snakes all the way down: varela calculus for self ...the autonomy of varela’s thinking what is...

■ Research Paper

Snakes all the Way Down: Varela’sCalculus for Self-Reference and thePraxis of Paradise

André Reichel*

European Center for Sustainability Research, Zeppelin University, Friedrichshafen, Germany

This contribution seeks to commemorate Francisco Varela’s formal conceptions ofself-reference, providing an overview of his writings while shedding some light in thepraxis of self-reference, from where a future research agenda can be derived.The architecture of Varela’s thinking, determined by the interrelated notions of autopoiesis,autonomy, closure and self-reference, was examined. The emphasis was on the develop-ment and expansions of his calculus for self-reference from George Spencer Brown’sLaws of Form. After dealing with some of the criticism launched at both works, an appraisalof the praxis of self-reference of Varela’s thinking in action was given. The outlook roundsup this contribution, shedding some light on a possible future research agenda forthe formalization of theory and praxis of self-reference. Copyright © 2011 John Wiley &Sons, Ltd.

Keywords Francisco Varela; self-reference; Laws of Form; closure; autonomy

INTRODUCTION

If everybody would agree that their currentreality is a reality, and that what we essentiallyshare is our capacity for constructing a reality,then perhaps we could agree on a meta-agreement for computing a reality that wouldmean survival and dignity for everybody onthe planet, rather than each group being soldon a particular way of doing things. Thus,

self-reference is, for me, the nerve of this logicof paradise . . .(Varela, 1976: 31)

Francisco Varela died 10 years ago and left uswith a rich body of work, radiating into manydifferent fields and problem areas, probably be-yond his dreams and hopes. This contributionseeks to commemorate Varela’s formal concep-tions of self-reference, providing an overview ofhis writings while shedding some light on thepraxis of self-reference, from where a future re-search agenda can be derived. The issues dis-cussed here will start from the originalarchitecture of Varela’s thinking across his 30

*Correspondence to: Dr André Reichel, European Center forSustainability Research, Zeppelin University, Am Seemooser Horn20, Friedrichshafen 88045, Germany.E-mail: [email protected]

Received 28 February 2011Accepted 29 July 2011Copyright © 2011 John Wiley & Sons, Ltd.

Systems Research and Behavioral ScienceSyst. Res. (2011)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/sres.1105

years of scholarly life to the intertwined notionsof autopoiesis, autonomy, closure and self-reference. We will then continue with his workon the formal aspects of self-reference asdeveloped in A Calculus for Self-reference (Varela,1975) and the extensions made in collaborationwith Joseph Goguen and Louis Kauffman. Thecriticisms launched at this part of Varela’s work,especially at its basis, the Laws of Form by GeorgeSpencer Brown (Spencer Brown, 1969), will becategorized and rebutted. In the final part, wewill dive into some of the many applications ofhis thinking, namely, in psychology, his owntheory of embodiment, and the application insocial systems theory by Niklas Luhmann (1995a).

The frequent use of direct and unabbreviatedquotations from Varela himself offers the readerthe possibility to assort and evaluate his originalideas with the conclusions we are drawing fromthem. The main argument encountered again andagain is that Varela provided a formal groundingfor dealing with self-reference, regardless of thediscipline one is affiliatedwith or the phenomenonat hand. This contribution demands an ‘openheart’ (Kauffman and Solzman, 1981: 256) and thewillingness to dive into the logic of paradise.

THE AUTONOMY OF VARELA’S THINKING

What is striking about Francisco Varela and hiswork is the great coherence of its architecture.This architecture rests on four interrelatednotions: autopoiesis, autonomy, closure and self-reference. All four notions reverberate through-out the 30 years of research Varela undertook,from the humble beginnings in Chile and theautopoiesis of living systems (Varela et al., 1974)to his work on phenomenology and philosophyof biology (Weber and Varela, 2002). All of hiswork contributed, in one way or another, tothe core question of biology, posed by ErwinSchrödinger: ‘What is life?’ (Schroedinger, 1944).Varela’s attempt of an answer led him to amagical mystery tour deep into philosophicalterritory, in fact, ‘into a more than 2500-year-oldphilosophical minefield about the nature ofreality and cognition’ (Brier, 1996: 231–232). This

quotation from Brier, although aiming at second-order cybernetics, is valid for the quest Varelawas following, because life and cognition are sointricately intertwined that the entire notion of a‘cybernetics of cybernetics’ only makes sensewhen connected to the living.

Starting with notably the most famous notionof the four, autopoiesis, its classic definition fromthe seminal paper by Varela et al. (1974: 188)indicates it as the production of a ‘unity by anetwork of productions of components which (i)participate recursively in the same network ofproductions of components which producedthese components, and (ii) realize the networkof productions as a unity in the space in whichthe components exist.’ The criteria for autopoiesis,that is, if we are in fact dealing with an autopoieticunit, have been simplified by Varela himself inhis essay ‘El fenómeno de la vida’, from whichLuisi (2003) quotes that they consist of ‘verifying(1) whether the system has a semi-permeableboundary that (2) is produced from within thesystem and (3) that encompasses reactions thatregenerate the components of the system.’ In orderto understand where autopoiesis comes from andwhat the motives of its ‘parents’ were, one has torecall the state of biology in the 1960s and 1970s.The dominant approach back then was gene-centrism, the idea that the living is determined byits genetic constitution, reducing Schrödinger’squestion to a mere counting of RNA, DNA andenzymes (Varela, 1996). The feeling of revolutionin biology and maybe in the whole of science asthe focus of interest started to shift ‘from causalunidirectional to mutualistic systemic thinking,from a preoccupation with the properties ofthe observed to the study of the properties ofthe observer’ (Howe and von Foerster, 1975: 1),coincided with the revolution in Chile’s politicalsystem, signified by the election of SalvadorAllende as president in 1970. All distinctions inscience that are drawn to understand the objectsof interest, in fact, all distinctions in all areas oflife, are drawn with a motive, for there ‘can beno distinction without motive, and there can beno motive unless contents are seen to differ invalue’ (Spencer Brown, 1969: 1). This idea that everydistinction, and thus every concept in science, in-cluding its understandings andmisunderstandings,

