The Mutual Information of University-Industry-Government Relations:
An Indicator of the Triple Helix Dynamics
Scientometrics, forthcoming
Loet Leydesdorff
Science & Technology Dynamics, University of Amsterdam
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam, The Netherlands
loet@leydesdorff.net ; http://www.leydesdorff.net/
Abstract
University-industry-government relations provide a networked
infrastructure for knowledge-based innovation systems. This infrastructure
organizes the dynamic fluxes locally and the knowledge base remains emergent
given these conditions. Whereas the relations between the institutions can be
measured as variables, the interacting fluxes generate a probabilistic entropy.
The mutual information among the three institutional dimensions provides us
with an indicator of this entropy. When this indicator is negative,
self-organization can be expected. The self-organizing dynamic may temporarily
be stabilized in the overlay of communications among the carrying agencies. The
various dynamics of Triple Helix relations at the global and national levels,
in different databases, and in different regions of the world, are
distinguished by applying this indicator to scientometric and webometric data.
1. Introduction
In 1953, Linus Pauling and Robert B. Corey proposed that DNA was made up of three chains, twisted around each other in ropelike helices (Pauling & Corey, 1953). A few months later, James Watson and Francis Crick proposed the double helix, which was then quickly accepted as the correct structure of DNA (Watson & Crick, 1953). This discovery led to a Nobel Prize (Watson, 1970).
Double helices can under circumstances stabilize in a coevolution, but triple helices may contain all kinds of chaotic behaviour (Poincaré, 1905). Triple Helix models continue to be useful in studying transition processes, for example, in crystallography and molecular biology. More recently, Richard Lewontin (2000) used the metaphor of a Triple Helix for modeling the relations between genes, organisms, and environments.
In a different context, Henry Etzkowitz and I introduced a Triple Helix model for the dynamics of university-industry-government relations (Etzkowitz & Leydesdorff, 1995). Our argument for using this neo-evolutionary model was that a knowledge-based regime of innovations can be expected to remain in transition. A Triple Helix can contain double helices as temporary stabilizations, but a system of three dynamics is meta-stabilized. Under specific conditions the next-order system of an overlay of communications can also be globalized and then exhibit self-organization. Globalization means in this context that the next-order (emerging) overlay gains priority in determining the dynamics of the underlying ones (on which it rests). Thus, a Triple Helix model may be sufficiently complex to encompass the different species of observable behaviour in the networks under study.
The advantages of using the Triple Helix model can be specified with reference to different research traditions. First, one is able to study specific configurations of university-industry-government relations as instantiations of the Triple Helix dynamics of a knowledge-based innovation system (Giddens, 1984; Leydesdorff & Etzkowitz, 1998). In this context of specification, the Triple Helix metaphor functions as a heuristics. The institutional configurations in knowledge-based systems can be considered as the outcome of three (functional) subdynamics of competitive systems: (a) the economic dynamic of wealth generation through exchange, (b) the knowledge-based dynamic of reconstruction and innovation over time, and (c) the political and managerial need and urge for normative control at the interfaces. The carriers of these three functions do no longer have to exhibit a one-to-one correspondence to industry, university, and government, respectively. The institutions can be expected to experiment with new formats in their mutual arrangements (Etzkowitz & Leydesdorff, 1997).
While the heuristic application of the Triple Helix metaphor can be made useful for the historical specification, the neo-evolutionary model of the two layers of functions and institutions operating upon each other opens a space of possible interactions. The evolutionary system has an option to reconstruct itself in the present with reference to the historical configurations that have occurred. The functional dimension can be provided with priority if a next-order system (e.g., a relevant selection environment) can be defined. Are the institutional arrangements still functional?
For example, participants who are entrained in co-evolutions of mutual shaping between two helices can be expected to ‘lock-in’ (David, 1985; Arthur, 1988). The internal perspectives of these participant-observers can be distinguished from the perspective of an external (that is, third) observer. The latter is able to evaluate. The switch to the external perspective enables the analyst to search for options emerging from interactions that cannot be perceived from within the co-evolution. The configuration under study can then be reconstructed on the basis of knowledge. Thus, a knowledge base for the reconstruction can emerge as different from an institutional rationale.
The two layers of functions and institutions can also be considered as degrees of freedom. For example, one can question whether a network at the institutional level is functionally efficient and whether it provides dynamic scale effects. (The latter can be considered as emergent synergies.) The functional perspective and the institutional perspective can be used for the optimization and the reorganization in different cycles.
