Аннотация: Origins of matrix analysis, alternative matrix analysis in Europe, practical use of matrixes, ideal matrix Thanks to new technologies of digital silicon wafers, we now have the opportunity to get acquainted with the Giulio Parigi"s book, which is now available in electronic archives of the Library of Congress in U.S., and it is of substantial interest in solving the problem of history-graphical interpretations of the birth of the risks matrix analysis in the management of systems in Europe. Long before the advent of the classical European tradition branch, there appeared and then was developed a special approach to matrix analysis. It was based on the practical use of matrices to analyze the risks in the management of systems that had profound economic implications. It can be regarded as a striking example - the birth of the practical use of the matrix analysis of risks in the management of systems - and it all can be found in a handwritten essay of Giulio Parigi (Julio Parigi) "Fronte capillata" ("The hairs on the forehead," old. Ital. / Spanish.).
Alexander A. Shemetev (copyright protected)
PhD (finance), MBA, MACFM /Master in Anti-Crisis
Financial Management/,
Master in Linguistics
The origin of the practical use of the risks matrix analysis
in managing the systems in Europe
Thanks to new technologies of digital silicon wafers, we now have the opportunity to get acquainted with the Giulio Parigi"s book, which is now available in electronic archives of the Library of Congress in U.S., and it is of substantial interest in solving the problem of history-graphical interpretations of the birth of the risks matrix analysis in the management of systems in Europe.
It should be said a few words about the fate of the manuscript. Until 1944 it was in a private collection of L.J. Rosenwald (Lessing J. Rosenwald), a famous collector of rare editions, who realized its cultural and historical significance and handed the manuscript to the Library of the U.S. Congress. According to the conclusion of expertise, the manuscript was created in the next time interval: from 1592 to 1608 A.D. Much of the book was written at the end of the XVI century and in the early XVII century; then it was supplemented with some pictures.
The examination confirmed the author of this work - Giulio Parigi, a practical mathematician who lifelong created military machines for the cities that were in the territory of modern Italy, as well as for the Spanish Empire. The manuscript is written in the Old Italian language with a high proportion of Old-Spanish, mainly classical Iberian dialect. The work itself is made in the form of the author's monograph with text and illustrations on one side so, that the reverse of the sheets remain blank for the next possible author"s or readers" records. One should also mention the lack of a clear numbering of the sheets in the manuscript. In this case, the numbering is based on the silicone matrix copy of the work, where the first digit is a lateral cover (matrix 1), second digit is a hardcover, the third - is the page after the spine and so on. Thus, the cover, made by the author himself after the hardcover, it turns out only on page 6, and the author's preface - 8. Calculated in this manner, the book has 601 matrix sheets .
Long before the advent of the classical European tradition branch, there appeared and then was developed a special approach to matrix analysis. It was based on the practical use of matrices to analyze the risks in the management of systems that had profound economic implications. It can be regarded as a striking example - the birth of the practical use of the matrix analysis of risks in the management of systems - and it all can be found in a handwritten essay of Giulio Parigi (Julio Parigi) "Fronte capillata" ("The hairs on the forehead," old. Ital. / Spanish.). This comic title describes the circus acrobat - a scientist who tries to understand the laws of mathematics and fortification, and because of this he rides a gun kernel dressed in the ancient Roman garb with his "hairs on the forehead," which in addition stand on end. This picture was drawn by the author on the first page of his manuscript.
The first rudiments of matrix analysis have appeared in ancient China. However, the "magic squares", as they were known in China and India, they were invented in 2200 BC presumably by Mr. Lo Shu, - all these matrix had little practical use. Then there was created an ideal matrix (sum of rows, columns and diagonals are equal to each other, and the sum always gives the same constant). Any deviation from the ideal matrix immediately reduced its value. The so-called "demonic" magic squares were also of high value - they are the matrixes, which coincided with constant sums of the numbers of broken diagonals. However, such matrixes were also out of wide practical usage.
In the European tradition, matrixes were used in the art till the end of XVII century - middle of the XVIII century .
Widespread practical use of analysis, based on matrixes, appeared in the second half of XIX century. Risks" matrix analysis was used mainly in the III quarter of the twentieth century. This is a classical branch of the matrix analysis development.
