PSYCHON:

a survey on automatic and voluntary control

Henrique Schützer Del Nero

Institute for Advanced Study-University of São Paulo

Alfredo Portinari Maranca

Polytechnic School - University of São Paulo

José Roberto Castilho Piqueira

Polytechnic School - University of São Paulo

ABSTRACT

The authors present here an architecture of seven coupling oscillators, called psychon, that, analyzed through the Theory of Dynamical Systems, and with some interesting computational results, can suggest alternatives to the problem of neural networks that change continuously depending on external informations, resetting parameters, and using non-linearities and the concept of structural stability as a source of variability and richness when risks and ambiguities are involved. Consciousness, here interepreted under the dychotomy voluntary x automatic control can have with these ideas more elements to be investigated in biological systems and, maybe, modeled in artificial-formal ones.

INTRODUCTION

Cognitive Science is one of the last efforts of our century to face the perplexities that surround the old dilemma that tries to explain how the mental "emerges" from the physical.

The mind conceived as an information-processing device opens a series of perspectives in spite of gathering multiple problems. The same problem occurs with notions such as intelligence, cognition and, at the top of the hill, consciousness.

It is far from simple to state that the mind is an information-processing device. First because the criteria that subserve the notion of information are formal ones. Adding the "processing" means nothing but a kind of rule, or system, that codifies or de-codifies information. Nothing is said about the nature of the objects that are carried through a channel, nor about the source, nor about the receiver. Only quantities are considered in their relative probabilities and converted into "bits". Whatever the objects may be, it doesn't imply that the quantities will vary according to their meanings or inclusiveness in one or other class. Briefly, information and process can be considered as abstract notions that prescribe and describe the modes a relation can be handled between several sets. Transformations must be considered twofold: in a formal, or syntactical way, and in a "content"or semantical way. In principle, considering the mind as an information-processing device privileges only the syntactical aspect of transformations. What the mind contents are, is not focused, as if one could believe that the taxonomy of our mental experiences is trustworthy. The world may not be made of these "objects" we presume to see or to feel or even to manipulate through our thinking.

On the other hand, considering semantical objects, like thoughts, feelings an so on, opens the dangerous dualistic door that has obscured science. The manipulation of semantical objects would be, according to this tradition, a separate realm that has its own logic. Or talking in a modern version, the level of the algorythm and of computation are dissociated of the level of implementation (functional separation).

The mental could be divided in three different categories: emotions, volitions and thoughts. Cognitive Science in a restrictive view would have to handle only with thoughts, but it would imply that "two thirds" of our "object" would remain homeless.

Good science prescribes that one should pursue a "liturgyc" way: from the simple to the complex, from the bottom to the upper level, from the linear to the non-linear, etc. That is why serious authors suggest that handling with cognitive phenomena must be preceded by a carefull asepsis: de-contextualize and de-affectize the data. Hystory, this way, is an outsider intruder in the persecuted world of ideal forms. But hystory too, is what tells us the initial or boundary conditions of the system under consideration. Even the most inocent deterministic system, a three bodies one, acting one to each other according to the gravitational rules behaves dramatically differently according to the point of departure. Is it possible to think of something that obeys the invariance of the universe, ommiting this "context" informations? Moreover, if attention and emotion are coefficients that modify the quantity and even the quality of one's acts, how can one legitimately suppose cognition deprived of hystorical and hysterical aspects. Hystory, here, means only the integer that, given the initial conditions, reports the systems flux. Hysterya, here, means the masks, or entities, that are candidates to substitute bounded or state variables.

Dynamical systems are so widespread as time inflicts its inexorable mark. There are always quantities that vary along the time. The decay of a radioactive isotope, the wrinkles of one's skin, the wisdom of the oldest. Food resources and starvation: the dammed Malthus' dysloyal non-linear variation; co-variation, mutual dependence and a rate of change that depends on time, from zero point till the end of integration, or desintegration, who knows? Why must be the mental something different. Syntactical rules could be considered rules that connect the neurons in one's brain. Semantical entities could be considered one's behavior or mental representations. But what about the semantical rules that stay in between syntactical and pragmatical ones? Is it reliable to state that mental "impressions"or sensations are the right candidates to substitute the state variables in a dynamical system? And if they are, what is the structure of the differential equations that govern this absurd integration: the numbers that feed these equations and the order of this system, considering a superposition of hierarchies: syntactical, semantical and pragmatical, or in another version what theory can handle with the structure of the system, define its variables and establish the domain of interpretation of these functions, i.e. the individuals that are invariantly, be in New York city, be in an aborigeneal society, apt to iterate the equations leading to a state? Briefly, how many colors can one see and how many are "cultural" and contingent "a posteriori" interpretations? What kind of primitives conjoin to tailor a human being, thoughtfull, "free" and emotionally driven?

