Introduction

The authors, in the 700th year from the birth of Giovanni Boccaccio, intend to celebrate the event by their proper means: statistical, numerical, computing, and cartographic techniques, as used in Geomatics. As the Decameron novels record time, places, and itineraries, it is easy to put in evidence the latter (with further evolution of synthesis of results).

Most of the medieval maps have a general “TO” shape. The “O” means the outer ring of waters, the ocean, which encloses the lands; the “T” is the general shape of the three continents, as related to the three sons of Noah. Indeed, in the Middle Age, the Earth was thought of as a globe mainly covered with water, with a number of islands comparatively small, a part of which was Oekoumene. So, it was thought as possible a plane representation of Oekoumene. This type of maps is clearly related to the views of Augustine about the City of God: evidently, the will of God has placed Christians at the centre of Oekoumene, as non-Christian peoples are relegated in outer spaces, even at the boundary of non-human beings.

Boccaccio’s world, from the cartographic viewpoint, is not the one of TO maps, but the one of portolanos for travelers and merchants. Boccaccio’s world is the one of Florentine merchants. Ptolemy’s Geographia had been translated from Greek to Arabian language in the ninth century; later, a Latin translation was made available in the early fourteenth century. Obviously, Boccaccio could not know about Geographia; however, in the period of Neapolitan apprenticeship, he was very interested in Mathematics and Astronomy, having as instructors Andalò del Negro and Paolo dell’Abaco, respectively. So, Boccaccio also wrote about Geography (De Canaria et insulis reliquis ultra Hispaniam in Oceano noviter repertis (1342) and De montibus, silvis, fontibus, lacubus, fluminibus, stagnis seu paludibus et de diversis nominibus maris (1374).

However, we also mean to have an interface between Geomatics and Humanistics, for hybridation of different areas.

Statistical and probabilistic methods, as presently employed in the field of social sciences, have been greatly enhanced by a larger availability of computation facilities in the last decades. For Linguistics, statistical methods have come into use in early decades of the past century (Markov 1913)). The great pupil of Čebyšëv examined the first 20,000 characters of Puškin’s “Evgenij Onjegin” with attention paid to the probability of alternance vowel/consonant. Later, Markov applied the same statistical technique to Aksakov’s “The childhood of Bogrov the grandson.” Many other scholars, after him, were interested to find out the real authors or the text analysis.

The famous method of “Markov’s chains” was extended to many fields.

In the present paper, the authors will use statistical and geomatical techniques to test geographical knowledge of Boccaccio, as shown in the travels described in the Decameron novels.

(Branca 1992) notes that geographical assessment of location is pursued with remarkable precision and in one of the most remarkable issues of “Boccaccio’s realism.”(Greppi 2010) has resumed geographical knowledge of Boccaccio in a dedicated dictionary. Also, the Italian IGM (Istituto Geografico Militare) managed in 2005 a conference about Boccaccio as a geographer, with a contribution of the medievalist Franco Cardini.

A visualization of Boccaccio’s world has been conceived starting with “density-equalizing maps,” a method due to (Gastner and Newman 2004). Worldmapper is a website which contains a number of these maps: each map is related to a particular subject. Tobler was an early user of cartograms, especially the “value-by-area” variety, in order to communicate spatial properties other than position and size in space (Tobler 1996).

The structure of Decameron

The Decameron (Boccaccio 2012) begins with the flight of ten young people (seven girls and three boys) from plague-stricken Florence in 1348. They retire to a rich, well-watered countryside, where, in the course of a fortnight, each member of the party has a turn as king or queen over the others, deciding in detail how their day shall be spent and directing their leisurely walks, their outdoor conversations, their dances and songs, and, above all, their alternate storytelling. This storytelling occupies 10 days of the fortnight (the rest being set aside for personal adornment or for religious devotions); hence, the title of the book itself, Decameron. The stories thus amount to 100 in all. Each of the days, moreover, ends with a canzone (song) for dancing sung by one of the storytellers (from: Encyclopedia Britannica).

