The flow of knowledge: Scientific contacts in formal ... - Science Direct

SOCIAL NETWORKS ELSEVIER

Social Networks 19 (1997) 271-283

The flow of knowledge: Scientific contacts in formal meetings 1 Sofia Liberman 2 Kurt Bernardo W o l f *'3 Centro Internacional de Ciencias A.C., Cuernavaca, Mexico

Abstract The scientific community organizes its relations into network patterns, where the nodes are individuals and the links are acquaintance and common work. Scientific meetings are marketplaces of specialized knowledge, where new links are established by exchange of information. The flow of knowledge is modelled by information transfer that may be calibrated through polling the participants on the number of 'contacts' they establish at such meetings. We indicate estimates of cost and efficiency of scientific meetings which may be important for helping science and technology funding agencies in developing countries to increase their community's impact in the world of science.

Keywords: Networks; Information exchange," Scientific contacts; Scientific communication and scientific meetings

1. Fostering scientific networks Scientists invest a considerable amount of their time in acquiring and disseminating new knowledge. The exchange of updated information and exploratory discussions on new developments are increasingly made at formal academic meetings, in-face-to-face conversations. The timeliness of this information is appreciated as a scientific asset. Publication in refereed journals is still considered as the most important validation of knowledge, and serves as the orderly archive of results. For the successful researcher it is obligatory to interact with his colleagues through other, more agile channels, such as conferences, schools, workshops and academic visits. This person-to-person communica-

* Corresponding author. Fax: (52-73) 17-3388. J Research sponsored by DGAPA UNAM Project IN301795. 2 Permanent address: Facultad de Psicologla, Universidad Nacional Aut6noma de M6xico. UNAM Mexico, D.F.C.P. 04510. 3 Permanent address: Instituto de Investigaciones en Matemfiticas Aplicadas y en Sistemas, UNAM. Apartado Postal 48-3, Cuernavaca, Morelos 62251, M6xico. 0378-8733/97/$17.00 Copyright © 1997 Published by Elsevier Science B.V. All rights reserved. PH S 0 3 7 8 - 8 7 3 3 ( 9 6 ) 0 0 3 0 3 - 6

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tion process has created an invisible organization or structure (Friedkin, 1978) in the scientific community, distinct from that of research institutions (Barney, 1985). Such structures have been studied by several sociologists of science and have been conceptualized among other theories as 'networks' (Boissevan, 1979). Traditionally, networks are studied in terms of their centrality and other topological characteristics. International science and technology development agencies have seen virtue in furthering the formation of networks among scientists in developing countries, and promote this process by offering grants to conference organizers. Groups of researchers in the South (i.e. less-developed countries) who work on similar problems are sometimes unaware of each other because their links are mostly with colleagues at mother institutions in the North (Schott, 1991), where many of their academic leaders have been educated. One prominent example of a network-promoting agency is the International Centre for Theoretical Physics (ICTP), in Trieste, Italy. It has allied projects such as the Third World Academy of Sciences (TWAS), which has fostered the Third World Network of Scientific Organizations (TWNSO). Part of Italy's aid to the developing countries is channelled through the Trieste institutions that offer grants specifically for scientific meetings attended by researchers and graduate students from countries within a cultural region. Recognized 'regions' are Latin America, Africa, South Asia, Middle East, etc. Within Latin America, similar efforts at regional integration are supported by specific grants from the Organization of American States (OAS), the Centro Latino Americano de Fisica (CLAF) and UNESCO. Networks created along such lines include the Red Latino Americana de Biologla (REDLAB), that has lead to fruitful exchange visits and joint patents in bioengineering, and a recently proposed Latin American Network of Regional Scientific Organizations, for physics and mathematics. To obtain international or regional funding, the organizers of scientific meetings must obtain matching support from national research and development agencies, such as the Consejo Nacional de Ciencia y Tecnologia (CONACYT) in Mexico and its counterparts in other countries. For this, they must convince the national authorities that it makes more economic sense (benefit/cost) to convene some particular meeting within the country than to send the interested researchers abroad, to some equivalent meeting elsewhere. It is thus important to quantify the flow of knowledge in networks of scientists in order to formulate the criteria to decide between the two strategies. As in other developing countries, the Mexican community of physicists works mostly (95%) in academic institutions (Aguilera-Granja et al., 1992). The funds that a researcher can obtain to attend meetings are not really scarce, and he attends meetings both abroad and at home. For example, the yearly national meetings of the Sociedad Mexicana de Fisica can draw 500 participants - - somewhat more than half of the active physicists in the country. It is a common observation that a large part of the meeting time he spends speaking pleasantries with old colleagues in the corridor or lounge but which are nonetheless important for the cohesiveness of the network. On the other hand, he will also make great efforts to procure the funds for attending a top international workshop outside the country, and while abroad, work to saturation. And, if he perceives a meeting as too dull for its expense, he will not attend. Different kinds of meetings occupy various niches in activating or extending the

