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Toward Physics of the Mind: Concepts, Emotions, Consciousness, and Symbols

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Mathematical approaches to modeling the mind since the 1950s are reviewed, including artificial intelligence, pattern recognition, and neural networks. I analyze difficulties faced by these algorithms and neural networks and relate them to the fundamental inconsistency of logic discovered by Gödel. Mathematical discussions are related to those in neurobiology, psychology, cognitive science, and philosophy. Higher cognitive functions are reviewed including concepts, emotions, instincts, understanding, imagination, intuition, consciousness. Then, I describe a mathematical formulation, unifying the mind mechanisms in a psychologically and neuro-biologically plausible system. A mechanism of the knowledge instinct drives our understanding of the world and serves as a foundation for higher cognitive functions. This mechanism relates aesthetic emotions and perception of beauty to “everyday” functioning of the mind. The article reviews mechanisms of human symbolic ability. I touch on future directions: joint evolution of the mind, language, consciousness, and cultures; mechanisms of differentiation and synthesis; a manifold of aesthetic emotions in music and differentiated instinct for knowledge. I concentrate on elucidating the first principles; review aspects of the theory that have been proven in laboratory research, relationships between the mind and brain; discuss unsolved problems, and outline a number of theoretical predictions, which will have to be tested in future mathematical simulations and neuro-biological research.
Hierarchical integrated language-cognition MF system. At each level in a hierarchy there are integrated language and cognition models. Similarities are integrated as products of language and cognition similarities. Initial models are fuzzy placeholders, so integration of language and cognition is sub-conscious. Association variables depend on both language and cognitive models and signals. Therefore language model learning helps cognitive model learning and v.v. Abstract cognitive concepts are grounded in abstract language concepts. cognitive models. Still, experience (cognitions) of the entire culture is accumulated in language. Evolution of culture is gradually accumulated in genes. Structure (9) gives a fuzzy placeholder for a cognitive model corresponding to each language model, and v.v. It enables independent learning of language and cognitive parts of models, while enhancing each other's learning. In this way, models of each type are gradually learned, cognition helps language, and language helps cognition. Knowledge is accumulated in culture through generations. Section 5.4 described the hierarchical MFT organization, as shown in Fig. 2. Combined with the mechanism of integrated models (9), it can integrate cognitive and language hierarchies as illustrated in Fig. 3. An amazing aspect of the human mind is that these two hierarchies are integrated in such a way that relationships among constituent models are preserved. For example, a cognitive model of a situation and the corresponding phrase model are constituted from lower-level models: objects and words. Correspondence between these objects and words in the object-word level is the same as between them, when they become constituent parts of the phrase-situation level model. And this holds true across tremendous number of the phrase-situation level models, using various combinations of the same words from the lower level. This amazing property of our mind seems so obvious, that nontrivial complexity of the required mechanism was noticed only recently [68]. Let us elaborate a bit. A dog can learn to bring shoes on command. The dog can associate shoes with a word "shoes". Does it mean dog's mind possesses models (9)? Try to teach a meaning of a word "rational" to a dog. Apparently, a dog can associate sounds with objects, which it sees in the world. A dog treats sounds just like other objects. But it does not possess a hierarchy of integrated models. In dog's mind, cognitive models are "grounded" in objects and situations in the world. But abstract concepts require grounding in other concepts, a hierarchy of concepts is required. According to [68], smartest apes after years of training, could possibly learn 2 levels of a hierarchy. Why is it so difficult? Higher levels of a hierarchy in the ape mind have no "ground". In the human mind, higher level language models are grounded in conversations with other people: Mutual understanding "assures" our mind of the reality of language hierarchy. A cognitive hierarchy is supported by a language hierarchy. Dawkins [99] called concept-models of the mind "memes" and emphasized that model selection will overtake gene selection because models are more efficient replicators. A mathematical description of this process, as interaction of language and cognition is a subject of this review. Cognitive models that proved useful in life and evolution cannot be directly transferred to the minds of the next generation. Only language models are transferred to the next generation. This separation between cognitive models and language models can be compared to separation between phenotypes and genotypes. In some ways this comparison could be deep and inspiring, in other ways, it is superficial and wrong. Because of space limitation, we will not pursue it here. Cognitive models created by each generation are accumulated in culture due to language. Cultural evolution selects useful models. Language accumulates cultural knowledge at all levels in a hierarchy of the mind. Due to integration
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Physics of Life Reviews 3 (2006) 23–55 www.elsevier.com/locate/plrev
Review
Toward physics of the mind:
Concepts, emotions, consciousness, and symbols
Leonid I. Perlovsky
Air Force Research Lab., 80 Scott Rd., Hanscom AFB, MA 01731, USA
Accepted 28 November 2005
Available online 20 January 2006
Abstract
Mathematical approaches to modeling the mind since the 1950s are reviewed, including artificial intelligence, pattern recogni-
tion, and neural networks. I analyze difficulties faced by these algorithms and neural networks and relate them to the fundamental
inconsistency of logic discovered by Gödel. Mathematical discussions are related to those in neurobiology, psychology, cognitive
science, and philosophy. Higher cognitive functions are reviewed including concepts, emotions, instincts, understanding, imagina-
tion, intuition, consciousness. Then, I describe a mathematical formulation, unifying the mind mechanisms in a psychologically
and neuro-biologically plausible system. A mechanism of the knowledge instinct drives our understanding of the world and serves
as a foundation for higher cognitive functions. This mechanism relates aesthetic emotions and perception of beauty to “everyday”
functioning of the mind. The article reviews mechanisms of human symbolic ability. I touch on future directions: joint evolution
of the mind, language, consciousness, and cultures; mechanisms of differentiation and synthesis; a manifold of aesthetic emotions
in music and differentiated instinct for knowledge. I concentrate on elucidating the first principles; review aspects of the theory
that have been proven in laboratory research, relationships between the mind and brain; discuss unsolved problems, and outline
a number of theoretical predictions, which will have to be tested in future mathematical simulations and neuro-biological research.
2005 Elsevier B.V. All rights reserved.
Keywords: The mind; Physics; Emotions; Concepts; Consciousness; The knowledge instinct
Contents
1. Physicsandthemind ...................................................................24
2. Logicvs.mind........................................................................25
3. Computational intelligencesince the 1950s: Complexity and logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4. Structuresofthemind...................................................................27
5. Modelingfieldtheory(MFT)..............................................................30
5.1. Theknowledgeinstinct.............................................................30
5.2. Dynamiclogic...................................................................32
5.3. Example of dynamic logic operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.4. MFT hierarchical organization . . . . . . . . . . . . ............................................33
*Tel. +781377 1728.
E-mail address: leonid.perlovsky@hanscom.af.mil.
1571-0645/$ – see front matter 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.plrev.2005.11.003
24 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
6. Symbolicculture ......................................................................35
6.1. Symbols in cognitivelinguistics, philosophy, and computational intelligence . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.2. Integration of language and cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7. Workingsof the mind: Current understanding, future research, predictions and tests . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.1. Cognition anddynamics of MFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.2. Elementary thought-process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.3. Understanding...................................................................41
7.4. Conscious andunconscious . . . . . . . . . . . . . . . . ..........................................41
7.5. Imagination.....................................................................45
7.6. Bodily instinctsand emotions . . . . . . . . . . . . .............................................46
7.7. Aestheticemotionsandtheinstinctforknowledge...........................................46
7.8. Beautifulandsublime..............................................................47
7.9. Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.10. Language, cognition, andsymbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7.11. Creativity, differentiation, and synthesis . . . ..............................................49
7.12. Teleology, causality, and the knowledge instinct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
7.13. Mind and brain,experimental evidence . . . . . .............................................50
7.14. Predictionsandtesting .............................................................50
Acknowledgements.........................................................................51
References...............................................................................51
1. Physics and the mind
Is a physical theory of the mind possible? What kind of physics would this be? I proceed assuming that the mind
and brain refer to the same physical system at different levels of description. This situation is not new to physics,
for example thermodynamics and statistical physics are also related to each other in this manner. Although a physi-
cist would prefer the most fundamental description level (elementary particles, strings ...), intermediate levels are
sometimes appropriate. Einstein once mentioned that he liked thermodynamics as physics defined at an intermediate
phenomenological level. The world is amenable to understanding at various levels. Understanding searched by physi-
cists is specific in certain ways: physics is a search for basic laws, a few universal “first principles” describing a wealth
of observed phenomena.
Many physicists are uncomfortable with the phrase “physics of the mind”, and I will attempt to overcome this initial
reaction. Some of the reasons for discomfort are obvious: the mind is perceived as deeply personal, something that no
equation will ever be able to describe, no computer will ever be able to simulate. Responding to this reservation, let me
mention that no particular individual mind is addressed here, rather this review considers the most general mechanisms
that act in every mind. The future will tell how close a physical theory could come to understanding individual minds.
Another reason for skepticism is that the mind is both diverse and unpredictable, therefore how can it be reduced to
few basic laws? Newton saw nothing wrong with developing physics of the mind, which he called spiritual substance.
However Newton failed and since then few physicists have dared to approach the subject. Recently, new data, new
intuitions, and new mathematical tools have emerged, and today we make a new attempt. We seek to identify a few
basic principles of the mind operation, formulate these principles mathematically, use them to explain a wealth of
known data, and make predictions that can be tested in the lab.
How the mind works has been the subject of discussions for millennia, from the Ancient Greek philosophers to
mathematicians and cognitive scientists of today. Words like mind, thought, imagination, emotion, concept present a
challenge: people use these words in many ways colloquially, but in cognitive science and in mathematics of intelli-
gence they have not been uniquely defined and their meaning is a subject of active research and ongoing debates [1].
Standardized definitions come at the end of the development of a theory (e.g., “force” was defined by Newton’s laws,
following centuries of less precise usage). Whereas the mind theory is under development, this review adheres to the
following guidance: we need to make sure that our proposals:
(1) correspond to the discussions in scientific and mathematical community,
(2) correspond to millennia of philosophical discussions and the general cultural usage,
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 25
(3) are clear and mathematically tractable, and
(4) that deviations or discrepancies in these proposals are noted and discussed.
According to the dictionary [2], which we take as a starting point, the mind includes conscious and unconscious
processes, especially thought, perception, emotion, will, memory, and imagination, and it originates in brain. These
constituent notions will be discussed throughout the paper. Specific neural mechanisms in the brain “implementing”
various mind functions constitute the relationship between the mind and brain; this is a contemporary formulation
of the millennia old mind-body problem. We will discuss possible relationships between the proposed mathematical
descriptions and neural structures in the brain.
A broad range of opinions exists about the mathematical methods suitable for the description of the mind. Founders
of artificial intelligence, including Allan Newell and Marvin Minsky, thought that formal logic was sufficient [3] and
that no specific mathematical techniques would be needed to describe the mind [4]. An opposite view was advocated
by Brian Josephson and Roger Penrose, suggesting that the mind cannot be understood within the current knowledge
of physics; new unknown yet physical phenomena will have to be accounted for explaining the working of the mind
[5,6]. Quantum computational processes were considered, which might take place in the brain [5,7,8]. Some authors
are developing a “classical physics” point of view in which there are few specific mathematical constructs, “the first
principles” of the mind. Among researchers taking this view are Grossberg, who suggests that the first principles in-
clude a resonant matching between bottom-up signals and top-down representations [9], and emotional evaluation of
conceptual contents [10]; Zadeh developing theory of granularity [11]; Meystel developing hierarchical multi-scale or-
ganization [12]; Edelman suggesting neuronal group selection [13]; and the author, suggesting the knowledge instinct,
aesthetic emotions, and dynamic logic [8,14,15] among the first principles of the mind. This review addresses mathe-
matical methods that can be realized by classical physics mechanisms. We review specific difficulties encountered by
previous attempts at mathematical modeling of the mind and recent developments overcoming these difficulties.
2. Logic vs. mind
For a long time people believed that intelligence is equivalent to conceptual understanding and reasoning. A part
of this belief was that the mind works according to logic. Although it is obvious that the mind is not logical, over the
course of the two millennia since Aristotle, many people have identified the power of intelligence with logic. Founders
of artificial intelligence in the 1950s and 1960s believed that by relying on rules of logic they would soon develop
computers with intelligence far exceeding the human mind.
The beginning of this story is usually attributed to Aristotle, the inventor of logic [16]. However, Aristotle did not
think that the mind works logically; he invented logic as a supreme way of argument, not as a theory of the mind. This
is clear from many Aristotelian writings, for example, in “Rhetoric for Alexander” Aristotle lists dozens of topics on
which Alexander had to speak publicly [17]. For each topic, Aristotle identified two opposite positions (e.g. make
peace or declare war; use torture or do not for extracting the truth, etc.). For each of the opposite positions, Aristotle
gives logical arguments, to argue either way. Clearly, for Aristotle, logic is a tool to express previously made decisions,
not the mechanism of the mind. Logic can only provide deductions from first principles, but cannot indicate what the
first principles should be. Logic, if you wish, is a tool for politicians. (Scientists, I would add, use logic to present their
results, but not to arrive at these results.) To explain the mind, Aristotle developed a theory of Forms, which will be
discussed later. But during the following centuries the subtleties of Aristotelian thoughts were not always understood.
With the advent of science, the idea that intelligence is equivalent to logic was gaining grounds. In the 19th century
mathematicians turned their attention to logic. George Boole noted what he thought was not completed in Aristotle’s
theory. The foundation of logic, since Aristotle, was a law of excluded middle (or excluded third): every statement
is either true or false, any middle alternative is excluded [18]. But Aristotle also emphasized that logical statements
should not be formulated too precisely (say, a measure of wheat should not be defined with an accuracy of a single
grain), that language implies the adequate accuracy, and everyone has his mind to decide what is reasonable.
Boole thought that the contradiction between exactness of the law of excluded middle and vagueness of language
should be corrected. A new branch of mathematics, formal logic was born. Prominent mathematicians contributed
to the development of formal logic, including George Boole, Gottlob Frege, Georg Cantor, Bertrand Russell, David
Hilbert, and Kurt Gödel. Logicians “threw away” uncertainty of language and founded formal mathematical logic
based on the law of excluded middle. Most of physicists today agree that exactness of mathematics is an insepara-
26 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
ble part of physics, but formal logicians went beyond this. Hilbert developed an approach named formalism, which
rejected the intuition as a part of scientific investigation and thought to define scientific objects formally in terms of
axioms or rules. Hilbert was sure that his logical theory also described mechanisms of the mind: “The fundamental
idea of my proof theory is none other than to describe the activity of our understanding, to make a protocol of the rules
according to which our thinking actually proceeds” [19]. In the 1900 he formulated famous Entscheidungsproblem: to
define a set of logical rules sufficient to prove all past and future mathematical theorems. This entailed formalization
of scientific creativity and the entire human thinking.
Almost as soon as Hilbert formulated his formalization program, the first hole appeared. In 1902 Russell exposed
an inconsistency of formal procedures by introducing a set Ras follows: Ris a set of all sets which are not members
of themselves.IsRa member of R? If it is not, then it should belong to Raccording to the definition, but if R
is a member of R, this contradicts the definition. Thus, either way we get a contradiction. This became known as
the Russell’s paradox. Its joking formulation is as follows: A barber shaves everybody who does not shave himself.