The important thing is what the author meant by the system. During the gradual transition from the era of the late Middle-Ages to the Renaissance, yet there was no economic science as a separate branch of human knowledge. The largest system was the city itself, which was an industrial, commercial, trade and military "hub". Particularly important system was the capital of a state, the loss of which meant the most significant crisis. "Theorization" of mathematics" sciences and its partition, the matrix calculation instead of pure notation, it was made much later, after almost 250 years after the publication of this manuscript book.
The conclusions and proposals of the book were, most likely, the ones to have been practically applied. There is a possibility of their application in the construction of a model of an ideal city-fortress " Bird-City " in the South American colony, and Peter-and-Paul Fortress in St. Petersburg was built largely under the laws of the Giulio Parigi"s inferred concept of ideal military fortification for commercial and political centers.
On page 412 Giulio Parigi describes the matrix depending cubes of different substances (water, stone, marble, iron, and alloys (iron and lead)) from a fraction of the ideal proportions to create defensive line systems (ill. 1).
Illustration 1 - The illustrated matrix of blocks of different substances
Under the systems" management in the manuscript it is included next.
First, under the system he understood the management of commercial, industrial and domestic infrastructure of the castle to be built in accordance with the ideal matrix. The most perfect system he thought the quadratic-matrix-system-location of this infrastructure as it is shown in a matrix with artistic illustrations (p. 336). The matrix is divided into zones: F - area outside of the matrix - it is considered to be an empty space; A -area of residential infrastructure, it corresponds to the extreme rows and columns of the matrix; B - zone of industrial-commercial infrastructure - it conforms to all the top interior columns and rows of the matrix, except for the center; Zone E - corresponds to the dislocation core of military infrastructure, this is the ideal center of the matrix; D is the area of commercial infrastructure, which is directly linked to the military (food stores, distribution networks for the military purposes and so on). Zone C represents only the military sector of infrastructure; the fortified zone G sector meets "the last stronghold" purposes, that must be used to resist if the city (outside the zone) will be busy with the enemy, - according to Giulio Parigi, - it is the lower right cell, which is located from the bottom up - just inside the cell at the matrix. When the ideal matrix is complied in practice, it should reduce to minimum the risk of a system"s demolishing due to the capture, and also due to other crises trends of the environment, by which he meant chiefly military crisis trends of the environment (ill. 2).
Illustration 2 - The illustrated matrix of ideal city"s risks minimization
Thus, based on matrix analysis Giulio Parigi developed, the ideal systems" management tries to minimize the risks of this very administration or management (of the old. Italian Maneggiare - "Get in hand (a tool)", "Something to do using one"s hands" and the old. Lat. Manus - "hand"). Get in or pick up an instrument intended to be used to create a system with minimal risk, at those times to fulfill this purpose the construction process was very much needed. It was necessary to know how many resources and "what goes where" for the construction in the process of construction. Giulio Parigi calculated it all on the basis of developed by him practical applications of matrix analysis.
In these conditions it was possible to calculate in advance the exact amount of resources needed, therefore, the exact amount of money that are needed to create a system with minimal risks, a system to be able to withstand the crisis changes in the environment, mainly, military expansion crisis.
Based on the matrix, according to Giulio Parigi, one can determine whether resources are enough to create the ideal system. If not - then Giulio Parigi offers a wide range of cheaper in the implementation not so "perfect systems", which are listed at the beginning of the book (pp. 46, 48, 54).
One of those "cheap" system, in terms of the amount of the necessary resources, is given in the form of broken triangle (p. 54). According to the calculations made with the transformation matrix, the creation of such a system would take very little resources, and, at the same time, the risks of this system with a limited set of inputs will be minimal possible.
Second, under a system management Giulio Parigi understood managing of set of siege weapons, in particular, based on matrix analysis.
At the same time, Giulio Parigi applied matrix analysis to create projects, schemes and designs of an ideal system. Primary, Giulio Parigi invented the Camera obscura principle, re-invented only by the late XVIII - early XIX century, when making a photo started to develop itself. Principle, described by Giulio Parigi, the Camera obscura principle is used today. A section in the manuscript of Giulio Parigi is devoted to the Camera obscura principle (p. 480 - 540). Giulio Parigi begins with an introduction to the reader with the principle of Camera obscura, which is in an exact copy of an image by an artist (p. 480). The image passes through a lens and projected onto a special treated canvas on which the artist displays a replica of the image (p. 480). However, Giulio Parigi considered such use of copying acceptable only for professional art, history and architecture. It was necessary not simply copy models when constructing models of systems, - it was necessary a high-precision copying.