So, the structure of Decameron consists of a narrative framework, in which the author tells the story of the “brigade” escaping from Florence in the villa, and a hundred short stories divided in 10 days.

The first day, the theme is free (Pampinea is the Queen).

The other themes are

  • the importance of fortune to achieve goal (Queen: Filomena)

  • the role of ingenuity for succeeding (Queen: Neifile)

  • the love stories that end sadly (King: Filostrato)

  • the love stories that end happily (Queen: Fiammetta)

  • the effectiveness of witty responses (Queen: Elissa)

  • the mockery of wives to husbands (King: Dioneo)

  • jokes of any kind (Queen: Lauretta)

  • human vices (Queen: Emilia)

  • liberal and magnificent actions (King: Panfilo)

Each storyteller is a determined character, for example, Fiammetta is passionate and jealous, whereas Philostratus is melancholic and Pampinea is an intellectual woman, and so on. In this paper, the authors study Boccaccio’s geography. The entire list of places and travels of the Decameron novels is written in Appendix 2.

Concerning representation: diffusion-based method for density-equalizing maps

Traditional thematic mapping, unlike standard reference maps which only show natural features, highlights the spatial distribution of a given item or of a specific characteristic (temperature, agricultural-related items, population density, etc.). It also shows variations in data over time, such as the history of a migration or the spread of a disease.

In short, a thematic map combines geographical data and the time variable linked to the relevant items. In addition, it makes plain relationships among the most important features and aids correlation analysis of geographical data.

In the actual creation of any thematic map, once both a specific physical area and a suitable cartographic projection have been selected (usually from equivalent projections, which preserve dimensional stability of the tested area), it is fundamental to perform an analysis of a number of sets of statistical data and to choose an appropriate method for representation of the variables. Color, for instance, is a major element in producing clear and effective maps.

However, the last few decades have seen an increase in the use of cartograms in which the tested area is not stable but may be distorted in order to convey information relating to the feature itself (anamorphic maps). Indeed, an anamorphic map is easier to understand and provides a better overview of a specific geographical question.

Many scholars have generated cartograms in which the dimensions of a given region would be proportionate to its population or to any other feature (or a statistical variable). However, this type of graphical rendering of statistical data makes it hard, at times, to recognize the areas under examination, as the constraints for assembling adjacent regions produce distortions, which may result in the map being difficult to use. Moreover, drawing such maps is a difficult computational task, requiring considerable time for calculations to be performed.

In view of this fact, M.T. Gastner and M.C. Newman of the Physics Department and Center for the Study of Complex Systems of the University of Michigan, in Ann Arbor, have presented a simple algorithm based on Elementary Physics, which allows easy-to-read cartograms to be produced (modified from (Gastner and Newman 2004)). The algorithm is based on the theory of diffusion, and for this reason, the cartograms are also known as “diffusion-based” or “anamorphic maps.”

For a distribution-based cartogram, distribution must be necessarily uniform, and after resizing areas so that they are proportionate to the variable, by definition, density is equal everywhere.

Given a particular distribution, one way to create a cartogram is to let the elements “flow” from areas of greater density to areas of lesser density, with the aim of equalizing overall density, as in any diffusion process of Elementary Physics (it can be easily proven that linear diffusion is simply a density equalization).

Moreover, since areas of interest have boundaries or coastlines (beyond which density is unknown or insignificant), interest often regards particular areas of the globe and not the entire globe itself. Here, a neutral threshold condition is applied, ensuring that the area of interest floats in a kind of sea of uniform densities, equal to the average of the densities of the entire area of interest (the tested area should remain constant during the diffusion process).

These intuitive considerations complete the description of the method used (the algorithm implementation, in contrast, requires computing operations which must be carried out in a relatively short time). Be this as it may, this remains a highly interesting tool for the representation and analysis of geographic data.

Places of the “heart”

The places of the heart is a common locution, recently adopted by thematic cartography to mean “preferences.” Places are listed according to Italian alphabetical order (as Boccaccio wrote them).

