hierarchies of symmetry had to be involved in some fashion, in my
opinion, because that is the way one can turn virtual energy into
observable energy (call it coherent integration, whatever). Leyton has
developed it on very rigorous group theoretic approach, so I think its
one of the discoveries of the century. His work has also been applied
to robotics, pattern recognition, and even to the way we "think" or
"conceive" (powerful dense nesting!).
Leyton's profound work is further exposed, a great many areas of physics
and human knowledge will be affected. Symmetry and broken symmetry
affect just about all major areas of physics, very profoundly. And the
Leyton Effect in turn affects symmetry and broken symmetry profoundly.
The definitive book
is: Michael Leyton,
Generative Theory of Shape,
Springer-Verlag, Berlin, 2001. Leyton develops a generative theory of
shape that has two properties regarded as fundamental to
transfer of structure and maximizing recoverability of the generative
operations. These two properties are particularly important in the
representation of complex
shape — which is the main concern of the book. The primary goal of the
theory is the conversion of complexity into understandability. For this
purpose, a mathematical theory is presented of how understandability is
created in a structure. This is achieved by developing a group-theoretic
approach to formalizing transfer and recoverability.
To handle complex shape, a new class of groups is developed, called
unfolding groups. These
unfold structure from a maximally collapsed version of that structure. A
principal aspect of the theory is that it develops a group-theoretic
formalization of major object-oriented concepts such as inheritance. The
result is an object-oriented theory
The algebraic theory is applied in detail to CAD, perception, and
robotics. In CAD, lengthy chapters are presented on mechanical and
architectural design. For example, using the theory of unfolding groups,
the book works in detail through the main stages of mechanical CAD/CAM:
part-design, assembly and machining. And within part-design, an
extensive algebraic analysis is given of sketching, alignment,
dimensioning, resolution, editing, sweeping, feature-addition, and
intent-management. The equivalent analysis is also done for
architectural design. In perception, extensive theories are given for
grouping and the main Gestalt motion phenomena (induced motion,
separation of systems, the Johannson relative/absolute motion effects);
as well as orientation and form. In robotics, several levels of analysis
are developed for manipulator structure, using the author's algebraic
theory of object-oriented structure.
"A Generative Theory of Shape" contains the full mathematical
theory of hierarchies of symmetry. It invents a new group-theoretic
approach to symmetry-breaking, that is the opposite of the conventional
approach. In the conventional approach, symmetry-breaking causes a
reduction in symmetry group. In the new approach, it causes the
creation of a larger symmetry group with an extra layer that NESTS the
For its impact on
understanding perception and the mind, see also Michael Leyton,
MIT Press, 1992.
Isn't this in some ways analogous to the way Rife's microscope worked?
once in awhile the good guys win one because they just plain get lucky!
Leyton has already developed the hierarchy of symmetries that I was
groping for. Further, he's done it in really good group theoretic work,
and it's already published (just not very well known, it seems). He's
applied it to the way we actually are able to perceive things, etc.
point is that broken symmetry at one level does (by his work) create a
higher level symmetry that nests around and over where one started.
Voila! That gets us coherently (symmetrical) in the observable state
from just adding up a whole bunch of subquantal (virtual) energy. It
also continues and gives us the symmetry (determinism) of the resulting
fields, etc. It's sorta the ultimate "self-ordering", even in the way
we think, perceive, and observe.
least my intuition was correct, and the entire notion of entropy has to
be revised for the hierarchy effect that occurs whenever symmetry is
broken at any level. That is presently missing entirely, at least as far
as I can discover. And it changes a whole bunch of other physics also!
Nice to have a very solid reference! I'll also make sure to point out
the tremendous importance of his work, because it really is!
should have the book in here in about two to three weeks.