Complexity and the Mind
George Kampis
Fujtisu Chair, Shool of Knowledge Science
Japan Advanced Institute for Science and Technology
We have to talk about simple systems and complex systems.
What is a Complex System? What is a Simple System?
Complex systems may be trendy, but most systems in scence are very simple.
Simple Systems
Examples for simple systems:
pendulum
- it can only do one thing, swinging.
LRC electric circuits
- have several "modes", i.e. oscillations
dynamical systems
- in the old-fashioned
sense, composed of elements like above
Why are they simple?
Well, if you don't know how to solve
them... they are complex.
Phenomenologically, based on what
we see as behavior, they are complex indeed.
But technically or methodologically,
they are very simple:
there is, in each
case, one master method of solution that fits them all
That is, all
kinds of LRC systems, all behaviors of "classic" dynamical systems (systems
for which most of the circuitry
in a TV set or a radio equipment is an example) are tractable
using the same technique.
And that is the method of the Fourier analysis of behaviors composed of oscillations.
Let us now see this from a different point of view. If there is one master
method, there is some kind of a generality involved here.
The concept by which to capture this is that of a law.
In other words, in every such system, you have a law,
or a covering law, i.e. one which covers several instances, in fact all instances.
The concept is usually explicated like this:
C1..Cn contingents,
such as initial conditions, boundary conditions, parameters, etc.
L1...Lm law statements,
which formulate how later events depend on earlier events, and so on
---------
E1
..Ek "explananda",
the time behaviors or other dependent variables to be explained
L is written very big here, and C-s are written small - we have the same
L for wide classes of events, only actualized by the C-s.
For several hundred years, this was the ideal of science, and all science
was imagined (perhaps still imagined by some today) like this.
For instance, "general laws of quantum mechanics", "general laws ogf
motion" such as Newtonian laws etc.
Complex sytstem
Most often they are conceived as nonlinear systems.
Nonlinear systems - the earlier examples were all linear systems (...).
Linear systems:
if
temporal behavior is specified in the form of differential equations, e.g.
as dx/dt =
f (x,t) etc for several variables
then a linear system is one where f (x, t) = ax + by +cz ......
but never ax2 + bxy
+... which are the nonliear systems.
Behavior of nonlinear systems
is very much studied but unlcear in many details (perhaps one reason why
they are called complex; it's the edge)
examples are: chaos
- initial conditions are everyting,
as opposed to pendulum
transient behaviors
- as opposed to attractors
(like oscillations)
non-stationary
behavior - which never gets the same
a famous example
is a cellular automaton (S. Wolfram) which can produce perhaps any desirable
patterns
among them all bit
combinations that can code for computations as in a PC (called Turing computations).
Are these complex because they are nonlinear?
This is one way of looking at the question indeed.
There is another way, look at the laws.
The above examples for complex systems also show that
we don't have general
laws here, or covering laws
each system has its
own law, a different law
the same, or a similar
kind of broad explanation scheme exists (i.e. diff.eq)
but the details are
very different here, no master method exists,and the role of "law"
is changing
for instance, in
chaos C is "big", and L is "small". Why? Because that's where responsibility
for the behavior lies.
and the L-s, the
equations have no generality, each time a different law -- more like a rule.
So, here is maybe a different definition of complex systems:
A complex system is one where laws break down, and where different rules apply
for every individual behavior.
Along these lines now, how complex can a complex system be? How far can
you get?
It
appears that we have a hierarchy here: cL,Cl, R.......... perhaps up to systems
which produce new R-s or L-s?
In fact, I am going to foward here the idea that some systems are so complex,
in this sense, that they indeed require a
large variety of rules, or rule
sets to describe them - by any reasonable definition of what is a "rule".
Here is a familiar example, to get the flavor of it: Evolution.
Rules describing
dinosaur systems
Rules describing
humans systems -- 70 million years difference.
You can say it's
just a different system. But in a very precise sense it is the same system
nevertheless.
The kind of definition
of complexity that we are interested here seeks to grasp this kind of identity.
Minds as complex systems
Here is the main point of this lecture: the mind (i.e. human and animal
mind) - the entire functional unit that controls thinking and behavior -
is probably
a complex system of the same kind I mentioned here.
By "probably" I
mean - we don't know... there are models and theories, but needless
to say,
today we don't
know exaclty how it all works in the mind.
I briefly review the usual picture to appreciate the idea. Usual = dominating....
up (or down) to bookstore level.
Current models of the mind
- functionalism
- neural nets
- verbal models
of philosophy and cognitive science
Functionalism
computer metaphor
of the mind, has many different names:
representational
theory, propositional theory, LoT, etc.
slight variations
but the essence is same
mind = machine
= computer program ("software for the brain")
realized as finite
automaton (FA).
How complex is
it? The definition says it all.
FA = set of states plus set of rules
mind - right kind of rule set (the right kind of program).
i.e. seeking a law conceived as a general rule set, a
general theory of the mind in computational terms
that covers all
instances (and all aspects) of behavior in all animals and all minds
e.g. perception (vision
etc), reasoning, planning, emotion and attitudes (fear, anger, belief), meaning.
Challenged by many;
in particular in the past 20 year- symbolic states are replaced by dynamic
states
Neural nets
Connectionism,
neurodynamics, NN.
Function as a distribute
network of nodes with adjustable connections between them
What representation/symbol/the
carrying out of a rule is for functionalism, is learning for NN.
