This article discusses the concept of mathematical metaphor as a tool for analyzing the formation of mathematical knowledge. It reflects on the work of Lakoff and Núñez as a reference point against which to rearticulate a richer notion of mathematical metaphor that can account for actual mathematical evolution. To reach its goal this article analyzes historical case studies, draws on cognitive research, and applies lessons from the history of metaphors in philosophy as analyzed by Derrida and de Man.

Contemporary psycholinguistic models place significant emphasis on the cognitive processes involved in the acquisition, recognition, and production of language but neglect many issues related to the representation of language-related information in the mental lexicon. In contrast, a central tenet of network science is that the structure of a network influences the processes that operate in that system, making process and representation inextricably connected. Here, we consider how the structure found across phonological networks of several languages from different language families may (...) influence language processing as we age and experience diseases that affect cognition during the typical and atypical acquisition of new words, during typical perception and production of speech in adults, and during language change over time. We conclude that the network science approach may not only provide insights into specific language processes but also provide a way to connect the work from these domains, which are becoming increasingly balkanized. (shrink)

Neurotrophins are a small family of dimeric secretory proteins in vertebrate neurons with a broad spectrum of functions. They are generated as pro‐proteins with a functionality that is distinct from the proteolytically processed form. The cellular responses of neurotrophins are mediated by three different types of receptor proteins, the receptor tyrosine kinases of the Trk family, the neurotrophin receptor p75NTR, which is a member of the tumor necrosis factor receptor (TNFR) superfamily, and sortilin, previously characterized as neurotensin receptor. Recent studies (...) have revealed an intriguing pattern: neurotrophins can elicit opposing signals utilising their variable configuration and different receptor types. BioEssays 28: 583–594, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

Morphological EvoDevo is a field of biological inquiry in which explicit relations between evolutionary patterns and growth or morphogenetic processes are made. Historically, morphological EvoDevo results from the coming together of several traditions, notably Naturphilosophie, embryology, the study of heterochrony, and developmental constraints. A special feature binding different approaches to morphological EvoDevo is the use of formalisms and mathematical models. Here we will introduce anatomical network analysis, a new approach centered on connectivity patterns formed by anatomical parts, with its own (...) concepts and tools specifically designed for the study of morphological EvoDevo questions. Riedl’s concept of burden is tightly related to the use of anatomical networks, providing a nexus between the evolutionary patterns and the structural constraints that shape them. (shrink)

The emerging area of network biology is seeking to provide insights into organizational principles of life. However, despite significant collaborative efforts, there is still typically a weak link between biological and computational scientists and a lack of understanding of the research issues across the disciplines. This results in the use of simple computational techniques of limited potential that are incapable of explaining these complex data. Hence, the danger is that the community might begin to view the topological properties of network (...) data as mere statistics, rather than rich sources of biological information. A further danger is that such views might result in the imposition of scientific doctrines, such as scale-free-centric (on the modeling side) and genome-centric (on the biological side) opinions onto this area. Here, we take a graph-theoretic perspective on protein-protein interaction networks and present a high-level overview of the area, commenting on possible challenges ahead. (shrink)

A model of a spatio-cultural sub-context (enfolded in a wider scope context) is presented in the form of a blue print of a Complex System with a two-stage decision engine at its core. The engine first attaches a meaning to analyzable datum, and then decides whether to keep or change it. It does not alter already stored meanings but is designed to search for data to be converted into additional stored meanings and improve the accuracy of correspondence of their spatial (...) and cultural range of relevance. Meaning is reduced to the choice of a strategy—a future continuum of events; a choice dependent on a unique Evolutionary Path, a past continuum of events specific enough to lead to the current temporarily stable state of a spatio-cultural category. It is a blue print for a program that can emulate decisions to initiate changes in the environment in which a collective of culture partners resides; changes consisting of movements from one location to another or in the layout of its current location. The model is proposed at a low cultural resolution and is applicable, after suitable modifications, to a majority of city/period pairs. However, any such model has to be city/period specific. It is illustrated with a design for analyzing changes in the Israeli city, in particular in Tel Aviv. (shrink)

