Theories and Metaphors of Cyberspace- Abstracts

Fractal Maps of Cyber-Markets

By Mag. Dr. Michael Schreiber

  • Univ. Assistant at the Dept. of Absatz/Marketing,
  • University of Economics and Business Administration
  • Vienna, Aug. 2,
  • A-1090 Austria/EU.
  • email:
  • Abstract:

    What is a cyberspace, a market, a model? The meaning of concepts can be defined by using distinctions. A refinement of this Aristotelian insight is combined with an ancient pattern from Yang Hsiung in order to model differences influencing decisions of cyberspace actors. The common consulting portfolio relating the attractiveness of markets to competitive strength is thus restructured to map evaluations of imports and exports of systems by permutation of binary and trinary ramifications of distinction. These lists of categories are then translated into generalized fractal decision-portfolios. These fractal forms of expression point to the issue of instable rankings of implications which can result in shifting models and evaluations of cognitive, social and ecologic implications of cyberspace. A research programme is outlined by proposing some theoretical and empirical operations.

    Abstract Image Resource: Cyber-Market Meta-Portfolio dd2322

    Introduction to Scaling Speculations

    Is automated communication triggering competing civilisatory transitions to orbital and tribal perspectives of competitive and cooperative relations? Is it necessary to push it? Or should one resist the virtual life as outlined in the anthology of James Brook and Iain Boali? Cyberspace in general and its impact on locations competing for market activity by high-tech-subvention in particular obviously deserve comprehensive observation. Thorbjoern Mann called for adoption of argumenative design approaches to public descisions. But such views are hard to define, as there are various tangled aspects to map. So it is not intended to present another listing of potentially relevant conceptualizations and observations here.

    The "virtual" cybernetic problem might be to conceptualize and anticipate higher order self-referent turning points of obvious trends caused by conscious and un-conscious adoptions of beliefs in cybernetic evaluations of thus distorted frameworks of causality. In the context of cyberspaced markets this could mean to prepare for disappointment caused by speculative exploitation of successful diffusions of plausible extrapolations of statistically significant causalities.

    This paper is about a chance to keep at least some elementary but surprisingly rewarding theoretical elaborations relatively concise. Specific issues need not obscure some of the basic fractal issues in mapping multidimensional phenomena like cyberspace or markets in general. While even concepts of what is to be discussed can lead to lengthy discussions it seems still possible to create rather simple models of the potentially oscillating re-evaluations enfolding in this new evolution of our understanding of articulation, automation, autonomy and arbitration. Further trivialization may become possible through further evolution and diffusion of theoretical and empirical tools. This version is plain text only except for the visual "bait" following the abstract. This seems necessary in order to stress the heuristic principle without inviting premature commercialisation of still unstandardized and untested pseudo-hyper-portfolios. The goal is not generate innocent fascination with typically beautiful fractal manifolds but to share some ideas concerning a means for a critical monitoring of such hyper-mediated market-research, promotion and consulting.

    Theoretical Formation and Emperical Evaluation of Models

    The Glossary on Cybernetics and Systems Theory offers definitions of various kinds of models but does not include the following approach.

    If models are compositions of forms of expressing relations among potential variableson the one hand and truthvalues fitting these relations to empirical observations on the other hand both ingredients deserve attention. Cyberspace-technology is obviously offering new tools for gathering and distributing data via for instance automatic real-time questionaire processing. The speed of net-diffusion created an urgency to arrive at non-military strategies for commercial, non-profit, public and private actors.

    Pure theory though challenged by potentially deepening changes of organized reality does not offer simple interfaces to ready made solutions of course. But it can contribute to redefinitions of the general forms used to express the variables breaking records so fast today.

