404
Progress of Theoretical Physics Supplement No. 99, 1989
How Animals Understand the Meaning of Indefinite Information
from Environments?
Hiroshi SHIMIZU and Y oko YAMAGUCHI
Faculty of Pharmaceutical Sciences, University of Tokyo, Tokyo 113
Animals, including human beings, have ability to understand the meaning of indefinite
information from environments. Thanks to this ability the animals have flexibility in their
behaviors for the environmental changes. Starting from a hypothesis that understanding of
the input (Shannonian) information is based on the self-organization of a neuronal representation, that is, a spatio-temporal pattern constituted of coherent activities of neurons encoding
a "figure", being separated from the "background" encoded by incoherent activities, the
conditions necessary for the understanding of indefinite information were discussed. The
crucial conditions revealed are that the neuronal system is incomplete or indefinite in a sense
that its rules for the self-organization of the neuronal activities are completed only after the
input of the environmental information and that it has an additional system named "self"
specific to relevantly self-organize dynamical "constraints" or "boundary conditions" for the
self-organization of the representation. For the simultaneous self-organizations of the
relevant constraints and the representation, a global circulation of activities must be selforganized between these two kinds of neuronal systems. Moreover, for the performance of
these functions, a specific kind of synergetic elements, "holon elements", are also necessary.
By means of a neuronal model, the visual perception of indefinite input signals is demonstrated. The results obtained are consistent with those recently observed in the visual cortex of
cats.
§ 1.
Introduction
Not only human beings but also wild animals frequently receive uncertain or
indefinite information from their environments. And they, more or less, have ability
to understand the meaning of such indefinite information. Here the indefiniteness of
the information is caused by the complex dynamics of the environment with indefinite
boundary conditions. Because of the indefinite boundary of the uncertain information, we are not able to relate such uncertainty to probabilities; the probability
concept is applicable only when a definite boundary is provided. This ability is also
the essential cause of the biological flexibility in their cognition of external information. Neither the von Neuman type computer nor the neural net with back propagation do not have such flexibility. In the present paper, by means of a neuronal model
that generates oscillations, we will study the essential mechanism to understand the
meaning of indefinite information, and will present a new kind of "biological computer" based on the discovered principle.
In any case, external information is more or less uncertain, and in the cognitive
process the uncertainty must be reduced. The uncertainty may be tentatively
Indefiniteness in Information Generation
405
classified as Shannonian uncertainty and semantic uncertainty. Shannonian uncertainty is defined as uncertainty caused by the selection of an arbitrary element from
a definite set of known elements as in the case of recognition of a character chosen
from an alphabet set. For the reduction of Shannonian uncertainty, a certain amount
of Shannonian information, that is, probability-based information, is needed, and such
Shannonian information is produced in the cognitive process. Semantic uncertainty,
on the other hand, is caused by the selection of one from an indefinite set of known and
unknown elements since we usually encounter an unexpected event or situation. The
indefinite set will be defined as a set with an indefinite boundary. Clearly, to know
the selected element not only Shannonian information but also semantic information
that describes the element is necessary.
Klir 1> pointed out that we are concerned with several kinds of information other
than probability-based Shannonian information. At any rate, Shannonian information is not sufficient for the self-operation of cognitive processes if external information has semantic uncertainty. What is needed for operational information is
possibility-based information. In the cognitive process semantic information must be
generated or created. (Semantic information could be regarded as such a type of
such possibility-based information.)
§ 2.
Self-incompleteness of biological systems
All the types of information input to acceptors have a Shannonian form. If only
input information with Shannonian uncertainty is perceived by an information acceptor, it is a self-complete acceptor in the following sense. To relate the input information to one of the known elements, the acceptor needs Shannonian information for
its self-operation. In such an acceptor all the types of Shannonian information which
are needed for the self-operation can be stored as fixed potentials or constraints fixed
for the self-organization of the potentials. In other words, the acceptor has prepared
all the types of operational information before input information is introduced, and
that the input Shannonian information has been transformed to the stored Shannonian
information. In this sense the acceptor is self-complete and self-referential in the strict
sense of the words. It is essentially closed against the outer world.
However, such a mechanism does not work for input information with semantic
uncertainty. It is by no means possible for any acceptor to store all the types of
operational information for unpredictable input. Therefore, if an information acceptor has the ability to perceive input information with semantic uncertainty, it means
that operational information is generated after the reception of the input information.
It also means that operational information is not determined by the acceptor alone.
In this sense, the acceptor is self-incomplete.
An immune system is a typical example of such a self-incomplete acceptor, where
a new type of antibody is produced in an immunological network as an "internal
image" of environment only after a new sort of environmental information, a new
type of antigen, is received. In addition, the immune system has learning ability and
is capable of recognizing known information by utilizing operational information that
has been fixed in the system.
