Time Distribution, Popularity, Diversity and Productivity of the Iconography of Venus in the Low Countries, France and Italy

8/12/2019 Time Distribution, Popularity, Diversity and Productivity of the Iconography of Venus in the Low Countries, France

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Research Paper 5 in the series Quantitative Iconography of Venus

Time distribution, popularity, diversity and

productivity of the iconography of Venus

of the Low Countries, France and Italy

byK. Bender

independent researcher

[email protected]

January 2011

Abstract

1. Introduction2. The data sets

3. Time distribution of artworks and artists4. Popularity and diversity of topics5. Productivity of artists6. Conclusions7. References

Abstract

The paper analyses quantitatively three large data sets of artworks (7473 in total) and their

artists (2374 in total) of the Low Countries, of France and of Italy from the 16th

century to the

present time. These data sets are convenient samples, compiled from available sources and

published in topical catalogues, where the artworks - sculptures, reliefs, paintings, frescoes,

drawings, prints and illustrations depicting Venus - are categorized into 18 main topicsaccording to her classical companions, her attributes and her allegories. The time series analysis

shows a clear shift of the peak production from the 16th

century in Italy to the 17th

century in the

Low Countries and the 18th

century in France. Topics Venus and Cupid and Venus and

Adonis are among the most popular ones in Italy and France during different periods, butVenus and Adonisis definitely the most popular topic in the Low Countries from 1600 to 1799.

Also the diversity of topics is different: there is a lower diversity in the Low Countries than in

France, with an intermediate value in Italy. A ranking of the ten most productive artists in each

region reveals that the artists of the Low Countries were more productive than their colleagues

in France, and those in France more than the artists in Italy. The productivity of artists in this

case study follows exactly the formula of Lotka, known as the law of scientific productivity:

60% of all artists in the samples create only one Venus-artwork. A plausible explanation is the

principle success breeds success.


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1. Introduction

Within the series of the Iconography of Venus from the Middle Ages to Modern Times,

Volume 3.1 The Venus of the Low Countrieswas recently published (Bender, 2010). It is

a Topical Catalogue of sculptures, reliefs, paintings, frescoes, drawings, prints andillustrations of identified artists of the Low Countries, which lists chronologically, in 18 main

topics, 2636 artworks of 728 artists. The methodology of the compilation is explained in the

Guideline of the catalogue and is the same applied to Volume 1.1 The Italian Venus (1840artworks of 649 Italian artists) and Volume 2.1 The French Venus (2997 artworks of 977

French artists) (Bender, 2007 & 2009a). The goal of this paper is to compare results of thequantitative analysis of the three catalogues, following the approach of Research Papers 1 to4 (Bender, 2008a, 2008b, 2009b and 2009c), which analysed or compared the two former

catalogues. The data sets, extracted from the catalogues, are not random' samples of the

indefinite number of artworks (the population) with the subject Venus created by anunknown number of artists, but convenient samples, biased by the information sources

available and consulted. However, the large size of the compilation is judged to yield fair

samples, allowing for a thoughtful application of non-parametric statistical techniques (see

e.g. Siegel, 1956). This means that the author assumes that larger or other samples would notyield statistically different results. Meta-analysis could be helpful to clarify this assumption.

2. The data sets

The full data set of The Venus of the Low Countries (short written: VLC) is presented in

contingency Table 1. For reasons of harmonization of all data sets, artworks created before

1500 and after 1999, which were compiled in the catalogue, are not included in Table 2,comparable to Tables 3 and 4 containing the harmonized data sets of The French Venus and

The Italian Venus (short written FV and IV), respectively. The tables list the number of

artworks (also called frequencies f) per period of 50 years from 1500-1549 to 1950-1999,distributed among 18 topics. Marginal totals and their percentages p for each topic and for

each period as well as the grand total are given. At the bottom of the tables are also given the

estimated number of artists with assumed maximal productivity in the period considered.