RESEARCH PAPER Syst. Res

Copyright © 2011 John Wiley & Sons, Ltd. Syst. Res (2011)DOI: 10.1002/sres

André Reichel

indicates its motive and cannot be understoodproperly without taking this into account willcome up in this contribution from time to time.Autonomy, turning to the second important no-

tion, ‘is the distinctive phenomenology resultingfrom an autopoietic organization: the realizationof the autopoietic organization is the product ofits operation’ (Varela et al., 1974: 188). Varelaillustrates autonomy with the example of theimmune system, which he views as autonomousdue to its autonomous functioning within theorganism. An autonomous system might nothave a clear-cut boundary like a cell membrane,but it has a boundary drawn in operation, thatis, in the way the system functions autonomouslyin relation to its environment (Varela, 1978: 80).Although he draws a distinction betweenautopoiesis and autonomy, restricting autopoiesisto biology and living systems, thus placing itlogically under autonomy (Varela, 1981: 14), thisdistinction can best be understood when onerecalls the underlying motives. Autopoiesis wasand is sought to be the central concept defining aliving system and providing an answer toSchrödinger’s question. The battlefield is biology,not any other scientific discipline. Regardless ofthis distinction, the importance of the notion ofautonomy, ‘that is, the assertion of the system’sidentity through its internal functioning and self-regulation’ (Varela, 1978: 77), can be seen through-out Varela’s work, from its centrality for theautopoiesis concept, where it was used to positionforces against genetic determinism (Fleischaker,1988: 39), to his work on identity and cognition.In order to understand the connection betweenthe living and its identity construction through(self-)cognition, autonomy as the ‘fundamental’condition of the living needs to be taken intoaccount (Varela, 1997: 73). Glanville notes, in anobituary for Varela, that the assertion of autonomywas not only a scientific matter for him, but also apersonal one, reflected in the turn towardsBuddhism and Continental philosophy (Glanville,2002: 67). Varela himself admitted that creating his‘own original science’ (Varela, 1996: 411) was amatter of staying true to himself, his past and hisroots. Again, no distinction is drawnwithout amotive.Autonomy is tied to the third notion, that

of closure. Axiomatically, Varela formulates his

closure thesis: Every autonomous system isorganizationally closed (Varela, 1978: 79). Whyshould that be substantial? Because the processof identity construction of an autonomoussystem is always one of closure from its environ-ment, and to close means to establish a perfectlycontained circular process producing itself,thus constituting its autonomy (Varela, 1997:73). The process of closing can be sketched byKauffman’s visualization of an arrow benttowards itself and, therefore, pointing to itsbeginning (Kauffman, 1987: 54). Closure thusdefines a unity that is produced by the containednetwork of interactions producing themselves ‘asa unity in the space in which the componentsexist by constituting and specifying the unity’sboundaries as a cleavage from the background’(Varela, 1981: 15; emphasis added). Accordingto Fleischaker (1988: 38), Varela replaced theoriginal closure adjective ‘organizational’ with‘operational’ somewhere around 1982, but appar-ently, he seems to use the terms interchangeably.This might be due to his rooting in biology andthat therein ‘organizational’ and ‘operational’ issynonymous or arise at the same time. However,through closure, intrasystemic coherence withoutthe need for central control emerges, whereasat the same time, closure from an environmentparadoxically implies dependency on thatenvironment (Varela, 1997: 73–78).

Closure now is leading to the last notionmentioned previously, that of self-reference. Fromwhat has already been said, it becomes clear thatany autopoietic system, in order to maintain itsautopoiesis (organization), needs some form ofclosure (distinction) from its environment, thusstating its autonomy from this environment.Closure, autonomy and, in fact, autopoiesisrequire a production of a boundary through theboundary, that is, presently drawing a distinctionwith the help of past drawings of a distinction.Only then the system can interact with itsenvironment without loss of identity (Varela,1981: 15–17). In other words, autonomous, self-producing systems construct their environment(draw a distinction) in order to be and staythemselves. Autonomy as self-rule throughclosure and self-production (autopoiesis) leadsto the insight that ‘the rules of operation are all

Syst. Res RESEARCH PAPER


Snakes all the Way Down

self-contained, there is no possibility of referringto the outside from inside the system’ (Varela,1997: 73). That is, the autonomous system canonly refer to itself; the arrow has been bentinwards and created a circular loop of self-creation. Luisi (2003: 51) terms the autonomousidentity of a closed autopoietic system as ‘auto-referential’, producing its own rules of existence.In such forms of closure, component interac-tions become fixed-point solutions1 of theautonomous system, where the fixed pointsare Eigenbehaviors or self-determined behaviorsexpressing systemic invariances against theenvironment specified by the system itself (vonFoerster, 2003). The system exhibiting suchEigenbehaviors becomes ‘aware’ of itself throughcognizing the drawing of the distinction betweenitself and its environment and the understandingof this distinction as an indication what the systemis and what it is not. As Kauffman (1987: 53) putsit, ‘[t]he self appears, and an indication of that selfthat can be seen as separate from the self. Any dis-tinction involves the self-reference of “the one whodistinguishes”. Therefore, self-reference and theidea of distinction are inseparable (hence concep-tually identical).’ So the ‘know it-self’ is crucialfor identity construction, for only through thisself-knowing the self thus constructed can detectthe presence of something foreign, and in fact,itself is the only point of reference for a closed sys-tem (autopoietic system, autonomous system) tobuild discriminations of what it is not. Throughself-reference, a system creates its own teleologyand, by doing so, reproduce itself indefinitely(Weber and Varela, 2002: 120). To conclude onself-reference, it has multivalued meanings,appearing (i) as a procedure applied to itself, (ii)a reflexive domain of systemic invariances and(iii) a fixed point of a system’s Eigenbehaviors(Soto-Andrade and Varela, 1984: 18).

All these notions—autopoiesis, autonomy,closure and self-reference—are intimately con-nected. In Spencer Brown’s words, they all can

be confused. All of them are arising from themain motive of Varela’s research, to give an an-swer to Schrödinger’s question about the natureof life. In order to answer this question, one hasto cope with issues of self-referencing, self-producing and self-closing systems that areautonomous with respect to their environment.When starting his journey towards the answerin the 1970s, there was no foundation toconceptualize these kinds of systems in a scien-tific manner. The turn from cybernetics towardscomputationalism, signified by John vonNeumann, in Varela’s view led the field furtheraway from dealing properly and respectfullywith the question (Varela, 1986: 117). The roadVarela was taking instead was a journey intothe heart of paradise: ‘That paradise is somethingvery concrete, founded on the logic of self-reference, on seeing that what we do is a reflectionof what we are’ (Varela, 1976: 31). As beautifuland aesthetic as his words may appear tothe reader, the task sketched by them led Varelato formulate a mathematical foundation of auton-omous systems. It is the main argument ofthis contribution that he not only succeeded indoing so but also provided a formal groundingfor those sciences dealing with self-referential,self-producing and self-closing autonomoussystems. We will retrace his steps and dive intothe heart of paradise Varela found for him and us.

