INTEGRATING LANGUAGE AND COGNITION NEW RESULTS IN COMPUTATIONAL INTELLIGENCE Leonid Perlovsky Technical Advisor, AFRL International Joint Conference on Neural Networks (IJCNN) July 2005 "The lecture material in this book is intended for strictly limited distribution to IJCNN2005 tutorial attendees only. This work is copyrighted by the tutorial speaker(s). No duplication of this work is permitted without the written consent of the author."

OUTLINE 1. Cognition 2. Modeling Field Theory (MFT) 3. Integration of cognition and language 4. Prolegomena to a theory of the mind 5. Evolution of language and culture (future directions)

DETAILED OUTLINE 1. Cognition – integration of real-time signals and a priori knowledge 1.1. physics and mathematics of the mind 1.2. genetic argument for the first principles 1.3. the nature of understanding “chair” hierarchy 1.4.combinatorial complexity (CC) – a fundamental problem? 1.5. CC since 1950s 1.6. CC vs. logic formal, multivalued and fuzzy logics fuzzy dynamic logic Aristotle vs. Russell: 1.7. mathematics vs. mind 1.8.structure of the mind: concepts, instincts, emotions, behavior 1.9. instinct for knowledge need for learning “knowledge emotion” = aesthetic emotion 2. Modeling Field Theory (MFT) of cognition 2.1. Instinct for knowledge = max similarity 2.2. Similarity as likelihood, as information 2.3. Dynamic Logic (DL) 2.4. Exersices, applications Recognition Tracking and CRB Fusion Prediction 2.5. Block-Diagrams 2.6. Example: patterns in images pattern with and without noise models finding pattern in noise, one object finding pattern in noise, three objects computational complexity: MFT vs. MHT 2.7. Hierarchical structure

DETAILED OUTLINE CONTINUATION 3.1. Language Language acquisition and complexity Language separate from cognition Hierarchy of language Application: search engine based on understanding 3.2. MFT of language Differentiating non-differentiable qualitative functions 4. Integration of cognition and language 4.1. Language vs. cognition 4.2. Past: AI and Chomskyan linguistics 4.3. Integrated models 4.4. Humboldt’s inner linguistic form 5. Prolegomena to a theory of the mind 5.1. Why mind and emotions? 5.2. From Plato to Lock 5.3. From Kant to Grossberg 5.4. MFT vs. Buddhism 5.5. MFT vs. biology 5.5. MFT dynamics: elementary thought process 5.6. Consciousness and unconscious 5.7. Cognition and understanding 5.8. MFT as multi-agent system 5.9.Semiotics: signs and symbols MFT theory of symbols Symbolic AI 5.10.Aesthetic emotions Beauty Intuition 6. Evolution of Culture 6.1. Origin and evolution of language 6.2. Evolution of concepts Split between conceptual and emotional 6.3. Creativity 6.4. Disintegration of cultures 6.5. Terrorist’s consciousness 6.6. Synthesis Mathematics of synthesis 6.7. Differentiation of emotions 6.8 Role of music in evolution of the mind 7.Publications

COGNITION Integration of real-time signals and existing (a priori) knowledge –From signals to concepts –From less knowledge to more knowledge

COGNITION Example: “this is a chair, it is for sitting” Understanding signals (visual, acoustic, text) –Identify objects in signals signals -> concepts; or sounds -> words –Associate objects with prior knowledge and with behavior chair is for sitting What in the mind help us do this? Representations, models, ontologies? –What are the nature of representations in the mind? –There are wooden chairs in the world, but no wood in the brain

COMBINATORIAL COMPLEXITY A FUNDAMENTAL PROBLEM? Cognition and language involve evaluating large numbers of combinations Associate pixels or samples into objects –A general problem Recognition, tracking, fusion, language… Combinatorial Complexity (CC): –Combinations of 100 elements are –This number ~ the size of the Universe all the events in the Universe during its entire life

COMBINATORIAL COMPLEXITY SINCE the 1950s CC was encountered for over 50 years Statistical pattern recognition and neural networks: CC of learning requirements Rule systems and AI, in the presence of variability: CC of rules –Minsky 1960s: Artificial Intelligence –Chomsky 1957: language mechanisms are rule systems Model-based systems, utilizing adaptive models: CC of computations (N and NP complete) –Chomsky 1981: language mechanisms are model-based (rules and parameters Current ontologies, “semantic web” are rule-systems –Evolvable ontologies will lead to CC