Issues involving the categorizing and observation of the artworks and estimated activity ofartists have been discussed in Research Paper 4 (Bender, 2009b). For the purpose of this

paper we summarize:

The categorizing in topics leads to a nominal scale:the artworks are grouped on thebasis of shared characteristics, which are called topics. This categorization is

mutually exclusive and exhaustive: each artwork belongs to only one topic and there

are no artworks left out. By its nature the nominal scale limits the possibilities of astatistical analysis of the data. The order of the topics does not matter.

The time scale is an interval scale and while the choice of a period of 50 years isconvenient, it is arbitrary; it can be justified by the crude approximate dates of

creation of many artworks and the presumably maximum length of activity of an

artist.


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Table 1. Full data set with topics and periods

of the Venus of the Low Countries.

TOPICS / PERIODS 1450- 1500- 1550- 1600- 1650- 1700- 1750- 1800- 1850- 1900- 1950- 2000- TOTAL p%

1 Allegories of Venus/Planet 5 25 69 40 7 3 15 2 1 167 6,33

2Apotheosis/...Worship of

Venus 7 30 22 13 3 4 4 3 1 87 3,3

3 Attributes of Venus 4 12 18 12 6 1 2 1 2 6 64 2,43

4Birth of Venus/...Venus

Marina 3 14 30 12 8 4 3 4 14 9 2 103 3,91

5Toilet/Bath/Venus

crouching9 21 22 6 3 3 3 1 68 2,58

6 Venus and Adonis 1 56 162 143 73 14 6 5 460 17,45

7Venus and Anchises,

Aeneas 2 9 14 10 2 3 1 41 1,56

8 Venus and Anteros/Cupid 16 48 103 75 39 12 17 7 1 1 1 320 12,14

9 Venus and Cupids 3 3 16 11 4 7 1 45 1,71

10Venus and Judgement of

Paris3 11 62 121 47 17 3 8 5 2 6 285 10,81

11 Venus and Mars 26 47 97 37 18 7 5 1 238 9,03

12Venus and other Gods,

etc 1 4 83 112 44 25 11 2 3 3 2 290 11

13 Venus and Psyche 18 9 4 1 32 1,21

14 Venus and Satyrs 4 10 27 14 8 1 1 65 2,47

15 Venus and Vulcan 6 8 46 23 5 3 1 2 94 3,57

16Venus asleep/...with the

Musician 11 25 12 10 1 1 3 11 1 75 2,84

17 Venus statues 10 7 26 10 1 6 2 6 27 95 3,60

18 Venus unaccompanied 1 19 18 17 2 5 6 5 9 16 9 107 4,06

TOTALS 4 84 444 920 575 262 81 68 59 56 65 18 2636 100

% 0,15 3,19 16,84 34,90 21,81 9,94 3,07 2,58 2,24 2,12 2,46 0,68 100

Number of Artists 4 39 94 203 145 62 37 33 27 39 40 5 728

% 0,55 5,36 12,91 27,88 19,92 8,52 5,08 4,53 3,71 5,36 5,49 0,69 100


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Table 2. Harmonized data set with topics and periods

of the Venus of the Low Countries.

