevant to understanding the potential of integrative simulations. We discuss the role of theory and modeling in different areas of physics and suggest that certain sub-disciplines of physics provide useful cultural analogies for imagining the future role of simulations in biological research. We examine philosophical issues related to modeling which consistently arise in discussions about integrative simulations and suggest a pragmatic viewpoint that balances a belief in philosophy with the recognition of the relative infancy of our state of philosophical understanding. Finally, we discuss community workflow and publication practices to allow research to be readily discoverable and amenable to incorporation into simulations. We argue that there are aligned incentives in widespread adoption of practices which will both advance the needs of integrative simulation efforts as well as other contemporary trends in the biological sciences, ranging from open science and data sharing to improving reproducibility.Comment: 10 page

Robust Computer Algebra, Theorem Proving, and Oracle AI

In the context of superintelligent AI systems, the term "oracle" has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety.Comment: 15 pages, 3 figure

Interior noise prediction methodology: ATDAC theory and validation

The Acoustical Theory for Design of Aircraft Cabins (ATDAC) is a computer program developed to predict interior noise levels inside aircraft and to evaluate the effects of different aircraft configurations on the aircraft acoustical environment. The primary motivation for development of this program is the special interior noise problems associated with advanced turboprop (ATP) aircraft where there is a tonal, low frequency noise problem. Prediction of interior noise levels requires knowledge of the energy sources, the transmission paths, and the relationship between the energy variable and the sound pressure level. The energy sources include engine noise, both airborne and structure-borne; turbulent boundary layer noise; and interior noise sources such as air conditioner noise and auxiliary power unit noise. Since propeller and engine noise prediction programs are widely available, they are not included in ATDAC. Airborne engine noise from any prediction or measurement may be input to this program. This report describes the theory and equations implemented in the ATDAC program