'Topological Geometrodynamics' and Consciousness

Date: Tue, 25 Jun 1996 02:50:57 -0700 (PDT)
From: Matti Pitkanen <matpitkanen@phcu.helsinki.fi>
To: quantum-d@teleport.com
Subject: 'Topological Geometrodynamics' and Consciousness


Basic ideas of TGD inspired theory of consciousness

Matti Pitkanen
Torkkelinkatu 21 B39 , 00530, Helsinki, Finland
E-mail  matpitkanen@phcu.helsinki.fi
homepage: http://blues.helsinki.fi/~matpitka/

June 25,  1996


1.   Quantum TGD very briefly
1.1. TGD as a generalization of string model
1.2  Configuration space concept
1.3  General coordinate invariance and the definition of Kahler
     function
1.4  Quantum states as spinor fields in CH
1.5  State function reduction as quantum jump between deterministic
     quantum histories
1.6. TGD inspired measurement theory
1.7. The concept of effective spacetime

2.   TGD inspired theory of consciousness
2.1  The problem of subjective time as key to the theory of
     consciousness
2.2  Some consequences

3.   Application to human consciousness
3.1  How to stay conscious?
3.2  Brain as a macroscopic quantum system
3.3  Jumps between quantum histories at the level of brain

4.   About cognitive aspects of consciousness
4.1  Thoughts as simulations
4.2  Vacuum degeneracy of the Kahler action
4.3  Nonuniqueness of the classical spacetime from vacuum degeneracy

5.   Summary

     Bibliography


Abstract


The basic assumption of T(opological) G(eometro)D(ynamics) is that
physical spacetimes are representable as surfaces of a certain
8-dimensional space M4+ x CP2, where M4+ is the future light cone
of Minkowski space and CP2 is complex projective space of two
complex dimensions. In the following the basic ideas of a TGD
inspired theory of consciousness are described shortly. The first
element is TGDish description of quantum states as deterministic
quantum histories and the description of state function reduction
as jump between two deterministic quantum histories. The second
element is the identification of quantum jump as act of free will/
conscious experience.  The contents of the conscious experience
are assumed to be determined by the region of spacetime to which
the nondeterminism of the quantum jump is localized. This provides
a natural identification of subjective time: the arrow of time
follows from the basic structure of TGD. The third element is the
generalization of quantum measurement theory so that it applies to
all systems in interaction with the surrounding world.  Finally,
the TGDish concept of spacetime provides the realization of the
idea of Penrose about biosystem as a quantum superposition of
macroscopically different geometries.


1. Quantum TGD very briefly

In the following only those aspects  of TGD relevant to the TGD
inspired theory of consciousness are reviewed. The interested reader
can get more detailed information from my  personal homepage, where
the  books 'Topological Geometrodynamics' and 'p-Adic numbers and
Topological Geometrodynamics' can be found  as ps-files. Also hypertext
representation of the basic ideas of TGD and p-adic TGD can be found
at the homepage.


1.1. TGD as a generalization of string model

Quantum TGD [TGD,padTGD] can be regarded as a generalization of string
model in the  sense that  point like particles are replaced  with
3-dimensional  surfaces (rather than one-dimensional strings)  of
certain 8-dimensional space H=M4+ x CP2, where M4+ is the future
light cone of Minkowski space and CP2 is the complex projective
space of two complex dimensions (4 real dimensions). The  orbit of
3-surface is  4-dimensional surface. A radical generalization of
the spacetime concept is involved. Macroscopic spacetime is regarded
as a macroscopic 4-surface in H and elementary particles correspond
to 'small' 3-surfaces with size of order Planck length. By gluing
small 3-surfaces by topological sum operation to macroscopic 3-surface
one obtains macroscopic spacetime containing particles as topological
inhomogeneities. Even macroscopic objects are regarded 3-surfaces
having outer boundaries and glued by topological sum contacts to the
larger background 3-surface so that TGD means a completely new manner
to interpret even the everyday world around us.  Needless to say,
TGD has nontrivial applications in all length scales.


