A Longitudinal Analysis of a Social Network of Intellectual History
AA Longitudinal Analysis of a Social Network of Intellectual History
Cindarella Petz, Raji Ghawi and J¨urgen Pfeffer
Bavarian School of Public PolicyTechnical University of Munich, Munich, GermanyEmail: { cindarella.petz, raji.ghawi, juergen.pfeffer } @tum.de Abstract —The history of intellectuals consists of a complicatedweb of influences and interconnections of philosophers, scientists,writers, their work, and ideas. How did these influences evolveover time? Who were the most influential scholars in a period?To answer these questions, we mined a network of influence ofover 12,500 intellectuals, extracted from the Linked Open Dataprovider YAGO. We enriched this network with a longitudinalperspective, and analysed time-sliced projections of the com-plete network differentiating between within-era, inter-era, andaccumulated-era networks. We thus identified various patternsof intellectuals and eras, and studied their development in time.We show which scholars were most influential in different eras,and who took prominent knowledge broker roles. One essentialfinding is that the highest impact of an era’s scholar was on theircontemporaries, as well as the inter-era influence of each periodwas strongest to its consecutive one. Further, we see quantitativeevidence that there was no re-discovery of Antiquity during theRenaissance, but a continuous reception since the Middle Ages.
I. INTRODUCTION“No self is of itself alone”, wrote Erwin Schr¨odinger in 1918[16] and noted, “It has a long chain of intellectual ancestors”.The history of intellectuals is comprised of a myriad of suchlong chains, embedded in a tapestry of competing influencesof “ageless” ideas, which - in the words of the French scholarBonaventura D’Argonne in 1699 - “embrace [...] the wholeworld” [10].To understand the dynamics of influence and spread of ideasthrough history, the embeddness and interconnections of schol-arship should be taken into account. A network approach offersto identify the most influential scholars via their positions ina network of intellectual influence through the history. Thisallows to study their social relations [26], [12], [20], and toprovide deep insights into the underlying social structure.A recent study by Ghawi et al. [6] addressed the analysisof such a social network of intellectual influence incorporatingover 12,500 scholars from international origins since the be-ginning of historiography. In this paper, we build upon [6], andextend the analysis of that network by incorporating a temporaldimension. We analyze the network of scholars dependent totheir time, adding a longitudinal perspective on how scholarsformed networks. As such, we opt for an inclusive, globalperspective on the history of intellectuals. This perspectiveof a vast longitudinal global network of intellectuals answersto recent discussions on not-global-enough research withinintellectual history [11]. We thus attempt to go beyond thetraditional “master narratives” [5] of a Western Europeancentrist view on intellectual history [24]. The goal of this paperis not only to understand how the influence relations amongscholars evolved over time, but also to get deep insights on their influence on historical periods. The questions we seek toanswer are: • How did these influence networks evolve over time? • Who were the most influential scholars in a period? • Which patterns of influence did emerge?To answer these questions, we analyze the evolution ofinfluences in time in order to identify periods and scholars,who stand out.The contributions of this paper are: • We incorporate a longitudinal perspective on the socialnetwork analysis of intellectuals based on a global peri-odization of history. • We identify patterns of influence, and their distribution inwithin-, inter-, and accumulated-era influence networks. • We identify influence signatures of scholars and eras. • We identify scholars with various knowledge broker roles.This paper is organized as follows. Section II reviewsrelated works. In Section III, we briefly outline the dataset’s characteristics and pre-processing. Section IV presentsthe network analysis of the entire network, and its time-sliced projections into partial influence networks (within-era,inter-era, and accumulated-era), featuring their basic networkmetrics, degree distribution and connectivity. In section V,we identify different influence patterns of scholars and eras.Section VI is devoted to the longitudinal analysis of brokerageroles in scholars. II. RELATED WORKThe term of intellectual history combines a plethora ofapproaches on discourse analysis, evolution of ideas, intellec-tual genealogies, and the history of books, various scientificdisciplines, political thought, and intellectual social context[27], [8]. These studies are usually limited to certain regionsor time spans as a trade-off for thorough comparative andtextual analysis. Endeavors to write a “Global IntellectualHistory” [17] were criticized for focusing on the more well-known intellectual thinkers despite including a transnationalcomparative perspective [23].Network Methodologies allow to analyze intellectual historyand as such the history of intellectuals as big data encompass-ing time and space with a focus on their inter-connections.So far, computational methods were used in the study ofcommunication networks of the respublica litteraria , in whichvarious studies modeled the Early Modern scholarly book andletter exchanges as networks. Among the first was “Mappingthe Republic of Letters” at Stanford University in 2008 [2]. a r X i v : . [ c s . S I] S e p ore recent studies incorporated a temporal perspective onthese epistolary networks [25].A recent study [6] proposed to study the entire history ofintellectuals with the means of a network approach. This paperdefined the most influential as those with the longest reachinginfluence (influence cascades), and identified as such Antiqueand Medieval Islam scholars, and as the one with the mostout-going influences, Karl Marx. In this paper, we extend thisanalysis by incorporating a temporal dimension, in order toestablish a deeper insight on how these influences evolved intime.Much research has been devoted to the area of longitudinalsocial networks [18], [14], [22], [13]. Longitudinal networkstudies aim at understanding how social structures developor change over time usually by employing panel data [12].Snapshots of the social network at different points in timeare analyzed in order to explain the changes in the socialstructure between two (or more) points in time, in terms ofthe characteristics of the actors, their positions in the network,or their former interactions.In this paper, we do not use the classical notion of networksnapshot, which is a static network depicted at a given pointin time. Rather, we split the time span (i.e., the history)into consecutive periods (eras), and embed the network nodes(actors) into the eras in which they lived. This way, the micro-level influence among actors can be viewed as a macro-levelinfluence among periods of history. This enables the analysisof the influence network within each era, between differenteras, and in an accumulative manner.In its core, a network of scholarly influence is a citation net-work, answering to who is influenced by whom [1]. However,in citation networks the influence is indirect , as the relationis originally among documents, from which a social relationamong the authors is inferred. In the data set used here, theinfluence relation is rather direct among intellectuals.III. DATA A. Data Acquisition and Preprocessing
The source of information used in this paper originatedYAGO (Yet Another Great Ontology) [15], a pioneering se-mantic knowledge base that links open data on people, cities,countries, and organizations from Wikipedia, WordNet, andGeoNames. At YAGO, an influence relation appears in termsof the influences predicate that relates a scholar to anotherwhen the latter is influenced by the ideas, thoughts, or worksof the former. The accuracy of this relation was evaluated byYAGO at 95%. We extracted a data set that encompasses allinfluence relationships available in YAGO, using appropriateSPARQL queries that implement social networks mining fromLOD techniques [7]. The result consisted of 22,818 directedlinks among 12,705 intellectuals, that made up the nodes andedges of our target social network of influence. In order toincorporate a time dimension to our analysis, we extractedbirth and death dates of each scholar. Some scholars hadmissing birth and/or death dates, which we deduced by sub-tracting 60 years from the death date, and vice versa, up to the symbolic year of 2020. When both dates were missing, wemanually verified them. During this process, we had to removesome entities, as they did not correspond to intellectuals.Those were either 1) concepts, e.g., ‘German philosophy’ and‘Megarian school’, 2) legendary characters, e.g., ‘Gilgamesh’and ‘Scheherazade’, or 3) bands e.g., ‘Rancid’ and ‘Tube’. Tothis end, we obtained a new data set of 12,577 actors withcomplete dates of birth and death.
B. Periodization
Introducing a longitudinal perspective, we opted for a peri-odization taking global events into account. Any periodizationis a construct of analysis, as each field of research has its owntimeline characterizing periods [21], which are dependent ondifferent caesura for the respective object of research [19].This complicates an overarching longitudinal perspective ona global scale. We used Osterhammel’s global periodization[19] to match the internationality of the scholars, and workedwith six consecutive periods (eras): Antiquity (up to 600 AD),Middle Ages (600, 1350), Early Modern Period (1350, 1760),Transitioning Period (1760, 1870), Modern Age (1870, 1945),and Contemporary Period (1945, 2020).One conceptual challenge was to map actors into eras. Manyactors fit to more than one period’s timeline. We opted for asingle era membership approach since it is more intuitive andeasier to conceive, and reduces the complexity of analysis andcomputations, while grasping the essential membership to anera of each scholar. It also offers adequate results when wecompare eras, since it avoids redundancy.In order to assign a single era to an actor, we used thefollowing method: We assumed that scholars would not beactive in the first 20 years of their lives. Therefore, wecalculated the mid point of the scholar’s lifespan ignoring thefirst 20 years of their age, then we assigned the era in whichthis mid point occurs.After this initial assignment process, we verified the globalvalidity of assignments by counting the number of influencelinks from one era to another. We observed that there weresome reverse links of eras, i.e., an influence relation from anactor in a recent era towards an actor assigned to an older era.Those anomaly cases (about 200) were basically due to: • Errors in dates: – some dates were stated in the Hijri calendar, insteadof the Gregorian calendar, and – some dates were BC and missing the negative sign. • Errors in direction of the relationship: source and targetactors were wrongly switched. • Inappropriate era-actor assignments.The anomalies due to errors have been manually corrected.The cases of inappropriate assignment were technically noterroneous. This usually happened when the influencer livedmuch longer than the influenced, elevating the influencer’speriod into a more recent one. We solved this by iterativelyre-assigning either the influencer backward to the era ofthe influenced, or the influenced forward to the era of the
500 1000 500 0 500 1000 1500
Year N o . A c t o r s AntiquityMiddleAgesEarlyModernPeriod 1300 1400 1500 1600 1700 1800 1900
Year
Year
Fig. 1. Number of actors alive in each year based on their assigned eras.