    Cyberspacing from Ancient Oracles to Consultant Portfolios

    Cyberspace offers benefits for users investing some extra effort but adds to the complexity of nearly all commercial and public decisions. Security, authenticity and copyrights, pricing related to tight bandwidth and rapid technical obsolescence, enforcement of local taboos and conservation of cultural diversity, ecologic impacts, employment, hyper-democracy, new issues keep emerging as transaction costs of organizing their discussion drop sharply.

    A convenient way to modell this and other categories relevant to such official and some personal decisions is to map the permutations of their basic distinctions. If such distinctions are combined as proposed in this paper a type of forms is genenerated, which shall be called matrix-portfolios. They could be related to at least five sources besides Mandelbrot and his contributions towards a fractal theory of nature:

    Aristoteles formalized the conventional approach to defining concepts by distinction from more general concepts. A cyberspace or a market could thus be thought of for instance as special quality spacetime locations for interactions of actors.

    The emerging problem of how to organize maps of overlapping indications is known for a long time too. About two thousand years ago Yang Hsiung invented a two-year-calendar reflecting the permutating forms of interaction based on trinary destinctions. According to Walters he offerd 3^3*3^3=27*27=729 fields later replaced as oracle by the 2^6=2^3*2^3=8*8=64 binary modell known as the I Ching. The calendar is presented as a cube of nine magic squares of 9*9 fields with number 365 in the middle.

    Modern consultants often implement double binary or double trinary portfolios mostly relating to measures of market-attractivity and relative competitive advantage. Situations characterized by distinctions like growing market-volume and big market-share are then interpreted as to call for the corresponding standard portfolio strategy to reinvest profits in order to grow own advantages with the market. Experts like Weinberg look for the trade-offs.

    Financial and real estate markets provide good examples for what happens if enough people trust their maps. Soros observes that groups of investors can contribute to shifting their markets whenever they evaluate empirical decisions in terms of theoretic distinctions and assumed causalities. The marketprice can rise because it has been rising or fall for no other reason than because it stopped rising or do a similar trick in the other direction.

    Selfreference and selfcontradiction in particular are thus likely to turn out to be the most critical issues of cybernetic study. The complete syntactic reconstruction of first level predicate calculus was based on primary not-the-same (neither-nor) operators like NAND or NOR. Spencer-Brown suggested laws of formation operating with the basic instrument of distinction and observing oscillating truth values at the outside of non-selfreferential logics. But we still have to arrive at a similarly convincing syntactic re-generation of axioms concerning prime-number-cryptography and higher order evaluations of qualified quantities.

    Such turbulence is still somehow alien to economic studies still nostalgic about the idea of efficient markets gravitating towards equilibriumof supply and demand for all quantities of qualities. Cyberspace is then trustingly associated with higher efficiencies in conventional domains of observation and is expected to become an ideal round-the-clock-clearing, open-to-all-everywhere market. A market in fact for every commercial, personal, hegemonial, ideological etc. carrier-content-product-service not only those recognized in the Apple portfolio as key players in the information economy. Years later this portfolio still covers a full page in a related hegemonial report of technology assessment.

    The catch is that revolutionary potential benefits for production, consumption, investment and regulation can be dangerous for established organizations. Additionally installed traps like high public and private debt, volatile currency markets accompanied by political and spiritual unrest call for caution and some theoretical hedging against trivial bull-stampedes over a collapsing need of tele-commuters and unemployed for mortgaged landmarks in cash-stripped cities.

    Some of the general interferences generated by such encounters might be presentably reflected in theoretic forms by blending the formulas of ancient and modern portfolios. This will be illustrated by a fractal reconstruction of a general market and a meta-map-distinction of cyberspace.

    Distinguishing Fractal Imports and Exports

    In order to simplify theory fractal methodology prefers to look for general generators contributing to scaling systems of explanation. One way to follow this idea is to look for operations central to all forms of organized intelligence interfacing natural and abstract causalities.

    Consciousness refers to tangled modalities of natural and cultural distinctions. It imports carriers from nature and contents from cultures by reading the implicit informational content by means of intelligent organs. It exports to nature by moving its surface in and around it while informing it according to organic and symbolic programs of self-regeneration.