1.2. Configuration space concept

The construction of quantum theory relies on the concept of configuration
space CH [TGD]. CH consists of all possible 3-surfaces in H=M4+ x CP2.
All topologies are allowed: in particular also surfaces with several
disjoint components are possible. Quantum theory reduces to the
construction of spinor geometry for CH.  This necessitates the
construction of metric and spinor structure. Physical states correspond
to some basis of spinor fields in CH. Physical requirements force
Kahler geometry, which means that the tangent space of CH allows
complexification and the representation of imaginary unit by
antisymmetric tensor satisfying the condition JJ= -g (counterpart of
ii=-1), where the product is defined via index contraction and g is
metric tensor. Kahler geometry can be coded into Kahler function K and
the task is to identify Kahler function somehow.


1.3 General coordinate invariance and the definition of Kahler
    function

In the  definition of the  Kahler function the basic  ingredient is
the requirement of General Coordinate Invariance, which is the
cornerstone of General Relativity, too.  4-dimensional  diffeomorphism
group Diff4 rather than 3-dimensional Diff3 is in question and one
encounters a problem since the points of CH correspond to 3-surfaces
rather than 4-surfaces. Somehow the definition of Kahler function should
associate a unique 4-dimensional surface to  a  given  3-surface for
Diff4 to act on. Here comes the  connection with ordinary quantum field
theories and string models.    One can define variational principle in
the set of  4-surfaces  of H  in terms of  so called Kahler action,
which is Diff4 invariant and defined in terms of imbedding space
geometry and can be regarded as a nonlinear counterpart of Maxwell
action.  The extremals of the  Kahler action satisfy Euler Lagrange
equations, which would define classical theory if ordinary QFT were in
question.  The idea is to define  Kahler function K(X3)   as absolute
minimum of the  Kahler action  for all 4-surfaces containing X3 as
submanifold (boundary of X3 belongs to the boundary of X4). This means
that one constructs all extremals of Kahler action going through X3 and
seeks  from this set  the extremal X4(X3) with the minimum value of
Kahler action. There is an obvious temptation to identify X4(X3)  as
classical spacetime so that classical physics becomes part of
configuration space geometry.

The absolute minimum spacetime surface X4(X3) need not be unique, which
means nondeterminism already at classical level. In fact, the properties
of Kahler action suggest that for certain critical 3-surfaces this is
the case. In present of N-fold degeneracy one can  replace the critical
3-surface X3 with N-fold replica of X3. This degeneracy and related
classical nondeterminism  might play important role in biosystems and
might imply the picture   proposed by Penrose.


1.4 Quantum states as spinor fields in CH

Quantum states correspond to spinor fields  in CH. It turns out that
spinor components span the  Fock-space  with the second quantized free
spinor fields of H on spacetime surface.  Diff4 invariance implies  that
the value of CH spinor field is same for all diffeorelated 3-surfaces on
X4(X3). Diff4 invariance with respect to time translations implies
deterministic time-evolution so that there is no need to postulate any
Schrodinger equation for configuration space spinor fields. What is
important is that quantum states correspond to entire deterministic
quantum histories rather than equal time snapshot of single
deterministic history.  This implies deep difference between TGD and
standard  quantum field theories.  The   problem of  defining the
concept of subjective time, when physical states are regarded as quantum
histories,  will be considered  later and  leads to the TGD inspired
theory of consciousness.


1.5. State function reduction as quantum jump between  deterministic
     quantum histories

Quantum jumps are an essential element in the interpretation of the
standard quantum theory.  Unless one is willing to adopt Many Universe
interpretation quantum jump (state function reduction) must be regarded
as  a spontaneous nondeterminism at the level of Schrodinger equation.
This kind of behavior is extremely awkward mathematically. In TGD
quantum jumps occur between  between deterministic quantum histories
and are  completely outside the realm of the geometric spacetime so
that determinism at the level of solutions of Schrodinger equation is
not lost. The paradoxes related with concept-pairs subjective/objective
disappear. Determinism is realized at the level of geometric spacetime
realm and nondeterminism at the level of state space. Objective worlds
correspond to deterministic quantum evolutions and, according to the
theory of consciousness to be formulated,  subjective experience
corresponds to the quantum jump between two objective worlds.