CC AND TYPES OF LOGIC CC is related to formal logic –Law of excluded third every logical statement is either true or false –There is no similarity measure between logical statements “between any two logical statement another one can fit” –CC is Gödel's “incompleteness” in a finite system Multivalued logic eliminated the “law of excluded third” –Still, it was based on the math. of formal logic –Excluded 3rd -> excluded (n+1) Fuzzy logic eliminated the “law of excluded third” –Fuzzy logic systems are either too fuzzy or too crisp –Adapt fuzziness for every statement at every step => CC

FUZZY DYNAMIC LOGIC Fuzzy dynamic logic –based on a similarity between models and signals / data Dynamic Logic unifies formal and fuzzy logic –initial “fuzzy model-concepts” dynamically evolve into “formal-logic or crisp model-concepts” Overcomes CC of model-based recognition –fast algorithms

ARISTOTLE VS. GÖDEL forms, logic, and language Aristotle –Logic: a supreme way of argument –Forms: representations in the mind Form-as-potentiality evolves into form-as-actuality Logic is valid for actualities, not for potentialities (Dynamic Logic) –Thought language and thinking to be closely linked Warned not to use overly precise statements in logic Language contains the necessary uncertainty From Boole to Russell: formalization of logic –Logicians eliminated from logic uncertainty of language –Hilbert: formalize rules of mathematical proofs forever Gödel (the 1930s) –Logic is not consistent Any statement can be proved true and false Aristotle and Alexander the Great

OUTLINE Cognition -Logic did not work, but the mind does -Structure of the mind Modeling Field Theory (MFT) of cognition Language Integration of cognition and language Prolegomena to a theory of the mind Future directions

STRUCTURE OF THE MIND Concepts –Models of objects, their relations, and situations –Evolved to satisfy instincts Instincts –Internal sensors (e.g. sugar level in blood) Emotions –Neural signals connecting instincts and concepts e.g. a hungry person sees food all around Behavior –Models of goals (desires) and muscle-movement… Hierarchy –Concept-models and behavior-models are organized in a “loose” hierarchy

THE KNOWLEDGE INSTINCT Model-concepts always have to be adapted –lighting, surrounding, new objects and situations –even when there is no concrete “bodily” needs Instinct for knowledge and understanding –Increase similarity between models and the world Emotions related to the knowledge instinct –Satisfaction or dissatisfaction change in similarity between models and world –Related not to bodily instincts harmony or disharmony (knowledge-world): aesthetic emotion

REASONS FOR PAST LIMITATIONS The basis of human intelligence is in combining conceptual understanding with emotional evaluation A long-standing cultural belief that emotions are opposite to thinking and intellectually inferior –“Stay cool to be smart” –Socrates, Plato, Aristotle –Reiterated by founders of Artificial Intelligence [Newell, Minsky]

OUTLINE Cognition – integration of real-time signals and a priori knowledge Modeling Field Theory (MFT) of cognition -Mathematics of MFT -Examples and applications: recognition, tracking, fusion, prediction Integration of cognition and language Prolegomena to a theory of the mind Future directions

Modeling Field Theory (MFT) A mathematical construct modeling the mind –A loose hierarchy of more and more general concepts –At every level: concepts, emotions, models, behavior –Top-down and bottom-up signals

MODELING FIELDS one layer in a MF hierarchy: from signals to objects Bottom-up signals –Pixels or samples (from sensor or retina) x(n), n = 1,…,N Top-Down, concept-models (objects…) M m (S m,n), parameters S m, m = 1, …; –Models predict expected signals from objects Goal: learn object-models and understand signals (knowledge instinct) –associate signals n with models m and find parameters S m –learn signal-contents of objects (and object properties)

THE KNOWLEDGE INSTINCT Knowledge instinct = maximization of similarity between signals and models Similarity between signals and models, L –L = l ({x}) = l (x(n)) –l (x(n)) = r(m) l (x(n) | M m (S m,n)) –l (x(n) | M m (S m,n)) is a conditional similarity for x(n) given m {n} are not independent, M(n) may depend on n’ CC: L contains M N items: all associations of pixels and models