Does the barber shave himself? Either answer to this question (yes or no) leads to a contradiction. This barber, like
Russell’s set can be logically defined, but cannot exist. For the next 25 years mathematicians where trying to develop
a self-consistent mathematical logic, free from the paradoxes of this type. But, in 1931, Gödel has proved that it is not
possible [20], formal logic was inconsistent, self-contradictory.
Belief in logic has deep psychological roots related to functioning of human mind. A major part of any perception
and cognition process is not accessible to consciousness directly. We are conscious about the “final states” of these
processes, which are perceived by our minds as “concepts” approximately obeying formal logic. For this reason
prominent mathematicians believed in logic. Even after the Gödelian proof, founders of artificial intelligence still
insisted that logic is sufficient to explain working of the mind. We will turn to this in the next section; for now, let us
just state that logic is not a fundamental mechanism of the mind, but the result of mind’s operations (in Section 5we
discuss mathematics of dynamic logic, which suggests a mathematical explanation of how logic appears from illogical
states).
3. Computational intelligence since the 1950s: Complexity and logic
Simple object perception involves signals from sensory organs and internal mind’s representations (memories) of
objects. During perception, the mind associates subsets of signals corresponding to objects with representations of
object. This produces object recognition; it activates brain signals leading to mental and behavioral responses, parts
of understanding.
Developing mathematical descriptions of the very first recognition step in this seemingly simple association–
recognition–understanding process has not been easy, a number of difficulties have been encountered during the past
fifty years. These difficulties were summarized under the notion of combinatorial complexity (CC) [21]. CC refers to
multiple combinations of various elements in a complex system; for example, recognition of a scene often requires
concurrent recognition of its multiple elements that could be encountered in various combinations. CC is prohibitive
because the number of combinations is very large: for example, consider 100 elements (not too large a number); the
number of combinations of 100 elements is 100100, exceeding the number of all elementary particle events in life of
the Universe; no computer would ever be able to compute that many combinations.
The problem was first identified in pattern recognition and classification research in the 1960s and was named
“the curse of dimensionality” [22]. It seemed that adaptive self-learning algorithms and neural networks could learn
solutions to any problem “on their own”, if provided with a sufficient number of training examples. The following
thirty years of developing adaptive statistical pattern recognition and neural network algorithms led to a conclusion that
the required number of training examples often was combinatorially large. Thus, self-learning approaches encountered
CC of learning requirements.
Rule-based systems were proposed in the 1970s to solve the problem of learning complexity [23,24]. An initial
idea was that rules would capture the required knowledge and eliminate a need for learning. However in presence
of variability, the number of rules grew; rules became contingent on other rules; combinations of rules had to be
considered; rule systems encountered CC of rules.
Beginning in the 1980s, model-based systems were proposed. They used models which depended on adaptive
parameters. The idea was to combine advantages of rules with learning–adaptivity by using adaptive models. The
knowledge was encapsulated in models, whereas unknown aspects of particular situations were to be learned by
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 27
fitting model parameters [25,26]. Fitting models to data required selecting data subsets corresponding to various
models. The number of subsets, however, is combinatorially large. A general popular algorithm for fitting models to
the data, multiple hypothesis testing [27], is known to face CC of computations. Model-based approaches encountered
computational CC (N and NP complete algorithms).
In subsequent research, CC was related to the type of logic, underlying various algorithms and neural networks [21].
Formal logic is based on the “law of excluded middle”, according to which every statement is either true or false
and nothing in between. Therefore, algorithms based on formal logic have to evaluate every little variation in data or
internal representations as a separate logical statement (hypothesis); a large number of combinations of these variations
causes combinatorial complexity. In fact, combinatorial complexity of algorithms based on logic is related to Gödel
theory: it is a manifestation of the inconsistency of logic in finite systems [28]. Multivalued logic and fuzzy logic
were proposed to overcome limitations related to the law of excluded third [29]. Yet the mathematics of multivalued
logic is no different in principle from formal logic, “excluded third” is substituted by “excluded n+1”. Fuzzy logic
encountered a difficulty related to the degree of fuzziness, if too much fuzziness is specified, the solution does not
achieve a needed accuracy, if too little, it will become similar to formal logic. Complex systems require different
degrees of fuzziness in various elements of system operations; searching for the appropriate degrees of fuzziness
among combinations of elements again would lead to CC. Is logic still possible after Gödel? Bruno Marchal recently
reviewed the contemporary state of this field [30], it appears that logic after Gödel is much more complicated and much
less logical than was assumed by founders of artificial intelligence. Also, CC is still unsolved within logic. Penrose
thought that Gödel’s results entail incomputability of the mind processes and testify for a need for new physics [31].
An opposite position in this review is that incomputability of logic does not entail incomputability of the mind. Logic
is not the basic mechanism of the mind.
Various manifestations of CC are all related to formal logic and Gödel theory. Rule systems rely on formal logic in
a most direct way. Self-learning algorithms and neural networks rely on logic in their training or learning procedures:
every training example is treated as a separate logical statement. Fuzzy logic systems rely on logic for setting degrees
of fuzziness. CC of mathematical approaches to the mind is related to the fundamental inconsistency of logic.
4. Structures of the mind
In the 1950s and 1960s developers of artificial intelligence naïvely believed that they would soon develop computers
exceeding human intelligence, and that the mathematics of logic was sufficient for this purpose. As we discussed, logic
does not work, but the mind works. So let us turn to the mechanisms of the mind discussed in psychology, philosophy,
cognitive science, and neurobiology. Possibly, we will find inspiration for developing mathematics needed for physics
of the mind and for intelligent computers. The main mechanisms of the mind include instincts, concepts, emotions,
and behavior.Let us look briefly at their current definitions in cognitive science and psychology.
While theories of life and intelligence are being developed, as mentioned, definitions of cognitive functions are
a subject of research and debates. Let me summarize few related definitions [2,32,33] as a starting point for further
elaboration. Instincts are innate capabilities, aptitudes, or behavior, which are complex, not learned, and normally
adaptive. In humans and higher animals, instincts are related to emotions.
We use the word “concept” to designate a common thread among words like concept, idea, understanding, thought,
or notion. Different authors use these words with different meanings or subtle differences. A common thread among
these words is an abstract, universal psychical entity that serves to designate a category or class of entities, events,
or relations. Concepts are abstract in that they treat individual entities as if they were identical. Emphasizing this
property, Middle Age philosophers used the term “universals”. Plato and Aristotle called them ideas or forms, and
considered them the basis for the mind’s understanding of the world. Similarly, Kant considered them a foundation
for the ability for understanding, the contents of pure reason. According to Jung, conscious concepts of the mind are
learned on the basis of inborn unconscious psychic structures, archetypes. Contemporary science often equates the
mechanism of concepts with internal representations of objects, their relationships, situations, etc.
Ray Jackendoff [34] considers the terms representation or symbol as too loaded with “thorny philosophical problem
of intentionality”, and uses the word model. I do not think we should be afraid of intentionality; John Searle emphasis
on intentionality as “aboutness” [35,36] is too narrow [37]. All brain mechanisms and mental functions are intentional;
in fact everything within a living being is a result of long evolution and has evolved with a certain intent, or better to
28 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
say, purpose. We are purposeful beings, and I will return to this discussion later. But I agree with Jackendoff that the
word model is most appropriate for concept or representation.
Emotions refer to both exaggeratedly expressive communications and to internal states related to feelings. Love,
hate, courage, fear, joy, sadness, pleasure and disgust can all be described in both psychological and physiological
terms. Emotion is the realm where thought and physiology are inextricably entwined, and where the self is insepara-
ble from individual perceptions of value and judgment toward others and ourselves. Emotions are sometimes regarded
as the antithesis of reason; as is suggested by phrases such as “appeal to emotion” or “don’t let your emotions take
over”. A distinctive and challenging fact about human beings is a potential for both opposition and entanglement
between will, emotion, and reason. It has also been suggested that there is no empirical support for any generalization
suggesting the antithesis between reason and emotion: indeed, anger or fear can often be thought of as a systematic
response to observed facts. What should be noted, however, is that the human psyche possesses many possible reac-
tions and perspective in regard to the internal and external world—often lying on a continuum—some of which may
involve the extreme of pure intellectual logic (often called “cold”), other the extreme of pure emotion unresponsive
to logical argument (“the heat of passion”). In any case, it should be clear that the relation between logic and argu-
ment on the one hand and emotion on the other, is still a matter of research. It has been noted by many that passion,
emotion, or feeling can add backing to an argument, even one based primarily on reason—particularly in regard to
religion or ideology, areas of human thought which frequently demand an all-or-nothing rejection or acceptance, that
is, the adoption of a comprehensive worldview partly backed by empirical argument and partly by feeling and passion.
Moreover, it has been suggested by several researchers (see e.g., D.S. Levine and S.J. Leven [38]) that typically there
is no “pure” decision or thought, that is, no thought based “purely” on intellectual logic or “purely” on emotion—most
decisions and cognitions are founded on a mixture of both.
An essential role of emotions in working of the mind was analyzed by many researchers, from various per-
spectives: philosophical (Rene Descartes [39], Immanuel Kant [40], Jean Paul Sartre [41]); analytical psychology
(Carl Jung [42]); psychological and neural (Stephen Grossberg and Daniel Levine [10], Andrew Ortony [43], Joseph
LeDoux [44]); philosophical–linguistic (Paul Griffiths [45]); neuro-physiological (Antonio Damasio [46]); and from
the learning and cognition perspective by the author [47]. Descartes attempted a scientific explanation of passions. He
rationalized emotions, explained them as objects, and related to physiological processes. According to Kant, emotions
are closely related to judgments about which individual experiences and perceptions correspond to which general con-
cepts and vice versa. The ability for judgment is a foundation of all higher spiritual abilities, including the beautiful
and sublime. Kant’s aesthetics is a foundation of aesthetic theories till this very day (we will continue this discussion
later). Sartre equated emotions, to a significant extent, with unconscious contents of the psyche; today this does not
seem to be adequate. Jung analyzed conscious and unconscious aspects of emotions. He emphasized undifferentiated
status of primitive fused emotion-concept-behavior psychic states in everyday functioning and their role in neuroses.
He also emphasized rational aspect of conscious differentiated emotions. Ortony explains emotions in terms of knowl-
edge representations and emphasizes abductive logic as a mechanism of inferencing other people’s emotions. LeDoux
analyses neural structures and pathways involved in emotional processing, especially in fear. Griffiths considers basic
emotions and their evolutionary development within social interactions. According to Damasio, emotions are primar-
ily bodily perceptions, and feelings of emotions in the brain invoke “bodily markers”. Grossberg and Levine consider
emotions as neural signals that relate instinctual and conceptual brain centers. In processes of perception and cogni-
tion, emotions evaluate concept-models of objects and situations for satisfaction or dissatisfaction of instinctual needs.
In Section 6, I discuss relationships of these various theories of emotions to mathematical descriptions in the next sec-
tion, here I just mention that this mathematical description closely corresponds to ideas of Kant, Jung, Grossberg and
Levine. Ideas of Sartre and Damasio were not elaborated mathematically.
Behavior is comprised of many mechanisms. Behavior is controlled by the endocrine system and the nervous
system. The complexity of the behavior of an organism is related to the complexity of its nervous system. In this
review I refer only to neurally controlled behavior; it involves mechanisms of negative feedback (e.g., when reaching
an object with a hand) and positive feedback (e.g. when making a decision). The first does not reach consciousness,
the second is potentially available to consciousness [9].
Even this very cursory review of basic notions illustrates that they are far from being crystal clear; some notions
may seem to contradict others. Below I summarize and simplify this discussion of basic mechanisms of the mind and
relate them to mathematical discussions in the next section. This summarization and simplification of the huge body
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 29
of discussions ongoing for millennia is inspired by trying to find unifying themes in commonsense understanding and
technical writings from ancient philosophers to today’s research in multiple disciplines.
Explaining basic mind mechanisms, let me repeat, requires no mysterious assumptions; each mechanism can be
described mathematically. Among the mind’s cognitive mechanisms, the most directly accessible to consciousness are
concepts. Concepts are like internal models of the objects and situations in the world; this analogy is quite literal, e.g.,
during visual perception of an object, a concept-model in our memory projects an image onto the visual cortex, which
is matched there to an image, projected from retina (this simplified description will be refined later).
Concepts serve for satisfaction of the basic instincts, which have emerged as survival mechanisms long before
concepts. Inborn, less adaptive, unconscious, and more automatic functioning often is referred to as instinctual. This
lumping together of various mechanisms is inappropriate for the developmentof physical theory, requiring mathemat-
ical description of the mind mechanisms. Grossberg and Levine [10] separated instincts as internal sensors indicating
the basic needs, from “instinctual behavior”, which should be described by appropriate mechanisms. Accordingly,
I use word “instincts” to describe mechanisms of internal sensors: for example, when a sugar level in blood goes
below a certain level an instinct “tells us” to eat. Such separation of instinct as “internal sensor” from “instinctual
behavior” helps explaining many cognitive functions.
How do we know about instinctual needs? We do not hear instinctual pronouncements or read dials of instinc-
tual sensors. Instincts are connected to cognition and behavior by emotions. Whereas in colloquial usage, emotions
are often understood as facial expressions, higher voice pitch, exaggerated gesticulation, these are outward signs of
emotions, serving for communication. A more fundamental role of emotions within the mind system is that emo-
tional signals evaluate concepts for the purpose of instinct satisfaction [10]. This emotional mechanism is crucial for
breaking out of the “vicious circle” of combinatorial complexity.
An inevitable conclusion from a mathematical analysis: humans and higher animals have a special instinct respon-
sible for cognition. Let me emphasize, this is not an abstract mathematical theorem, but a conclusion from the basic
knowledge of the mind operations as described in thousands of publications. Clearly, humans and animals engage into
exploratory behavior,even when basic bodily needs, like eating, are satisfied. Biologists and psychologists discussed
various aspects of this behavior. Harry Harlow discovered that monkeys as well as humans have the drive for pos-
itive stimulation, regardless of satisfaction of drives such as hunger [48]; David Berlyne discussed curiosity in this
regard [49]; Leon Festinger, introduced the notion of cognitive dissonance and described many experiments on the
drive of humans to reduce dissonance [50]. Until recently, however, it was not mentioned among “basic instincts”
on a par with instincts for food and procreation. The reasons were that it was difficult to define, and that its funda-
mental nature was not obvious. The fundamental nature of this mechanism is related to the fact that our knowledge
always has to be modified to fit the current situations. One rarely sees exactly the same object: illumination, angles,
surrounding objects are usually different; therefore, adaptation–learning is required. A mathematical formulation of
the mind mechanisms makes obvious the fundamental nature of our desire for knowledge.In fact virtually all learning
and adaptive algorithms (tens of thousands of publications) maximize correspondence between the algorithm internal
structure (knowledge in a wide sense) and objects of recognition. Concept-models that our mind uses for understand-
ing the world are in a constant need of adaptation. Knowledge is not just a static state; it is in a constant process of
adaptation and learning. Without adaptation of concept-models we will not be able to understand the ever-changing
surrounding world. We will not be able to orient ourselves or satisfy any of the bodily needs. Therefore, we have
an inborn need, a drive, an instinct to improve our knowledge. I call it the knowledge instinct. Mathematically it is
described as a maximization of a similarity measure between concept-models and the world (as it is sensed by sensory
organs; also the very sensing is usually adapted and shaped during perception).