S. Liberman, K.B. Wolf~Social Networks 19 (1997) 271-283

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communication links of each participant with colleagues in the larger community, social and scientific networks being often intertwined. In Mexico, as in most Latin countries, personal acquaintance and frequent contact is crucial for most joint enterprises in social life (Adler Lomnitz, 1977) and (McPherson et al., 1992). Funding agencies prefer of course, that the communications be kept strictly scientific, and it is in the interests of the national ones to optimize the transmission of scientific knowledge from abroad to home. We develop here an empirical model where a cost per unit can be proposed and estimated. This paper analyzes the responses of Mexican academic researchers in physics and in mathematics to an interview and a questionnaire about the number and quality of contacts established at formal scientific meetings: conferences, schools, workshops and visits. (The precise definition of 'contact' will be given below.) We interpret the results in the context of the prevailing mores and habits of each of the two fields. We introduce a network-matrix model and divide the population attending a scientific event into Mexican and Alien (home and foreign). This division is arbitrary of course, and applies equally well to regional and extra-regional, South and North, or academic and industrial subpopulations in a meeting.

2. Creation and accumulation of knowledge The community of scientists, as a developing neural network, has over decades adjusted its own organization to enhance the efficiency in creating, transmitting and accumulating knowledge. There is much parallelism in the communication structure, successive abstraction by ganglial nodes, short and long-term memory. The higher functions are diffusely localized on the scale of the brain or community, but highly distributed on the scale of individual neurons or researchers. On the scale of the communication time, the whole structure becomes endowed with the qualities of collective consciousness. The Creation of scientific knowledge is the quintessence of research. To belong to the corpus of science, a scientific result is required to pass a validation procedure: somebody else - - a peer or better - - should be able to understand the logic of a new theorem or the reliability of an experimental result. The academic community has converged on the procedure of peer-review in scientific journals. Also respectable are conjectures of plausible but still unproven results that conform to prevailing paradigms, provided they are identified as such in the text or in the context of oral discussion. The accumulation of knowledge takes place inside living scientists, aided by personal written files (often in a jumble of notes and preprints kept without apparent order in drawers and shelves whose organization reflects the corresponding structures of associative memory in the brain). Accumulation of knowledge is also a function of humanity at large and takes place in libraries with journal collections and scientific books classified by subject matter, and compressed abstracts on computer files transmittable by electronic mail. The amount of scientific knowledge accumulated in an individual is at best perceived only intuitively by his more experienced peers. Evaluation committees in academic institutions quantify a researcher's standing by

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(sometimes crudely) summing points based on the list of desiderata for an ideal researcher. This is becoming firmly established in Latin American countries with the provision of grants to excellence. The list includes the number of articles in refereed journals of international standing (articles in national science journals are less appreciated), the number of citations in the Science Citation Index, the number of lectures and of participations in scientific meetings. The organizers of scientific meetings now routinely issue academic certificates for those participants who have covered their subscription fee, who have lectured by invitation or contribution etc. Scientific meetings, attended or organized, are thus rated on a numerical scale as a measure of the productivity of each scientist. Although it is agreed that such numbers and mini-diplomas only partially describe the actual knowledge and potential wisdom of an individual, they have grudgingly acquired the status of accepted units for production and accumulation of scientific knowledge. Since these units receive a corresponding economic reward, the benefit-to-cost ratio for scientific contacts may be quantified with a model for knowledge transmission.