DYNAMIC LOGIC (DL) non-combinatorial solution Start with a set of signals and unknown object-models –any parameter values S m –associate object-model with its contents (signal composition) –(1)f(m|n) = r(m) l (n|m) / r(m') l (n|m') Improve parameter estimation –(2)S m = S m +  f(m|n) [  ln l (n|m)/  M m ]*[  M m /  S m ] (  determines speed of convergence) –learn signal-contents of objects Continue iterations (1)-(2). Theorem: MF is a converging system - similarity increases on each iteration - aesthetic emotion is positive during learning

OUTLINE Cognition Modeling Field Theory (MFT) -Mathematics of MFT -Examples Integration of cognition and language Prolegomena to a theory of the mind Future directions

EXAMPLE FINDING PATTERNS IN IMAGES

DIFFICULTY: SIGNAL BELOW NOISE Object Image y Object Image + Noise y x x

Multiple Hypothesis Testing (MHT) approach: try all possible ways of fitting model to the data PRIOR STATE-OF-THE-ART Computational complexity For a 100 x 100 pixel image: Number of Objects Number of Computations

DL FINDS OBJECT BELOW CLUTTER Y X SNR = -2.0 dB

DYNAMIC LOGIC EXAMPLE y (m) Range x (m) Cross-range DL starts with uncertain knowledge, and similar to human mind does not sort through all possibilities, but converges rapidly on exact solution Object invisible to human eye By integrating data with the knowledge-model DL finds an object below noise

Three objects in noise object 1 object 2 object 3 SNR dB dB dB MULTIPLE OBJECT DETECTION y y x x 3 Object Image + Clutter3 Object Image

MULTIPLE TARGET DETECTION DL WORKING EXAMPLE x y DL starts with uncertain knowledge, and similar to human mind does not sort through all possibilities like an MHT, but converges rapidly on exact solution

COMPUTATIONAL REQUIREMENTS COMPARED Dynamic Logic (DL) vs. Classical State-of-the-art Multiple Hypothesis Testing (MHT) Based on 100 x 100 pixel image 10 8 vs x10 8 vs x10 8 vs Number of Objects Number of Computations DL vs. MHT Previously un-computable ( ), can now be computed ( 3x10 8 ) This pertains to many complex information-finding problems

OTHER ASPECTS OF COGNITION Many applications were developed -Recognition -Signal Processing -Spectrum Estimation -Inverse Scattering -Tracking -Fusion -Search Engines -Bioinformatics -Prediction Each application requires appropriate models

MFT/DL SENSOR FUSION Difficult part: association of data among sensors –Which sample in one sensor corresponds to which sample in another sensor? MFT/DL for sensor fusion requires no new conceptual development Multiple sensor data require multiple sensor models –Data: n -> (s,n); X(n) -> X(s,n) –Models M m (n) -> M m (s,n) Note: this solves the difficult problem of concurrent detection, tracking, and fusion

FINANCIAL PREDICTION Data are available for free Difficulty: too many parameters –Markets * instruments ~ 100 to 1000 –Time intervals ~ *10 –Predictions in shortest time, estimate hundreds of parameters from few data points, impossible? Select few best variables for each single prediction Predicted crash following 9/11

MFT/DL FOR COGNITION SUMMARY Cognition –Integrating knowledge and signals Knowledge = concepts = models Knowledge instinct = similarity(models, data) Aesthetic emotion = change in similarity Emotional intelligence –combination of conceptual knowledge and emotional evaluation Applications –Recognition, tracking, fusion, bioinformatics, prediction

MFT HIERARCHICAL STRUCTURE At every level of hierarchy –Bottom-up signals are lower-level-concepts –Top-down signals are concept-models –Behavior-actions (including adaptation) Similarity measures Models Action/Adaptation Models Action/Adaptation Similarity measures

OUTLINE Cognition Modeling Field Theory and Dynamic Logic Integration of cognition and language Prolegomena to a theory of the mind Future directions

