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本文探讨了数学、物理和生物学中各种形式的内在随机性。首先,阐述了数学中不含时的数学内随机性(如多解性、非循环性、不定性、任意性、不可判定性等)与含时的数学内随机性(如表现在确定的非线性常微分方程、迭代方程的解对初始条件和参数改变的敏感性上的内随机性)。接着,分析了物理学中宏观混沌、统计涨落、物质波、真空激发、量子起伏等内随机性和相互独立、均匀对称的内随机性。最后,介绍了生物学中的遗传、生灭、更新与进化过程以及生物功能方面的内随机性。
This article explores the various forms of internal randomness in mathematics, physics and biology. First of all, it expounds the mathematical randomness (such as multi-solution, non-cyclic, indefinite, arbitrary, indefinable, etc.) Linear ordinary differential equations, the stochasticity of the solution of the iterative equations to the initial conditions and the sensitivity of the parameters to change). Then, we analyze the internal randomness of macroscopic chaos, statistical fluctuation, material wave, vacuum excitation and quantum fluctuation in physics, which are independent and symmetrical. Finally, we introduce the internal randomness in the biology of genetics, birth and death, renewal and evolution, and biological function.