A view of evolution is presented in this paper (a two paper series), intended as a methodological infrastructure for modeling spatio-cultural systems (the design outline of such a model is presented in paper II). A motivation for the re-articulation of evolution as information dynamics is the phenomenologically discovered prerequisite of embedding a meaning-attributing apparatus in any and all models of spatio-cultural systems. An evolution is construed as the dynamics of a complex system comprised of memory devices, connected in an ordered (...) fashion (not randomly) by information-exchanges. An information-exchange transpires when the recipient system adopts a strategy (a continuum of events) that eventually changes its structure; namely, after the exchange, it contains and conveys different information. These memory devices—sub-systems—are also similarly constructed complex system. Only a part of the information is retained by a system in its physical-memory storage, which eventually loses this function too, when the ability to retrieve a common enough structure is lost. The entire amount of information is a system’s structure of connections (information exchanges); it is contained (apparently stored) dynamically when a system is observed in a temporarily stable state. This temporary permanence—robustness and resilience—is attained dynamically; namely, enabled by changes taking place in its sub-systems and in each of their sub-systems. Therefore, for modeling such a system a multi-layer/multi-scale approach is preferable. It enables the addition and subtraction of an interim scale and the consideration of such a scale as a micro or a macro (thus initiating a maneuver up or down scale) according to an ad-hoc requirement of the model, which imitates an envisaged sub system (called an ‘Inner World’), to which a certain range of decisions is relegated. This dynamics is driven (in time) by dynamically originated information growth, as defined by Shannon; i.e. by the fact that each of certain state transitions have occurred sometime in the past of the system just so and not otherwise, and by the fact that they have occurred in a certain order. Therefore, each ‘history’ and memory retrieval availability of information is unique, and thus can be used to differentiate meanings. Hence, there cannot be a comprehensive solution to the meaning attribution model-design challenge. However, the observation that at the core of each envisaged complex system, moving in time according to a rounded logic, there is an information manipulating device, operating necessarily according to a Boolean logic, can be copied into the design of a model. This observation enables, therefore, the embedding of a specific, locally fitted, meaning attributing device, which is an information manipulating mechanism (it splices/attaches one segment of information to another—its meaning). However, this is just a framework; the actual solution has still to be found locally—for each subject system. Such a solution is demonstrated for the change in location or layout in the Israeli city in paper II. (shrink)

Network theory is applied across the sciences to study phenomena as diverse as the spread of SARS, the topology of the cell, the structure of the Internet and job search behaviour. Underlying the study of networks is graph theory. Whether the graph represents a network of neurons, cells, friends or firms, it displays features that exclusively depend on the mathematical properties of the graph itself. However, the way in which graph theory is implemented to the modelling of networks differs significantly (...) across scientific fields. This article compares the economics variant of network theory with those of other fields. It shows how the methodology employed by economists to model networks is shaped by two explanatory desiderata: that the explanandum phenomenon is based on micro-economic foundations and that the explanation is general. (shrink)

Our understanding of how evolution acts on biological networks remains patchy, as is our knowledge of how that action is best identified, modelled and understood. Starting with network structure and the evolution of protein–protein interaction networks, we briefly survey the ways in which network evolution is being addressed in the fields of systems biology, development and ecology. The approaches highlighted demonstrate a movement away from a focus on network topology towards a more integrated view, placing biological properties centre‐stage. We argue (...) that there remains great potential in a closer synergy between evolutionary biology and biological network analysis, although that may require the development of novel approaches and even different analogies for biological networks themselves. (shrink)

This paper offers a contribution to debates around integrative aspects of systems biology and engages with issues related to the circumstances under which physicists look at biological problems. We use oral history as one of the methodological tools to gather the empirical material, conducting interviews with physicists working in systems biology. The interviews were conducted at several institutions in Brazil, Germany, Israel and the U.S. Biological research has been increasingly dependent on computational methods, high-throughput technologies, and multidisciplinary skills. Quantitative scientists (...) are joining biological departments and collaborations between physicists and biologists are particularly vigorous. This state of affairs raises a number of questions, such as: What are the circumstances under which physicists approach biological problems in systems biology? What kind of interdisciplinary challenges must be tackled? The paper suggests that, concerning physicists’ move to work on biological systems, there are common reasons to move, the transition must be understood in terms of degrees, physicists have a rationale for simplifying systems, and distinct conceptions of model and modeling strategies are recurrent. We identified problems regarding linguistic clarity and integration of epistemological aims. We conclude that cultural unconformities within the systems biology community have important consequences to the flow of scientific knowledge. (shrink)