LANGUAGE WORDS, CONCEPTS AND GOALS Language is a hierarchy –Sounds or letters, words, phrases,… Models (e.g. phrases made up of words) –Simplistic “bag”-model a set or collection of words –More complex real-language models Modeling Fields and DL of language

LANGUAGE AND COMPLEXITY Chomsky: linguistics should study the mind mechanisms of language (1957) Chomsky’s language mechanisms –In forefront of mathematical ideas at the time time –1957: rule-based –1981: model-based (rules and parameters) –1995: minimalist, language and cognition Pinker: language instinct (the 1990s) Kirby: language evolution (2002) Combinatorial complexity –For the same reason as all rule-based and model-based methods

INTEGRATION OF COGNITION AND LANGUAGE Human mind is the only example of language and abstract cognition –Possibly they are only possible together –Cognition does not exist without communication? Past attempts based on logic did not work –We are conscious about “final results” of language mechanisms ~ logical concepts –We are not conscious about fuzzy mechanisms involved in language Future: sub-conceptual, sub-conscious integration

INTEGRATED LANGUAGE AND COGNITION Where language and cognition come together? –A fuzzy concept m has linguistic and cognitive-sensory models M m = { M m sensory,M m linguistic }; –language and cognition are fused at fuzzy pre-conceptual level before concepts are learned Understanding language and sensory data –Initial models are fuzzy blobs –linguistic models have empty “slots” for cognitive model (objects and situations) and v.v. –language participates in cognition and v.v. L & C help learning and understanding each other –help associating signals, words, models, and behavior

INNER LINGUISTIC FORM HUMBOLDT, the 1830s In the 1830s Humboldt discussed two types of linguistic forms –words’ outer linguistic form (dictionary) – a formal designation –and inner linguistic form (???) – creative, full of potential This remained a mystery for rule-based AI, structural linguistics, Chomskyan linguistics –rule-based approaches using the mathematics of logic make no difference between formal and creative In MFT / DL there is a difference –static form of learned (converged) concept-models –dynamic form of fuzzy concepts, with creative learning potential, emotional content, and unconscious content

OUTLINE Cognition Modeling Field Theory (MFT) of cognition Language Integration of cognition and language Prolegomena to a theory of the mind Future directions

WHY MIND AND EMOTIONS? A lot about the mind can be explained: concepts, instincts, emotions, conscious and unconscious, intuition, aesthetic ability,… –but, isn’t it sufficient to solve mathematical equations or to code a computer and execute the code? A simple yet profound question –the answer is in history and practice of science –Newton laws do not contain all of the classical mechanics –Maxwell equations do not exhaust radars and radio-communication –a physical intuition about the system is needed –an intuition about MFT was derived from biological, linguistic, cognitive, neuro-physiological, and psychological insights into human mind Practical engineering applications of DLA require biological, linguistic, cognitive, neuro-physiological, and psychological insights in addition to mathematics

MF DYNAMICS A large number of model-concepts compete for incoming signals Uncertainty in models corresponds to uncertainty in associations f(m|n) Eventually, one model (m') wins a competition for a subset {n'} of input signals Upon convergence, all input signals {n} are divided into subsets, each associated with one model-object Fuzzy a priori concepts (unconscious) become crisp concepts (conscious) –dynamic logic, Aristotelian forms, Jungian archetypes, Grossberg resonance Elementary thought process

CONSCIOUSNESS AND UNCONSCIOUS Jung: conscious concepts and unconscious archetypes Grossberg: models attaining a resonant state (winning the competition for signals) reach consciousness MFT: fuzzy mechanisms (DL) are unconscious, crisp concept-models, adapted and matched to data are conscious

SYMBOL “A most misused word in our culture” (T. Deacon) Cultural and religious symbols –Provoke wars and make piece Traffic Signs

SIGNS AND SYMBOLS Signs: stand for something else –non-adaptive entities (mathematics, AI) –brain signals insensitive to context (Pribram) Symbols –general culture: deeply affect psyche –psychological processes connecting conscious and unconscious (Jung) –brain signals sensitive to context (Pribram) –signs (mathematics, AI): mixed up –processes of sign interpretation MFT: mathematics of symbol-processes –elementary thought process

