Cognitive Mechanics: Natural Intelligence Beyond Biology and Computation

Jon DoyleDepartment of Computer ScienceNorth Carolina State University

Box 8206, Raleigh, NC 27965-8206, USAJon Doyle@ncsu.edu

Abstract

Framing traditional disputes between computational and bi-ological approaches to understanding cognition in terms ofa divide between natural and engineering inspirations artifi-cially restricts the notion of nature to biology. One need notrestrict natural inspiration to biology, however. One can findcommon ground between the two approaches in mechanics,which underlies and provides important extensions to bothconceptions.

Introduction

The computational conception of cognition has come in forcriticism on several grounds, including undesirable brittle-ness in capacities; the large efforts needed to manually for-malize and represent human knowledge; the nonuniformityevident in needing different learning methods for each dif-ferent representation and task; and a lack of direct con-nection with neurophysiological realizations (though somecount this as a strength rather than as a weakness). Theseweaknesses of the computational conception are often con-trasted with the strengths of biological conceptions, whichin the popular artificial neural network frameworks haveboasted of robust behaviors insensitive to small perturba-tions in situation or mental state; relatively universal anduniform learning methods, at least in comparison to com-putational conceptions; and structures that fit well with bothanimal physiology and evolutionary theories.

Critics of biological conceptions of cognition in turnhave pointed out that unstructured neural conceptions lackready interpretation or explanation in linguistic terms; thatuniform learning methods sometimes require long trainingtimes in comparison with specific symbolic methods; andthat universality of learning methods is trivial to obtain.These weaknesses of biological conceptions are in turn con-trasted with notable strengths of computational conceptions,namely expressive and independently intelligible represen-tations of statements in natural and formal human languages;ready provision of explanations of mental states and theirchanges; straightforward cognitive computations that appearclose to some introspective accounts of human experience;and direct provision for innate abilities and structure.

Copyright c© 2008 by Jon Doyle. All rights reserved.

I believe that some of the respective strengths of the bio-logical and computational approaches come from the samenatural source, namely mechanics, and that one can seekfruitful combinations of the two and add further strengthsby looking to concepts of mechanics that have not playedmuch of a role in either approach to date.

Cognitive Mechanics

The brief position statement offered here draws on Extend-ing Mechanics to Minds (Doyle 2006), which applies mod-ern axiomatic rational mechanics to psychology and arguesthat mechanical concepts, such as force, mass, and work,provide a useful vocabulary supplementing ones from com-putation and neurophysiology for describing and character-izing cognition and other mental processes.

Only a few of the axioms of modern rational mechanics(Noll 1958; 1973; Truesdell 1991) embed assumptions aboutthe continuum nature of space and time. One can separatethese continuum assumptions from the rest of the contentto obtain axioms that characterize almost all of the familiarproperties of mechanical concepts in a way that is indepen-dent of continuum assumptions. The resulting mechanics re-produces standard mechanics as a special case, in which thefamiliar continuum assumptions need apply only to physicalspace and time.

The broadened mechanics also applies to nontraditionalmechanical systems that characterize time, space, mass, andforce with discrete structures that are mathematically quitesimilar to the vector space structures used to characterizetraditional mechanics. Some common formalizations of dis-crete cognitive architectures studied in artificial intelligencecan be recast in these structures and observed to satisfy themechanical axioms. Minds that satisfy the axioms of me-chanics are mechanical systems, so use of mechanical con-cepts to describe such minds involves no use of metaphor.

Hybrid combinations of discrete and continuous mechan-ical systems, such as persons with bodies and minds thateach form mechanical systems, can also form mechanicalsystems in the broadened mechanics.

Just as physical materials appear in different kinds withdifferent characteristics, so also do mental materials makingup different kinds of minds. In particular, cognitive architec-tures with different characteristics can correspond to differ-ent mechanical materials. Indeed, physical materials appear

in such variety that a particular mental material can be moresimilar to a particular physical material than that physicalmaterial is to some other physical material.

Transcending Rigid Kinematics

Development of Turing’s (1936) mathematical model ofan intelligent human mathematician engaged in calculationproduced the modern theory of symbolic and numeric com-putation, in which discrete symbols and rules govern dis-crete movement through finite or infinite machine states.In developing its application to cognition, one can replacesymbols with logical or quasi-logical statements, behav-ioral rules by inference rules, and machine configurationsby memory lists and structures, and one can combine suchdiscrete structures with finite numerical values to obtainBayesian networks and update rules.

At its base, however, Turing’s computational conception,like the earlier calculation-oriented efforts of Babbage andLovelace, views thinking in terms of movements and con-figurations of clockwork-like machines. In traditional me-chanical clocks, of course, gears shift from one configura-tion to another in discrete steps. Modern stored-programcomputers behave much the same, except that the configura-tions are those of discrete switching circuits. In clocks, as incomputers, the motive power that produces these changes ofconfiguration is irrelevant to the operation except when thepower fails and the machine stops.

From a mechanical point of view, the computational ap-proach is limited to properties of rigid kinematical systems.The discrete configurations correspond to symbols, and ex-plicitly so in Newell and Simon’s (1976) physical symbolsystem hypothesis about the nature of intelligence. Thisrigid kinematical approach contributes to the observed brit-tleness of computational approaches. In the mechanicalworld in which we live, most things deform a bit when sub-ject to ordinary forces, and few things exhibit perfect rigid-ity. Turing insisted explicitly on something close to inde-formability in his model of computation, basing the restric-tion to finite tape alphabets on the need to avoid one symbolshading off into another, just as a deformed “j” can resemblean “i”.