Emotions evaluating satisfaction or dissatisfaction of the knowledge instinct are not directly related to bodily needs.
Therefore, they are “spiritual” or aesthetic emotions. These aesthetic emotions are not peculiar to perception of art;
they are inseparable from every act of perception and cognition. Conceptual–emotional understanding of the world
results in actions in the outside world or within the mind. In this review we only discuss an internal behavior within the
mind, the behavior of learning and understanding the world; the behavior of increasing knowledge. A mathematical
theory of conceptual–emotional recognition and understanding is presented in the next section. Later, it is related to
intuition, imagination, conscious, and unconscious; to an ability of the mind to think, to operate with symbols and
signs. The mind involves a hierarchy of multiple levels of concept-models, from simple perceptual elements (like
edges, or moving dots), to concept-models of objects, to relationships among objects, to complex scenes, and up the
hierarchy ... toward the concept-models of the meaning of life and purpose of our existence. Hence the tremendous
30 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
complexity of the mind, yet relatively few basic principles of the mind organization go a long way explaining this
system.
I would like to add a side comment. In neural, cognitive, and psychological literature about the mind and brain, one
often encounters a statement that the brain is a kludge, a nonelegant, nonoptimal design, a concoction of modules that
appeared in evolution first for one purpose, then were used for a different purpose, etc. [51–54]. These statements are
made usually by nonmathematicians, whose ideas about mathematical optimality and elegance are at best naive (we
discussed that in this line of research many considered formal logic as the peak of optimality and elegance, already
after Gödel proved its mathematical inconsistency). Mathematical analysis of evolution demonstrates just the oppo-
site [55], there was more than enough information for evolution to attain optimality. The mind is often optimal [56].
Among those preaching nonoptimality of the brain and mind, no one produced a computer program working better
or more optimally than the mind. Therefore, it is reasonable to consider mathematically optimal methods for mod-
eling the mind (of course, mathematical descriptions have been compared with experimental data, and continuous
comparison of theory and experiments is an essential part of physics).
5. Modeling field theory (MFT)
Modeling field theory mathematically implements the mechanisms of the mind discussed above. It is a multi-level,
hetero-hierarchical system [8]. The mind is not a strict hierarchy; there are multiple feedback connections among
adjacent levels, hence the term hetero-hierarchy. At each level in MFT there are concept-models encapsulating the
mind’s knowledge; they generate so-called top–down neural signals, interacting with input, bottom–up signals. These
interactions are governed by the knowledge instinct, which drives concept-model learning, adaptation, and formation
of new concept-models for better correspondence to the input signals.
This section describes a basic mechanism of interaction between two adjacent hierarchical levels of bottom–up and
top–down signals (fields of neural activation; in this aspect MFT follows [57]); sometimes, it will be more convenient
to talk about these two signal-levels as an input to and output from a (single) processing-level. At each level, output
signals are concepts recognized in (or formed from) input signals. Input signals are associated with (or recognized,
or grouped into) concepts according to the models and the knowledge instinct at this level. This general structure of
MFT corresponds to our knowledge of neural structures in the brain; still, in this review we do not map mathemat-
ical mechanisms in all their details to specific neurons or synaptic connections. The knowledge instinct is described
mathematically as maximization of a similarity measure. In the process of learning and understanding input signals,
models are adapted for better representation of the input signals so that similarity between the models and signals
increases. This increase in similarity satisfies the knowledge instinct and is felt as aesthetic emotions.
5.1. The knowledge instinct
At a particular hierarchical level, we enumerate neurons by index n=1,...,N. These neurons receive bottom–up
input signals, X(n), from lower levels in the processing hierarchy. X(n) is a field of bottom–up neuronal synapse acti-
vations, coming from neurons at a lower level. Each neuron has a number of synapses; for generality, we describe each
neuron activation as a set of numbers, X(n) ={Xd(n), d =1,...,D}. Top–down, or priming signals to these neurons
are sent by concept-models, Mh(Sh,n); we enumerate models by index h=1,...,H. Each model is characterized
by its parameters, Sh; in the neuron structure of the brain they are encoded by strength of synaptic connections, math-
ematically, we describe them as a set of numbers, Sh={Sa
h,a=1,...,A}. Models represent signals in the following
way. Say, signal X(n), is coming from sensory neurons activated by object h, characterized by parameters Sh. These
parameters may include position, orientation, or lighting of an object h. Model Mh(Sh,n) predicts a value X(n) of a
signal at neuron n. For example, during visual perception, a neuron nin the visual cortex receives a signal X(n) from
retina and a priming signal Mh(Sh,n) from an object–concept-model h. A neuron nis activated if both bottom–up
signal from lower-level-input and top–down priming signal are strong. Various models compete for evidence in the
bottom–up signals, while adapting their parameters for better match as described below. This is a simplified descrip-
tion of perception. The most benign everyday visual perception uses many levels from retina to object perception.
The MFT premise is that the same laws describe the basic interaction dynamics at each level. Perception of minute
features, or everyday objects, or cognition of complex abstract concepts is due to the same mechanism described be-
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 31
low. Perception and cognition involve models and learning. In perception, models correspond to objects; in cognition
models correspond to relationships and situations.
Learning is an essential part of perception and cognition, and it is driven by the knowledge instinct. It increases
a similarity measure between the sets of models and signals, L({X},{M}). The similarity measure is a function of
model parameters and associations between the input bottom–up signals and top–down, concept-model signals. For
concreteness I refer here to an object perception using a simplified terminology, as if perception of objects in retinal
signals occurs in a single level.
In constructing a mathematical description of the similarity measure, it is important to acknowledge two principles
(which are almost obvious). First, the visual field content is unknown before perception occurred and second, it may
contain any of a number of objects. Important information could be contained in any bottom–up signal; therefore, the
similarity measure is constructed so that it accounts for all bottom–up signals, X(n),
(1)L{X},{M}=
nN
lX(n).
This expression contains a product of partial similarities, l(X(n)), over all bottom–up signals; therefore it forces
the mind to account for every signal (even if one term in the product is zero, the product is zero, the similarity is
low and the knowledge instinct is not satisfied); this is a reflection of the first principle. Second, before perception
occurs, the mind does not know which object gave rise to a signal from a particular retinal neuron. Therefore a
partial similarity measure is constructed so that it treats each model as an alternative (a sum over models) for each
input neuron signal. Its constituent elements are conditional partial similarities between signal X(n) and model Mh,
l(X(n)|h). This measure is “conditional” on object hbeing present, [58] therefore, when combining these quantities
into the overall similarity measure, L, they are multiplied by r(h), which represent a probabilistic measure of object
hactually being present. Combining these elements with the two principles noted above, a similarity measure is
constructed as follows [59]:
(2)L{X},{M}=
nN
hH
r(h)lX(n)|h.
The structure of (2) follows standard principles of the probability theory: a summation is taken over alternatives, h,
and various pieces of evidence, n, are multiplied. This expression is not necessarily a probability, but it has a proba-
bilistic structure. If learning is successful, it approximates probabilistic description and leads to near-optimal Bayesian
decisions. The name “conditional partial similarity” for l(X(n)|h) (or simply l(n|h)) follows the probabilistic termi-
nology. If learning is successful, l(n|h) becomes a conditional probability density function, a probabilistic measure
that signal in neuron noriginated from object h. Then Lis a total likelihood of observing signals {X(n)}coming from
objects described by models {Mh}. Coefficients r(h), called priors in probability theory, contain preliminary biases or
expectations, expected objects hhave relatively high r(h) values; their true values are usually unknown and should
be learned, like other parameters Sh.
We note that in probability theory, a product of probabilities usually assumes that evidence is independent. Ex-
pression (2) contains a product over n, but it does not assume independence among various signals X(n). There is a
dependence among signals due to models: each model Mh(Sh,n) predicts expected signal values in many neurons n.
During the learning process, concept-models are constantly modified. In this review we consider a case when
functional forms of models, Mh(Sh,n), are all fixed and learning–adaptation involves only model parameters, Sh.
More complicated structural learning of models is considered in [60,61]. From time to time a system forms a new
concept, while retaining an old one as well; alternatively, old concepts are sometimes merged or eliminated. This
requires a modification of the similarity measure (2); the reason is that more models always result in a better fit between
the models and data. This is a well-known problem, it is addressed by reducing similarity (2) using a “skeptic penalty
function”, p(N, M) that grows with the number of models M, and this growth is steeper for a smaller amount of
data N. For example, an asymptotically unbiased maximum likelihood estimation leads to multiplicative p(N, M) =
exp(Npar/2), where Npar is a total number of adaptive parameters in all models (this penalty function is known as
Akaike Information Criterion, see [8] for further discussion and references).
32 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
5.2. Dynamic logic
The learning process consists in estimating model parameters Sand associating signals with concepts by maximiz-
ing the similarity (2). Note, all possible combinations of signals and models are accounted for in expression (2). This
can be seen by expanding a sum in (2), and multiplying all the terms; it would result in HNitems, a huge number.
This is the number of combinations between all signals (N) and all models (H). Here is the source of CC of many
algorithms used in the past. For example, multiple hypothesis testing algorithms attempts to maximize similarity L
over model parameters and associations between signals and models, in two steps. First it takes one of the HNitems,
which is one particular association between signals and models; and maximizes it over model parameters. Second, the
largest item is selected (that is the best association for the best set of parameters). Such a program inevitably faces a
wall of CC, the number of computations on the order of HN.
Modeling field theory solves this problem by using dynamic logic [8,62]. An important aspect of dynamic logic is
matching vagueness or fuzziness of similarity measures to the uncertainty of models. Initially, parameter values are
not known, and uncertainty of models is high; so is the fuzziness of the similarity measures. In the process of learning,
models become more accurate, and the similarity measure more crisp, the value of the similarity increases. This is the
mechanism of dynamic logic.
Mathematically it is described as follows. First, assign any values to unknown parameters, {Sh}. Then, compute
association variables f(h|n),
(3)f(h|n) =r(h)lX(n)|h
hH
r(h)lX(n)|h.
Eq. (3) looks like the Bayes formula for a posteriori probabilities; if l(n|h) in the result of learning become conditional
likelihoods, f(h|n) become Bayesian probabilities for signal noriginating from object h. The dynamic logic of the
Modeling Fields (MF) is defined as follows:
(4)df(h|n)/dt=f(h|n)
hHδhhf(h
|n)·lnl(n|h)/∂MhMh/∂ Sh·dSh/dt,
(5)dSh/dt=
nN
f(h|n)lnl(n|h)/∂MhMh/∂ Sh,
here
(6)δhhis 1ifh=h,
0 otherwise.
Parameter tis the time of the internal dynamics of the MF system (like a number of internal iterations). Gaussian-shape
functions can often be used for conditional partial similarities,
(7)l(n|h) =GX(n)|Mh(Sh,n),Ch.
Here Gis a Gaussian function with mean Mhand covariance matrix Ch. Note, a “Gaussian assumption” is often used
in statistics; it assumes that signal distribution is Gaussian. This is not the case in (7): here signal is not assumed to be
Gaussian. Eq. (7) is valid if deviations between the model Mand signal Xare Gaussian; these deviations usually are
due to many random causes and, therefore, Gaussian. If they are not Gaussian, appropriate functions could be used. If
there is no information about functional shapes of conditional partial similarities, still (7) is a good choice, it is not a
limiting assumption: a weighted sum of Gaussians in (2) can approximate any positive function, like similarity.
Covariance matrices, Ch,in(7) are estimated like other unknown parameters. Their initial values should be large,
corresponding to uncertainty in knowledge of models, Mh. As parameter values and models improve, covariances
are reduced to intrinsic differences between models and signals (due to sensor errors, or model inaccuracies). As
covariances get smaller, similarities get crisper, closer to delta-functions; association variables (3) get closer to crisp
{0,1}values, and dynamic logic solutions converge to crisp logic. This process of concurrent parameter improvement
and convergence of similarity to a crisp logical function is an essential part of dynamic logic. This is the mechanism
of dynamic logic combining fuzzy and crisp logic.
The dynamic evolution of fuzziness from largeto small is the reason for the name “dynamic logic”. Mathematically,
this mechanism helps avoiding local maxima during convergence [8], and psychologically it explains many properties
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 33
of the mind, as discussed in Section 6 [63]. Whichever functional shapes are used for conditional partial similarities,
they ought to allow for this process of matched convergence in parameter values and similarity crispness.
The following theorem was proved [8].
Theorem. Eqs. (3)(6) define a convergent dynamic MF system with stationary states defined by max{Sh}L.
It follows that the stationary states of an MF system are the maximum similarity states satisfying the knowledge
instinct. When partial similarities are specified as probability density functions (pdf), or likelihoods, the stationary val-
ues of parameters {Sh}are asymptotically unbiased and efficient estimates of these parameters [64]. A computational
complexity of the MF method is linear in N.
In plain English, this means that dynamic logic is a convergentprocess. It converges to the maximum of similarity,
and therefore satisfies the knowledge instinct. Several aspects of MFT convergence are discussed below (in Sec-
tions 5.3, 5.4, and 6.1). If likelihood is used as similarity, parameter values are estimated efficiently (that is, in most
cases, parameters cannot be better learned using any other procedure). Moreover, as a part of the above theorem, it is
proven that the similarity measure increases at each iteration. The psychological interpretation is that the knowledge
instinct is satisfied at each step: a modeling field system with dynamic logic enjoys learning.
5.3. Example of dynamic logic operations
Finding patterns below noise can be an exceedingly complex problem. If an exact pattern shape is not known and
depends on unknown parameters, these parameters should be found by fitting the pattern model to the data. However,
when the locations and orientations of patterns are not known, it is not clear which subset of the data points should
be selected for fitting. A standard approach for solving this kind of problem, which has already been discussed,
is multiple hypothesis testing [27]. Here, since all combinations of subsets and models are exhaustively searched,
it faces the problem of combinatorial complexity. In the current example, we are looking for “smile” and “frown”
patterns in noise shown in Fig. 1(a) without noise, and in Fig. 1(b) with noise, as actually measured. Each pattern
is characterized by a 3-parameter parabolic shape. The image size in this example is 100 ×100 points, and the true
number of patterns is 3, which is not known. Therefore, at least 4 patterns should be fit to the data, to decide that
3 patterns fit best. Fitting 4 ×3=12 parameters to 100 ×100 grid by a brute-force testing would take about 1032 to
1040 operations, a prohibitive computational complexity.
To apply MFT and dynamic logic to this problem one needs to develop parametric adaptive models of expected
patterns. The models and conditional partial similarities for this case are described in details in [65]: a uniform model
for noise, Gaussian blobs for highly-fuzzy, poorly resolved patterns, and parabolic models for “smiles” and “frowns”.