2. The representation of a Triple Helix dynamics
A Triple Helix configuration can be depicted statically using social network analysis or in more general terms, as partially overlapping sets (e.g., Venn-diagrams; see also figure 2 below). While a Triple Helix dynamics can be expected to remain in flux, the geometrical representation focuses necessarily on one subdynamics or another by taking a perspective. For example, one can measure instantiations of a Triple Helix in terms of variables or trajectories along the time axis. An evolutionary system, however, can go through reconstructions of the complex system in the present. The system is complex at different levels, since the various subdynamics can be recombined algorithmically.
How can the values of the variables at each moment in time be related to the dynamic operation over time? Using a calculus one can study changes in the value of a variable (x = a) in relation to changes in the variable (dx/dt). Following a suggestion of Bar-Hillel (1955), Leydesdorff (1995) proposed to use information calculus for this purpose. In this study, I elaborate this calculus for Triple Helix dynamics, but let me first explain the concept of the mutual information in three dimensions using graphical representations.
Already in 1979, Goguen and Varela proposed a representation of a complex and self-organizing system using a holographic model of three interacting dynamics:
Figure 1
A schematic depiction of a complex system by Goguen & Varela (1979)
At each step (i-1, i, i+1), the emerging system is composed of interaction effects among the previous stages of the three participating systems. In addition, however, to the recursion of the interaction among the helices, a model of university-industry-government relations should encompass the recursive dynamics within each of the helices along their respective time axes. The differences in these subdynamics may break the symmetries suggested by this representation.
Let us develop a model that is both interactive and recursive step by step. First, consider three helices as sets that overlap in the intersections, as follows:
Figure 2
A Triple Helix configuration with positive overlap among the subsystems
In this configuration, the three helices share a common ground or origin in the overlap area indicated in the figure as i. Under conditions, however, this overlap can become zero or even negative. This configuration can be depicted as follows:
 |
Figure 3
A Triple Helix configuration with negative overlap among the subsystems
In this representation, the three helices have differentiated to such an extent that the communality i has been dissolved. This system operates over time in terms of different communications at the respective interfaces (e.g., ijk). If all the interfaces operate, one can consider the result as the emergence of a ‘hypercycle’ (Figure 4). The hypercyclic configuration integrates the three systems in a distributed mode. It fails to integrate completely, or one can also say that the integration remains subsymbolic.
Figure 4
Ex post integration in an ‘emerging’ hypercycle by recombining different interactions
This configuration can be expected to exhibit ‘self-organizing’ properties because the various transmissions are no longer integrated at a single place. Since a common domain of instantaneous integration is lacking, each integration leads at the same time to a re-differentiation. Integration fails in this configuration at each moment in time, but it may take place over the time dimension.
It can be shown that under the condition of a lack of overlap among the three sets, the mutual information in three dimensions is negative (Abramson, 1963). From the perspective of each binary interface, the third dimension remains then ‘latent’ as a structural given in the background. This third system entertains interfaces with each of the first two, but not directly (or less so) with their interaction. The structural function of the third system remains beyond the control of each two relating systems, but this latent structure in the network reduces the uncertainty that prevails when the first two systems interact.
In the Triple Helix model of university-industry-government relations the hypercyclic integration can be identified as an overlay of negotiations and exchange relations among the institutional carriers of the Triple Helix dynamics. Insofar as the hypercycle operates it functions as a virtual feedback on the network of relations among the institutional agents at each moment in time.
4. Methodology
The mutual information in the three dimensions of the Triple Helix enables us to measure networks at each moment in time in terms of probability distributions and to evaluate the measurement results in terms of the dynamics. Unlike co-variation, correlation or co-occurrence measurements, the mutual information is defined in the case of interactions among three dimensions. However, the mutual information in three dimensions can no longer be considered as a similarity measure. It informs us about the size and the sign of the probabilistic entropy generated by the interactions within the complex system.
Conceptually, the generation of a negative entropy corresponds with the idea of complexity that is contained or ‘self-organized’ in a network of relations that lacks central coordination. The network system may then be able to propel itself in an evolutionary mode by alternating and recombining the various subdynamics. The reduction of the uncertainty is a result of the bi-lateral relations operating upon each other. The network contains more uncertainty-reducing structure than is visible for the interacting agents at their respective interfaces. This negative entropy is generated because the flux is constrained by the existing structure of institutional relations.
How does this relate to the measurement? Triple Helix relations can be measured in terms of relevant variables (e.g., budgets, collaborations, citations). From this perspective, the historical description of a specific configuration can be considered as measurement with only nominal variables (that is, words used for the description). In detailed (“thick”) descriptions, one is able to evaluate whether something was the case or not. However, one can often specify the intensity of the relationship at a more aggregated level using measurement scales more refined than the binary one. To which extent was something the case?