An especially unpleasant paradox for theoretician is that conventional
determinism makes theoretician  useless! If only single deterministic
history is actually realized then the mental constructs of theoretician
are in principle not testable since it is not possible to compare
different time evolutions. If quantum jumps between different
deterministic histories are possible it becomes possible to genuinely
test theories. In  the proposed picture one avoids also the question
about  the initial values of dynamical variables  at the moment of big
bang.


1.6. TGD inspired measurement theory

TGD suggests also a generalization of the  standard quantum measurement
theory and this generalization  adds additional elements  to the TGD
inspired theory of consciousness.

The standard measurement theory postulates that quantum subsystem in
interaction with the measuring system goes to the eigenstate of the
measured observables and if the experiment is repeated (the measurement
interaction  does not change in time) no further quantum jumps occur.

The TGDish generalization is following. Quantum measurement theory
applies to any subsystem in interaction with  its environment. The
fundamental observable is the density matrix of the subsystem obtained
by integrating over the degrees of freedom associated with the environment.
The negentropy associated with this density matrix could be regarded as
a measure for the amount of selfknowledge obtained via the interaction
with the environment. When subsystem measures its own density matrix it
goes to an eigenstate of the  density matrix. Since the eigenstates of
the density maximize the negentropy  one can say that subsystem tends to
maximize its self knowledge.

The ordinary entropy maximation principle  of thermodynamics  seems to
be closely related to the negentropy maximation principle. Ordinary
thermodynamic negentropy measures the knowledge of observer from the
external world. Assume for simplicity that external world consists of
an ensemble of quantum systems in interaction. The interaction implies
that these systems are continually performing quantum jumps to maximize
their self knowledge. The nondeterminism of quantum jump however implies
that the knowledge of the observer decreases gradually implying the
increase of thermodynamical entropy.


1.7. The concept of effective spacetime

CH spinor fields cannot be localized to single 3-surface so that in
quantum states can be regarded as superpositions of infinitely many 3-
surfaces, or equivalently, classical spacetimes, which are absolute
minima of  Kahler action.  The general structure of quantum field
theories suggests that it should be possible to define quantum average
spacetime as an absolute minimum of so called effective action.  It
seems natural to identify this effective spacetime as the counterpart
of the observed classical spacetime.  In fact, the symmetries of Kahler
action dictate the form of the effective action to very high degree.
The properties of Kahler action, in particular the analogy with spin
glass phase, motivate the hypothesis that effective spacetime obeys p-
adic rather than real topology below certain length scale L(p) [padTGD].
Effective space time is assumed to  consist of regions of different p-
adic prime  p glued together along their boundaries. p-Adic hypothesis
leads to highly successful predictions for elementary particle masses
and simple argument shows that p-adic QFT should be free of ultraviolet
divergences.  p-Adic concepts might have highly nontrivial applications
to biosystems [padTGD,homepage], too.


2. TGD inspired theory of consciousness

TGD inspired theory of consciousness contains 3 basic elements.

 a) The interpretation of quantum jump as the act of free will or
    equivalently as a moment of consciousness. Consciousness is here
    defined as 'pure alertness': no cognitive abilities such as
    memory and thinking need be involved.

 b) The generalization of the ordinary quantum measurement theory
    (already described) so that it applies to the interaction of any
    subsystem with the surrounding world.

 c) The properties of Kahler function, in particular its vacuum
    degeneracy, suggest a more concrete description of thinking
    systems as macroscopic quantum systems. Details about various
    developments can be found from my homepage.