    These operations of consciousness interface inner and outer systems of observation including various levels of self-reference but always refering to the two times two original modes of

    1) natural and

    2) cultural types of

    a) import and

    b) export.

    The perspective of relative selfreference established by comparing two maps of distinctions concerning the same imports and exports of carriers and contents is the guiding star of this fractal approach to market-definition tested here.

    The specific mathematical operation defining the actual form of calculating selfreferent relations is not discussed here. Deeper theoretical analysis might look at the quaternion-form of stating rules relating variables. Such Hamiltonian perspective would integrate one basic value and three imaginary components into one set of values to be processed by the to be defined calculus. The first simulations referred to in this presentation have added and multiplied natural and rational numbers only.

    Prototyping Fractal Forms of General and Particular Markets

    A general Marketing approach to decisions related to overlapping distinctions can build on classic and contemporary portfolios while focussing on the meta-distinctions influencing the evaluations of imports and exports. If all considered dimensions are related to both import and export evaluations a comprehensive table of all interactions can be generated. The decision of actors are thus analyzed by modelling all potential permutations of some of the distinctions the actors use in order to relate to imports and exports. A general design can forsee only scaling levels of binary distinction or can try to establish a fundamental pattern of mixing criteria geared for different types of ramification like binary or trinary distinctions. A list of permutated combinations forms describes the tops of the columns of this matrix. A transposition can form the descriptions on one side of the rows. This basic dd-map refers to distinctions concerning the imports and exports of a system.

    Note: The letters dd indicate the two basic meta-distinctions defining the proposed map. They are not to be confused with a symbol in a marginal difference calculus or any fractal dimension D which might for instance be computed by relating proportions between logarithmic measures for iterations of empirical or simulated distinctions - which will not be attempted here. Edgar Peters already used fractals to challenge the efficient market hypothesis of traditional economics.

    A pre-quantitative implementation of this form of expressing statements about competitive environments can start with a two level distinction refering to both imports to and exports from a special quality timespace defined by some formal superimposition of relations between such imports and exports. The two levels will be called value of prospect-quality and value of code-quality. Both are already complex results of interferences among all four modes of conscious and un-conscious operation in nature-based societies.

    • Prospect-quality as a measure of rising or falling demand for exports and entries and exits of competing importers can be defined as binary or trinary.

    • Code-quality on the other hand is geared at mapping the stability of codes used to evaluate prospects. It is either just another prospect-quality and thus easy to map or can be regarded as a special form of achievement of actors shaping their market. If this is the case a distinguished form of values could be appropriate leading to inclusion of a value for stability of coding available for im- or exports.

    Special implementations of models of general markets starting with balanced mappings of imports and exports, binary evaluation of prospect-distinctions but an articulated para-neutral predisposition for stable coding shall be called dd23-Market-Maps.

    The next step is to conceptualize a more realistic reconstruction of distinguished im- and exports. While it is possible to create complex tables up to 243*243 (27*9=243) fields rather easily within the 256 columns limits of familiar spread-sheets it is instructive to concentrate on less complex forms of distinguished interactions. In order to provide a simple interface for potential adopters only four generalized elementary distinctions of conventional market practice are included in the following elaborations. This results in four distinctions among imports and four distinctions about exports of analyzed systems which can be interpreted as more detailled articulations of prospect- and code-qualities which are never-the-less achieved by similar socio-ecologic organization of conscious and un-conscious distinctions.

    a) Productmarket-Expandability: A distinction reflecting evaluations of the potential volume of future interactions.

    b) Pricing-Convertability: A distinction reflecting evaluations of the shifting values of future interactions.

    c) Promotion-Imageability: A distinction reflecting evaluations of the advantages enjoyed or disadvantages carried by actors in relation to others arranging similar transactions.

    d) Placedistribution-Sustainability: A distinction reflecting evaluations of the logistically managed level of sustainability of transactions.

