TOWARDS PHYSICS OF THE MINDлекция 1, лекция 2

Dr. Leonid PerlovskyHarvard University

Novosibirsk State University

2014

OUTLINE

• Physics of the mind, what it is

• The first principles

• Mathematical models and experiments

• Cognitive algorithms and engineering applications

• Future research directions

PHYSICS OF LIFE REVIEWS

• Elsevier

• Impact Factor = 9.5

• Thomson Reuter rating #3 in the world among 85 journals in biophysics

PHYSICS OF THE MIND, WHAT IT IS

• First principles describing a wide area of reality

• Mathematical models making testable predictions

• Psychology, cognitive science, neurophysiology- Experimental physics of the mind

• Is physics of the mind possible?

• We can identify a few basic principles of the mind- Formulate mathematically- Explain a wealth of known data- Make predictions and test in the lab

FIRST PRINCIPLES

• Mechanisms of - Instincts, emotions, concepts

- Hierarchy

• Higher emotions and cognition- The knowledge instinct

- Abstract concepts

- Beautiful

• Language and cognition- Emotions of speech prosody

- Music

• Few principles describe a wide area of reality

MATHEMATICAL MODEL OF CONCEPTS

•Concepts are neural representations (memories)

•Perception: match memories to sensor patterns

•Mathematics: dynamic logic (DL)- DL is a process-logic, “from vague to crisp”- Vague representations match visual perceptions

•Experimental proof- Discuss in few minutes

DYNAMIC LOGIC (DL)

• Mathematical models of mind since the 1950s failed - Artificial intelligence, pattern recognition, neural networks…

• Reason: Combinatorial Complexity (CC) of matching memories and sensor patterns

- More computations than the size of the Universe

• CC is equivalent to Gödelian incompleteness in a finite system

- Logic is the reason for failures

• DL, a vague-to-crisp process eliminates CC

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DYNAMIC LOGIC illustration: perception of objects below noise

CC, unsolvable for decades

EXPERIMENTAL PROOF OF DL

•Посмотрите на предмет перед Вами и запомните

• Закройте глаза и вспомните предмет во всех деталях- Всех деталей не вспомнить!

- Воображаемый предмет расплывчат!

•Воображаемый предмет – это нейронная проекция представления на зрительную кору, следовательно- Представления расплывчаты

- Процесс восприятия = «от расплывчатого к конкретному» = ДЛ

•Bar et al, PNAS (2006) (имаджинг эксперименты)- Доказали что ДЛ адекватная модель восприятия

- Восприятие – 0.6 сек, процесс ДЛ и расплывчатые состояния недоступны субъективному сознанию

ARISTOTLE VS. GÖDEL AND DL

• 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 are closely linked• 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

COGNITIVE ALGORITHMS AND ENGINEERING APPLICATIONS

• Engineering problems have been solved, unsolvable for decades:

• Patterns under noise• Tracking moving objects under noise• Learning and recognition of situations• Integration of disparate data• Data mining integrating data sources• Integration of language and cognition• Future

- Correlation of genes and disease beyond 1 gene- Adaptive cybersecurity

MATHEMATICAL MODELS OF INSTINCTS AND EMOTIONS

• Instincts- Sensors measuring vital parameters

- Indicating safe range

- E.g. sugar level in blood

• Emotions - When unsafe, neural signals are sent to decision regions

- These neural signals are felt as emotions

- Low sugar level in blood is felt as emotion of hunger

• Grossberg and Levine, 1987

KNOWLEDGE INSTINCT (KI)

• Adequate representations are necessary for survival

• KI drives to improve representations (knowledge)

• KI mathematical model - Maximize similarity between concepts and percepts

- Cannot be solved w/o DL

• KI satisfaction – aesthetic emotions

- related to knowledge not to bodily needs (“spiritual”)

- not only in museum, but in every act of perception

HIERARCHY OF THE MIND

situations

objects

abstract ideas

sensory-motor signals

…

• Concepts at every level unify lower-level concepts

The “highest model”

HIERARCHY OF THE MIND

situations

objects

abstract ideas

sensory-motor signals

…

• Higher level abstract concepts are - vague and unconscious- only understood due to language

• Concepts at every level unify lower-level concepts

The “highest model”

HIERARCHY OF THE MIND

situations

objects

abstract ideas

sensory-motor signals

… • Concepts at the top unify entire life experience- meaning of life- satisfaction of KI – emotion of the beautiful

• Higher level abstract concepts are - vague and unconscious- only understood due to language

• Concepts at every level unify lower-level concepts

The “highest model”