The number of computer operations in this example was about 1010. Thus, a problem that was not solvable due to CC
becomes solvable using dynamic logic.
During an adaptation process, initial fuzzy and uncertain models are associated with structures in the input signals,
and fuzzy models become more definite and crisp with successive iterations. The type, shape, and number, of models
are selected so that the internal representation within the system is similar to input signals: the MF concept-models
represent structure-objects in the signals. The figure below illustrates operations of dynamic logic. In Fig. 1(a) true
“smile” and “frown” patterns are shown without noise; (b) actual image available for recognition (signal is below
noise, signal-to-noise ratio is between 2dBand 0.7dB); (c) an initial fuzzy model, a large fuzziness corresponds
to uncertainty of knowledge; (d) through (h) show improved models at various iteration stages (total of 22 iterations).
Every five iterations the algorithm tried to increase or decrease the number of pattern-models. Between iterations (d)
and (e) the algorithm decided, that it needs three Gaussian models for the “best” fit. There are several types of models:
one uniform model describing noise (it is not shown) and a variable number of blob models and parabolic models,
which number, location, and curvature are estimated from the data. Until about stage (g) the algorithm used simple
blob models, at (g) and beyond, the algorithm decided that it needs more complex parabolic models to describe the
data. Iterations stopped at (h), when similarity stopped increasing.
5.4. MFT hierarchical organization
Above, we described a single processing level in a hierarchical MFT system. At each level of a hierarchy there
are input signals from lower levels, models, similarity measures (2), emotions, which are changes in similarity (2),
34 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
Fig. 1. Finding “smile” and “frown” patterns in noise, an example of dynamic logic operation: (a) true “smile” and “frown” patterns are shown
without noise; (b) actual image available for recognition (signal is below noise, signal-to-noise ratio is between 2dBand 0.7dB); (c) an initial
fuzzy blob-model, the fuzziness corresponds to uncertainty of knowledge; (d) through (h) show improved models at various iteration stages (total of
22 iterations). Between stages (d) and (e) the algorithm tried to fit the data with more than one model and decided, that it needs three blob-models to
“understand” the content of the data. There are several types of models: one uniform model describing noise (it is not shown) and a variable number
of blob-models and parabolic models, which number, location, and curvature are estimated from the data. Until about stage (g) the algorithm
“thought” in terms of simple blob models, at (g) and beyond, the algorithm decided that it needs more complex parabolic models to describe the
data. Iterations stopped at (h), when similarity (2) stopped increasing. This example is discussed in more details in [65].
and actions; actions include adaptation, behavior satisfying the knowledge instinct—maximization of similarity,
Eqs. (3)–(6). An input to each level is a set of signals X(n), or in neural terminology, an input field of neuronal
activations. The result of signal processing at a given level are activated models, or concepts hrecognized in the input
signals n; these models along with the corresponding instinctual signals and emotions may activate behavioral models
and generate behavior at this level.
The activated models initiate other actions. They serve as input signals to the next processing level, where more
general concept-models are recognized or created. Output signals from a given level, serving as input to the next level,
could be model activation signals, ah, defined as
(8)ah=
nN
f(h|n).
Alternatively, output signals may include model parameters. The hierarchical MF system is illustrated in Fig. 2. Within
the hierarchy of the mind, each concept-model finds its “mental” meaning and purpose at a higher level (in addition
to other purposes). For example, consider a concept-model “chair”. It has a “behavioral” purpose of initiating sitting
behavior (if sitting is required by the body), this is the “bodily” purpose at the same hierarchical level. In addition,
it has a “purely mental” purpose at a higher level in the hierarchy, a purpose of helping to recognize a more general
concept, say of a “concert hall”, which model contains rows of chairs.
Models at higher levels in the hierarchy are more general than models at lower levels. For example, at the very
bottom of the hierarchy, if we consider vision system, models correspond (roughly speaking) to retinal ganglion cells
and perform similar functions; they detect simple features in the visual field; at higher levels, models correspond to
functions performed at V1 and higher up in the visual cortex, that is detection of more complex features, such as
contrast edges, their directions, elementary moves, etc. Visual hierarchical structures and models are studied in details
[9,66], these models can be used in MFT. At still higher cognitive levels, models correspond to objects, to relationships
among objects, to situations, and relationships among situations, etc. [8]. Still higher up are even more general models
of complex cultural notions and relationships, like family, love, friendship, and abstract concepts, like law, rationality,
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 35
Fig. 2. Hierarchical MF system. At each level of a hierarchy there are models, similarity measures, and actions (including adaptation, maximizing the
knowledge instinct—similarity). High levels of partial similarity measures correspond to concepts recognized at a given level. Concept activations
are output signals at this level and they become input signals to the next level, propagating knowledge up the hierarchy.
etc. Contents of these models correspond to cultural wealth of knowledge, including writings of Shakespeare and
Tolstoy; mechanisms of the development of these models are reviewed in the next section. At the top of the hierarchy
of the mind, according to Kantian analysis [67], are models of the meaning and purpose of our existence, unifying our
knowledge, and the corresponding behavioral models aimed at achieving this meaning.
From time to time, as discussed, a system forms a new concept or eliminates an old one. Many pattern recognition
algorithms and neural networks luck this important ability of the mind. It can be modeled mathematically in several
ways; adaptive resonance theory (ART) uses vigilance threshold, which is compared to a similarity measure [57].
A somewhat different mechanism of MFT works as follows. At every level, the system always keeps a reserve of
vague (fuzzy) inactive concept-models (with large covariance, C,Eq.(7)). They are inactive in that their parameters
are not adapted to the data, therefore their similarities to signals are low. Yet, because of a large fuzziness (covariance)
the similarities are not exactly zero. When a new signal does not fit well into any of the active models, its similarities
to inactive models automatically increase (because first, every piece of data is accounted for see Ref. [58], and second,
inactive models are vague-fuzzy and potentially can “grab” every signal that does not fit into more specific, less fuzzy,
active models). When the activation signal ahof Eq. (8) for an inactive model, h, exceeds a certain threshold, the
model is activated. Similarly, when an activation signal for a particular model falls below a threshold, the model
is deactivated. Thresholds for activation and deactivation are set usually based on information existing at a higher
hierarchical level (prior information, system resources, numbers of activated models of various types, etc.). Activation
signals for active models at a particular level {ah}form a “neuronal field”, which serve as input signals to the next
level, where more abstract and more general concepts are formed, and so on along the hierarchy toward higher models
of meaning and purpose.
6. Symbolic culture
6.1. Symbols in cognitive linguistics, philosophy, and computational intelligence
“Symbol is the most misused word in our culture” [68]. We use this word in trivial cases referring to traffic signs,
and in the most profound cases to cultural and religious symbols. Charles Peirce considered symbols to be a particular
type of signs [69]. He concentrated on the process of sign interpretation, which he conceived as a triadic relationship
of sign, object, and interpretant. Interpretant is similar to what we call today a representation of the object in the mind.
Peircian approach, however, was inconsistent. He classified signs into symbols, indexes, and icons. Icons have mean-
ings due to resemblance to the signified (objects, situations, etc.), indexes have meanings by direct connection to the
signified, and symbols have meaning due to arbitrary conventional agreements. However, identifying “resemblance”
turned out a complex problem; pattern recognition algorithms based on simple resemblances do not work. Similarly
problematic was an idea of “arbitrary” symbols, as we discuss later.
When scientists attempted to understand symbols in the development of semiotics, the two functions, understanding
language and understanding world, were often mixed up, as if cognition was provided by language. This tendency
was strengthened by considering logic to be the mechanism of both, language and cognition. According to Bertrand
Russell, language is equivalent to axiomatic logic, “[a word-name is] merelyto indicate what we are speaking about;
36 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
[it] is no part of the fact asserted... it is merely part of the symbolism by which we express our thought” [70].
Logical positivism centered on “the elimination of metaphysics through the logical analysis of language”—according
to Rudolf Carnap [71] logic was sufficient for the analysis of language. We have already analyzed roots of this belief
in logic.
Similar understanding of relationships among symbol, language, logic, and the mind can be traced in semiotics of
Ferdinand Saussure and in structuralism. A simplistic idea that words are labels for objects falls apart as soon as we
consider words for abstract ideas, say, “rational”. Saussure tried to resolve this problem by saying that “the linguistic
sign does not unite a thing and a name, but a concept and a sound image” [72]. Here, both aspects of the sign exist in
the mind and the real world is taking a back sit. Like in formal logic, relationships between mathematical objects and
the world are arbitrary. Similarly, Saussure emphasized the arbitrariness of the sign, relationships between words and
objects in the world are arbitrary conventions.
This idea later heavily influenced Structuralism, and evolved into arbitrariness of communication codes in general.
Since communication codes contain cultural values, some concluded that cultural values are arbitrary. “There may be
an objective, empiricist reality out there, but there is no universal, objective way of perceiving and making sense of it.
What passes for reality in any culture is the product of the culture’s codes, so “reality” is always already encoded, it is
never “raw” [73]. This circle of ideas served as a platform for Jacques Derrida’s attacks on structuralism [74]. Since
any statement is based on some cultural structures and values, it can be dismissed as having no objective validity, as
“arbitrary” or as “local”. Here we review attempts [60,61] to give answer to this question: How is it possible to have
anything of truth and value? How our mind constructs symbols, which have psychological values and are not reducible
to arbitrary signs.
A path toward such understanding was not straight. The first move towards mathematical models of language and
cognition was in opposite directions. It took a while for science, first, to appreciate that language and cognition were
not one and the same, and later to realize that their relationships require scientific elucidation. In the second half of
the 20th century Noam Chomsky reoriented linguistics toward studies of innate mind mechanisms [75]. “Nativists”
(as followers of Chomsky are called today) emphasized that mechanisms of language were separate from the rest
of cognition. In the 1960s and 1970s they used mathematics of logical rules, similar to artificial intelligence. In the
1980s Chomsky proposed a new mathematical paradigm in linguistics, rules and parameters [76]. This was similar
to model-based systems emerging in mathematical studies of cognition. In 1990s, Chomsky’s minimalist program
called for simplifying rule structure of the mind mechanism of language [77]. It moved language closer to other
mind mechanisms, closer to cognition, but stopped at an interface between language and cognition. Nativist linguists,
following Chomsky, emphasized that cognition and language abilities are different: they are located in different brain
areas and they might have emerged along separate paths in evolution [78]. Learning language models is driven by
the language instinct, separate from the knowledge instinct. Chomsky’s linguistics still assumed that meanings appear
independently from language, and a mix-up of signs and symbols continued; motivational forces of symbols were
ignored.
Cognitive linguistics emerged in the 1970s to address some of these limitations of the nativist approach. “Cog-
nitivists” wanted to unify language with cognition and explain creation of meanings. They were looking for simpler
innate structures than those postulated by nativists. These simpler structures would be sufficient, scientists thought, be-
cause they will combine language and cognition, combine innate structures with learning from experience (to a much
larger extent than nativists postulated). Cognitivists gradually moved away from heavy logical bias of the previous
structuralist thinking, which could be characterized by
“the meaning of a word can be exhaustively decomposed into finite set of conditions ... necessary and sufficient
...[79]
George Lakoff emphasized that abstract concepts used by the mind for understanding the world have metaphorical
structure [80]. Metaphors were not just poetic tools, but an important mechanism of the mind for creating new abstract
meanings. Lakoff’ analysis brought this cultural knowledge, advanced by Fyodor Dostoevsky and Friedrich Nietzsche,
within the mainstream of science. There was still a big gap between Lakoff’ analysis of metaphors [81] on one hand
and neural and mathematical mechanisms on the other. The “Metaphors we live by” is a metaphorical book in that it
begs the question: Who is that homunculus in the mind, interpreting the metaphorical theater of the mind? What are
the mechanisms of metaphorical thinking?
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 37
In works of Jackendoff [79], Langacker [82],Talmy[83], and other cognitive linguists [84] it was recognized that
old divisions dominating linguistics were insufficient. Dichotomies of meanings (semantic-pragmatic), dichotomies
of hierarchical structures (superordinate-subordinate) were limiting scientific discourse and had to be overcome. Con-
sider the following opinions on meaning creation:
“in a hierarchical structure of meaning determination the superordinate concept is a necessary condition for the
subordinate one ... COLOR is a necessary condition for determining the meaning or RED” [79]
“The base of predication is nothing more than ...domains which the prediction actually invokes and requires” [82]
These examples illustrate attempts to overcome old dichotomies and at the same time difficulties encountered
along this path. Both examples are influenced by logical bias. Attempts to implement mathematically mechanisms
assumed by these examples would lead to combinatorial complexity. To put it jovially, problems of meaning and
hierarchy still reminded the old question about the chicken and the egg, what came first? If superordinate concepts
come before subordinate ones, where do they come from? Are we born with the concept COLOR in our minds?
If predictions invoke domains, where do domains come from? These complex questions with millennial pedigrees
are answered mathematically in the following sections. Here I give a brief psychological preview of the answer,
accounting for contemporary development in dynamic logic, neurobiology, and language evolution. Hierarchy and
meaning emerge jointly with cognition and language. In processes of evolution and individual learning, superordinate
concepts (COLOR) are vaguer, less specific, and less conscious than subordinate ones (RED). RED can be vividly
perceived, but COLOR cannot be perceived. RED can be perceived by animals. But, the concept COLOR can only
emerge in the human mind, due to joint operation of language and cognition.
Elman [85] emphasized that cognitively driven, use-based language acquisition is possible, using connectionist
(neural network) mechanisms. The main argument was that the innate mechanisms of connectionist architectures can
be much simpler than logical rules postulated by nativists. But what exactly is “simpler”? Elman himself emphasized
this other side of the story. The connectionist neural network is not an off-the-shelf product, but SNR neural network
carefully designed for language acquisition (Elman [86]). Moreover, SNR does not perform “general” language ac-
quisition, but a specific type of learning it was designed for. Elman emphasized a hard learned lesson: “there is no ...
general purpose learning algorithm that works equally well across domains” [85, p. 1]. We already discussed this in
Sections 2 and 3.
Jackendoff in his recent research [98] concentrated on unifying language and cognition. He developed detailed
models for such unification; however, his logical structures face combinatorial complexity.
We have, however, reasons to believe that the mind does work, and that there are the first principles of the mind
organization [87] leading to an ability for creating symbols. SNR neural network cannot be an example for such a gen-
eral principle: according to analysis in previous sections, SNR will face combinatorial complexity, when exposed to
complex learning. It will not scale up to real human brain. Elman [88] is among the first to admit this. Still, SNR can be
used to elucidate the general principles. Among such principles is evolution of abstract notions from vague and fuzzy
toward specific and concrete (Elman [85, p. 14]; Olguin and Tomasello [89]; Tomasello and Olguin [90]). Dynamic
logic systematically utilizes this principle. We already addressed another important principle of the mind organiza-
tion discussed recently by Nolfi et al. [91], learning is motivated by internal drives. There is an important difference,
however, between Elman [88] discussion of nonspecific emergence and the purposeful emergence mechanisms of the
instinct for knowledge.