    This level of complexity can be accomodated in various ways. If all dimensions are reflected in trinary ramification of -1, 0, +1 subsets of rows and columns a large but still PC-computable matrix of 81*81 (3^4*3^4) emerges. If all are simplified to -1, +1 differences a small 16*16 (2^4*2^4) table is sufficient to map all potential interactions. If stable rates of convertibility are defined as desirable an intermediate formation of distinction featuring one trinary and three binary distinctions could be called adequately biased. This could be called a dd2322-Market-Map or simply a 24*24 matrix. This 24*24 matrix looks different if the para-neutral trinary distinction is located at different levels of hierarchy in relation to the other three distinctions mapped as binary in the portfolio.

    General Arbitrage and the 24*24 Matrix

    A general market was defined as a double set of combined distinctions evaluating imports to and exports from a set of contexts specified by aggregation of such distinctions. In this general context all market transactions can be interpreted as arbitrage of matrix functionality in the context of distinctions characterizing evaluations of importers and exporters of distinguished systems. Every actor is thus in principal comparable to a state or multinational enterprise which is liquid in some foreign currencies and is selecting the most attractive markets for its talents.

    The 24*24 basic matrix is only one among other potential implementations of a symmetric dimension distinction portfolio. Markets gain distinction if specific matrixes are sustained. They can then be able to ignore distinctions to be sought or evaded in other implementations of otherwise similar markets. The self-reference-loops of evolving distinction are obvious. A general theory of markets expects distinguished markets to behave differently under similar changes of contexts evaluated according to different distinctions.

    Meta-Modelling Diffusion and Implications of Cyberspace

    The basic metaphor of virtuality is a difference in space-time which does not matter in regard to a level of interaction. The implementation of increasingly self-organizing cybernetics to interacting levels of codes and machines on nano-scales is the secret of life and the modern prototypes of cyberspace on the internet. Pragmatic definitions are well on their track if they manage to follow the actual way automated communication will affect their clients positions of interest. The common denominator of such definitory efforts is likely to cover some observable anchorpoints of the civil agreements concerning the management of conflicts over peaks of bandwidth and cusps of critical, criminal or culture-shock content. But even a specialists snap-shot has probably no choice but to face the fact that not only some office equipment but also a lot of jobs might be obsolete soon. The new space of automated chip-communication is starting to cannibalize various peripheries and layers of distribution that are currently consuming payed and paying and unpaid time. Everything can happen if all ages, genders, believers and non-believers, free and arrested, of all races at all places would be invited to learn more about how they can benefit via cyberspace. At some places or everywhere in the worst case. Naive deregulation ideology blended with grey and illegal economies can turn the resulting matrix into an algorithmic cybertax empire without army or bureaucracy and consequently rich enough to support the law-enforcement-process-providers and the ones without cash innocently as long as they play by the complex but fair and decent rules. The discussion about the distribution of workloads and the heritage of literatures has just begun to stretch its wings.

    The initial differences resulting from specific politics of linking markets to cyberspaces can be modelled by introducing cyberspace as a new categoric distinction among other specific portfolios of distinctions or by tracing its impact on the elementary categories of general markets conceptualized here. >p> A categoric approach could inquire if one or more traditional categories of distinguished markets - like physical distance - will become obsolete by cyber-spacing more of their relations.

    A trivial application of the proposed 24*24 map would be for instance to assume that cyberspace would be adopted in some relation to the numerical output of fields characterized by distinctions actually found in empirical settings.

    A more challenging perspective would be to suggest values for specific empirical conditions that can be translated in numerical guidelines for investment in or divestment from product-service-markets. One approach would be to "cyber-scenario-map" the distinctions used in PIMS-Research.

