The man of knowledge must be able not only to love his enemies but also to hate his friends.

*Friedrich Nietzsche*

The Polish Jew Chaim Zelig Slonimski (1810-1904), a Hebrew publisher, astronomer, inventor, and science author, commenced his activities with calculating machines around 1838, when he, visiting Byelostok, heard that a Jew had spent there several days, collecting subscriptions for tables of calculations, which he had invented. The tables had no success, but Chaim decided to try to produce something better, and having once taken the idea into his head, it was soon accomplished. He returned home and designed a machine to perform addition and subtraction, but he had not the means to complete his instrument.

In the late 1830s Chaim Zelig Slonimski settled permanently in Warsaw as a guest in the home of Abraham Jakub Stern, the popular mathematician and inventor of various machines (including calculating). This occurred for the young author and scholar who had recently been divorced, thanks to Stern, who wanted him as a son-in-law for his youngest daughter, Sara Gitel. The match was finalized at the beginning of 1842, one month before Stern’s death. There is no doubt, that Slonimski was heavily influenced by his mentor and father-in-law Stern, but besides this valuable legacy, Slonimski must have been a very smart man, judging by the rest of his life.

Three calculating machines were invented and produced by Slonimski before 1843, one for addition and subtraction, one logarithmic device, and one for multiplication. The first account of his calculating devices is from September 1839, when he wrote to a friend, that he had built a calculating machine and that he was working on a 20-digit logarithmic device.

It seems Slonimski demonstrated firstly the adding machine, because in the June 1840 issue of the Vilnius newspaper *Kuryer Litewski* was announced (at that time Slonimski was in Vilnius to publish his mathematical handbook):

*A Jew Slonimski born in Bialystok, recently invented a small machine for calculating, which thanks to its dimensions (length 10 inches, width 3 inches and 1 inch height), comfort, and low price deserves to be widely used. Everybody who knows digits only can, with the help of this machine, make calculations easily, fast, and without need to think. This machine can be seen at the inventor’s residence, where he is now working on a new machine for calculating logarithms. With the help of this machine one can simply and comfortably find the differences of Bruget logarithms, as well as natural logarithms up to 14 decimal digits*.

The adding machine was presented also in 1841 in Königsberg, where Slonimski was invited through the recommendation of Bessel, the great astronomer, who taught at the university. Slonimski got permission to expose for inspection, in the university building, his calculating machine and had the pleasure to see it highly approved by the whole faculty. Slonimski obviously described (or demonstrated) his logarithmic device also, because there is a letter from Carl Gustav Jacobi to his brother, asking for support for Slonimski to demonstrate it in St. Petersburg.

The multiplication machine was based on a newly discovered theorem from number theory, called the *Slonimski Theorem*. The operation of the multiplication machine, which is more important, has been described by Slonimski himself in Russian. In principle, it was an implementation of multiplication tables, which resulted from the application of the theorem. Since the amount of related numbers was not that large, they were put on the cylinders, which—when moved appropriately—were showing the multiplication results in small windows.

Slonimski’s machines got high recognition during his lifetime. In August 1844, he brought his machines to Berlin, where he demonstrated them first to some prominent scientist as Alexander von Humboldt, Friedrich Bessel, Johann Encke, and others, then to the *Royal Prussian Academy of Sciences*, and his work was highly appreciated. The accurate results of his machines gained him here the same approbation, and although he did not communicate the theoretical principles on which the whole rests, yet, Humboldt recommended him to Friedrich Wilhelm IV, King of Prussia, where he saw, at his representation, his machines highly approved. Humboldt even intended to provide him with material means so that he could settle in Berlin and then occupy the chair of mathematics in one of the Prussian universities, but family circumstances prevented Slonimski from taking advantage of this offer.

In the same 1844, Slonimski published an article on calculating machines in the *Journal für die reine und angewandte Mathematik*, vol. 26, 1844, pp. 184–190 (see article of Slonimski). In 1845 an article “Selig Slonimski and His Calculating Instrument” was published in *Illustrierte Zeitung*, Leipzig, vol. 5, no. 110, 1845, pp. 90–92 (see article of Slonimski).

