Artikkeli Theory of Futuribles

Artikkeli Pentti Malaskai and Ilkka Virtanenii Theory of Futuribles

Each field of scientific knowledge has its intrinsic canon of sufficient legitimation. Knowing about the future is no exception; futurological canon legitimizes beliefs and opinions about the future as knowledge of the future. At the moment, however, this canon is more implicit in a plethora of approaches, mindsets, and methodologies applied in futures studies than explicitly stated. Con- ception of the futures manifold is implicit in many approaches and mindsets of the futurological inquiry, and to study it is the object of the paper. Instead of considering the future as a single pre-determined case, a fan of possible futures, called futuribles is considered as a proper object of futurological conjecture. The manifold conceptualization of the future has a long history from Luis de Molina and others in the 16th century to Bertrand de Jouvenel in the 1950s and 60s. The logical theory based on the manifold conceptualization has not as yet, however, been fully analyzed. The authors develop a general set-theoretic construction, called a theory of futuribles for futures knowledge inquiry. New concepts of futures space, futures galaxy and futures multiverse as well as synoptic difference and distance, local and egocentric transitivity of the distance measure are deduced. Key words: futuribles, theory of futuribles, futures manifold, futures knowledge, scenario, futures space, synopsis, synoptic distance, local and egocentric transitivity

Introduction sal theory of truth to be referred to by all the sciences; each of them has its A wish to know about the future is kno- intrinsic canon of necessary and suffi- wn to be human intellectual charac- cient legitimation, and the canons are teristic since Antic Greece and Rome, not fully compatible with each other. as Robert Nisbet1, Wendell Bell2, Ossip In sciences, however, one canon shall K. Flechtheim3, and Sirkka Heinonen4 not be contradictory with another, even among numerous others have pointed though there is no ultimate authority out. Interest in the future can be traced but only open scientific discussion back even to the ancestors of Homo to resolve discrepancies that might Sapiens, as exemplified for instance appear. No canon can be internally by Y. Coppens with archeological fin- inconsistent or against the laws of Na- dings5, by Riane Eisler with her studies ture. Knowing about the future makes of women’s roles and the construction no exception in these respects. of social systems6, or Tom Lombardo7 in In another respect, however, kno- his essay on the prehistoric evolution wing about future is different from of future consciousness. One can say knowing about the past and present. that the future was invented by the Unlike the past or present, the future emerging consciousness of mind at does not materialize to our senses, the dawn of humankind. when a desire to know about it appears Scientific knowledge is nothing else in the human mind. Knowing about the than a well grounded true belief. All past and present can be grounded on sciences from mathematics or natu- factual material evidence, but conjec- ral sciences to social and humanistic turing the future relies on non-factual sciences stick in this as an epistemo- and intentional data. logical commitment. It means that a Futurological inquiry has its intrin- subjective belief, intuition or opinion sic canon for legitimizing beliefs and is accepted as objective knowledge opinions about the future as knowled- when there is sufficient evidence to ge. At the moment the futurological “legitimate” that the belief is true and canon is more implicitly present in a credible. However, there is no univer- plethora of case studies, approaches,

10 2-3/05 mindsets, and methodologies app- The essence of intentionality was lied in futures studies, than explicitly well articulated by Ossip. K. Flecht- stated. An updated source for the heim in his book Der Kampf um die methods is found in the Millennium Zukunft3. According to Flechtheim the project’s publication Futures Rese- scientific discipline, that he as the first arch Methodology Version 2.08. There one called futurology in the 1940s, is, however, a need for basic futures intents to contribute to (op.cit. p.9): research to recognize that ‘knowledge eliminating war and institutionalizing of the future’ is generalization of the peace, eradicating hunger and poverty knowledge of the past and present. and stabilizing world population, de- In this paper the authors develop mocratization of societies, protecting a general set-theoretic construction, Nature from over-exploitation, and hu- called a theory of futuribles for futures mans from themselves, and preventing knowledge inquiry. alienation by giving rise to new creative Knowing about future Homo humanus. The modern futures studies have no objections to these Future is no entity but a continuously intentional challenges today. unfolding process, to be forethought in Ossip K. Flechtheim also outlined the mind scenery. The past constraints four presumptions necessary for ac- the future unfolding - the future re- complishing the intentional challenge members some of the past - but the past of futurology (op.cit, p.16). The first never fully determines the future cour- assumption holds that the world is se. The future is not a deterministic considered dynamic whereby not only consequence of the past, but there are its temporal states change but also its many factors at any time which have basic structures generating the states effects on the realization; the factors do change and new options of human may be random “fluctuations”, chance interest emerge from the changes. “disturbances” or natural “shocks”, Secondly, the possible changes are “structural change”, or human “inter- partly recognizable beforehand and the ventions”, etc. In system language the directions and speeds of the changes future process is under-determined can in some instances be roughly pre- by the past and its realizations will be dictable. Thirdly, antithetical forecasts determined behind the curtain of ge- and projections also have some value; neric indeterminacy. Knowledge about they can contribute to the clarification such a contingent “under-determined of problems and to specifying time, object” is necessarily uncertain, i.e. place, area, or degree of probability knowledge of the future is irreducibly and consequences of crises. Fourthly, contingent. within the frame of the conditions de- Futurological knowledge is “true” if termined by the past there is a freedom it asserts something that is not impos- for human choice to make an effect on sible in the material world, or somet- the future and to create alternatives hing that is not impossible for humans and shape the future unfolding. Also to make real. The wide use of foresight understanding of what is necessary methods and material produced by fu- and out of human reach, or possible tures studies indicate that scientifically and desired, or what is unnecessary grounded contingent knowledge is im- and avoidable contributes essentially portant and vital to modern societies. to shaping the future. We can well agree Futurological inquiry is concerned also with these presumptions today. particularly with intentional human The possibility to intervene by free deeds and their effects. Intentionality will in the course of the future and to is one of the aspects which make the pursue human intentions is a funda- futures study essentially more general mental commitment but not always than natural science or other studies easily accepted. A strongly contro- of non-intentional objects. versial dispute about the possibility