BEAUTY

• The highest aesthetic emotion, beautiful • improvement of the highest concepts (at the top of the

hierarchy)• feel emotion of beautiful

• Beautiful “reminds” us of our purposiveness• the “top” concepts unify all our experience• Vague and unconscious• perceived as our purpose (“aimless purposiveness”)• Scientific beauty – valid and general theory (or experiment)

• Beauty is separate from sex (different instincts)• sex uses all our abilities, including beauty

LANGUAGE AND COGNITION DUAL HIERARCHY

situations

objects

abstract ideas

COGNITION

phrases

words

abstract words/phrases

LANGUAGE

sensory-motor signals

…

SURROUNDINGLANGUAGE

words for objects

phrases for situations

language sounds

language descriptions of abstract thoughts

… …

sensory-motor language models

• Language is crisp and conscious w/o life experience, because it exists around ready-made

• Cognition cannot be learned w/o language

(1) abstract concepts do not exist in the world ready-made

(2) cognition is only grounded in experience at the very bottom

• The Dual model requires dynamic logic

• We also need emotional motivation

ЭСТЕТИЧЕСКИЕ ЭМОЦИИ

• Красота

• Эмоции в музыке

• Эмоции звука голоса (мелодия интонации)

• Когнитивные диссонансы

КОГНИТИВНЫЕ ДИССОНАНСЫ

• Cognitive dissonance, CD - A most significant development in 20th c. psychology- Discomfort due to holding contradictory knowledge- Contradictions are unpleasant and discarded- Every new word would be discarded before proved useful- Как могла возникнуть культура?

Миллионы противоречий

• Emotions of speech prosody (melody of intonation)- A motivation to overcome CD- Connects language and cognition- В каждом слове – эмоциональная конфетка

• Культуры различаются эмоциональностью

ЯЗЫК И ЭМОЦИИ

• У животных понимание-эмоция-действие-голос неразделены- Голос => действие- Язык не может возникнуть

• У человека возникла отдельная система эмоций- Эмоции в коре мозга, частично осознанные,

контролируют звук голоса- Эмоции голоса частично отделились от

неконтролируемых эмоций, и мог возникнуть язык

• Противоречие!!: эмоции предотвращают язык, и всё же необходимы для языка

MUSICAL EMOTIONS(C. Darwin: “the greatest mystery”)

• Музыка возникла из просодии языка - Звук голоса разделился- Семантическая часть - язык- Эмоциональная часть - музыка

• Психика (душа) разделилась- Единство души необходимо для выживания (КД необходимо преодолевать)- У животных есть единство, но нет детального понимания- Разделение души для человека - болезненно

• Musical emotions help to- Overcome CD, and create unity of mind- Hold contradictory knowledge - CD between trust, love, betrayal are addressed by many songs- Фуги Баха – КД жизни и смерти

• Why musical emotions are so powerful?• Knowledge contradicts instincts and other knowledge• We live in these contradictions• Music enables human evolution

• Experimentally confirmed

INTUITION

• Complex states of perception-feeling • vague partly-conscious representations• conceptual and emotional content is

undifferentiated

• Artistic intuition • composer: sounds and their relations to psyche• painter: colors, shapes and relations to psyche• writer: words and their relations to psyche

INTUITION: Physics vs. Math.

Mathematical intuition is about– Structure and consistency within the theory

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

DIFFERENTIATION AND SYNTHESIS

• The knowledge instinct–Two mechanisms: differentiation and synthesis

• Differentiation –Down the hierarchy: more detailed concepts–Separate concepts from emotions

• Synthesis –Up the hierarchy, more unity, concepts closer to emotions–Connect knowledge to life–Connect concepts and emotions

Connect language and cognitionMeaning: concepts acquire meaning at the next level

EMOTIONALITY OF LANGUAGESAND CULTURES

• Conceptual content of culture: words, phrases–Easily borrowed among cultures

• Emotional content of culture–In voice sound (melody of speech)–Determined by grammar–Cannot be borrowed among cultures

• English language (Diff. > Synthesis)–Weak connection between conceptual and emotional (since 15 c)–Pragmatic, good for science, but may lead to loss of values and

identity crisis (which actually goes on)

• Arabic language (Synthesis > Diff.)–Strong connection between conceptual and emotional–Cultural immobility, but strong feel of identity (synthesis)

EVOLUTION OF MUSIC AND CONSCIOUSNESS

Psalmody, antiphon, респонсориум since 5th c. BCE (впервые в Исайе, 7в. днэ) – Основа церковной музыки до сего дня – Возникает современное сознание с противоречиями – Противоречия в музыке богослужения помогают человеку принять их в своей

душе Консонансы и диссонансы

Tonal system evolved (14th to 19th c.) for – Реформация, 16в., поместила противоречия Бога и Дьявола в сердце человека– Необходима новая церковная музыка с более сильными эмоциями– Необходим новый синтез концепций и эмоций– В музыке Баха личное соединяется с «высшим»