3. Transmission mechanisms and times

The transmission of knowledge occupies a very substantial portion of the academic working time. Discussing new ideas among colleagues, attending seminars and symposia, teaching courses to new disciples and publication of new papers and books are the visible manifestations of this activity. There are written and oral transmission channels for scientific knowledge. The information placed in a refereed journal goes through the outer cycle of knowledge reproduction: the period between its creation by an author and the reading of the results by unknown colleagues ranges from 2 to 3 years for pure mathematics, 6 to 12 months for physics, and down to 3 months for rapid publication journals in hot fields. This can be seen comparing the reception and publication dates of scientific articles in major journals. At least double of this time would be necessary for feedback in the community if the outer cycle of journal literature were the only means of communication between scientists. The inner cycle (Liberman and Wolf, 1990) of ongoing frontier research is shorter, and is mostly oral 4. Open, specialized academic meetings provide timely information to an audience that is efficiently pre-selected by academic interest and by the networks of the organizers, invited speakers and key participants. Face-to-face discussions with colleagues in research sessions that share a common mathematical language become a friendly tennis match where the ball acquires substance with each exchange. The oral information gained by attending a meeting overlaps partially with that contained in preprints or articles soon to appear in the journal literature. The latter are much more precise (and are quotable), but the former include vital morsels of knowl4 The role of preprints in the academic community can be placed in other intermediate categories. In academia they are normallyacceptedas plausible results, not yet formallyvalidated.


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edge such as: which mathematical techniques are more appropriate for a problem, what the dead ends are, and when a problem is worthwhile to start with. If a participant of a topical scientific meeting has the skill, he will understand the pattern of advancement in his area, spot the hot fields, and direct his own research accordingly. Periodic conferences, topical workshops and specialized schools have become routine academic activity. Adam Smith's invisible hand of maximum personal profits (academic and economic) is at play in this conscious self-organization of scientific endeavour. This pattern is not new. The famous Solvay conferences in Brussels began before World War I, knitting the founders of quantum mechanics and special relativity. In fact, scientists have gathered since the salons of the Encyclopedists, but only in the last two or three decades has international travel become so accessible. Having lowered its cost, this mode of communication has become attractive for the scientific community. The price of long-distance text communication is also dropping. Phone calls and faxes are commonplace and electronic mail has brought its cost practically down to zero. Such wired communications however, are hardly seen as a substitute for old-fashioned conversation. Face-to-face talk conveys qualities of context and depth to the knowledge that is exchanged; the scientist will remember the core subject of a conversation better because of associative memory aids such as the voice emphasis of his colleague, his body language and posture, and even such peripherals as the conference excursion during the time the informal comments were made. Formal academic meetings such as conferences, schools and workshops create personal links between individual scientists that are durable and will support later reactivation by wired messages.

4. Prototypes of formal meetings Having placed the role of formal scientific meetings in the context of the normal activity of a professional scientist, we focus on the patterns of knowledge transfer. We denote by M = ( m i j ) the interaction matrix of interpersonal ties (Breiger, 1974). The value of the matrix element mij (in the intersection of the i th column in the j t h row) is the number of information units conveyed from the i th talker to the jth listener. These values can only be positive or zero; diagonal elements are understood to be zero. When the meeting has n participants, the matrix has n rows labelled by i and n columns labelled by j, as shown in Fig. 1. The matrix M need not be symmetric. A good lecturer produces a row whose sum of A l v a r e z

B a k e r

C h a n g

Alvarez

0

2

2

Baker Chang

I

0

I

2

0

0

Zfifiiga

I

0

2

LISTENER

TALKER

Z

Fig. I. I n t e r a c t i o n m a t r i x .

fi 1

g a

o°'

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S. Liberman, K.B. Wolf/Social Networks 19 (1997) 271-283 CONFERENCE

SCtIOOL

WORKStlOP

t

Fig. 2. Prototype network patterns of scientific meetings.