406
H. Shimizu andY. Yamaguchi
Since any input information has a Shannonian form, it is therefore crucial for
self-incomplete acceptors to have internal dynamics to transform the input Shannonian information into semantic information utilized for its self-operation. How is
the semantic information obtained from the input Shannonian information?
§ 3.
Definition of semantic information
Semantic information may be defined as information that has some meaning or
function. This definition however is insufficient, since any information can be defined
only in relation to a system where the information is utilized. We must ask what the
meaning or function is. Clearly, if we define a system where the information is
generated or transformed, then we can ask the meaning or function of the information
for the system itself.
In addition to this, there are the following characteristics in semantic information: (1) the semantic separation of input information into a figure (the meaningful
part) and ground or background (the meaningless part), (2) the articulation of
meaning (figure) according to stored concept, (3) the holonic character of meaning,
namely the cyclic dependence of meaning between the whole and the elements of
information and (4) the mutual dependence between the structure and the meaning of
information. These properties are caused not only from cooperative but also from
multiple functions or meanings of the information elements. A relevant function or
meaning will be chosen from the multiple functional or semantic states of the elements
cooperatively, depending on the structure of the information.
On the other hand, Shannonian information is composed of elements which are
essentially independent and have no cooperativity. In addition, they have no multiple
characteristics as described above. These differences between semantic and Shannonian information will suggest to us a mechanism required for the transformation
from Shannonian to semantic information.
Information transformation in a self-incomplete system leads to the representation of semantic information. The representation, or more exactly the representation with semantic separation depends on attention.
§ 4.
Semantic transformation of Shannonian information
To make our problems clear, let us consider a simple example; namely a painter
is painting a picture on a white canvas with fine black dots. We tentatively assume
that the canvas is a Shannonian information space and is constituted of fine meshed
spaces called elementary spaces, and that elementary signals, or the elements of
Shannonian information in the form of dot, are introduced one by one to relevant
elementary spaces. A TV station is reporting the painting process with a TV camera
and sending it to a TV viewer. We will call the painter, the TV station and the TV
viewer the information creator, carrier and acceptor, respectively. From time to
time the carrier reports the condition of the canvas, namely, the positions of black and
white elementary spaces in the Shannonian information space. Therefore, for the
carrier, there is no semantic uncertainty in the elementary signals in the canvas, since
Indefiniteness in Information Generation
407
the carrier's task is only to report the positions of black and white elementary spaces
that are equally definite and important. This is the situation of Shannon & Weaver's
communication theory.
However, this is not the case for the creator nor for the acceptor. They are
concerned with semantic information. For the painter, the white space of the original canvas has no definite meaning. Namely, it is an uncertain space, and the
painter's task is to reduce the semantic uncertainty of the canvas with black dots.
For the creator black elementary spaces are entirely different from white ones in the
degree of semantic uncertainty, and only the former are regarded as elementary
symbols. (It is the symmetry breaking of the meaning of information between black
and white spaces.) This is also the case for the acceptor.
The painter and viewer assume invisible connections between some of the black
dots to generate a figure: i.e., semantic information, and the figure is distinguished
from the unconnected part, a ground or background. The elementary meaning of a
dot, an elementary symbol, depends on its connections with others. However, neither
such connections nor the elementary meanings can be explicitly shown in the Shannonian information spaces, the canvas and the TV; only the relative positions of the
black and white elementary signals are indicated there. It means that the Shannonian information space is insufficient to represent semantic information.
Therefore, to indicate the meanings of the elementary symbols, we are required
to add a new dimension to the information spaces, and the meaning of the elementary
symbols is represented by the position of the "semantic coordinate" of the new
dimension. Consequently, we have a generalized information space; i.e., semantic
information space constituted of a Shannonian subspace and a semantic coordinate
axis perpendicular to it. One of the simplest expressions of the semantic information
space is an assembly of elements with a
hypercolumn-like structure as shown in
Fig. 1. The semantic coordinate axis is
taken in the direction of hypercolumn,
that is the direction perpendicular to the
Shannonian subspace. Each dot constituting a border of a figure is regarded
as a line element with a specific orientation encoded in each column, and this is
the elementary meaning given to the dot.
Evidently, the orientation is determined
by the connections of the dot with other
dots. When the dot is regarded as a
part of background, its position in the
semantic coordinate is indefinite. This
occurs when the dot has no definite connections with others.
Fig. 1. Hypercolumn-like structure is schematicalThe transformation of input Shanly illustrated based on a parallel processor
nonian
information, elementary signals,
model of visual information processing,
to semantic information will be treated
Holovision!Hl
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408
H. Shimizu and Y. Yamaguchi
as the self-organization of a dynamical pattern in the semantic information space of
a parallel processor constituted of elementary processors with a hypercolumn-like
internal structure. Normally the self-organization starts from an uncertain state.