Michael Tomasello [92,93] suggests that the first principle of the human mind organization, the most important
mechanism of the human brain required to learn language is not language specific, but more broadly cultural and
social. It is our ability to perceive other people as intentional agents. We understand that other people have intentions
and plans to achieve them, we can figure out what these intentions and plans are. This is the foundation for our
entire symbolic culture. Mathematical or neural mechanisms of this ability are not known. In the following sections
I describe a mathematical theory of joint learning of cognition and language. Its most important premise is that we
are born with an innate drive, an instinct for knowledge. It determines the purposiveness of our existence, our higher
mental abilities, and our ability to create symbolic culture. It is mathematically possible that a significant aspect
of this drive is to acquire knowledge about other people’ intentions and plans. It would be a fascinating enterprise to
38 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
establish relationships between these two theories through mathematical modeling, neural research, and psychological
laboratory experimentation.
Let us summarize goals and achievements of cognitive linguistics. Connectionist architectures demonstrated that
complex syntax patterns can be learned without explicit rules and without explicit examples. They demonstrated
elements of joint language learning and meaning creation (cognition). Still these type architectures face CC and do
not scale up. Motivational forces inherent to symbols, which were recognized by Saussure and analytic psychology,
made inroads into linguistics and psychology. Still, symbols and signs continue to be mixed up.
Learning cognitive models, as discussed in Section 5is driven by the knowledge instinct. Most importantly,
cognition is about objects and situations in the surrounding world, whereas mechanisms of acquiring and using lan-
guage identified in cognitive linguistics are about language, not about the world. Today, we still do not know neural
mechanisms combining language with cognition, nor their locations in the brain; and until recently, no mathemat-
ical mechanisms were suggested for unifying new findings in cognitive linguistics and computational intelligence.
Researchers in cognition, linguistics, evolutionary linguistics, computational semiotics came to appreciation that lan-
guage cannot be understood separately from thinking about the world [60,94–96]. Similar ideas are becoming accepted
by Chomsky and by nativist linguists [97,98]. The next section discusses steps toward mathematical theory of symbols
integrating cognition and language.
6.2. Integration of language and cognition
Integration of language and cognition in MFT [60,61] is attained by integrating cognitive and language models, so
that a concept-model (in (1) through (5))Mhis given by
(9)Mh=MC
h,ML
h.
Here MC
hdenotes a cognitive part of the model of an object or situation in the world (like models in example, Fig. 1),
and ML
his a language part of the model. Mathematical mechanisms of integrating cognition and language require
extension of MFT considered in [60]. Consider now this integrated model as the mind’s mechanism of integrating
language and cognition. A data stream constantly comes into the mind from all sensory perceptions; every part of
this data stream is constantly evaluated and associated with models (9) according to the mechanisms of dynamic
logic described in previous sections. At the beginning, the models are fuzzy; cognitivemodels vaguely correspond to
uncertain undifferentiated sensory perceptions. Language models vaguely correspond to sounds. This is approximately
a state of the mind of a newborn baby. First, models of simple perceptions differentiate; objects are distinguished in
visual perception. Language sounds are differentiated from other sounds. In (9) some cognitive models become crisper
than other cognitive models. Until about one year of age, perception models corresponding to simple objects become
crisper at a faster rate than language models.
Gradually, models are adapted, their correspondence to specific signals improve, selectivity to language signals
and nonlanguage sounds is enhanced. Language models are associated with words (sentences, etc.), and cognitive
models are associated with objects and situations of perception and cognition. Between the first and second year of
life the speed of adaptation of language models tremendously accelerates and overtakes learning of cognitive models.
By the age of 5 or 7, a child knows tremendous number of language models (words, rules of grammar), which attained
differentiated, crisp status. But it will take the rest of his life to associate them with real life situations and acquire
highly differentiated crisp cognitive models.
Association between language and cognitive models occurs before any of the models attain a high degree of speci-
ficity characteristic of the grown-up conscious concepts. Language and cognition are integrated at a pre-conscious
level. Certain language models evolve faster than their corresponding cognitive models and vice versa. Correspond-
ingly, uncertainty and fuzziness of the two aspects of integrated models may significantly differ. Still, existence of
crisp language models helps to identify relevant objects and situations in the world, and therefore, speeds up learn-
ing and adaptation of the corresponding cognitive models and v.v. This was suggested as a mechanism of interaction
between language and cognition [60,61]. Both abilities enhance each other.
This mechanism of interaction between language and cognition was suggested for ontological development and
learning in each human individual, as well as for biological evolution of the human specie, and for evolution of
cultures. Few human individuals succeed in connecting the entire wealth of language models with crisp and conscious
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 39
Fig. 3. Hierarchical integrated language-cognition MF system. At each level in a hierarchy there are integrated language and cognition models.
Similarities are integrated as products of language and cognition similarities. Initial models are fuzzy placeholders, so integration of language and
cognition is sub-conscious. Association variables depend on both language and cognitive models and signals. Therefore language model learning
helps cognitive model learning and v.v. Abstract cognitive concepts are grounded in abstract language concepts.
cognitive models. Still, experience (cognitions) of the entire culture is accumulated in language. Evolution of culture
is gradually accumulated in genes.
Structure (9) gives a fuzzy placeholder for a cognitive model corresponding to each language model, and v.v. It
enables independent learning of language and cognitive parts of models, while enhancing each other’s learning. In this
way, models of each type are gradually learned, cognition helps language, and language helps cognition. Knowledge
is accumulated in culture through generations.
Section 5.4 described the hierarchical MFT organization, as shown in Fig. 2. Combined with the mechanism of
integrated models (9), it can integrate cognitive and language hierarchies as illustrated in Fig. 3. An amazing aspect of
the human mind is that these two hierarchies are integrated in such a way that relationships among constituent models
are preserved. For example, a cognitive model of a situation and the corresponding phrase model are constituted from
lower-level models: objects and words. Correspondence between these objects and words in the object-word level is
the same as between them, when they become constituent parts of the phrase-situation level model. And this holds
true across tremendous number of the phrase-situation level models, using various combinations of the same words
from the lower level. This amazing property of our mind seems so obvious, that nontrivial complexity of the required
mechanism was noticed only recently [68].
Let us elaborate a bit. A dog can learn to bring shoes on command. The dog can associate shoes with a word
“shoes”. Does it mean dog’s mind possesses models (9)? Try to teach a meaning of a word “rational” to a dog.
Apparently, a dog can associate sounds with objects, which it sees in the world. A dog treats sounds just like other
objects. But it does not possess a hierarchy of integrated models. In dog’s mind, cognitive models are “grounded” in
objects and situations in the world. But abstract concepts require grounding in other concepts, a hierarchy of concepts
is required. According to [68], smartest apes after years of training, could possibly learn 2 levels of a hierarchy. Why
is it so difficult? Higher levels of a hierarchy in the ape mind have no “ground”. In the human mind, higher level
language models are grounded in conversations with other people: Mutual understanding “assures” our mind of the
reality of language hierarchy. A cognitive hierarchy is supported by a language hierarchy.
Dawkins [99] called concept-models of the mind “memes” and emphasized that model selection will overtake gene
selection because models are more efficient replicators. A mathematical description of this process, as interaction of
language and cognition is a subject of this review. Cognitive models that proved useful in life and evolution cannot be
directly transferred to the minds of the next generation. Only language models are transferred to the next generation.
This separation between cognitive models and language models can be compared to separation between phenotypes
and genotypes. In some ways this comparison could be deep and inspiring, in other ways, it is superficial and wrong.
Because of space limitation, we will not pursue it here.
Cognitive models created by each generation are accumulated in culture due to language. Cultural evolution selects
useful models. Language accumulates cultural knowledge at all levels in a hierarchy of the mind. Due to integration
40 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
of language and cognition, language provides grounding for abstract high-level cognitive models. But, this requires
that every next generation connects language and cognitive models in individual minds. Every generation has to learn
differentiated conscious cognitive models corresponding to the level of differentiation accumulated in language and
culture. Possibly, an essential inborn difference between human and animal minds is that we possess structures similar
to Eq. (9). This might be sufficient for evolution of symbolic culture.
Is it possible to prove these assertions? Current research in evolution of languages and cultures uses mathematical
simulations of communities of interacting agents [96] and related statistical models [100,101]. It was shown that a
compositional hierarchical language (with phrases composed from words) evolves from noncompositional languages
given a structure similar to Eq. (9) under certain conditions [102]. This research was limited by an assumption of pre-
existing cognitive models. Combining these results with MFT toward self-evolving integrated hierarchical cognitive-
language system was initiated in [103–105].
7. Workings of the mind: Current understanding, future research, predictions and tests
I review here how the mathematical descriptions are related to a variety of the mind functions. I would like to
illustrate that current understanding of the mind merits a status of the new area of physics: The mind is described
mathematically, on one hand without mysticism, and on the other hand, without reductionism, in general agreement
with cognitive science, psychology, and philosophy. A variety of the mind phenomena are understood from few basic
principles; some long-standing controversies in psychology, philosophy, and aesthetics are resolved; and specific
predictions are made that will be tested in laboratory and mathematical simulations. Among the first principles of the
mind is the knowledge instinct, which is described mathematically as maximization of similarity between concept-
models and the world. This principle leads to a better understanding of the mind functioning, and to solving previously
unsolved problems associated with higher mind functions, including consciousness, feelings of sublime, and beauty.
In addition to studying basic mechanisms of isolated minds, I address research in language and culture evolution
involving simulation of interacting minds.
7.1. Cognition and dynamics of MFT
Eqs. (3)–(6) describe an elementary process of perception or cognition, which maximizes knowledge. Knowledge
is measured by similarity between concept-models and the world. In this process a large number of model-concepts
compete for incoming signals, models are modified and new ones are formed, and eventually, connections are es-
tablished between signal subsets on the one hand, and model-concepts on the other. Perception refers to processes
in which the input signals come from sensory organs and model-concepts correspond to objects in the surrounding
world. Cognition refers to higher levels in the hierarchy where the input signals are activation signals from concepts
cognized (activated) at lower levels, whereas model-concepts are more complex, abstract, and correspond to situations
and relationships among lower-level concepts.
This process is described by dynamic logic. Its salient mathematical property is a correspondence between uncer-
tainty in models and vagueness–fuzziness in associations f(h|n). During perception, as long as model parameters
do not correspond to actual objects, there is no match between models and signals; many models poorly match many
objects, and associations remain fuzzy. Eventually, one model (h)wins a competition for a subset {n}of input signals
X(n), when parameter values match object properties; f(h
|n) values become close to 1 for n∈{n}and 0 for n/∈{n}.
Upon the convergence, the entire set of input signals {n}is approximately divided into subsets, each associated with
one model-object. Initial fuzzy concepts become crisp concepts, approximately obeying formal logic. The general
mathematical laws of cognition and perception are similar.
7.2. Elementary thought-process
Thought-processes or thinking involvesa number of sub-processes and attributes, including internal representations
and their manipulation, attention, memory, concept formation, knowledge, generalization, recognition, understanding,
meaning, prediction, imagination, intuition, emotion, decisions, reasoning, goals, behavior, conscious and unconscious
[8,9,12]. A “minimal” subset of these processes has to involve mechanisms for afferent and efferent signals [9],in
other words, bottom–up and top–down signals coming from outside (external sensor signals) and from inside (internal
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 41
representation signals). According to Carpenter and Grossberg [57] every recognition and concept formation process
involves a “resonance” between these two types of signals. In MFT, at every level in a hierarchy, the afferent signals
are represented by the input signal field X, and the efferent signals are represented by the modeling field signals Mh;
resonances correspond to high similarity measures l(n|h) for some subsets of {n}that are “recognized” as concepts (or
objects) h. The mechanism leading to the resonances, Eqs. (3)–(6), is an elementary thought-process. In this process,
subsets of signals corresponding to objects or situations are understood as concepts, signals acquire meanings.
Kant’s three volumes on theory of the mind, Critique of Pure Reason, Critique of Judgment, and Critique of
Practical Reason [40,106,107] describe the structure of the mind similarly to MFT. Pure reason or the faculty of
understanding contains concept-models. The faculty of judgment, or emotions, establishes correspondences between
models and data about the world acquired by sensory organs (in Kant’s terminology, between general concepts and
individual events). Practical reason contains models of behavior. Kant was first to recognize that emotions are an
inseparable part of cognition. The only missing link in Kantian theory is the knowledge instinct. Kant underappreciated
a pervading need for concept adaptation; he considered concepts as given a priori.
A dynamic aspect of working of the mind, described by dynamic logic, was first given by Aristotle [108].He
described thinking as a learning process in which an a priori form-as-potentiality (fuzzy model) meets matter (sensory
signals) and becomes a form-as-actuality (a concept of the mind). He pointed out an important aspect of dynamic logic,
reduction of fuzziness during learning: Forms-potentialities are fuzzy (do not obey logic), whereas forms-actualities
are logical.
History preserved for us evidence of Aristotle’s foresight. When Alexander the Great, Aristotelian pupil, was
fighting in Persia, he wrote to his teacher: “Aristotle, I heard you are writing books now. Are you going to make our
secret knowledge public?” In a reply letter Aristotle wrote: “Alexander, do not worry: nobody will understand” [109].
7.3. Understanding
In the elementary thought process, subsets in the incoming signals are associated with recognized models, which
are understood as objects or situations. In other words signal subsets acquire meaning, for example, a subset of retinal
signals acquires a meaning of a chair. There are several aspects to understanding and meaning. First, object-models
are connected (by emotional signals [8,10]) to instincts that they might satisfy, and also to behavioral models that can
make use of them for instinct satisfaction. Second, an object is understood in the context of a more general situation
in the next hierarchical level consisting of more general concept-models, which accepts as input-signals the results of
object recognition. That is, each recognized object-model sends (in neural terminology, activates) an output signal;
and a set of these signals comprises input signals for the next level models, which “cognize” more general concept-
models, like relations and situations. And this process continues up and up the hierarchy of the mind toward the
most general models a system could come up with, such as models of universe (scientific theories), models of self
(psychological concepts), models of meaning of existence (philosophical concepts), models of a priori transcendent
intelligent subject (theological concepts).
7.4. Conscious and unconscious
Why is there consciousness? Why would a feature like consciousness appear in the process of evolution? The
answer to this question seems clear: consciousness directs the will and results in a better adaptation for survival. In
simple situations, when only minimal adaptation is required, an instinct directly wired to action is sufficient, and
unconscious processes can efficiently allocate resources and will. However, in complex situations, when adaptation
is complicated, various instincts might contradict one another. Undifferentiated unconscious psychic functions result
in ambivalence and ambitendency; every position entails its own negation, leading to an inhibition. This inhibition
cannot be resolved by unconscious that does not differentiate among alternatives. Direction is impossible without dif-
ferentiation. Consciousness is needed to resolve an instinctual impasse by suppressing some processes and allocating
power to others. By differentiating alternatives, consciousness can direct a psychological function to a goal.
We are not conscious about most of organism functioning; blood flow, breathing, workings of heart and stomach
are unconscious, at least as long as they work as appropriate. The same is true about most of the processes in the
brain and mind. We are not conscious about fuzzy models competing for evidence in retinal signals, etc. We become
conscious about concepts, only during resonance, when a model-concept matches bottom-up signals and become crisp.
