Current physics commonly qualifies the Earth system as ‘complex’ because it includes numerous different processes operating over a large range of spatial scales, often modelled as exhibiting non-linear chaotic response dynamics and power scaling laws. This characterization is based on the fundamental assumption that the Earth’s complexity could, in principle, be modeled by (surrogated by) a numerical algorithm if enough computing power were granted. Yet, similar numerical algorithms also surrogate different systems having the same processes and dynamics, such as Mars or Jupiter, although being qualitatively different from the Earth system. Here, I argue that understanding the Earth as a complex system requires a consideration of the Gaia hypothesis: the Earth is a complex system because it instantiates life—and therefore an autopoietic, metabolic-repair (M,R) organization—at a planetary scale. This implies that the Earth’s complexity has formal equivalence to a self-referential system that inherently is non-algorithmic and, therefore, cannot be surrogated and simulated in a Turing machine. I discuss the consequences of this, with reference to in-silico climate models, tipping points, planetary boundaries, and planetary feedback loops as units of adaptive evolution and selection.

中文翻译：

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地球的复杂性是不可计算的：缩放定律、非线性和混沌的极限

当前物理学通常将地球系统称为“复杂”，因为它包括在大范围空间尺度上运行的许多不同过程，通常建模为表现出非线性混沌响应动力学和功率缩放定律。这种表征基于这样一个基本假设，即如果授予足够的计算能力，地球的复杂性原则上可以由数值算法（由其替代）建模。然而，类似的数值算法也可以替代具有相同过程和动力学的不同系统，例如火星或木星，尽管它们在性质上与地球系统不同。在这里，我认为将地球理解为一个复杂的系统需要考虑盖亚假设：地球是一个复杂的系统，因为它实例化了生命——因此是一个自创生的，代谢修复（M，R）组织——在全球范围内。这意味着地球的复杂性与本质上是非算法的自我参照系统具有形式上的等价性，因此无法在图灵机中替代和模拟。我将参考计算机模拟气候模型、临界点、行星边界和行星反馈回路作为适应性进化和选择的单位来讨论其后果。