Absolute frequency

Places of the heart

Absolute frequency

Places of the heart

1

Abruzzo

1

Castellammare di Stabia

1

Acquamorta (present-day Monte di Procida)

1

Cathai (today China)

2

Acri

1

Cephalonia

1

Agrigento

1

Certaldo, Garbo (province of Florence)

1

Albissola

1

Chiarenza (Romania, Peloponnese)

8

Alexandria

1

Chios

2

Amalfi

6

Cyprus

1

Anagni

1

Classe (province of Ravenna)

1

Ancona

2

Cluny

1

Antiochia

1

Corfu (formerly island of Gurfo)

1

Antwerp

1

Cornwall

1

Aragona

1

Corsignano (hamlet of Pienza)

2

Arezzo

1

Constantinople (sea before)

1

Argo (Peloponnese)

1

Cremona

2

Armenia

4

Crete

1

Assisi

1

deserts of Thebais (Egypt)

1

Asti

1

Aegina

2

Athens

2

Faenza

1

Avignone

1

Famagosta

3

Babylon

1

Fano

2

Barberia

2

Ferrara

1

Barcelona

1

Flanders

1

Barletta

2

Fiesole

1

Benevento

45

Florence

1

Berlinzone (Land of Bengodi)

1

Mouth of the Magra

1

Bitonto

1

Forlimpopoli

8

Bologna

1

France

1

Borgo San Lorenzo

1

Friuli

1

Burgundy

1

Gaeta

1

Brescia

1

Weles

1

Brindisi

8

Genoa

1

Bruges

2

Jerusalem

1

Buonconvento (province of Siena)

1

Gharb (Island of Malta)

1

Calais

2

Granada

1

Campi Bisenzio

1

Gascony

1

Candia (Island of Crete)

1

Imola

1

Cappadocia

1

India

1

Capsa (Tunisia)

2

The Hell

1

Carthage

2

England

1

Castel Guglielmo (province of Rovigo)

1

Ireland

1

Ischia

1

Puglia (Apulia)

1

Laiazzo (today Ayas in Turkey)

1

(The) Purgatory

1

Lamporecchio (province of Pistoia)

1

Radicofani (province of Siena)

1

Laterina (province of Arezzo)

1

Ravello

1

Lerici

2

Ravenna

2

Lipari

1

Reggio Calabria

1

Livorno

1

Rimini

3

Lombardy

3

Rhodes

3

London

11

Rome

3

Lunigiana

2

Romagna

1

Majorca

1

Rossiglione (Rossillon, France)

1

Mar Egeo

4

Salerno

1

Marca d’Ancona

2

Saluzzo

1

Marseilles

2

Sardinia

2

Messina

1

Scalea

3

Milan

1

Scotland

1

Molese (the area of Mola di Bari)

7

Sicily

1

Modena

5

Siena

2

Monaco

1

Smirne

1

Monferrato

2

Spain

1

Montpellier

1

Stanford

1

Mugello

1

Susa (in Tunisia)

8

Naples

1

The Holy Land

1

Narbonne

1

Truffia, Buffia and Menzogna Territory

1

Paphos

1

Ticino (river near Pavia)

6

Palermo

1

Torrenieri (a hamlet of Montalcino)

1

Paradise

5

Tuscany

15

Paris

1

Trani

5

Pavia

2

Trapani

1

Persia

1

Tresanti (province of Florence)

4

Perugia

1

Treviso

2

Pisa

2

Tunisia

2

Pistoia

1

Udine

1

Pontremoli

1

Ustica

1

Ponza

1

Valbona (a hamlet of Berceto or Collagno, province of Parma or province of Reggio Emilia)

3

Prato

1

Valdarno

1

Procida

3

Venice

2

Provence

2

Verona

Needless to say, Florence comes out on top, followed, some way behind, by Paris (with roughly a third of the mentions of Florence) and by

  • Rome

  • Alexandria, Bologna, Genoa, Naples

  • Cyprus, Palermo, Sicily

  • Pavia, Siena, Tuscany

  • Crete, Perugia, Salerno

(with between nearly one quarter to one tenth of mentions, approximately), with at last many items, triple, double, or single.

