A Model of The Quantum Mind

Diaa A Ahmed

e-mail: diahmed@yahoo.com

Cairo August 1986, revised Amsterdam 1999

A Model of the "Quantum Mind" was introduced in conjunction with the study of the "Quantum Topology"; the theory of the quantum space on the basis of theory of sets. Some new development are based on the logical structure of the "Yoga Sutras of Patanjali"; the ancient text on Yoga Psychology that describes the development of states of the mind that have the nature of existence itself. Quantum structure of the mind is based on the ortholattice structure of the quantum set and orthological structure of the sutras and formation of the topological solitons/instantons that are relevant to living systems.

Quantum Logic

The system of Yoga Sutras is subject to quantum logic ( P , m ); every proposition correspond to some event in the field and these propositions are subject to the formalism of quantum logic.

The Group

The Homotopy group gives the set of soliton states S. The group admits a representation in Hilbert orthologic; continuous unitary representation. The group connects a logical structure to every topological structure; the group admits quantum logic.

Topological Solitons

These nontrivial solutions follows from nonlinearity of the field that gives rise to stable structures -stable configuration of the fields- for purely topological reasons that lead to purely topological conservation laws that do not follow from Noether theorem and this leads to a kind of motion that is nondissipative; I think that precisely these solutions must play the dominant role in consciousness. The vacuum state of the field is a linear combination of such soliton-instanton states.

Comments on The Sutras

A                                     : Questions.
A and B                           : Conjugate mapping.
Distinction of A and B    : A <-------> B compatible questions.
Relationship of A and B : The set of morphisms A -------> B, define a category L.

It is convenient to embed it in an orthomodular structure ( Hilbert ortholattice ),

Property : A family of orthogonal projectors { P_a } on Hilbert space H_a.
Observable : B ----------^A---------> L, A morphism in the category of the complete ortholattices.
Group : Logical symmetry.

B----------^A----------L
aut (B) | | aut (L)
B----------A----------L

The Model

( 1 ) First we construct an ortholattice of properties L for consciousness, and the impermitivity system,

B----------^A----------L
s (g) | | s (g)
B----------^A----------L

( 2 ) The homotopy group G admits a representation in the logic; unitary projective, L admits the observables of the soliton type solutions. ( L, satisfies an impermitivity system based on G ).
( 3 ) The topology induced by the action of G on L can be used to classify A in
the logic. ( Group Manifold Formulation ).

An Example

A set of properties for consciousness like [ friendliness, strength, intellect, etc.] contain noncommuting elements; transcendence and hearing.
Body ( matter field ) is a property of the lattice, space ( field vacuum ) is another property; relationship of the two is a morphism B -------> A , that defines a category L. We can write such morphism taking vac. state vectors < in, vac | out, vac > , < in, vac | out, vac > = - i d / d B_m < out, vac | in, vac >
= < out, vac | S | in, vac > .

The morphism is accompanied by creation of the source S.
Lightness is another property of the lattice; we may guess at an appropriate solution; gravi-photon soliton states. The source can be mapped into such soliton states,

S -------> G_ph .

Note 1997: Quantum mind is the source of intuition; that discriminates the set into subsets, giving each a different flavor and realizes their morphism. It sees all the histories in a functional space and when chooses a particular one, attention actualizes and project it.
Computations are performed on the fabrics of topology, and stable structures -solitons- store the information and play the role in providing a macroscopic quantum computer -DNA- and macroscopic quantum effects.
All these morphisms are implicit in the set and the logic that is chosen is the logic of complexity; quantum logic.

A R Marlow, Mathematical Foundations of Quantum Theory, Academic Press 1978.
J C Taylor, Gauge Theories of Weak Interactions, Cambridge 1976.
L Lopes, Gauge Field Theories, Pergamon 1981.
Swami Hariharananda Aranya, Yoga Philosophy of Patanjali, SUNY Press 1983.