In contrast, neural models of cognition following fromthe work of McCulloch and Pitts (1943) and von Neumann(1958) regard the imprecision of symbol boundaries as con-tributing to robustness. Even though one can sometimesread or design symbols into the structures and states of neu-ral networks, as in (Touretzky and Hinton 1985), one usu-ally expects the meaning of concepts to shift somewhat withchanges in one’s environment or activities. This sort of de-formation is offered as a strength of neural net approaches.

Indeed, models of some types of learning explicitly in-volve mathematical structures found in the mechanics ofdeformable materials. Construction of support-vector ma-chines, for example, involves computing a Gram matrixfrom a set of data points in the course of finding a separatingembedding of the original data into a larger space. In me-chanics, the intrinsic configuration of a body consists of theset of distances between each pair of body points. Deforma-tions of bodies consist of changes in intrinsic configurations.

The Gram matrix of a body of data is one representation ofthe intrinsic configuration of the data, so the support-vectortechnique amounts to finding a deformation of the body ofdata that separates the classes of interest.

Characterizing Realistic Dynamics

Many neural models are tied to a specific level of detailand do not in themselves support abstract and higher-levelcharacterizations of mind. Modern mechanics, in contrast,gives central roles to constitutive assumptions that charac-terize properties, such as elasticity, incompressibility, polar-ization, and rigidity, that differentiate the variety of specialtypes of materials and that are critical to understanding be-haviors independent of the precise identity of the materialsexhibiting them.

One example of an important mechanical property is men-tal inertia or resistance to change. Neurophysiological an-swers to questions about how minds change primarily in-volve schemes of neural parameter adjustments, and to amuch smaller extent, ideas about growth or death of neuronsand neural structures. Although such physiological changesmight mediate mental changes, they do not answer questionsabout mental change any more than sets of character inser-tions and deletions answer questions about how Lincoln re-vised drafts of his Gettysburg address.

Even foregoing questions about motivations of change,neural biology does not provide good answers to questionsabout the effort, difficulty, or rate of change. These playmajor roles in understanding realistic notions of rationality.The idealized rational agent assumed in economics and epis-temology exhibits perfect epistemic omniscience and con-sistency, and is capable of assimilating new information andmaking perfect decisions instantaneously. Realistic rational-ity, in contrast, suffers limitations: reasoning and delibera-tion require effort and concentration, actions must be takendespite persistent inconsistency and ignorance, and learningtakes time and slows as habits accumulate.

Mechanics provides concepts for understanding theselimitations in natural terms (Doyle 2009). Some limitationsarise from the mental mass associated with some aspects ofmemory. All mass generates inertial forces that limit themotion resultant from a given force. Other limitations arisefrom bounds on the amount of work that can be performed ineffecting change. Mechanics measures work in terms of theforce applied across the distance traveled. This notion pro-vides a natural measure of effort in mental mechanical sys-tems as well, which in simple kinds of minds corresponds tothe number of changes to memory made in the course of rea-soning. Some limits on the rate of work stem from boundson the magnitude of forces acting in a system. Natural mate-rials generate forces bounded by the size and mass of bodies,and such limitations are evident in realistic mental materi-als as well, in which reasoning rules or other mechanismschange bounded numbers of conclusions and in which sen-sor dimensionality and Shannon channel capacity limit themagnitude of forces.

Some mental materials exhibit forms of constitutionalrigidity, such as cognitive architectures in which some typesof conclusions are always drawn automatically regardless

of the rules or other knowledge possessed by the reasoner.Elastic and refractory forces are exhibited by other mentalmaterials. In reasoners making use of nonmonotonic defaultrules and dependency-based revision and restoration opera-tions, for example, the “rest configuration” of defeated de-fault assumptions can be restored on the removal of the as-sumption defeaters, and the existence of alternate support forconclusions can resist removal of the conclusion in the firstplace. The common multiplicity of conclusion sets gener-ated by multiple nonmonotonic defaults means that removalof deforming defeaters can let the reasoner rebound to men-tal states other than those existing prior to imposition of thedefeaters. The elasticity characteristic of default reasoningis thus also often accompanied by some amount of plas-ticity. Rigidity and elasticity can aid in reasoning, but canalso impede it. In particular, when reasoning habits gener-ate distracting conclusions that divert the reasoner from itsgoals, focusing attention on those goals requires generationof forces to counteract the distractions. In such cases, boththe creation and removal of the distraction involve work onthe part of the reasoner.

Conclusion

One can trace some of the comparative strengths and weak-nesses of computational and biological approaches in arti-ficial intelligence to the provision for or lack of importantcharacteristics of mechanical systems. As one might ex-pect from the kinematic appearance of computation, somekinematic characteristics of materials are easier to identifyin computational approaches than in superficial biologicalmodels, and account for some of the advantages of compu-tational relative to biological approaches. Similarly, somecontinuum characteristics of materials are more easily iden-tified in neurophysiological models, and account for some ofthe advantages of biological over computational approaches.

Mechanics provides concepts including mass, force,work, and elasticity that go beyond the standard con-cepts provided by current computational and biological ap-proaches. Augmenting computational and biological analy-ses with mechanical concepts promises to illuminate betterthe full richness of mental materials and phenomena and soimprove our understanding of mind. Fulfilling this promisewill likely require progress on developing the mathematicalanalysis of discrete and hybrid mechanics in ways that paral-lel past progress on the mathematical analysis of continuumphysics.

Acknowledgments

The author’s preparation of this paper was aided by a SASInstitute Professorship endowment.

References

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