This Research Bulletin has been published in Annals of the Association of American Geographers, 90 (1), (2000), 123-134.
"You cannot have a geography of anything that is unconnected. No connections, no geography"
Peter Gould (1991: 4)
John Rennie Short & Yeong-Hyun Kim (1999: 38)
INTRODUCTION: THE EARTH AT NIGHT
During the Apollo space flights it was reported that one of the astronauts, looking back to Earth, expressed amazement that he could see no boundaries. This new view of our world as the 'blue planet' (famously captured in NASA photo 22727 of the whole and unshadowed globe (Cosgrove, 1991: 127)) contradicted the taken-for-granted, state-centric Ptolemaic model or image of world-space which modern people carry around in their heads of grids, graticule and territorial boundaries (see Cosgrove, 1994). As a further jolt to the arrogance of modernity, it was soon accepted as a truism that the only 'man-made' artefact visible from space was the ancient Great Wall of China. Interestingly, the latter is not strictly correct: viewing Earth from space at night (as the Earth turns away from the Sun), modern settlements are clearly visible as pin-pricks of electric light on a black canvass1. Consisting of a broad swath girdling the mid-latitudes of the northern hemisphere plus many oases of light elsewhere, the globality of modern society is clear for all to see in the photo prints communicated back to Earth of lights delimiting a global pattern of cities.
The fact that these 'outside views' of Earth identified a world-space of settlements but not the more familiar world-space of countries has contributed to the growth of contemporary 'one world' rhetoric2 (other examples are 'Spaceship Earth' or 'Whole Earth') which has culminated in 'borderless world' theories of globalization. Of course, geographies do not depend upon visibility and therefore states being missing from space flight photographs tells us nothing about the current power of states to affect world geography. They do, however, augment the possibility for metageographic change. Metageography consists of the 'spatial structures through which people order their knowledge of the world' (Lewis & Wigen, 1997: ix) and in the modern world this has been notably Euro-centric and state-based in character3. It is this mosaic spatial structure which the night-time photographs challenge: first and foremost people live in settlements, collecting these together to form states is made to seem somehow secondary. In this paper we consider the largest pinpricks of light, the world cities as settlements with transnational functions which materially challenge states and their territories. They exist in a world of flows, linkages, connections and relations; an alternative metageography of networks rather than the mosaic of states.
This paper reports upon a preliminary investigation into measuring this new metageography of inter-city relations. Such a modest goal is made necessary because of a critical empirical deficit within the world city literature: the flows, linkages, connections and relations are only conspicuous because of their general absence in world city research. We designate this to be the 'Achilles heel' of this research school.
ATTRIBUTES WITHOUT RELATIONS: RESEARCH CLUSTERS IN WORLD CITY STUDIES
Studies of world cities are generally full of information which facilitate evaluations of individual cities and comparative analyses of several cities. The problem is that the data upon which this is based has been overwhelmingly derived from measures of attributes (Taylor, 1999). Such information is useful for estimating the general importance of cities and for studying intra-city processes but it tells us nothing directly about relations between cities. Hence cities can be ranked by attributes but a hierarchical ordering requires a different type of data based upon measures of relations between cities (Taylor, 1997). It is the dearth of relational data which is the 'dirty little secret' (Short et al., 1996) of this field of research.
This situation can be interpreted as follows: there has been an accumulation of knowledge on world city formation but we know very little about world city network formation4. In other words we know about the nodes but not the links in this new metageography. Of course, a proper understanding requires integrated knowledge of both nodes and links. Hence, our brief reviews of the main clusters of world city research has two purposes: first to illustrate the pervasive nature of the Achilles heel and second, to find world city formation processes which can direct our search for information on world city network formation processes.
