Theory of Dimensions

This chapter concerns dimensions as the term is used in the physical sciences today. Some key points made are: (i) Quantities of the same kind have the same dimension; but that two quantities have the same dimension does not necessarily mean they are of the same kind. (ii) The dimension of a quantity is not determined for a single quantity in isolation, but relative to a system of quantities and the relations that hold between them. (iii) Dimensions, units, and quantities are distinct notions. In this article, I explain how dimensions, units, and quantities are involved in the design of coherent systems of units; the account involves the equations of physics. When the use of a coherent system of units can be presumed, dimensional analysis is a powerful logico-mathematical method for deriving equations and relations in physics, and for parameterizing equations in terms of dimensionless parameters, which allows identifying physically similar systems. The source of the information yielded by dimensional analysis is not yet well understood in philosophy of physics. This chapter aims to reveal the role of dimensions not only in applications of dimensional analysis to obtain information by involving the principle of dimensional homogeneity, but to the role of dimensions in encoding information about physical relationships in the language of dimensions, specifically via the feature of coherence of a system of units. Philosophers of mathematics and philosophers of science have been concerned to address the question of the effectiveness of mathematics in science. It is argued here that no philosophical analysis of the question of the applicability of mathematics to science is complete without including dimensions and dimensional analysis in the picture

Theory of Dimensions

This chapter concerns dimensions as the term is used in the physical sciences today. Some key points made are: (i) Quantities of the same kind have the same dimension; but that two quantities have the same dimension does not necessarily mean they are of the same kind. (ii) The dimension of a quantity is not determined for a single quantity in isolation, but relative to a system of quantities and the relations that hold between them. (iii) Dimensions, units, and quantities are distinct notions. In this article, I explain how dimensions, units, and quantities are involved in the design of coherent systems of units; the account involves the equations of physics. When the use of a coherent system of units can be presumed, dimensional analysis is a powerful logico-mathematical method for deriving equations and relations in physics, and for parameterizing equations in terms of dimensionless parameters, which allows identifying physically similar systems. The source of the information yielded by dimensional analysis is not yet well understood in philosophy of physics. This chapter aims to reveal the role of dimensions not only in applications of dimensional analysis to obtain information by involving the principle of dimensional homogeneity, but to the role of dimensions in encoding information about physical relationships in the language of dimensions, specifically via the feature of coherence of a system of units. Philosophers of mathematics and philosophers of science have been concerned to address the question of the effectiveness of mathematics in science. It is argued here that no philosophical analysis of the question of the applicability of mathematics to science is complete without including dimensions and dimensional analysis in the picture

Relations Between Units and Relations Between Quantities

The proposed revision to the International System of Units contains two features that are bound to be of special interest to those concerned with foundational questions in philosophy of science. These are that the proposed system of international units ("New SI") can be defined (i) without drawing a distinction between base units and derived units, and (ii) without restricting (or, even, specifying) the means by which the value of the quantities associated with the units are to be established. In this paper, I address the question of the role of base units in light of the New SI: Do the "base units" of the SI play any essential role anymore, if they are neither at the bottom of a hierarchy of definitions themselves, nor the only units that figure in the statements fixing the numerical values of the "defining constants" ? The answer I develop and present (a qualified yes and no) also shows why it is important to retain the distinction between dimensions and quantities. I argue for an appreciation of the role of dimensions in understanding issues related to systems of units

"Pictures, Models, and Measures" A contribution to Invited Symposium: "Wittgenstein's Picture Theory" at the 2015 Pacific APA Meeting

Putting Wittgenstein's writing into an historical context that includes scientific and technological developments as well as cultural and intellectual works can be helpful in understanding some of Wittgenstein's works. I focus on the Tractatus Logico-Philosophicus in particular in this paper, and on topics related to pictures and models: the development of audio recording technologies, the development of miniature scale models that were both aesthetically pleasing and scientifically useful, particularly in the forensics of traffic accidents, and the culmination of a centuries-long effort to articulate the method behind the use of physical modeling, i.e., the formulation of a concept presented in 1914 and dubbed "physically similar systems.