11 2-3/05 of free will took place in the Catholic and social, cultural and environmental Church towards the close of the 16th issues. century9, and this has relevance also Presumptions of determinism, pre- to modern futurological discussion. determination, or prophesying do not The debate was fuelled especially by belong to the futurological knowledge Luis de Molina’s book Concordia10 creation. Predicting, forecasting, ex- published in 1589, where this scholar trapolating, simulation and decision offered a logical explanation for free modeling, and planning procedures will, foreknowledge and predestination. are instead valuable approaches in He argued for freedom and indeter- futurological inquiry. Their use calls, minism in the world and he has been however, for more careful considera- credited with introducing a concept tion of validity and reliability than for of ‘conditional future contingents’ or instance in natural science studies. “futuribilia” (Molina Luis de 9). It is not, Predicting the moon orbit around the however, sure that the term futuribilia earth in astronomy is relatively easy was really coined by de Molina even because there are no intentions or though he was the father of the idea; possibilities to change the orbit deli- his important texts have as yet not berately, and predicting the orbit of a been studied rigorously enough from satellite is possible because the pre- the modern futures studies point of vailing intentions are well known and viewiii. strictly managed. Human societies are Conception of futuribles different, fortunately! De Jouvenel presented also the De Jouvenel, in his classic The Art of following important assertion. If an 11 Conjecture (p.15) and Flechtheim, exhaustive enumeration of the possible 12 in his History and Futurology (p. futures at any hypothetical present 105) referred to de Molina. Bertrand could be assumed possible, it would de Jouvenel picked up the idea of “fu- lead to the untenable consequence turibilia” and combined “future” and that there is a progressive reduction “possibility” together into a new term of uncertainty of futures knowledge “futurible”. in general. Therefore, there is no time De Jouvenel deﬁned futuribles as a at which we can enumerate the fu- fan of possible futures, and he states turibles exhaustively, concluded de that futuribles designate what seems Jouvenel. to be the object of thought when the Futurible-conception, i.e. the ma- mind is directed towards the future (op. nifold of possible futures, is well ac- cit p. 18 and 20). This indicates that cepted in modern futurological inquiry. the futuribles is a “multifold object” Growth of the popularity of scenario of forethought. Our mind is unable to writing since the 1960s demonstra- grasp with certainty the things which tes this well, as exempliﬁed by the will be or all intentions which may sample of the references13 of recog- intervene in the process, but it can nized experts, such as Michel Godet, conjecture possible alternatives. There Ian Wilson, Eleonora Masini, Jerome are many states of affairs which we Glenn and Theodore Gordon, and by have no reason to regard impossible several reports to the Club of Rome in the future; it follows, in accordance since the 1972. Possibilities which with the law of contradiction, that we the conceptualization offers to futures can regard them as possible. A possible studies have not as yet, however, been future state enters into the class of comprehensively utilized. “futuribles” only if it originates from The objective of this study is to the present. Futurible is an element present a logical framework of the of analytical and semantic construc- futurible-conception which is called tion of the futures process comprising a theory of futuribles. The theory economic and technological, political is deduced from the morphological

12 2-3/05 setting called a generic table of the is a symbolic representation of the futures space. future, i.e. it is a kind of a map. But Map analogy the “futures cartography” is still in its infancy. There are no standards The study approach is illustrated with for symbols of social issues, or how an analogy of ordinary mapping which to present, for instance political re- everybody is familiar to. A map tells us lationships and power dependencies something but not everything about and qualitative transformations. There scenery assuming that one can read the are no criteria for which issues really map and interpret its messages. The matter in the future or which of them map is a source of information about would generally be important enough to the scenery, a symbolic replica of some be selected for a mapping. In addition it characters of it. There is a relation- might be desirable that a futures map ship between the map’s designs and is more of a playground for competi- symbols and the real scenery at some tion and action than a description of level of coarseness and vagueness. A the state of affairs as such. When the map is not the territory. One cannot intentional points matter, the futures walk on the map, and neither are trees cartography aims at a unique product growing nor lakes opening before one’s for a given purpose. All this does not eyes on the map or smells and sounds make, however, futures mapping any sensed as in the real scenery. The less important in general. Futures map is anyhow useful when planning studies can benefit from the analogy a project in the scenery or wishing to of mapping. foreknow what kinds of experience Requisite coarseness of resolution one might be able to sense there and is an important logical aspect in any possibilities different places would be mapping. In a geographical map the- suitable for. re may be both elementary items of Robert Osserman offers an excellent the scenery, e.g. a tree, or a cliff, and general account of mapping in his book also some larger units of scenery like 14 Poetry of the universe . In an analo- forests of different kinds, swamps, gous way we see the futures manifold fields, water systems, industrial areas, as a symbolic representation of the housing areas, etc. Different types are future, i.e. it is a kind of a map. often mutually exclusive, i.e. if there Were similar maps of futures scenery is a lake there is no road in the same available or were it possible to design place, and if a swamp then no corn field, them, they would certainly be of ser- but this is not always a necessity. In a vice to our undertakings for the future swamp there may be forest, and a road and foreseeing possible options of the can go along a river bank or cross a future. lake. Logical separateness and mutual In geographical mapping the ele- exclusiveness is a vital methodological mentary symbols and patterns of the character to be preserved. This re- map represent different elements of the quirement can be fulfilled by defining scenery, e.g. trees, lakes, meadows, compound scenery types of richer cliffs, buildings, roads, or spatial rela- information. A scenery type ‘swamp tions between the elements like height with fir forest’, or ‘lake with a bridge differences, distances, steepness, etc. and road across’ serves as an example During the centennial time of deve- of finer resolution. On the other hand, lopment in cartography it has become the resolution can be made coarser by possible to agree internationally on withholding information that does not common standards for map design, matter, as is often done for instance on i.e. symbols used, ways to represent highway maps. Unavoidable vagueness spatial relationships, or scales of the is left in any mapping, which may be maps. managed somehow with a diversity of In the same way a futures manifold maps. Vagueness is for sure also una-