1. Early studies: from Cosmopolitanism to Corporate Economy. Peter Hall (1966) initiated the modern study of world cities with a very comprehensive study of the attributes - politics, trade, communication facilities, finance, culture, technology and higher education - which placed London, Paris, Randstad-Holland, Rhine-Ruhr, Moscow, New York and Tokyo at the top of the world urban hierarchy. Stephen Hymer (1972) initiated the 'economic turn' in world city studies which has continued to dominate down to the present. In an emerging global economy, he argued that corporate control mechanisms were crucial hence multinational corporation headquarters tend to be concentrated in the "world's major cities - New York, London, Paris, Bonn and Tokyo . along with Moscow and Peking" (page 50). Using the distribution of headquarters to rank cities has become commonplace (e.g. Feagin & Smith, 1987; Meijer, 1993; Short et al., 1996) but although such attribute data can define the relative importance of cities it cannot specify a hierarchy within a network.
2. Command centres and basing points: the New International Division of Labour and World City Hypothesis. Most studies of world urban hierarchies have drawn inspiration from John Friedmann's (Friedmann & Wolff, 1982; Friedmann, 1986) seminal world city hypothesis. Following Cohen's (1981) new hierarchy of predominant (New York, Tokyo, London) and secondary level (Osaka, Rhine-Ruhr, Chicago, Paris, Frankfurt and Zurich) world cities, Friedmann drew his ideas from the organizational implications for capital from Frobel et al.'s (1980) New International Division of Labour. The restructuring of industrial production in the 1970s posed new problems for capital which world cities helped solve by becoming both command centres and basing points for capital in its perennial movement around the globe. Friedmann's hierarchy is frequently cited for its pedagogic and heuristic worth, but it is particularly weak because it is based upon a limited attributive survey of key parameters, which in themselves were either difficult to measure and calibrate, or not all "used in every case": finance; MNC headquarters; business services; manufacturing activity; transportation; and population (Friedmann, 1986: 72). Many have now developed elaborate critiques of Friedmann's original hierarchy (e.g. Beaverstock et al., 2000; Korff, 1986; Taylor, 1997), and he himself (1995) has noted some of its limitations but has not discouraged subsequent research which has allocated cities to hierarchies based upon their command and control criteria, by measuring attributes of world cities and then ranking them in order of magnitude (e.g. Brotchie et al., 1995; Daniels, 1993; Fujita, 1991; Fu-Chen Lo & Yue-Man Yeung, 1998; London Planning Advisory Committee, 1991; Lyons & Salmon, 1995; Meijer, 1993; Shacker, 1994).
3. International Financial Centres. The rise of global financial markets has been one of the most noted elements of economic globalization and their articulation in international financial centres has stimulated a particular strand of world city research. The pioneering work of Reed (1981) produced the first major quantitative analysis of world cities Using a multi-variate analysis of over fifty financial, cultural, economic, geographical and political attributes in 76 cities, between 1900-1980, Reed produced an evolving hierarchy of international financial centres. Like Friedmann's (1986), this hierarchy has been widely discussed for its pedagogic value (e.g. Drennan, 1996; The Economist, 1998; Thrift, 1987), but its principal weakness is that it neglects relations between financial centres. No matter how sophisticated an analysis of attribute data, only rankings can be produced so that a hierarchy of world city financial centre relations can only be inferred. Furthermore, the recent addition of considering the functions of financial intermediaries, with no inter-financial centre data analysis whatsoever, as advocated by Meyer (1998), does not constitute a "world city hierarchy of financial centres" (page 428).
4. The producer service complex and the 'triad' of global cities. International financial centres can be represented as an 'unpacking' of the world city concept, Saskia Sassen's (1991) concept of global city is the beginning of a repacking. As well as financial services, she identifies the production of other advanced producer services (e. g. accountancy, advertising, insurance, commercial law, etc.) creating complexes of theoretical and practical knowledges as epitomised by London, New York and Tokyo. It is the necessity of these localised complexes for servicing global capital which creates the concentration of functions we know as world cities. However, although Sassen interprets this triad of cities as the apex of a global urban hierarchy, her analyses are wholly dependent upon attribute data. The result of her many studies (Sassen, 1994a, 1994b, 1995) is a rich knowledge of the triad in comparative terms but with no direct evidence of relations between the three cities or between them and other cities5.