2.1. The problem of subjective time as a key to the theory of
     consciousness

The replacement of quantum state with quantum history raises a problem.
If states are quantum histories how it is possible to   define  the
concept of subjective time  at all? The concept of quantum jump suggests
a solution of the problem. Assume that any quantum system is conscious
only during the quantum jump and that the contents of consciousness are
determined by the properties of the initial and final quantum histories.
Identify  the conscious 'I' as the region the configuration space CH,
where nondeterminism of the quantum jump is located.  Assuming  that this
region corresponds to some finite region of space M4+  the value of the
subjective time can be defined as  average value of the time variable in
this region. This definition associates in a natural manner time duration
with the conscious experience. The localizability of nondeterminism to a
finite spacetime region holds true if small deformation of 3-surface X3
(quantum jump) does not change the corresponding  classical spacetime
surface X4(X3) in regions faraway from X3. This kind of assumption does
not necessarily hold true for initial value sensitive systems.  One can
however replace X4(X3) with the quantum average spacetime in the proposed
definition: it would not be too surprising if   quantum jump would affect
the properties of some finite region of  the quantum averaged  spacetime,
only.

The arrow of time  can  be understood in this picture easily. Imbedding
space is cartesian product of future light cone M4+ (empty Robertson-
Walker type cosmology) and CP2.  The boundary of the future light cone
corresponds to the moment of big bang and for a given value of light
cone proper time  a there is much more room in the future than in the
past so that in the long run the subjective time associated with the
quantum jump  is bound to increase.

I found the proposed definition of subjective time   when writing this
essay. There is also a more formal approach for identifying subjective
time [TGD,padTGD] described in detail in my homepage.  Imbedding space
is cartesian product of future light cone M4+ with CP2 and M4+  breaks
exact Poincare invariance globally.  Poincare transformations do not
commute with Diff4 transformations since Poincare transform of absolute
minimum spacetime surface is in general not absolute minimum spacetime
surface.

One can however define Diff4 invariant Poincare transformations so that
infinitesimal Poincare transformations act as ordinary infinitesimal
Poincare transformations on 3-surfaces, which are intersections of
spacetime surface with M4+ proper time  a=constant hyperboloids.
Outside the hyperboloid the transformations induce deformation of
absolute minimum spacetime. One can select the value of a freely and
one-parameter family of unitarily related, non-orthogonal energy
momentum eigenstate basis results. Non-trivial  S-matrix  for state
basis a1 and a2 can be defined in obvious manner. The identification
of a as subjective time is suggestive. It is  however not obvious to
what degree these two definitions overlap and the previous definition,
although somewhat imprecise, seems to be more fundamental.


2.2. Some consequences

The proposed  identification for the  act of free will as quantum jump
or equivalently as a moment of consciousness resolves many paradoxes
related to the  phenomenon of consciousness.

 a) Moments of consciousness form a discrete sequence rather than
    a continuous stream. One can say that there is only single
    universal consciousness, whose 'I' at a given  moment of
    consciousness  corresponds to the region of nondeterminism
    associated with that particular quantum jump. There is obvious
    parallel with the Brahman=Atman identity of Eastern religions
    and also with the experience of oneness associated with mystic
    experiences. 'You' is 'Me' at a different moment. The reason why
    I cannot remember being 'You' is that the memories are coded
    into the quantum state and are expected to correspond to that
    region of spacetime where nondeterminism is located. Since our
    'I's correspond to different spacetime regions I cannot have
    any memories of being You.
 b) The  idea about parallel streams of consciousness is simply
    wrong in this picture.  This removes several  problems related
    to consciousness. It is easy to understand why separate units
    of consciousness cannot communicate directly: they do not exist
    simultaneously.
    A solution to the  conceptual problems raised by the study of
    split brain patients emerges.  For  split brain patients  either
    left of right half of the  brain is conscious at time but not
    both. Different brain halves seem to  have even different plans
    of future and the transition between two different 'Me's  takes
    place instantaneously.
    If both brain halves are assumed to correspond to continuous streams
    of consciousness one ends up with a hopeless  mess.  Which of these
    halves corresponds to the 'actual Me'. Does the nondominating half
    correspond to a second 'Me'?   What happens, when second half begins
    to dominate as the 'actual Me'?
 c) The possibility that lower units of consciousness  form larger units
    of consciousness (without knowing it!) is not excluded.  The two
    brain halves of a  healthy person obviously do so. The collective
    behavior of an ant society might has explanation in terms of higher
    consciousness associated with the society. Similarly,  our own
    consciousness  could be regarded as that associated with a  society
    of cells. The formation of higher states of consciousness might occur
    even at the level of human society and  could be even crucial for
    the development of civilization and  the formation of language.
 d) The basic  assumption is  that the contents of the experience is
    determined from the properties of the  initial and final states in
    the region of CH where the nondeterminism is located. This implies
    that sensory experience measures always changes rather than static
    properties. Sensory experience seems to have this kind of nature. In
    principle, all sensory qualia should be related to the properties of
    the initial and final states in the quantum jump. In some instances,
    the quantum jumps cause negligible change in the properties of the
    external world (consider vision  as an example) so that sensory
    experience can be said to give rather faithful picture of some
    aspects of the objective world.
 e) Negentropy maximation principle  poses restrictions on free will:
    the interaction with  environment gives the alternatives between
    (eigenstate basis of the density matrix), from which subsystem can
    select one. For ensembles various alternatives have different
    probabilities given by standard quantum theory.


