Izvorni znanstveni članak
Ruggiero Giuseppe Boscovich / Ruđer Josip Bošković Breve memoria sul lotto di Roma (1765)
Ivica Martinović
; Dubrovnik, Hrvatska
Sažetak
Here published is the editio princeps of Bošković’s manuscript Breve memoria sul lotto di Roma, which in caligraphic transcription is kept at the Bancroft Library within the University of California at Berkeley, the collection Boscovich Papers, call number Carton 1, Part 1: no. 65, Folder 1:82.
The transcription of Bošković’s manuscript Breve memoria sul lotto di Roma is accompanied by notes and introduction. The latter contains the following: (1) description of the manuscript and the status of its research; (2) outline of the contents of Bošković’s writing in the field of game theory; (3) assessment of the manuscript’s purpose and messages.
The authorship of the writing is undisputable: Bošković signed his dedication to Cardinal Federico Marcello Lante Montefeltro della Rovere. The manuscript also contains the place and date when it was written. Dedication is dated: “Bagnaja 26 Luglio 1765.” [“Bagnaia 26 July 1765”]. This means that Bošković, professor at the Pavia University at the time, composed the memorial during his leave for the purpose of healing a leg wound in the nearby thermal baths in Viterbo. In June he left Pavia and went to Viterbo, and the manuscript proves that after Viterbo he visited the cardinal’s country residence, Villa di Bagnaia, where he remained until the end of July 1765.
Indeed, as confirmed by the title page of the manuscript, Bošković presented the memorial personally to Cardinal Lante “in his magnificent villa” (presentata a Sua Eminenza Il Signor Cardinal Lante nella sua magnifica Villa di Bagnaja).
Among various explanations of lottery, Cardinal Lante showed interest in the mathematical principles of the game, and thus encouraged the professor of mathematics to compose a short memorial (breve memoria) of mathematical nature. With this goal in mind, Bošković divided his treatise into three parts. In the first, he expounded the notions of the sets of two, three, four and five winning numbers (ambo, terna, quaterna, cinquina), and also calculated their maximum number for a lottery in which 90 numbers are drawn.
In the second part, he discussed the Roman lottery as a theoretical model (in se stesso) or, as explicitly formulated by Bošković, “independently of the costs of the contractors for the officials and for other purposes, and of the amount the contractors pay to the ruler when the game is leased.”
Bošković in detail described the four types of lottery winnings in Roman tombola:
1. when simple numbers are drawn in a series of drawings (semplici numeri);
2. when the number is selected (numero eletto);
3. when five numbers are drawn out together, and the game involves a set of two
winning numbers (ambo);
4. when five numbers are drawn out together, and the game involves a set of three winning numbers (terna).
For these four types of tombola, the Ragusan then examined whether the requested equality of participants in the game is honoured. After mathematical analysis, his conclusion reads: “In any case, the game remains unequal, with loss for the players and gain for the lottery contractor.” In order to re-establish equality in the game, Bošković suggests that the price of every tombola ticket should be diminished by percent for which mathematical analysis has established to indicate the degree of inequality in the game.
In such a model the game is unfair for the players, whilst the lottery contractor is the only party winning. For this reason, the relationshipbetween the given revenue and the usual costs should be discussed. By far the largest of all costs is the price of the annual licence that the contractors pay to the Papal Treasury to the amount of 142,000 scudi, whilst the overall lottery annual expenses are estimated at 200,000 scudi. Thus in the third part of his treatise Sul lotto Bošković iscussed the gains and losses of this game with regard to the contract, according to which lottery was played on the New Year in papal Rome (relativamente al suo presente appalto in Roma). He first estimated the outcomes for each of the four types of tombola, assuming that the total revenue from lottery amounted to 500,000 scudi. For the first two games involving drawn and selected numbers, he estimated that the contractor had an annual loss of 89,000 scudi, and with the ambo only the loss would be 33,000 scudi. Exception would be the terna, bringing a substantial profit of 80,000 scudi to the contractor.
The amount of the estimated loss or gain per game depends, naturally, on the level of the realised revenue, i.e. on the number of the lottery tickets sold. What maintains the contractor is the terna, and his total profit today may be approximated from 30 to 40 thousand scudi per year, Bošković estimated.
In the final part, Bošković remained open for more enquiries on behalf of the cardinal: “With the help of a few exposed principles, the character of this game is easily understood, and they may also facilitate the solving of many other problems.”
This third part of Bošković’s memorial proved of utmost interest to Cardinal Lante, prefect of the Congregation “for the good regiment” (Congregatio bonae regiminis), therefore, Papal minister of economy, as the sustenance and financial effects of the Roman lottery were in the domain of his direct responsibilities. Although Bošković showed modesty in characterising his memorial as a “small trifle” (questa piccola bagattelletta), he submitted a writing suited to the basic interests of the Papal minister of economy.
Ključne riječi
Ruđer Bošković; theory of probability; game theory; Roman lottery; Federico Marcello Lante; Congregation for the good regiment / Congregatio bonae regiminis; ethics; political philosophy; economics
Hrčak ID:
220260
URI
Datum izdavanja:
12.3.2019.
Posjeta: 876 *