Next year, in April of 1845, he presented the multiplication machine to the *Academy of Sciences* in St. Petersburg, and obtained its recommendation for the *Demidov Prize* of the Second Grade (The Second Grade prize amounted to 2500 Rubles. For comparison, one should say that a university scholarship of 20 Roubles per 1 month could easily cover a student’s living and educational expenditures.), which was awarded to him on 24 June 1845. Moreover, the President of the Academy, Министр Граф Серге́й Ува́ров, presented the inventor before the Emperor, and a few days afterward the following Ukase (decree) appeared:

*Ukase to the Senate.
The Hebrew, Selig Slonimski, born in the city of Bialystok, is hereby, in approval of the high merits which his learned and useful labours in the Mathematical branch have gained, raised to the rank of an Honorary Citizen.
Nicolas I.
Peterhof, 26 July, 1845.*

In 1847 Slonimski applied for a patent in the USA (see the petition of Slonimski), stating that there was a company in New York— Neustadt and Barnett (of two Jews from Warsaw named Samuel J. Neustadt and David Barnett), who were interested in financing his invention and they apparently paid $300—at that time a very large sum of money—in order to get a patent. For unknown reasons, this application was unsuccessful. Barnett managed however to obtain a Great Britain patent on Slonimski’s behalf for the adding device and the third model of his multiplying device (British patent number 11441 of 1847). By a stroke of luck, Slonimski managed to sell the rights of the manufacture of his adding machine to England for £400. He invested the money in the acquisition of a fruit orchard in the town of Tomashov.

The theorem of Slonimski is derived from the Farey numbers (a sequence of the irreducible irrational numbers a/b where b<=n, which belongs to the segment /0, 1/ and is arranged in increasing order). Using this theorem, Slonimski composed a table with 280 columns, each of which contained 9 numbers. The table was engraved on the cylinders; as the main component of the device, these cylinders can both revolve around the axis (the shaft) and move (reciprocate) along it. Aside from the main cylinders, there are also 2 small cylinders with digits from 0 to 9 on one of them and the letters a, b, c, d, together with digits 1 to 7 on the other. The cylinders are driven with the use of handles, and fastened to the shaft end. While the small cylinders are immobile, the main cylinders are moved along their axis with toothed gearing, driven with screws, and mounted on the cover. There are also handles on the cover, which set the numbers (multiplicands).

The whole instrument is made of a flat wooden box, similar to a chessboard, 40 cm long, 33 cm wide, and 5 cm high. On the cover of the machine, there are 11 rows of windows. The first (lower) window shows the multiplicand. When the number is set in the first row, both letters and numbers appear in the windows of the second and third rows. Their combination is the code, which informs the operator which screw should be turned (and which cylinder is to be shifted). After this, windows 4-11 show the resulting numbers. The 4th row shows the product of multiplication by 2, the 5th by 3, the 6th by 4, etc. Finally, the products of all ranks are displayed. After adding them to paper, the desired product is obtained. Apparently, the convenience of this method was rather questionable, and it is no wonder, that there is no evidence of its systematic practical use.

More importantly, this machine was the only available device for discrete calculating. The basic principle of its work was the theory of numbers, rather than complicated mechanism alone. It was the *mathematical art* of the device, which was so highly appreciated by the Academy, and personally by the famous mathematician Ostrogradsky. As the Academy report noted, “the discovery of the basic feature of multiple numbers was the principle but not the only condition for composing this calculating machine… The inventor also should arrange the aforementioned 280 types in proper order and also invent a phantom key (the code). Finally, the surface of each of the six cylinders is covered with a complicated system of 2280 numbers and 600 letters with indicators. This artificial ordering demonstrates the shrewdness of its author’s mind, which raises Mr. Slonimski’s device to the level of an analytical mathematical instrument. It is not just a calculator, of which the main idea is represented by the numbers of its pinions.”

The Academy commissioned Slonimski to publish the proof of his theorem, together with a detailed description of the machine in the Russian language. The task was performed within a short time, and the book appeared in 1845.

Later on, other inventors made similar devices—August Leopold Crelle, Henry Knight, Herschell Filipowski. In 1881, a Russian Jew—the mathematician Zebi Hirsch Joffe, created a popular counting tool (a set, consisting of 70 rectangular bars with totally of 280 columns on all sides), named Joffe’s Counting Bars, based on Slonimski’s theorem.

For his calculating machine for addition and subtraction, the so-called arithmetical machine (see the patent drawing below), Slonimski also obtained a patent (Привилегия Слонимскаго) on 24 November 1845, for the period of ten years (see the patent of Slonimski RU1845-11).

A working example of Slonimski’s adding machine, made by the Warsaw mechanic and optician Jakob Pik, survived to the present and is kept in the collection of Museum of the Jagiellonian University, Poland (see below the photos of the device).