FROM THE LAWS OF FORM TO A CALCULUSFOR SELF-REFERENCE

Whenever there is an autopoietic, that is, self-producing entity, this entity needs to close onitself, draw a distinction between the environ-ment and itself and, through that, indicate whatit is and what it is not. This whole circularprocess is autonomous, without reference toanything outside itself, and it is self-referential.The hardships with self-reference have all thesame root: the distinction between actor oroperand, and that which is acted or operatedupon, collapses. The system thus constituted isof its own making, its own product and producer.This autopoietic ontology gives rise to a severeepistemological crisis, the ‘minefield’ as stated

1 Fixed points are solutions to an equation of the form f(x) = x. Varela(1979a: 171) gives an illustrative example by Heinz von Foerster of afixed point in the linguistic domain: “This sentence has thirty-threeletters”, where the sentence S has its only fixed point solution forn= 33 letters, that is, the form of the sentence is identical with whatit indicates.



André Reichel

previously: the introduction of the observer asbeing inseparable from the observation, evenworse, the observer observing and thus creatingboth the observer and what is observed. Varelaframed the problem like this: the peculiarity ofsuch systems ‘lies in being self-indicative in agiven domain, in standing out of a background bytheir own means, in being autonomous as the strictmeaning of the word enounces’ (Varela, 1975: 5;emphasis added). For Varela, the problem offormulating a conceptual foundation for this typeof system could only be solved by basing it firmlyon its self-indicational grounds. Precisely becauseof that, his attention turned to George SpencerBrown, the Laws of Form and the calculus ofindication (Spencer Brown, 1969).Much has been written about George Spencer

Brown and the Laws of Form. Kauffman (2002:50) sees it as ‘a lucid exposition of the founda-tions of mathematics. It embodies a movementfrom creativity, to creation, to symbol, to systemand language and thought and self.’ The initialmotivation of Spencer Brown, however, was ofa very earthly matter: the scheduling of trains intunnels (Marks-Tarlow et al., 2002). The algebraicequations he developed sometimes needed torefer to themselves, resulting in paradoxicalsolutions in which the Aristotelian tertium nondatur could not hold. The results oscillatedbetween true and false or, in Spencer Brown’sterms, marked and unmarked. In order to dealwith this, Spencer Brown worked backwards inmathematics, beyond its Boolean foundation inlogic, and arrived at ‘seemingly the most basicsymbol system possible, involving only the voidand a distinction in the void’ (Robertson, 1999:44). The apodictic start into the first chapter ofLaws of Form begins with the idea of distinction,and that by drawing a distinction, an indicationis made to what is marked or named by thedistinction. Both distinction and indication cometogether, bring forth each other (Spencer Brown,1969: 1). When Spencer Brown speaks of the formof distinction, and that this is to be taken as theform, the notion of ‘form’ reflects the Aristoteliandistinction between form and matter. A form iswhat bounds ‘things’; that is, the form constitutestheir boundary and in fact themselves—inVarela’s case, the autonomous system, and in

Spencer Brown’s case, the very fundament ofmathematical reasoning (Russell, 1946: 162). Thenotion of boundary thereby is also very basic:In drawing a distinction, a space with two sepa-rated realms comes into existence, and in orderto reach one side from the other, one has to crossthe boundary. The definition of distinction as per-fect continence strongly resonates with the ideasof closure and autonomy mentioned before. Themotive of distinguishing, for example, a livingcell from its environment is to uphold its autopoi-esis, thus giving a value to it that differs from thevalue of its environment. From these very basicideas of distinction, indication and continence,two situations almost naturally emerge, buildingthe basic axioms of the calculus of indication. Thefirst situation occurs when a distinction that hasbeen drawn is indicated again. This is a meredescription of what is already obvious and notchanging anything, like writing the name of thedistinction on its outside: the law of calling—‘the value of a call made again is the value ofthe call.’ The second situation is sometimes notso easy to comprehend. Spencer Brown developsa bridge between his two axioms out of the lawof calling and what he stated before. Rememberthat a distinction is always drawn with a motive;that is, it is of a value that differs fromwhat is notdistinguished. Whenever this is the case, a dis-tinction is drawn in order to name the differingvalues. If a call is made, the call is of value andcan be recalled over and over again withoutchanging its value. To call is to draw a distinc-tion, thus creating a boundary and crossing itto the side that is of value, naming it as valuableor, in other words, as marked. The second situ-ation now is that of crossing the boundary again,and that crossing can only lead into the un-marked state: the law of crossing—‘the value ofa crossing made again is not the value of a cross-ing.’ These two axioms are representing theJanus-faced nature of distinctions. Distinctionscan be both descriptive and merely naming whatis distinguished, as well as operational: draw adistinction (Schiltz, 2007: 11).

The notation of the calculus of indication isalso very basic. The mark of distinction,referred to as the cross, is a diagonally croppedrectangle with its right vertical side denoting




the distinction and the upper horizontal sidedenoting the indication. The law of calling canthen be pictured as follows:

�j �j ¼ �j (1)

The law of crossing translates into the following:

�j�j ¼ (2)

The unmarked state is not given a sign butdenoted by a blank space. With this one symboland the absence of it, and the two axioms, theentire calculus of indication develops.2

Spencer Brown stopped his work when self-reference was encountered. Chapters 11 and 12of the Laws of Form deals with what he calls ‘re-entry’, that is, what happens when the distinctionis inserted in itself, the oscillations of values frommarked to unmarked. This behavior arises fromthe following expression:

f ¼ f�j (3)

When f is taken to be the marked state andinserted on the right-hand side, what followsfrom the law of calling is a cancellation of thatside, thus resulting in the paradoxical situationwhere the marked state is identical or, as GeorgeSpencer Brown sees the equal sign, can be con-fused with the unmarked state of the void:

f ¼�j ⇒ f�j ¼�j�j ¼ ⇒ f ¼ (4)

If the unmarked state is now inserted, the re-sult is the marked state and so on. For everyodd number of crosses or marks, there appearsto be some-thing from no-thing (Robertson,1999: 255); in fact, both are identical in the formof re-entry. George Spencer Brown’s ‘most out-standing contribution’ (Varela, 1979a: 138) was

the realization that this behavior was in factequivalent to that of imaginary numbers, that is,numbers that have an imaginary part i of theform i2 =�1. Although in normal mathematics,these numbers were interpreted as being ‘orthog-onal’ to the real numbers, Spencer Brown inter-preted his re-entering expressions as oscillationsin time. Whereas the calculus produces spaceby the injunction to draw a distinction, by re-entering the calculus into itself, it produces time.Although Spencer Brown finished his work there,Varela decided to start his journey right here.

