Projection, symmetry, and natural kinds

“…Dynamical kinds were first defined in [ 68 ], and have since been applied explicitly to problems of model validation [ 69 ] and causal discovery [ 70 ]. The dynamical kinds theory partitions the space of dynamical systems into equivalence classes—dynamical kinds—on the basis of dynamical symmetry.…”

Section: Related Workmentioning

confidence: 99%

“…The composition of any two dynamical symmetries (by successive intervention on the variables of a system) is itself a dynamical symmetry, and for any given system, its dynamical symmetries typically exhibit nontrivial algebraic structure under composition. It is the collection of symmetries and their structure under composition that characterizes a dynamical kind [ 68 ].…”

Section: Related Workmentioning

confidence: 99%

A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Shea-Blymyer

Roy

Jantzen

2021

Entropy

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Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.

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“…The third does leave us with a residual problem of the naturalness of kinds: how do we ascertain without already knowing all of the variables involved whether two things are sufficiently similar in their causal structure? This is one of the questions posed by [24] as an "epistemic" problem of natural kinds, and the "dynamical kinds" solution explored in [25][26][27] provides just the sort of test we're looking for.…”

Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

Scientific Variables

Jantzen

2021

Philosophies

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Despite their centrality to the scientific enterprise, both the nature of scientific variables and their relation to inductive inference remain obscure. I suggest that scientific variables should be viewed as equivalence classes of sets of physical states mapped to representations (often real numbers) in a structure preserving fashion, and argue that most scientific variables introduced to expand the degrees of freedom in terms of which we describe the world can be seen as products of an algorithmic inductive inference first identified by William W. Rozeboom. This inference algorithm depends upon a notion of natural kind previously left unexplicated. By appealing to dynamical kinds—equivalence classes of causal system characterized by the interventions which commute with their time evolution—to fill this gap, we attain a complete algorithm. I demonstrate the efficacy of this algorithm in a series of experiments involving the percolation of water through granular soils that result in the induction of three novel variables. Finally, I argue that variables obtained through this sort of inductive inference are guaranteed to satisfy a variety of norms that in turn suit them for use in further scientific inferences.

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Projection, symmetry, and natural kinds

Cited by 14 publications

References 41 publications

Introduction to the foundations of causal discovery

Introduction to the foundations of causal discovery

A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Scientific Variables

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