Center for Nonlinear Science, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017, USA.
Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor's Circle, Winnipeg, MB, R3T 5V6, Canada; Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey.
Prog Biophys Mol Biol. 2018 Mar;133:30-35. doi: 10.1016/j.pbiomolbio.2017.10.005. Epub 2017 Oct 31.
A unifying principle underlies the organization of physical and biological systems. It relates to a well-known topological theorem which succinctly states that an activity on a planar circumference projects to two activities with "matching description" into a sphere. Here we ask: what does "matching description" mean? Has it something to do with "identity"? Going through different formulations of the principle of identity, we describe diverse possible meanings of the term "matching description". We demonstrate that the concepts of "sameness", "equality", "belonging together" stand for intertwined levels with mutual interactions. By showing that "matching" description is a very general and malleable concept, we provide a novel testable approach to "identity" that yields helpful insights into physical and biological matters. Indeed, we illustrate how a novel mathematical approach derived from the Borsuk-Ulam theorem, termed bio-BUT, might explain the astonishing biological "multiplicity from identity" of evolving living beings as well as their biochemical arrangements.
一个统一的原则是物理和生物系统的组织。它涉及到一个著名的拓扑定理，简洁地说，一个在平面圆周上的活动投影到一个球上有“匹配描述”的两个活动。在这里我们问：“匹配描述”是什么意思？它与“同一性”有关吗？通过研究同一性原理的不同表述，我们描述了“匹配描述”一词的多种可能含义。我们证明了“相同”、“平等”、“归属”等概念代表了相互交织、相互作用的层次。通过表明“匹配”描述是一个非常通用和灵活的概念，我们为“同一性”提供了一种新颖的可测试方法，为物理和生物学问题提供了有帮助的见解。事实上，我们说明了如何从 Borsuk-Ulam 定理中推导出一种新的数学方法，称为生物 BUT（bio-BUT），它可以解释生物进化的生物体及其生化排列的惊人的“同一性中的多样性”。