A calculus for self-reference (Varela, 1975) is anextension of the calculus of indication, motivatedby Varela’s work on living systems and how toformalize their key characteristics, namely, theirself-referential nature. In a way, this work is aprime example of how Spencer Brown’s Laws ofForm can be extended and, in fact, applied toother realms than mathematics. The emphasison and embracing of self-reference, driven byVarela’s motive of finding a conceptual founda-tion for the autonomous systems he was dealingwith as a researcher, changed the indicationalperspective insofar as self-reference, the ‘end’ ofthe Laws of Form, is now as constitutional for itas the primary distinction Spencer Brown made.Robertson (1999: 53) noted that this ‘is . . . anexplicit creation of a new calculus in whichself-reference will be the core.’

Varela (1975: 5) himself describes self-referenceas ‘awkward’ and that ‘one may find the axioms[of a calculus for self-reference] in the expla-nation, the brain writing its own theory, a cellcomputing its own computer, the observer inthe observed, the snake eating its own tail in aceaseless generative process.’ This strengthensthe claim made before that self-reference, self-production, circularity and autonomy are inter-twined and emerge from each other. Wheneverthere is closure, that is, a distinction, that whatis constituted by this closure indicates itself andthus refers to itself and produces itself, and itdoes so without reference to anything other thanitself: it does so autonomous. This restated defi-nition of autonomy is important because Varelauses this notion as the core of his new calculus:‘Let there be a third state, distinguishable in theform, distinct from the marked and unmarked

2 The reader is advised to work through Laws of Form herself andspend “delightful days” (Beer, 1969: 1329) with a pen and some paper,watching the world unfolds itself in front of one’s eyes.



André Reichel

states. Let this state arise autonomously, thatis, by self-indication: Call this third state appear-ing in a distinction the autonomous state’ (Varela,1975: 7; emphasis added). Like autopoietic sys-tems arise autonomously, that is, by themselvesthrough the process of the network of inter-actions in their domains, so is the case with thecalculus of these systems. It is a state in the form,arising from the indicational perspective whenturned towards itself. The notation Varela haschosen for this third state in the form refers toSpencer Brown’s rewriting of

Here, the re-entry of the distinction between aand b is inserted under a, denoted by f and result-ing in an infinite nesting of crosses indicatingthe distinction between a and b.3 The f can beconfused with a horizontal ‘hook’ attached tothe bottom of the cross containing the distinctionbetween a and b, pointing to where the wholeexpression should be inserted. This ‘self-cross’resembles the ancient symbol of the Uroboros, aserpent eating its own tail:

In his Arithmetics of Closure, Varela togetherwith Goguen develops another form of graphicsrepresenting both indicational as well as self-indicational expressions: the tree (Varela andGoguen, 1978: 308–310). The expression of

��ajbj

can thus be written as

denoting the containment operation at b and theplacement of a under its cross and the crosscontaining it and b. Similarly, the re-entrantexpression (5) is then transformed into

Consequently, the re-entrant expression (3) isthen perfectly symbolizing the process of closure,the arrow bent towards itself:

The autonomous state, as the third state in theform, represents a description of the re-enteringexpression, that is, of itself, as well as an injunc-tion to re-enter autonomously from any environ-mental conditions and thus create itself by itself.Just as the mark of indication, the cross havingtwo meanings—to name it as a cross (a distinc-tion, a cross) and to demand a crossing (to drawa distinction, cross!)—the mark of re-enteringindications, the Uroboros has two meanings: toname the spatial pattern as re-entry (an indica-tion entering its own indicational space, a self-cross) and to demand re-entry (to re-enter one’sown indicational space, self-cross!). There aresnakes all the way down (Kauffman, 2002:58), and they have to bite their own tail. Theform of re-entry can thus be viewed as anEigenform, a self-determined or autonomousform, a solution to a non-numeric equation de-scribing the act of distinguishing oneself from

3 This is done by applying consequences C1, C4, C5 and the initial J2 ofthe primary algebra (Spencer Brown, 1969: 55).

(5)

(6)

(7)

(8)

(9)

(10)




its environment. Varela (1979a: 125) himselfmakes the connection to time Spencer Brownalready mentioned and exposes the doublenature of self-reference and its confusion of oper-ator and operand: ‘We have to pay attention tothe fact that the double nature of self-reference,its blending of operand and operator, cannot beconceived of outside of time as a process in whichtwo states alternate. . . Both aspects are evident inthe idea of autopoiesis: the invariance of a unityand the indefinite recursion underlying theinvariance. Therefore we find a peculiar equiv-alence of self-reference and time, insofar asself-reference cannot be conceived outside time,and time comes in whenever self-reference isallowed.’ This is exactly the conceptual founda-tion Varela needed for the question posed bySchrödinger. Life itself is autonomous; it arisesout of itself and cannot be reduced to anythingoutside or inside its own creative, repetitiveloop, where end products are fed back into thesystem as new points of departure (Marks-Tarlowet al., 2002).

In the original article (Varela, 1975), afterdeveloping and proving its initials, consequencesand theorems, Varela exemplifies several uses ofhis calculus. First, because every higher-orderexpression, that is, re-entrant expressions, caneither be reduced to the autonomous state orthe unmarked state (second-order expressionslike (3)) or reduced to one simple expression, thatis, marked, unmarked or autonomous (third-order expressions like (5)), the calculus ‘not onlyshows that all self-referential situations can in-deed be treated on an equal footing as belongingessentially to one class, but also shows a wayto decide when an apparently self-referentialsituation is truly such’ (Varela, 1975: 20). Oneapplication developed by Kauffman (1978) isthe simplification of digital circuits, where thecalculus for self-reference is used for valid net-work transformations without changing theirglobal properties.