5. The Los Angeles school. A part of the postmodern and cultural 'turns' in geography and urban planning has been the rise of the so-called 'California school' or 'LA school' (if one wishes to highlight the conceptual shift from the famous largely positivist Chicago School of the early 20th Century) which is returning the world city concept back towards Hall's originally broader formation (examples of famous works include: Davis, 1990; Soja, 1989 and 1996; Scott, 1988; Jameson, 1992; and Scott & Soja, 1986). However, by focusing on a single city, Los Angeles as archtypal, paradigmatic, or the 'celebrity city' of contemporary world city processes (the place where it 'all comes together' (Soja, 1989: 8)), relations between cities have not surfaced in this broad research agenda. Nevertheless, one strand within this school is relevant to this review. Michael Storper's 'theory of the urban economy: the social organization of economic reflexivity" (1997: 244) is centred upon the proximity in places serving as vital innovation centres for capital. The city is treated by Storper (1997: 222) as a "privileged site" for reflexivity to occur, because of their embedded knowledge and learning structures. Going beyond producer services to specialised manufacture with Hollywood as the classic 'privileged site', this work, nevertheless does not treat the wider spatial role of cities so that their connections in the economy of flows remains invisible. Whilst reference is made to the "society of cities" (page 222), inter-city relations is precisely what is absent from this work. Economic reflexivity need not be strictly local and territorial; we agree with Amin & Thrift (1992), that there is critical reflexivity embedded and reproduced through global corporate networks: or as we would like to put it, through the relational network of world cities.
In summary, the world cities literature is seriously unbalanced: it has a surfeit of interesting theoretical concepts for treating the nodes of the world city network but these exist alongside a deficit in empirical concern for measuring relations between the nodes.
WORLD CITIES IN A NETWORK SOCIETY
One author in particular has attempted to advance theoretical knowledge of the world city network. Manuel Castells (1996) conceptualises the contemporary informational economy as operating through a space of flows which constitute a network society. This operates at several levels, one of which is the world city network. Thus, instead of the static world city concepts considered above - centres, points, complexes, sites - Castells conceptualises world cities as processes 'by which centres of production and consumption of advanced services, and their ancillary local societies, are connected in a global network' (page 380). Hence, cities accumulate and retain wealth, control and power, because of what flows through them, rather than what remains static within (as typically measured with attribute data).
It was not part of Castells' (1996) brief to engage in new data generation and therefore, despite its subject, his work reflects the prevailing use of attribute data (Taylor, 1999). His chief use of data to specify his space of flows is a very broad grained (one origin, nine destinations) set of information from Federal Express originally analysed by Michelson & Wheeler (1994: 382-3). Hence, Castells does not constitute an empirical advance on the previous study with respect to the world city network. Nevertheless, along with the other theoretical studies of the nodes, Castells provides a framework for our empirical work on world city network formation in a space of relations. World cities are produced by relations of corporate networking activities and connectivity between cities based upon knowledge complexes and economic reflexivity. These fruitful concepts notwithstanding, the key to unlocking the 'spaces of relations' of world cities is new data collection (Smith & Timberlake, 1995a, 1995b).
GLOBAL OFFICE LOCATION STRATEGIES
The only published data available for studying relations between cities at a global scale are international airline passenger statistics. Not surprisingly, therefore, empirical studies which present networks of world cities have focused upon this source (Keeling, 1995; Kunzmann, 1998; Rimmer, 1998). There are, however, serious limitations to these statistics as descriptions of relations between world cities (Taylor, 1999). The two major ones are first, that the information includes much more than trips associated with world city processes (e.g. tourism), and second, important inter-city trips within countries are not recorded in international data (e.g. New York-Toronto does feature in the data, New York-Los Angeles does not).