As has been discussed in our study of holovision, 2l- 4l the elementary signals of
Shannonian information introduced to some of the elementary processors on the
Shannonian subspace make the semantic states of the elementary processors uncertain. This initial uncertainty of the elementary processors, a type of semantic
uncertainty, is represented by a distributed or fuzzy activities of a set of columns,
a "hypercolumn". The set of columns share a common input of the elementary signal
and yields the indefinite semantic states. (The number of "columns" in a "hypercolumn" could also be indefinite.) However, this is by no means sufficient for the
information transformation because semantic separation between a figure and background is still indefinite.
§ 5.
Dynamical representations of semantic information
Haken suggested that a figure may be expressed in the brain by an order parameter, a dynamical order of neuronal activities. 10) We have extended this idea as
follows in our studies on holovision: The figure is expressed by coherent dynamics while
the ground is expressed by an incoherent one. The key concept is that the coincidence
in the timing leads to dynamical connections and vice versa.
By combining this idea with the preceding description of semantic information
space, we may assume that self-incomplete acceptors have a semantic information
generator (SIG), a kind of synergetic system composed of specific kinds of synergetic
elements with multiple functional or semantic states and that the selection of the
semantic state of the elements depends on connections among them. We have named
such elements holon elements. A hypercolumn with many columns is a typical
example of such a holon element. Generally the number of semantic states is not
always definite. It could be increased. Rolon elements can produce functional
coordinations among them by the self-organization of coherence.
One of the merits of assuming that the figure is represented by the coherent
dynamics of holon elements is that the holonic property (3) of semantic structure is
satisfied by means of the cyclic causality between the whole and elements. Furthermore this assumption makes the mechanism of semantic separation clear. Namely,
the semantic separation in the activities of holon elements can be brought by "constraints" generated inside the acceptor.
§ 6.
Function of "self" in self-incomplete systems
To accept information with semantic uncertainty, a self-incomplete acceptor
must have indefinite possibilities for the organization of elementary signals to a figure.
More concretely, the acceptor must prepare an excess amount of connection rules to
be applied to the formation of various kinds of connections among elementary signals.
This may be compared to a spider web which has an optimal structure with a suitable
amount of excess connections to catch an indefinite insect. The spider web itself is
Indefiniteness in Information Generation
409
an expression of the possibility of catching various kinds of targets.
In ideal cases, halon elements in the SIG of an acceptor must have indefinite
degrees of freedom in their expression of elementary meaning. It means that,
effectively, an infinitely large number of semantic states are present in a halon
element. Such multiplicity of semantic states associated with an indefinite variety of
connections will result in indefinite complexity which is needed to accept indefinite
information as coherent dynamics self-organized in the SIG. Of course, this is an
ideal case, and there are limitations at a certain level in real acceptors.
At any rate, to self-organize a figure, coherent dynamics, in the SIG, a selfincomplete acceptor must suppress the excess degrees of freedom in the possible
dynamics and make halon elements select their semantic states according to the
relevance to the figure. For the purpose of the suppression relevant constraints are
needed. A self-incomplete acceptor must create the constraints.
More generally, any self-incomplete acceptor must have a specific dynamics for
the creation of constraints. This means that other than an SIG the self-incomplete
acceptor has another synergetic system, "self", that specifically works for the selforganization of new constraints. The "self" will be composed of two parts, an
organizer of (dynamical) constraints and a storage of long-term memory, or more
briefly, a constraints-organizer and a memory-storage. The elementary processors
constituting the constraints-organizer and the memory-storage will be tentatively
named "macro-halon" and "memory-halon" elements, respectively.
§ 7.
Creation of semantic constraints
If only a small part of input signals can be connected to a figure under stored
constraints of a known concept, the greater part is left in an uncertain state. Quasi
periodic or chaotic oscillations with a complex form will emerge in the greater part
of the SIG. In such a case the self will try to "discover" more order in the SIG by
creating new types of constraints. When relevant constraints are created by macroholons in the constraints-organizer, the self-organization of semantic information in
the SIG will converge to produce global coherence or entrainment between the
organizer and the SIG. This global coherence is caused by the global circulation of
consistent activities emerging between these two types of dynamics. We shall call
this phenomenon a global entrainment or the emergence of a global circulation mode
in the acceptor. After the formation of the global entrainment, irrelevant dynamics
of the all kinds of halon elements in the SIG and self will be spontaneously excluded
or compressed because the activities in the global circulation governs the dynamics of
all the elements.
In the above process the long-term memory in the memory storage may give some
influence to the dynamics of macro-holons to sparate a figure from ground. The
creation of a new kind of constraints has been discussed by us in essentially the same
principle. 4 > When relevant concepts have been stored as long-term memory, they
would work as a type of constraint for the self-organization of constraints in the
constraints-organizer. In such cases, a global circulation mode will entrain the
dynamics of memory-holons that contribute to its formation. In general we would
410
H. Shimizu andY. Yamaguchi
have a hierarchy of constraints as schematically demonstrated by Mandara.