Second, the self-cross can be interpreted eitheras the spatial form of re-entry, thus providingan economic notation for an infinite arrangementof nested crosses, or as the temporal form ofits unfolding dynamic, thus giving rise to anoscillation in time between markedness and

unmarkedness (Varela, 1975: 21). This has beenfurther developed in Principles of Biological Auton-omy (Varela, 1979a) and Form Dynamics (Kauffmanand Varela, 1980) with the notion of ‘waveformarithmetic’ and is in fact a new extension of Lawsof Form. The idea is that the re-entrant expression(3), as the basic form of re-entry and interpretedas a dynamic unfolding, gives rise to two differentoscillations, depending on the initial value (eithermarked or unmarked). These so-called waveformsi and j can be written as

with m denoting markedness (the cross) and ndenoting unmarkedness (the void). What is inter-esting about these waveforms is that they arefixed points for the marked state combined to

ij ¼ l l l l l l l⋯

which according to the law of calling can be con-densed to one cross. Thus, the temporality of thewaveform, arising from the spatial form of theself-cross and the autonomous state it signifies,collapses into the spatial form of the cross andthe marked state it signifies: ‘The fixed points ofthe operator represent the spatial view of theoscillation, while its associated sequences repre-sents the temporal context’ (Varela, 1979a: 153).This sheds light on the issue of infinity and self-reference, because self-reference is the infinite infinite guise (Kauffman, 1987: 53) and vice versa:infinity, in autonomous systems, is a temporalunfolding of a finite Eigenform, that is, thesystem’s invariances against its environment.Infinity in self-reference does not grow acrossall borders, which is always a problem in math-ematics when dealing with real systems, butrather grows ‘within’: f embodies a copy of itselfwithin itself, thus stating its autonomy againstits environment over and over again.

Third, the calculus for self-reference canbe interpreted as a three-valued logic, just asSpencer Brown’s calculus of indication can beinterpreted as propositional logic. Such a logicof self-reference abandons the tertium non datur

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of two-valued logic systems, as a can be ¬ a inautonomous systems (Varela, 1975: 21). Varelacites Günther (1967) and his interpretation ofa third value as time, however, claims that thecalculus for self-reference is, just as the calculusof indication on which it rests, on a level deeperthan logic. Space is created by drawing a distinc-tion and thus making an indication. By insertingthe distinction in the space it indicates, that is,by self-indication, time emerges, which can beconfused with self-reference. There is no logicinvolved on this level; logic is something that isdeveloped from this with a motive. Varela fullydeveloped a three-valued logic in a separatework (Varela, 1979b), but his main intentionwas beyond logic. Both his newly developedlogic and the calculus for self-reference carryingit were seen by him as linguistic carriers fordescribing, modelling and simulation of self-referential systems. Varela’s own motive of draw-ing his distinctions the way he did is indicatedonce again by himself, and this motive is theapplication of the calculus in order to come toterms with self-referential, self-closing and self-producing autonomous systems and, ultimately,pay due respect to the riddle of the living.These few remarks show that, just as the cal-

culus of indication, Varela’s calculus for self-reference (the calculus of self-indication) can beinterpreted in many ways. It has to be noted here,however, that it is neither a three-valued logicnor a theory of autonomous systems nor a guidein self-referential situations. It can be all of thatand more, if there is a motive to confuse it forthat. What it actually is might best be describedas a formal notation for ‘the relation between aform (or figure) and its dynamic unfoldment (orvibration)’ (Varela, 1979a: 113; emphasis added)and an abstract concept of a system whose struc-ture is maintained through the self-productionof and through that structure. In the words ofKauffman (2002: 57–58), it is ‘the ancient mytho-logical symbol of the worm ouroboros embeddedin a mathematical, non-numerical calculus.’

CRITICISMS AND A REBUTTAL

The simple idea, that by drawing a distinction auniverse is created and that by inserting this

distinction in the space indicated by it the auton-omy of the living arises, received much praise asthe quotations before have shown. Of course,criticism also is abundant, and the most severearguments against the ‘Flaws of Form’ (Culland Frank, 1979) and the ‘awkward calculus ofawkwardness’ (Kaehr, 1980) need to be encoun-tered here. These arguments can be summarizedas non-originality, notational ambiguity and theproblem of infinity.

The arguments against the originality or non-originality of the indicational perspective reston the claim that nothing new is introduced tomathematics by it; in fact, the standard Booleanalgebra is only developed from a different view-point without much merits. Also, the blendingof operator and operand with the symbol of thecross is supposed to give rise to ambiguity incalculation (Cull and Frank, 1979). The firstmistake this type of critique is making is the con-fusion of the indicational perspective with a formof logic. The calculus of indication, however, isnot a logical calculus. Kauffman and Solzman(1981: 254) sees it as ‘is an empirical case studyof the consequences of distinguishing, begun assimply as we (and presumably Spencer-Brown)know how.’ The motive of Spencer Brown todraw his distinctions the way he did was thesearch for the simplest beginning, an inquiry intothe nature of arithmetics, into the ‘sociology ofnumbers’ before any number is constructed. Thegeometry of the arithmetic developed in Laws ofForm has no numerical measure; it is as basic asone can get. It provides a view on how ‘things’of whatever kinds are constructed, come intobeing and merge into another. It is the foundationof anything, of some-thing from no-thing, ofbecoming being (Schiltz, 2007: 11). Boolean alge-bra cannot deliver that, because it is ‘already’constructed from something deeper than itself.In other words, Boole’s system is not autono-mous. The notation Spencer Brown introduced,which in turn is ‘just’ a continuation of theidea of a distinction drawn in a plain and thusestablishing some indicational space of perfectcontinence, is giving rise to a very clear systemof markings and transformations. It is as unam-biguous as math can get, and the ‘ambiguity’from the blending of operator and operand is at




best a virtual one, because there ‘are neitheroperators nor operands in the primary arith-metic; just marks, expressions and changes dueto the transformation rules of calling and cross-ing. We can view the mark of distinction as anoperator if we like to’ (Kauffman and Solzman,1981: 254–255; emphasis added), that is, if wehave a motive to do so and this is saying moreabout the one drawing a particular distinctionthan about the notation of distinction. However,as Kauffman notes against Cull and Frank(1979: 202), mathematics is not independentfrom notation, and notation is nothing near‘insubstantial’. The invention of the zero ornegative numbers or, especially fitting whendealing with the calculus of indication, theimaginary numbers are prime examples of hownotational novelty enables mathematics to tackleproblems formerly thought unsolvable.