42 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
To put it more accurately, crisper models are better accessible by consciousness. In psychic functioning, evolutionary
directions and our personal goals are to increase consciousness. But, this is largely unconscious, because our direct
knowledge of ourselves is limited to consciousness. This fact creates a lot of confusion about consciousness. So, what
is consciousness?
Consciousness is an awareness or perception of inward psychological facts, a subjective experience of sensing,
feelings, or thoughts. This definition is taken from the Webster’s Dictionary. But, a more detailed, scientific analysis
of consciousness has proven to be difficult. For a long time it seemedobvious that consciousness completely pervades
our entire mental life, or at least its main aspects. Now, we know that this idea is wrong, and the main reason for this
misconception has been analyzed and understood: We are conscious only about what we are conscious of, and it is
extremely difficult to notice anything else.
Misconceptions about consciousness noted by Jaynes [110] include: consciousness is nothing but a property of
matter, or a property of living things, or a property of neural systems. These three “explanations” attempted to dismiss
consciousness as an epiphenomenon, an unimportant quality of something else. They are useless because the prob-
lem is in explaining the relationships of consciousness to matter, to life, and to neural systems. These dismissals of
consciousness are not very different from saying that there is no consciousness; but, of course, this statement refutes
itself (if somebody makes such a statement unconsciously, there is no point of discussing it). A dualistic position is
that consciousness belongs to the world of ideas and has nothing to do with the world of matter. But the scientific
problem is in explaining the consciousness as a natural-science phenomenon; that is to relate consciousness and the
material world. Searle [111] suggested that any explanation of consciousness has to account for it being real and based
on physical mechanisms in the brain. Among properties of consciousness requiring explanation he listed unity and
intentionality (we perceive our consciousness as being unified in the space of our perceptions and in the time of our
life; consciousness is about something; this “about” points to its intentionality).
In his book on consciousness, Searle [112] reviewed recent attempts to explain consciousness, and came to the con-
clusion that little progress was made during the 1990s. Penrose [5] suggested that consciousness cannot be explained
by known physical laws of matter. His arguments descend from Gödel’s proofs of inconsistency and incompleteness
of logic. We have already mentioned that this, however, only proves [28] that the mind is not a system of logical rules.
Knowledge of consciousness is primarily of introspective origin. Understanding of consciousness requires differen-
tiating conscious and unconscious psychic processes, so we need to understand what is psychic, what is unconscious,
and what is consciousness. Our experiences can be divided into somatic and psychic. A will modifying instinctual
reflexes indicates a presence of psyche, but not necessarily consciousness. Often, we associate consciousness with a
subjective perception of free will. Consciousness about somatic experiences is limited by the unknown in the outer
world. Similarly, consciousness about psychic experiences is limited by the unknown in psyche, or unconscious.
Roughly speaking, there are three conscious/unconscious levels of psychic contents:
(1) contents that can be recalled and made conscious voluntarily (memories);
(2) contents that are not under voluntary control, we know about them because they spontaneously irrupt into con-
sciousness; and
(3) contents inaccessible to consciousness.
We know about the latter through scientific deductions.
Consciousness is not a simple phenomenon, but a complicated differentiated process. Jung differentiated four types
of consciousness related to experiences of feelings (emotions), thoughts (concepts), sensations, and intuitions [42].
In addition to these four psychic functions, consciousness is characterized by the attitude: Introverted, concentrated
mainly on the inner experience, or extroverted, concentrated mainly on the outer experience. Interplay of various
conscious and unconscious levels of psychic functions and attitudes results in a number of types of consciousness;
interactions of these types with individual memories and experiences make consciousness dependent on the entire
individual experience producing variability among individuals. The reviewed theories of the mind only touched on
relationships between concepts and consciousness. An idea that better differentiated, crisper model-concepts are more
conscious is close to Jung’s views. Mechanisms of other types of consciousness are less understood and their mathe-
matical descriptions belong to future. Future research would also address emergence in evolution of different types of
consciousness, elaborating on Jungian ideas.
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 43
Totality and undividedness of consciousness are important adaptive properties needed to concentrate power on the
most important goal at every moment. This is illustrated, for example, by clinical cases of divided consciousness and
multiple personalities, resulting in maladaptation up to a complete loss of functionality. Simple consciousness needs
only to operate with relatively few concepts. Humans need more differentiation for selecting more specific goals in
more complex environment. The scientific quest is to explain these opposite tendencies of consciousness: how does
consciousness pursues undividedness and differentiation at once? There is no mystery, the knowledge instinct together
with the hierarchical structure of the mind hold the key to the answer. Whereas every level pursues differentiation,
totality belongs to the highest levels of the hierarchy. Future research will have to address these mechanisms in their
fascinating details.
Intentionality is a property of referring to something else, and consciousness is about something. This “aboutness”
many philosophers refer to as intentionality. In everyday life, when we hear an opinion we do not just collate it in our
memory and relate to other opinions (like a pseudo-scientist in a comedy); this would not lead very far. We wish to
know what are the aims and intentions associated with this opinion. Mechanisms of perceiving intent versus specific
words were studied by Valerie Reyna and Charles Brainerd, who discuss the contrast between gist and verbatim
systems of memory and decision making [113]. Often, we perceive the intent of what are said better then specific
words, even if the words are chosen to disguise the intent behind causal reasoning. The desire to know and the ability
to perceive the goal indicates that in psyche, final standpoint or purpose is more important than the causal one. This
intentionality of psyche was already emphasized by Aristotle in his discussions of the end cause of forms of the
mind [108]. Intentionality of consciousness is more fundamental than “aboutness”, it is purposiveness [114].
The intentional property of consciousness led many philosophers during the last decades to believe that intention-
ality is a unique and most important characteristic of consciousness: according to Searle, only conscious beings could
be intentional. But, the mechanism of the knowledge instinct leads to an opposite conclusion. Intentionality is a fun-
damental property of life: even a simplest living being is a result of long evolution and its every component, say a
gene, or a protein has a purpose and intent. In particular, every model-concept has evolved with an intent or purpose to
recognize a particular type of signal (event, message, concept) and to act accordingly (e.g., send recognition message
to other parts of the brain and to behavioral models). Aristotle was the first to explain the intentionality of the mind
this way; he argued that intentionality should be explained through the a priori contents of the mind [115]. Possibly,
future theoretical developments of mechanisms of the knowledge instinct will explain the minds intentionality and
purposiveness in its complexity.
Is there any specific relationship between consciousness and intentionality? If so, it is just the opposite of Searle’s
hypothesis of intentionality implying consciousness. Affective, subconscious, lower-bodily-level emotional responses
are concerned with immediate survival, utilitarian goals, and therefore are intentional in the most straightforward
way. A higher-intellectual-level consciousness is not concerned with the immediate survival, but with the overall
understanding of the world, with knowledge and beauty; it can afford to be impartial, abstract, and less immediately-
intentional than the rest of the psyche; its intentions might be directed toward meanings and purposes of life. As
we discuss few pages below, the highest creative aspect of individual consciousness and the abilities of perceiving
beautiful and sublime are intentional without any specific, lower-level utilitarian goal, they are intentional toward self-
realization, toward future-self beyond current-self. Due to the current mathematical theories reviewed in this article
we can more accurately manipulate these metaphorical descriptions to obtain solutions to long-standing philosophical
problems. In addition, we can identify directions for concrete studies of these metaphors in future mathematical
simulations and laboratory experiments.
Unity of consciousness refers to conscious mental states being parts of a unified sequence and simultaneous
conscious events are perceived as unified into a coherent picture. Searle’s unity is close to what Kant called “the
transcendental unity of apperception”. In MFT, this internal perception is explained as all perceptions, due to a prop-
erty of the special model involved in consciousness, called Ego by psychologists. The properties of Ego-model explain
the properties of consciousness. When certain properties of consciousness seem difficult to explain, we should follow
the example of Kant, we should turn the question around and ask: Which properties of Ego model would explain the
phenomenological properties of consciousness?
Let us begin the analysis of the structures of the Ego-model and the process of its adaptation to the constantly
changing world, from evolutionary-preceding simpler forms. What is the initial state of consciousness: an undifferen-
tiated unity or a “booming, buzzing confusion” [116]? Or, let us make a step back in the evolutionary development
and ask, what is the initial state of pre-conscious psyche? Or, let us move back even further toward evolution of
44 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
sensory systems and perception. When building a robot for a factory floor, why provide it with a sensor? Obviously,
such an expensive thing as a sensor is needed to achieve specific goals: to sense the environment with the purpose to
accomplish specific tasks. Providing a robot with a sensor goes together with an ability to utilize sensory data.
Similarly, in the process of evolution, sensory abilities emerged together with perception abilities. A natural
evolution of sensory abilities could not result in a “booming, buzzing confusion”, but must result in evolutionary
advantageous abilities to avoid danger, attain food, etc. Primitive perception abilities (observed in primitive animals)
are limited to few types of concept-objects (light-dark, warm-cold, edible-nonedible, dangerous-attractive ...) and are
directly “wired” to proper actions. When perception functions evolve further, beyond immediate actions, it is through
the development of complex internal model-concepts, which unify simpler object-models into a unified and flexible
model of the world. Only at this point of possessing relatively complicated differentiated concept-models composed
of a large number of sub-models, an intelligent system can experience a “booming, buzzing confusion”, if it faces
a new type of environment. A primitive system is simply incapable of perceiving confusion: It perceives only those
“things” for which it has concept-models and if its perceptions do not correspond to reality, it just does not survive
without experiencing confusion. When a baby is born, it undergoes a tremendous change of environment, most likely
without much conscious confusion. The original state of consciousness is undifferentiated unity. It possesses a single
modality of primordial undifferentiated Self-World.
The initial unity of psyche limited abilities of the mind, and further development proceeded through differentia-
tion of psychic functions or modalities (concepts, emotions, behavior); they were further differentiated into multiple
concept-models, etc. This accelerated adaptation. Differentiation of consciousness is a relatively recent process[110,
120].
Consciousness is about aspects of concept-models (of the environment, self, past, present, future plans, and alter-
natives) and emotions [117] to which we can direct our attention. As already mentioned, MFT explains consciousness
as a specialized Ego-model. Within this model, consciousness can direct attention at will. This conscious control of
will is called the free will. A subjective feeling of free will is a most cherished property of our psyche. Most of us
feel that this is what makes us different from inanimate objects and simple forms of life. And this property is a most
difficult one to explain rationally or to describe mathematically. But, let us see how far we can go towards understand-
ing this phenomenon. We know that raw percepts are often not conscious. As mentioned already, for example, in the
visual system, we are conscious about the final processing stage, the integrated crisp model, and unconscious about
intermediate processing. We are unconscious about eye receptive fields; about details of visual perception of motion
and color as far as it takes place in our brain separately from the main visual cortex, etc. [66]. In most cases, we are
conscious only about the integrated scene, crisp objects, etc.
These properties of consciousness follow from properties of concept-models, they have conscious (crisp) and un-
conscious (fuzzy) parts, which are accessible and inaccessible to consciousness, that is to Ego-model. In pre-scientific
literature about mechanisms of the mind there was a popular idea of homunculus, a little mind, inside our mind, which
perceived our perceptions and made them available to our mind. This naive view is amazingly close to actual scientific
explanation. The fundamental difference is that the scientific explanation does not need an infinite chain of homunculi
inside homunculi. Instead, there is a hierarchy of the mind models with their conscious and unconscious aspects. The
higher in the hierarchy, the less is the conscious differentiated aspect of the models. Until at the top of the hierarchy
there are mostly unconscious models of the meaning of our existence (which we discuss later).
Our internal perceptions of consciousness due to Ego-model “perceive” crisp conscious parts of other models
similar to models of perception “perceive” objects in the world. The properties of consciousness as we perceive them,
such as continuity and identity of consciousness, are due to properties of the Ego-model. What is known about this
“consciousness”-model? Since Freud, a certain complex of psychological functions was called Ego. Jung considered
Ego to be based on a more general model or archetype of Self. Jungian archetypes are psychic structures (models)
of a primordial origin, which are mostly inaccessible to consciousness, but determine the structure of our psyche.
In this way, archetypes are similar to other models, e.g., receptive fields of the retina are not consciously perceived,
but determine the structure of visual perception. The Self archetype determines our phenomenological subjective
perception of ourselves, and in addition, structures our psyche in many different ways, which are far from being
completely understood. An important phenomenological property of Self is the perception of uniqueness and in-
divisibility (hence, the word individual).
Consciousness, to a significant extent, coincides with the conscious part of the archetype-model of Self. A con-
scious part of Self belongs to Ego. Not everything within Ego (as defined by Freud) is conscious. Individuality as a
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 45
total character distinguishing an individual from others is a main characteristic of Ego. Not all aspects of individuality
are conscious, so, the relationships among the discussed models can be summarized to some extent, as:
Consciousness Individuality Ego Self Psyche.
Thesign“” here means “is a part of”. Consciousness-model is a subject of free will; it possesses, controls, and
directs free will. Free will is limited by laws of nature in the outer world and in the inner world by the unconscious
aspects of Self. Free will belongs to consciousness, but not to the conscious and unconscious totality of the psyche.
Clearly, much of the above discussion still has a long way to go to mathematical modeling and laboratory experimen-
tation; but it does not seem anymore as mystery beyond future physics of the mind.
Many contemporary philosophers consider subjective nature of consciousness to be an impenetrable barrier to
scientific investigation. Chalmers differentiated hard and easy questions about consciousness [118] as follows. Easy
questions, that will be answered better and better, are concerned with brain mechanisms: which brain structures are
responsible for consciousness? Hard questions, that no progress can be expected about, are concerned with the sub-
jective nature of consciousness and qualia, subjective feelings associated with every conscious perception. Nagel
described it dramatically with a question: “What is it like to be a bat?” [119] But I disagree. I do not think these
questions are hard. These questions are not mysteries; they are just wrong questions for a scientific theory. Newton,
while describing the laws of planet motion, did not ask: “What is it like to be a planet?” (even so, something like this
feeling is a part of scientific intuition). The subjective nature of consciousness is not a mystery. It is explained due
to the subjective nature of the concept-models that we are conscious of. The subjectivity is the result of combined a
priority and adaptivity of the consciousness-model, the unique genetic a priori structures of psyche together with our
unique individual experiences. I consider the only hard questions about consciousness to be free will and the nature
of creativity.
Let us summarize. Most of the mind’s operations are not accessible to consciousness. We definitely know that
neural firings and connections cannot be perceived consciously. In the foundations of the mind there are material
processes in the brain inaccessible to consciousness. Jung suggested that conscious concepts are developed by the
mind based on genetically inherited structures, archetypes, which are inaccessible to consciousness [42,120]. Gross-
berg [9] suggested that only signals and models attaining a resonant state (that is signals matching models) can reach
consciousness. It was further detailed by Taylor [121]; he related consciousness to the mind being a control mecha-
nism of the mind and body. A part of this mechanism is a prediction model. When this model predictions differ from
sensory observations, this difference may reach a resonant state, which we are consciousness about. To summarize
the above analyses, the mind mechanisms, described in MFT by dynamic logic and fuzzy models, are not acces-
sible to consciousness. Final results of dynamic logic processes, resonant states characterized by crisp models and
corresponding signals are accessible to consciousness.