Illustration 3 - The offered by Giulio Parigi Camera obscura principle
with using a matrix and without it
To do this, the scientist develops an accurate image transfer matrix, using which it was possible to focus a point on a canvas, or a line, - depending on the stage of precision copying. The such-like principle is used in modern digital cameras, in which there is also a digital matrix correction, which sets clear boundaries of images.
To focus the image, in addition to the matrix, it was used also a leverage system - to receive a precise angle of the shadow drop when copying. The paper shows the practical application of the matrix when using a framework to copy, in which some certain cells are made for high-precision-copy (p. 492) (at the modern digital copying technologies at a certain impulse cell-point the impulse code should be clearly distinguishable from the pulse codes of adjacent elements of picture matrix; at the times of Giulio Parigi they didn"t distinguish this matrix clearly - they distinguished clearly only a certain cell-point for a high-precision-copy; then they distinguished another certain cell-point or a line, and et cetera, - until the high-precision-copying process will not be completed).
There is a comparison in the manuscript - the comparison of copies of an image without using a discrete framework (very blurry image) (p. 494) with an image obtained using the framework (p. 492). You, my dear Reader, may see such comparison at an illustration above. Of course, the practical application of matrix analysis, that wasn"t developed then both methodically and methodologically, - it adversely affected the completeness of the application of modern for Giulio Parigi methods of matrix analysis.
The classic application of the Camera obscura method is given on page 500 in the book: there is illustrated how to receive an image from a light passing through a lens in a perfectly dark room on a sample of copying of an image copy of a Gothic cathedral in the details.
Giulio Parigi uses the image of a young child as an artist, implying that even a little boy can handle with the copying of complex images in Camera obscura (first photo-cameras were made in a form of such-like dark rooms, where the high-precision-copying-process lasted for many minutes, together with this, the "object for photography" wasn"t allowed as much as even move; the difference of such first photo-cameras from the original method of Giulio Parigi (1598) was in that fact, that an artist was needed, - an artist who could be not much skilled in an art. In this case, there was eliminated a risk somebody will move during the process of "photocopying", and so there was an opportunity to easily copy not just images of small objects and people inside a "dark room", - there is also an interesting fact that there was a possibility to copy wide-scale, big objects in a bright sunlight). Discrete-matrix apparatus is needed only when copying models of complex systems - to minimize the risk of errors in the construction of models, the errors that arise from natural inaccuracy in copying schemes and drawings (ill. 4).
Illustration 4 - The optical analysis of an ideal system
A variant of matrix analysis - is the matrix for calculation of the dependence between such parameters as volume and characteristics of the ball, baffle and throat of a gun; the bastion wall thickness and other factors (p. 44). The analysis can reveal the perfect construction for the system with minimal risks for different baseline characteristics and applications. Thus there is a counter-action to the risk of a system"s destruction - by means of an ideal system creation that would satisfy the conditions put in a certain matrix, i.e., it is the model for an ideal system that is calculated with the use of matrix. At the same time, Giulio Parigi considers the risk for artillery to miss the missiles to the enemy. To minimize this risk, in his opinion, a more complex geometry of wall should be used to increase the coverage area for all the defensive artillery weapons.
The Drawing matrixes author proposes to compare by using the optical slits in the selected discrete units through which a light ray is projected, - this is how an analysis of an ideal system "perfectness" should be made, the author says (p. 516) (ill. 4)..
On pages 260 - 262 there is a matrix that shows the depending between the required amounts of iron, stone, steel, specialists in certain designs of loopholes in the calculation of the ideal number of guns. A consequence of the matrix"s calculation is to establish the cost of the project, which is reflected in its resource-intensive. The author tried to identify the diagonal relationship between the columns, which can be clearly seen in his notes (ill. 5).
Illustration 5 - The G. Parigi attempt to reveal the diagonal inter-dependences of an ideal matrix
Giulio Parigi considered: the biggest risk for a system - is in a variety of risks that can occur simultaneously, such as during an analog cassette bombing of system, when the minimal risk of negative effects of a projectile is maximized at the expense of plurality of projectiles. On page 318 the author describes the gun for a massive cluster bombing of castles, the materials for the creation and operation of which can be calculated from the matrix analysis. The author offers two types of cassette- cluster-like bombings: With the cassette-gun, or by adaptation of the supply mechanism for fireworks to massive launch of missiles filled with high explosive shells prototypes (in the explosion there sprayed gas; while the risk of misses is minimized by a set of missiles, explosive gas and fission products in the explosive element (the analog of the nails)). Giulio Parigi describes in an allegorical way, that the risk of cluster bomb systems comparable to the risk, which gives the devil to the world, setting fire for masquerade to disguise the ship in which he swims (p. 352) (ill. 6).