ML EM T MR CA
Fig. 2. Percentage of received influences in each era. influencer. As a result, each actor is assigned to exactly oneera, such that no reverse links of eras exist. The final cleaneddataset consists of 22,485 influence links among 12,506 actors.IV. ANALYSISFigure 1 shows each era’s continuous density of scholarsbased on their lifespan.With scholars embedded in their respective eras, the entireinfluence network can be time-sliced: we projected it intoseveral partial networks based on the source era (of theinfluencer) and target era (of the influenced scholar). Whenthe source and target eras are the same, we called the partialnetwork a within-era influence network. When the source andtarget eras are different, we called the partial network an inter-era influence network. There are no reverse links from a laterera to a previous one due to pre-processing.After time-slicing the whole network, we received sixwithin-era networks corresponding to all the six eras, and15 inter-era networks, corresponding to all chronologicallyordered but not necessarily consecutive pairs of different eras.Additionally, we constructed six accumulated-era influencenetworks of all scholars living up to and including the targetera.Figure 2 shows the proportion of influence links amongall pairs of eras. There, we can make already two majorobservations for inter- and within-era influence relations: Forone, the highest fraction of influence received by scholars of each era come from its own era. This means that the internalimpact of any era is in general higher than its external impact.In absolute numbers, the vast majority of links occur withinthe Contemporary era, followed by links from Modern Age toContemporary, and within Modern Age, which is clearly owedto the increased amount of scholars in these periods.The inter-era influences of each period is strongest to itsconsecutive period. As our earliest period, Antiquity receivesonly influence links from itself, whereas the influence receivedin the Middle Ages are 82% internal, and 18% from An-tiquity. Subsequently, the amount of the within-era influenceshrinks throughout the consecutive periods, but still remainsthe biggest influence. Noteworthy here is the high proportionof influences of Antiquity on the Early Modern Period, whichrepresents their increased reception during the Renaissance.However, the proportionately many links of Antiquity to theMiddle Ages reassert the shift in historical research that theRenaissance did not “re-discover” Antiquity, but was receivedbefore in the Middle Ages as well [4, p. 3-4].
A. Within-Eras Influence Networks
In the following, we analysed the six within-era influencenetworks, which represent the internal impact of an era. Weextracted the following metrics, as shown in Table I: • Number of nodes N , and edges E , and density D . • Average out-degree (= avg. in-degree due to the propertiesof a directed graph) • Max. in-degree, max. out-degree, and max. degree. • WCC: number of weakly connected components. • LWCC: size of the largest weakly connected component. • SCC: number of strongly connected components, whenthe number of nodes is > ). • Reciprocity and transitivity.We included NA in Table I in order to contain that thenumber of nodes N in a within-era network could be lessthan the number of actors of that era A . This is owed to thefact that not all scholars of an era necessarily participatedin its within-era influence network. Some scholars influencedor were influenced by actors of different eras only. However,around 80% of scholars in each era were active in these within-era networks. The highest value of 86% of the Middle Agesrefer to their relative self-containment as an era, as well as ABLE IM
ETRICS OF W ITHIN -E RA N ETWORKS
Era A ML EM T MR C N
219 303 610 761 2102 6081
N/A
82% 86% 81% 70% 73% 85% E
327 387 694 927 2806 7960Density .0068 .0042 .0019 .0016 .0006 .0002avg. out-degree 1.49 1.28 1.14 1.22 1.33 1.31max in-degree 12 9 17 27 21 26max out-degree 20 16 23 32 68 58max degree 32 20 32 41 73 58WCC 11 21 94 108 208 582Largest WCC 179 233 245 436 1495 437982% 77% 40% 57% 71% 72%SCC 0 2 6 8 31 38Reciprocity 0 0.005 0.023 0.028 0.036 0.014Transitivity 0.064 0.066 0.071 0.042 0.029 0.017 the lowest value in the Transitioning period of 70% to itshigh out-going influences.Over all eras, the amount of nodes and edges steadilyincreased, while the density of networks decreased. On av-erage, the out-degree is relatively stable around 1.25, wherethe highest value of 1.5 occurs in Antiquity, and the lowestof 1.14 in the Early Modern period. When we compare theevolution of the max. out-degree in time, we find that theexpected continuous increase did not always hold due to twoexceptionally high observations at Antiquity and Modern Age.Mutual ties among contemporaries were in general very low.We can report none in Antiquity, and only one in the MiddleAges between Avicenna and Al-Brn. In the Early Modernperiod, eight mutual relations were observed, including e.g.Gottfried Leibniz (1646-1716) and David Bernoulli (1700-1782), whereas 13 mutual relations in the Transitioning period,such as Friedrich Engels (1820-1895) and Karl Marx (1818-1883), or Johann Goethe (1749-1832) and Friedrich Schelling(1775-1854). In the Modern Age, the number of mutual tiesincreased to 51 (e.g. Jean-Paul Sartre (1905-1980) and Simonede Beauvoir (1908-1986)); and to 54 in the Contemporaryperiod.