The arguments against the careless use ofinfinities arising from re-entry, especially inVarela’s calculus for self-reference, have beenstated most severely by Kaehr (1980), a formerstudent of Gotthard Günther. He claims that thedream of second-order cybernetics, and buildingon that also of Varela, would be to turn a straightline into a circle in infinity. Through the introduc-tion of self-reference, a series of markednessturned unmarkedness and so on grows, as arecursive expression, to indefinite length.According to Kaehr and his motive, which iswith the realization of artificial intelligence, thisis thinkable but not operational, that is, self-reference cannot be constructed in the real worldlike that. As has been argued, infinity in the cal-culus for self-reference, through the re-entry of adistinction in its own indicational space, is notgrowing ‘beyond borders’ but reaffirms theautonomy of what is self-indicated against itsenvironment. Expression (5), for example, reaf-firms that there is an a in the context of b in everdeeper spaces, that is, time and time again thusturning it into a stable, self-determined value. Itmight be a motivational error to suppose thatthis could not be realized, which might be thecase for artificial intelligence, but for any otherintelligence, for any other living system, it is notproblematic at all. It happens quite effortlesslyall the time around us. This motivational error

confuses a problem in mathematics—how toconstruct an infinite series that bites itself inits tail—with a problem beyond mathematics(Kauffman, 1996: 297–299).

The rebuttal of the criticisms launched at theindicational and self-indicational perspectivesmight appear as a form of dogmatic romanticismbecause both Spencer Brown as well as Varelause a very lively and colourful language, attract-ive to some, mystical blabbering to others. In fact,a subtle criticism throughout the reminiscence ofthe Laws of Form and the idea of self-referencethat captured Varela’s mind is aiming at theway these ideas are presented (Kauffman andSolzman, 1981: 254, Kauffman, 1996: 299). Bothhave turned, in their writing and thinking, toEastern philosophy. The Laws are inherentlyDaoist, and Varela, very early in his life, becamea Buddhist. Whatever impacts these spiritualleanings might have had on the ideas, and theysurely have as nothing is distinguished withoutmotive, the reasons both Spencer Brown andVarela had to resort to the language they wereusing is given in the problem they were facedwith. When going back to the simplest thinkableorigin, in Varela’s case, ‘to find the simplestpossible way to symbolize a reality which expli-citly includes self-reference’ (Robertson, 1999:53), one encounters the limits of thinking whichare drawn in language. Glanville (2002: 70–71)says it very precisely: ‘[W]hen I accept that I havereached a fundamental—that there are no moredistinctions—I have drawn the re-entrant distinc-tion “that there are no more distinctions to bedrawn”. And, when I accept that I have reachedthe Universal, I accept that I have drawn all dis-tinctions, by drawing the re-entrant distinction“that there are no more distinctions to bedrawn”’. This is the point where probably bothSpencer Brown and Varela realized that the‘form’ is a symbol for the world that cannot bereferred to from anywhere else but itself. Every-thing that follows rests on some-thing fromno-thing, that is, from referencing itself fromwithin itself. In a Foucauldian sense, when youtake away all the masks of reality, you end upwith what reality is: a pile of masks referring tothemselves. The Laws of Form and their calculusfor self-reference are anti-essentialist to the bone



André Reichel

or, better, to the form. The form marks the end oflanguage and description as well as the start ofit. It is an offer for the ‘empirically mindedscholar’ to follow what can be taken out ofthe form ‘with an open heart’ (Kauffman andSolzman, 1981: 256) and apply it to the seemingirrationality of the real world. This offer for prac-tice and application, that immediately followsfrom the basic ideas of indication and self-indication,which are in themselves empirically valid andexperienced all around in the living, is probablythe most overlooked part in Spencer Brown’sand Varela’s work.Quite contrary to the arguments against and

for the language used in Varela’s elaboration ofthe calculus for self-reference and his theory ofautonomous systems, the major breakthrough inbiology, the science dealing with Schrödinger’squestion, did not occur because of its overtlymathematical nature. The research programmeVarela laid out in his Principles of Biological Auton-omy was largely unanswered by mainstreamscience, probably because of the challenges itposed to so many established concepts, ‘perhapstoo many to be widely embraced, perhaps toofar ahead of its time’ (Krippendorf, 2002: 95).What is also striking to note is that in later years,Varela did not explicitly work on or use hisformal system for self-reference. It is rather moreimplicitly resonating in the language he uses thanin any formal description. Maybe it was too farahead of the time, even for him. Maybe it was aWittgensteinian ladder he had to take in orderto climb to the playing field of self-reference,and that could be thrown away afterwards. Onecan also argue that his Buddhist worldview thathe found for him in the 1970s is the bridge overwhich he came to the extended calculus andfurther to enaction theory (Brier, 2002: 81). Thus,the calculus for self-reference and the Laws ofForm can be on one side of the distinction, whereashis later work is on the other. As we know, both canbe confused and might well prove to be identicalin the form. Whatever may be the case, the coremotive of Varela (1979b: 141) should not beforgotten: ‘I have taken the Calculus of Indica-tions as a starting point in an attempt to produceadequate tools to deal with self-referentialsituations. Self-reference is, of course, of great

historical importance; it was responsible for amajor crisis in mathematical thinking at the turnof the century. More recently, with the develop-ment of cybernetics and systems theory, otheraspects of self-referential situations have becomeapparent, namely, the fact that many highly rele-vant systems have a self-referential organization.’The key problem when dealing with ‘system-wholes’ that produce themselves autonomouslythrough the production of a boundary is that ofself-reference. In developing a rich body offormal foundations for self-reference, Varela infact provided the grounds on which any theoryof autopoietic systems can and has to stand.Autopoietic systems, as Schiltz points out, havetheir own self-production as the Eigenform oftheir ‘basal unrest, the abbreviated expression ofthe system’s concern with getting around itsnon-identity’(Schiltz, 2007: 21), that is, reaffirm-ing its autonomy in relation to an environmentwhile constantly crossing the boundary of whatthe system is and what it is not. Varela’s workon self-reference, his many-faceted self-indicationalperspective, does provide a grounding not only‘for every description of any universe’ (Varela,1975: 22) but also on all self-referential systemsof whatever kind.