3. Application to human consciousness


3.1.  How to stay conscious?

Quantum measurement theory states that if the interaction between
subsystem and  environment does not change with time the system performs
just quantum jump and  remains in the resulting state after that. Since
consciousness is associated with quantum jumps  subsystem must fall into
an  nonconscious state unless the interaction with environment changes in
time. This is just what seems to occur. When we want to sleep we find some
peaceful place and minimize the interaction with the environment. We get
sleepy, when hearing boring lecturer.  Constant sensory stimulation leads
rapidly to the  disappearance of the sensory experience: to avoid the
disappearance of visual field our eyes in  fact perform  small motion all
the time. Insects can see only a moving object. Brain can however  stay
conscious by generating nerve pulses leading to hallucinatory experiences.
Similar phenomenon seems to occur at the level of nerve cells: when
sensory stimulation stays constant nerve cell ceases to fire.


3.2. Brain as a macroscopic quantum system

The idea of Penrose and Hameroff about brain as macroscopic quantum
system fits nicely with previous ideas.  For instance, one could
understand mental illness quantum mechanically as a loss of quantum
coherence in brain so that some regions of brain  have lost their
ability to  be in quantum coherent states. This loss of coherence could
be perhaps detected in the EEG as a loss of spatial coherence.  The
phenomenon of side personalities could be understood also: single
personality corresponds to some part of brain being conscious while
the remaining parts are nonconscious.  The  splitting of personality to
separate personalities could also understood as a partial of macroscopic
quantum coherence: for split brain patients this splitting is caused
artificially.  The ability (of, say, actors) to create
temporally new side personalities  might have explanation as  the
ability of the brain to form new quantum subsystems.

3.3. Jumps between quantum histories at the level of brain

In quantum jump between histories also the past of the system defined
in terms of  the effective quantum average space time changes. There is
evidence for this kind of change. In experiments, where the subject
person decides to do something, say  to take pencil from the table,
neurological activity begins about one second before the conscious
decision.  Materialistic interpretation is that consciousness is  a
passive spectator  and conscious experience is a by-product of a
deterministic time evolution. The alternative interpretation is based
on assumption that the process of taking pencil into hand is macroscopic
quantum jump between two widely different spatial configurations and
the corresponding histories.  The new history necessarily leads in a
deterministic manner to a final state, where person has pencil in his
hand.  Since this process must occur smoothly,  the new history must
differ from the old one already before the moment of decision so that
neurological process begin before the moment of decision. This
interpretation allows to deduce that brain is able to change its past
in the time scale of order one second.  A stronger conclusion is that
the dimension for the region of  nondeterminism is typically of order
one  second in time like direction and therefore the subjective duration
associated with a typical conscious experience. Interested reader can
find a discussion of Libet and Kornhuber experiments in my homepage
[padTGD]. Also the Ping-Pong example  of Penrose is discussed in terms
of TGDish concept of quantum jump.

Note that in all situations, where free will actually occurs, one can
argue that free will is just an illusion since the deterministic time
development in the final state history indeed leads continuously from
initial to  the final state. This observation perhaps explains why the
concept of free will has turned out to be apparently unnecessary element
in objective science.