A carefull analysis must be done in order to separate all the elyptical questions put above. Cognitive Science and any kind of decent attempt to grasp the mental from the darkness age will have to deal with these problems.

Consciousness will be the cornerstone of this labor. It will push us to face the relation between volitions and automatisms. Voluntary behavior is what precludes any model to be legitimately called a "cognitive" one. Recruiting these pairs to the arena will heat the debate between models and mind. This is the aim of this work, if you don't mind.

PLAN OF THE TOPICS

Considering the imense contingency of epistemic, ontological, biological, computational and mathematical problems involved in our proposal, there is here a guide to the work.

Section 1 deals with the problem of consciousness considered as a problem of volition and control.

Section 2 deals with the relation between voluntary and automatic control, from the natural and the artificial view.

Section 3 deals with the problem os ambiguity as a mark of culture and on how cortical plasticity has evolved to provide a rich, but strongly non-linear, tool to handle with this. Semantic ambiguity is presumed as a strong thesis to be possibly mapped unto bifurcations parameters values. To understand this proposal one has to know what stability, from the structural point of view means.

Section 4 explains the notions of structural stability and of bifurcations

Section 5 proposes a definition of organization based upon a rate of change os state variables (rapid dynamic) and of parameters (slow dynamic). The informational measure of the complexity of the system is defined through entropy.

Section 6 explains what information is and explains the thermodynamic and the informational notion of entropy.

Section 7 presents the Hodkin-Huxley model of the neuron as an oscillator and some tranformations that can be made in the model through the van der Pol non-linear oscillator.

Section 8 shows a model of neuron based upon thermodynamic notions

Section 9 relates three ways to see the relation between mind and brain: dualistic "models", traditional AI models and neural networks.

Section 10 defends the neural network models as better epistemic and ontologycal way to model the Central Nervous System and the mind

Section 11 has some criticisms about the lack of a rich source of continuosly dynamical changing in neural nets proposing architectures that have "real"dynamical properties: coupling oscillators

Section 12 explains the basic notions of an oscillator, ways of connection and a taxonomy inspired in telecomunications and clock-signal generators

Section 13 proposes an architecture of 7 coupling oscilltors called psychon.

Section 14 shows some mathematical problems involved with such an architecture.

Section 15 shows some simulations seeking two kinds of bifurcations: one based on frequencies other based on friction coefficients.

Section 16 tries to establish a relation between decision and bifurcations in the frequencies space. Problems tied to decision under risk, from the normative and the descriptive point of view are quickly presented. Consciousness is reafirmed as an decision makig device that appears progressively in the natural scale as way to solve ambiguities. Some problems of Godel's Theorems and Turing machines are discussed as speculation about the relation between the model and the emergence of mind

Section 17 tries to establish a learning rule based upon modifications of friction coefficients

Section 18 shows some relations between pulse to frequency transformations and defend the use of Fourier series as tool to integrate two rival outputs

Section 19 defends some ideas based upon the analogical x digital debate concerning neurons: local potentials and action potentials.

Section 20 shows some ideas of qualitative deviant behavior (psychiatric disorders) that are treated through quantitative modifications of neurotransmitters

Section 21 returns to the debate of ambiguity in the semantical sense and bifurcations in the mathematical sense. Structural non-stability is defended as a source of qualitative modification depending on slight variations of parameters.The relevance of these ideas to Psychology and mainly to Psychiatry are put.

Section 22 reviews some ideas about the function of sleep and dreams in cognitive systems

Section 23 proposes a dream algorythm in our architecture that deals with long term learning, categorization and organization.

Section 24 tries to establish the discussion about the nature of inputs in PSYCHON. The dychotomy semantic x sintactic is replaced based on information criteria. A semantic way to treat information is suggested

Section 25 Deals with virtual hierarchies of PSYCHONS as a way to reach "voluntary"control. A metaphor based upon OSI-model is recruited.

