Department of Biology, Memorial University of Newfoundland, St. John's, NL, A1B 3X9, Canada.
International Center for the Philosophy of Information, Xi'an Jiaotong University, Xi'an, 710049, China; Chemin Du College 1, 1865, Les Diablerets, Switzerland.
Biosystems. 2021 Jun;204:104395. doi: 10.1016/j.biosystems.2021.104395. Epub 2021 Feb 25.
Mathematics is a powerful tool to express the computable part of the reality of the physical world. For living systems, mathematical relations emerge internally as an abstracting capacity in the course of development and adaptation to the external world. All living systems possess internal coding structures which represent their embedded description. They are anticipatory in the sense that the embedded description generates deterministic model of their behavior. If the model does not provide a correct result, they can evolve through the acquisition of new statements inside the embedded description that overcome limitations of the existing model. The newly generated statements acquire meaning in and from the changing environment. The growth of complexity, being a consequence of the internal active adaptation to externality performed by the systems, increases the amount of external work and generates the observed patterns of spatiotemporal structures of evolving systems. In living systems, the symbolic memory constraints are dynamic processes in themselves, co-evolving with the other components of biological systems. Separation of the symbolic memory and the dynamic laws (defined as the epistemic cut), required for self-replication of biological systems, forms the basis for their onto-epistemic relation to reality. In this regard, living systems possess their own internal abstracting capacity and invent mathematics. The digital structure of the genetic code is a manifestation of this mathematics.
数学是表达物理世界可计算部分的有力工具。对于生命系统来说，数学关系是在发展和适应外部世界的过程中作为一种抽象能力而内在出现的。所有生命系统都具有内部编码结构，这些结构代表了它们的嵌入式描述。它们具有前瞻性，因为嵌入式描述生成了它们行为的确定性模型。如果模型没有提供正确的结果，它们可以通过在嵌入式描述中获取新的语句来进化，这些新的语句克服了现有模型的局限性。新生成的语句在不断变化的环境中获得意义。复杂性的增长是系统对外在性进行内部主动适应的结果，增加了外部工作量，并产生了进化系统时空结构的观察模式。在生命系统中，符号记忆约束本身就是动态过程，与生物系统的其他组成部分共同进化。符号记忆和动态规律（定义为认识的分割）的分离是生物系统自我复制所必需的，这构成了它们与现实的本体认识论关系的基础。在这方面，生命系统拥有自己的内部抽象能力，并发明了数学。遗传密码的数字结构就是这种数学的体现。
