Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Living Structure Down to Earth and Up to Heaven: Christopher Alexander   Discovered by Christopher Alexander, living structure is a physical
phenomenon, through which the quality of the built environment or artifacts can
be judged objectively. It bears two distinguished properties just like a tree:
"far more small things than large ones" across all scales, and "more or less
similar things" on each scale. As a physical phenomenon, and mathematical
concept, living structure is essentially empirical, discovered and developed
from miniscule observation in nature- and human-made things, and it affects our
daily lives in some substantial ways, such as where to put a table or a flower
vase in a room, helping us to make beautiful things and environments. Living
structure is not only empirical, but also philosophical and visionary, enabling
us to see the world and space in more meaningful ways. This paper is intended
to defend living structure as a physical phenomenon, clarifying some common
questions and misgivings surrounding Alexander's design thoughts, such as the
objective or structural nature of beauty, building styles advocated by
Alexander, and mysterious nature of his concepts. We first illustrate living
structure - essentially organized complexity, as advocated by the late Jane
Jacobs (1916-2006) - that is governed by two fundamental laws (scaling law and
Tobler's law), and generated in some step by step fashion by two design
principles (differentiation and adaptation) through the 15 structural
properties. We then verify why living structure is primarily empirical, drawing
evidence from Alexander's own work, as well as our case studies applied to the
Earth's surface including cities, streets, and buildings, and two logos. Before
reaching conclusions, we concentrate on the most mysterious part of Alexander's
work - the hypothesized "I" - as a substance that pervasively exists
everywhere, in order to make better sense of living structure in our minds.

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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: math