elements is large; a good listener shows the same property in his column. The total number of information units received at the meeting by an attending listener j is the sum of elements in the jth column, cj = mi,j + m2, j + ... + mn, j = ~ i m i , j . To describe the most common information exchange patterns, we divide scientific meetings into conferences, schools, workshops and visits (Liberman et al., 1991). (Other names such as congress, encounter or symposium will not be used separately.) By this division we characterize in Fig. 2 the following prototypical network patterns with their representing matrices. We consider a Conference to be typically a five-day meeting, where 50-150 independent participants gather to lecture, listen and talk to each other, establishing links and exchanging information at random. The links at a conference follow the pattern between the nodes pictured in Fig. 2a. The representing matrix M that contains units of information exchange is generated by salting 1's randomly on an initial field of O's, The average of the sums of column elements, c = Ej c i / n = "~i,j m i , j / n , is the average number of knowledge units received by the average participant. The value of c is a lower bound for the average number of links established by the average node in the network of the meeting. The actual number may be higher because the participants can establish social links that need not carry scientific information. A School is typically a 1-2 week meeting where a small group of invited speakers offers structured courses to a larger audience of listeners: graduate students, junior researchers and their own peers. The speakers' set is privileged because they can form links at low cost: they can choose future students from the crowd, suggest problems to many ears and reaffirm their leading position in the field by signing their availability for further meetings. Yet the speaker gives more scientific information than what he receives because his audience is large. The prototype network structure is shown in Fig. 2b. In the corresponding interaction matrix, the sum of elements of the speakers' rows have distinctly larger values than the sums of non-speakers' rows. A Workshop is typically a five-day meeting, where a small number of groups of researchers, convene to discuss a common topic or problem, and where all individuals talk randomly to each other. The participating groups are visible as closely linked clusters of nodes, in Fig. 2c. To the extent that the individuals in each research group work closely together before and after the workshop, the number of links established by each group is the sum of those made by its individual members. The interaction matrix of workshops may be thus decomposed into submatrices reflecting the interaction between these groups. Let us now form the group-interaction matrix M R, whose rows


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and columns are labelled by the research groups a, b, c .... If there are N research groups, the group-interaction matrix M g is a N × N matrix. The element Magb is the sum of the entries of the interaction matrix M between individuals, of elements mij with i in the subset a, and j in the subset b. Research groups thus behave as individuals with a larger communication capacity. The meetings most people attend generally have characteristics belonging to more than one of these three prototypes. Actual conferences usually have a subset of speakers or otherwise prominent individuals; under these conditions an attraction set for links characteristic of schools will appear. When attended by institutional groups or cliques, conferences will yield a partial clumping of links characteristic of workshops. Actual workshops usually include oral presentations by the various group leaders; these enhance the link structure of schools. Finally, at actual schools, speakers and students mingle outside lecture hours preferentially by institutional groups, so the random 'conference' background will be larger within some diagonal submatrices. If we assume there is no interaction between the prototypical patterns, the interaction matrices of actual meeting will be linear combinations of the prototype interaction patterns. All linear parameters, such as the averages of the sums of elements by columns and average of submatrix blocks, will follow the linear combination of their matrices. As control situations for normal scientific interactive activity outside formal meetings, we also considered the following two situations that base and bound the scale of information exchange numbers. A Visit is typically a 1-4 week stay of one scientist at a host research institute, who devotes all of his time to interact with a colleague or group, without the duress of lecture time limits, in accordance with the host institute's normal activity. Saturation is the natural limit on the efforts of any average scientist who tries to interact with everybody at a meeting. Productive scientific conversations require frequent activation of associative memory patterns of abstract concepts, for the fleeting recall of a definition, a theorem or a reference; mental fatigue sets in after an honest eight-hour day of scientific work. (Still, people at meetings will gather at the bar and often revert to writing formulas on napkins.) The average sum of columns c in the individual interaction matrix M cannot exceed the bound of saturation. As we indicated in Section 1, we are interested in separating the participants of a meeting into two subgroups: home and foreign. The groups in the audience are generally of different sizes. Let there be n participants, a fraction At of which is from home (0 < At < 1). The n × n interaction matrix of the meeting M is divided into four submatrices. In Fig. 3 we show this division and write inside the boxes the number of elements of each submatrix.

\us~

~,,

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FROM HOME FOREIGN

FROM HOME

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Fig. 3. Group-interaction matrix.

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For the 'home' and 'foreign' teams we have the 2 X 2 group-interaction matrix of Fig. 3. The net gain of knowledge for the home country is in the lower left element of this interaction matrix.