MFT OF SYMBOLS Example: a written word "chair" –The mind interprets it to refer to an entity in the world, or the concept "chair" in the mind This is a simplified description of a thinking process Elementary thought process is a symbol process –involves consciousness and unconscious, concepts and emotions –much more complicated than envisioned by founders of “symbolic AI” Two parallel hierarchies of Cognition and Language –A dog can learn word-object connection –A chimp can learn elements of 2 levels? –Only human mind has multi-level hierarchy

SYMBOLIC ABILITY Integrated hierarchies of Cognition and Language –High level cognition is only possible due to language –Language is only possible due to cognition Similarity Action Similarity Action Similarity cognition language M M M M

SYMBOLS and “SYMBOLIC AI” Founders of “symbolic AI” believed that by using “symbolic” mathematical notations they would penetrate into the mystery of the mind –But mathematical symbols are just notations (signs) –Not psychic processes This explains why “symbolic AI” was not successful This also illustrates the power of language over thinking –Wittgenstein called it “bewitchment (of thinking) by language”

AESTHETIC EMOTIONS Not related to bodily satisfaction Satisfy instincts for knowledge and language –learning concepts and learning language Not just what artists do Guide every perception and cognition process Perceived as feeling of harmony-disharmony –satisfaction-dissatisfaction Maximize similarity between models and world –between our understanding of how things ought to be and how they actually are in the surrounding world; Kant: aesthetic emotions

BEAUTY Harmony is an elementary aesthetic emotion –higher aesthetic emotions are involved in the development of more complex “ higher ” models The highest forms of aesthetic emotion, beauty –related to the most general and most important models –models of the meaning of our existence, of our purposiveness or intentionality –beautiful object stimulates improvement of the highest models of meaning Beautiful “ reminds ” us of our purposiveness –Kant called beauty “ aimless purposiveness ” : not related to bodily purposes –he was dissatisfied by not being able to give a positive definition: knowledge instinct –absence of positive definition remained a major source of confusion in philosophical aesthetics till this very day Beauty is separate from sex, but sex makes use of all our abilities, including beauty

INTUITION Complex states of perception-feeling of unconscious fuzzy processes –involves fuzzy unconscious concept-models –in process of being learned and adapted toward crisp and conscious models, a theory –conceptual and emotional content is undifferentiated –such models satisfy or dissatisfy the knowledge instinct before they are accessible to consciousness, hence the complex emotional feel of an intuition Artistic intuition is about – composer: sounds and their relationships to psyche – painter: colors, shapes and their relationships to psyche – writer: words and their relationships to psyche

INTUITION: Physics vs. Math. Mathematical intuition is about –Structure and consistency within the theory –Relationships to a priori content of psyche Physical intuition is about –The real world, first principles of its organization, and mathematics describing it Beauty of a physical theory discussed by physicists –Related to satisfying knowledge instinct the feeling of purpose in the world

OUTLINE Cognition Modeling Field Theory (MFT) of cognition Language Integration of cognition and language Prolegomena to a theory of the mind Future directions -Evolution of culture

EVOLUTION Genetic evolution simulations (1980s - ) –Using basic genetic mechanisms to explore genetic evolution –Artificial Life, evolution models: Bak and Sneppen, Tierra, Avida –Genes and memes (cultural concepts) Cultural evolution –Evolution of languages –Evolution of concepts vs. evolution of genes Culture evolves much faster than genetic evolution (~10,000 years) –Concepts are propagated through language Cognitive-models are not transferred to the next generation Language-models are Each individual –receives language models from culture –has to develop cognitive models from language models

MECHANISMS OF CULTURAL EVOLUTION Differentiation and synthesis Differentiation –Fuzzy concepts become detail and clear Synthesis –Integrate cognition and language {M C, M L } –Language evolved toward crisp, unemotional compare to animal cries: undifferentiated concept-emotion –Emotions integrate L & C –This is why music is so important Bach and Eminem integrate collective consciousness

SPLIT BETWEEN CONCEPTUAL AND EMOTIONAL Dissociation between language and cognition –Might prevail for the entire culture Words maintain their “ formal ” meanings –Relationships to other words Words loose their “ real ” meanings –Connection to cognition, unconscious, and emotions Conceptual and emotional dissociate –Concepts are sophisticated but “ un-emotional ” –Language is easy to use to say “ smart ” things but they are meaningless, unrelated to instinctual life