A ML EM T MR C0100200300400500600700
11 21 94 108 208 582
No. of Weakly Connected Components
A ML EM T MR C020406080100
Relative size of largest WCC
Fig. 3. Weakly connected components in within-era influence networks
Figure 3 shows the number of weakly connected compo-nents (WCCs) in the within-era networks of each era, and therelative size of the largest ones w.r.t the whole correspondingnetwork. The number of WCCs increased gradually over theconsecutive eras. In general, the networks consisted of onegiant component, which encompassed the majority of nodes,while the rest of components were relatively smaller. Thiswas particularly developed in Antiquity and Middle Ages,where the giant component constitute of 82% and 77% of
TABLE IIT OP ACTORS , PER ERA , BASED ON OUT - DEGREE IN WITHIN - ERAINFLUENCE NETWORKS . Antiquity MiddleAges EarlyModernPlato 20 Avicenna 16 John Locke 23Aesop 13 Muhammad 11 Ren Descartes 22Pythagoras 10 Al-Ghazali 11 Isaac Newton 15Plotinus 10 Ban Ms 8 Hugo Grotius 13Euhemerus 10 J. S. Eriugena 8 Leibniz 11Transition Modern ContemporaryGoethe 32 Nietzsche 68 Vladimir Nabokov 58Hegel 29 Jules Verne 35 Friedrich Hayek 50Lord Byron 24 Henri Bergson 35 Richard Pryor 50Immanuel Kant 22 Leo Tolstoy 24 Jacques Derrida 48von Schelling 17 Edmund Husserl 22 Michel Foucault 47 the nodes, while the second largest were at 6% and 3%,respectively. The Early Modern period constitutes an exceptionto this giant component rule: the largest one was at 40% only,and the second largest at 16%. Looking at their composi-tion, the first consisted of natural scientists, mathematicians,and philosophers, such as Descartes, Newton, and Leibniz,while the smaller one compromised of artists and painters,such as Rembrandt and Raphael. The single giant componentphenomenon appeared again in subsequent eras. For instance,in the Transitioning period, there were 108 WCCs, wherethe largest two incorporated 57% and 1.3% of the nodes.In Modern and Contemporary age, the largest componentscomprised about 70% of nodes.
Who was most influential on their contemporaries?
TableII lists the top five scholars per era based on their out-degreein the within-era influence networks. The highest within-eraout-degree over all times was achieved by Friedrich Nietzsche(1844-1900) of the Modern Age with 68 outgoing influencelinks to other scholars of his era.
B. Inter-Era Influence NetworksInter-era influence networks are partial networks wherethe source era is preceding the target era. We interpretedthese networks as bipartite, as the actors belong to differentgroups, the source era and the target era. Therefore, only edgesbetween nodes sets are possible.