It is noted that input signals may be classified into plural figures that are connected with different concepts. In such cases, the corresponding kinds of coherent
dynamics will be observed. If, however, the figures are further organized into a
global figure by the creation of new constraints in the organizer, we shall have only
one type of coherent dynamics.
As pointed out by Kryukov 5> and by Koerner, 6 > hippocampus may bind different
items together according to attention by means of entrainment. Hippocampus may be
a kind of organizer of dynamical constraints. Exactly speaking, hippocampus is a
central actor in the self-organization of a global circulation mode in the brain, since
it binds the activities of various fields of cortex in the form of coherent oscillations.
§ 8.
A neuronal model of the self-incomplete system
Let us discuss dynamical changes that occur spontaneously in a self-incomplete
acceptor after external information is introduced. The following model will be
proposed for the sake of a concrete description of our thinking at a crude level. We
like to assume that information composed of elementary signals is fed in the Shannonian subspace of the SIG of an acceptor as if it were a painting with dots on a
canvas. The elementary signals are introduced one by one to some of the halon
elements, hypercolumns, placed in each elementary space of the Shannonian subspace.
Each hypercolumn is constituted of a number of columns encoding elementary
meanings to be given to an elementary symbol.
Each column has three types of excitatory cell, a simple cell (S-cell) sensitive to
a line element with a specific orientation and two kinds of terminal cell (T -cell) that
are respectively sensitive to different ends of a line of the same orientation. There
are inhibitory interactions among these three cells. Therefore, only one is strongly
active while the other two are suppressed. Moreover, there are inhibitory interactions among S-cells in the same hypercolumn. We assume that S-cells have shortrange interactions only with those in the neighboring hypercolumns; as shown in Fig.
2(a) interactions are excitatory among S-cells with the same orientations and inhibitory among those with different orientations. On the other hand, as shown in Fig.
2(b) T-cells have long-range excitatory interactions with S-cells in the direction of the
line and inhibitory ones with those in the reverse direction.
Besides these three types of excitatory cells, inhibitory cells are also present in
each column. The inhibitory cells have interactions with the above three excitatory
cells. The functions of the inhibitory cells are, first, to avoid the excitatory cells to
stay in their maximum activity and, second, to generate rhythmic oscillations if the
activity of the column exceeds a certain (but controllable) threshold level that reflects
significance of a received signal. Due to the long-range interactions of the T-cells
and S-cells, longer lines are expressed by more coherent and stronger activities of
S-cells than shorter lines.
An elementary signal introduced to a hypercolumn only weakly excites all the
excitatory cells in all the columns belonging to the hypercolumn. This initial uncertainty of a hypercolumn corresponds to the situation that the elementary meaning of
Indefiniteness in Information Generation
411
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Fig. 2(a). Connections among S-cells are shown in
each set of orientation specificity. Open circles denote S-cells. Solid and broken lines
respectively represent excitatory and
inhibitory connections, respectively. The orientation specificity in the activity of S-cell
coincides with the direction of excitatory connections. S-cells in the same hypercolumn
inhibit the others.
Fig. 2(b). Connections among T-cells (circles) and
S-cells (ovals) are shown. There are two cells,
Ta and Tb, corresponding to both ends of a
line. Solid lines with black points and broken
lines with white points respectively denote the
excitatory and inhibitory connections. Shaded cells indicate that they are activated.
a dot on the painter's canvas is uncertain unless its connections with the other dots are
decided_ Therefore, initially, all the possible meanings must be prepared, It means
that all the possible connection rules are ready for use and that the self-organization
of semantic information starts from the initial uncertainty that is an expression of all
the possibilities of the SIG, The start from the initial uncertainty is crucial to the
transformation of input Shannonian information, probability-based information, to
semantic information that is a type of possibility-based information_
§ 9.
Dynamical properties of the "self"
The functions of macro-halon elements in the self are to self-organize constraints
(in a dynamical form) for the self-organization of a figure in the SIG. When a set of
relevant constraints are formed, a global circulation of activities will emerge between
the self and SIG and the dynamics of the both subsystems become coherent. It is the
self-organization of the global circulation mode in the acceptor. For the formation
412
H. Shimizu andY. Yamaguchi.
of the set of constraints, the macro-holons receive only characteristic features of
self-organizing information from the SIG and separate it into a figure and ground by
relevantly connecting the received features by producing a relevant conceptual
expression based on the alternation and combination with partial compression of
suitable concepts stored in the memory storage. Consequently, the macro-holon
elements encode elementary meanings that are more abstract than those in holon
elements in the SIG. In the process of the self-organization of the conceptual expression, by adjusting a threshold level, the macro-holons themselves are also able to
decide signals to be fed back to the SIG for the circulation of activities. A similar
idea was proposed by Koerner. 6> This means that the constraints organizer decide a
level of significance incorporating to semantic information and leads to suitable
separation between the figure and ground.