7.5. Imagination
Imagination involves excitation of a neural pattern in a sensory cortex in absence of an actual sensory stimulation.
For example, visual imagination involves excitation of visual cortex, say, with closed eyes [9,66]. Imagination was
long considered a part of thinking processes; Kant [40] emphasized the role of imagination in the thought process,
he called thinking “a play of cognitive functions of imagination and understanding”. Whereas pattern recognition and
artificial intelligence algorithms of recent past would not know how to relate to this [3,4], Carpenter and Grossberg
resonance model [57] and the MFT dynamics both describe imagination as an inseparable part of thinking. Imagined
patterns are top–down signals that prime the perception cortex areas (priming is a neural terminology for making
neurons to be more readily excited). In MFT, the imagined neural patterns are given by models Mh.
Visual imagination, as mentioned, can be “internally perceived” with closed eyes. The same process can be math-
ematically modeled at higher cognitive levels, where it involves models of complex situations or plans. Similarly,
models of behavior at higher levels of the hierarchy can be activated without actually propagating their output signals
down to actual muscle movements and to actual acts in the world. In other words, behavior can be imagined, along
with its consequences, it can be evaluated, and this is the essence of plans. Sometimes, imagination involves detailed
alternative courses of actions considered and evaluated consciously. Sometimes, imagination may involve fuzzy or
vague, barely conscious models, which reach consciousness only after they converge to a “reasonable” course of ac-
tion, which can be consciously evaluated. From a mathematical standpoint, this latter mechanism must predominate,
46 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
conscious evaluation cannot involve all possible courses of action; it would lead to combinatorial complexity and
impasse. It remains to be proven in brain studies, which will identify the exact brain regions and neural mechanisms
involved.
In agreement with neural data, MFT adds details to Kantian description: thinking is a play of top–down higher-
hierarchical-level imagination and bottom–up lower-level understanding. Kant identified this “play” [described by
(3)–(6)] as a source of aesthetic emotion. Kant used the word “play”, when he was uncertain about the exact mecha-
nism; this mechanism, according to our suggestion, is the knowledge instinct and dynamic logic.
7.6. Bodily instincts and emotions
The functioning of the mind and brain cannot be understood in isolation from the system’s “bodily needs”. For
example, a biological system (and any autonomous system) needs to replenish its energy resources (eat). This and
other fundamental unconditional needs are indicated to the system by instincts and emotions. As we discussed, scien-
tific terminology in this area is still evolving; for our purpose of making a step toward uncovering neural mechanisms
of the mind, we describe instincts mathematically as internal sensors, which measurements directly indicate uncon-
ditional needs of an organism. For example, instinct for food measures sugar level in blood, and related emotional
signals are perceived by psyche as “hunger”; they activate behavioral models related to food searching and eating.
Bodily instinctual influences on workings of the mind modify the object-perception process (3)–(6) in such a way that
desired objects get enhanced recognition. This is the reason a hungry person “sees food all around”. In MFT it can
be accomplished by modifying priors, r(h) in Eqs. (2), (3) according to the degree to which an object of type hcan
satisfy a particular instinct [122]. Details of these mechanisms are not considered here.
7.7. Aesthetic emotions and the instinct for knowledge
Recognizing objects in the environment and understanding their meaning is so important for survival that a spe-
cial instinct evolved for this purpose. This instinct for learning and improving concept-models I call the instinct for
knowledge. In MFT it is described by maximization of similarity between the models and the world, Eq. (2).Emo-
tions related to satisfaction–dissatisfaction of this instinct are perceived by us as harmony–disharmony (between our
understanding of how things ought to be and how they actually are in the surrounding world). According to Kant [40]
these are aesthetic emotions (emotions that are not related directly to satisfaction or dissatisfaction of bodily needs).
The instinct for knowledge makes little kids, cubs, and piglets jump around and play fight. Their inborn models of
behavior must adapt to their body weights, objects, and animals around them long before the instincts of hunger and
fear will use the models for direct aims of survival. Childish behavior just makes the work of the knowledge instinct
more observable; to varying degrees, this instinct continues acting throughout our lives. All the time we are bringing
our internal models into correspondence with the world. In adult life, when our perception and understanding of the
surrounding world is adequate, aesthetic emotions are barely perceptible: the mind just does its job. Similarly, we do
not usually notice adequate performance of our breathing muscles and satisfaction of the breathing instinct. However,
if breathing is difficult, negative emotions immediately reach consciousness. The same is true about the knowledge
instinct and aesthetic emotions: if we do not understand the surroundings, if objects around do not correspond to
our expectations, negative emotions immediately reach consciousness. We perceive these emotions as disharmony
between our knowledge and the world. Thriller movies exploit the instinct for knowledge: they are mainly based on
violating our expectations; their personages are shown in situations, when knowledge of the world is inadequate for
survival.
Let me emphasize again, aesthetic emotions are not peculiar to art and artists, they are inseparable from every act
of perception and cognition. In everyday life we usually do not notice them. Aesthetic emotions become noticeable at
higher cognitive levels in the mind hierarchy, when cognition is not automatic, but requires conscious effort. Damasio
view [46] of emotions defined by visceral mechanisms, as far as discussing higher cognitive functions, seems erro-
neous in taking secondary effects for the primary mechanisms. People often devote their spare time to increasing their
knowledge, even if it is not related to their job and a possibility of promotion. Pragmatic interests could be involved:
knowledge makes us more attractive to friends and could help find sexual partners. Still, there is a remainder, a pure
joy of knowledge, aesthetic emotions satisfying the knowledge instinct.
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 47
7.8. Beautiful and sublime
Contemporary cognitive science is at a complete loss when trying to explain the highest human abilities, the most
important and cherished abilities to create and perceive beautiful and sublime experiences. Their role in the working
of the mind is not understood. MFT explains that simple harmony is an elementary aesthetic emotion related to
improvement of object-models. Higher aesthetic emotions are related to the development and improvement of more
complex “higher” models at higher levels of the mind hierarchy. The highest forms of aesthetic emotion are related
to the most general and most important models near the top of the hierarchy. According to Kantian analysis [40,123],
among the highest models are models of the meaning of our existence, of our purposiveness or intentionality, and
beauty is related to improving these models.
Models of our purposiveness are largely fuzzy and unconscious. Some people, at some points in their life, may
believe that their life purpose is finite and concrete, for example to make a lot of money, or build a loving family
and bring up good children. These models are aimed at satisfying powerful instincts, but not the knowledge instinct,
and they do not reflect the highest human aspirations. Everyone who has achieved a finite goal of making money
or raising good children knows that this is not the end of his or her aspirations. The reason is that everyone has an
ineffable feeling of partaking in the infinite, while at the same time knowing that our material existence is finite.
This contradiction cannot be resolved. For this reason models of our purpose and meaning cannot be made crisp and
conscious, they will forever remain fuzzy and partly unconscious.
Everyday life gives us little evidence to develop models of meaning and purposiveness of our existence. People
are dying every day and often from random causes. Nevertheless, life itself demands belief in one’s purpose; without
such a belief it is easier to get drunk or take drugs than to read this article. These issues are not new; philosophers and
theologists expounded them from time immemorial. The knowledge instinct theory gives us a scientific approach to
the eternal quest for the meaning. We perceive an object or a situation as beautiful, when it stimulates improvement of
the highest models of meaning. Beautiful is what “reminds” us of our purposiveness. This is true about perception of
beauty in a flower or in an art object. Just an example, R. Buckminster Fuller, an architect, best known for inventing
the geodesic dome wrote: “When I’m working on a problem, I never think about beauty. I think only how to solve the
problem. But when I have finished, if the solution is not beautiful, I know it is wrong.[124]. The MFT explanation
of the nature of beautiful helps understanding an exact meaning of this statement and resolves a number of mysteries
and contradictions in contemporary aesthetics [125,126].
The feeling of spiritually sublime is similar and different from beautiful. Whereas beautiful is related to improve-
ment of the models of cognition, sublime is related to improvement of the models of behavior realizing the highest
meaning in our life. Beautiful and sublime are not finite. MFT tells us that mathematically, improvement of complex
models is related to choices from infinite number of possibilities. A mathematician may consider 100100, or million
to the millionth power as a finite number. But for a physicist, a number that exceeds all elementary events in the life
of the Universe is infinite. A choice from infinity is infinitely complex and contains infinite information. Therefore,
choices of beautiful and sublime contain infinite information. This is not a metaphor, but exact mathematical fact.
Beauty is at once objective and subjective. It really exists, cultures and individuals cannot exist without the ability for
beauty, and still, it cannot be described by any finite algorithm or a set of rules.
Beauty of a physical theory discussed sometimes by physicists is similar in its infinity to beauty in an artwork. For
a physicist, beauty of a physical theory is related to improving the models of the meaning in our understanding of the
universe. This satisfies a scientist’s quest for the purpose, which he identifies with the purpose in the world.
7.9. Intuition
Intuitions include inner perceptions of object-models, imaginations produced by them, and their relationships with
objects in the world. They include also higher-level models of relationships among simpler models. Intuitions involve
fuzzy unconscious concept-models, which are in a state of being formed, learned, and being adapted toward crisp and
conscious models (say, a theory). Conceptual contents of fuzzy models are undifferentiated and partly unconscious.
Similarly, conceptual and emotional contents of these fuzzy mind states are undifferentiated; concepts and emotions
are mixed up. Fuzzy mind states may satisfy or dissatisfy the knowledge instinct in varying degrees before they become
differentiated and accessible to consciousness, hence the vague complex emotional-cognitive feel of an intuition.
Contents of intuitive states differ among people, but the main mechanism of intuition is the same among artists
48 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
and scientists. Composer’s intuitions are mostly about sounds and their relationships to psyche. Painter’s intuitions
are mostly about colors and shapes and their relationships to psyche. Writer’s intuitions are about words, or more
generally, about language and its relationships to psyche. Mathematical intuition is about structure and consistency
within a theory, and about relationships between the theory and a priori content of psyche. Physical intuition is about
the real world, first principles of its organization, and mathematics describing it.
7.10. Language, cognition, and symbols
Why is the word “symbol” used in such opposite ways: to denote trivial objects, like traffic signs or mathematical
notations, and also to denote objects affecting entire cultures over millennia, like Magen David, Cross, or Crescent?
Let us compare in this regard opinions of two founders of contemporary semiotics, Charles Peirce and Ferdinand
De Saussure. Peirce classified signs into symbols, indexes, and icons [127]. Icons have meanings due to resemblance
to the signified (objects, situations, etc.), indexes have meanings by direct connection to the signified, and symbols
have meaning due to arbitrary conventional agreements. Saussure used different terminology, he emphasized that the
sign receives meaning due to arbitrary conventions [128], whereas symbol implies motivation.
Both Peirce and Saussure wanted to understand the process in which signs acquire meanings. Both of them failed:
workings of the mind were not known at the time. Consider Peircian icons; they resemble objects or situations be-
cause of specific mechanisms of perception and recognition in our mind. These mechanisms should be analyzed and
understood as an essential part of meaning creation. Peircian assumption that icons in themselves resemble situations
in the world is too simplistic. Algorithms based on this assumption led to irresolvable difficulties related to combina-
torial complexity. Similarly, arbitrariness emphasized by Peirce and Saussure did not lead to algorithms of meaning
creation. Arbitrary signs have no grounding in real world. Meanings cannot be created by unmotivated choices on
the interconnections of arbitrary signs, this type of choices lead to combinatorial complexity. In infinite systems, they
lead to Gödelian contradictions. Similarly, mechanismsof meaning creation were not found by founders of “symbolic
artificial intelligence”, when they used the motivationally loaded word “symbol” for arbitrary mathematical notations.
Mathematical notations, just because they are called symbols, do not hold a key to the mystery of cultural and psy-
chological symbols. Multiple meanings of the word “symbol” misguided their intuition. This is an example of what
Wittgenstein called “bewitchment by language”.
The MF theory emphasizes that meaning creation consists in bringing unconscious into consciousness in the
process of model adaptation. This process is “motivated” by the instinct for knowledge. The motivated meaning cre-
ation, connecting conscious and unconscious, is consistent with Jungian explanations of the nature of symbols [120].
This motivates to use the word symbol for the processes of meaning creation,and to use the word sign for conventional
or nonadaptive entities. This corresponds to Pribram’s [129] interpretation of signs, as nonadaptive neural signals with
fixed meanings.
Meanings are created by symbol-processes in the mind. Language plays special role in these processes. Language
accumulates cultural knowledge of the world. Through communication among people, language provides grounding
for abstract model-concepts at higher levels in the mind hierarchy. The mechanism of this relationship between lan-
guage and cognition is joint language-cognitive models. These joint models are organized in parallel hierarchies of
language models (words, texts) and cognitive models (world representations in the mind). Near the bottom of these
hierarchies words refer to objects. Higher up, complex texts refer to complex situations. An amazing result of the
described mechanism is that words within texts refer to objects within situations, and this reference at higher lev-
els corresponds to the words-objects relationships at lower levels. Because of this multi-level hierarchical structure,
maintaining meaningful relationships throughout the hierarchy, language is a coherent structure and not a set of ar-
bitrary notations for arbitrary relationships. This meaning–maintaining hierarchy makes possible “the infinite use of
finite means”. We do not know to which extent the hierarchies are inborn or created by mechanisms, which construct
higher levels from lower ones. Brighton et al. [102] results could be interpreted in the following way: a higher level is
predicted from a lower one. Future research will study this conjecture in more details [105,130].
Cultural evolution results in selection and preservation in language of important meanings. Importance of meanings
of various models and texts is based in culture; meanings and their importance are “biased” by culture; these biases
constitute culture. But the deconstruction idea that meanings are arbitrary is unscientific. Scientific quest is to explain
creation of meanings and the reviewed research makes steps in this direction.
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 49
A symbol-process involves conscious and unconscious, concepts and emotions, inborn models-archetypes and
models learned from culture, language, and cognition. Symbol processes continue up and up the hierarchy of models
and mind toward the most general models. Due to language, they continue in culture through many generations. In
semiotics this process is called semiosis, a continuous process of creating and interpreting the world outside (and
inside our mind). Symbols are processes creating meanings.
7.11. Creativity, differentiation, and synthesis
Creativity is an ability to improve and create new model-concepts. In a small degree it is present in everyday per-
ception and cognition. Usually the words “creativity”, “creative”, or “discovery” are applied to improving or creating
new model-concepts at higher cognitive levels, concepts that are important for the entire society or culture. A crisp
and specific model could only match a specific content; therefore it cannot lead to creation of new contents. Creativity
and discovery, according to Section 5, involve vague, fuzzy models, which are made more crisp and clear. It occurs,
therefore, at the border between consciousness and unconscious. A similar nature of creative process, involving con-
sciousness and unconscious, was discussed by Jung [120]. Creativity usually involves intuition, as discussed above:
fuzzy undifferentiated feelings-concepts.
