Coin finds in Bulgaria for half a century: 19101959


Jordan Tabov
with Kliment Vassilev and Asen Velchev · Sofia · 2006 

This is a preliminary publication of the draft version of a paper submitted to a Bulgarian scientific journal. The final version will be published later.


If a coin has been struck by Tsar Ivan Alexander (13301371), we attribute it to two intervals: (1340, 1360] and (1360, 1380].In the same ways a function will be defined corresponding to each coin from CFBP19101959. Finally all these functions should be summarized. 

Fig. 1: Graph of the individual unitstep function of a coin, struck by Tsar Ivan Shishman (13711393). 
To ensure that the graphs of the individual functions for all the coins “enclose” rectangles of the same area, i.e. that all they have equal contribution to the final result, we multiply the values of each IUSF by a coefficient, dependent on the number of intervals where the respective function is nonzero. We multiply by 60 the function of a coin attributed to a single interval and by 30 or 20 when the intervals of dating of the coin are 2 or 3 respectively. Thus the area of the rectangle between the abscissa and the graph of the function of any coin is constantly 1200. 
This can be expressed mathematically in the following way: IUSF (t; coin) = 
whereis the dating period of the respective coin; t is not a particular year but a unit interval:(20 years each); n is the number of unit intervals in the period , i.e. the “length” of it. Summarizing all individual functions we obtain the CDCFBP19101959. I.e.: CDC(t)=Σ IUSF(t; coin). 
The so constructed CDC is a function of time only, because the set of coins CFBP19101959 is fixed and the summing up includes all the coin’s IUSF. The number of the IUSFs is such that the use of computer technology becomes expedient. The MS Excel package can be used conveniently for adding them up and drawing the graph of their sum CDC. More details are given in Tabov and Tabova, 2004, Tabov et al., 2005, pp. 103107, Tabov et al., 2004a, pp. 99104 and Tabov et al., 2004b, pp. 257261.The graph of the derived CDCFBP19101959 is very convenient to make analyses and to draw conclusions. 
This graph, represented in Figure 2, is obtained by using builtin tools of MS Excel. 

Fig. 2: The graph of the Chronological Distribution of Coins Found in Bulgaria and Published 19101959 
Comparing them to the graph in Fig. 2, we conclude that the differences between the shapes of the three graphs are very small: the high peaks and the deep downs are distributed in the same way.  
Fig. 3: Chronological Distribution of Coins Found in Bulgaria and Published CDCFBP19101934. 
It might be checked that the sequence of the CDC for the first 26, 27, …, 40, …, 49 years “approaches” the CDCFBP19101959. On the basis of this observation it is natural to expect that: 

Fig. 4: Chronological Distribution of Coins Found in Bulgaria and Published 19101950. 
1. Further data adding would not change the main properties of the graph in Fig. 2, especially the distribution of the minima and maxima and the ratio between their values.





From Anastasius I to Maurice (491602)


From Phocas to Constantine IV (602685)


From Justinian II to Michael II (685829)


From Theophilus to Nicephorus II Phocas (829969)


From John I Tzimisces to Nicephorus III (9691081)


From Alexius I Comnenus to Alexius III (10811195) 

Fig. 5: Data on the Byzantine coins from the collection of the British Museum, tabulated by A. P. Kazhdan

The right column of the table defines a function, which in fact is a simple version of what we call here Chronological Distribution of Coins (CDC). We distributed the data from the above table in 20year time units in the manner described in § 3, put it in a new MS Excel’s worksheet and made the graph of what we entered in the computer. The graph is shown in Fig. 6: 
This graph provides us information on the Chronological Distribution of the Byzantine coins from the period 4911195 considered by Kazhdan. The table in Fig. 5 and the graph in Fig. 6 represent (almost) the same information.Comparing them we notice the advantages of the visualised presentation in Fig. 6 in comparison with the systematized numerical information in Fig. 5.  
Fig. 6: Chronological Distribution of Byzantine coins from the collection of the British Museum according to Kazhdan (Kazhdan, 1954, pp. 164188). 
Such an approach and the specialized software used for visualization of the data give our study various advantages. Since the “basic intervals” in the table in Fig. 5 (about 100 years and more) are longer than those used in our construction, the function in Fig. 6 is rougher. Nevertheless the table gave Kazhdan the opportunity to notice a peculiarity: the period 8th10th century is presented by lesser amounts of coins. The analogous table and graph in Fig. 7 and Fig. 8 constructed for the Byzantine coins from the collection of count I. I. Tolstoy (Tolstoy, 19121914) show the same peculiarity. 
From Anastasius I to Maurice (491602) 

