The Tom Bearden

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Date: Thu, 30 Jan 2003 22:07:59 -0600



Yes, Leyton's 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!).


Hopefully, once 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, A Generative Theory of Shape, Springer-Verlag, Berlin, 2001.  Leyton develops a generative theory of shape that has two properties regarded as fundamental to intelligence—maximizing 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 of geometry.
     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 preceding group.

For its impact on understanding perception and the mind, see also Michael Leyton, Symmetry, Causality, Mind, MIT Press, 1992.


Best wishes,




Isn't this in some ways analogous to the way Rife's microscope worked?




Tony and Marcia,

Well, once in awhile the good guys win one because they just plain get lucky!

Prof. 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.

But the 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.

So at 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!

Anyway, I should have the book in here in about two to three weeks.