4. About cognitive aspects of consciousness

The proposed definition of consciousness does says nothing about
cognitive aspects of human consciousness. Only some kind of elementary
awareness should  be associated with the quantum jumps occurring  at
elementary particle level. Very probably  electron cannot remember its
past experiences whereas  memory  and thinking are  crucial aspects of
the ordinary human consciousness.   TGD however provides general clues
for understanding also the cognitive aspects of the mind. Rather
remarkably,  several very general ideas combine together in natural
manner in TGDish framework:

 a) The idea of Penrose  about biosystem as a quantum superposition of
    macroscopically different classical spacetimes.
 b) Description of thinking system as quantum critical system.
 c) Description of macroscopic  quantum jump as quantum analog of phase
    transition.
 d) Catastrophe theory of Thom.


4.1. Thoughts as simulations

The basic feature of cognitive functions seems to be the simulation of
possible histories. Memory corresponds to simulation of past and future
plans and predictions to the simulation of the future.  The arrow of
time probably explains why the simulation of past is so reliable that we
speak of actual memories rather than  predictions of past. The possible
nonuniqueness of the classical spacetime  and related classical
nondeterminism  suggests a possible  origin for the simulatory aspects of
consciousness. The basic idea is  following. If the classical spacetime
associated with a  given 3-surface X3 is nonunique one must specify
besides X3 also some minimum number of other  3-surfaces at the selected
orbit X4(X3) of X3 to specify classical spacetime completely. This
minimal set of 3-surfaces  could be regarded as a discrete  simulation
for the time development of  X3 and thus as an elementary thought. In
the following this argument is developed in more detail.


4.2. Vacuum degeneracy of the  Kahler action

Perhaps the most fundamental property of Kahler action is its vacuum
degeneracy.  Kahler action allows enormous  numbers of vacuum extremals.
Any 4-surface with CP2 projection for which the induced Kahler form
of CP2 vanishes has vanishing Kahler field and Kahler action (which
is nonlinear counterpart of Maxwell action) and is therefore vacuum
extremal. The submanifolds of CP2 for which induced Kahler form vanishes
are called Lagrange manifolds and in general they are two-dimensional
submanifolds of CP2.

More familiar example is provided by the  n-dimensional  Lagrange
manifold of phase space spanned by the coordinates (qi,pi), i=1,..,n.
For instance, pi= const submanifolds and any manifolds obtained from
these manifolds by applying canonical transformations are Lagrange
manifolds.

Vacuum extremals allow the diffeomorphisms of M4 and canonical
transformations of CP2 as symmetries.  All   possible topologies
allowed by the imbeddability requirement are possible so that the
vacuum degeneracy is enormous. The vacuum degeneracy suggests
strongly that for some critical 3-surfaces absolute minimum spacetime
is not unique as the following arguments intend to show.


4.3. Nonuniqueness of the classical spacetime from vacuum degeneracy

Absolute minimum spacetimes is in general not vacuum extremal but one
can expect that in some cases it could be regarded as  a small
deformation of some vacuum extremal. It can however happen that for
some critical 3-surface there are two or more topologies giving same
value of Kahler action (also several minima with same topology could
occur). Critical surfaces are just those 3-surfaces,  where the
topological or other characteristics of the absolute minimum spacetime
surface change discontinuously. In this kind of situation one encounters
the problem of selecting between several alternatives and  there seems
to be no manner to fix uniquely the correct classical spacetime. The
only  way out of difficulty is the extension of configuration space so
that it becomes N-sheeted at the points X3  for which absolute minimum
is N-fold  degenerate.  At quantum level this classical nondeterminism
corresponds to additional discrete degrees of freedom labeled by integer
n=1,..,N.

The nonuniqueness of the classical spacetime  induces the nonuniqueness
of the effective spacetime since one can define the average spacetime
in many manners by fixing in some continuous manner the classical
spacetime associated with the critical 3-surfaces X3. In general
quantum states can be regarded as superpositions over these different
effective spacetimes. Following Penrose it is tempting to identify this
quantum superposition for effective spacetime geometries as  a
fundamental property of biosystems. Stating it differently: evolution
would favor the formation of macroscopic quantum critical systems.