Studying the global location strategies of advanced producer service firms is an alternative approach for describing world city networks which overcomes these problems. Firms who provide business services on a global scale have to decide on the distribution of their practitioners and professionals across world cities. Setting up an office is an expensive undertaking but is a necessary investment if the firm believes that a particular city is a place where it must locate in order to fulfil its corporate goals. Hence the office geographies of advanced producer firms provide a strategic insight into world city processes by interpreting intra-firm office networks as inter-city relations. In this argument, world city network formation consists of the aggregate of the global location strategies of major advanced producer service firms.
Information on the office networks of firms can be obtained through investigating a variety of sources such as company web sites, internal directories, handbooks for customers and trade publications. Data on the distributions of offices for 74 companies (covering accountancy, advertising, banking/finance and commercial law) in 263 cities has been collected. An initial analysis of this data identified the 143 major office centres in the set of cities and of these 55 have been designated world cities on the basis of the number, size and importance of their offices (for details of this classification exercise, see Beaverstock et al., 1999a) . No other such roster of world cities exists; it is used here as the basic framework for studying the world city network.
AN INTER-CITY GLOBAL NETWORK
The roster of 55 world cities is divided into three levels of service provision comprising 10 Alpha cities, 10 Beta cities, and 35 Gamma cities6. Only the Alpha cities - Chicago, Frankfurt, Hong Kong, London, Los Angeles, Milan, New York. Paris, Singapore and Tokyo - are used in this section to illustrate how office geographies can define inter-city relations. Note the geographical spread of these top ten world cities; they are distributed relatively evenly across three regions we have previously identified as the major 'globalization arenas': northern America, western Europe, and Pacific Asia (Beaverstock et al., 1999b). World city network patterns are constructed for these Alpha world cities using simple presence/absence data for the largest 46 firms in the data (all the firms have offices in 15 or more different cities).
Shared presences are shown in Table 1. Each cell in this inter-city matrix indicates the number of firms which have offices in both cities. Thus London and New York 'share' 45 firms, only one firm in the data does not have offices in both of these cities. Obviously these two cities are the places to be for a corporate service firm with serious global pretensions. This finding is not, of course, at all surprising; interest comes when lower levels of inter-city relations are explored. In Figure 1 the highest twenty shared presences are depicted at two levels of relation. The higher level picks out Sassen's (1991) trio of global cities - London, New York, Tokyo - as a triangular relationship but note that in addition Hong Kong also has such a relationship with London and New York. Bringing in the lower level of relations, London and New York have shared presences with eight other cities in all, but note again the high Pacific Asia profile in this data: Singapore joins with Tokyo and Hong Kong showing relations with five other cities, the same level as Paris. This contrasts with the US world cities below New York; Los Angeles is in the next to bottom class of shared presences with Frankfurt and Milan, and Chicago stands all alone with no inter-city relations at the minimum level for inclusion in the diagram. This pattern can be interpreted in terms of the different degrees of political fragmentation in the three major globalization arenas. In the most fragmented, Pacific Asia, there is no dominant world city so that presences are needed in at least three cities to cover the region: Hong Kong for China, Singapore for south east Asia, and Tokyo for Japan (Taylor, 2000). In contrast, northern America consists largely of a single state so that one city can suffice for a presence in that market. The result is that New York throws a shadow effect over other US world cities. In between, western Europe is becoming more unified politically but numerous national markets remain so that London does not dominate its regional hinterland to the same degree as New York.
Shared presences define a symmetric matrix, sizes are shown but not the direction of inter-city relations. In contrast, Table 2 is an asymmetric matrix showing probabilities of connections. Each cell contains the probability that a firm in city A will have an office in city B. Thus Table 2 shows that if you do business with a Chicago-based firm, then there is a 0.91 probability that that firm will also have an office in Frankfurt. On the other hand, go to a Frankfurt-based firm and the probability of it having an office in Chicago is only 0.66. Such asymmetry is represented by vectors in Figures 2 and 3. Primary vectors are defined by probabilities above 0.95 and all cities connect to London and New York at this level (Figure 2). As in Figure 1, only Tokyo and Hong Kong reach this highest category of connection but with only one link each. Again, it is more interesting to look at the lower level relations and these are shown in Figure 3. This diagram reinforces the interpretation concerning the three globalization arenas presented above: Chicago and Los Angeles have no inward vectors from the other arenas in what is largely a Eurasian pattern of connections. Vectors to the Pacific Asian cities dominate but Frankfurt and Paris also have a reasonable number of inward vectors.