We will treat here a simple case where the semantic states of the macro-holon
elements encode a specific direction of a line terminal in the Shannonian subspace.
On the other hand, the specificity of the position in the Shannonian subspace in the SIG
is only roughly given in the self in order to make relevant correspondences between
the features of the conceptual expression and the representation in the self and SIG,
respectively, based on competitions in the formation of dynamical connections. A
pair of macro-holon elements encoding reciprocal directions specificity a line of the
corresponding orientation. The connected elements generate coherent rhythmic
activities. More generally, conceptual expressions composed of several line segments can be expressed by the coherent rhythmic activities of such elements.
§ 10.
Dynamical connections between the self and SIG
Now we will explain about rules to connect the dynamics of the SIG and the self.
Every T -cell in the SIG is assumed to have a connection with macro-holon elements
having a corresponding direction specificity. In other words, one macro-holon element is connected with all T -cells that have the same direction specificity all over the
Shannonian subspace. We assume that an upward and downward connections are
present between the macro-holon element and the T -cell. A pair of the two kind of
connections will be called a "channel". Each channel transmits signals in both the
directions of bottom-up and top-down. The channels are gated according to a
competitive dynamics in each group of channels to a common macro-holon element.
The initial values of the channels between the T-cells and macro-holon elements are
uniformly given. The magnitudes of individual channels evolve according to the
relative magnitudes of signals going through them and of the extent of dynamical
coherence between the bottom-up and top-down signals transmitted from both sides of
individual channels. At the final state of the competition processes one macro-holon
element has only one open channel with the T -cell that has the strongest and most
coherent signal. The other channels are closed. The dynamical gating is parallel
processed and lead every macro-holon elements to try to get a single connection with
the most suitable T-cell. On the other hand, when there is no significant difference in
the magnitude and coherence of signals in the group, the initial state of uniform or
fuzzy connections is maintained in the group. It means that a piece of information
Indefiniteness in Information Generation
413
must be added to the information to the SIG.
For the coordination of macro-halon elements, the following connection rules are
assumed. Pairs of elements with reciprocal directions are inherently connected with
one another to denote a line. Within the self, excitatory connections between any
two elements are strengthened when their channels to the SIG are established with
T -cells at the same position in the Shannonian subspace. This rule allows the self to
coordinate its activity according to the continuity of the figure in the SIG.
§ 11.
Global circulation of activities for semantic consistency
If connection rules "prepared" in the SIG are applied without any control, many
types of connections will be formed at the same time among halon elements.
Therefore, at this stage, disordered oscillations appear in the SIG because of the
absence of definite constraints that determine semantic separation between figure and
ground.
Then, only from T-cells, activated beyond a threshold level signals are transmitted to the "self", reporting the characteristic features of connections being selforganized in the SIG. And the number of T-cells that transmit signals could be
controlled by adjusting the level of the threshold. The macro-halon elements in the
self have a set of paired T-cells for the opposite directions and are connected with the
all halon elements in the SIG. They also form a spider web structure and will
self-organize a rhizome-like dynamical structure connected at apices and at crossing
points.
Macro-halon elements that have received signals from the SIG are excited and
produce initial uncertainty. This leads to the evocation of various concepts in
long-term memory in the self. Then, the selection of a relevant concept from the list
of stored items occurs with mutual competition among the stored ones. The selected
concept will control in the formation of a dynamical rhizome-like structure as internal
constraints. When the evocation is sufficiently strong, dynamical connections among
the macro-halon elements are fixed instantly and the rhythmic oscillations of the
macro-halon elements work as dynamical constraints for the self-organization of
dynamical order, semantic information, in the SIG. Primarily from activated cells in
macro-halon elements their oscillations are sent back to the T-cells that are transmitting signals to the former and increase their excitement. The increased activity of
the T-cells is then further fed back to S-cells connected with excitatory interactions,
increasing their excitation. Finally, the SIG and the self generate strongly rhythmic
oscillations that are synchronized by means of global entrainment between these two
subsystems. When input signals are separated into plural figures, the figures are
represented by different dynamical orders connected at the same time with the self with
different circulation loops. Generally no dynamical coherence is present among such
orders unless they are related to each other by the formation of a new sort of
constraints.
