One way to resolve the actuation problem of metaphorical language change is
to provide a statistical profile of metaphorical constructions and generative
rules with antecedent conditions. Based on arguments from the view of language
as complex systems and the dynamic view of metaphor, this paper argues that
metaphorical language change qualifies as a self-organized criticality state
and the linguistic expressions of a metaphor can be profiled as a fractal with
spatio-temporal correlations. Synchronously, these metaphorical expressions
self-organize into a self-similar, scale-invariant fractal that follows a
power-law distribution; temporally, long range inter-dependence constrains the
self-organization process by the way of transformation rules that are intrinsic
of a language system. This argument is verified in the paper with statistical
analyses of twelve randomly selected Chinese verb metaphors in a large-scale
diachronic corpus.

通过大规模的历时语料统计分析，本文论证了随机选择的 12 个中文动词隐喻在时间和空间上符合自组织临界状态和分形自我相似的规律。

隐喻语言变化是自组织临界性

Metaphorical Language Change Is Self-Organized Criticality

Introduced by the late Per Bak and his colleagues, self-organized criticality
(SOC) has been one of the most stimulating concepts to come out of statistical
mechanics and condensed matter theory in the last few decades, and has played a
significant role in the development of complexity science. SOC, and more
generally fractals and power laws, have attacted much comment, ranging from the
very positive to the polemical. The other papers in this special issue
(Aschwanden et al, 2014; McAteer et al, 2014; Sharma et al, 2015) showcase the
considerable body of observations in solar, magnetospheric and fusion plasma
inspired by the SOC idea, and expose the fertile role the new paradigm has
played in approaches to modeling and understanding multiscale plasma
instabilities. This very broad impact, and the necessary process of adapting a
scientific hypothesis to the conditions of a given physical system, has meant
that SOC as studied in these fields has sometimes differed significantly from
the definition originally given by its creators. In Bak's own field of
theoretical physics there are significant observational and theoretical open
questions, even 25 years on (Pruessner, 2012). One aim of the present review is
to address the dichotomy between the great reception SOC has received in some
areas, and its shortcomings, as they became manifest in the controversies it
triggered. Our article tries to clear up what we think are misunderstandings of
SOC in fields more remote from its origins in statistical mechanics, condensed
matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original
papers.

本文通过重新访问 Bak，Tang 和 Wiesenfeld 的原始论文，试图澄清我们认为的关于 SOC 在统计力学、凝聚态和动力学系统之外的领域被误解的情况。

自组织临界性的 25 年：概念和争议

25 Years of Self-Organized Criticality: Concepts and Controversies

We present a systematic analysis of statistical properties of turbulent
current and vorticity structures at a given time using cluster analysis. The
data stems from numerical simulations of decaying three-dimensional (3D)
magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic
field; the magnetic Prandtl number is taken equal to unity, and we use a
periodic box with grids of up to 1536^3 points, and with Taylor Reynolds
numbers up to 1100. The initial conditions are either an X-point configuration
embedded in 3D, the so-called Orszag-Tang vortex, or an
Arn'old-Beltrami-Childress configuration with a fully helical velocity and
magnetic field. In each case two snapshots are analyzed, separated by one
turn-over time, starting just after the peak of dissipation. We show that the
algorithm is able to select a large number of structures (in excess of 8,000)
for each snapshot and that the statistical properties of these clusters are
remarkably similar for the two snapshots as well as for the two flows under
study in terms of scaling laws for the cluster characteristics, with the
structures in the vorticity and in the current behaving in the same way. We
also study the effect of Reynolds number on cluster statistics, and we finally
analyze the properties of these clusters in terms of their velocity-magnetic
field correlation. Self-organized criticality features have been identified in
the dissipative range of scales. A different scaling arises in the inertial
range, which cannot be identified for the moment with a known self-organized
criticality class consistent with MHD. We suggest that this range can be
governed by turbulence dynamics as opposed to criticality, and propose an
interpretation of intermittency in terms of propagation of local instabilities.

本研究通过簇分析系统地分析了湍流电流和涡流结构的统计特性，同时研究了雷诺数对簇统计的影响以及如何解释间歇性，并发现自组织临界性特征在可耗散尺度范围内。