    The implicit key problem of a general theory of markets is of course the most interesting domain of study to be indicated here. This would be the formulation of a market theory concerning cyber-effects of theoretic assumptions on real parameters of net diffusion and total economic performance among clusters of convertibilities and time-investor-migration.

    Volatile Re-evaluations of Markets Linking to Cyberspace

    Phenomena calling for redefinitions of the categories defining related markets can shift the values of options in thus reformed portfolios. Such effects have already been included when selecting the categories used to construct the 24*24 matrix. It suggests potentials of positive or negative values associated with communicable advantages and sustainability. The aggregated values of the fields marking computations of potential effects of distinguished transactions change if these factors are excluded. A solid margin can turn into a huge loss if the context is shifted.

    Similar effects are of course likely to occur whenever rough estimates of effects of cyberspace are adopted. New entries or external shocks like unexpected re-evaluations of currencies can trigger re-shifts of such estimations. This could in turn result in exaggerations of contrarian evaluations of portfolio-positions so familair from accelerations and busts of the business cycle. Such disappointments seem more probable if low-dimensional portfolios are used, which can react sharply to introductions of new distinctions.

    A more optimistic twin hypothesis could be formulated as: Robust scenarios and sustainable strategies could be formulated by defining high-dimensional maps and selecting only markets satisfying more complex combinations of criteria including at least distinctions concerning volume, convertibility, image and ecology in relation to imports to and exports from markets in general and cyberspace-markets in particular.

    Recognizing Speculators in Markets and Cyberspace

    One of the pre-conditions of heavy oscillation in evaluations of prices would be even wider participation in trading of future values of portfolios. New safe forms of cyber-currencies could pave the way towards such manic involvement beyond the budgets of mutual investment. Theory postpones calling these margins and just notes the possibility to reframe discussions of speculation in the wider context of a variety of co-mapped distinctions. The four basic distinctions of the 24*24 matrix can be used to re-identify some key actors in markets and cyberspace by refering to four oscillatory loops of speculative re-evaluation. A basic typology could thus procede by seperating the following background oscillations of emerging cyberspace-markts.

    a) The expandability loop is the domain of employers who create turbulence by entering growing markets and exiting shrinking ones.

    b) The convertibility loop is the domain of investors who create turbulence by buying rising rights and selling rights falling in worth.

    c) The imageability loop is the domain of persons who create turbulence by entering and exiting identifications according to part-conscious processing of dissonant suggestions.

    d) The sustainability loop is the domain of public actors who create turbulence by offering sustainable or non-sustainable redistributions of benefits and costs of real-estate-and qualification-sustainment.

    These four types of actors can of course further customize their portfolios by adopting the distinctions characteristic to other types of actors or by refering to other complexities specified according to ideosyncratic or organized needs. One way to monitor this is of course to blow up the number of permutated dimensions defining the portfolio-map.


    One way to outpace empirical assignments of truthvalues to the theoretic forms outlined here, is to call a qualitative balance of rates of diffusion an underpriced asset. This means a lot and at least the following. Full experience of cyberspace involves importing from and exporting to cyberspace aswell as importing and exporting peripheral carriers and contents as products and services aswell as participation in the philosophic investigation and civil regulation of this ecologically and symbolically distinguished market for indicated distinctions.

    To partake in the simulation of this breadth of participation can be one of the noble ambitions of employers, investors, persons and governments of the next decade. But there is a gap between potential benefits and un-employed frustration. Disappointment with short term benefits in relation to costs of re-employment could coincide with mounting ecologic stress and penny-wise turn-around efforts of governments falling into each others arms in desperate search for credi-ta-bility.

    dd-Maps might offer some perspective when looking for ways to reposition local markets in relation to others. The hyped new options affecting cyberspace and sustainability will surely deserve special attention but will have to be discussed in a multitude of context-portfolios reflecting global competitive pressures on local industries and lifestyles.

    Estimation of Parameters and Empirical Observations

    This approach to theory would suggest to feedback maps of the criteria pre-defining the decisions of actors to the actors. Actual complexities of relevant levels of distinction aswell as their value-parameters might be roughly estimated by discussion of current rules of thumb among actual market-managers.

    A market-manager might be called whoever is responsible for tracking the appropriateness of distinctions refering to imports and exports of a distinguishing system. The dd-maps suggested offer potentially relevant distinctions for commercial and political actors while providing for personal areas of advantage and preference. The modell is thus turned into a tool to organize permutations of distinctions regarded as currently relevant by actors. Empirical observations can then monitor the evolution of competitive environments and managed operations by relating them to the map of all possible situations considered.

    Historic analysis can focus for instance on the evolution of national currencies and revenues from real-estate-taxation in relation to the uninhibited and planned growth of markets and pools of competence during specific ecologic and communicational transformations.

    Statistically testable formulations of the model could work with historic data about cyberspaces already operated and other relevant markets. Concurrent analysis is difficult inspite of faster reporting as change-processes are accelerated too.


    Cyberspace was related to a scalingly generalized theoretic reconstruction of the market-metaphor. This fractal property allowed the formulation of general distinctions for operations in theoretical and empirical interface systems to the net-vortex. Emerging issues of specialized theories can thereby be related to logic, natural, social and psychologic laws of autonomous re-definitions of conscious experiences. The proposed approach tries to offer a fractal tool for the suggested comparisons of maps of potential evolutions of contexts. It indicates a possible path to syntactic reconstructions of multi-predicate logics as well as interfaces to natural and social resources invested by personal and organizational decisions.

    Market theories could thus be understood as specific implementations of a general theory modelling the effects of diverging theoretical evaluations of empirical parameters re-influencing the theoretical evaluations and empirical parameters.

    Applications of such a general theory of markets to cyberspace can proceed by mapping basic types of evaluated distinctions which are used in relating theoretic assumptions to decision portfolios which are in turn reaffecting the basically evaluated distinctions. It is a form for recalling historical examples of astonishment, boom and crash.

    Appendix 1: How to ddn-Map With a Spread-Sheet-Like Tool

    Create a table between a row and a column providing sums of combinations of values relevant either to potential imports of a system or to potential exportsfrom its boundaries. Create a ranking of categories relevant to the potential contexts to be itemized in the rows and columns. Enter specific combinations of values reflecting the ranked categories for each item of the rows and columns. If all permutations of potential values are reflected in the rows and columns a relatively comprehensive map of the potential contexts of transaction can be constructed by computing algebraic combinations of row and column values for each cell of the matrix.

    Appendix 2: How to Tune ddn-Maps

    A standard spread sheet offered the possibility to name the rows and columns and fill the table with formulas simply calling for an addition of the names. Display of zeroes and grid could be turned off with your software too. Reduced width of column can sometimes display a special character # for longer strings - so the shorter strings of positive values stand out clearly patterned. To a professional mathematician these zero-ed in manifolds might look not at all like Hartog-areas.

    The suggestive impact of ddn-meta-portfolios can be increased substantially if the potential contexts are arranged by grouping together items showing the same values for specific categories of distinctions. In the case of trinary distinctions this means to create sequences of -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1 instead of just repeating -1, 0, 1, -1, 0, 1 etc. Users of colour displays can further enhance the drama of simulated re-evaluations of interactions by defining negative values as red etc. 3D-columns offer a nice way to map the relative values of market interactions reflecting the impacts of distinctions among their contexts of import and export. But even if only actually observed transactions are included basic distortions of the map generated by hierarchic structures of distinction will stand in the way of trivialized interpretations of such graphs.


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    George SPENCER-BROWN: Laws of Form. 1979.

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    Glossary on Cybernetics and Systems Theory SC/INdexASC.html

    Some other sources influencing the author have been listed in previous papers which can be downloaded by pointing a worldwideweb browser at the URLocator: at/usr/absatz/schreiber/