Pop-song is a mechanism of synthesis– Integrates conceptual (lyric) and emotional (melody)– Also, differentiates emotions (любви, измены, верности…)– Bach might be too complex for many everyday needs– Human consciousness requires synthesis immediately

Rap is a simplified, but powerful mechanism of synthesis– Style and content like ancient Greek dithyrambs of Dionysian cult

Эволюция музыки и сознания идёт параллельно

FUTURE DIRECTIONS

• Mathematical development and simulation of cultures–DL in Hierarchy, mechanisms of synthesis–Computer models of language & cognition evolution, add emotions of prosody–Evolution of music–Joint evolution of language, cognition, music, and cultures

• Psycholinguistic and cognitive experiments–Measure emotionality of various languages and cultures–Measure musical emotions

• Cultural evolution – study effects of languages and music

• Improve human condition around the globe–Diagnose cultural states (up, down, stagnation), measure differentiation, synthesis, hierarch–Develop predictive cultural models, integrate spiritual and material causes–Identify language and music effects that can advance consciousness and reduce tensions

• Human-computer interaction, robotics–Acquire cultural knowledge–Enable culturally-sensitive communication–Help us understand ourselves–Help us understand each other

BACK UP

• Engineering example: learning situations (3)

• Math. Model of the Mind (3)

• Aristotle, Beauty, Intuition, (3)

• Evolution of Music and Consciousness (2)

• Evolution of Culture, mean field approximation (6)

• Terrorist’s consciousness

• Future Directions

SITUATIONSDATA (RANDOM)

obje

cts

Situations (random)

LEARNING SITUATIONS DATA (SORTED)

obje

cts

Situations (sorted)

SITUATION LEARNING: ERRORS

SITUATIONS AND ABSTRACT IDEAS

• This algorithm learns abstract ideas at every level of the hierarchy

• Lower level of ideas = “objects”

• Next higher level of more abstract ideas = “situations”

• Fundamental mathematical breakthrough- Discrete problem is formulated and solved as continuous problem (DL)

MATH. MODEL OF CONCEPTS

• The knowledge instinct = maximize similarity between signals, x(n), and concepts, M(m)

• Similarity between signals and concepts, L• L = l ({x}) = l (x(n))

• l (x(n)) = r(m) l (x(n) | Mm(Sm,n))

• l (x(n) | Mm(Sm,n)) is a conditional similarity for x(n) given m• {n} are not independent, M(n) may depend on n’

• CC: L contains MN items: all associations of signals and concepts (LOGIC)

n

m

DYNAMIC LOGIC (DL) non-combinatorial solution

• Start with a set of signals and unknown concepts- any parameter values Sm

- associate concepts with their contents (signals)

- (1) f(m|n) = r(m) l (n|m) / r(m') l (n|m')

• Improve parameter estimation

- (2) Sm = Sm + f(m|n) [ln l (n|m)/Mm]*[Mm/Sm]

( determines speed of convergence)

- learn signal-contents of concepts

• Continue iterations (1)-(2). Theorem: DL converges- similarity increases on each iteration- aesthetic emotions are positive during learning

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MATH. MODEL OF LANGUAGE, COGNITION, & HIERARCHY

• How language and cognition interact- A concept m has vague cognitive and crisp language parts

Mm = { Mmcognitive, Mm

language };

- This model requires DL

• Ontogenetic development- Before 1-3 y.a. both representations are vague

- After 5 y.a. language is crisp, cognitive rep. are learned from vague to crisp guided by language

• Hierarchy, a product of similarity over layers, h

- L = l hh

MEAN FIELD THEORY OF CULTURAL EVOLUTION

• Differentiation, D, synthesis, S, hierarchy, H

• dD/dt = a D G(S); G(S) = (S - S0) exp(-(S-S0) / S1)

• dS/dt = -bD + dH

• H = H0 + e*t,

• Only few solutions

DYNAMIC CULTURE

Average synthesis, high differentiation; oscillating solutionKnowledge accumulates; no stability

TRADITIONAL CULTURE

High synthesis, low differentiation; stable solutionStagnation, stability increases

INTERACTING CULTURES

• Two cultures– dynamic and traditional

– slow exchange by D and S

dDk/dt = ak Dk G(Sk) + xkDk

dSk/dt = -bkDk + dkHk + ykSk

Hk = H0k + ek*t

INTERACTING CULTURES

Knowledge accumulation + stability

1) Early: Dynamic culture affects traditional culture, no reciprocity2) Later: 2 dynamic cultures stabilize each other

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 19th century• Fascists and communists in the 20th century• Current Moslem terrorists