The adding device consists of two rectangular brass plates, in which there are curved incisions showing wheel dials. It has seven 24-teeth wheels, which can be rotated by means of a stylus, each corresponding to one decimal position. Windows above the incisions allow the display of results. On one side, the machine is used for additions (top plate), and on the other side, it is used for subtractions (back plate).

On the circumference are drilled 24 holes, appearing across the digits, and permitting the operator to advance the wheels from 1 to 9 units with the use of the stylus. A ribbon spring above each wheel, composed of a band, stops the uncontrolled advancement of the wheel. The teeth located between the wheels partially overlap, an important detail for the transmission of a carry. They are alternately placed above or below each other depending on the side that is used.

Slonimski’s design has a significant flaw—tens carry needed to be manually transmitted for each position, and if the operator was not careful, mistakes could be made.

Despite its flaws, it seems Slonimski’s adding device had a significant impact on the development of calculating devices, because only a year later, after Slonimski received a patent in St. Petersburg for his adding device, Heinrich Kummer designed in the same St. Petersburg a slide adder or what it’s now called a Kummer or Troncet type adder. Slide adders of this type became the most popular adding devices, and were manufactured for more than a century until the mid-1970s.

It seems after selling the rights to his calculating devices in 1847, Slonimski was no longer developing them, and transferred his efforts to other inventions.

#### Biography of Chaim Zelig Slonimski

Chaim Zelig Slonimski (also known by many name variations through Hebrew, Yiddish, Polish, and the funny Russian version *Зиновий Яковлевич Слонимский*) was born in a poor orthodox Jewish family on 31 March 1810, in Byelostok (*Byelostok* or *Bialystok* was one of the many towns in Russian Empire (now in Poland), that had a significant (almost 70%) Jewish population), in the Grodno Governorate of the Russian Empire.

He was the oldest son of Rabbi Avraham Ya’akov Bishka (1785–c. 1860), who belonged to a family of rabbis, who were writers, publishers, and printers, and his wife Leah (Neches) Bishka, daughter of Rabbi Yehiel Neches, an owner of a well-known House of Study (house of prayer) in Byelostok.

Avraham Bishka, also known as Bishke, ”Yankeleh” and “The Slonimer”, was a son of Rabbi Binyamin Bishka Hakohen Katz, a publisher, and printer. Avraham also was a scholar and teacher, but made his living as a pedlar of glassware, and made barely enough by it to support his numerous family. It is believed that Avraham worked (or was born) in Slonim (Слоним, another town in Russian Empire (now in Belarus), that had a significant Jewish population), and “The Slonimer” description became adapted by his descendants as “Slonimski”.

Besides the oldest son—Chaim Zelig, Avraham and Leah Bishka had a daughter, Zimke, and two younger sons, Avraham Avrom (who became a textile manufacturer and merchant), and Jonha (who had a glass shop).

Chaim’s family provided him with a good Talmudic education (he studied at the House of Study of his grandfather Yehiel Neches), and at an early age, he already looked upon as a smart boy and demonstrated an interest in mathematics.

There is an interesting (although lacking documentary corroboration) family story, told by Nicolas Slonimsky, a grandchild of Chaim Zelig Slonimski, concerning a solar eclipse that occurred near Bialystok, when Chaim was a boy. Let’s see:

*There was a total eclipse of the sun in the region of Bialystok on September 7, 1820, when my grandfather was ten years old, a date which would bear eloquent testimony to his precocity.
A German astronomical expedition was set up on the site; shiny telescopes adorned the landscape; the weather was perfect for the observation of the celestial phenomenon. The villagers looked with apprehension mixed with wonder at the primly dressed German scientists.
My grandfather, then a boy of tender years, watched the proceedings with unabated curiosity. A German astronomer was moved to speak to him (the Yiddish-speaking natives could understand elementary German without difficulty). ‘The sun will gradually become smaller and smaller, and soon it will be completely blotted out. But you must not be afraid,’ the German reassured the boy. ‘After a few minutes of total darkness, sunlight will return.’ My grandfather listened to the German’s explanations with due respect, and then said, in passable school German: ‘I know all that. What I cannot comprehend, however, is how you expect to make any worthwhile observations of the corona without a double diffraction lens.’ The German was startled. ‘Where did you learn all this?’ he asked in utter astonishment. ‘Why, every street urchin in the village knows such elementary stuff,’ was the reply.
The astronomer dispatched a report to the Berlin Academy of Sciences, in which he declared that Bialystok was the most civilized community in the world, and he advanced the theory that this extraordinary state of knowledge amid a largely illiterate population was due to the preservation through the centuries of secret rabbinical doctrines dealing with celestial phenomena.*