Relations Between Units and Relations Between Quantities

The proposed revision to the International System of Units contains two features that are bound to be of special interest to those concerned with foundational questions in philosophy of science. These are that the proposed system of international units ("New SI") can be defined (i) without drawing a distinction between base units and derived units, and (ii) without restricting (or, even, specifying) the means by which the value of the quantities associated with the units are to be established. In this paper, I address the question of the role of base units in light of the New SI: Do the "base units" of the SI play any essential role anymore, if they are neither at the bottom of a hierarchy of definitions themselves, nor the only units that figure in the statements fixing the numerical values of the "defining constants" ? The answer I develop and present (a qualified yes and no) also shows why it is important to retain the distinction between dimensions and quantities. I argue for an appreciation of the role of dimensions in understanding issues related to systems of units

Scale Modeling (Chapter 32, _Routledge Handbook of Philosophy of Engineering_)

This chapter describes the role of scale modeling in engineering and related sciences. Accounts of scale modeling in philosophy rarely provide a correct description of how the practice is actually employed in engineering. This chapter corrects misconceptions about scale modeling often found in the philosophical literature. It also provides an informal explanation of how and why scale modeling works, when it does, in terms of an analogy between geometric similarity of plane figures and similarity of physically similar systems, which is founded on physics rather than on geometry. The key idea is to identify the relevant ratios responsible for the kind of similarity that is of interest, and then to characterize similarity in terms of a set of ratios that are the same (i.e., identical, or invariant) between the model system and the system it models. References to more extended treatments are provided for further reading

Movement and habitat use of two aquatic turtles (\u3cem\u3eGraptemys geographic\u3c/em\u3e and \u3cem\u3eTrachemys scripta\u3c/em\u3e) in an urban landscape

Our study focuses on the spatial ecology and seasonal habitat use of two aquatic turtles in order to understand the manner in which upland habitat use by humans shapes the aquatic activity, movement, and habitat selection of these species in an urban setting. We used radiotelemetry to follow 15 female Graptemys geographica (common map turtle) and each of ten male and female Trachemys scripta (red-eared slider) living in a man-made canal within a highly urbanized region of Indianapolis, IN, USA. During the active season (between May and September) of 2002, we located 33 of the 35 individuals a total of 934 times and determined the total range of activity, mean movement, and daily movement for each individuals. We also analyzed turtle locations relative to the upland habitat types (commercial, residential, river, road, woodlot, and open) surrounding the canal and determined that the turtles spent a disproportionate amount of time in woodland and commercial habitats and avoided the road-associated portions of the canal. We also located 21 of the turtles during hibernation (February 2003), and determined that an even greater proportion of individuals hibernated in woodland-bordered portions of the canal. Our results clearly indicate that turtle habitat selection is influenced by human activities; sound conservation and management of turtle populations in urban habitats will require the incorporation of spatial ecology and habitat use data

Scale Modeling (Chapter 32, _Routledge Handbook of Philosophy of Engineering_)

This chapter describes the role of scale modeling in engineering and related sciences. Accounts of scale modeling in philosophy rarely provide a correct description of how the practice is actually employed in engineering. This chapter corrects misconceptions about scale modeling often found in the philosophical literature. It also provides an informal explanation of how and why scale modeling works, when it does, in terms of an analogy between geometric similarity of plane figures and similarity of physically similar systems, which is founded on physics rather than on geometry. The key idea is to identify the relevant ratios responsible for the kind of similarity that is of interest, and then to characterize similarity in terms of a set of ratios that are the same (i.e., identical, or invariant) between the model system and the system it models. References to more extended treatments are provided for further reading

HLA Class-II Associated HIV Polymorphisms Predict Escape from CD4+ T Cell Responses.

Antiretroviral therapy, antibody and CD8+ T cell-mediated responses targeting human immunodeficiency virus-1 (HIV-1) exert selection pressure on the virus necessitating escape; however, the ability of CD4+ T cells to exert selective pressure remains unclear. Using a computational approach on HIV gag/pol/nef sequences and HLA-II allelic data, we identified 29 HLA-II associated HIV sequence polymorphisms or adaptations (HLA-AP) in an African cohort of chronically HIV-infected individuals. Epitopes encompassing the predicted adaptation (AE) or its non-adapted (NAE) version were evaluated for immunogenicity. Using a CD8-depleted IFN-γ ELISpot assay, we determined that the magnitude of CD4+ T cell responses to the predicted epitopes in controllers was higher compared to non-controllers (p<0.0001). However, regardless of the group, the magnitude of responses to AE was lower as compared to NAE (p<0.0001). CD4+ T cell responses in patients with acute HIV infection (AHI) demonstrated poor immunogenicity towards AE as compared to NAE encoded by their transmitted founder virus. Longitudinal data in AHI off antiretroviral therapy demonstrated sequence changes that were biologically confirmed to represent CD4+ escape mutations. These data demonstrate an innovative application of HLA-associated polymorphisms to identify biologically relevant CD4+ epitopes and suggests CD4+ T cells are active participants in driving HIV evolution