Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications

Napoletani, Domenico; Panza, Marco; Struppa, Daniele C.

doi:10.1090/noti1102

Cited by 16 publications

(17 citation statements)

References 27 publications

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“…3 how the process of forcing optimality and its effectiveness can be reinterpreted in light of Brandt's principle, and we have argued that this principle governs most agnostic, data-driven methods. In this Section we explore the appropriateness of using such methods, consistent with Brandt's principle, to solve problems about historical phenomena (introduced in [29]). We perform this analysis by looking at one of the organizing principles that have been suggested in recent years to make sense of biological processes, the so called principle of developmental inertia [25].…”

Section: Data Analysis Of Historical Phenomenamentioning

confidence: 99%

“…In [29] we suggested that biology and social sciences could be preferred domains of exploration of data analysis, as sciences concerned with "historical phenomena", i.e. phenomena significantly constrained by their past, historical development.…”

Section: Data Analysis Of Historical Phenomenamentioning

confidence: 99%

“…phenomena significantly constrained by their past, historical development. We briefly argued moreover that it is possible to describe historical phenomena as "those phenomena whose development can only be constrained locally (in time and/or space) by (potentially multiple) optimization processes acting on subsets of variables, and in such a way that the functions to be optimized change over long periods of time" [29]. This characterization was motivated by an analysis of fitness landscapes in evolutionary biology.…”

Section: Data Analysis Of Historical Phenomenamentioning

confidence: 99%

“…In a series of previous papers [26,27,28,29] we described what we called the 'microarray paradigm' and we showed that there are specific methodological motifs that structure the approach of data analysis to scientific problems. By 'microarray paradigm' we referred to the belief that sufficiently large data collected from a phe-nomenon allows answering any question about the phenomenon itself.…”

Section: Introductionmentioning

confidence: 99%

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Forcing Optimality and Brandt’s Principle

Napoletani

Panza

Struppa

2017

Boston Studies in the Philosophy and History of Science

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We argue that many optimization methods can be viewed as representatives of "forcing", a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. From these considerations, we extrapolate a principle for general data analysis methods, what we call 'Brandt's principle', namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle.

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Section: Data Analysis Of Historical Phenomenamentioning

confidence: 99%

Section: Data Analysis Of Historical Phenomenamentioning

confidence: 99%

Section: Data Analysis Of Historical Phenomenamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Forcing Optimality and Brandt’s Principle

Napoletani

Panza

Struppa

2017

Boston Studies in the Philosophy and History of Science

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“…The advent of informatics and its fast development has allowed for new ways of doing mathematics and applying mathematics (Napoletani et al 2014). In the field of mathematics education these new ways of thinking have also been noticed and have been the focus of research .…”

Section: Final Considerationsmentioning

confidence: 99%

Mathematical Modelling in Education Research and Practice

Stillman¹,

Blum²,

Biembengut³

2015

International Perspectives on the Teaching and Learning of Mathematical Modelling

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This book series will publish various books from different theoretical perspectives around the world focusing on Teaching and Learning of Mathematical Modelling at Secondary and Tertiary level. The proceedings of the biennial conference called ICTMA, organised by the ICMI affiliated Study Group ICTMA (International Community of Teachers of Mathematical Modelling and Applications) will also be published in this series. These proceedings display the worldwide state-of-the-art in this field and will be of interest for a wider audience than the conference participants.ICTMA is a worldwide unique group, in which not only mathematics educators aiming for education at school level are included but also applied mathematicians interested in teaching and learning modelling at tertiary level are represented. ICTMA discusses all aspects related to Teaching and Learning of Mathematical Modelling at Secondary and Tertiary Level, e.g. usage of technology in modelling, psychological aspects of modelling and its teaching, modelling competencies, modelling examples and courses, teacher education and teacher education courses. More information about this series at

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Do We Need a Critical Evaluation of the Role of Mathematics in Data Science?

Allo

2019

The 2018 Yearbook of the Digital Ethics Lab

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Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications

Cited by 16 publications

References 27 publications

Forcing Optimality and Brandt’s Principle

Forcing Optimality and Brandt’s Principle

Mathematical Modelling in Education Research and Practice

Do We Need a Critical Evaluation of the Role of Mathematics in Data Science?

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