TABLE IIIM
ETRICS OF INTER - ERAS INFLUENCE NETWORKS source → N E N s N t D in-degree out degreetarget avg max avg maxA → MA 82 87 38 44 .052 1.98 7 2.29 12A → EM 117 145 46 71 .044 2.04 7 3.15 19A → T 66 66 29 37 .062 1.78 5 2.28 11A → MA 101 114 42 59 .046 1.93 11 2.71 23A → C 169 177 49 120 .030 1.47 6 3.61 46ML → EM 149 144 66 83 .026 1.73 9 2.18 21ML → T 52 36 22 30 .055 1.20 5 1.64 6ML → MR 77 62 27 50 .046 1.24 4 2.30 12ML → C 146 121 50 96 .025 1.26 6 2.42 34EM → T 392 432 159 233 .012 1.85 16 2.72 24EM → MR 262 269 101 161 .016 1.67 13 2.66 15EM → C 437 432 125 312 .011 1.38 7 3.46 35T → MR 1,111 1,373 436 675 .005 2.03 19 3.15 53T → C 888 1,041 212 676 .007 1.54 9 4.91 112MR → C 3,817 4,885 1,271 2,546 .002 1.92 17 3.84 78 able III shows the metrics for those inter-era influencenetworks. In general, each era had the most links with itsconsecutive era, and additionally with the Contemporaryperiod’s scholars. Exception to this rule was Antiquity, whichsaw its first peak with the Early Modern period relating toRenaissance interests. Their densities were again decreasingthrough the combinations, except for those periods that hadless links to other periods, such as the Middle Ages to theTransitioning period.
Which scholar influenced a successive era the most?
TableIV shows the scholars with the highest degrees in the inter-eranetworks. Noteworthy here is Karl Marx, who had the highestout-degree over all times from the Transitioning period to theContemporary age, followed by modern philosopher FriedrichNietzsche and Martin Heidegger on Contemporary scholars.
C. Accumulative Influence Networks
For each era, we constructed an accumulative influencenetwork of all influence links among scholars who lived upto and including that era. We performed essential social net-work analysis on these six accumulated-eras networks, whichcombine the internal and external impact of eras. The finalnetwork of Contemporary Age is the same as the completenetwork over all periods [6].Fig. 4 shows the best connected scholars for each era, thatinfluence at least 10 others, in the final accumulated network.We clearly see two joined networks of hubs. The right part isvery diverse in terms of including different eras and differentfields such as philosophy, theology and science scholars. Theleft part consists mainly of writers since the long 19. Century(1789-1914); Alexander Pushkin (1799-1837) is one of theeldest nodes there. This writers’ network shows little diversityto other historical periods and consists mostly of Modern andContemporary age writers. That writers are less connected tothe philosophy, theology, and science scholars shows that thesegroups referenced themselves more consistently.Table V shows the metrics of accumulated-era networks. Re-garding node degrees change over consecutively accumulatederas, we observe that at all eras the maximum out-degree is
TABLE IVT
OP SCHOLARS WITH HIGHEST OUT - DEGREE IN THE INTER - ERANETWORKS s → t First Rank Second RankA → ML Aristotle 12 Augustine of Hippo 6A → EM Aristotle 19 Plato 14A → T Aristotle 11 Plato 9A → MR Plato 23 Aristotle 16A → C Aristotle 46 Plato 32ML → EM Ibn Tufail 21 Thomas Aquinas 9ML → T Petrarch 6 Dante Alighieri 5ML → MR Dante Alighieri 12 Thomas Aquinas 11ML → C Thomas Aquinas 34 Dante Alighieri 10EM → T J. J. Rousseau 24 Shakespeare 21EM → MR Baruch Spinoza 15 Shakespeare 15EM → C Shakespeare 35 David Hume 25T → MR Immanuel Kant 53 Karl Marx 43T → C Karl Marx 112 Hegel 67MR → C Nietzsche 78 Martin Heidegger 73
SchellingChestertonOrwellJoyceTolstoy Goethe Hegel Tufail BaconDescartesSpinozaFreudSchopenhauerNietzsche Plato HobbesKant SmithRousseauDiderot EngelsPushkin HusserlVoltaire LockeMarxVicoSartreTurgenev Beckett BenjaminKierkegaard HeideggerAquinas Arendt DurkheimWeberDeweyWittgenstein GadamerPeirce JaspersCusaProust Beauvoir BergsonNabokov CamusBorges MagnusCalvoBlanchot Lévi-StraussLeibnizJamesMerleau-PontyHumeShestovHemingway Scheler Mill Santayana StraussKojèveBenthamRilke Bataille LevinasMacedonskiMinulescuGraciánTzara Jacobi Cantillon Voegelin
AntiquityMiddle AgesEarly Modern PeriodTransition PeriodModern AgeContemporary History
Fig. 4. Network of the most influential actors with at least 10 out-goinginfluences. Node size = proximity prestige, node color = era, links within anera are colored with the color of the era, the other links are gray. greater than the maximum in-degree. Moreover, those maxi-mum degrees continuously increase over eras, in contrast towithin-era networks. The average out degree changes slightlyover time, taking its lowest value of 1.45 at Middle Ages, andhighest value of 1.8 at Contemporary age. Noteworthy is thedrastic collapse of the largest Weak Component in the EarlyModern period, which was steadily rising since.
