Coherence, complexity and creativity: the dynamics of decision making F. Tito Arecchi e-mail:
[email protected] homepage:www.inoa.it/home/arecchi
New economic windows 2008 Salerno, 19-21 June 2008
Why in science meaning appears irrelevant but only measurable details and repeatible phenomena make sense ,and all the rest is a “miracle”
1-
HOW WE SEE: PROCESSING VISUAL EVENTS ;
2- THE SCIENTIFIC INSIGHT
Visual perception: paths and times
Motor and language areas 800 ms PFC=prefrontal cortex 200-800 ms V5 WHERE? (Motion, Space relations )
V4 WHAT? (Shape,Colour) retina
LGB
t=0
200 ms Primary visual cortex V1
Feature binding (W. Singer)
Each circle represents a receptive field which detects an elementary detail (e.g. a vertical bar)
ART = Adaptive Resonance Theory ( cooperation between input and past memories)
NO ! Syntax of symbols (handled by a Turing machine)?
6
1-
HOW WE SEE: PROCESSING VISUAL EVENTS ;
2- THE SCIENTIFIC INSIGHT
The words of science (Galileo, 1610) ordinary
Physi cal language
language flavour colour shape
APPLE
weight Position and velocity of atoms
Determinism = predictability ( Newton 1687; Laplace 1812 ) = unique trajectory ( initial condition (
) starting from a precise ).
ON THE CONTRARY: Unpredictability (Poincaré 1890) ………
Nonlinear dynamics with 3 or more bodies (Poincaré,1890)
(DETERMINISTIC CHAOS)
Transverse stability of trajectory (
) .
Left regular motion; right chaotic motion with information loss (
: trajectories from initial conditions
distinct from
Rate of information loss = K (from Kolmogorov).
).
Chaotic dynamics : control transverse instability reduced or reversed by external controls
For ever
New descriptive level =
Code change
2 msec
PERCEPTION : RELIABLE IF LONG , BUT NOT INFINITE , LIFETIME !!
200 msec
ε=0.104 (less than coupling for spontaneous synchronization); entropy vs time for two inputs of short duration ( one ),and increasing amplitude A. On the right, two new features:
i) collective excitability to a short trigger; ii) excitation lasting a finite time slot, around 5
ii) is a collective synchronization state lasting for a time depending on - A (bottom-up input) and - ε (top-down tune of coupling)
From perception (sensorial input) to cognition (conceptual input)
Living being = semiotic agent ; embedded in an environment, it changes the descriptive code in order to stabilize the cognitive dynamics.
Complexity It is measurable,provided one sticks to a single code : rather to be called COMPLICATION C. of a string (Chaitin-65) = n°of bits of the shortest programme wh ich evaluates the string and then stops. Max C of an n bit string=n (random case) Let us plot C as a function of K
C
random
K
CHANGE OF
C
CODE = CREATIVITY Partial chaos control (additional variables suggested COMPUTATION
by environment) SEMIOSIS
SCIENTIFIC THEORY
Kepler-Newton BACON programme by H. Simon
K
Bayes theorem
P(h | data) = P(h) [P(data |h) / P(data)]
A-posteriori experimental measurements A-priori model
BAYES Fitness= probability mountain
final condition INFORMATION
a-posteriori prob. a-priori prob.
initial
Darwin = Bayesian strategy
condition
Semantic complexity
MEANING
INFORMATION complication STOP!!!
Bayes without semiosis
creativity (change model to stabilize chaotic agent-environment dynamics )
From BAYES to HILBERT ; then GOEDEL Theorems undecidable
Goedel
Hilbert model
P ( data | h ) =
∫ d (data )δ (data − F (h )) = 1
∆data
Theorems decidable
formal rule
axioms
From BAYES to POPPER : what falsification means
P(h | data) = P(h) [P(data |h) / P(data)]
A scientific theory is falsified if for some data it occurs
P(data |h) / P(data)< 1
From what we have discussed : search for meaning, i.e. creative decision, is
NON-Bayesian, NON-Hilbertian, NON-Popperian
Firenze around the Cathedral Dome Scientific questions: 1.how many stones? 2.how many working days? 3.size and coordinates Etc. etc
all barely relevant to grasp the aesthetic feeling as one watches the city from the hill
…The world is complex, that is , not grasped by a unique model How to choose among alternative models? -
arbitrarily (kind of oracle) = relativism,
or - along some guidelines (fertility and latitude of the new explanation; useful outcomes ) = stabilizing chaotic agent-environment dynamics: hint of an ontology
A
Hermeneutic circle (closed lexicon):
B
as Turing machine Limited repertoire- No information loss
B
A
e.g. locust (G. Laurent)
time
A
Hermeneutic spiral (adjustable lexicon)
B
beyond Turing Unlimited repertoire- Information swapping) e.g. rabbit (W. Freeman)
Infinite use (in course of time) of finite resources
We are embodied ; our freedom is CONDITIONAL (-Aristotle: thought and desire play a coordinate roleNicomachean Ethics, -Vico: poetic wisdom is the result of perception, memory and imagination- The New Science ) NOT ABSOLUTE (as instead in Kant: freedom= independency from cause-effect chains = not-caused cause- Critique of Practical Reason).