THE PRAXIS OF SELF-REFERENCE

Ten years after Varela’s untimely death andmore than 35 years after Calculus, the greatpromise of the logic of paradise is still to un-fold. There are some hints where we can findtraces of it. These hints stem from psychology,Varela’s own theory of embodiment, and theplayful use of self-referential logic in socialsystems.

In psychology, it was Gregory Bateson whointroduced the notion of ‘double bind’ whilestudying the communication patterns in familiesof schizophrenics (Bateson, 1972: 271–278). Adouble bind exists when in a continuing patternof communication, that is, a situation with no exitoption, a certain behavior B is produced and, inturn, the opposite behavior ¬B is also produced.




This situation is clearly self-referential and canbe depicted as

In the classic situation of the mother demand-ing, in a verbal form, ‘love me’, while at thesame time, in body gestures, signalling ‘do notlove me’, the resulting Eigenbehavior is of thekind ‘love me love me not love me not loveme not. . .’ Expression (14) is clearly neither‘love me’ nor ‘love me not’; it is, in this specificsituation, an undesired autonomous state of thedouble bind that produces a pathological con-text (Varela, 1979a: 198). For example, for fam-ily therapy, it is clear then that such asituation cannot be solved by focusing on wholoves who or who does not but on the newstate that is emerging as an Eigenbehavior ofthe situation. As a waveform, it resembles i,and it should be remembered that in combi-nation with j, it constitutes the fixed point forthe marked state. If the initial marked state is‘love me’, there is hope that by combining thetwo waveform patterns, that is, by contrasting‘love me’ with ‘love me not’ simultaneously, themarked state, that is, ‘love me’, shouldoccur. In a therapeutic context, this wouldimply confronting the mother who says ‘loveme’ with ‘would you want me not to loveyou’. This is clearly paradoxical as the entireunfoldment of the situation; however, it wouldcreate the fixed point necessary for ‘love me’to stabilize itself. In a very similar manner,Ronald Laing, having some connections toSpencer Brown, described the structures ofhuman relations as inextricable knots (Laing,1970). The famous ‘Jack and Jill’ story describesa situation where, for example, Jack is hurtby thinking that Jill thinks he is hurtingher by being hurt by thinking . . . and Jill is hurtby thinking that Jack thinks she is hurting himby being hurt by thinking . . . The oscillation ofboth feeling hurt by the assumption whythe other is feeling hurt is the Eigenbehaviorof Jack and Jill, which is neither Jack and hisfeelings nor Jill and her feelings but the

insertion of Jack is hurt by the fact that Jill ishurt into Jack’s hurt:

To assume the ‘waveform solution’ for thissituation would mean to question Jack why heloves Jill (hurt is marked, love is unmarked), thusgiving rise to the marked state. It would be aninteresting move to find a method for formulat-ing social situations of self-referential nature asthese kinds of stories, or ‘riddles’, as SpencerBrown did with Lewis Caroll’s last sorites andapply the calculus on it (Spencer Brown, 1969:123–124).

As stated before, Varela himself turned to-wards self-reference as praxis without naming ei-ther his calculus or the formal aspects of his workon autonomous systems. However, he stayedwithin his central notions especially that of au-tonomy when dealing with the nature of the liv-ing, and the reciprocal, that is, self-referringconstruction of identity, which becomes a (fixed?)point of reference for a domain of interactions.Whatever the parts of such an emerging system-whole may be, they can and must referencetheir interactions towards the system’s identity(Varela, 1997: 73). Via this form of self-reference,the system, and Varela’s (1997: 83) thinking,moves towards cognition that ‘happens at thelevel of a behavioral entity and not, as in thebasic cellular self, as a spatially bounded entity.The key in this cognitive process is the nervoussystem through its neuro-logic. In other words,the cognitive self is the manner in which theorganism, through its own self-produced activity,becomes a distinct entity in space, but alwayscoupled to its corresponding environment fromwhich it remains nevertheless distinct.’ Fromhere, it is a small step to the notion of ‘embodi-ment’, the realization that life and cognition areembodied; that is, the system is the reflection ofthe distinction between system and environmentwithin the system and thus, and only thus, thesystem ‘knows’ that it is not alone and . . . is. Ina scientific manner, Varela describes this as the

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enmeshed network of nervous system, the bodyand their environment, and that the only properunderstanding of life, cognition and mind is thatof mutually embedded systems (Thompson andVarela, 2001: 423). In a more personal manner,taking notes of his experience with his liver trans-plantation, he reaffirms the organism’s embodi-ment as a double quality of being a functionalbiological machine, but also by being lived . . .by someone who draws a distinction, placingthe body within the space indicated and at thesame time switching between intimacy of yourown self and a decentred intersubjectivity depend-ing on whom you interact with that is not the selfthat . . . (Varela, 2001). This can be notated as

andwhichmight be reduced to a simple expressionas in

While reading his later work on enaction and em-bodiment, the formal background summed up inPrinciples of Biological Autonomy reverberatesthrough the reader’s mind. To formulate theproblem of consciousness as embodied cognitionand apply the formal notations developedby Varela does indeed indicate an entire new re-search agenda for the cognitive sciences and, infact, pose a new path to answering Schrödinger’squestion.However, there is more from self-reference

than the field the calculus motivationally origi-nated. The last field of praxis for the calculusfor self-reference, therefore, is that of social sys-tems. Luhmann (1995a) borrowed heavily fromSpencer Brown and Varela, especially as regardsthe ideas of re-entry, autonomy, autopoiesis andclosure in stating his theory of social systems. Hisuse of the concept of autopoiesis as well as theindicational perspective systems as distinctionsentering their own indicational domain resonatestrongly with all that has been argued before.However, the application of the idea of autonomythrough self-production and self-indication, that