For example, when comparing science parks, one may be able to count instances in which government agencies were involved in these academic-industry relations, and to which extent. In other cases, one may be able to measure more precisely, for example, along a scale. The measurement can be based on various measurement scales, but the networks can always be compared as relative frequency distributions. Independently of the answer to the question how the network relations are operationalized and measured, the observations of Triple Helix configurations can thereafter be organized in a three-dimensional array using the format visualized in Figure 5:
 |
Figure 5
The three-dimensions of measurement in a Triple Helix configuration and their combinations
Different variables can also be measured in more than one of the three institutional dimensions. This leads to a co-variation or mutual information between the dimensions. However complicated the data gathering may be, this does not affect these methods for analyzing Triple Helix data in terms of the three dimensions indicated in Figure 5. Methodological questions about the data collections and the measurement can thus be distinguished from methodological questions with respect to the data analysis. This study focuses on the development of an indicator that can be used after and relatively independently of how the data were collected.
In general, network data can be considered as relative frequency distributions. A relative frequency distribution can be written as a probability distribution. The description of the network data in terms of probability distributions enables us to use Shannon’s (1948) mathematical theory of communication. A probability distribution contains an uncertainty. The expected information content of the message that these events have happened with this observed frequency distribution, can be expressed in terms of bits of information using the Shannon-formulas (Abramson, 1963; Theil, 1972; Leydesdorff, 1995).
The mutual information between two dimensions of the probability distribution (for example, in university-industry (UI) relations) is then equal to the transmission (T) of the uncertainty (Theil, 1972):
TUI = HU + HI – HUI
The relationship reduces the uncertainty for the two relating systems (with –HUI).
Abramson (1963, at p. 129) showed that the mutual information in three dimensions can be derived as:
TUIG = HU + HI + HG – HUI – HIG – HUG + HUIG
Note that the uncertainty of the variables measured in each of the interacting systems (HU, HI, and HG) is reduced at the system’s level by the relations at the interfaces between them, but the three-dimensional uncertainty adds positively to the uncertainty that prevails. Because of this alteration of the signs, the three-dimensional transmission can become negative. As noted, this reduction of the uncertainty by the negative transmission is a result of the network configuration of bi-lateral relations that develops without central coordination (Figure 4).
5. Results
In order to show the usefulness of this indicator, I will apply it to relatively straightforward data like search results with the terms ‘university,’ ‘industry,’ ‘government,’ and their combinations with Boolean AND operators in various databases. As noted, the measurement problems in the data collections are backgrounded in favour of the data analysis. The data collection is based on raw search strategies that result in approximate figures, but which serve us here mainly for the illustration of the argument.
The research question behind the searches is whether and the extent to which the relations among these retrieval terms enable us to reveal a Triple Helix dynamics operating. At which level can a self-propelling dynamic of network relations be observed, and to what extent? I first turn to the Internet for retrieving relevant time-series data and then use also the Science Citation Index to measure these relations at national and international levels.
5.1 The Triple Helix at the Internet
University-industry-government relations can be measured at the Internet, for example, in terms of the occurrences and co-occurrences of the words ‘university,’ ‘industry,’ and ‘government’ (Leydesdorff & Curran, 2000). Using various search engines, Bar-Ilan (2001) showed, among other things, how sensitive the Internet is to measurements at different moments in time (Rousseau, 1999). However, the AltaVista Advanced Search Engine has remained the sole search engine that enables the analyst to combine the various search options with specific time frames (e.g., years) so that time series of data in various dimensions can conveniently be generated (Leydesdorff, 2001a).[1]
The search terms ‘university,’ ‘industry,’ ‘government,’ and their combinations with Boolean AND-operators were used for the years 1993-2001. All searches were performed on the 24th of March 2002, and during the data collection the stability of the Altavista Advanced Search Engine was checked at least once an hour for its stability (Rousseau, 1999). The results of these searches are shown in Figure 6.
 |
Figure 6
Results of searches using the AltaVista Advanced Search Engine
Figure 6 first shows that the Internet continues to expand rapidly. In Figure 7 the continuous growth of the number of all documents in the AltaVista domain is shown using a logarithmic scale. Remember that AltaVista provides only one specific representation of the data at the Internet (Butler, 2000; cf. Leydesdorff, 2001a).
 |
Figure 7
The exponential growth curve of the AltaVista domain during the period 1993-2001
When the data is organized in a three-dimensional array as explained above, the transmission in three dimensions T(uig) can be calculated straightforwardly for each year.[2] This leads to Figure 8.