5. Scientific contacts

During the annual Intemational Colloquium on Group Theoretical Methods in Physics of 1979, held in Austin, Texas, Nobel prize winner Eugene P. Wigner was surrounded, as usual, by several eager young physicists and mathematicians, each of whom kept pressing on the Princeton Professor their latest group theoretical scheme (Prof. Wigner sometimes did give very valuable advice). Yet, he refused to receive any more preprints from the crowd into his slim but full briefcase. • But will you r e m e m b e r my assumptions and derivation? • I f y o u r result is important, I will.

And sometimes he did. Scientific knowledge cannot be cut into cubes. We have used the term 'unit of information' in a deliberately figurative way. Yet, after many years of attending meetings of various types, a working scientist has an intuitive idea of how much benefit he obtains from participating in one or another such public and formal academic activity. With the purpose of quantifying this essentially subjective estimate, we interviewed a random sample of 32 physicists and 32 mathematicians with Ph.D.s at their respective institutes at the Universidad Nacional Aut6noma de Mexico, in Mexico City. To focus our questions, we used the following definition: Contact is a useful piece of information, a personal communication bounded in time, retained in the researcher's memory or briefcase, which generates some later action, ranging from immediately influencing his research work to expanding his general scientific culture. In the interviews we applied a questionnaire after the previous definitions were read to him. We asked for the number of contacts received by the respondent at each type of meeting, (conferences, schools and workshops), during visits and his saturation. We also asked for his number of publications, seniority and other curricular and personal data for possible future correlation with scientific productivity. We used this supplementary information to eliminate four physicists and four mathematicians from the data base because they were atypical in one or more respects, belonging to the top of the academic hyperactives or elders with no publications 5 The interviewed scientists confirmed that their participation in meetings is essential for their research. Several hesitated to assign numerical values to the amount of information they obtain at a meeting and some researchers preferred not to give answers in some cases; these cases were dismissed. The number of contacts most researchers quoted were one-digit numbers. Barring here a deeper correlation analysis, the number 5 The results reported by Liberman et al., 1991 on physicists included three individuals with very high numbers of reported contacts.


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Table 1 Means and standard errors for number of contacts reported in the samples of physicists and mathematicians in the three scientific meeting prototypes Sample

Physicists

Meeting

National

International

Mathematicians National

International

Con~rence School Wo~shop Allmeetings

3.1±0,6 4.0±0.9 3.4±0.8 3.4±0.4

4.7±0.7 4.0±0.9 4.8±0.9 4.5±0.5

4.7±0.8 4.3±1.1 4.54-1.0 4.54-0.5

5.84-1.2 5.44-1.5 6.34-1.5 5.94-0.8

of contacts reported appears to be independent of seniority. In Table 1 we show the means and standard errors for the number of contacts reported by physicists and mathematicians at national and international conferences, schools and workshops, excluding zeros (no answer). Table 2 contains the number of contacts in visits and individual saturation levels. The standard errors in the data sets are under 20% of the mean, so a degree of objectivity in these numbers can be claimed. From the entries of Table 1 we see over standard errors that: the home scientists rate international meetings as 30% more efficient than national ones for personal knowledge acquisition; • mathematicians report some 20% more contacts than physicists; saturation bounds give diminishing returns for long meetings. In anticipation of the next section, let us remark that the means of Table 1 are c, the average sum of rows or columns in the representing matrix of the meeting. Before returning to the matrix model, however, we comment on the above statements. Researchers in Mexico report that meetings abroad provide some 30% more scientific contacts than meetings at home. There are at least two good and valid reasons for this: First and objectively, there are excellent international meetings in the North, attended by the very top world scientists. The extra effort spent in finding a larger grant for travel abroad, makes the researcher objectively choose these top meetings a n d / o r meetings in precisely his field of research and network, where a common scientific language is spoken enhancing the communication flow. Second and subjectively, having spent the effort in getting there, he will make sure to get his worth in contacts. There are other reasons why national conferences are lower in scientific esteem: national meetings are cheaper to attend, but their quality may be uneven; specialized formal national workshops are rarer because the interested audience is smaller. The strategy to raise the

Table 2 Means and standard errors for number of contacts reported in visits and saturation Sample

Physicists

Mathematicians

One week visit One month id.

