Degrees of Freedom Problem: 40 Years and Counting

blessinghomoeopathAI and Robotics

Nov 30, 2013 (3 years and 9 months ago)

85 views

brain

spine

muscles

skeleton

Degrees of Freedom Problem: 40 Years and Counting

10
12

10
9

10
2

10
3

DF Problem

(e.g., muscle DF >>> CM DF)


many DF state space

few DF control space

CM

3

articulation

phonation

respiration

producing
any

single phoneme
involves ≈ 70
muscles

PE at Ohio State (1963
-
1964)

Coached

Collaborated

Taught

Studied

Experimental and Physiological Psychology at Ohio State
(1964
-
1967)

Fall, 1965

PE at Loughborough College (now University)

Why Action?

speak
(hear)

hear
(speak)

Spring
1969

UConn 1967, Haskins 1970

1
st

epiphany (1952)
:

Invariance is in articulation, not acoustics.

Object of perception is gesture, not sound.

2
nd

epiphany (1985):


Inconstant motor commands implicate abstract motor invariants.
Speech production
-
perception is a special module.

Spring

1973

Two gifts

Turvey “Preliminaries to a theory of action with reference to vision.” (’75), ’77

Fowler & Turvey “Skill acquisition: An event approach with special reference
to searching for the optimum of a function of several variables.” (’77) ’78

Fowler “Timing control in speech production” ’77

Turvey, Shaw, & Mace “Issues in a theory of action: degrees of freedom,
coordinative structures, and coalitions” ‘79

Fitch, Tuller, Turvey “The Bernstein perspective: I. The problems of degrees
of freedom and context
-
conditioned variability. II. The concept of muscle
linkage or coordinative structure. III. Timing of coordinative structures with
special reference to perception. (’78), ‘82


Fowler, Rubin, Remez, & Turvey ”Implications for speech production of a
general theory of action.” ’80

Saltzman “On levels of sensorimotor representation” ‘77

Fitch & Turvey “On the control of activity: Some remarks from an ecological
point of view.” ‘77

1974
-
75: Guggenheim

Biofizica, Bernstein, Gibson, coordinative
structure

(a group of muscles, often spanning
several joints, constrained to act as a single
[tunable. cyclic
-
like] functional unit)


flows

forces

“How do flows constrain forces?”

“How does light get into muscle?


Address
-
specific
control?Address
-
approximate
control?Address
-
less control?

cortical
keyboard

spinal
keyboard

A Panoply of Issues

I(d
2

/dt
2
)

time

force field given

F

I(d
2

/dt
2
)

time

force field desired

“Bend force
-
field given to obtain force
-
field required”

A minimally intelligent executive intervening minimally

An elegant theory of executive ignorance

No loans of intelligence (no set points, no programs, no
inference engines)

Action must be “direct” if perception is

Not hierarchy, but dual heterarchies


Strong
heterarchy

On a drive to Haskins: “It’s a physics problem”

Solution to Bernstein’s problem
: Not neurophysiology, not cybernetics,
not artificial intelligence, but physics.
But what kind of physics
?

Kugler, Kelso, & Turvey “On the
concept of coordinative structures
as dissipative structures” ‘80

Physics of self
-
organization:
Nonlinear, nonequilibrium
thermodynamics

Kugler, Kelso, & Turvey “On the
control and coordination of
naturally developing systems.” ‘82


On first occurrence

For /baeb/, lips adjust to
complete utterance, not tongue


For /baez/, tongue adjusts to
complete utterance, not lips

Kelso,
Tuller
, Bateson, & Fowler, 1984

freeze jaw
while closing

upper lip DF
“compensates”
for lost jaw DF

Functionally specific cooperation
of speech articulators

Frank’s 2
nd

Gift

C (Collective/Cooperative Level)

B (Boundary Conditions)

A (Atomistic Level)

Coordinative structures as 3
-
tiered

Coordination as emergent from competition and cooperation:
Haskins research scientists as von Holst’s (1935) fish

Kugler & Turvey “Information, natural law, and the
self
-
assembly of rhythmic movement” 1987 (pp.480)

Coordinative structures are S
-
O ( HKB Equation: Elementary Coordination Law)

0

Symmetry
:

reflectional

time
-
translational

The Potential

The Motion

The Formalism

The Noise

f

V
(
f
)

π

-
π

The Strategy

Recognize
: Even in complex situations Nature obeys simple laws

Pursue
: A phenomenological, aggregated description of the highest level

Frequency

f

π

0

Criteria of non
-
equilibrium
phase transition
: modality,
inaccessibility, sudden jumps,
hysteresis, critical slowing
down, critical fluctuations

The Experiments

tract variables

articulators

constrictions variable
in location, degree

“planning” dynamics

“execution” dynamics

coordinate transformation

intended
gestures

articulatory dynamics

perceive
gestures

[
Phonetic Module
]


Intrinsic Timing, Articulatory Phonology

task specific

special purpose

autonomous

dynamic

Action Units

Task Dynamics

Basic phonological unit
:
articulatory

gesture, a dynamical system with a
characteristic set of parameter values.

An utterance
: an ensemble of potentially
overlapping gestural units


Phonetic
and
phonological
as micro and
macro descriptions of the same system

A Haskins Legacy

?

Today?

Executive ignorance
(on
-
line assembly of feedback
laws),
minimal intervention
(uncontrolled manifold)
(Todorov, 2004)

Rate of entropy production
as coordination selection
principle
(Frank 2011)

Impredicativity of S
-
O
(Chemero in press)

Intentional dynamics
(Shaw & Kinsella
-
Shaw,1988,
in press)

(Warren 2009)

perception
-
action

(West
2009)

Renormalization,
fractal calculus