CREATIVITY At the border of conscious and unconscious Archetypes should be connected to consciousness –To be useful for cognition Collective concepts–language should be connected to –The wealth of conceptual knowledge (other concepts) –Unconscious and emotions Creativity in everyday life and in high art –Connects conscious and unconscious

DISINTEGRATION OF CULTURES Split between conceptual and emotional –When important concepts are severed from emotions –There is nothing to sacrifice one ’ s life for Split may dominate the entire culture –Occurs periodically throughout history –Was a mechanism of decay of old civilizations –Old cultures grew sophisticated and refined but got severed from instinctual sources of life Ancient Acadians, Babylonians, Egyptians, Greeks, Romans … –New cultures ( “ barbarians ” ) were not refined, but vigorous Their simple concepts were strongly linked to instincts, “ fused ”

TERRORIST’S CONSCIOUSNESS Ancient consciousness was “ fused ” –Concepts, emotions, and actions were one Undifferentiated, fuzzy psychic structures –Psychic conflicts were unconscious and projected outside Gods, other tribes, other people Complexity of today ’ s world is “ too much ” for many –Evolution of culture and differentiation Internalization of conflicts: too difficult –Reaction: relapse into fused consciousness Undifferentiated, fuzzy, but simple and synthetic The recent terrorist ’ s consciousness is “ fused ” –European terrorists in the 19 th century –Fascists and communists in the 20 th century –Current Moslem terrorists

SYNTHESIS Creativity, life, and vigor requires synthesis –Emotional and conceptual, conscious and unconscious –In every individual Lost synthesis and meaning leads to drugs and personal disintegration –In the entire culture Lost synthesis and meaning leads to cultural disintegration Historical evolution of consciousness –From primitive, fuzzy, and fused to differentiated and refined –Interrupted when synthesis is lost Individual consciousness –Combining differentiation and synthesis –Jung called individuation, “the highest purpose in every life”

MATHEMATICS OF SYNTHESIS Integrating a wealth of concepts –Undifferentiated knowledge instinct “likelihood maximization” –Differentiated knowledge instinct Likelihood involves “local” relationships among concepts Highly-valued concepts Highly valued concepts acquire properties of instincts –Affect adaptation, differentiation, and cognition of other concepts Differentiated forms of knowledge instinct –All concepts are emotionally related –This requires “continuum” of emotions (music) –Differentiated emotions connect diverse concepts

ROLE OF MUSIC IN EVOLUTION OF THE MIND Melody of human voice contains vital information –About people’s world views and mutual compatibility –Exploits mechanical properties of human inner ear Consonances and dissonances Tonal system evolved (14 th to 19 th c.) for –Differentiation of emotions –Synthesis of conceptual and emotional –Bach integrates personal concerns with “the highest” Pop-song is a mechanism of synthesis –Integrates conceptual (lyric) and emotional (melody) –Also, differentiates emotions –Bach concerns are too complex for many everyday needs –Human consciousness requires synthesis immediately Rap is a simplified, but powerful mechanism of synthesis –Exactly like ancient Greek dithyrambs of Dionysian cult

PREDICTIONS AND TESTING of MFT/DL theory of the mind General neural mechanisms of the elementary thought process –confirmed by neural and psychological experiments –includes neural mechanisms for bottom-up (sensory) signals, top-down (“imagination”) model-signals, and the resonant matching between the two Adaptive modeling abilities –well studied: adaptive parameters are synaptic connections Instinctual learning mechanisms –studied in psychology and linguistics Emerging method: simulation of multi-agent evolving systems Ongoing and future research will confirm, disprove, or suggest modifications to –similarity measure as a foundation of knowledge and language instincts –mechanisms of model parameterization and parameter adaptation –dynamics of fuzziness during perception/cognition/learning –mechanisms of language and cognition integration –mechanisms of differentiation and synthesis

THE END Can we describe mathematically and build simulation models for evolution of all of these?