This is the first time inter-city relations on a global scale have been studied in this way. As expected of such initial research, several opportunities for further investigations are suggested, not least using more cities and more sophisticated network analysis to tease out further features of world city network formation. However, the outstanding finding of this work is the New York shadow effect, which has obvious policy implications for US cities promoting themselves as global cities.
CASE STUDY: LONDON'S GLOBAL REACH
There is no published study which assesses the global capacity of a world city in terms of its relations with other world cities. The producer service office geography data set is particularly suited for such an exercise; here we illustrate this with a brief case study of London.
The data we employ for London differs from that used in the last section in three ways: First, it is obvious that we will be considering only London-based firms which means one of the firms used previously is dropped. In addition, there is information on smaller London-based firms which are analysed here creating a total of 69 firms in all. Second, we will consider all 55 world cities in our roster. Third, for many firms there is richer information than simply whether they are present or absent in a city. Further information can provide interval level measurement, such as numbers of practitioners or professionals employed by a firm across all its offices, or ordinal level measures where the importance of offices can be allocated to ranked classes on the basis of given functions. In order to combine this data into a single, comparable set of measures, all three levels - interval, ordinal and nominal (presence/absence) - have to be combined as a single ordinal scale. For every world city, each firm is scored as one of the following: (0) absence; (1) presence, and where additional information is available it indicates only minor presence; (2) additional information indicates medium presence in a city; and (3) additional information indicates major presence in a city. In making boundary decisions with the additional information, we were careful to be sensitive to the range of data; for large accountancy firms minor was defined as less than 20 practitioners in a city, major as over 50, for law firms the equivalent figures were 10 and 20. Through this approach we can move beyond simple geographies of presence to geographies of the level of the producer services available in a city.
For each of the producer service sectors represented in our data, levels of service are summed for London-based firms in each of the other 54 world cities. This provides an estimate of the level of external service which can be expected when doing business in another world city from London. In Table 3 the top ten world cities are ranked in terms of service available for each of the producer services represented in our data. As would be expected, the Alpha cities, identified in the last section, figure prominently in these ranking with New York first or first equal in all four sectors. However, other world cities now make an appearance: the notable examples are the key political cities of Washington, DC and Brussels featuring prominently in law, Dusseldorf easily out-ranking Germany's Alpha world city in accountancy, and, generally Britain's old imperial links being represented by Sydney and Toronto in several lists. Average levels of linkage have been computed from standardised sector scores (city totals as percentage of maximum possible (i.e. 3 (maximum score) x number of firms in a given sector)) showing all the Alpha cities in London's top ten except Chicago. Given also Los Angeles' bottom ranking in the list, this can be interpreted as the New York shadow effect operating even from London.
Average levels of linkage with London, when computed for all other world cities, provide an illustration of London's global reach within the world city network. These average percentages range from a top score of 87 for New York, followed by Paris (68) and Hong Kong (64), to the lowest score for Minneapolis of only 15 with Osaka (21) and Munich (22) just above the bottom. Using these averages world cities can be divided into five groups in terms of the intensity of their relations with London. Out on its own is New York, the 'prime link', followed by Paris and Hong Kong as the other two 'major links'. Below these three and with scores all over 50 come 9 'important links'. The remainder of the cities are divided between 18 'medium links' (36-50) and the remaining 24 'minor links'. These links are arrayed in Figure 4 showing a relatively even distribution across the three globalization arenas and their adjacent regions, the New York shadow effect notwithstanding.
This case study has shown how analysis of global office location strategies can begin to order relations between world cities and locate a given city within the world city network.
CONCLUSION: META-GEOGRAPHIC DYSTOPIA?