Who was the most influential intellectual in an era?
Figure5 shows the evolution of the ten most influential scholars inthe complete network based on their out-degree progressingin the accumulative networks.The top two ranks of the most prolific scholars were consis-tently taken over by Antique philosophers Plato, and Aristotle(who among contemporaries was only in rank 6) Contem-porary scholars came on third rank in the Middle Ages(Avicenna), in the Early Modern period (Ibn Tufail, JohnLocke, Ren Descartes), and in the Transitioning period (JohnLocke, Johann Goethe). This changed in the Modern Age,when Transitioning period scholars Immanuel Kant and Hegeltook the first ranks. Aristotle still remained in the top five. Thehighest out-degree over all times is observed at Contemporary
TABLE VM
ETRICS OF A CCUMULATIVE -E RA N ETWORKS
Era A ML EM T MR C N
219 552 1,227 2,141 4,697 12,506 E
327 801 1,784 3,245 7,869 22,485 N src
54 155 388 677 1,501 3,890 N inner
71 178 353 597 1,331 3,080 N sink
94 219 486 867 1,865 5,536Density .0068 .0026 .0012 .0007 .0004 .0001avg. out-degree 1.49 1.45 1.45 1.5 1.68 1.80max in-degree 12 16 26 38 48 48max out-degree 20 24 41 52 75 158max degree 32 36 50 60 116 196WCC 11 30 110 211 390 817Largest WCC 179 441 797 1513 3550 1019282% 80% 65% 71% 76% 81%SCC 0 2 8 16 47 85Reciprocity 0 0.002 0.010 0.014 0.019 0.011Transitivity 0.064 0.067 0.064 0.056 0.039 0.021 u t - d e g r ee Fig. 5. Top 10 of the most influential intellectuals of the complete networkbased on their out-degree, and their progression in the accumulated-eranetworks. age, where Karl Marx had 158 outgoing influence links toother scholars of all eras, followed by Nietzsche, Hegel andKant. V. P
ATTERNS OF I NFLUENCE OVER E RAS
In this section, we study the influence patterns of scholarsover eras. We construct influence signatures based on howmuch on average a scholar influenced an era, and whichpatterns of directed influences characterize an era.
1) Influence Power of Scholars:
For each scholar, we con-struct their influence signature as a sequence of their influencelinks towards each era starting from their own. For example,the influence signature of Aristotle was [10 , , , , , ,which meant, he had 10 influence links within Antiquity, 12links towards the Middle Ages, etc. Using those signatures,we define the longitudinal influence power of a scholar asthe average of their influence signature. A scholar wouldhave a high influence power when he has (1) a high numberof influence links (2) over all or many eras. In contrast,having few influence links over several eras, or many linksover few eras would give low value of this influence powermeasure. For example, with an average around 19 bothAristotle and Shakespeare had similar influence powers. Inabsolute numbers, Aristotle had almost twice the number ofShakespeare’s influence links (114 to 73, respectively). WhileAristotle influenced all 6 eras, and Shakespeare only 4, theratio of the links per era decreased for Aristotle, resultingin their similar influence powers. This measure provides anindicator of the influence power of an intellectual throughouthistory, and combines both the intensity and the diversity ofinfluence.It also allows us to compare scholars from different eras.Table VI shows the top 5 scholars based on the longitudinalinfluence power. Here, Aristotle, Thomas Aquinas, WilliamShakespeare, Karl Marx, Friedrich Nietzsche and the writerVladimir Nabokov (1899-1977) are identified by their in- fluence power as the most influential intellectuals of theirrespective periods. The highest longitudinal influence powersover all times had Nietzsche (73), followed by Nabokov (58)and Marx (52). TABLE VIT OP ACTORS BASED ON THE LONGITUDINAL INFLUENCE POWER . Antiquity MiddleAges EarlyModernAristotle 19.0 Thomas Aquinas 12.6 William Shakespeare 18.2Plato 17.0 Dante Alighieri 6.0 Baruch Spinoza 14.8Augustine of Hippo 6.0 Ibn Tufail 5.8 Ren Descartes 14.0Plotinus 4.7 Avicenna 4.6 John Locke 13.0Heraclitus 4.2 Al-Ghazali 3.6 David Hume 12.5Transition ModernAge ContemporaryKarl Marx 52.6 Friedrich Nietzsche 73.0 Vladimir Nabokov 58.0Hegel 45.7 Martin Heidegger 45.0 Friedrich Hayek 50.0Immanuel Kant 45.0 Ludwig Wittgenstein 40.0 Richard Pryor 50.0Sren Kierkegaard 25.3 James Joyce 39.5 Jacques Derrida 48.0Fyodor Dostoyevsky 23.0 Sigmund Freud 32.0 Michel Foucault 47.0
2) Influence Patterns:
Which directed influences were mostcommon in an era? We derive to these influence patterns oferas by replacing any non-zero entries by X of the scholar’sinfluence signatures, and aggregate all occurrences of eachpattern for each era. We thus ignore the actual values ofinfluence (intensity), but keep the temporal effect (diversity).For example, the influence pattern [ X, , · · · , means thatthe scholarly influences goes to the first (own) era only,with no influence on other eras. The pattern [ X, X, · · · , X ] signifies that the influence is distributed over all applicableeras, regardless of the actual values. Table VII gives the toppatterns of each era with the pattern’s frequency of occurrencewith regard to the respective era. TABLE VIIT
OP FREQUENT INFLUENCE PATTERNS OF ERAS ( FROM LEFT TO RIGHT ) A ML EM T MR CAntiquity × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × For example, for the Middle Ages the most frequent patternwas [ − , X, , , , , which represents that 56% of scholarsonly influenced contemporaries with no influences on othereras. Over all eras, the most common pattern was of within-erainfluence, followed by the influence on the consecutive period.Exception to this rule was the Modern period, which had thisule reversed, and an higher influence on the Contemporaryperiod than on its own. Since the Early Modern period, thepattern of influencing all successive eras including its ownbecomes more frequent (from 7% on), and rising in eachsuccessive period. VI. B ROKERAGE R OLE
Which roles had scholars in regard to their influence onothers?
We look at roles by following the brokerage approachby Gould and Fernandez [9] by analyzing non-transitive triads,in which a node A has a tie to node B, and B has a tie tonode C, but there is no tie between A and C. In these triads,B is thought to play a structural role called a broker .The possible roles are shown in Figure 6, which are adaptedfrom the work of Gould and Fernandez in [9], and Everettand Borgatti [3]. This allows us to consider to what extenta node’s importance is based on joining two nodes that aremembers of the node’s own era, or on joining others outsidetheir group. We interpret nodal membership in groups as eras. A
1. Liaison 2. Gatekeeper 3. Representative 4. Coodinator
BC A BC A BC A BC
Fig. 6. Brokerage Roles of the top right node of each triad, adapted fromGould and Fernandez (1989) [9].
In Table VIII, we analyse the above described brokerageroles for each period. Over all eras, 23% of all scholars onaverage had at least one of the above described brokerageroles. Since the Early Modern period, the amount of scholarswith exactly one brokerage role stays very stable on about 12-13%, slightly higher in the Antiquity and Middle Ages. Boththe first and the last of the periods could have a maximum of 2different brokerage roles, because pre-processing didn’t allowreverse links. Therefore, Representative and Liaison brokeragewas impossible for Contemporary, as well as Liaison andGatekeeper brokerage for Antiquity. Coordinator and Gate-keeper roles represent the scholars importance within theirown period. Gatekeeper had inter-period influences, and in turninfluenced their contemporaries. The scholars with the highestscores for Gatekeeper in their respective periods were medievalpolymath Avicenna (980-1037), Early Modern philosopherRen Descartes (1596-1650), and Immanuel Kant (1724-1804),Friedrich Nietzsche (1844-1900), and Michel Foucault (1926-1984). The highest scores of Coordinators had Plato, againAvicenna, John Locke (1632-1704), Johann Goethe (1749-1832), again Friedrich Nietzsche, and contemporary horrorwriter Stephen King (born 1947). As Coordinators, these The fifth brokerage role, the
Consultant , where A and C belong to oneperiod, and B belongs to another, is not possible in our network, as we didn’tallow reverse influences of a more recent period onto a previous one by pre-processing. scholars represented an within-period influence. Liaison bro-kers would have the longest time frame of influence, whichincludes three successive periods. Highest scores had Do-minican friar Thomas Aquinas (1225-1274), Early Modernphilosopher Baruch Spinoza (1632-1677), and again ImmanuelKant and Friedrich Nietzsche as Liaisons. Representatives tookthe reverse role of an Gatekeeper: They had an within-erainfluence, that spread to a successive era. Here, Plato, ThomasAquinas, David Hume (1711-1776), Karl Marx (1818-1883)and Martin Heidegger (1889-1976) stood out.From Middle to Modern Age, the amount of scholars withall four brokerage roles steadily increased. Noteworthy herewere Thomas Aquinas (Middle Ages), Gottfried Leibniz (EarlyModern Period), Georg Hegel (Transitioning Period), andMartin Heidegger (Modern Age), who appeared most oftenin super brokerage roles: They combined Liaison, Gatekeeper,Representative, and Coordinator roles alike in their respectiveperiods. Surprisingly though, scholars with 3 brokerage roleswere roughly ten times less common than those with allbrokerages (compare Table VIII).
TABLE VIIIN
UMBER AND FRACTION OF ACTORS TAKING
1, 2, 3 OR ROLES
No. of Roles 1 2 3 4Antiquity 55 (21%) 30 (11%)MiddleAges 62 (18%) 32 (9%) 12 (3%)EarlyModern 101 (13%) 51 (7%) 2 (0.3%) 38 (5%)Transition 136 (12%) 87 (8%) 6 (0.8%) 70 (6%)ModernAge 363 (13%) 269 (9%) 5 (0.7%) 200 (7%)Contemporary 879 (12%) 536 (7%)overall 1,596 1,005 13 32012.8% 8.0% 0.1% 2.6%
VII. CONCLUSIONSIn this paper, we incorporated a longitudinal aspect in thestudy of the influence networks of scholars. First, we extractedtheir social network of influence from YAGO, a pioneeringdata source of Linked Open Data. Rigorous pre-processingresulted in a network of 12,705 intellectuals with 22,818 edges,including information on each scholar’s era. We opted for aglobal approach to the periodization of history, resulting in sixconsecutive eras to study.Our main question was whether we could identify pat-terns of influence, and their change over time. Therefore weperformed essential network analysis on every time-slicedprojection of the entire network in within-era, inter-era, andaccumulated-era influence networks. We investigated theirsocial network metrics, degree distribution and connectivity.An influence pattern throughout all eras was that the internalimpact of any era was higher than its external impact. The vastmajority of scholars influenced scholars of their own period(= within-era influence) with an relatively stable average out-degree. There were only few instances of reciprocity. Whenaccumulating eras, the max. degrees drastically increased.However, over all eras, the maximum out-degree stayed greaterthan the maximum in-degree. In inter-era influence networks,each era influenced most its consecutive one, and additionallythe Contemporary period. Exception to this rule was a spike inhe absolute links of antique influences on the Early ModernPeriod, representing the increased reception of antique scholarsduring the Renaissance. However, proportionally Antiquity’sinfluence on Early Modernity was as high as on the MiddleAges, which reasserts the shift in historical research that theRenaissance thinkers did not “re-discover” Antiquity, but thatmedieval scholars also received it [4, p. 3-4].With a longitudinal perspective, we can add a more pro-nounced view on who the most influential intellectuals were.The scholar with the highest out-degree over all periodson contemporaries (= within-era) was Modern age scholarFriedrich Nietzsche. Plato in Antiquity, Avicenna in the MiddleAges, John Locke in the Early Modern period, Johann Goethein the Transition period and Vladimir Nabokov in Contempo-rary were the most influential on the contemporaries of theirrespective periods.When accumulating eras, the most influential intellectualsof an era change: there, Plato was the most influential forAntiquity and the Middle Ages, Aristotle for the Early Modernand Transitioning period, Immanuel Kant for Modern Age.In the Contemporary period, and therefore for the completenetwork of intellectuals, it was Karl Marx.In the inter-era network analysis, Transitioning periodscholar Karl Marx had the highest out-degree over all times tothe Contemporary age. Second places over all time took Mod-ern intellectuals Friedrich Nietzsche and Martin Heidegger onthe Contemporary period.We constructed the longitudinal influence power of intel-lectuals based on the average of their influences on eras,which favours consistency of influence. Here, again Aristotle,Thomas Aquinas, William Shakespeare, Karl Marx, FriedrichNietzsche and Vladimir Nabokov were the most consistentlyinfluential intellectuals of their respective periods. The highestinfluences had Nietzsche, Nabokov, and Marx.In terms of knowledge brokering, we could identify Co-ordinator, Gatekeeper, Representative and Liasion knowledgebrokers, whom we interpreted as passing influence betweenand within eras. We found scholars with all four differentbrokerage roles were medieval scholar Thomas Aquinas, EarlyModern polygraph Gottfried Leibniz, Georg Hegel of theTransitioning Period, and the Modern philosopher MartinHeidegger.This study of the longitudinal patterns of influence suchis suited to further the insights on the interconnections ofinfluence of thinkers, and the dynamics of eras alike.Therefore we plan to study the evolution of communities inthese accumulated networks in future work. In addition, welike to compare this YAGO network of intellectual influencewith a more detailed network of scholars based on the mainbooks on intellectual history, in order to establish their differ-ences and insights on this field.R
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