In order to create the activity in the self relevant to the figure self-organized in
the SIG of our present model, the following suppression mechanism is assumed. As
a measure of relevancy, the degree of selection of the channels to individual macro-
414
H. Shimizu andY. Yamaguchi
halon elements of the self is utilized for the following reason. The highest degree of
selection, i.e., definite selection of channels to a macro-halon element means that a
feature specifically related to the element emerges definitely in the SIG. On the other
hand when no such a definite feature appears in the SIG, the channels still remain at
the initial uncertain (and semantically uniform) state. The selection of the channels
to individual macro-halon elements determines the selection of suppression of irrelevant activities of the elements.
It should be noted that the selection of the channels is advanced not only by the
state in the SIG but also feedback signals from the activated elements in the self.
Furthermore, the activities in the self change according to the relevancy to those in
the SIG. Thus, the self creates coherent dynamics within itself to be relevant to that
of the SIG. The feedback signals from the self give dynamical constraints to selected
T -cells and S-cells connected to them. The entrainment between th~ halon and
macro-holon elements enhances consistent dynamics and suppresses inconsistent ones.
The degree of the entrainment thus gives a global measure of consistency. This is a
natural consequence of neuronal oscillators as pointed out by us in the study of
holovision. 2H>
§ 12.
Comparisons with experimental evidence
If input signals are new and are not connected immediately with a stored concept,
no definite entrainment will be established either in the SIG or in the stored concept
in the self. As a result their oscillations are still uncertain with a low level activation. It is noted that the neural activities in such indefinite states are significantly
lower than those in entrained definite states. Freeman7' reported that the olfactory
bulb shows chaos-like oscillations when
Self
a new odor is introduced and that they
become rhythmic after learning the odor.
He also showed that the sychronized
oscillations of neuronal activities appear
between the bulb and olfactory cortex,
prepyriform, after the odor has been
learned. These results will support our
model.
Entrainment of the activities
between the SIG and self through a
global circulation loop of entrainment as
schematically shown in Fig. 3 (which we
have named the holonic loop or semantic
loop) is a fundamental mechanism to
Fig. 3. A schematic representation of circulation
support a convergence from an uncerof information in a global circulation loop
tain state to a new semantic state where
between an SIG and Self. The cognitive procnot only a new type of semantic inforess is completed when the dynamical coherence
mation is formed in the form of coherent
is established between the two kinds of sysoscillations but also a new set of contems.
Indefiniteness in Information Generation
415
straints, encoding a new concept, is created. The creation of the constraints will
correspond to the creation of short-term memory and will be transferred to long-term
memory after long term potentiation.
§ 13.
Computer experiments
For the elucidation of the above scheme, computer experiments were carried out.
The model was however simplified as follows. Elementary signals are introduced to
a binary array of 8 X 8 square lattices. The SIG has correspondingly an 8 x 8 array of
hypercolumns in its Shannonian subspace. Each hypercolumn has four columns, the
subelements, provideS-cells of 4 kinds of line orientations and T-cells of 8 directions
of line ends. The self includes 8 kinds of macro-holon elements which encode
"elementary constraints" specifying the directions of lines of 4 orientations. In the
present model each of the macro-holon elements four subelements. Therefore, as a
whole, the self is composed of 16 subelements, macro-holon subelements, corresponding to the subelements of the macro-holons for such specification of line ends. Then
one line with an orientation could be connected with two pairs of macro-holon
subelements. Either of the subelements has channels to all T-cells with the corresponding direction. The two subelements for the same direction are distinguished
from each other with respect to the preference for the T-cells in the Shannonian
subspace of the SIG in the competitive selection of channels. The territory of each
subelement is not discretely divided but a fuzzy separation with a gradual change was
assumed for the sake of flexible connections. The gradient is given in the same
direction of the "receptive field" of the macro-holon subelenments but is just opposite
between the two subelements. For the sake of simplicity, we assumed that "unit
processors" such as S-cells and T -cells are connected with their proper inhibitory cells
and that this is also the case for macro-holon subelements.
Basic equations for the dynamics of unit processors such as S-cells, T-cells and
self subelements are given by the following type of differential equations:
(1)
and
(2)
with
P(z)=0.5{tanh(c(z- ,u)}+0.5,
z=(x;, y;).
(3)
In Eq. (1), X; and y; respectively represent activities of excitatory and inhibitory parts
of the i-th unit processor. In Eqs. (1) and (2), r represents the damping constant and
a, ao, (3 and f3o are also constant parameters. I; in Eq. (1) varies according to the
input from the outside of the unit processor. The last term on the left-hand side of
Eq. (1) denotes connections where the j-th unit processor gives input to the i-th one
with a weight wu. Connections are assumed not only within the same subsystem but
also between the different subsystems, the SIG and the self. An output from any
416
H. Shimizu andY. Yamaguchi
(a)
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Fig. 4. (a) An example of computer experiments. Input signals and self-organized information in the
SIG obtained by decoding the activities of S-, Ta- and Tb-cells. The sizes of symbols show the
magnitudes of activity of individual units. Small bars and arrows respectively show the orientations of lines and the directions of line ends. The self-organized image in the SIG appears as a set
of bars. (b) Left: magnitudes of channels between macro-holon subelements and T-cells in the
SIG. The channels for a common macro-halon subelement is shown in each plane. Arrows are
shown at the position of the corresponding T-cell and its size shows the magnitude of channel.