TOPICS / PERIODS 1500-49

1550-99

1600-49

1650-99

1700-49

1750-99

1800-49

1850-99

1900-49

1950-99

TOTAL p%


2 Apotheosis/...Worship of Venus 7 30 22 13 3 4 4 3 1 87 3,333 Attributes of Venus 4 12 18 12 6 1 2 1 2 58 2,22

4 Birth of Venus/...Venus Marina 3 14 30 12 8 4 3 4 14 9 101 3,86

5 Toilet/Bath/Venus crouching 9 21 22 6 3 3 3 1 68 2,60

6 Venus and Adonis 1 56 162 143 73 14 6 5 46017,5

7 Venus and Anchises, Aeneas 2 9 14 10 2 3 1 41 1,57

8 Venus and Anteros/Cupid 16 48 103 75 39 12 17 7 1 1 31912,2

9 Venus and Cupids 3 3 16 11 4 7 1 45 1,72

10 Venus and Judgement of Paris 11 62 121 47 17 3 8 5 2 6 28210,7

11 Venus and Mars 26 47 97 37 18 7 5 1 238 9,10

12 Venus and other Gods, etc 4 83 112 44 25 11 2 3 3 2 28911,0

13 Venus and Psyche 18 9 4 1 32 1,22

14 Venus and Satyrs 4 10 27 14 8 1 1 65 2,49

15 Venus and Vulcan 6 8 46 23 5 3 1 2 94 3,60

16 Venus asleep/... with Musician 11 25 12 10 1 1 3 11 1 75 2,87

17 Venus statues 10 7 26 10 1 6 2 6 27 95 3,63

18 Venus unaccompanied 1 19 18 17 2 5 6 5 9 16 98 3,75

TOTALS 84 444 920 575 262 81 68 59 56 65 2614 100

% 3,21 16,98 35,20 22,00 10,02 3,10 2,60 2,26 2,14 2,49 100

Number of artists 39 94 203 145 62 37 33 27 39 40 719

% 5,42 13,07 28,23 20,17 8,62 5,15 4,59 3,76 5,42 5,56 100


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Table 3. Harmonized data set with topics and periods

of the French Venus.


1550-99

1600-49

1650-99

1700-49

1750-99

1800-49

1850-99

1900-49

1950-99

TOTAL p%


2 Apotheosis/...Worship of Venus 4 3 2 18 50 19 16 4 116 4,08

3 Attributes of Venus 1 2 2 6 5 44 9 10 11 4 943,31

4 Birth of Venus/...Venus Marina 1 12 21 41 68 33 48 71 21 316 11,1

5 Toilet/Bath/Venus crouching 3 8 6 37 66 24 40 12 3 199 7,00

6 Venus and Adonis 9 23 26 37 52 30 16 5 198 6,97


8 Venus and Anteros/Cupid 8 7 20 77 146 49 65 24 396 13,9

9 Venus and Cupids 1 1 8 13 37 10 15 3 88 3,10

10 Venus and Judgement of Paris 3 6 18 12 14 36 28 20 37 5 182 6,30

11 Venus and Mars 3 9 8 23 25 34 31 2 135 4,75

12 Venus and other Gods, etc 1 5 13 19 54 81 39 15 8 1 236 8,30

13 Venus and Psyche 8 4 26 13 12 7 6 76 2,67

14 Venus and Satyrs 6 4 8 6 4 2 2 32 1,1315 Venus and Vulcan 6 12 43 33 8 2 2 106 3,73

16 Venus asleep/...with the Musician 2 5 5 13 34 14 7 8 2 90 3,17

17 Venus statues 0 1 4 17 22 17 23 31 25 30 170 5,98


TOTALS 9 60 137 210 483 785 383 327 286 162 2842 100

% 0,317 2,11 4,82 7,39 16,0 27,6 13,5 11,5 10,1 5,70 100

Number of Artists 9 21 43 66 108 198 150 156 92 65 908

% 0,99 2,31 4,74 7,27 11,89 21,81 16,52 17,18 10,13 7,16 100


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Table 4. Harmonized data set with topics and periods of the Italian Venus.