2.74- 0.6 5.04-1.2

2.7 4- 0.3 6.9-t-0.9

One day saturation One week id.

2.4 4- 0.2 6.64-0.9

2.2 + 0.3 5.9+ 1.1

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Table 3 Supplementary data on physicists and mathematicians for studying productivity per author Sample

Physicists

Mathematicians

Seniority a Meetings abroad b Meetings at home b Publications c Articles of one author o Authors per article d

16 + 1.6 1.4 + 0.2 1.8 _+0.2 32.4 _+4.3 16.3% 2.9

17.4 _+2.1 1.4 + 0.3 2.0_+0.4 16.1 _+2.4 56.5% 1.5

a In years. Per year. c Total production. d Data from Bosch et al. (1987), Boldfi (1987).

scientific standard of national meetings is presently quite clear: upgrade meetings at home to the status of international meetings. This can and has been done only in fields where there exists a national research group with the required international presence to convene such meetings. It is of interest to comment on the 20% difference between the number of contacts reported by physicists and by mathematicians in the context of other scientometric indicators. We do not subscribe to the evaluation of individual researchers by their scientometric data, but we accept that for statistical ensembles of researchers these numbers do have objective meanings and, indeed, set the standard. In Table 3 we collect the data from our interviews in the groups of physicists and mathematicians. Within standard error they have the same seniority and meeting habits, but present a 2:1 proportion in their mean number of publications. We compiled the rest of the data in Table 3 from the periodic reports of the institutes where the interviews took place. Physicists indeed author twice as many articles as mathematicians do, but every article has twice as many authors. So the production per author is the same in physics as in mathematics, vindicating that talent is equally distributed. But the talent to exchange information at meetings should then be also equal, unless other factors exist. The moderately increased (20%) number of contacts reported by the mathematicians in their meetings may be due to the general slowness of their outer cycle of knowledge reproduction by journals (approximately 2 - 3 years as mentioned above); some information is therefore shunted to the faster inner cycle, where it is orally hawked at meetings, and where the participants work closer to their saturation level. The saturation bounds for the number of contacts per day and per week, together with the diminishing returns of longer visits, suggest interesting analogies with fatigue in the learning processes. Mathematicians still use preferentially blackboard and chalk in their public presentations because, they say, it adjusts better to the comprehension rhythm of the audience, who proceed by association to imprint their long-time memory with the new abstract constructs. On the other hand, physicists use mostly overhead transparency projectors; they flash sheets of messy algebra and graphs without really expecting the audience to remember everything. The aim is to convey an idea as tangibly as possible, as a landscape and as a phenomenological fact.

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Evidently, meetings are a time of intense mental and social activity for the participants. Three to five days seems to be the preferred range for the duration of conferences and workshops; schools very often run for two and sometimes for three weeks; longer affairs are extremely tiresome. Four meetings a year is the consensual habit of the scientists we interviewed, i.e. 4 weeks per year or 10% of the total institutional working time is spent in meetings. One respondent assured us that there is a place in hell for bad scientists, where they are forced to attend conference after conference, for all eternity.

6. Flow and cost of knowledge When a meeting has n participants, the total number of contacts traded is the sum of elements in the interaction matrix, m t ° t = ~i,j mi,j = cn. These are the entries of Table 1, where c is the average number of contacts reported by the researchers for each type of meeting, or linear combination of them. We indicate the 2 × 2 group interaction matrix of home (h) and foreign ( f ) participants as follows (refer to Fig. 4). Let the number of home participants at a meeting be n h = pro. The net trade of knowledge into the country will be a proportion /z(1 - tt) of cn, namely the group-interaction matrix element mth = (1 -- tz)cn = (1 -- It)cn h. This trade grows linearly with the home team contact capacity c and with the total number of home participants n h. The total information trade cannot grow more than linearly with the number of participants because the average participant will not absorb more than his contact capacity c. The meeting whose group-interaction matrix is discussed can take place at a home site or at a foreign site. Let us use primed letters for the interaction matrix of the home team at a foreign site. Note that c' > c by some 30% and that the proportion of home scientists at a given foreign meeting, /Z, is usually small. A home team of n,, scientists will bring back /zth = (1 - k g ) c ' n ' , or approximately c'n' contacts. The dilemma between sending home delegations to foreign meetings or encouraging the organization of equivalent meetings at home, will depend on the cost per perceived contact. To organize the cost estimate, for a home or foreign scientist to participate in a meeting held at a home or at a foreign site we consider the expenses of round-trip travel tickets and lodging. There are different prices for home travel and international travel, as there are for lodging. The home participants of a home meeting, moreover, bear their proportion of overhead expense for the meeting's organization and its infrastructure. A typical five-day conference in central Mexico could have the following, nominal values in US dollars. The home participants travel expenses are $50 and lodging $350. Foreign participants from the US, Latin America and Europe would pay $750 for travel, the same as Mexican envoys to a meeting abroad. Lodging in Northern cities may be