Right top: the magnitudes of activities of macro-halon subelements. Right bottom: connections
among macro-halon subelements. They are symmetric. Connections between each pair of ? and
.r are significantly established.
subelement is given by the sigmoidal function P in Eq. (3). Quantities, c and fl.
respectively represent the gradient and the threshold of function P. Details in
mathematical equations used will be given elsewhere (in preparation). The equations
were numerically calculated with a high-speed computer by using the Runge-KuttaGill method. Some simple and typical examples will be shown below.
The cognition of input signals as a line segment is demonstrated in Figs. 4 and 5.
The activities of subelements in the final state are shown in Fig. 4. A line and its
Indefiniteness in Information Generation
417
1.0
0.0
0.0
Fig. 5(a). Temporal evolution of a spatial pattern in the activity of S-cells representing a line segment.
S·cells in this figure are those active and placed along the line segment seen in Fig. 4(a). The
vertical and horizontal axes respectively show the magnitude of activity and the time. The
oblique axis on the left-hand side represents the sites of S·cells along the line segment.
0.0
Fig. 5(b). Temporal evolution of spatial pattern in the activity of S-cells at the same position as in Fig.
5(a) but with the different orientation specificity.
418
H. Shimizu and Y. Yamaguchi
1.0
0.0
Fig. 5(c). Temporal evolution of spatial pattern in the activity of T-cells at the same position as in
Fig. 5(a). The oscillation appears at a point of a line terminal.
1.0
0.0
0.0
Fig. 5(d). Temporal evolution of weights of channels among a self-unit and T-cells shown in Fig. 5(c).
Only one channel achieves a full magnitude.
Indefiniteness in Information Generation
419
1.0
0.0
2
0.0
TIME
32.0
Fig. 5(e). Activities of macro-holon subelements. 16 macro-holon subelements are plotted in the
order of their corresponding directions; 1<--, 2 ", 3 J., 4 '», 5--+, 6/', 7 t, 8 '\, 9<--, 10 J, 11 J., 12 \,
13--+, 14/', 15 t, and 16 '- (shown along the oblique axis). Four macro-holon subelements (2, 6, 10,
14) are mutually synchronized while others are suppressed.
1.0
0.0
5
4
3
2
1
0.0
TIME
32.0
Fig. 5(f). The coincidence function defined by a product between two variables as a measure of
coherence of temporal evolution.
1) between two neighboring S-cells representing the line segment; 2) between two S-cells repre·
senting the same line but placed far from each other; 3) between an S-cell in the line segment and
an activated macro-holon subelement (2) in the self; 4) between two macro-holon subelements (2, 6);
5) between two macro-holon subelements (2, 10).
420
H. Shimizu andY. Yamaguchi
terminals are self-organized in the SIG with semantic separation from the background. The weights for the selection of channels between the self and the SIG show
that two T -cells activated in the SIG are selectively connected with corresponding
macro-holon subelements. On the other hand channels to irrelevant macro-holon
subelements are left almost unchanged. The macro-holon subelements with relevant
directions indicate greater activity than the others. In the self connections are
established among macro-holon subelements for the same direction, though some
irrelevant connections weakly contribute to a noisy background.
Figures 5(a) ~(f) illustrate the time evolution of the activities of the subelements
before reaching the final states shown in Fig. 4. It is seen in Fig. 5(a) that the S-cells
representing the line segment generate synchronized oscillations. Damped or independent oscillations with small amplitudes are generated by S-cells at irrelevant
sites as shown in Fig. 5(b). AT-cell representing the line segment is activated to give
an oscillation as shown in Fig. 5(c). The time evolutions of some channels are
indicated in Fig. 5(d). It should be noted that the rate of evolution is slower than that
of rhythmic activities as it is a consequence of integration of those rhythmic activities.
Generally an irreversible process occurs in our model being accompanied by
autocatalytic enhancement of coherent dynamics. The initial uncertain state of
channels converges to the final state where only a few T-cells are selectively connected with macro-holon subelements. Figure 5(e) shows that in the self only the
macro-holon subelements with relevant directions are activated, and, furthermore,
that the activated macro-holon subelements are in mutual synchronization.
The degrees of dynamical coherence among several types of elementary processors in the SIG and self are compared in Fig. 5(f). As a measure of the coherence, a
quantity "coincidence" is defined by the product of two rhythmic variables. S-cells
representing the same line segment have regular and coherent rhythmic activities.