Some absences are noteworthy:

  • in Tuscany, Lucca (a town of tricksters, in Dante’s Divine Comedy, Hell, canto XXI)

  • in the Emilia Romagna region, Parma, Piacenza and Reggio Emilia

  • in Veneto, Padua and Vicenza (besides Trieste in the Venezia Giulia region)

  • in Lombardy, Bergamo, Como, Crema, Cremona, Lodi, Monza, and Mantova (that is, only Brescia, Milan, and Pavia)

  • in Piedmont, all but Monferrato, Asti, and Saluzzo (and especially Turin)

  • in Apulia, Bari, Lecce, and Taranto

  • in Sicily, Catania, Enna, and Syracuse

Other facts are remarkable:

  • Boccaccio’s geography is limited to Europe, the Mediterranean Sea, North Africa, and Near East, going into Asia and reaching Armenia, Persia, India, and China, though making no mention of Tibet, or Siam (today’s Thailand), or Japan, which are in turn mentioned by Polo

  • Africa (Saharan and Sub-Saharan) is never cited, despite the growing concern for its circumnavigation, as evidenced by the unsuccessful journey of the Vivaldi brothers from Genoa as well as by the imaginary journey of Dante’s Ulysses (Comedy, The Hell, canto XXVI)

  • In Europe, no mention for German and for Slavonic worlds (in that age, only Scandinavia and Russia could be regarded as marginal): of its peripheral areas, all ports of British Isles are recorded, as is Ireland, though not Portugal

  • In the Mediterranean Sea, almost all its islands are mentioned, though not Elba (nor any other small islands of Tuscany), nor even Corsica, despite these being the nearest to Florence and TuscanyFootnote 2

  • Two places are purely imaginary: the Terre di Menzogna (the Lands of Lies) and the Lands of Berlinzone

  • Three novels deal with Hell,Footnote 3 Purgatory, and Paradise (along the lines of the cantos in the Divine Comedy,Footnote 4 and the garden in the Decameron Cornice resembles the Paradise on Earth depicted in Dante’s masterpiece

  • Nothing is said about travels to the MoonFootnote 5

Here follow some images showing

the frequency diagram of the so-called places of the heart (Figs. 1 and 2)

  • the geographical location of the said places of the heart in Italy (in two different depictions, natural and anamorphicFootnote 6) (Fig. 3a, b)

  • the location of the same places of the heart in Boccaccio’s world (with both modes of representation) (Figs. 3a and 4b).

    Fig. 1
    figure 1

    The places of the heart in Italy of the Decameron: a frequency diagram

    Full size image
    Fig. 2
    figure 2

    The places of the heart in Italy plotted in function of the kilometric distance from Florence

    Full size image
    Fig. 3
    figure 3

    a The places of the heart in Italy of the Decameron: a classical thematic map. b The places of the heart in Italy of the Decameron: an anamorphic chart

    Full size image
    Fig. 4
    figure 4

    a The places of the heart in Boccaccio’s world: a classical thematic map. b The places of the heart in Boccaccio’s world: an anamorphic chart

    Full size image

As far as Boccaccio’s world is concerned then, it is confined, apart from India and China, solely to a part of Europe, to the Mediterranean Sea, and to North Africa and the Near East. For this reason too, a normal map (with its meridians and parallels) would include large areas with no involvement in the novels (since only Italy, France, and a few other countries are spoken of, the overall result would make the map difficult to read) (Figs. 3a and 4a). Notice how in the anamorphic representation some Italian regions, e.g., Sardinia, Apulia, and Calabria, are greatly reduced. This type of cartographic representation immediately highlights that in these regions are present only a few places of the heart or none.