1550-99

1600-49

1650-99

1700-49

1750-99

1800-49

1850-99

1900-49

1950-99

TOTAL p %

1 Allegories of Venus/Planet 9 7 9 2 2 2 3 1 35 1,97

2 Apotheosis/...Worship of Venus 7 4 3 7 8 11 6 3 2 51 2,87

3 Attributes of Venus 20 13 3 4 7 4 4 2 57 3,21

4 Birth of Venus/...Venus Marina 15 18 13 11 5 5 4 1 9 11 92 5,18

5 Toilet/Bath/Venus crouching 6 24 20 9 0 7 2 1 2 71 4,00

6 Venus and Adonis 22 62 53 31 39 26 4 1 1 239 13,5


8 Venus and Anteros/Cupid 60 74 56 29 30 18 22 5 2 296 16,7

9 Venus and Cupids 13 5 5 12 8 9 52 2,93

10 Venus and Judgement of Paris 26 25 15 16 13 7 4 3 3 5 117 6,59

11 Venus and Mars 29 35 19 11 11 12 5 3 125 7,04

12 Venus and other Gods, etc 20 27 16 13 12 24 11 3 126 7,10

13 Venus and Psyche 40 2 1 4 6 2 55 3,10

14 Venus and Satyrs 2 11 8 9 16 5 51 2,87

15 Venus and Vulcan 22 15 13 11 17 10 290 5,07

16 Venus asleep/... with Musician 10 13 5 3 1 3 3 2 4 44 2,45

17 Venus statues 12 9 5 4 4 5 14 6 5 5 69 3,89


TOTALS 355 371 268 195 187 164 91 31 40 73 1775 100

% 20,0 20,9 15,1 10,0 10,5 9,23 5,13 1,75 2,25 4,11 100

Number of artists 95 91 82 62 54 61 41 23 37 45 591

% 16,07 15,40 13,87 10,49 9,14 10,32 6,94 3,89 6,26 7,61 100

3.Time distribution of artworks and artists

Fig.1 shows the column graph of total frequencies of artworks and estimated number of

artists in the Low Countries (VLC) in each period of 50 years as given in Table 1. The

trendlines are the moving averages calculated for two periods. This figure can be comparedwith Figs. 1 & 2 of Research Paper 3 (Bender, 2008b), but it is more interesting to present

together all the relative frequencies (percentages orproportional frequencies p) of artworks

as given in the harmonized data of Tables 2, 3 and 4 (Fig.2). The trendlines show clearly the

shift of the peak production in the 16th

century in Italy (IV) to the 17th

century in the Low


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Countries (VLC) and to the 18th century in France (FV). A similar trend is found for theestimated relative numbers of artists in the three regions (Fig.3). For both variables (artworks

and artists) the peak is much higher and sharper in the Low Countries than in France or Italy.

The relative number of artists in the Low Countries reaches its maximum value of 28% in1600-49 when this variable was only 5% in France and 14% in Italy. But 150 years later, the

Low Countries had a value as low as 5%, while France had its maximum with 22%. Fig.4

with the cumulative relative frequencies of artworks per period is even more illustrative forthe time distribution among the three regions: the Low Countries follow quiteclosely Italy

and both reach 55% of their total production in period 1600-49, while France reaches this

value only in period 1750-99.

0

100

200

300

400

500

600

700

800

900

1000

1450-

99

1500-

49

1550-

99

1600-

49

1650-

99

1700-

49

1750-

99

1800-

49

1850-

99

1900-

49

1950-

99

2000-

10

Time periods

Numbers

Artworks VLC

Artists VLCTrendline artworks

Trendline artists

Fig.1 Absolute frequencies of artworks and estimated number of artists

in periods of 50 years for Venus of the Low Countries (VLC).


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0

5

10

15

20

25

30

35

40

1500-49 1550-99 1600-49 1650-99 1700-49 1750-99 1800-49 1850-99 1900-49 1950-99

Time periods

Relativefreque

ncies

% VLC

% FV% IV

Trendline VLC

Trendline FV

Trendline IV

Fig.2 Relative frequencies of artworks in periods of 50 years of the iconography of

Venus in the Low Countries (VLC), in France (FV) and in Italy (IV).


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0

5

10

15

20

25

30

1500-

49

1550-

99

1600-

49

1650-

99

1700-

49

1750-

99

1800-

49

1850-

99

1900-

49

1950-

99

Time periods

Relativenumber % VLC

% FV

% IVTrendline VLC

Trendline FV

Trendline IV

Fig.3 Relative number of artists in periods of 50 years inthe iconography of Venus inthe Low Countries (VLC), in France (FV) and in Italy (IV).


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0

10

20

30

40

50

60

70

80

90

100

1500-49 1550-99 1600-49 1650-99 1700-49 1750-99 1800-49 1850-99 1900-49 1950-99

Time periods

Cumulativerelative

frequencies

cum%VLCcum%FV

cum%IV

Fig.4 Cumulative relative frequencies of Venus artworks per period

in the Low Countries (VLC), in France (FV) and in Italy (IV).