There is close analogy with phase transitions and catastrophe theory.
Kahler function  is completely analogous with thermodynamical free
energy. Typically free energy depends on  state variables x,.. and
external parameters (a,b,..). Simplest situation corresponds to van
der Waals equation of state with one state variable x and two  external
parameters (a,b). The minimization is performed with respect to state
variables x keeping  (a,b) constant.  The 2-dimensional surface of
minima is many sheeted in some region of (x,a,b)-space and  looks
locally like cusp catastrophe.   For  cusp catastrophe 3 solutions to
the  extremization conditions exist in  cusp region. For generic x only
one of these is absolute minimum. The situation changes however on the
Maxwell line, where two branches have same value of free energy and
where phase transition occurs. This simple picture generalizes to higher
dimensional situation and as Thom has shown the description of  cusp
catastrophe can always be reduced to the canonical description using
only 3 coordinates. More complicated catastrophes can be constructed
from cusps but  as far as  discontinuous jumps in  x are considered,
cusps are the basic catastrophes.

In the  present infinite-dimensional context the external parameters are
the configuration space coordinates specifying the 3-surface X3 and are
held constant in the minimization of Kahler action. The state variables
correspond to the coordinates specifying 4-surface X4 going through X3.
For vacuum surfaces X3, which have vanishing induced Kahler field,
there exist infinite number of vacuum surfaces with varying topologies
going through X3 and the  deformations  of these surfaces give  good
candidates for the absolute minimum. At critical 3-surfaces the nature
of the  absolute minimum surface changes: for instance, the topology of
this surface can change. The preceding argument applies to vacuum X3s
but also for X3 sufficiently close to vacuums situation is expected to
be same by continuity.

Cusp catastrophe implies that there are two different  effective
spacetimes associated with X3 so that the point of the  extended
configuration space is completely described by  associating a binary
digit with the critical surface.  For multicatastrophes (say one
catastrophe per tubulin dimer in microtubule) a sequence of binary
digits describes the situation. One can easily imagine that thinking
system could perform  quantum computation using the quantum states
specified by these binary sequences. This binary structure should
somehow reflect itself in the properties of the effective spacetime
and it is very tempting to speculate that the binary structure of
microtubules (tubulin dimers have two possible conformations)  is
related to  these  binary  sequences.  This argument suggests that
biosystems should correspond to 3-surfaces near to vacuum extremals.
One can  generate negative Kahler action by deforming vacuum extremal
so that Kahler electric fields are generated: this leads to the
generation of ordinary electric fields, too. Perhaps the the important
role  of electric fields in biosystems is closely related to the
minimization of Kahler action. Possible applications along these lines
are  considered on my homepage.


5. Summary

This brief essay gives only the basic ideas of TGD inspired theory of
conscious and intelligent systems, which have gradually developed
during last 10 years or so. Interested readers can find more detailed
discussions on my homepage, where also applications of TGD to the
description of biosystems can be found. Of course, all these
developments are highly speculative and I am happy if these ideas can
serve as an inspiration for someone else, who has  been caught by
the fascinating problem of consciousness.


Bibliography

TGD:    M. Pitkanen (1990):  Topological Geometrodynamics. Internal
        Report HU-TFT-IR-90-4 (Helsinki University).  Summary  of
        Topological Geometrodynamics in book form. Book contains
        construction of Quantum TGD, 'classical' TGD and  applications
        to various branches of physics.


padTGD: M. Pitkanen (1995):  Topological Geometrodynamics and p-Adic
        Numbers}. Internal Report HU-TFT-IR-95-5 (Helsinki University).
        Report on application of p-adic numbers in attempts to
        understand  quantum field theory limit of TGD. Chapters 4-9
        are especially interesting as far sa this paper is considered.

Updated versions of both reports are available as ps-files at

     http://blues.helsinki.fi/~matpitka/

where also can be found hypertext representation of basic ideas and
concepts of TGD.