When, however, all the territories (or proper groupings of the same, if too small singularly) are given at a unitary (and non-zero) weight, and one unit is added to all counties involved, so as not to distort the result, the resulting sum gives an anamorphic chart much less deformed than the natural map and hence much easier to read. Moreover, this procedure does not alter data, but simply transfers the digits representing them, that is a shift of origin (a standard procedure, together with the change of scale, in cartography) (Figs. 3b and 4b). Notice how the anamorphic representation shows the Italian areas more warped than the rest of the Mediterranean zones because of the same consideration of the previous figure. Indeed, the characteristic deformation of the anamorphic representation strictly depends on the involved geographic zone.

Further proof of the non-randomness of the places of the heart is provided by Boccaccio himself, as seen if we examine the giornate (days), in the columns, and the order of narration of the novels, in the rows, by the ten storytellers, whose names—1 to 10—are in alphabetical order (Table 1 and Table 2). Indeed, connection analysis, performed by calculating the contingencies and Bonferroni indices, by itself shows the almost complete independence among giornate (days of tales) and the order of narration. It must be borne in mind, moreover, that the contingencies and Bonferroni indices merely serve to reject independence, computing the differences between double frequencies and the product of corresponding marginal frequencies (equality of these values is the condition of independence). Elementary computation gives rather low values for all Bonferroni’s indices (unilateral and bilateral).Footnote 7

Table 1 Table of speakers by day (columns) and order of narration
Full size table
Table 2 The same table with numerical values (according to the alphabetical order of the names of the speakers)
Full size table

The travel routes

The list of travel routes will show the basic unity of Boccaccio’s world (Italian and otherwise), detecting in it a unique cluster, albeit, to varying degrees, a jagged one.

1st day

Tale

Route

1

A: Prato–Burgundy; B: Burgundy–Tuscany

2

Paris–Rome–Paris

5

France–Monferrato–Genoa

9

Gascony–The Holy Land–Cyprus

2nd day

Tale

Route

1

Florence–Treviso–Florence

2

Asti–Bologna–Ferrara–Asti

3

A: Florence–London–Florence; B: Florence–London–Rome–Florence–London–Florence

4

Ravello–Cyprus–Constantinople–Cefalonia–Corfù–Trani–Ravello

5

Perugia–Rome–Perugia

6

A: Palermo–Lipari–Ponza–Lunigiana–Lerici–Palermo; B: Palermo–Lipari–Ponza–Genoa–Lunigiana–Lerici–Palermo; C: Palermo–Lipari–Ponza–Lerici–Palermo

7

Alexandria–Majorca–Peloponnesus–Athens–Egina–Chios–Rhodes–Cyprus–Famagosta–Alexandria–Gharb

8

Paris–Calais–London–Weles–Ireland–Weles–London–Paris

9

A: Genoa–Paris–Genoa–Alexandria–Genoa; B: Genoa–Alexandria–Genoa

10

A: Pisa–Monaco; B: Pisa–Monaco–Pisa

3rd day

Tale

Route

1

Lamporecchio (province of Pistoia)–Florence–Lamporecchio (province of Pistoia)

3

Florence–Genoa–Florence

4

Paris–Florence

5

Pistoia–Milan–Pistoia

7

Florence–Ancona–Cyprus–Ancona–Florence

9

A: Rossillon (in France)–Paris–Florence; B: Rossillon (in France)–Paris–Rossillon (in France)–Florence

10

Capsa (in Tunisia)–deserts of Thebais (in Egypt)–Capsa (in Tunisia)

4th day

Tale

Route

2

Imola–Venice

3

A: Marseilles–Crete; B: Marseilles–Crete–Rhodes

4

A: Messina–Ustica–Messina; B: Tunisia–Ustica

5

Messina–Naples

8

Florence–Paris–Florence

10

Salerno–Amalfi–Salerno

5th day

Tale

Route

1

A: Cyprus–Rhodes–Crete–Cyprus; B: Rhodes–Crete–Rhodes

2

A: Lipari–Tunisia–Lipari; B: Lipari–Susa (in Tunisia)–Tunisia–Lipari

3

Rome–Anagni–Rome

5

Fano–Faenza

6

A: Ischia–Palermo; B: Procida–Ischia–Palermo

7

A: Armenia–Trapani–Armenia; B: Armenia–Trapani–Rome–Trapani–Armenia; C: Trapani–Armenia

