Learning from the Shape of Data

This paper examines the epistemic value of using topological methods to study the "shape" of data sets. It is argued that the category theoretic notion of "functoriality" aids in translating visual intuitions about structure in data into precise, computable descriptions of real-world systems

On Einstein Algebras and Relativistic Spacetimes

In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson (2012, 2015) and Weatherall (2015), the two are equivalent theories.Comment: 20 page

Learning from the Shape of Data

To make sense of large data sets, we often look for patterns in how data points are ``shaped” in the space of possible measurement outcomes. The emerging field of topological data analysis (TDA) offers a toolkit for formalizing the process of identifying such shapes. This paper aims to discover why and how the resulting analysis should be understood as reflecting significant features of the systems that generated the data. I argue that a particular feature of TDA---its functoriality---is what enables TDA to translate visual intuitions about structure in data into precise, computationally tractable descriptions of real-world systems

In Epistemic Networks, is Less Really More?

We show that previous results from epistemic network models (Zollman, 2007, 2010; Kummerfeld and Zollman, 2015) showing the benefits of decreased connectivity in epistemic networks are not robust across changes in parameter values. Our findings motivate discussion about whether and how such models can inform real-world epistemic communities. As we argue, only robust results from epistemic network models should be used to generate advice for the real-world, and, in particular, decreasing connectivity is a robustly poor recommendation

In Epistemic Networks, is Less Really More?

We show that previous results from epistemic network models (Zollman, 2007, 2010; Kummerfeld and Zollman, 2015) showing the benefits of decreased connectivity in epistemic networks are not robust across changes in parameter values. Our findings motivate discussion about whether and how such models can inform real-world epistemic communities. As we argue, only robust results from epistemic network models should be used to generate advice for the real-world, and, in particular, decreasing connectivity is a robustly poor recommendation

On Einstein Algebras and Relativistic Spacetimes

In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson (2012, 2015) and Weatherall (2015), the two are equivalent theories

Why Be Regular? Part I

We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who argues that the non-regular "position" and "momentum" representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We how that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods

Why Be Regular? Part I

We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who argues that the non-regular "position" and "momentum" representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We how that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods

In Epistemic Networks, Is Less Really More?

We show that previous results from epistemic network models by Kevin J. S. Zollman and Erich Kummerfeld showing the benefits of decreased connectivity in epistemic networks are not robust across changes in parameter values. Our findings motivate discussion about whether and how such models can inform real world epistemic communitie