Figure 8
Mutual information in three dimensions (‘university,’ ‘industry,’ ‘government’) as measured using the AltaVista Advanced Search Engine. (The trend line is based on the values for 1994-2000 only; r2 = 0.95.)
Figure 8 shows that the values for T(uig) are always negative, but the curve decreases linearly during the period 1994-2000. This period witnessed the booming and the potential self-organization of the so-called new economy. The decrease of the value of the transmission in three dimensions is steady during this period (r2 = 0.95). Perhaps the flattening of the curve in recent years illustrates that the process of endogenous expansion of the Internet has been interrupted temporarily as the e-business has gone into a recession. Note that this change in the dynamics is not noticeable upon visual inspection of the growth data in Figures 6 and 7.
5.2 Testing for Systemness in the Overlay of Triple Helix Relations
What does the effect of increasingly negative values for T(uig) teach us when compared to the descriptive statistics? Does it indicate the self-organization of a virtual dimension in the overlay of relations generated by the co-occurrences? Can this, indeed, be considered as an indication of increasing self-organization of the system of relations? Are the underlying data in each of the helices also being reorganized by the emerging system at the overlay level?
Emerging systemness in data sets can be tested against the alternative of historical development of the elements of the system along the time axis (Leydesdorff, 1995). While the overlay in the Triple Helix model may exhibit systemness, the carrying institutions continue to develop historically; but the overlay system would then provide another selection environment for them at the global level, that is, in a (historically changing) present. Negative entropy first indicates that the overlay system provides the carrying systems with information relevant to reduce the uncertainty in the present. But has this feedback also become stabilized as a systemic subdynamic?
In the case of emerging systemness, one can expect a data set increasingly to contain the Markov property. The Markov property states that the current state of a system is the best prediction of its next stage.[3] If systemness is not achieved, however, the normalized sum of the longitudinal predictions for the various elements provides us with the best prediction for a next state. These two hypotheses (of systemic development versus independent development of the elements, respectively) can be tested against each other for predicting next year’s data. When the predicted values are subsequently observed, the quality of the two predictions can be evaluated (e.g., Leydesdorff & Oomes, 1999; Riba-Vilanova & Leydesdorff, 2001).[4]
This test was applied using the time series data 1993-2000 for the prediction of 2001 data. Comparison with the observed data for 2001 led to the following results:
|
prediction of the value in 2001 |
7 categories (U, I, G, UI, UG, IG, UIG) |
four categories (UI, UG, IG, UIG) |
three categories (UI, UG, IG) |
|
on the basis of the univariate time series (1993-2000) |
2.06 |
5.93 |
5.06 |
|
on the basis of the previous year (2000) (Markov property) |
2.83 |
5.54 |
4.15 |
|
hypothesis of systemness |
- 0.77 (rejected) |
0.39
|
0.91
|
Table 1
Testing the hypothesis of systemness in the Triple Helix overlay of University-Industry-Government Relations. (All values are in millibits of information.)
The results show that the prediction of the 2001 data on the basis of the same data for the previous year (Markov property assumed) is inferior to the prediction on the basis of the time series of the various categories in the case of considering the whole system of seven search categories (second column of Table 1). Thus, the hypothesis that the representation would develop as a system is rejected.
When the analysis is limited to the three bi-lateral relations (right column of Table 1), the hypothesis of systemness in the data is corroborated. The quality of this latter prediction is worsened by including the trilateral relations (middle column). Similar results were obtained when using the prediction of data for the year 2000 on the basis of the time-series 1993-1999, but the results were then even more pronounced.[5]
In summary, these results suggest that the system of representations of university-industry-government relations at the Internet is developing as a set of bilateral relations. The bilateral relations generate a negative entropy and in this sense enable the global system to self-organize the complexity in the data using a virtual overlay of network relations. This development, however, has slowed down recently.
5.3 The Triple Helix in the Science Citation Index (2000)
In the next application of the mutual information in three dimensions on Triple Helix data, I used the 1,432,401 corporate addresses on the CD-Rom version of the Science Citation Index 2000. These addresses point to 725,354 records contained in this database on a total of 778,446 items. Only 3.7 % of these records contain no address information.[6] Our research focuses on the international coauthorship relations in this data, but we will report on that project elsewhere (Wagner & Leydesdorff, 2003). Here, I focus on University-Industry-Government relations in this data set.