Section 26 discusses the biologycal plausibility of the model and many of its limitations .

SECTION 1 CONSCIOUSNESS AS VOLUNTARY CONTROL

Consciousnesss is one of the main problems tied to the "replication" of cognitive abilities through artificial architectures.

Several startegies may be followed to handle with this problem. We suppose that denying consciousness as a pseudo-problem or re-affirming it in spite of having no idea on how to model it are both bad extremes.

Consciousness in our view must be seen first of all with two lenses: first it must be seen as function; second it must be seen as the set of properties that it predicates.

Definition 1 : consciousness represents an evolutionary gain (function)

Definition 2: consciousness represents an internal model that represents concrete and virtual, conter-intuitive (conterfactual) worlds. These representations are objects of manipulation by an agent (one's identity) that has the sensation of acting freely of constraint (free-will, volition). Even the most elaborated theory of optimization doesn't give account of one's acts because not always his, or her, voluntary, hence conscious, acts pursue optimization. But they always represent decision

Definition 3: Consciousness represents multiple models of multiple worlds, acting upon them through suposed freely volitions. The agent that acts upon representations not always optimize a decision but almost always decide. Hence, decision is one of the main marks of consciousness, and maybe its crucial evolutionary meaning.

Definition 4: Decision is one of the main functions of consciousness

Definition 5: Ambiguity is read in the cognitive domain as indecidibility

Definition 6: Culture and contingent situations are full of ambiguity

Hence: Consciousness appears the more culture makes ambiguity proliferate.

The more upper levels are recruited to eleiminate ambiguity, the more "consciousness"is involved.

The more ambiguity and indecidibility are present, hence recruiting upper levels, the more voluntary the process. The steps that must be present till the system "decides" accumulates the freedom sensation, hence the voluntary aspect of decision.

Godel's theorem affirms that there is always a certain degree of incompleteness and indecidibility in a system and this is what gives the looping problem in Turing machines (the stop problem)

Then, meta-levels must be recruited in order to solve the problem. One of

the tricks to prevent the looping problem in a Turing machine is the usage of a deterministic stochastic device (what in theoretical terms doesn't solve the Godel's problem of existence of a proposition that cannot be proved by the system) or of a quantum device (oraculi).

Consciousness within this view may be seen as the name one gives to the progressive appearence of levels of decision within systems that are forbidden to stop in an indecidible point, that means maximum ambiguity and paralisates every behavior (in optimal terms)

Let us explain this ideas within the scope of this brief pages.

Pre-wired, hereditary mechanisms are modeled to respond in a quick monotonous way. This systems in artificial-mathematical terms use to be linear, or if non-linear, parameters are set to mantain the system far from bifurcations zones.We risk to suggest that pre-wired systems are conservative in hamiltonianian terms.

The tasks however a system has to face are not always simple, and learning must be necessary, and also in situ, or on line, adaptation. The more comples a system and an environment is, the more on-line adaptation and learning are necessary. This enriches the systems behavior but pays the cost of introducing sttructures, from the mathematical point of view that tend to behave strangely. Non-linearities associated with sensibility to the initial conditions gives rise to "deterministic chaos". This is the peak of a mountain of difficulties a system has, qualitative abrupt transitions in the state-space that undermines predictability. Bifurcations are in our view the mathematical correlate of ambiguity in each level, i.e, slight perturbations give dramatically different behaviors.

The architecture we are going to propose needs not necessarily chaos to enrich its behavior but uses the dichotomy structuraly stabe x unstable and ordinary x bifurcation parameters value as a source of inspiration to treat ambiguity, decision under risk taking account of normative (optimal ) and descriptive issues. Consciousness this is way is seen as an adaptive device that happens to manage decision problems when ambiguities and undecidibility are involved. The kind of mathematical problems, the neural natural and artificial structure that underlies these problems and the criteria one could adopt to manage the decision problem at the syntactical and at the semantical levels will be focused on in the next sections.

SECTION 2: VOLUNTARY x AUTOMATIC CONTROL

From the above said it is a plain fact that every artificial architecture that tries to model "cognitive" structures is an "automatic" device. Difficult notions like control in its automatic and voluntary fashion are discussed in this topic.

