Darwin, nós temos um grave problema epistemológico: sua teoria da evolução não pode ser matematizada!

The Reasonable Ineffectiveness of Mathematics in the Biological Sciences

by Seymour Garte 1,* Perry Marshall 2 and Stuart Kauffman 3

1 Department Pharmacology and Toxicology, School of Pharmacy, Rutgers University, Piscataway, NJ 08854, USA

2 Evolution 2.0, Oak Park, IL 60301, USA

3 The Institute for Systems Biology, Seattle, WA 98109-5263, USA

* Author to whom correspondence should be addressed.

Entropy 2025, 27(3), 280; https://doi.org/10.3390/e27030280

Submission received: 24 December 2024 / Revised: 26 February 2025 / Accepted: 5 March 2025 / Published: 7 March 2025

Image/Imagem

Abstract

The known laws of nature in the physical sciences are well expressed in the language of mathematics, a fact that caused Eugene Wigner to wonder at the “unreasonable effectiveness” of mathematical concepts to explain physical phenomena. The biological sciences, in contrast, have resisted the formulation of precise mathematical laws that model the complexity of the living world. The limits of mathematics in biology are discussed as stemming from the impossibility of constructing a deterministic “Laplacian” model and the failure of set theory to capture the creative nature of evolutionary processes in the biosphere. Indeed, biology transcends the limits of computation. This leads to a necessity of finding new formalisms to describe biological reality, with or without strictly mathematical approaches. In the former case, mathematical expressions that do not demand numerical equivalence (equations) provide useful information without exact predictions. Examples of approximations without equal signs are given. The ineffectiveness of mathematics in biology is an invitation to expand the limits of science and to see that the creativity of nature transcends mathematical formalism.

Keywords: mathematical laws; set theory; third transition

FREE PDF GRATIS: Entropy

Darwin, a ilusão de design na natureza inspira novo material no esqueleto de vidro de uma esponja do mar

Auxetic behavior and energy absorption characteristics of a lattice structure inspired by deep-sea sponge

Jiaming Ma, Hongru Zhang, Ting-Uei Lee, Hongjia Lu, Yi Min Xie, Ngoc San Ha

Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia

Received 16 September 2024, Revised 23 December 2024, Accepted 27 December 2024, Available online 27 December 2024, Version of Record 2 January 2025.

https://doi.org/10.1016/j.compstruct.2024.118835 

Image/Imagem:

The silica skeleton of a Venus’ flower basket sea sponge (Euplectella aspergillum). Credit: RMIT University

Abstract

Auxetic metamaterials, characterized by their lateral contraction under compression, have seen notable progress in recent years, largely due to advancements in 3D printing technologies. However, their practical application remains constrained by limited design versatility, moderate improvements in negative Poisson’s ratio (NPR), and relatively low structural stiffness. To address these challenges, a bio-inspired lattice structure (BLS) has been developed, drawing inspiration from the skeletal system of deep-sea hexactinellid sponges, renowned for their exceptional energy absorption capabilities, stiffness, and mechanical properties. Although this structure exhibits auxetic behavior, a comprehensive understanding of its mechanical performance, including its auxetic properties, remains incomplete. In this study, we systematically explore the auxetic behavior, stiffness, and energy absorption properties of the BLS through a combination of quasi-static compression experiments and detailed numerical simulations using finite element analysis. The experimental results reveal that the BLS outperforms conventional auxetic structures, such as re-entrant hexagonal honeycombs, in terms of NPR, stiffness, and energy absorption capacity. Furthermore, a parametric study is conducted to evaluate the influence of geometric variations, such as member thickness and spacing, on the mechanical performance of the BLS. These findings demonstrate that the BLS has the potential to pioneer a new class of auxetic materials, offering superior mechanical properties and broad applicability in engineering fields that require enhanced energy absorption and structural stiffness under compressive loading.

Keywords

Metamaterial Negative Poisson’s ratio Bio-inspired structure Auxetic 3D printing

FREE PDF GRATIS: Composite Structures