Riccardo Petrella (1995), sometimes referred to as 'the official futurist of the European Union' (p. 21), has warned of the rise of a 'wealthy archipelago of city regions ... surrounded by an impoverished lumpenplanet' (p. 21). He envisages CR-30 (the top 30 most powerful city regions) replacing G-7 (the top 7 most powerful states) by presiding over a new global governance by 2025. Such a scenario is given credence by contemporary world cities being implicated in the current increased polarisation of wealth and wages which has accompanied economic globalization. World city practitioners and professionals operating in a global labour market have demanded and received 'global wages' (largely in the form of bonuses) to create a new income category of the 'waged rich'; with reference to London, Adonis & Pollard (1997) have called them the new 'Super Class'.
Petrella sets out his global apartheid dystopia as a warning about current trends so as to alert us of the dangers ahead. But cities do not have to play the bête noire role of the future. It is within cosmopolitan cities that cultural tensions can be best managed and creatively developed. Certainly modern states, in their ambition to be nation-states, have an appalling record in dealing with matters of cultural difference. But the key point is that this is not a simple matter of cities versus states (Taylor, 2000). World cities are not eliminating the power of states, they are part of a global restructuring which is 'rescaling' power relations in which states will change and adapt as they have done many times in previous restucturings (Brenner, 1998). The 'renegotiations' going on between London's world role and the UK state economy, between New York's world role and the US state economy and with all other world cities and their encompassing territorial 'home' economies, are part of a broader change affecting the balance between networks and territories in the global space-economy. All we have illustrated in this paper is how we can begin empirical analysis of networks to set alongside the traditional economic geography concern for comparative advantage between states. Our one firm conclusion is that in the new millennium we cannot afford to ignore the new metageography which is the world city network.
We would like to thank the Economic and Social Research Council for funding this research (R000222050). Thank you to the anonymous referees for their comments.
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1. For a photo of the Network of European cities at night see 'Europe at night', W.T. Sullivan and Hansen, Planetarium; Science Photo Library (see Rogers, 1997: 171).
2. We are aware that there is a danger that these rhetorics can de-humanise and decontextualise the world and that one has to be careful and critical about, "the modes and metaphors of representation within which geographical discourse is framed" (Cosgrove & Rogers, 1991: 37).
3. Denis Cosgrove (1991: 127) points to the Eurocentric nature of maps compared to the view of Earth from space. Discussing NASA photo 22727 he observes that; "The photo de-centres Europe and the Atlantic, to the advantage of Africa, the least 'significant' of all the continents in the conventional system .. Thus, our most familiar global image today privileges the 'Third World' and the 'South' . Earth is no longer an extension of European earth".
4. Richard Rogers in his Cities for a small planet (1997: 175) discusses "Networks of cities across the world", but in the context of sustainable development; " . sharing knowledge, technologies, services and recycled resources, and framing joint policies that both respect local cultures and implement common environmental objectives". He concludes the book by saying simply that, "Cities that are beautiful, safe and equitable are within our grasp".
5. In her latest article Saskia Sassen (1999) argues that "London and New York Triumph" in the world city hierarchy and then makes an argument that "a leaner system dominated by a handful of cities is evolving". Immediately under London and New York she places Frankfurt, Tokyo and Hong Kong, and under them she places Singapore and Sydney. However, again this is a house of cards because it is not based on direct evidence of relations between the cited cities.
6. Keeping with our image of the Earth from space with lights delimiting a global pattern or constellation of cities we have classified the world cities as one does with stars: Alpha (the brightest), Beta (second brightest) or Gamma (third brightest).
Table 1: Relations between Alpha World Cities: Shared firm presences
Table 2: Matrix of office presence linkage indices for Alpha World Cities
Table 3: Top ten ranked office linkages to London by advanced producer services
Figure 1: Shared presences among Alpha world cities
Figure 2: Primary vectors (probabilities of links) among Alpha world cities
Figure 3: Secondary vectors (probabilities of links) among Alpha world cities
Figure 4: World city links to London
Edited and posted on the web on 28th July 1999