Precision is a very far concept the more one tries to reach the so called "superior functions"of the Central Nervous System. It is difficult to defend a strong point of view. Some ask if the best way is not to avoid such problem, waiting for more data. Others propose that such questions have to be faced, otherwise data will not appear, simply because one doesn't have to grasp them from the empirical blocks. We know that there are many speculations when one tries to model cognitive phenomena. Moreover, it is a fact that high-order functions, like thoughts, intelligence, consciousness and pathologies can be a strange set of problems to artificial modelers: engineers, physicists, etc. They have to handled by physicians and biologysts till the ammount of empirical data become clear and high enough to be formalized and simulated. If one has the will to face "cognitive" phenomena it is better to begin with vision, or olfaction, or mouvement. Consciousness is under suspicion until today, because it can be one of the last oncepts of another era. Everything in the artificial real must be automatic and voluntary control, based upon conscious manipulation of some sort of representations, are to be discarded as soon as formalisms and science reaches these last frontiers.

Strategy 1: abandon the high-order functions, mainly consciousness and volitions, waiting form more biologycal data

Strategy 2: try to propose thought-experiments based upon some invariant notions of the physiscal systems, combined with some biologycal knowledge, seraching for a feed-back mouvement regarding neurobiology: first one states how it might be and then one seeks if it is. Refutations based on arguments and proofs are welcome but arbitraryly prejudices are not in the spirit of scientific inquiry. We consider strategy 1 good science but we addopt strategy 2 as way of integration between some specialists: multidisciplinary cognitive science.

Muldisciplinary efforts are of two sorts:

1) a posteriori: a psychologyst may do reserach on a topic a with data ask a mathematician to formalize or to a computer scientist to simulate. A physicist may have a psychologycal interpretation of a quantum phenomena in spite of having no idea of the level the CNS is supposed to work (Quantum phenomena may not be the major problems in the CNS).

2) a priori: some specialist may have common ideas based upon some similarities they see between their disciplines. The genesis of this work comes from three different sources: cognitive deviance (psychopathology), dynamical systems and computers science and we addopt multidisciplinary 2 the way of working. Why? Because there are plenty dychotomies in our work that seem elusive: von Neumann x neural nets models, neural x computational models, quantitative variation x qualitative behavior, and the pharmacologycal treatment of psychiatric disorders, e.g. anxiety, depression, obsessive-compulsive disorder (OCD) and schizophrenia.

Briefly, computer science asks about the nature of representations (symbols) in a cognitive architecture and the rules that are used to manipulate them.

Dynamical Systems Theory approaches the problem of qualitative variation according to subtle quantiataive changes in bifurcation's values in deterministic systems, i.e. systems that doesn't have quantum limitations of measure and can be, in principle, be described by differential equations.

Psychiatry furnishes an astonishing organ: the mind and its deviances. We don't know where it is located, somewhere between nature and culture, and we know it becomes sick. Mainly, the best way to handle with organic or "endogenous"psychiaric disorders is to use drugs that act in the synaptic cleft. They promote quantiatative variations in the neural signallinfg mechanisms, and allow the patient to recover or to ammeliorate, reporting drastic qualitative inner feelings, thoughts and experiences.

A depressive patient may relate an inner qualitative sad mood, experience mad thoughts of ruin and may see no exit to his, or her life. Quantitative variations of nor-adrenalin and serotonin, through the usage of antidepressant drugs, usually are followed of relief of the symptoms and of dramatic qualiative variations of the mood and thoughts. Examples like this are common in all other pathologies.

Why is the mind and hence its deviances implemented in neural structure and what gives rise to collective behaviors and inner experiences that change dramatically suggesting strong non-linearities? Our approach is that in spite of the gap between our undestanding of syntactical rules (rules of connection) between neurons, and semantical rules (rueles of connection) between mental blocks ( like thoughts, feelings,) the rule that underlies the first may be approximately the same that underlies the second. In this way we are strongly reductionists and henceforth we suggest a model that though the most basic rules can enlight the undertsanding of some obscure properties like volition, representation and conscious control.

Reduction means that the system must be deterministic in a certain sense. This is what we expect from objects that are supposed to be investigated though scientific inquiry. But being thermodinamically open, or being mathematically non-linear, or being complex from the statistical point of view, means that predicatability may be insane, and sometimes non-linearities are read as "emergence"and "dissociation" of categories. Hence the mental and at the top consciousness, represented here by voluntary control, are supposed to be an other real, or a functional new object that accidentally is implemented in a brain