is, through closure and self-reference, was noteasily conceived. Varela himself was very scep-tical when using, for example, the notion ofautopoiesis for social systems. Instead of autopoi-esis, autonomy for Varela (1981: 15) appearedto be the more exact property for a wider classof self-referential systems, including social sys-tems: ‘From what l have said l believe that theseproposals are category mistakes: they confuseautopoiesis with autonomy. Instead, I suggest totake the lessons offered by the autonomy of livingsystems and convert them into an operationalcharacterization of autonomy in general, livingand otherwise. Autonomous systems, then, aremechanistic (dynamic) systems defined by theirorganization. What is common to all autonomoussystems is that they are organizationally closed.’As has been already stated, both notions are sointricately connected that this may come acrossas hairsplitting; however, it is hairsplittingwith a motive. As Luisi points out, the start ofautopoiesis in biology was not easy; in fact, itwas more regarded as being ‘philosophy’ ratherthan science. Moreover, the sudden upspring inthe 1980s of autopoietic notions in social sciences‘not always in a very rigorous way’ providedthe entire set of ideas with a certain ‘new-agey’shine, which probably was even deepened bythe language of self-reference Varela took fromSpencer Brown and Heinz von Foerster (Luisi,2003: 50). Also, there were some heavy biasesagainst the way Luhmann applied the notionof autopoiesis for social systems, foremostexpressed by Mingers (1989, 2002). When readingthrough Mingers’ arguments, however, his mainobjections are not likely to hold against whatLuhmann actually did. Mingers objection can becondensed to two questions that he might regardas not properly solvable in the formal definition ofautopoiesis: what do social systems produce?Whatare the components of social systems? We do notwant to dive toomuch into theMingers’ arguments,as King and Thornhill (2003) have effectivelyrejected them quite thoroughly, but let Luhmannanswer these questions himself: ‘Social systemsuse communication as their particular modeof autopoietic reproduction. Their elements arecommunications which are recursively producedand reproduced by a network of communications

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andwhich cannot exist outside of such a network.Communications are not “living” units, they arenot “conscious” units, they are not “actions”.Their unity [of the autopoietic system] requires asynthesis of three selections: namely, information,utterance and understanding (including misun-derstanding). This synthesis [unity] is producedby the network of communication, not by somekind of inherent power of consciousness, orby the inherent quality of the information.’(Luhmann, 1986: 174) The network of communi-cation is producing the boundary of the socialsystem. It does so by processing a synthesis of

whereas this form is the unity of the social system.This form, at the same time, provides for continu-ation of communication in the network ofcommunication, thus continuing unity produc-tion. The form needs to show re-entry; that is,information enters utterance and understanding,thus re-entering the distinctions made. The unityof communication, the boundary of the socialsystem, is produced through understanding theutterance of information as communication.Luhmann’s application of autopoietic thoughtwas in fact not metaphorical at all but followedStafford Beer’s ‘yo-yo model’ (Beer, 1970: 118)

and climbed up the ladder of abstractiontowards a general theory of autopoietic systemsas the foundation of theories of psychic andsocial systems (Luhmann, 1986: 172). However,we are not so much interested here in Luhmann’sgreatest efforts—namely, to free sociologyfrom its humanist prejudices, its reliance ongeography to indicate the space of society andthe subject/object distinction that haunted manysciences (Luhmann, 1992)—but focus on hisembracing of self-reference as key feature ofsocial systems and the indicational perspectiveas best suited for developing a conceptual

foundation of them. Baecker (2006: 125) isdrawing heavily on self-referential logic and theindicational notation for developing an arrayof forms for organization and managementsciences (Baecker, 2006). For him, the form ofdistinction can be confused for ‘a simple devicethat consists in picturing operations withincontexts, these contexts being operations thatthemselves call on further contexts.’ In drawingthe form of the firm, Baecker assigns value notonly to the different sides indicated but also tothe re-entering operation itself, resulting in thefollowing form

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André Reichel

where work, business, corporate culture, commu-nication and ethics are distinct re-entering opera-tions, each of differing value to what is re-enteredwith them. Although being more or less a usefulheuristic to focus observation of the firm ondifferent aspects of interests, Baecker (2006: 137)concludes that the next step for such a ‘distinctionview’ of the firm would be ‘to envision a kind ofcontextual mathematics as a means of analysingphenomena and constructing observations as acontribution to organizational practice.’ Thisis clearly calling for a formal grounding, andVarela’s work could play a significant role in this.4

All these forms of self-referential praxis showthe richness of what springs from Varela’s think-ing and his move from first-order to formalizedsecond-order descriptions. Luhmann (1995b: 52)himself demands such a move, going beyondwhat is to be found in the Laws of Form and thecalculus of indication. We argue, and hope tohave proven it as fact, that Francisco Varelaachieved that move and made the first steps intoa new world of formal descriptions.

OUTLOOK

From where we stand now, on the pinnacle ofself-reference, looking down the valleys of para-dise, what remains of Francisco Varela, whatcan and needs to be done? Varela’s (1976: 31)dance with the world led him to the insight thatin order ‘to understand the whole of us and theworld, we have to participate with the wholeof us.’ This call for participation resonateswith the nature of the indicational perspectivehe deepened and widened to the calculus forself-reference and what he termed the logic ofparadise, ‘the possibility of a common survivalwith dignity of humankind’ (Varela, 1976: 31).The praxis of self-reference, and his formalnotation and system, can be valid across manyscales of self-referential systems. The furtherformalization of these systems, and in fact,the scientific fields that are dealing with them,

is not hindered by any inaccessible barrier, notanymore. In Varela’s (1981: 19) own words,‘there is no reason why there could be no math-ematical theory of circular systemic processes.It surely entails some conceptual and formalreadjustements, but no more so, say, than a rigor-ous theory of vagueness.’ Two roads are laidout to be explored. The first is the formalizationof theories currently ‘under-formalized’. Froma self-indicational perspective theories, for ex-ample, from the social sciences and psychology,the so-called ‘soft’ sciences could be reformulatedin a notation close to the calculus for self-reference.For sociology, Luhmann and Baecker came near-est to that, and there appears to be fertile groundto continue the work. The second road is theformalization of empirical phenomena, that is, toapply the self-indicational perspective directly tosocial situations as in the psychological examplesgiven. Can we, for example, use the calculus forself-reference in the way Varela envisioned it, todetermine whether or not we see self-reference,and if so, if that is a contender for a system’sEigenform? If a system’s Eigenform can bedetermined, we can understand what drives itsidentity construction and how this is done. Bothroads will meet and cross each other severaltimes, like an oscillation unfolding from the formof self-reference, the Uroboros itself. Theory thatcan be contrasted with practice can be contrastedwith theory and so forth until we reach a betterunderstanding of the self-referential systems weencounter. There is plenty of territory to bediscovered in this land of paradise. To give Varela(1981: 22) the last words: ‘So far, we have givensubstance to only a few item of this researchprogramme. The rest is yet to unfold.’

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snakes all the way down: varela calculus for self ...the autonomy of varela’s thinking what is...

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