This paper offers a contribution to debates around integrative aspects of systems biology and engages with issues related to the circumstances under which physicists look at biological problems. We use oral history as one of the methodological tools to gather the empirical material, conducting interviews with physicists working in systems biology. The interviews were conducted at several institutions in Brazil, Germany, Israel and the U.S. Biological research has been increasingly dependent on computational methods, high-throughput technologies, and multidisciplinary skills. Quantitative scientists (...) are joining biological departments and collaborations between physicists and biologists are particularly vigorous. This state of affairs raises a number of questions, such as: What are the circumstances under which physicists approach biological problems in systems biology? What kind of interdisciplinary challenges must be tackled? The paper suggests that, concerning physicists’ move to work on biological systems, there are common reasons to move, the transition must be understood in terms of degrees, physicists have a rationale for simplifying systems, and distinct conceptions of model and modeling strategies are recurrent. We identified problems regarding linguistic clarity and integration of epistemological aims. We conclude that cultural unconformities within the systems biology community have important consequences to the flow of scientific knowledge. (shrink)

This article maps a controversy in network science over the last 15 years, dividing the field about the epistemic status of a central notion, scale-freeness. The article accounts for the two main disputes, in 2005 and in 2018, as they unfolded in academic publications and on social media. This article analyzes the conflict, and the reasons why it reignited in 2018, to the surprise of many. It is argued that the concept of complex networks is shared by the distinct subcultures (...) of theorists and experimentalists; and that these subcultures have incompatible approaches to knowledge: nomothetic and idiographic. Following Galison, this article contends that network science is a trading zone where theorists and experimentalists can trade knowledge across the epistemic divide. (shrink)

We present two case studies from contemporary biology in which we observe conflicts between established and emerging approaches. The first case study discusses the relation between molecular biology and systems biology regarding the explanation of cellular processes, while the second deals with phylogenetic systematics and the challenge posed by recent network approaches to established ideas of evolutionary processes. We show that the emergence of new fields is in both cases driven by the development of high-throughput data generation technologies and the (...) transfer of modeling techniques from other fields. New and emerging views are characterized by different philosophies of nature, i.e. by different ontological and methodological assumptions and epistemic values and virtues. This results in a kind of conflict we call “epistemic competition” that manifests in two ways: On the one hand, opponents engage in mutual critique and defense of their fundamental assumptions. On the other hand, they compete for the acceptance and integration of the knowledge they provide by a broader scientific community. Despite an initial rhetoric of replacement, the views as well as the respective audiences come to be seen as more clearly distinct during the course of the debate. Hence, we observe—contrary to many other accounts of scientific change—that conflict results in the formation of new niches of research, leading to co-existence and perceived complementarity of approaches. Our model thus contributes to the understanding of the pluralization of the scientific landscape. (shrink)

Concerns with the use of engineering approaches in biology have recently been raised. I examine two related challenges to biological research that I call the synchronic and diachronic underdetermination problem. The former refers to challenges associated with the inference of design principles underlying system capacities when the synchronic relations between lower-level processes and higher-level systems capacities are degenerate. The diachronic underdetermination problem regards the problem of reverse engineering a system where the non-linear relations between system capacities and lower-level mechanisms are (...) changing over time. Braun and Marom argue that recent insights to biological complexity leave the aim of reverse engineering hopeless - in principle as well as in practice. While I support their call for systemic approaches to capture the dynamic nature of living systems, I take issue with the conflation of reverse engineering with naïve reductionism. I clarify how the notion of design principles can be more broadly conceived and argue that reverse engineering is compatible with a dynamic view of organisms. It may even help to facilitate an integrated account that bridges the gap between mechanistic and systems approaches. (shrink)