Namely, their activities are characterized by a high coincidence. A considerable
extent of coincidence is also observed between an S-cell and a relevantly connected
macro-holon subelement, though they generate not so regular oscillations. The
figure indicates that coherence is also present among the activities of relevant
macro-holon subelements. The spontaneous formation of coherence among oscillating activities of unit processors leads to figure-ground separation. It means the
formation of a global circulation loop through the relevant parts of the activities in
the SIG and the self. The semantic information is thus represented by a coherent
rhythmic pattern in the acceptor produced by entrained oscillations among relevant
unit processors.
Figure 6 shows the results for the cognition of two line segments from introduced
elementary signals. In this case the two separate line segments in the SIG independently have connections with relevant macro-holon subelements. And the macrohalon subelements for the same direction are independently connected with T -cells of
the two lines self-organized in the SIG. Thus, connections among the unit processors
are not additively established. The calculated coincidence demonstrates that two
S-cells respectively belonging to different line segments show mutually independent
oscillations.
Figure 7 shows an example for the cognition of a corner. A set of constraints
421
Indefiniteness in Information Generation
(a)
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input
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connetions within the self
channels between the SIG and the self
(c)
1.0
0.0
2
1
0.0
TIME
32.0
Fig. 6. (a) An example of computer experiments. Two line segments with corresponding terminals
are organized in the SIG. (b) Left: magnitudes of channels between macro-holon subelements and
T-cells in the SIG. Right top: Activities of macro-holon subelements. Right bottom: Connections
among macro-holon sublements. No significant connection appears. (c) The coincidence 1)
between two active S-cells in a line segment. 2) between two active S-cells each of which belongs
to a different line segment. The variation in the amplitude in 2) means the independence in the
frequency and phase between the two S-cells.
422
H. Shimizu andY. Yamaguchi
(a)
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connetions within the self
channels between the SIG and the self
Fig. 7. An example of computer experiment for cognition of a corner. The final state in the SIG (a)
and in channels between the SIG and the self and in the self (b).
corresponding to a corner must be created in the self from the stored elementary
constraints. The figure illustrates that connections appear among the macro-holon
subelements that are spontaneously connected with T-cells with different directions at
the same position (that is a corner point) of the Shannonian subspace in the SIG. The
formation of the corner is demonstrated by the appearance of a new synchronization
state among related macro-holon subelements and T- and S-cells in the SIG. It means
the spontaneous formation of a global circulation loop with a new type of (generated)
constraints occurs in our system. This is the self-organization of constraints in the
system.
§ 14.
Concluding remarks
In the present paper we proposed a model for the information processing where
constraints are flexibly self-organized according to the input information and to the
state of the SIG. Our model shows a great flexibility in the recognition of input
Indefiniteness in Information Generation
423
signals with semantic uncertainty. Consequently, it includes not only phase-locking
among oscillators but also the reorganization processes of connections among elementary oscillators. Those multivariate processes are well organized in hierarchical
information processing by means of a global circulation of activities. This model
will be therefore related to the formation of short-term memory of vision under the
control of hippocampus.
The dynamical properties of our model could be compared with those reported
recently. In particular with the observations of coherent oscillations of simple cells
in the visual cortex of cat.8 >·9 > The idea that the coherent oscillation is self-organized
when simple cells form a representation of a line with a specific orientation or a
pattern was originally proposed is our previous work 2 > and is also included in the
present paper.
Now, let us go back to our original problem, "Why are human beings and animals
capable of understanding the meaning of indefinite information given from their
environments?" The answer is that they have ability to create relevant "constraints"
for the self-organization of semantic information in them after they receive the
environmental information. What are necessary conditions for it? The present
paper shows that (1) they must have indefinite states in their information system, (2)
the information system must be composed of, at least, two subsystems, where the
semantic information (a representation of the environmental signals) and the constraints (a conceptual pattern) are respectively self-organized and (3) the convergence
of a global circulation of activities makes the consistency between these two.
It would be interesting to point out that the concept of "void" or "nothing" in the
Zen thoughts is essentially identical to unlimitted indefiniteness in our internal state.
Acknowledgements
From 1970 to 1976 one of the authors, H. S., worked in Kyushu University as a
professor in the Department of Biology and spent most impressive days with Professor H. Mori in the rapid progress of physics on self-organization, since our dream was
to understand essential properties of the life based on the fusion of physics and
biology. He knows the most of the fundamental ideas of his present activities were
obtained during these days in stimulating discussions with Professor Mori. Therefore, it is his pleasure and happiness to dedicate the present paper to Professor Mori
for the memory of our good days.
The authors thank Mr. G. Taga and Mr. H. Hasegawa for their discussion and
cooperation. The authors would like to express their gratitude to Professor H.
Haken and Professor E. Koerner for their helpful discussion and kind encouragements.
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2)
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424
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