PUBLICATIONS OXFORD UNIVERSITY PRESS Future together with Fernando Fontanari: Emotional mechanisms in evolution; Creation of meanings in evolution

PUBLICATIONS New book is coming: –The Knowledge Instinct

BACK UP MFT and inverse problems Cognition and understanding From Plato to Locke From Kant to Grossberg Mechanisms of evolution MFT and Buddhism

MFT VS. INVERSE SCATTERING Inverse Scattering in Physics –reconstruction of target properties by “propagating back” scattered fields –usually complicated, ill-posed problems (exception: CATSCAN) Biological systems (mind) solve this problem all the time –by utilizing prior information (in feedback neural pathways) Classical Tikhonov’s inversion cannot use knowledge –regularization parameter (  ) is a constant –Morozov’s modification can utilize prior estimate of errors for  Inverse Scattering using MFT –can utilize any prior knowledge (  became an operator) –utilizes prior knowledge adaptively (  depends on parameters)

COGNITION AND UNDERSTANDING Incoming signals, {x,w} are associated with model-concepts (m) –creating phenomena (of the MFT-mind), which are understood as objects, situations, phrases,… –in other words signal subsets acquire meaning (e.g., a subset of retinal signals acquires a meaning of a chair) Several aspects of understanding and meaning –concept-models are connected (by emotional signals) to instincts and to behavioral models that can make use of them for satisfaction of bodily instincts –an object is understood in the context of a more general situation in the next layer consisting of more general concept-models (satisfaction of knowledge instinct) each recognized concept-model (phenomenon) sends (in neural terminology: activates) an output signal a set of these signals comprises input signals for the next layer models, which ‘cognize’ more general concept-models this process continues up and up the hierarchy towards the most general models: 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)

FROM PLATO TO LOCKE Realism: –Plato: ability for thinking is based on a priori Ideas –Aristotle: ability for thinking is based on a priori (dynamic) Forms an a priori form-as-potentiality (fuzzy model) meets matter (signals) and becomes a form-as-actuality (a concept) actualities obey logic, potentialities do not Nominalism –Antisthenes (contemporary of Plato) there are no a priori ideas, just names for similar things –Occam (14 th c.) Ideas are linguistic phenomena devoid of reality –Locke (17 th c.) A newborn mind is a “blank page”

FROM KANT TO GROSSBERG Kant: three primary a priori abilities –Reason = understanding (models of cognition) –Practical Reason = behavior (models of behavior) –Judgment = emotions (similarity) –“We only know phenomena (concepts), not things-in-themselves” Jung –Conscious concepts are developed based on inherited structures of the mind, archetypes, inaccessible to consciousness Chomsky –Inborn structures, not “general intelligence” Grossberg –Models attaining a resonant state (winning the competition for signals and becoming crisp in this process) reach consciousness

MECHANISMS OF CONCEPT EVOLUTION Differentiation, synthesis, and language transmission Differentiation –Fuzzy contents become detail and clear –A priori models, archetypes are closely connected to unconscious needs, to emotions, to behavior Concepts have meanings Cultural and generational propagation of concepts through language –Integration of language and cognition is not perfect Language instinct is separate from knowledge instinct Propagation of concepts through language –A newborn child encounters highly-developed language –Synthesis: cognitive and language models {M C, M L } are connected individually –No guarantee that language model-concepts are properly integrated with the adequate cognitive model-concepts in every individual And we know this imperfection occurs in real life Meanings might be lost Some people speak well, but do not quite understand and v.v.

MFT AND BUDDHISM Fundamental Buddhist notion of “Maya” –the world of phenomena, “Maya”, is meaningless deception –penetrates into the depths of perception and cognition –phenomena are not identical to things-in-themselves Fundamental Buddhist notion of “Emptiness” –“consciousness of bodhisattva wonders at perception of emptiness in any object” (Dalai Lama 1993) –any object is first of all a phenomenon accessible to cognition –value of any object for satisfying the “lower” bodily instincts is much less than its value for satisfying higher needs, knowledge instinct –Bodhisattva’s consciousness is directed by knowledge instinct –concentration on “emptiness” does not mean emotional emptiness, but the opposite, the fullness with highest emotions related to the knowledge instinct, beauty and spiritually sublime