4. Popularity and diversity of topics

The popularity of topics among the three regions can be visualized by ranking the relativefrequencies from high to low of the Venus of the Low Countries (VLC) and by comparing

this ranking to the relative frequencies of the French Venus (FV) and the Italian Venus

(IV) (Fig.5). The differences are better highlighted when plotting the cumulative relativefrequencies (Fig.6)

1. VLC reaches a production of 52% with 4 topics: 6.Adonis, 8.Cupids,

12.Others and 10.Paris. The French Venus reaches only 43% with its 4 major topics:

8.Cupid, 4.Birth, 18.Unaccompanied and 12.Othersand the Italian Venus has 46% for its 4

1The use of the line diagram is for easy visual understanding only and does not imply an interval-scale of the

variable topics.


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major topics: 8.Cupid, 6.Adonis, 18.Unaccompaniedand 12.Others. In other words: VLC hasa lower diversity than FV, with IV in an intermediate position: a straight line from top-left

(100%) to bottom-right in Fig. 6 would mean an equal distribution among all topics

or total uniformity.

0

2

4

6

8

10

12

14

16

18

20

6.Ad

onis

8.Cu

pid

12.Others

10.Paris

11.Mars

1.Alleg

ories

4.Bi

rth

18.Unacc

.

17.Statues

15.Vulc

an

2.Ap

othe

osis

16.Asle

ep

5.To

ilet

14.Satyrs

3.Attribu

tes

9.Cu

pids

7.Ae

neas

13.Psyche

Topics

Relativefrequencies

VLC

FV

IV

Fig.5 Relative frequencies of topics ranked from high to lowfor the Venus of the Low Countries (VLC)

compared to those of the French Venus (FV) and the Italian Venus (IV).


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0

10

20

30

40

50

60

70

80

90

100

6.Adonis

8.Cupid

12.Oth

ers

10.Paris

11.Mars

1.Allego

ries

4.Birth

18.Una

cc.

17.Stat

ues

15.Vul

can

2.Ap

otheosis

16.Asl

eep

5.To

ilet

14.Sa

tyrs

3.Attribu

tes

9.Cupids

7.Aen

eas

13.Psy

che

Topics

Cumulativerela

tivefrequencies

VLC

FVIV

Fig.6 Cumulative relative frequencies of topics,

ranked from high to low for the Venus of the Low Countries (VLC)

and compared to the French Venus (FV) and the Italian Venus (IV).

To analyse in detail the change in popularity, like in Research Paper 4, the popularity ratio:

the ratio of the frequency f of artworks of each topic to the frequency of the mode(highest frequency) is defined.Table 5 lists the observed and calculated data for the period

1500-18992and Fig.7 shows graphically the calculated popularity ratios.

2A comparison beyond 1899 is unavailing because there are too many zero frequencies for topics in the 20 th

century.


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Table 5. Frequenciesfand popularity ratiosof topics for the whole period 1500-1899

of the Venus of the Low Countries (VLC), of France (FV) and of Italy (IV).

VLC FV IVTopics

f ratio f ratio f ratio

1.Allegories 164 0,36 43 0,12 35 0,12

2.Apotheosis 83 0,18 112 0,3 49 0,17

3.Attributes 56 0,12 79 0,21 55 0,19

4.Birth 78 0,17 224 0,6 72 0,24

5.Toilet 67 0,15 184 0,49 69 0,236.Adonis 460 1 193 0,52 238 0,81

7.Aeneas 40 0,09 81 0,22 45 0,15

8.Cupid 317 0,69 372 1 294 1

9.Cupids 45 0,1 85 0,23 52 0,18

10.Paris 274 0,6 140 0,38 109 0,37

11.Mars 237 0,52 133 0,36 122 0,41

12.Others 284 0,62 227 0,61 126 0,43

13.Psyche 32 0,07 70 0,19 55 0,19

14.Satyrs 64 0,14 30 0,08 51 0,17

15.Vulcan 94 0,2 104 0,28 90 0,31

16.Asleep 63 0,14 80 0,22 38 0,1317.Statues 62 0,13 115 0,31 59 0,2

18.Unaccom. 73 0,16 125 0,34 103 0,35

Total 2493 2397 1662

Some striking differences of popularity are summarized:

o Topic 8.Cupid is less popular in the Low Countries, where Topic 6.Adonis isdefinitely the most popular topic;

o Topic 4.Birth of Venusand Topic 5.Toilet of Venusare much more popular in France(topic 4 includes titles such as Venus on the waves, Venus on the waters, etc.);

o Topic 10.Judgement of Paris scores higher in the Low Countries, partly due to thepopularity of the preparatory event The marriage of Peleus and Thetis (51 works ofa total of 274, see Bender, 2010, pp.91-93);

o Topic 12.Venus with Others is popular in both the Low Countries and France, but inthe former region Venus with Bacchus and Ceresis dominant in this topic (121 worksof a total of 284, see Bender, 2010, pp.115-122), while in France Graces-Nymphsand

Mercuryscore higher;

o Topic 1.Allegories is more popular in the Low Countries, while Topic 18.Venusunaccompanied scores higher in France and Italy.


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0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1.Alleg

ories

2.Ap

otheosis

3.Attrib

utes

4.Birth

5.T

oilet

6.Ad

onis

7.Aeneas

8.C

upid

9.Cu

pids

10.Pa

ris

11.Mars

12.Others

13.Psyche

14.Satyrs

15.Vulc

an

16.Asle

ep

17.Statues

18.Unac

com

.

Topics

Popula

rityratio

VLC

FV

IV

Fig.7 Comparison of popularity ratios of topics

among the Venus of the Low Countries (VLC), of France (FV) and of Italy (IV)

for the whole period 1500-1899

A further analysis of the changing popularity with time is made for Topics 6.Adonis and

8.Cupid. In each period the popularity ratios of these topics are calculated using the mode

(the highest frequency) of the period. Fig. 8 shows that Topic 6.Adoniswas very popular fromperiod 1550-99 onwards till the end of the 17

thcentury in all regions and still till the end of

the 18th

century in both Italy and the Low Countries. Fig. 9 illustrates that Topic 8.Cupidwasseldom very popular in the Low Countries. The conclusion is that Topic 6.Venus and Adonis

3

3The myth ofVenus and Adonisis told by Ovidius in Book 10 of his Metamorphoses. This work was well-

known from the Middle Ages onwards, edited in numerous ways, mostly illustrated, and translated in many

European languages. Some editions were conceived as a kind of dictionary who is who in mythology. Sluijter

(1986) counts 24 editions or reprints in Dutch language from 1566 till 1679. Many of these editions were

specifically targeted towards artists for their instruction. Sluijter also discusses in depth the allegory and the

different possible meanings given to the pictorial representation of the myth. There is no doubt that the large

production of the topic was tailored to meet the request of the open market.


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and Topic 8.Venus and Cupidshare together the top-popularity over the whole period 1555-1899 in the three regions, but with Topic 6.Venus and Adonisdefinitely most popular in the

Low Countries in the 17th

and 18th

centuries.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1500-49 1550-99 1600-49 1650-99 1700-49 1750-99 1800-49 1850-99

Time periods

Popularity ratio

6.Adonis VLC

6.Adonis FV

6.Adonis IV

Fig. 8 Popularity ratios of Topic 6.Venus and Adonisversus time periods



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0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1500-49 1550-99 1600-49 1650-99 1700-49 1750-99 1800-49 1850-99

Time periods

Popularityratio

8.Cupid VLC

8.Cupid FV

8.Cupid IV

Fig. 9 Popularity ratios of Topic 8.Venus and Cupidversus time periods


Four measures of diversity, applicable to nominal scales or categories (Weisberg, 1992), were

calculated in Research Paper 4 (Bender 2009b, p.17-18 and Table 4) and are repeated inTable 6 for VLC and compared to the values calculated for FV and IV in the whole period1500-1999 and the short period 1900-1999 where frequencies are less or zero for several

topics.

a. Variation ratioV = 1-fmode/N

where fmodeis the highest frequency of all topics and N is the grand total.V is 0 if all objects are in one category or topic (f = N) and is 1-N/K for uniform distribution

and thus approaches 1 if the total number of topics K becomes very large. V is easy to

compute but does not take into account the full distribution of categories. V is lowest for


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VLC in the whole period since its mode frequency is highest, but VLC has a higher diversityin period 1900-1999 compared to FV and IV.

b. Index of diversity

D = 1-p12-p2

2-p3

2-pK

2= 1-pk

2

where p is the proportional or relative frequency and = sum for all k.