The creative jump is not arbitrary, but guided by the situation in which we are embedded. We re-adjust the code until we find a satisfactory reading of the world around us.
The notion of scale number
0.85
Adult height = Gauss
1.70
3.40
metre
number
Income = Pareto
0.1
1
10
income ( units: 10 k-euro/year)
Sherlock Holmes
vs
Father Brown
Two styles of criminal investigation
Reduction of complexity by code change 1- electricity; magnetism; optics
Maxwell equations
2- Mendeleev table
Quantum atom (Bohr,Pauli)
3 - zoo of more than 100 elementary particles
SU (3)- quarks (M Gell Mann)
4–scaling laws in phase transitions
Renormalization Group (K.Wilson)
Analytical Linguistics and Neurocognitive Linguistics Analytical linguistics denotes numerous schools ( "generative grammar", "cognitive grammar", etc., etc.) ;it describes various properties of things that people say. Neurocognitive linguistics has different objectives: to discover the mental operations that underlie the processes of speaking and understanding, the processes by which our brains learn to use language, and the brain structures that make these processes possible.
The two approaches are not in conflict . Rather, they complement each other. The following table identifies some differences between them. But it is a simplified account since 'analytical linguistics' covers a range of different schools of thought
Analytical Linguistics
Neurocognitive Linguistics
Works with the first two kinds of evidence.
•Works with all four kinds of evidence.
•
Attempts to describe linguistic data. •
•The object of investigation is either "language" (arguably an illusory object) or "the ideal speakerhearer", clearly an illusory object.
Tends to view words and other linguistic units as objects or stored symbols. •
Views grammar as sets of rules. •
Likes to analyze forms as much as possible, eliminating redundancy. (True for some versions of analytical linguistics.) •
Bottom Line: Describe properties of linguistic products (spoken and/or written).
Examines linguistic data as evidence for the structure of the cortical information system. •
The object of investigation is the neurocognitive system of the typical person. •
Views linguistic units in terms of distributed connections in a network. •
Views linguistic information as a system of connections organized in a network. •
Recognizes that the human brain automatically learns complex composites as units, with all their redundancy. •
Bottom Line: Describe the cognitive system which produces and understands and learns how to do so.
The four bases of linguistic reality: First Base. The organs and processes of speech production. There is a high degree of correlation between movements of the speech-producing organs (tongue, lips, etc.) and the resulting patterns of sound waves. Thus, the phonetician is able to transcribe and analyze speech of any human language. Such analysis is essential for getting to second base. Second Base. The things people say and write, which are also things that people can comprehend. We call them 'texts', either written or spoken discourse. The analysis of such material is the task of analytical linguistics. Third Base. Linguistic processes. These include speaking and understanding and related processes, especially learning. (Compare operational and developmental plausibility.) Fourth Base . The neurocognitive basis of language — the human brain. (Compare neurological plausibility .)
• • • ·
• • •
Plausibility Requirements for a neurocognitive theory of language The demands for a neurocognitive theory go beyond those considered in linguistics , including these plausibility requirements: (1) Operational plausibility The linguistic system has to be able to operate in real time to produce and understand speech. Rejects as unrealistic the proposal that our cognitive systems have a non-operating 'competence model' that is accessed somehow by a separate 'performance model'. (2) Developmental plausibility · The theory must allow for the learning and development we observe in normal children around the world. (3) Neurological plausibility · The theory must be compatible with what is known about the brain, providing : (i) A hypothesis of how neural structures represent, use, and acquire linguistic information. (ii) At the systems level, the localization of functions in the cortex and the connections among the subsystems which perform higher level functions like those involved in language processing.