13 2-3/05 voidable in futures mapping, and to a of GDP” illustrate futures issues and certain degree it can be managed by variable names. Each issue is itemized choosing the coarseness of resolution into mutually exclusive, alternative accordingly, but as noted earlier, an possibilities of the issue variety. The enumeration of the futuribles is not items of the issue variety are called possible and knowledge of the future value elements of the variable and the is at no time converging towards a total set of them forms the domain of “real” future. the variable in the study. A futures map is a generic design of Let the futures variables be denoted the futures manifold and a symbolic by Xi, (i = 1, 2,…, K), where K is the representation of what might unfold or number of identiﬁed variables. The be realized by human interventions in domain of the value elements of va- the material world. riable Xi is a set of the varieties {xij|j=1, 2,…, n }, where n is the number of the Generic design of futures i i different values of Xi. manifold When an issue is apt to quantitative Futures manifold measurement, the value elements of the variable are quantities. Futures Designing a futures map starts by variables may also be measurable only identifying the issues which are regar- on an ordinal scale, or it may represent ded as vital and relevant in the study; plain qualitative aspects of the future they are called futures variables. Each on a nominal scale. If all the values in variable has a name tag, e.g. “econo- a domain are the same, i.e. the variable mic growth”, “export”, “aging rate of has only one value, the variable is called population”, “literacy rate”, “dema- a futures constant; for instance, until terialization”, “equality”, “rebound”, today the planetary conditions of the “environmental stress”, “energy need”, Earth have been generally regarded “material consumption”, “technology as constant; nowadays the possibility development”, “welfare productivity

Figure 1. Illustration of the futures manifold as a coordinate system

14 2-3/05 of an irreversible climate change has row i of the table is designated and to transformed that aspect from a futures each value element xij of the variable Xi constant to the class of variable. A va- a cell (i, j) in that row is designated. The riable having a domain of a few values resulting table of the manifold is called only may be taken to serve as a futures the generic table. The generic table parameter; the parameter can be used obviously has K rows and a number for partitioning the futures space into ni cells in each of the rows. A design of mutually exclusive sub-spaces. The the generic table is illustrated in Figure partition can be seen as analogous to 2. The generic table and the coordinate presenting a map of the Globe with the system are isomorphic equivalents of maps of the Eastern hemisphere and the futures manifold . Western hemisphere. In summary we In Figure 2, the bottom row has only get a definition of the futures manifold one value element in the domain; the (1) to (3): respective issue is a constant futures Let the collection of the futures va- background and the variable a futures riables Xi be symbolically denoted by constant. The next two variables just the variable set X. We then have above the bottom row have three value (1) elements and the second variable has four cells in its domain. They repre- The value domains of the variables sent a conventional futures variable are with a given domain. The uppermost (2) Xi = {xij | j = 1,...,ni }, i = 1,...,K. variable has two values. This variable The elementary system defined by (1) could be regarded, if relevant, as a and (2) is called a futures manifold . It futures parameter. With the values of can be interpreted as a K-dimensional the parameter the manifold in Figure coordinate system “spanned” by the 2 can be partitioned into two mutually variable set X. The futures manifold exclusive sub-manifolds, as will be can be symbolically presented as a explained later. set of “K-dimensional Cartesian points” Figure 3 shows a concrete example , i.e. of a generic table taken from an EU study15. For layout reasons the table (3) = { x X | x X X x X x ... x X }. P P 1 2 K in Figure 3 is presented in a “trans- In Figure 1 the coordinate system of posed form”, i.e. the five (K=5) futures the futures manifold is schematically variables appear horizontally and their illustrated, with points ( ). value domains (with 4 to 5 cells) ver- Generic table of the futures tically. The non-shaded cells in the manifold table combined represent a point in the K-dimensional futures space. The system of (1) to (3) is possible to The generic table is a morphological represent alternatively in the form of map of future “sceneries”, i.e. repre- a table. For each futures variable Xi a

Figure 2. Generic table design of a futures manifold

15 2-3/05 Figure 3. Generic table of an EU study; the futurible of the non-shaded cells is called the “Laissez faire” future in the study. The table layout is transposed as indicated in the text. (Source: Scenarios Europe 2010) sentations of the possible futures. mean resolution indicates the total Each futures issue or a variable has expressiveness of the manifold under multiple varieties, i.e. each row of the study. table has different number of cells. The Syntactic design of futures number of the cells in a variable row gives an indication of the coarseness mapping of resolution of the issue presentation. An element of the futures manifold The more cells there are, the finer is in (3) and equivalently a point in the the resolution, and vice versa. coordinate system in Figure 1 is cal- If the number of the variables in the led a synopsis. In the generic table it generic table is K and the ith variable is defined as follows: a synopsis is an has ni value elements, then the total exhaustive and exclusive collection of number of cells in the table is M given values of the successive variables, i.e. by equation (4): the synopsis is a design composed of K . one and only one cell from each variable (4) M = ∑ n i = K n . i = 1 row of the table. Formally a synopsis, Metaphorically, the number of fu- Fq, is defined by (5): tures variables K refers to the exten- (5) sion of the futures space – the bigger In formula (5), N stands for the ma- K the farer the horizon of the space ximum number of separate synopses. from a centre.K The mean number of It depends on the number of the pos- . the cellsM = per∑ n i row=K n .implies the mean sible values of the variables in their issue resolution.i = 1 The number M, i.e. domains according to the multiplica- the product of the extension and the tion formula (6) (5) Fq = (x 1q1, x 2q2 ,..., x KqK), q = 1,...,N; q 1 { 1,...,n i}, i = 1,...,K.

16 2-3/05 K notation of = {Dq}. (6) N = ni = n1 x n2 x ...x nK. q i = 1 With the D -table notation a synop- There may be some bans which sis Fq of can be presented with a negate the simultaneous presence of scalar product operation (denoted by ·) some values of distinct variables whe- between a row of the generic table in q refore the number of feasible synopses (3) and of the Dirac’s Delta table D : may be smaller than the number of all (7). synopses N. The given generic table q As defined above, the symbol D i in forms the background of the study and Formula (7) denotes the ith row vector synopses. Therefore a synopsis inclu- q th of the table D and Xi is the i row of des also information of the particular the generic table . The operation in address of the elements (row and cell (7) results in a vector Fq whose com- number) picked for it. For example, ponents are scalar products of the row one synopsis of the table in Figure 2 vectors of the tables Dq and . There is (x11, x21, x31, x41, x51). To show this is one to one correspondence between synopsis on the background of the this result and the previous notations whole table we present the table as of { } and {F }. q q q q a long row of all variables one after . . . The futures space F = is {F qdefined|q = 1,...,N as } = {(D 1 X1 , D 2 X2 ,...,D K XK ) | q = 1,...,N } = D ° . the other as follows: [(x11, 0),(x21, 0, 0, the set of all synopsizes {Fq} spanned 0),(x31, 0, 0),(x41, 0, 0),(x51)]. This pre- by the whole generic table . With the sentation shows what other choices notation of the futures space will are possible on the same background have a simple expression as a “multip- and that the choice made is a picking lication” operation (denoted by symbol of this certain alternative. ) with the generic table For rationalizing this notation the ° following Dirac’s Delta type table Dq (8). q is introduced. D is a table with the Futurible - a basic unit of futures same number of rows and cells and the same format as the generic tab- mapping le. Each cell value of the Dq-table is The synopsis concept belongs to the either 0 or 1 in such a way that each syntactic design of futures mapping; row contains one and only one 1. Let it is a logical form of a possible future. the ith row (i = 1,2,...,K) of the Dq-table Synopsis and futurible are synony- q mous equivalents in the sense that be denoted by D i and let us further assume that it has its non-zero ele- futurible is a semantic counterpart of synopsis. Futurible refers to the con- ment in the position pi ∈ ({1,2,..., ni}, q q tent, while synopsis gives the logical i.e. D ipi = 1 and D ij = 0, when j ≠ pi. q form in which the content is to be pre- The table element D ipi can be used to sented. The whole set of synopses in pick a cell value xipi from address pi of (8) also means the fan of the futuribles the futures variable Xi in the generic q mapped onto the generic table , and table. Together all the D i -rows with F denotes also a futurible. i = 1,..., K and pi = 1,2,..., ni pick an q exhaustive set of the value elements of Each futures variable defines an in- the futures variables that constitutes a dependent dimension of the future into synopsis. The Dirac’s Delta table thus which direction the futures stories can defines the formal picking of a specific be told and varied within the domain synopsis from the set of all synopses of the variable. The generic table with within the generic table. The set of all its K variables spans a K-dimensional Dirac’s Delta tables is presented by a futures space, where each futurible

q . q . q . q . (7) Fq = (D i Xi |i = 1,2,...,K ) = (D 1 X1 , D 2 X2 ,...,D K XK ). q q q . . . (8) F = {Fq|q = 1,...,N } = {(D 1 X1 , D 2 X2 ,...,D K XK ) | q = 1,...,N } = D ° .

17 2-3/05 represents a map of a possible future value there is a synoptic difference “scenery”. and a synoptic distance between them. It is plausible, as mentioned earlier, Semantically, the values of a variable that relations of one kind or another differ from each other qualitatively, and may exist between futures variables the same holds necessarily also with denying a possibility of some values to the differences between the futuribles. coexist. In addition, constraints may Therefore a distance from one futurible occur also between futuribles to follow to another can not be defined in any each other. Some futurible may be a metric sense. The only quantitative necessary condition for another one, information concerning the differences and this in turn to yet another one etc., is the number of the variables which while constraints of another type may assume different values in the cor- deny a succession between futuribles. responding futuribles. The concepts For instance, the present which in the of synoptic difference and distance of logical sense is also a synopsis and a futuribles are based on this informa- “futurible”, is a necessary though not tion within the generic table. sufficient condition for any futures The synoptic difference between to come. The present does not prede- the futuribles Fp and Fq is defined as termine the course of the successive follows. Let Fp and Fq be two synopses futuribles, but neither does it leave the of the futuribles and consider the va- course of the future unconstrained. lues xipi and xiqi, respectively, which a From the synopsis of the present seve- certain futures variable Xi has in these ral possibilities are open for futuribles synopses. Let furtheri define ai diffe- to unfold. Some possible courses of rence relationi pq such that pq = 0, if the future may divert from each other xipi=xiqi, and pq =1 otherwise. Using this irreversibly depending on the different relation, a synoptic difference (vector) constraints, while other courses may ∆(Fp, Fq) for the futuribles Fp and Fq is pass through the same futuribles. It defined in (9): is, in addition, well grounded to assu- (9). me that in the course of the future a Now we can use the number of given futurible may be reachable from components which are equal to 1 in several preceding ones but not from the synoptic difference (9) to define whichever futuribles. A possible chain the synoptic distance between the of futuribles is called a course of the two futuribles. The synoptic distance future. Futuribles as well as futures indicates how many future variables courses may be attached with specific there are in the futuribles, which differ attributes such as probable, desirable, in values from each other. The synoptic avoidable, non-feasible, or a threat, a distance thus is an integer between utopia or a dystopia. 0 and K. Synoptic difference and synoptic Formally, the synoptic distance, distance denoted by d(Fp, Fq), can be defined with The futures variables are most fre- the help of the synoptic difference: quently qualitative issues “measured (10). on nominal scales”. We can speak The synoptic distance (10) is a well- about a synoptic difference between defined distance-type measure in the futuribles only in a specific meaning. sense that it fulfills all the properties When one or more futures variables required for a distance measure: of two futuribles assume a different

1 2 K (9) ∆ (Fp, Fq) = ( pq , pq ,..., pq ) ; p, q = 1,...,N . K K . i 2 i (10) d (Fp, Fq) = ∆(Fp, Fq ) ∆(Fp, Fq ) = ∑ ( pq ) = ∑ pq . i = 1 i = 1

18 2-3/05 (i) Non-negativity and reﬂexivity: of the space at a distance C from the

d(Fp, Fq) ≥ 0; center so that 0 ≤ C ≤ K. d(Fp, Fq) = 0 if and only if Fp = Fq The number of the 1-close futuribles (ii) Symmetry: around the center is obviously d(Fp, Fq) = d(Fq, Fp) (11). (iii)Triangle inequality: i.e. the total number (M) of the cells in |d(F , F ) - d(F , F )|≤ d(F , F ) ≤ p r r q p q the generic table minus the number d(F , F ) + d(F , F ). p r r q (K) of the futures variables (or rows The properties (i) and (ii) are direct in the table). consequences from the definition (10), For the 2-close futuribles we get: proof of the validity of the triangle inequality is also straightforward but is (12). omitted here. On the other hand, the The last sum expression is used as synoptic distance does not possess a shorthand version of the preceding such common properties of a relati- double sum. on as additivity and transitivity. The The general formula for the number synoptic distance is in a sense analo- of the C-close futuribles (0 ≤ C ≤ K) can gical to the L1-norm (absolute value be shown to be norm) in the Euclidian space. (13). C-close futuribles where again the last sum expression Futuribles at the distance C between is used as a shortened notation for the each other are said to be C-close. When multiple product sum expression. the futuribles are 1-close they differ For the number of the most remote, only by one value element of one va- K-close futuribles at the horizon, one riable, and when they are C-close the gets the factorial form number of the variables with different K (14) NK = (n1 -1)(n2 -1) ... (nK -1) = (ni -1). values is C. i = 1 Let us choose some of the futuribles The C-close futuribles are located in of the futures space to represent the a same orbit, but they are Z-close to present or a hypothetical present. The each other, where Z is not a constant number of other futuribles at a given but obtains different values from zero distance from this centre point can to 2C or K taking the smaller of the easily be calculated. Obviously, the two. This reflects the non-transitive synoptic distance from the centre to character of the synoptic distance and itself is zero and the distance to the C-closeness relation: the relation is most remote futuribles within the reflexive and symmetric, but it is not “horizon” is given by the extension transitive for reasons stemming from number K of the futures manifold. All the synoptic difference. The closeness futuribles are distributed in the orbits relation is also non-additive, but it still

K K (11) N1 = (n1 - 1 ) + (n2 - 1 ) + ...+ (nK - 1 ) = ∑ (ni - 1 ) = ∑ ni - K = M - K , i = 1 i = 1

(12) N2 = (n1 - 1 )(n2 - 1 ) + (n1 - 1 )(n3 - 1 ) +...+ (nK -1 - 1 )(nK - 1 ) K - 1 K = ∑ (ni - 1 ) ∑ (nj - 1 ) = ∑ (ni - 1 )(nj - 1 ) . i = 1 j = i + 1 j > i

K - C +1 K - C +2 K -1 K (13) N = (n - 1) (n - 1) ... (n - 1) (n - 1) C ∑ i1 ∑ i2 ∑ iC-1 ∑ iC i1 = 1 i2 = i1+1 iC-1 = iC-2+1 iC = iC-1+1

= (n - 1)(n - 1) ... (n - 1)(n - 1) , ∑ i1 i2 iC-1 iC i1 < i2 <...< iC-1< iC

19 2-3/05 obeys the triangular equation as the the “cosmos” of the futures space looks synoptic distance does (see property similar in every “direction” and similar (iii) before). from every synopsis. The symmetry The distance (or closeness) of any may be broken, however, by bringing

two futuribles Fp and Fq, denoted by the past, present, and future into Cpq, can formally be expressed using the “cosmos”. The present is a centre the Delta tables as follows futurible in an egocentric mapping K of the futures space; the centre may p . q (15) Cpq = K - ∑ D i D i , also represent a hypothetical present where the generali = 1 (ith) term in the instead of one just being experienced. sum expression is the scalar product Figure 4 gives a graphical illustration of the ith row vectors of the tables Dp of the futures space of the generic table and Dq, respectively, and it reveals in Figure 2 and the distribution of the whether the ith value elements in the futuribles in C-close orbits of different distances, 0 ≤ C ≤ K. The outermost (C two futuribles Fp and Fq are the same (the scalar product equals to one) or = K) orbit remains empty, due to the not (the scalar product is zero). The fact that the fifth variable of the table complete distribution of distances bet- is a futures constant. ween any two futuribles is determined The C-close futuribles are different using the generalized products of the qualitatively and semantically, which Delta tables, cf. definition (8) above, is of no concern to the closeness me- and their scalar products: asure. Semantically, the differences may mean anything from crucial or (16). epoch making change to a small shift In the last expression of Formula of orientation or change of resolution p q . p q p q 2 2 (Cpq)N x N = (K - (D D ) (D D ))N x N = (K - (D D(16), ) = K - is (D a ND ×)N . -matrix having K as all ° ° ° ° 2 of an issue. The theory of futuribles (C ) = (K - (D p D q ) . (D p D q )) of= its(K -elements (D p D q )2 =and K - (D D )2 .denotes the pq N x N ° ° N x N ° ° p q 2 does not concern the semantics but N×N -matrix of the elements (D °D ) . only syntax of the futures mapping. The futures space defined by the As observed earlier, the distance generic table is most symmetric. Each between the futuribles is not additive synopsis is surrounded by equal num- or transitive in general. However, it is ber of other synopses at the same dis- possible to find sub-sets of futuribles in tance from it. Metaphorically speaking, the futures space where the closeness

(16) p q . p q p q 2 2 (Cpq)N x N = (K - (D °D ) (D °D ))N x N = (K - (D °D ) = K - (D °D ) .

Figure 4. The futures space of the futuribles spanned by the generic table in Figure 2.

20 2-3/05 relation is both additive and transitive. the separate values of the parameter By additivity and transitivity is meant the futures manifold can be partitio- that the triangular relation is an equa- ned into separate “hemispheres” of the tion between the distances of any three manifolds. With the two values of the futuribles Fp, Fq, Fr, i.e. variable X1, for instance, the generic (17) C = C + C . table of the futures manifold in Figure pq pr r q 2 can be partitioned into two exclusive When additivity and transitivity are sub-manifolds as, say, a “Northern” applied to a directed net of successi- and a “Southern” hemisphere of the ve futuribles and when they hold on futures space. In Figure 5 the mani- triples of futuribles which immediately fold of Figure 2 is partitioned into two. follow each other, we call them local As compared to the original futures additivity and transitivity. Another manifold, it is to be noted, that the special form of additivity and transiti- extension of the sub-manifolds has vity which can be defined on a futures decreased to four, and the constant space is called egocentric additivity and value of the variable X , which is the egocentric transitivity, respectively. In 5 same in all 72 futuribles, is depicted these relations one of the three futu- as a common background for both ribles, Fp is fixed (“choice of the origin”) 0 hemispheres. and the triangular relation refers (the Figure 6 gives a graphical illustration equality form) to this center futurible: of the two hemispheres of sub-mani- Cp q = Cp r + Crq. Egocentrically additive 0 0 folds presented in the generic tables and transitive sub-spaces are at the of Figure 5. As in Figure 4, the futu- base of scenario approaches, and there ribles are distributed on C-close orbits is an algorithmic way to determine around a center for different values them based on the N×N matrix (C ). pq of 0 ≤ C ≤ K. Because of the common The locally additive and transitive futures background variable X , the sub-spaces are analogical to those of 5 dimension of both sub-manifolds is the one-dimensional sub-spaces of four (K = 4). The outermost orbits (C = higher-dimensional spaces in the case 4) of the hemispheres are empty. This of Euclidian metrics. is because the first variable X1 has the Transformations of the futures role of a partitioning parameter and manifold its value element in each hemisphere becomes in turn a futures constant

Partitioning the futures space (x11 for the ﬁrst hemisphere and x12 for A futures variable can be used as a the second). The numbers of futuribles parameter, as mentioned earlier. With in different orbits are N0 = 1, N1 = 7,

Figure 5. Partitioned futures manifolds with the variable X1 as the parameter and the variable X5 as a constant futures background

21 2-3/05 Figure 6. Illustration of the partitioning of the futures manifold into two hemispheres

N2 = 16, N3 = 12 and N4 = 0 for both other purpose. Using the map analogy, hemispheres. the transformations can be interpreted Other transformations as a choice of the scale. By letting the domains of the va- Futures manifold as a map may be riables be variant but keeping the more or less expressive in relation to number of the variables fixed we attain the futures issues envisioned in two a generalization of the futures space ways. Maps may be needed to show concept called a futures galaxy. A set deformation of societies in a more or of futures spaces with the same variab- less coarse way. This capability will be le set is called a futures galaxy. The achieved with transformations of the dimension of the galaxy is the same preliminary generic table in futures as the dimension of its future spaces, mapping. There are two options to do i.e. the number of the variables (K). the transformations and they may also It is worth noting that in the galactic be combined. transformation the synoptic distance First, the value domain of some va- remains defined. riable may be extended by adding new If the galaxy consists of the future value elements for instance by splitting spaces 1, 2,..., P of K-dimension, some previous value element into more where each p, p =1,2,...,P is a set of the detailed parts, or the domain can be futuribles Fpi, i = 1, ... , Np, the galaxy made coarser by removing some value can be formally denoted by (18). elements. The number of the futures Another transformation of a generic variables, i.e. the issues of the future, table is more profound than that of remains fixed in this transformation the galactic transformation. In that and only the variety of the value options transformation new variables are ad- of one or more variables are changed. ded to the table, i.e. the futures space The transformations may be relevant is extended by dimension, or vice versa in order to change the coarseness of some variable is deleted from it whe- resolution of some issues or for some reby the futures space is contracted. P P Np (18) O = F1 F2 ... FP = FP = {Fpi } . p =1 p =1 i =1

22 2-3/05 Figure 7. A thirteen-dimensional extension of the ﬁve-dimensional futures space of gure 3 (source: Scenarios Europe 2010)

23 2-3/05 The synoptic distance is no longer ding process which has been going on defined between the futuribles of the in the past and is continuing through transformed and the primary galaxy. the present. A study of the known Each transformed generic table of the and unknown forces and dynamics second kind defines a futures galaxy of which drive the process belongs to the its own extension. The infinite set of the phenomenology of futures studies and futures galaxies of different extension not to the present syntactical study. is called a futures multiverse. The theory of futuribles is, however, The futures manifold design in Fi- a framework where in the trace of the gure 7 was used recently in an EU- process can be made visible so to speak. study14 and it illustrates the futurible, The process within the framework of futures space and futures multiverse the futures manifold is a directed di- concept. The futures space in Figure graph of successive futuribles going 7 is a 13-dimensional extension of the through a hypothetical present. A five-dimensional space presented in digraph of the futuribles leading to Figure 3. The new variables are non- the present from the past represents shaded and the primary five variables correspondingly a history course. The shaded. The set of the darker-shaded present is a futurible breaking the value elements show the “Laissez faire” symmetry of the manifold. We omit the futurible in the primary space. For formal presentation here and illustrate layout reasons the generic table of the the process view by a digraph of the extended space is again presented in history and future course on the fu- the transposed form. turible map in Figure 8. In the figure it is assumed that the course goes via Histories and scenarios in the 1-close successive futuribles where the futures space sense of “successiveness” comes from Future as a process the semantics of the issues or from the phenomenological dynamics. As stated earlier the future is not a The number of the different courses state or an entity but rather an unfol- of the future originating from a hypot-

Figure 8. A digraph of a history course and a future course via a hypothetical presen

24 2-3/05 hetical present depends on the expres- It might further be unrealistic to siveness of the manifold and on the assume that a feasible course of the other hand on the assumed dynamics future would consist of a repetition of and constraints of the process. one and the same futurible, neither Systemic dynamics of the process would a course returning cyclically back to some earlier futurible match of the future well with our experience. The process A few remarks will be made about the of the future is irreversible. There are dynamics of future unfolding. If we do non-linear attractor dynamics which not have any pre-understanding of it, are interesting to think about as a we may assume that the process is a futures process. An attractor means random walk process from one futurible a bounded set of futuribles which the to the next with plain disorder of ran- course of successive chains of futu- domness as the law. This is, however, ribles may asymptotically approach hardly a satisfactory point of departure from different origins of the course. The for a futures study. By breaking the character of the attractor may be for symmetry with an introduction the instance a constant ﬁxed point futu- present as a special point, we also as- rible or a set of cyclically interchanging sume the past and present somehow futuribles. Today’s Western political conditions the unfolding of the future. drive toward capitalism, democracy It seems reasonable to assume that a and individual human rights may be feasible future course is a descendant seen as universal attractors of human of the present. Furthermore it is ob- development. But an attractor may vious that the process of future cannot also be a set of chaotically changing bring about anything against the laws futuribles within a bounded set. And of nature which thus constrains the non-linear dynamics may bring along feasibility of the futurible chain and unexpected bifurcations from one type the choice of one after the other. of a future to another attractor type,

Figure 9. Egocentrically transitive futures digraph with multiple scenarios from a hypothetical present

25 2-3/05 and in addition to attractors also a the futuribles most remote from the complete disorder may be a possible present. course. Scenario is one of the basic con- Knowing the dynamics of the process cepts in futures studies It is used in requires knowing its kinetic charac- somewhat different meanings, but it teristics. Kinetics determines which always refers to alternatives of the futurible succeeds when the preceding future. Multiple scenarios and a fan ones are given. Kinetics determines of futuribles are almost synonyms. how the preceding futuribles condition Often a scenario is used to mean the the next to follow. Social kinetic con- same as a futurible, i.e. some point ditioning means that a futurible does in Figure 9, e.g. F14. Sometimes the not only carry information about the scenario approach considers a futures prevailing state but also about how course to the targeted end point from the unfolding will take place. the present, e.g. the route F1→ F2 →F5 F or F F F F to the end Deliberate intervention → 14 1→ 2 → 11 → 14 point F14. As illustrated in the figure Even if we understand some of the there are usually several alternative systemic dynamics of unfolding and routes to a targeted point, i.e. there can present it explicitly as a dynamic are several scenarios to consider. system, much of the dynamics will It is then natural to compare not only always remain beyond our knowledge the end points but also the alternative and comprehension. This makes pre- courses with each other assuming that diction a difficult task in any accurate one has foreknowledge about what it sense. Chaos dynamics may also be- would mean to take this route or anot- come a temporary reality that makes her. Some course may be regarded as prediction in the longer run impossible more probable than others, another even when the short run prediction is may be seen as more desirable and possible. However, future’s unfolding yet another one undesirable or threa- is considered to be at the reach of tening. This kind of valuing belongs to human interventions and free will to the semantics of futures study. some extent, too in futures studies. A sample of the vast literature of strategic Concluding remarks management exemplifies this16. It is necessary that the syntactical theory of Knowing about the future has a diffe- futuribles should also allow presenting rent canon of legitimation than that of human intervention and choices in the knowing the past and present, it can map of the future. For this purpose we be regarded as more general in the take into use the egocentrically transi- scientific sense because of the intentio- tive sub-space defined earlier. nal characteristic of knowledge of the Figure 9 represents one such sub- future. These ontological premises of space taken apart from the futures the futures knowledge was discussed space in Figure 4. The sub-space is based on some classics of the futures directional from and to a futurible of the studies. A logical construction based hypothetical present. There are several on a morphological setting called the sub-spaces possible to choose from generic table of the futures manifold was developed and a syntactic the- fig.4, only one of them (F1) presented in the figure. There are in general fu- ory of futuribles was presented. The turibles at different distances from the concept of futures space, galaxy and present, cf. the orbits at distances C = futures multiverse has been derived 1, 2, 3, and 4. Between the triplets of and synoptic difference and distan- the consecutive futuribles which are ce between futuribles in the futures connected with arrows, the egocentric space is mathematically formalized. transitivity condition holds. There are Local and egocentric transitivity of the several routes or futures courses to distance measure formulated gives

26 2-3/05 the consistent logic of scenarios and by the authors.17 The present paper, futures courses and an explanation to however, is a more comprehensive and history courses of “historibles” as well. deeper analysis on the subject. It also The formalism developed in this paper links the analysis closely to the general was ﬁrstly introduced in a recent article discourse of futures studies.