M.Irm,lm,,l m,.hIra, I Fig. 4. Group-interactionmatrix of home and foreign participants.

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typically $600. From the data of the tables and the simple considerations above, we find that the cost of an international contact, obtained by sending a home researcher to a meeting abroad is $270 (with c'= 5 and /x' near to zero). At home, the cost per international contact at a meeting (with ~ = ~I and c = 4) is $200. If at that meeting the home team achieves an international standard c = 5, then the cost per contact drops to $160, excluding organization expenses. In fact, the expenses of the organizers must come from the difference between spending $1350 per participant at a meeting abroad to obtain c' contacts, and spending $400 per participant for international contacts received at home where the home participants only absorb c contacts. When the number of scientific contacts is the same, c = c', and the proportion is the optimal, /z = ½, the saving for the country is $275 per participant. This is the amount that may be invested in the organization of the meeting within the country. It includes lodging and travel expenses for some of the prominent foreign participants, communications (and sometimes secretarial staff) for the local organizing committee, printed material, mail, coffee, program amenities, etc. To lower local travel expenses the conference site should be located near to the communication cost centroid of the country's scientific community. The country that is host to an international meeting and has a sizable proportion of peer participants, obtains the largest transfer of knowledge; its funding agencies disemburse organization costs that are (or should be) sensibly commensurate with the additional benefit. The interest of the home funding agencies to funnel scientific knowledge into the country lies in raising the values in the 'home' column of the representing matrix, and lowering that column in the cost matrix. The purpose of the regional funding agencies is to foster the formation of links between researchers with cultural and geographic affinity, so that resources can be pooled and critical research masses kindled (Adler Lomnitz et al., 1987). The drive to this aim may be academic, political, ideological or economic, as are other efforts for multinational integration to common market entities. The division between home and foreign participants still applies with the regional criterion, but since the average home-to-home travel cost increases, regional conferences offer a thinner economic advantage.

7. Concluding remarks The transfer of specialized knowledge is a recognized activity in the scientific community; in formal scientific meetings there is a selective distribution of information through the networks of academic researchers in a persistent, self-organizing pattern. The existing networks follow the needs for reciprocal exchange assuming everybody has the same access to this information through his links, and assuming every scientist works for the advancement of knowledge as well as for individual advance in academic and economic standing. Within this structure, scientists in developing countries that belong to international networks use their links for the transcendence of their work. The study of the frequency and cost of scientific contacts for Mexican scientists, and the tactics for their acquisition, should permit a coherent strategy to further the transfer of knowledge into the country.


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With the drop in the cost of travel, attending international meetings has become a recognized part of the normal activity of researchers that drives the inner cycle of scientific knowledge reproduction. We model meetings with two populations exchanging units of information - - contacts - - by a matrix divided into blocks of home and foreign participants. The average column sum is the consensus value of information transfer measured in 'contacts' that were responded by a sample of physicists and mathematicians; it is bounded by the saturation value for an individual. International meetings are rated higher than national ones, as are articles in international journals versus national ones. The context of the discussion suggests that the present preferences for meeting schemes at home and abroad, are in equilibrium with their present cost and usefulness to the academic community. Scientific communication can play a very important role in the advancement of science in developing countries. In the fields where home groups have international presence, the hosting of international meetings is an economically attractive proposition. The empirical application of these results was developed as one of the efficiency criteria for meetings organized by the Centro Internacional de Fisica y Matem~ticas Aplicadas (presently Centro Internacional de Ciencias A.C.) in terms of communication between scientists.

References

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