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.

The traditional practice of establishing morphological types and investigating morphological organization has found new support from evolutionary developmental biology (evo-devo), especially with respect to the notion of body plans. Despite recurring claims that typology is at odds with evolutionary thinking, evo-devo offers mechanistic explanations of the evolutionary origin, transformation, and evolvability of morphological organization. In parallel, philosophers have developed non-essentialist conceptions of natural kinds that permit kinds to exhibit variation and undergo change. This not only facilitates a construal of species (...) and higher taxa as natural kinds, but also broadens our perspective on the diversity of kinds found in biology. There are many different natural kinds relevant to the investigative and explanatory aims of evo-devo, including homologues and developmental modules. (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)

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)

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)

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)

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)

The comprehension of living organisms in all their complexity poses a major challenge to the biological sciences. Recently, systems biology has been proposed as a new candidate in the development of such a comprehension. The main objective of this paper is to address what systems biology is and how it is practised. To this end, the basic tools of a systems biological approach are explored and illustrated. In addition, it is questioned whether systems biology ‘revolutionizes’ molecular biology and ‘transcends’ its (...) assumed reductionism. The strength of this claim appears to depend on how molecular and systems biology are characterised and on how reductionism is interpreted. Doing credit to molecular biology and to methodological reductionism, it is argued that the distinction between molecular and systems biology is gradual rather than sharp. As such, the classical challenge in biology to manage, interpret and integrate biological data into functional wholes is further intensified by systems biology’s use of modelling and bioinformatics, and by its scale enlargement. (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)

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)

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)