Fearful Symmetry: Is God a Geometer?

Book by Ian Stewart and Martin Golubitsky, cited for symmetry breaking concepts used to explain structure-preserving transformations in physics.

Extracted from this book

Claims (11)

Structure-preserving transformations are the secret of all artistic and constructive human-inspired acts of creation.
Claim that the same process that creates natural living structure also underlies human artistic and architectural creativity.
The creation of morphological novelty, biological invention, artistic creation, architectural invention ... may all be understood as products of a relatively simple process of intensifying existing latent centers.
Claim that the emergence of new forms, often considered mysterious, is explainable through repeated intensification of latent structure.
The fifteen properties appear in nature as a direct result of repeated structure-preserving transformations unfolding the wholeness.
Interpretation that the geometric properties of living structure are not arbitrary but arise inevitably from the smooth unfolding process.
The fifteen properties are the fifteen ways in which centers can enliven one another.
Recapitulation of the Book 1 definition, linking the properties to the mutual intensification of centers.
The fifteen transformations provide the base transformations from which, in practice, all structure-preserving transformation are made.
Assertion that the fifteen specific transformation types form a complete palette for all structure-preserving differentiation.
The intricate and beautiful structure of living centers comes about naturally, and most of the time without effort, as a result of the repeated application of structure-preserving transformations to the wholeness which exists.
Central interpretive claim of the chapter, asserting that living structure is an effortless natural outcome of structure-preserving transformations.
The structure we know as living structure is just that kind of structure which has unfolded smoothly and naturally, arising step by step from what exists, preserving the structure of what exists.
Defines living structure as the product of a truthful unfolding process that respects and preserves existing wholeness.
The system acts to preserve as much of its structure as possible, removing as few symmetries as possible when symmetry breaking occurs.
Physical principle interpreted as a form of structure-preserving transformation, explaining phenomena like buckling and dew drops.
This horn of plenty is inexhaustible, and we may conceive an everlasting fountain of novelty without ever having to beat ourselves over the head for the sake of novelty per se.
Optimistic view that respecting wholeness generates endless novelty, conquering the fear that structure-preservation is merely conservative.
What is more structure-preserving and what is less so is, in principle, an objective matter.
Assertion that the distinction between structure-preserving and structure-destroying is objective, not merely subjective opinion.
Within the framework of wholeness, value is an objective phenomenon which arises inevitably from the degree to which unfolding has been truthful—guided by the fifteen structure-preserving transformations.
A new view of ethics and aesthetics where goodness is equated to smooth unfolding from existing wholeness.

Findings (4)

Drawing the structure first increases inter-rater agreement on structure-preserving judgments, even when drawings differ
People who first attempted to draw the perceived structure of a configuration showed higher agreement about which transformations are structure-preserving, despite drawing different aspects of the field of centers.
Sequence of all structure-preserving transformations almost always beautiful; a single bad transformation causes ugliness and is hard to recover from
In laboratory studies, repeated structure-preserving transformations led to beautiful results, while a single structure-destroying step disrupted the unfolding and proved very difficult to repair.
Third transformation in lower row of octagon unanimously rated structure-destroying (8/8 people)
The third transformation of the lower row was unanimously judged as structure-destroying by all eight participants.
Upper row octagon transformations unanimously rated structure-preserving (8/8 people)
In a rating study, the transformations in the upper row of an octagon were unanimously judged as structure-preserving by all eight participants.

Hypotheses (1)

If the evolution of the natural world follows a step-by-step process in which each step is structure-preserving, then the fifteen properties will appear more and more often, and the degree of life in the wholeness will increase steadily.
Conditional statement linking smooth unfolding to the progressive emergence of the fifteen properties and increased life.

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Thinkers (2)

thinker

Ian Stewart
authored
Mathematician and co-author of Fearful Symmetry, cited for symmetry breaking concepts.
Martin Golubitsky
authored
Mathematician and co-author of Fearful Symmetry, cited for symmetry breaking concepts.

Concepts (1)

concept

Structure-Preserving Transformations
cites
Chapter 2 of Volume 2 of The Nature of Order, introducing structure-preserving transformations as the mechanism by which living structure arises naturally through unfolding wholeness.