Creativity is driven by the knowledge instinct. Two main mechanisms of creativity, the components of the knowl-
edge instinct, are differentiation and synthesis. Differentiation is a process of creating new, more specific and more
detailed concept-models from simpler, less differentiated and less conscious models. Mathematical mechanisms of
differentiation were discussed in Section 5. The role of language in differentiation of cognition was discussed in
Section 6, as mentioned, this research is in its infancy and a subject of future research.
Synthesis is a process of connecting detailed crisp concept-models to the unconscious, instincts, and emotions.
The need for synthesis comes from the fact that most of our concept-models are acquired from language. The entire
conceptual content of the culture is transmitted from generation to generation through language; cognitive concept-
models cannot be transmitted directly from brain to brain. Therefore, concepts acquired from language have to be used
by individual minds to create cognitive concepts. The mechanism of integrating cognition and language, discussed in
Section 6, explains that language concepts could be detailed and conscious; but not necessarily connected to equally
detailed cognitive concepts, to emotions, and to the knowledge instinct. Connecting language and cognition involves
differentiating cognitive models, developing cognitive models, whose differentiation and consciousness approaches
that of language models. Every child acquires language between one and seven, but it takes the rest of life to connect
abstract language models to cognitive concept-models, to emotions, instincts, and to the life’s needs. This is the process
of synthesis; it integrates language and cognition, concepts and emotions, conscious and unconscious, instinctual and
learned. Current research directions discussed in Section 6are just touching on these mechanisms of synthesis. It is
largely an area for future research.
Another aspect of synthesis, essential for creativity, is developing a unified whole within psyche, a feel and intuition
of purpose and meaning of existence. It is necessary for concentrating will, for survival, for achieving individual goals,
and in particular for satisfying the knowledge instinct by differentiating knowledge. Concept-models of purpose and
meaning, as discussed are near the top of the mind hierarchy; they are mostly unconscious and related to feelings
of beautiful and sublime. A condition of synthesis is correspondence among a large number of concept-models.
A knowledge instinct as discussed in Section 5is a single measure of correspondence between all the concept-models
and all the experiences-data about the world. This is, of course, a simplification. Certain concept-models have high
value for psyche (e.g., family, success, certain political causes) and they affect recognition and understanding of other
concepts. This is a mechanism of differentiation of the knowledge instinct. Satisfaction of the knowledge instinct
therefore is not measured by a single aesthetic emotion, but by a large number of aesthetic emotions. The entire
wealth of our knowledge should be brought into correspondence with itself, this requires a manifold of aesthetic
emotions. Differentiation of emotions is performed by music [126], but this is beyond the scope of the review.
There is an opposition between differentiation and synthesis in individual minds as well as in the collective psyche.
This opposition leads to complex evolution of cultures. Differentiated concepts acquire meaning in connections with
instinctual and unconscious, in synthesis. In evolution of the mind, differentiation is the essence of the development
of the mind and consciousness, but it may bring about a split between conscious and unconscious, between emotional
and conceptual, between language and cognition. Differentiated and refined models existing in language may loose
connection with cognitive models, with people’s instinctual needs. If the split affects collective psyche, it leads to a loss
50 L.I. Perlovsky/ Physics of Life Reviews 3 (2006) 23–55
of the creative potential of a community or nation. This was the mechanism of death of great ancient civilizations.
The development of culture, the very interest of life requires combining differentiation and synthesis. Evolution of the
mind and cultures is determined by this complex nonlinear interaction: One factor prevails, then another [126].This
is an area for future research.
7.12. Teleology, causality, and the knowledge instinct
Teleology explains the Universe in terms of purposes. In many religious teachings, it is a basic argument for the
existence of God: If there is purpose, an ultimate Designer must exist. Therefore, teleology is a hot point of debates
between creationists and evolutionists: Is there a purpose in the world? Evolutionists assume that the only explanation
is causal. Newton laws gave a perfect causal explanation for the motion of planets: A planet moves from moment
to moment under the influence of a gravitational force. Similarly, today science explains motions of all particles and
fields according to causal laws, and there are exact mathematical expressions for fields, forces and their motions.
Causality explains what happens in the next moment as a result of forces acting in the previous moment. Scientists
accept this causal explanation and oppose to teleological explanations in terms of purposes. The very basis of science,
it seems, is on the side of causality, and religion is on the side of teleology.
However, at the level of the first physical principles this is wrong. The contradiction between causality and teleology
does not exist at the very basic level of fundamental physics. The laws of physics, from classical Newtonian laws to
quantum superstrings, can be formulated equally as causal or as teleological. An example of teleological principle
in physics is energy minimization, particles move so that energy is minimized. As if particles in each moment know
their purpose: to minimize the energy. The most general physical laws are formulated as minimization of action.
Action is a more general physical entity than energy; it is an intuitive name for a mathematical expression called
Lagrangian. Causal dynamics, motions of particles, quantum strings, and superstrings are determined by minimizing
Lagrangian-action [131]. A particle under force moves from point to point as if it knows its final purpose, to minimize
Lagrangian-action. Causal dynamics and teleology are two sides of the same coin.
The knowledge instinct is similar to these most general physical laws: evolution of the mind is guided by maximiza-
tion of knowledge. A mathematical structure of similarity (2) or its continuous version [59] is similar to Lagrangian,
and it plays a similar role; it bridges causal dynamic logic of cognition and teleological principle of maximum
knowledge. Similarly to fundamental physics, dynamics and teleology are equivalent: Dynamic logic follows from
maximization of knowledge and vice versa. Ideas, concept-models change under the “force” of dynamic logic, as
if they know the purpose: Maximum knowledge. One does not have to choose between scientific explanation and
teleological purpose: Causal dynamics and teleology are equivalent.
7.13. Mind and brain, experimental evidence
Historically, the mind is described in psychological and philosophical terms, whereas the brain is described in
terms of neurobiology and medicine. Within scientific exploration the mind and brain are different description levels
of the same system. Establishing relationships between these descriptions is of great scientific interest. Today we
approach solutions to this challenge [132], which eluded Newton in his attempt to establish physics of “spiritual
substance” [133]. Detailed discussion of established relationships between the mind and brain is beyond the scope of
this review. We briefly mention the main known and unknown facts and give references for future reading. Adaptive
modeling abilities are well studied with adaptive parameters identified with synaptic connections [134]; instinctual
learning mechanisms have been studied in psychology and linguistics [68,76,98,135]. General neural mechanisms of
the elementary thought process (which are similar in MFT and ART [57]) include neural mechanisms for bottom–up
(sensory) signals, top–down imagination model-signals, and the resonant matching between the two; these have been
confirmed by neural and psychological experiments [136]. Ongoing research address relationships between neural
processes and consciousness [121,132,137]. Relating MFT to brain mechanisms in details is a subject of ongoing and
future research.
7.14. Predictions and testing
Ongoing and future research will confirm, disprove, or suggest modifications to specific mechanisms considered
in Sections 5 and 6. These mechanisms include model parameterization and parameter adaptation, reduction of fuzzi-
L.I. Perlovsky / Physics of Life Reviews 3 (2006) 23–55 51
ness during learning, and the similarity measure described by Eq. (2) as a foundation of the knowledge instinct and
aesthetic emotion. Other mechanisms include on one hand, relationships between psychological and neural mecha-
nisms of learning and, on the other hand, aesthetic feelings of harmony and emotions of beautiful and sublime. Future
research will also investigate the validity of the dual integrated structure of model-concepts described by Eq. (9) as
a foundation for interaction between cognition and language and for symbolic ability. A step in this direction will be
to demonstrate in simulations that this mechanism actually integrates cognition and language without combinatorial
complexity. Specific neural systems will need to be related to mathematical descriptions as well as to psychological
descriptions in terms of subjective experiences and observable behavior. Ongoing simulation research addresses the
evolution of models jointly with the evolution of language [138]. Also being investigated are the ways that MFT and
the knowledge instinct relate to behavioral psychology and to the specific brain areas involved in emotional reward
and punishment during learning [139]. Interesting unsolved problems include: detailed mechanisms of interactions be-
tween cognitive hierarchy and language hierarchy [60,61]; differentiatedforms of the knowledge instinct, the infinite
variety of aesthetic emotions perceived in music, their relationships to mechanisms of synthesis [126]; and interactions
of differentiation and synthesis in the development of the mind during cultural evolution. Future experimental research
will need to examine, in detail, the nature of hierarchical interactions, including mechanisms of learning hierarchy, to
what extent the hierarchy is inborn vs. adaptively learned, and the hierarchy of the knowledge instinct.
Acknowledgements
It is my pleasure to thank people whose thoughts, ideas, encouragement, and support shaped this review: R. Brock-
ett, G. Carpenter, A. Chernyakov, R. Deming, V. Dmitriev, F. Fontanari, M. Frank-Kamenetskii, W. Freeman, K. Fuku-
naga, L. Garvin, I. Ginzburg, R. Gudwin, S. Greineder, S. Grossberg, M. Karpovsky, S. Kashin, D. Levine, L. Levitin,
R. Linnehan, T. Luginbuhl, A. Meystel, S. Middleton, K. Moore, C. Mutz, A. Ovsich, R. Payne, N. Pechersky,
I. Perlovsky, V. Petrov, C. Plum, J. Rumer, E. Schakhnovich, W. Schoendorf, N. Shokhirev, J. Sjogren, D. Skatrud,
R. Streit, E. Taborsky, I. Ternovsky, T. Ternovsky, E. Tichovolsky, B. Weijers, D. Vinkovetsky, Y. Vinkovetsky, P. Wer-
bos, M. Xiarhos, L. Zadeh, G. Zainiev. I am thankful to anonymous referees for many suggestions that benefited this
review.
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describe mathematically as a continuous flow of signals, for example, a flow of visual stimuli in time and space; then, it is convenient instead
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... Generally, the emotions can be divided into basic emotions which include fear, anger, fear, sadness, joy, and another sets that are considered as the specialization of the basic emotions, for examples elation, regret, pride, shame (Bonala, 2009). Emotions can be described as an excessive expression of feelings which can be expressed both mentally and physically (Perlovsky, 2006). It can also be considered as a situation where thought and physiology are intimately intertwined affecting one's overall judgments. ...
... Generally, the emotions can be divided into basic emotions which include fear, anger, fear, sadness, joy, and another sets that are considered as the specialization of the basic emotions, for examples elation, regret, pride, shame (Bonala, 2009). Emotions can be described as an excessive expression of feelings which can be expressed both mentally and physically (Perlovsky, 2006). It can also be considered as a situation where thought and physiology are intimately intertwined affecting one's overall judgments. ...
... Generally, the emotions can be divided into basic emotions which include fear, anger, fear, sadness, joy, and another sets that are considered as the specialization of the basic emotions, for examples elation, regret, pride, shame (Bonala, 2009). Emotions can be described as an excessive expression of feelings which can be expressed both mentally and physically (Perlovsky, 2006). It can also be considered as a situation where thought and physiology are intimately intertwined affecting one's overall judgments. ...
... One possibility, predicated on a number of theories from the (neuro)aesthetics literature, is that the perceptual models we survey may in effect be placeholders for principled instantiations of the perceptual or representational 'priors' [60][61][62] that guide most quotidian activity. In this formulation, the distinctiveness of beautiful images is deviation from commonly held perceptual priors, and is thus a form of a perceptual 'surprise' -enough to trigger learning, but not so incommensurately out-of-domain as to be uninterpretable [63][64][65][66][67]. Another possibility, predicated on seminal work in 'affective prediction' [3] and 'micro-valences' [68], is that the perceptual models we survey may contain statistical proxies of common value. ...
Article
To propose a mathematical model of consciousness and will, we first simulated the inverted qualia with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia on the neural network. In other words, the qualia were individual-dependent and considered difficult as an indicator of consciousness and will. To solve that difficulty, we introduce a probability space and a random variable into a set of qualia and define a human language for events. Based on this idea of human language, consciousness and will are modeled. In this proposal, future actions are randomly selected from the comparison between "recognition of events" by external observation and past episodic memory, and the actual "recognition of actions" is regarded as the occurrence of consciousness. The basic formula is also derived. This proposal is compared with other past philosophical discussions.
Thesis
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L’objectif de la thèse est de valider la pertinence concrète d’un exercice de pensée consistant à lire les simulations de gestion de crise comme un jeu (Henriot 1983, 1989), et à identifier les manifestations ludiques et les leviers pour agir sur eux, à travers un protocole d’observation qui limite les risques de surimposer la catégorie mentale du jeu là où elle n’a pas sa place (Harviainen 2013).En effet, la capacité des jeux à servir une ambition pédagogique est bien établie (Winnicott 1975, Piaget 1945, Brougère 1995, Daniau 2005, Alvarez 2007, Hamayon 2012, 2015), et les simulations et les jeux sont désormais courants en matière de préparation à la gestion de crise. IMT Mines d’Alès développe depuis des années un simulateur pédagogique de cellule communale de gestion de crise (Tena-Chollet 2012, Lapierre 2016, Limousin 2017, Frealle 2018, Sauvagnargues et al. 2019). Pendant 2 à 6 heures, une dizaine de participants sont placés dans une situation de crise virtuelle et doivent recueillir des informations qui leur permettent de comprendre la situation et ses évolutions, prendre les décisions et délivrer des instructions à des opérateurs susceptibles d’agir sur le terrain, et ce, en résistant au stress, à la pression d’autorités supérieures et aux médias.Le parti-pris de la thèse est de cerner au mieux la nature ludique de la simulation de gestion de crise, malgré le fait que l’engagement des participants dans le jeu n’est pas totalement conscient (Huizinga 1938, Caillois 1958). Nous proposons le concept de ‘’ludicité’’, pour désigner les manifestations d’une attitude ludique (Henriot 1989) dans une situation qui n’est pas déclarée comme étant un jeu.Nous mettons au point un protocole d’observation de la ludicité mobilisant toute une palette d’instruments permettant d’observer ce qui se joue dans plusieurs simulations. La vidéo-analyse qualitative (Knoblauch 2012) des effusions émotionnelles (Goffman 1961) qui libèrent une tension entre la simulation et la réalité qui lui sert de modèle, y tient une place centrale en lien avec une typologie en vingt-six manifestations d’attitudes ludiques prévisibles (Franck 2012, Kapp 2013, Suits 2014, etc).L’analyse permet de confirmer que la ludicité se trouve bien dans les simulations elles-mêmes, et pas simplement dans le regard de l’observateur, et de valider la pertinence de la typologie proposée et l’efficacité du protocole mis au point. Elle met également en évidence des structures de l’espace-temps ludique ainsi que l’existence de fonctions ludiques activant la dynamique de jeu au sein de la mécanique de la simulation (Van Gennep 1909, Harviainen 2012). Elle explore enfin les émotions éprouvées (Pelissolo 2007), notamment les plaisirs ludiques et ce que les joueurs mettent en jeu durant la simulation, entre engagement et distance (Mermet & Zaccaï-Reyners 2015), entre ludicité et lucidité.A l’issue de ce travail, les limites du protocole d’observation sont discutées, et les moyens d'activer les cadres ludiques de la simulation (Lieberoth 2015) sans dénaturer la simulation sont envisagés.
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