Captured in the
paradigm of "synaptic modification", with universal learning rules.
A law; a simple
system, a general model, where "one size fits all";
again: language processing,
experience and qualities ("pain","red"), motor control, problem solving,
etc.
Verbal models
a mixed, freestyle
category
philosophy, philosophy
of mind, cognitive science,cognitive psychology
talk about "naturalism",
"supervenient levels", "qualia", "understanding", "intentionality"
in general, talk
about various "mental states" - now what are they?
This is a logical
next question, but it implies that they are looking here for a theory of
the mental state,
i.e. concevied
a kind of stuff, such as a dog is a kind of animal
and indeed this
is the case.
Open a book and
see: anwering one question (eg. about intentionality) is anwering all
questions: "how the mind works"
which means seeking
universal law statements
Summary: theories of the mind as a simple system. But it should not (cannot)
stay at that.
Complex Minds
3 reasons to consider the mind as complex:
(1) [weak] historical:
assuming a parallel, we see that theory of mind is at a (pre-)Newtonian phase,
still looking for the master trick.
(2) [stronger]
nonlinear systems can be used for modelling the mind and can offer a full
spectrum of complexity
(3) [strong] minds
use mental models; causal structures which are complex
ad (1) this is not a real argument
just because other
systems were recognized as complex, it does not, by itself, imply the mind
should be complex too
but, of course,
the mind was concieved by what was at hand, and that has changed a
lot; the conception of the mind was not even reconsidered, so far.
so a sharper reading
is that there is a task here
ad (2) e.g. nonlinear systems such as very high dimensional systems
their study has
just began
in chaos and elsewhere,
the concern is with attractors, i.e. with stationary long time - behaviors
simple systems,
as well as low-dimensional dynamical systems are dominated by attractor structures
in very hight dimensional
systems the concept of atttactor can lose its significance
- infinitely long
lived transients (....?)
- "chameleon"systems
capable of simualting many, perhaps every, different systems (or lower dimension)
emergent levels
level = aggregate
e.g. in physics, molecular motion vs. solid body
emergent levels
in very high dimensional systems
temorary coalitions
of variables acting together
one example is synchrony
an aggregate, which
follows a separate rule
Complex system = at the "high end" we find heterogeneous systems, where
several different dynamical behaviors are possible
from the phenomenal
point of view, different systems
Dynamical systems can approach this... although currently no universal method
for generating such behaviors is known.
Mental models as complex, causal structures
So far we have seen that nonlinear systems can be complex
Now we are going to discuss grounds why minds are complex
Mental models
The particular theory of the mind
that I am advancing here is that of "mental models"
In a first, perhaps naive form suggested
by K. Craik in 1943.
The idea is that the mind contains
a small-scale replica of the world, ie. functionally it contains a little
world
Many people like to imagine this as
a mock-up model - the model of a house is a house, with windows, people....
But not as a static picture, or even
as a movie.....rather, a generative model
where some, selected, properties of the model are identical with that
of the modelled, and
the other properties of the mental model are consequences, i.e. are generated
from here
A famous example. P.N. Johnson-Laird
reasoning about syllogisms.
"Every Banker is an Athlete"
"No Chancellor is a Banker" --- what
follows from this?
About 5% of all people can solve this.
J-L explains this by assuming that
instead of A,B,C we represent tokens or "pebbles" that stand for them, and
that the mind
spontaneously animates and dramatizes the relation of these objects to
obtain various solutions.
Successful in the past 20 years as
a general model of the mind, not just in reasoning.
The example is quite static, but now
consider the Mental Model of an episode E1.
A mental model as a specific causal system must be able to re-animate that
episode.
An episode is like a small dynamical system: it has variables (that stand
for the objects and persons)
it has rules, for representing actions
as elements of what we can call a generative history.
The resulting picture is a so-called narrative model of the mind - a narrative
that consists of what happens with the actors.
Each narrative tells a different story: each representation needs a separate
dynamics, as in the case of dinosaur/man.
Consider now another episode
E2 for which this dynamics is different, and then consider a series
of episodes E2..... En etc.
What do we have here?
A series of different kinds of dynamical systems -
i.e.
our mind, as a complex system, appears to be able to generate every
element of such a series.
In short, our mind as a causal system
is/must be complex in a sense that goes beyond what can be represented by
a single
set of rules - its dynamics must be able to support the generation of several
different rule sets.
Just how that is accomplished (or approiximated), is not the subject of
this talk.
What I was trying to tell here is THAT the mind is a complex system of this
kind,
and to characterize it, from a phenomenological, birds-eye point of view.
Conclusions
Complex systems exist, not just in physics but everywhere.
Or, taking seriously what I have said earlier: complex systems in physics
(meaning nonlinear systems of the kind discussed
in the beginning) are perhaps not
really complex, after all.
"Real" complexity may reside in many-dimensional nonlinear systems, and
in natural systems like minds that can build different episodes
or (more precisely) mental models
of different episodes.
In other words, the suggestion is something like this: there are several
big leaps in science.
There is a quantum jump from simple to (moderately) complex systems - ie
. to systems of a few dimensions, and another
(or perhaps several further) quantum
jumps to very high dimensional systems and to complex natural systems such
as minds.
If that is true, we can expect to hear more from these systems at the higher
end of complexity in the future.