An attempt was made to organize all these addresses automatically in terms of their attribution to university-industry-government relations. The routine first attributed a university label to addresses that contained the abbreviations ‘UNIV’ or ‘COLL.’ Once an attribution was made, the record was set aside before further attributions were made. The remaining addresses were subsequently labeled as ‘industrial’ if they contained one of the following identifiers ‘CORP’, ‘INC’, ‘LTD’, ‘SA’ or ‘AG’. Thereafter, the file was scanned for the identifiers of public research institutions using ‘NATL’, ‘NACL’, ‘NAZL’, ‘GOVT’, ‘MINIST’, ‘ACAD’, ‘INST’, ‘NIH’, ‘HOSP’, ‘HOP ‘, ‘EUROPEAN’, ‘US’, ‘CNRS’, ‘CERN’, ‘INRA’, and ‘BUNDES’ as identifiers.
This relatively simple procedure enabled us to identify 1,239,848, that is 86.6% of the total number of address records, in terms of their origin as ‘university,’ ‘industry,’ or ‘government.’ However, these results remain statistically approximate figures. The distribution is exhibited in Table 2:
|
|
Number of records |
Percentage |
|
‘University’ |
878,427 |
61.3 |
|
‘Industry’ |
46,952 |
3.3 |
|
‘Government’ |
314,469 |
22.0 |
|
– (not identified) |
192,553 |
13.4 |
|
Total |
1,432,401 |
100 |
Table 2
Number of records in the Science Citation Index 2000 that could be attributed with a Triple Helix label using a routine
The addresses refer thus identified to 676,511 (93.3%) of the 725,354 records in the database that contain address information. Furthermore, the address information also contains the country names. For the purpose of this study, records containing an address in England, Scotland, Wales or Northern Ireland were additionally labeled ‘UK,’ and analogously a dataset for the EU was composed containing all records with addresses in the 15 member states. The label ‘Scandinavia’ was added to all records containing an address in Norway, Sweden, Denmark, and Finland. A subset of the 120,086 internationally co-authored papers could analogously be defined.
For all these subsets a three-dimensional transmission of Triple Helix relations can be calculated. The results of this calculation are shown in Table 3.
|
|
number |
% titles retrieved |
T(uig) in mbits |
UI |
UG |
IG |
UIG |
Univers |
Industry |
Govern |
|
All |
676511 |
93.3 |
-77.0 |
16270 |
108919 |
4359 |
5201 |
543123 |
41242 |
232096 |
|
|
|
|
|
|
|
|
|
|
|
|
|
USA |
232571 |
92.5 |
-74.4 |
7200 |
37834 |
1782 |
2666 |
200149 |
18154 |
66416 |
|
EU |
257376 |
93.0 |
-50.1 |
4455 |
52112 |
1485 |
2028 |
206747 |
11192 |
101545 |
|
|
|
|
|
|
|
|
|
|
|
|
|
UK |
68404 |
93.1 |
-63.1 |
1719 |
13098 |
394 |
690 |
54823 |
3970 |
26202 |
|
Germany |
61017 |
94.7 |
-43.4 |
1028 |
14003 |
407 |
664 |
51283 |
2799 |
23701 |
|
France |
41112 |
90.3 |
-52.1 |
439 |
11593 |
452 |
530 |
26133 |
1928 |
26595 |
|
Scandinavia |
30939 |
95.8 |
-31.6 |
490 |
8477 |
162 |
371 |
26542 |
1263 |
13005 |
|
Italy |
28958 |
89.9 |
-29.4 |
362 |
7133 |
87 |
262 |
25633 |
905 |
10526 |
|
Netherlands |
18357 |
95.3 |
-25.4 |
372 |
4482 |
106 |
259 |
16379 |
863 |
6593 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Japan |
67715 |
97.9 |
-92.1 |
4147 |
12492 |
954 |
1311 |
56534 |
9732 |
21664 |
|
PR China |
22116 |
99.5 |
-14.9 |
237 |
4610 |
68 |
114 |
18196 |
480 |
8583 |
|
Taiwan |
8390 |
97.4 |
-17.1 |
148 |
2163 |
19 |
52 |
7454 |
250 |
3120 |
|
Singapore |
2931 |
99.0 |
-23.9 |
104 |
476 |
7 |
17 |
2598 |
145 |
809 |
|
S. Korea |
12038 |
98.3 |
-40.1 |
351 |
2341 |
87 |
91 |
10345 |
676 |
3978 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Russia |
22767 |
98.6 |
-24.2 |
76 |
6315 |
162 |
138 |
11507 |
478 |
17611 |
|
India |
10916 |
89.2 |
-78.1 |
97 |
1813 |
61 |
55 |
6099 |
407 |
6492 |
|
Brazil |
9120 |
91.0 |
-22.4 |
137 |
1727 |
32 |
52 |
7968 |
267 |
2885 |
|
|
|
|
|