This index shows the degree of concentration of the larger categories, because squaring the

proportion p gives emphasis to the larger values. Or one could call it also a measure of

heterogeneity. D is 0 if all objects are in one category (zero heterogeneity) or approaches 1

for K very large. The values of D are similar as those of V in both periods.

c. Index of qualitative variation

IQV = D/[(K-1)/K]

IQV has the advantage to apply for comparison between samples of different number K of

topics. This is the case in period 1900-1999 and the values confirm the results obtained with

V or D.

d. Standardized uncertainty or entropy

J = - pklog(pk)/log(K)

This measure of spread, also called 'efficiency', is based on information theory and gauges

how much information is conveyed by the distribution. There is no uncertainty if all objectsfall into one category (J = 0 for p = 1), but the greater the spread the more uncertainty or the

higher the entropy, with J=1 for total uniformity. Or in other words: there is less entropy if

the distribution is more non-uniform and uncertainty is highest when all possible 'events' areequiprobable. The uncertainty or entropy J has a stronger theoretical basis and is preferred in

literature. All calculated values of J confirm the results of the other measures.

In other words: the simplest measure of diversity gives the same information as the morecomplex calculations: for the whole period 1500-1999 VLC is less diverse than FV, with IV

in an intermediate position; but for the period 1900-1999 VLC is more diverse than FV andIV has the lowest diversity. The latter result, however, may be biased given the small samples

of VLC and IV.


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Table 6. Measures of diversity of the iconography of Venus

of the Low Countries (VLC), of France (FV) and of Italy (IV).

VLC FV IVDescription / Periods

1500-

19991900-

1999

1500-

19991900-

1999

1500-

19991900-

1999

grand total N 2614 121 2842 448 1775 113

number of topics K 18 14 18 17 18 12

mode Topic 6 Topic 17 Topic 8 Topic 18 Topic 8 Topic 18

frequency fmode 460 33 396 149 296 55

variation ratio V 0.824 0.727 0.861 0.667 0.833 0.513

index of diversity D 0.908 0.828 0.924 0.816 0.917 0.714

index of qualitative variation

IQV 0.961 0.892 0.979 0.867 0.971 0.779

standardized uncertainty

or entropy J0.901 0.771 0.941 0.733 0.930 0.688

5. Productivity of artists

The average productivity of the artists can be simply expressed as the grand total N ofartworks to the grand total number of artists. Thus 2636/728 = 3,62 in the Low Countries,

2997/977 = 3,06 in France and 1840/649 = 2,85 in Italy or using the harmonized data sets ofTables 2, 3 and 4: 2614/719 = 3,63 , 2842/908 = 3,13 and 1775/591 = 3,00 respectively.

Another way is to calculate the mean productivity per period of 50 years and derive the meanvalue for all periods: 2,91 for VLC, 2,89 for FV and 2,66 for IV (Fig. 10). Given the large

variation of productivity per period, these overall means in the three regions are not

significant different. Of more interest is the ranking of the ten most productive artists in eachregion: Table 7 illustrates that the productivity of the top-ten artists in the Low Countries was

definitely higher than in France and Italy and seven more artists of the Low Countries with a

production higher than 23 works could be added to the list. The ranking would slightlychange when the level of identification of the works is considered (see Research Paper 2,

Table 2 for the Italian Venus, in Bender, 2008b).


