As nature scales, complexity gives way to universal law.
Why shouldn’t an ecosystem be just as beautifully perfect as an ideal gas, and why can’t ecologists have as much predicting power as a physicist? The answers to these questions just might be “it is,” and “they can.” But only when viewed from a particular perspective.
When we plotted average evolutionary distance against species number, we found the power law lurking in yet another dimension of ecology: The distance increased rapidly at first, then began to slow in the same manner as the species-area curve.3 The reasons for this behavior are not clear at the moment. One possibility is that both spatial and temporal scaling behaviors are affected by a “burstiness,” in which periods of stasis are punctuated by rapid periods of diversification. In our bacterial trees we found that these bursty expansions have a fractal distribution, also described by a power law, and they could point to radiations of species through both time and space.
The power laws we see for evolutionary distance and diversification point once again to a simple, mechanistic, and relatively detail-free view of ecology at the biggest scales. They’re just not quite as simple as what has been proposed for spatial patterns. They take at least one step back down the spectrum toward needing real ecological and evolutionary mechanisms to explain macroecological patterns.More.
Rob Sheldon writes to say,
I ran into power-laws when we analyzed particle spectra (plasma distribution functions) both near the earth and far away in the solar wind. It turned out that regular (integer power) diffusion equations don’t give power laws, but “fractional diffusion” equations do. The difference is that differential equations with integer powers are local, only affecting by things nearby, but fractional differential equations are “non-local”, affected by global changes.
Global spatial effects are the bane of materialism, Einstein called them “spooky action-at-a-distance” and in his famous EPR paper, attempted to disprove them. Global temporal effects are likewise troublesome to materialists.
It is as if one can predict the future and adjust one’s behavior accordingly. In psychology we call that ability “consciousness”. In physics we call that a non-causal relationship, “a spacelike” separation in spacetime. In philosophy we call it teleology.
In this article, ecology seems to show lots of power laws, and nobody is sure how to explain it. Their explanation of “maximum entropy” might as well be “maximum teleology”, since it is a global property being described.
Yet another proof that materialism is not just misguided, but wrong.
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