8

A: Ravenna–Classe (province of Ravenna); B: The Hell–Classe (province of Ravenna)

6th day

Tale

Route

2

Rome–Florence

5

Mugello–Florence

10

Venice–Florence–(imaginary) countries of Truffia, Buffia, and Menzogna–Florence

7th day

Tale

Route

1

Florence–Fiesole

7

Paris–Bologna

10

Siena–The Hell–Siena

8th day

Tale

Route

1

Milan–Genoa–Milan

7

Paris–Florence

10

Florence–Salerno–Palermo–Naples–Palermo–Florence–Ferrara

9th day

Tale

Route

4

A: Marca d’Ancona–Siena–Buonconvento (province of Siena)–Siena; B: Siena–Buonconvento (province of Siena)–Corsignano (hamlet of Pienza)

9

Laiazzo (today Ayas in Turkey)–Antiochia–Jerusalem–Antiochia–Laiazzo (today Ayas in Turkey)

10

Barletta–Bitonto

10th day

Tale

Route

1

Spain–Tuscany

2

A: Radicofani (province of Siena)–Rome; B: Cluny–Rome–Radicofani (province of Siena)–Rome

4

Bologna–Modena–Bologna–Modena–Bologna

6

A: Florence–Castellammare di Stabia; B: Castellammare di Stabia–Naples–Apulia

8

Rome–Athens–Rome

9

A: Alexandria–Milan–Pavia–Alexandria; B: Pavia–Genoa–Acri–Alexandria–Pavia (by magics)

10

Saluzzo–Bologna–Saluzzo

In the images, a single cluster can be recognized, even if variously indented. Switching from the connection matrix (Fig. 5) (putting places in alphabetical order, while keeping Florence at the bottom of the list and dissecting it, in order to highlight its centrality) to the reordered one (Fig. 6) (by graph theory), having recognized some regional affiliations (Florence and Pisa in Tuscany, Fano in the Marche region, Bitonto in Apulia, Jerusalem in the Holy Land, and the deserts of Thebaid in Egypt), the clearly resulting sole cluster representing Boccaccio’s world stands out.

Fig. 5
figure 5

Connection (alphabetical) matrix

Full size image
Fig. 6
figure 6

Connection reordered matrix

Full size image

Beware: the images, output of a graph computational program, are to be read in a qualitative way, in order to show the substantial unity of Boccaccio’s world. The places are labeled according to (Italian) alphabetical order form Acri (no. 1) to Venice (no. 90). Figure 5 shows the correspondent connection matrixFootnote 8, and Fig. 6 represents the same matrix reordered using an ordering algorithm of Cuthill-McKee type for sparse matricesFootnote 9 (George and Liu 1981).

Final remarks

The 700th year from the birth of Boccaccio was a useful pretext to investigate how Geomatics could approach the study of a humanistic topic. Since Decameron novels deal with place, itineraries, and travels, they proved to be an ideal study case to verify the hybridation among Geomatics and Literature. Thematic maps show a synthetic information about the travels described in the literary work, and they give in a clear image the amplitude of geography of Boccaccio’s novels (i.e., the Mediterranean area).

Moreover, the anamorphic description of the travels allows to give with the geographic information also the weight of the information itself. A future work could concern the travel times of the analyzed travel routes.

The authors hope that this could be one of many other “mixed studies” among science not similar but, in some way, complementary.

Our analysis can be summarized in the words of (Branca 1992): “a new World Atlas opens from novel to novel.” But the center of these worlds is always Florence; moreover, for some reasons, Eastern Europe, beyond Constantinople, is quite ignored.