Illustration 6 - The philosophy of fire
Giulio Parigi, in his manuscript, also creates a detailed drawing of Colt-like-pistol with drum cartridge (p. 286) (ill. 7).
Illustration 7 - Colt pistol, a sample from 1598 year
And also Giulio Parigi, in his manuscript, describes the anti-chivalry-mines (p. 220) (ill. 8).
Illustration 8 - The anti-chivalry-mines
And also Giulio Parigi, in his manuscript, describes the scheme of mines these anti-chivalry-mines (p. 202). The author also gives the type of the bastion, which analogue was later often used in the construction of Russian cities in the future periods of time (p. 136) (ill. 9).
Illustration 9 - The fast in installing bastion
In general, at the end of the Middle-Ages in Europe, there was created an alternative for the future matrix analysis, based on first-hand - in the practical applications of this type of analysis. The author abandoned the theoretical framework of diagonal relationship among the columns in one of his matrices, the matrix needed to be used to calculate the resource requirements for the organization and systems" management, because, apparently, he could not find a practical application of this theoretical construct. Giulio Parigi"s Matrix risk analysis in the systems" management was, in fact, an analysis of the systems themselves by comparing them with the standards based on the matrix. Consequently, using the basis of this analysis, one could calculate the quantity and quality of standard resources that are needed to create a system: stones, wood, metal (iron and alloys), gunpowder and other components. As a result, the world received a theory of ideal systems" building, the systems that are most resistant to the main risk for the environment of those times - the risk of military intervention.
So, for example, the first fortress on the territory of present-day Yekaterinburg city in Russia, the city primary built during Peter the Great times, the main city was also created on the principles described by Giulio Parigi (iI. 9, 10, 11 (straightening of the fortress into a rectangular shape in the mountainous terrain), 12).
Illustration 10 - An ideal fortress at river
Illustration 11 - Straightening of the fortress into a rectangular shape in the mountainous terrain
Illustration 12 - Surrounding of fortress with a picket fence
Management, at those times, was perceived on the basis of its practical value - "to pick up the tools" to create a system to minimize the risks .
List of sources used:
1) Giulio Parigi Fronte capillata, LJRC MS 27 # R1363, 1598, 601p.
2) Lamberini D. Two projects: a sketchbook on military architecture and the Frederick Hart papers / / Record of activities and research reports, Washington: National Gallery of Art, 2004
![Illustration 1 – The illustrated matrix of blocks of different substances [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris1illjustrirowannajamatricablokowweshestwwsootnosheniisriskami.jpg)
![Illustration 2 - The illustrated matrix of ideal city's risks minimization [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris2illjustrirowannajamatricaminimizaciiriskowidealxnogogoroda.jpg)
![Illustration 3 – The offered by Giulio Parigi Camera obscura principle with using a matrix and without it [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris3cameraobscurasmatricejibez.jpg)
![Illustration 4 – The optical analysis of an ideal system [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris4opticheskijanalizidealxnojsistemy.jpg)
![Illustration 5 – The G. Parigi attempt to reveal the diagonal inter-dependences of an ideal matrix [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris5popytkawyjawlenijadiagonalxnojzawisimostiidealxnojmatricy.jpg)
![Illustration 6 – The philosophy of fire [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris6filosofijaognja.jpg)
![Illustration 7 – Colt pistol, a sample from 1598 year [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris7kolxt1598goda.jpg)
![Illustration 8 – The anti-chivalry-mines [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris8protiwokawalerijskieminy.jpg)
![Illustration 9 – The fast in installing bastion [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris9bystroustanawliwaemyjbastion.jpg)
![Illustration 10 – An ideal fortress at river [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris10idealxnajakrepostxnareke.jpg)
![Illustration 11 – Straightening of the fortress into a rectangular shape in the mountainous terrain [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris11wyrawniwaniekwadratomkrepostiwuslowijahgor.jpg)
![Illustration 12 – Surrounding of fortress with a picket fence [Giulio Parigi]](/img/s/shemetew_a_a/alexanderashemetevmatrixanalysisoriginsineurope/ris12obneseniechastokolomkrepostej.jpg)