This paper offers a contribution to debates around integrative aspects of systems biology and engages with issues related to the circumstances under which physicists look at biological problems. We use oral history as one of the methodological tools to gather the empirical material, conducting interviews with physicists working in systems biology. The interviews were conducted at several institutions in Brazil, Germany, Israel and the U.S. Biological research has been increasingly dependent on computational methods, high-throughput technologies, and multidisciplinary skills. Quantitative scientists (...) are joining biological departments and collaborations between physicists and biologists are particularly vigorous. This state of affairs raises a number of questions, such as: What are the circumstances under which physicists approach biological problems in systems biology? What kind of interdisciplinary challenges must be tackled? The paper suggests that, concerning physicists’ move to work on biological systems, there are common reasons to move, the transition must be understood in terms of degrees, physicists have a rationale for simplifying systems, and distinct conceptions of model and modeling strategies are recurrent. We identified problems regarding linguistic clarity and integration of epistemological aims. We conclude that cultural unconformities within the systems biology community have important consequences to the flow of scientific knowledge. (shrink)

Despite the importance of network analysis in biological practice, dominant models of scientific explanation do not account satisfactorily for how this family of explanations gain their explanatory power in every specific application. This insufficiency is particularly salient in the study of the ecology of the microbiome. Drawing on Coyte et al. (2015) study of the ecology of the microbiome, Deulofeu et al. (2021) argue that these explanations are neither mechanistic, nor purely mathematical, yet they are substantially empirical. Building on their (...) criticisms, in the present work we make a step further elucidating this kind of explanations with a general analytical framework according to which scientific explanations are ampliative, specialized embeddings (ASE), which has recently been successfully applied to other biological subfields. We use ASE to reconstruct in detail the Coyte et al.’s case study and on its basis, we claim that network explanations of the ecology of the microbiome, and other similar explanations in ecology, gain their epistemological force in virtue of their capacity to embed biological phenomena in non-accidental generalizations that are simultaneously ampliative and specialized. (shrink)

A number of areas of biology raise questions about what is of value in the natural environment and how we ought to behave towards it: conservation biology, environmental science, and ecology, to name a few. Based on my experience teaching students from these and similar majors, I argue that the field of environmental ethics has much to teach these students. They come to me with pent-up questions and a feeling that more is needed to fully engage in their subjects, and (...) I believe some exposure to environmental ethics can help focus their interests and goals. I identify three primary areas in which environmental ethics can con- tribute to their education. The first is an examination of who (or what) should be considered to be part of our moral community (i.e., the community to whom we owe direct duties). Is it humans only? Or does it include all sentient life? Or all life? Or ecosystems considered holistically? Often, readings implicitly assume one or more of these answers; the goal is to make the student more sensitive to these implicit claims and to get them to think about the different reasons that support them. The second area, related to the first, is the application of the different answers concerning the extent of the ethical community to real environmental issues and problems. Students need to be aware of how the different answers concerning the moral community can imply conflicting answers for how we should act in certain cases and to think about ways to move toward conflict resolution. The third area in which environmental ethics can contribute is a more conceptual one, focusing on central concepts such as biodiversity, sustainability, species, and ecosystems. Exploring and evaluating various meanings of these terms will make students more reflective and thoughtful citizens and biologists, sensitive to the implications that different conceptual choices make. (shrink)

With the emergence of systems biology the notion of organizing principles is being highlighted as a key research aim. Researchers attempt to ‘reverse engineer’ the functional organization of biological systems using methodologies from mathematics, engineering and computer science while taking advantage of data produced by new experimental techniques. While systems biology is a relatively new approach, the quest for general principles of biological organization dates back to systems theoretic approaches in early and mid-20th century. The aim of this paper is (...) to draw on this historical background in order to increase the understanding of the motivation behind the systems theoretic approach and to clarify different epistemic aims within systems biology. We pinpoint key aspects of earlier approaches that also underlie the current practice. These are i) the focus on relational and system-level properties, ii) the inherent critique of reductionism and fragmentation of knowledge resulting from overspecialization, and iii) the insight that the ideal of formulating abstract organizing principles is complementary to, rather than conflicting with, the aim of formulating detailed explanations of biological mechanisms. We argue that looking back not only helps us understand the current practice but also points to possible future directions for systems biology. (shrink)