According to custom, peculiar to the Eastern European Jews, to unite the children early in wedlock, Chaim’s marriage was arranged when he was only sixteen, and on his eighteenth birthday, he was given a wife. She was Reiza Rivhas Neches (probably his distant relative) from Zabludow (a small town with a large Jewish community near Byelostok). As usual, the father-in-law took the young couple to his wooden house, located in the market of Zabłudów (where he had a grocery), to pass there the first part of their married life. Chaim and Reiza soon had two daughters.

In Zabludow the teenager continued his rabbinical studies, but his attention was soon attracted by Maimonides’ treatise *Kiddush Hachodesh*, and its calculations and astronomical observations captivated his mind. Then he came across the *Naaveh Kodesh* of Rabbi Shimon Waltosh, a treatise on geometry, trigonometry, and stereometry, and mastered it for a short time. The next was the Hebrew translation of *Elements of Geometry* of Euclid by Rabbi Baruch Sclower, then the *Shebilay Derakiah* of Rabbi Elijahu Heches, a rare mathematical treatise, then the Euler’s *Algebra*, then the Mennig’s *Cursus of Mathematics*, in four volumes (he needed two months to finish this ponderous work). Another opportunity brought him together with a pharmacist in Bialystok, who volunteered to teach him German.

In 1831 the three years, during which time his father-in-law had engaged to support him and his family, were passed, and being without means, and without any business, dreary prospects were before Chaim. Nothing remained for him than to accept the place of bookkeeper with his brother, who owned a glass manufacture, some 60 km from Bialystok, deep in the woods. For a year and a half, every hope of progress was taken from him, no book, a lot of boring work. Fortunately, he found the mathematical works of Abel Berrias in eighteen volumes, and in the deep hour of the night only was he able to pursue his beloved studies.

Sometime in 1831 or 1832, knowing that the Jewish literature had no works in that line, and that the Eastern European Jews had no opportunity to study mathematical works in a foreign language, Chaim undertook to write a whole course of mathematics, both the pure and applied, in the Hebrew language. Thus he wrote a manuscript, *Mosede Hokmah (On the Principles of Mathematics)*, but nobody would have ever heard of that hidden knowledge if a kind Providence had not furnished him an opportunity. In 1833 his brother sent him on a business trip to Grodno, the governorate center. There Chaim met Eliezer Rosenthal (1794-1868), a famous Jewish book collector, who encouraged him and advised him to go to Wilna (Vilnius, the capital of modern Lithuania), where there is a Jewish printing office and a host of learned men, who will help him to get his works published.

Thus in 1834 Slonimski traveled to Wilna and asked for financial support from the first men of the local Jewish community. A subscription list was opened, but by reason of the poverty of the Jews it had not much success. The printers were not enterprising enough to take hold of a new work in Jewish literature. The expenditure of a thousand roubles appalled them, and thus Chaim was forced to publish only one part (which treats of Algebra) of his great work.

From Wilna Slonimski went to Minsk, where the young mathematician enjoyed the most marked attention, and encouraged by his first success in mathematics, he returned to Zabludow. Although he drew upon himself already, by the publication of scientific works, the name of a Berliner (sectarian), as they called him tauntingly in his small town, and although his wife felt greatly chagrined by the danger which the orthodox reputation of her husband run, yet she relaxed in her opposition, when the silvery sound of 75 roubles struck upon her ear. A year and a half he passed now under his domestic roof, enjoying greater freedom for study. He ordered several books from Leipzig, for a pamphlet on Halley’s comet, which he intended to publish.

Thus in 1835 Slonimski released *Sefer Kukba di-Shebit*, a collection of essays on the Halley comet and other astronomy related topics such as the laws of Kepler and Newton. This work significantly increased his popularity, because Halley’s comet was a widely discussed topic as the return of this periodic comet was expected in 1835. Rapaport, Reggio, Geiger, and other scholars, began to correspond with him, and from all parts, he received encouraging words.

In 1836 Chaim Zelig visited again Wilna and Warsaw, where he passed a few weeks with the mathematician Abraham Stern, and went from there to Königsberg. Stern, a prominent member of the local community, became his patron.