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1

1,5

2

2,5

3

3,5

4

4,5

5

1500-

49

1550-

99

1600-

49

1650-

99

1700-

49

1750-

99

1800-

49

1850-

99

1900-

49

1950-

99

Time periods

Meanproductivityperartist

VLC mean=2,91

FV mean=2,89

IV mean=2,66

Fig. 10 Mean productivity per artist



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Table 7. Ranking of the ten most productive artists in each region:

in the Low Countries (VLC), in France (IV) and in Italy (IV)

(f= number of artworks; r= rank within the region)

VLC FV IVName Period Rank

f r f r f r

1. BOUCHER, Franois 1703-1770 100 273 100

2. RUBENS, Peter Paul 1577-1640 36 98 100

3. ARMAN, F. 1928-2003 26 71 26

4. VAN HAARLEM, Cornelis C. 1562-1638 23 64 65

5. NATOIRE, Charles Joseph 1700-1777 21 58 216. GOLTZIUS, Hendrick 1558-1617 21 57 58

7. DE LAIRESSE, Gerard 1641-1711 20 55 56

8. RODIN, Auguste 1840-1917 20 54 20

9. SPRANGER, Bartholomeus 1546-1611 20 54 55

10. BLOEMAERT, Abraham 1566-1651 18 49 50

11. VAN BALEN (I), Hendrick 1572-1632 18 49 50

12. POUSSIN, Nicolas 1594-1665 18 48 18

13. VAN DYCK, Antoon 1599-1641 17 46 47

14. WTEWAEL, Joachim 1566-1638 17 46 47

15. DE PASSE (I), Chrispijn c1565-1637 16 44 45

16. ALBANI, Francesco 1578-1660 15 42 10017. FRAGONARD, Jean Honor 1732-1806 15 41 15

18. CAMBIASO, Luca 1527-1585 13 36 86

19. Vecellio, TIZIANO c1488-1575 13 35 83

20. BOUCHARDON, Edm 1698-1762 12 33 12

21. GIORDANO, Luca 1632-1705 11 30 71

22. ROMANO, Giulio c1492-1546 10 28 67

23.RAIMONDI, Marcantonio c1480-c1527 10 27 64

24.RICCI, Sebastiano 1639-1734 10 27 64

25. RENOIR, Pierre Auguste 1841-1919 10 26 10

26. DEMARTEAU (I), Gilles 1722-1776 9 25 927. Sanzio, RAFFAELLO 1483-1520 9 25 60

28. VERONESE, Paolo c1528-1588 9 25 60

29. PRUDHON, Pierre Paul 1758-1823 8 23 8

30. CANOVA, Antonio 1757-1822 8 23 55


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Already in Research Paper 1 (p.7, Fig.4) (Bender, 2008a) the observation was made that 57%of artists created only one work, 17% only two works, etc. This observation fitted perfectly

the formula of Lotka, known as the law of scientific productivity4, for the Italian Venus in

Research Paper 2 (p.3-4, Fig.3 in Bender, 2008b) and for the French Venus in ResearchPaper 3 (p.10-12, Table 4 and Fig.11 in Bender, 2009b). Also the data of the Venus of the

Low Countries fit the formula of Lotka very well.

Table 8 summarizes all the observed data for the three regions and Table 9 all the calculatedvalues of the empirical parameters Cand aof the inverse power equation of Lotka:

y = C / xa

whereyis the relative or proportional number of artists who createdxworks.Thus forx = 1, C = y. Lotka suggested that the power exponent anearly always equals 2 in

which case the equation is an inverse square law. Egghe (2005) shows that the theoreticalvalue of C is 0.6079 if a = 2 and that the observed value y forx = 1 is always lower than

the theoretical value of C ifa = 2.Egghe also explains that the function is scale-free and can

be applied to any 'item' or 'product', regardless its evolution in time.The determination of the constant Cand the power exponent afor a given data set can be

done in two ways:

1 by logarithmic transformation of the data and using the classical linear regressiontechnique (or 'least squares method', applied for instance automatically in the trend-line

functionality in 'charts' of MS-Excel); the technique also offers a measure of goodness-of-fit

between the equation and the observed data, commonly called the correlation coefficient 0

Documents

Time Distribution, Popularity, Diversity and Productivity of the Iconography of Venus in the Low Countries, France and Italy