Notes i Professor (emer.), Turku School of Econom- on her initial work on the concept of the ics and Business Administration future (Futurum-futura) in 16th century ii Professor, University of Vaasa Latin mainly in Jesuits’ texts starting from iii We are grateful to Dr. Eleonora Barbieri de Molina and advancing through analysis Masini for invaluable information based of later texts

References

1 Robert Nisbet, History of the Idea of 12 Ossip K. Flechtheim, History and Progress, Basic books, N.Y. 1980 (new Futurology, Verlag Anton Hain Meisenheim ed. 1994, New Brunswick: Transaction am Glan, Germany, 1966 Publishers) 13 Jerome C. Glenn and Theodore J. Gordon 2 Wendell Bell, Foundations of futures (2003), Futures Research Methodology studies, Vol I-II, New Brunswick. Version 2.0, AC/UNU Millennium Project Transaction books, 1997 report, gives an account of the methods 3 Ossip K. Flechtheim, Der Kampf und die of futures studies. Michel Godet (2001), Zukunft, 2. Augabe, 1971 in his book Creating Futures: Scenario 4 Sirkka Heinonen Prometheus Revisited, Planning as a Strategic Management Tool, FUTU, Yliopistopaino, Helsinki 1999 Economica, London, explains the general morphological design and application of 5 Coppens, Y, Brain, locomotion, diet and scenarios. Jerome C. Glenn and Theodore culture: how primate , by chance , became J. Gordon (2000), 1999 State of the Future, a man. In Changeux J-P, Chavallion J. AC/UNU Millennium Project report, has (eds), Origin of the human brains. p. 4-12, a chapter of scenario research and an Oxford, 1995 extensive review of bibliography. Eleonora 6 Eisler, Riane. The Chalice and the Blade: Barbieri Masini (1994), Why Futures Our History, Our Future. San Francisco: Studies?, Grey Seal Books, London, Harper & Row, 1987. updated in 2000 in French, Penser le 7 Tom Lombardo, The Evolution of Futur, Dunod, is a widely recognized text Future Consciousness, http://www. book of scenarios. The list of the reports to odysseyofthefuture.net/listing/ the Club of Rome can be found via Internet ReadingEvolFutConscious.pdf in http://www.clubofrome.org/archive/ 8 Jerome C. Glenn and Theodore J. Gordon, reports.php. Edward Cornish’s (2004) Futures Research Methodology Version book, Futuring. Exploration of the Future, 2.0, AC/UNU Millennium Project. WFS Washington is a general reading of 9 Congregatio de Auxiliis. Catholic modern futures inquiry recognized already Encyclopedia. /Luis de Molina. http:// as a classic in the genre. Robert J. Lemper, www.newadvent.org/cathen/04238a. Steven W. Popper and Steven C. Bankes htm and Molina Luis de, http://www3. (2003), Shaping the Next Hundred Years, nd.edu/~afreddos/papers/molina.htm RAND, presents new advances in applied 10 Luis de Molina, Liberi arbitrii cum gratiae futuring. donis, divina praescientia, providentia, 14 Robert Osserman (1994), The Poetry of the predestinatione et reprobatione Concordia, Universe, A Mathematical Explanation of known simply as Concordia, Lisbon, 1589, the Universe, Bantam Doubleday Publ. http://www3.nd.edu/~afreddos/papers/ 15 Scenarios Europe 2010, ES/FSU, July molina.htm. 1999 11 Bertrand de Jouvenel, The Art of Conjecture, Basic Books, N.Y. 1967

27 2-3/05 16 Hugues de Jouvenel (2004), in his book in strategic leadership. An Invitatation to Foresight, Futuribles 17 Malaska, Pentti and Ilkka Virtanen (2005). Perspectives Paris, states that the future Orienteering in the futures universe: A is a realm of freedom, of power and of map-analogy-based set-theoretic approach will. And hence it is a land to be explored to the theory of futuribles. In Contributions and a land to be built as well. Robert S. to Accounting, Finance and Management Kaplan and David P. Norton (2001), in their Science. Essays in Honour of Professor book The Strategy Focused Organization, Timo Salmi. Acta Wasaensia No. 143, Harvard Business School Publ., Boston, 261-284. Eds Erkki K. Laitinen and Teija incorporate a concept of strategic map Laitinen. and show how it is effectively used for making strategy to work in organizations. Ian Wilson (2003), in The Subtle Art of Strategy, Praeger, London, gives an account of scenarios in corporate strategic planning and managerial experience. Henry Minzberg, Bruce Ahlsrand and Joseph Lampel (1998), Strategy Safari, Prentice Hall, is a comprehensive analysis of the development of corporate strategic thinking. Karin Holstius and Pentti Malaska (2004), in their study Advanced Strategic Thinking: Visionary Management, Publications of the Turku School of Economics and Business Administration, available electronically http://www.tukkk. ﬁ/julkaisut/vk/Ae8_2004.pdf, analyze origination and development of strategic thinking and envisioning “futures territory”

28 2-3/05