When in 1836 Slonimski returned to Zabludow, his domestic troubles got worse and worse (his wife’s family was against his scientific pursuits), and only the last remedy, so frequently used among the Polish Jews, remained to him, to divorce himself from his wife. Deprived of all means and the only support for his small children, at the end of 1836 he returned to Bialystok, his native place, and poverty in all its nakedness starred him in the face.

But his ill-luck had reached its climax, and fortune began from now to smile on him. Abraham Stern got information of his misfortune, and with parental kindness, he invited Slonimski and his family to his house in Warsaw, and highly recommended him to the local Jewish community. Thus Slonimski obtained a permanent situation among the numerous beneficial societies of the Polish capital and get the support of Itshak Shimon Rosen, a prominent banker.

Moreover, later Stern offered him the hand of his youngest daughter, Sara (Salomea) Gitel (1824–1897). Thus in early 1842 Slonimski married Stern’s beloved daughter. They had five children: Abraham Jakub (1845-1849), Leonid Ludwig Zelig (1 Nov. 1849-1918), Michal (b. 1850), Stanislaw (1853-1916), and Josef (1860-1934).

In 1838 Slonimski’s work on astronomy, *The History of the Heavens*, appeared in Warsaw with introductions in Polish by two prominent Polish astronomers.

Financial troubles constantly plagued Slonimski, and the ability to organize his affairs was completely alien to him. In the late 1840s by a stroke of luck, he managed to sell the rights of the manufacture of his adding machine to England for £400, a huge sum for the time. He invested the money in the acquisition of a fruit orchard in the town of Tomashov, and engaged in gardening and making experiments in the preparation of pottery on a new method invented by him.

In the 1850s and 1860s, Slonimski continued his scientific pursuits. In 1853 he invented a chemical process for plating iron vessels with lead. In 1856 he designed an electrochemical device for sending quadruple telegrams, which enabled simultaneous double transmission and reception—four active communication channels were open through one wire at the same time. In April 1858, he addressed a letter to the Directorate of the Russian Ministry of Transportation, in which he revealed a thorough understanding of the processes that take place in duplex telegraphy, and for the first time proposed a method to obviate certain difficulties of simultaneous transmission of messages over the wire. Despite the novelty of his proposal and the feasibility of its practical application, he failed to obtain the necessary funds for his experiments. In 1859 Slonimski published a separate brochure containing a detailed description of his method. The system of multiple telegraphy, which was used by Lord Kelvin in 1858, was based on Slonimski’s discovery. Later, the same invention was repeated by Thomas Edison, who could hardly have known anything about Slonimski’s work.

In 1863 Chaim Zelig Slonimski was appointed government censor of Hebrew books in Zhitomir and was named inspector of the rabbinical seminary (a government-sponsored rabbinical school). He served as an inspector for 12 years, until the Russian authorities closed such seminaries down.

First in history, Slonimski began writing and publishing science books in Hebrew to enlighten the Jewish population in Eastern Europe. He started publishing a popular science magazine, *Ha-Zefirah*, 1862, in Hebrew, which continued after his death, till 1931. Ha-Zefirah was a cultural event of prime importance in the Jewish community because of the vast amount of miscellaneous information that was generously spread across its pages. Until the last decade of the 19th century, Slonimski strove to develop a broad Jewish scientific discourse that would be accessible to as many educated Jews as possible.

Chaim Zelig Slonimski was an idealistic, but impractical genius. Let’s look at how he is described in the *Энциклопедический словарь Брокгауза и Ефрона* (The Brockhaus and Efron Encyclopedic Dictionary is a comprehensive multi-volume encyclopedia in Russian), published in 1900 (one of the editors of this encyclopedia was his son Leonid Ludwig), when he was still living:

*The mathematical gifts and inventive power with which Slonimski astounded both theoretical and practical scientists in his youth, were not exploited by him in full, partly because of the unfavorable living conditions of Russian Jews and partly because of Slonimski’s own intellectual idiosyncrasies. Once he had found the solution of a specific problem…, he was in no hurry to publish his findings… and often laid them aside for many years until the foreign scientific periodicals announced these inventions as new accomplishments of some Western scientist.*

Chaim Zelig Slonimski carried on in excellent mental and physical health well into his tenth decade (he inherited his longevity from his grandfather, Yehiel Neches, who also lived to 95, and his grandchild, the composer Nicolas Slonimsky, died in 1995 at the age of 101). He died on 15 May 1904, in Warsaw. His gravestone in the Jewish cemetery on Okopowa str. in Warsaw is still preserved (see the nearby image).