From Phocas to Constantine IV (602685) 

From Justinian II to Michael II (685829) 

From Theophilus to Michael III (829867) 

Fig. 7: Data on the Byzantine coins from the collection of count I. I. Tolstoy, tabulated by A. P. Kazhdan. 
Considering further the generalized data of finds of Byzantine coins Kazhdan makes the following conclusion: “Considering the data in these catalogues one may suppose that at the border between 7th and 8th century Byzantium had entered in a period of significant economical alterations, which found expression in diminishing the intensity of minting. 

Fig. 8: Chronological Distribution of the Byzantine coins included in the collection of count I. I. Tolstoy. 
This conclusion, however, remains hypothetical and should be seriously checked out. The matter is that the collections always have subjective and random character: in particular the more common is one or another kind of coins, the minder is the collector’s interest in it. Therefore there are mostly rare coins in the collections. Moreover the coins struck by the Comnens and Palaeologs during the last centuries of the empire are of minder interest for the collectors than the earlier ones. All these factors of course deform the picture and therefore the catalogue data should be verified with the data in the publications on archaeological excavations and collective coin finds… Having in mind all these facts, all the following reasoning and calculations might have preliminary and tentative character, even though it seems to me that the mass character of the coin finds is a certain guarantee for the relevancy of the conclusions deduced on the base of analyses of the numismatic material.” (Kazhdan, 1954, p. 167) Following this logic Kazhdan directs his attention to publications on archaeological excavations and collective coin finds and uses their data to confirm his expectations that (this phrase deserves to be repeated) “the mass character of the coin finds is a certain guarantee for the relevancy of the conclusions deduced on the base of analyses of the numismatic material.” Kazhdan finds out that the numismatic material found by excavations and treasure findings has the same property – negligible quantity of coins from 8th and 9th century. Details can be found by the readers in his article (Kazhdan, 1954, pp. 164188). It is important to notice that in his research he involves data for more than 50000 Byzantine coins; we put all them together and construct their Chronological Distribution in the interval (500, 1000]. 
Its graph is shown in Fig. 9: Thus Kazhdan convincingly shows the existence of a “monetary crisis” in the Byzantine history. It comprises the period 8th9th century. 

Fig. 9: Chronological Distribution of all Byzantine coins considered in the article of Kazhdan (Kazhdan, 1954, pp. 164188) 
Similar conclusion is proved also by the data of R. Lazer (Lazer, 1980) (cited by A. Romanchuk in Romanchuk, 2003, pp. 132137) on Roman and early Byzantine coins (1641 coins in total) excavated in East Germany, and the results of V. Kropotkin (Kropotkin, 1961 and Kropotkin, 1962) on finds of the same type coins on the territory of the exUSSR and East Europe (11729 coins in total). The number (given by V. Kropotkin) of Byzantine coins found in East Europe and dated to 8th9th century is clear enough: 2 coins from 8th century and 11 from 9th century (Kropotkin, 1962 – table 1). This phenomenon appears to be a serious scientific problem, because the life in a city, even a small one, is impossible without coins. The majority of the citizens do not produce agricultural products like bread, milk, meat, etc and they should purchase their food, needing money for this. It’s known that in some countries instead of money were used leathers; but as far as it is known from the sources in Byzantium for “money” were used only coins. Hence in Constantinople and other big cities of the empire, especially in Serdica (Sofia) and Philippopolis (Plovdiv), which are in Bulgaria today, there should have been monetary circulation. Hence coins were struck in Byzantium for sure. But where they are? Why the archaeologists don’t find them in Bulgaria? 
References  
Fedorov S., Fomenko A. T. (1986) Statistical Estimation of Chronological Nearness of Historical Texts. Journal of Soviet Mathematics, Vol. 32, № 6, pp. 668675. 
I would like to write a Comment
to this text:
