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87-610: Curtas were considered the best portable calculators available until they were displaced by electronic calculators in the 1970s. The Curta was conceived by Curt Herzstark in the 1930s in Vienna , Austria . By 1938, he had filed a key patent, covering his complemented stepped drum. This single drum replaced the multiple drums, typically around 10 or so, of contemporary calculators, and it enabled not only addition, but subtraction through nines complement math, essentially subtracting by adding. The nines' complement math breakthrough eliminated

174-529: A dissertation Specimen Quaestionum Philosophicarum ex Jure collectarum ( An Essay of Collected Philosophical Problems of Right ), arguing for both a theoretical and a pedagogical relationship between philosophy and law. After one year of legal studies, he was awarded his bachelor's degree in Law on 28 September 1665. His dissertation was titled De conditionibus ( On Conditions ). In early 1666, at age 19, Leibniz wrote his first book, De Arte Combinatoria ( On

261-416: A mathematician , philosopher , scientist and diplomat who is credited, alongside Sir Isaac Newton , with the invention of calculus in addition to many other branches of mathematics , such as binary arithmetic, and statistics . Leibniz has been called the "last universal genius" due to his knowledge and skills in different fields and because such people became much less common after his lifetime with

348-455: A mechanical pocket calculator (the Curta ). Herzstark was born in Vienna , the son of Marie and Samuel Jakob Herzstark. His father was Jewish and his mother, born a Catholic, converted to Lutheranism and raised Herzstark Lutheran. In 1938, while he was technical manager of his father's company Rechenmaschinenwerk Austria Herzstark & Co., Herzstark had already completed the design of

435-421: A Curta was designed by Marcus Wu that could be produced on a 3D printer. The Curta's fine tolerances were beyond the ability of printer technology of 2017 to produce to scale, so the printed Curta was about the size of a coffee can and weighed about three pounds. Curt Herzstark Curt Herzstark (January 26, 1902 – October 27, 1988) was an Austrian engineer. During World War II , he designed plans for

522-575: A drawing of the construction of his calculator, so that the Nazis could ultimately give the machine to the Führer as a gift after the successful end of the war. The preferential treatment this allowed ensured that he survived his stay at Buchenwald until the camp's liberation in 1945, by which time he had redrawn the complete construction from memory. Herzstark died in Nendeln , Liechtenstein . The Curta

609-726: A fair part of his assigned task: when the material Leibniz had written and collected for his history of the House of Brunswick was finally published in the 19th century, it filled three volumes. Leibniz was appointed Librarian of the Herzog August Library in Wolfenbüttel , Lower Saxony , in 1691. In 1708, John Keill , writing in the journal of the Royal Society and with Newton's presumed blessing, accused Leibniz of having plagiarised Newton's calculus. Thus began

696-511: A geometry book as an example to explain his reasoning. If this book was copied from an infinite chain of copies, there must be some reason for the content of the book. Leibniz concluded that there must be the " monas monadum " or God. The ontological essence of a monad is its irreducible simplicity. Unlike atoms, monads possess no material or spatial character. They also differ from atoms by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of

783-604: A journal article titled "New System of the Nature and Communication of Substances". Between 1695 and 1705, he composed his New Essays on Human Understanding , a lengthy commentary on John Locke 's 1690 An Essay Concerning Human Understanding , but upon learning of Locke's 1704 death, lost the desire to publish it, so that the New Essays were not published until 1765. The Monadologie , composed in 1714 and published posthumously, consists of 90 aphorisms. Leibniz also wrote

870-612: A key role in advancing his mathematical and scientific reputation, which in turn enhanced his eminence in diplomacy, history, theology, and philosophy. The Elector Ernest Augustus commissioned Leibniz to write a history of the House of Brunswick, going back to the time of Charlemagne or earlier, hoping that the resulting book would advance his dynastic ambitions. From 1687 to 1690, Leibniz traveled extensively in Germany, Austria, and Italy, seeking and finding archival materials bearing on this project. Decades went by but no history appeared;

957-725: A large collection of mechanical calculators, among them over 100 Curta calculators. A part of his collections is on display at the Enter Museum in Solothurn , Switzerland. In 2016 he donated a Curta calculator to the Yad Vashem Museum in Jerusalem. The Curta plays a role in William Gibson 's Pattern Recognition (2003) as a piece of historic computing machinery as well as a crucial "trade" item. In 2016

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1044-546: A meticulous study (informed by the 1999 additions to the critical edition) of all of Leibniz's philosophical writings up to 1688, Mercer (2001) disagreed with Couturat's reading. Leibniz met Baruch Spinoza in 1676, read some of his unpublished writings, and had since been influenced by some of Spinoza's ideas. While Leibniz befriended him and admired Spinoza's powerful intellect, he was also dismayed by Spinoza's conclusions, especially when these were inconsistent with Christian orthodoxy. Unlike Descartes and Spinoza, Leibniz had

1131-409: A philosopher, he was a leading representative of 17th-century rationalism and idealism . As a mathematician, his major achievement was the development of the main ideas of differential and integral calculus , independently of Isaac Newton 's contemporaneous developments. Mathematicians have consistently favored Leibniz's notation as the conventional and more exact expression of calculus. In

1218-410: A post he held for the rest of his life. Leibniz served three consecutive rulers of the House of Brunswick as historian, political adviser, and most consequentially, as librarian of the ducal library. He thenceforth employed his pen on all the various political, historical, and theological matters involving the House of Brunswick; the resulting documents form a valuable part of the historical record for

1305-652: A related mission to the English government in London, early in 1673. There Leibniz came into acquaintance of Henry Oldenburg and John Collins . He met with the Royal Society where he demonstrated a calculating machine that he had designed and had been building since 1670. The machine was able to execute all four basic operations (adding, subtracting, multiplying, and dividing), and the society quickly made him an external member. The mission ended abruptly when news of

1392-676: A role in the initiatives and negotiations leading up to that Act, but not always an effective one. For example, something he published anonymously in England, thinking to promote the Brunswick cause, was formally censured by the British Parliament . The Brunswicks tolerated the enormous effort Leibniz devoted to intellectual pursuits unrelated to his duties as a courtier, pursuits such as perfecting calculus, writing about other mathematics, logic, physics, and philosophy, and keeping up

1479-546: A short paper, "Primae veritates" ("First Truths"), first published by Louis Couturat in 1903 (pp. 518–523) summarizing his views on metaphysics . The paper is undated; that he wrote it while in Vienna in 1689 was determined only in 1999, when the ongoing critical edition finally published Leibniz's philosophical writings for the period 1677–1690. Couturat's reading of this paper influenced much 20th-century thinking about Leibniz, especially among analytic philosophers . After

1566-443: A six-digit revolution counter, and an eleven-digit result counter. According to the advertising literature, it weighs only 8 ounces (230 g). Serial number 70154, produced in 1969, weighs 245 grams (8.6 oz). The larger Type II Curta, introduced in 1954, has eleven digits for data entry, an eight-digit revolution counter, and a fifteen-digit result counter. The Curta was popular among contestants in sports car rallies during

1653-625: A two-year residence in Vienna , where he was appointed Imperial Court Councillor to the Habsburgs . On the death of Queen Anne in 1714, Elector George Louis became King George I of Great Britain , under the terms of the 1701 Act of Settlement. Even though Leibniz had done much to bring about this happy event, it was not to be his hour of glory. Despite the intercession of the Princess of Wales, Caroline of Ansbach, George I forbade Leibniz to join him in London until he completed at least one volume of

1740-467: A university education in philosophy. He was influenced by his Leipzig professor Jakob Thomasius , who also supervised his BA thesis in philosophy. Leibniz also read Francisco Suárez , a Spanish Jesuit respected even in Lutheran universities. Leibniz was deeply interested in the new methods and conclusions of Descartes, Huygens, Newton, and Boyle , but the established philosophical ideas in which he

1827-462: A vast correspondence. He began working on calculus in 1674; the earliest evidence of its use in his surviving notebooks is 1675. By 1677 he had a coherent system in hand, but did not publish it until 1684. Leibniz's most important mathematical papers were published between 1682 and 1692, usually in a journal which he and Otto Mencke founded in 1682, the Acta Eruditorum . That journal played

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1914-594: A wide variety of advanced philosophical and theological works—ones that he would not have otherwise been able to read until his college years. Access to his father's library, largely written in Latin , also led to his proficiency in the Latin language, which he achieved by the age of 12. At the age of 13 he composed 300 hexameters of Latin verse in a single morning for a special event at school. In April 1661 he enrolled in his father's former university at age 14. There he

2001-420: Is referenced in chapter four of William Gibson 's Pattern Recognition . The chapter is entitled 'Math Grenades', which refers to protagonist Cayce Pollard mistaking a box of them for hand grenades at first glance. Notes Further reading Gottfried Leibniz Gottfried Wilhelm Leibniz or Leibnitz (1 July 1646 [ O.S. 21 June] – 14 November 1716) was a German polymath active as

2088-402: Is a descendant of Gottfried Leibniz 's Stepped Reckoner and Charles Thomas's Arithmometer , accumulating values on cogs, which are added or complemented by a stepped drum mechanism. Numbers are entered using slides (one slide per digit) on the side of the device. The revolution counter and result counter reside around the shiftable carriage, at the top of the machine. A single turn of

2175-475: Is exercised within natural laws, where choices are merely contingently necessary and to be decided in the event by a "wonderful spontaneity" that provides individuals with an escape from rigorous predestination. For Leibniz, "God is an absolutely perfect being". He describes this perfection later in section VI as the simplest form of something with the most substantial outcome (VI). Along these lines, he declares that every type of perfection "pertains to him (God) in

2262-410: Is force, while space , matter , and motion are merely phenomenal. He argued, against Newton, that space , time , and motion are completely relative: "As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions." Einstein, who called himself a "Leibnizian", wrote in

2349-535: Is made of an infinite number of simple substances known as monads. Monads can also be compared to the corpuscles of the mechanical philosophy of René Descartes and others. These simple substances or monads are the "ultimate units of existence in nature". Monads have no parts but still exist by the qualities that they have. These qualities are continuously changing over time, and each monad is unique. They are also not affected by time and are subject to only creation and annihilation. Monads are centers of force ; substance

2436-522: Is really worth something, then we will give it to the Führer as a present after we win the war. Then, surely, you will be made an Aryan.' For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it. In the camp, Herzstark was able to develop working drawings for a manufacturable device. Buchenwald

2523-518: The Leibniz wheel , later used in the arithmometer , the first mass-produced mechanical calculator. In philosophy and theology , Leibniz is most noted for his optimism , i.e. his conclusion that our world is, in a qualified sense, the best possible world that God could have created , a view sometimes lampooned by other thinkers, such as Voltaire in his satirical novella Candide . Leibniz, along with René Descartes and Baruch Spinoza ,

2610-594: The Thirty Years' War had left German-speaking Europe exhausted, fragmented, and economically backward. Leibniz proposed to protect German-speaking Europe by distracting Louis as follows: France would be invited to take Egypt as a stepping stone towards an eventual conquest of the Dutch East Indies . In return, France would agree to leave Germany and the Netherlands undisturbed. This plan obtained

2697-557: The Théodicée of 1710 was published in his lifetime. Leibniz dated his beginning as a philosopher to his Discourse on Metaphysics , which he composed in 1686 as a commentary on a running dispute between Nicolas Malebranche and Antoine Arnauld . This led to an extensive correspondence with Arnauld; it and the Discourse were not published until the 19th century. In 1695, Leibniz made his public entrée into European philosophy with

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2784-454: The calculus priority dispute which darkened the remainder of Leibniz's life. A formal investigation by the Royal Society (in which Newton was an unacknowledged participant), undertaken in response to Leibniz's demand for a retraction, upheld Keill's charge. Historians of mathematics writing since 1900 or so have tended to acquit Leibniz, pointing to important differences between Leibniz's and Newton's versions of calculus. In 1712, Leibniz began

2871-410: The principle of sufficient reason . Using the principle of reasoning, Leibniz concluded that the first reason of all things is God. All that we see and experience is subject to change, and the fact that this world is contingent can be explained by the possibility of the world being arranged differently in space and time. The contingent world must have some necessary reason for its existence. Leibniz uses

2958-419: The 1960s, 1970s and into the 1980s. Even after the introduction of the electronic calculator for other purposes, they were used in time-speed-distance (TSD) rallies to aid in computation of times to checkpoints, distances off-course and so on, since the early electronic calculators did not fare well with the bounces and jolts of rallying. The Curta was also favored by commercial and general-aviation pilots before

3045-402: The 1970s. The Curta, however, lives on, being a highly popular collectible, with thousands of machines working just as smoothly as they did at the time of their manufacture. An estimated 140,000 Curta calculators were made (80,000 Type I and 60,000 Type II). According to Curt Herzstark, the last Curta was produced in 1972. The Curta Type I was sold for $ 125 in the later years of production, and

3132-410: The 20th century, Leibniz's notions of the law of continuity and transcendental law of homogeneity found a consistent mathematical formulation by means of non-standard analysis . He was also a pioneer in the field of mechanical calculators . While working on adding automatic multiplication and division to Pascal's calculator , he was the first to describe a pinwheel calculator in 1685 and invented

3219-526: The British. Thus Leibniz went to Paris in 1672. Soon after arriving, he met Dutch physicist and mathematician Christiaan Huygens and realised that his own knowledge of mathematics and physics was patchy. With Huygens as his mentor, he began a program of self-study that soon pushed him to making major contributions to both subjects, including discovering his version of the differential and integral calculus . He met Nicolas Malebranche and Antoine Arnauld ,

3306-614: The Combinatorial Art ), the first part of which was also his habilitation thesis in Philosophy, which he defended in March 1666. De Arte Combinatoria was inspired by Ramon Llull 's Ars Magna and contained a proof of the existence of God , cast in geometrical form, and based on the argument from motion . His next goal was to earn his license and Doctorate in Law, which normally required three years of study. In 1666,

3393-649: The Curta, but could not manufacture it due to the Nazi German annexation of Austria . Instead, the company was ordered to make measuring devices for the German Army . In 1943, perhaps influenced by the fact that his father was a liberal Jew , the Nazis arrested him for "helping Jews and subversive elements" and "indecent contacts with Aryan women" and sent him to the Buchenwald concentration camp . However,

3480-584: The Elector in the hope of obtaining employment. The stratagem worked; the Elector asked Leibniz to assist with the redrafting of the legal code for the Electorate. In 1669, Leibniz was appointed assessor in the Court of Appeal. Although von Boyneburg died late in 1672, Leibniz remained under the employment of his widow until she dismissed him in 1674. Von Boyneburg did much to promote Leibniz's reputation, and

3567-689: The Elector's cautious support. In 1672, the French government invited Leibniz to Paris for discussion, but the plan was soon overtaken by the outbreak of the Franco-Dutch War and became irrelevant. Napoleon's failed invasion of Egypt in 1798 can be seen as an unwitting, late implementation of Leibniz's plan, after the Eastern hemisphere colonial supremacy in Europe had already passed from the Dutch to

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3654-437: The Elector's death (12 February 1673) reached them. Leibniz promptly returned to Paris and not, as had been planned, to Mainz. The sudden deaths of his two patrons in the same winter meant that Leibniz had to find a new basis for his career. In this regard, a 1669 invitation from Duke John Frederick of Brunswick to visit Hanover proved to have been fateful. Leibniz had declined the invitation, but had begun corresponding with

3741-693: The Russian Tsar Peter the Great stopped in Bad Pyrmont and met Leibniz, who took interest in Russian matters since 1708 and was appointed advisor in 1711. Leibniz died in Hanover in 1716. At the time, he was so out of favor that neither George I (who happened to be near Hanover at that time) nor any fellow courtier other than his personal secretary attended the funeral. Even though Leibniz

3828-462: The Type II was sold for $ 175. While only 3% of Curtas were returned to the factory for warranty repair, a small, but significant number of buyers returned their Curtas in pieces, having attempted to disassemble them. Reassembling the machine was more difficult, requiring intimate knowledge of the orientation of, and installation order for, each part and sub-assembly, plus special guides designed to hold

3915-853: The University of Leipzig turned down Leibniz's doctoral application and refused to grant him a Doctorate in Law, most likely due to his relative youth. Leibniz subsequently left Leipzig. Leibniz then enrolled in the University of Altdorf and quickly submitted a thesis, which he had probably been working on earlier in Leipzig. The title of his thesis was Disputatio Inauguralis de Casibus Perplexis in Jure ( Inaugural Disputation on Ambiguous Legal Cases ). Leibniz earned his license to practice law and his Doctorate in Law in November 1666. He next declined

4002-442: The advent of electronic calculators because of its precision and the user's ability to confirm the accuracy of their manipulations via the revolution counter. Because calculations such as weight and balance are critical for safe flight, precise results free of pilot error are essential. The Curta calculator is very popular among collectors and can be purchased on many platforms. The Swiss entrepreneur and collector Peter Regenass holds

4089-416: The best of all masters" and he will know when his good succeeds, so we, therefore, must act in conformity to his good will—or as much of it as we understand (IV). In our view of God, Leibniz declares that we cannot admire the work solely because of the maker, lest we mar the glory and love God in doing so. Instead, we must admire the maker for the work he has done (II). Effectively, Leibniz states that if we say

4176-634: The coming of the Industrial Revolution and the spread of specialized labor. He is a prominent figure in both the history of philosophy and the history of mathematics . He wrote works on philosophy , theology , ethics , politics , law , history , philology , games , music , and other studies. Leibniz also made major contributions to physics and technology , and anticipated notions that surfaced much later in probability theory , biology , medicine , geology , psychology , linguistics and computer science . Leibniz contributed to

4263-431: The company, so that, should anyone sue, they would be suing Herzstark, not the company, thereby protecting themselves at Herzstark's expense. This ploy now backfired: without the patent rights, they could manufacture nothing. Herzstark was able to negotiate a new agreement, and money continued to flow to him. Curtas were considered the best portable calculators available until they were displaced by electronic calculators in

4350-401: The consort of her grandson, the future George II . To each of these women he was correspondent, adviser, and friend. In turn, they all approved of Leibniz more than did their spouses and the future king George I of Great Britain . The population of Hanover was only about 10,000, and its provinciality eventually grated on Leibniz. Nevertheless, to be a major courtier to the House of Brunswick

4437-430: The crank adds the input number to the result counter, at any carriage position, and increments the corresponding digit of the revolution counter. Pulling the crank upwards slightly before turning performs a subtraction instead of an addition. Multiplication, division, and other functions require a series of crank and carriage-shifting operations. The Type I Curta has eight digits for data entry (known as "setting sliders"),

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4524-573: The duke in 1671. In 1673, the duke offered Leibniz the post of counsellor. Leibniz very reluctantly accepted the position two years later, only after it became clear that no employment was forthcoming in Paris, whose intellectual stimulation he relished, or with the Habsburg imperial court. In 1675 he tried to get admitted to the French Academy of Sciences as a foreign honorary member, but it

4611-582: The exercise of their free will . God does not arbitrarily inflict pain and suffering on humans; rather he permits both moral evil (sin) and physical evil (pain and suffering) as the necessary consequences of metaphysical evil (imperfection), as a means by which humans can identify and correct their erroneous decisions, and as a contrast to true good. Further, although human actions flow from prior causes that ultimately arise in God and therefore are known to God as metaphysical certainties, an individual's free will

4698-577: The fair sum he left to his sole heir, his sister's stepson, proved that the Brunswicks had paid him fairly well. In his diplomatic endeavors, he at times verged on the unscrupulous, as was often the case with professional diplomats of his day. On several occasions, Leibniz backdated and altered personal manuscripts, actions which put him in a bad light during the calculus controversy . He was charming, well-mannered, and not without humor and imagination. He had many friends and admirers all over Europe. He

4785-436: The field of library science by developing a cataloguing system while working at the Herzog August Library in Wolfenbüttel , Germany, that served as a model for many of Europe's largest libraries. His contributions to a wide range of subjects were scattered in various learned journals , in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German. As

4872-422: The highest degree" (I). Even though his types of perfections are not specifically drawn out, Leibniz highlights the one thing that, to him, does certify imperfections and proves that God is perfect: "that one acts imperfectly if he acts with less perfection than he is capable of", and since God is a perfect being, he cannot act imperfectly (III). Because God cannot act imperfectly, the decisions he makes pertaining to

4959-531: The history of the Brunswick family his father had commissioned nearly 30 years earlier. Moreover, for George I to include Leibniz in his London court would have been deemed insulting to Newton, who was seen as having won the calculus priority dispute and whose standing in British official circles could not have been higher. Finally, his dear friend and defender, the Dowager Electress Sophia, died in 1714. In 1716, while traveling in northern Europe,

5046-487: The introduction to Max Jammer 's book Concepts of Space that Leibnizianism was superior to Newtonianism, and his ideas would have dominated over Newton's had it not been for the poor technological tools of the time; Joseph Agassi argues that Leibniz paved the way for Einstein's theory of relativity . Leibniz's proof of God can be summarized in the Théodicée . Reason is governed by the principle of contradiction and

5133-508: The journey from London to Hanover, Leibniz stopped in The Hague where he met van Leeuwenhoek , the discoverer of microorganisms. He also spent several days in intense discussion with Spinoza , who had just completed, but had not published, his masterwork, the Ethics . Spinoza died very shortly after Leibniz's visit. In 1677, he was promoted, at his request, to Privy Counselor of Justice,

5220-624: The latter's memoranda and letters began to attract favorable notice. After Leibniz's service to the Elector there soon followed a diplomatic role. He published an essay, under the pseudonym of a fictitious Polish nobleman, arguing (unsuccessfully) for the German candidate for the Polish crown. The main force in European geopolitics during Leibniz's adult life was the ambition of Louis XIV of France , backed by French military and economic might. Meanwhile,

5307-400: The leading French philosophers of the day, and studied the writings of Descartes and Pascal , unpublished as well as published. He befriended a German mathematician, Ehrenfried Walther von Tschirnhaus ; they corresponded for the rest of their lives. When it became clear that France would not implement its part of Leibniz's Egyptian plan, the Elector sent his nephew, escorted by Leibniz, on

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5394-525: The manufacture of the device, and soon a newly formed company, Contina AG Mauren, began production in Liechtenstein. It was not long before Herzstark's financial backers, thinking they had got from him all they needed, conspired to force him out by reducing the value of all of the company's existing stock to zero, including his one-third interest. These were the same people who had earlier elected not to have Herzstark transfer ownership of his patents to

5481-496: The next Elector became quite annoyed at Leibniz's apparent dilatoriness. Leibniz never finished the project, in part because of his huge output on many other fronts, but also because he insisted on writing a meticulously researched and erudite book based on archival sources, when his patrons would have been quite happy with a short popular book, one perhaps little more than a genealogy with commentary, to be completed in three years or less. They never knew that he had in fact carried out

5568-483: The offer of an academic appointment at Altdorf, saying that "my thoughts were turned in an entirely different direction". As an adult, Leibniz often introduced himself as "Gottfried von Leibniz". Many posthumously published editions of his writings presented his name on the title page as " Freiherr G. W. von Leibniz." However, no document has ever been found from any contemporary government that stated his appointment to any form of nobility . Leibniz's first position

5655-510: The only way we can truly love God is by being content "with all that comes to us according to his will" (IV). Because God is "an absolutely perfect being" (I), Leibniz argues that God would be acting imperfectly if he acted with any less perfection than what he is able of (III). His syllogism then ends with the statement that God has made the world perfectly in all ways. This also affects how we should view God and his will. Leibniz states that, in lieu of God's will, we have to understand that God "is

5742-644: The period. Leibniz began promoting a project to use windmills to improve the mining operations in the Harz Mountains. This project did little to improve mining operations and was shut down by Duke Ernst August in 1685. Among the few people in north Germany to accept Leibniz were the Electress Sophia of Hanover (1630–1714), her daughter Sophia Charlotte of Hanover (1668–1705), the Queen of Prussia and his avowed disciple, and Caroline of Ansbach ,

5829-402: The pieces in place during assembly. Many identical-looking parts, each with slightly different dimensions, required test fitting and selection as well as special tools to adjust to design tolerances. The machines have a high curiosity value; in 2016 they sold for around US$ 1,000, but buyers paid as much as US$ 1,900 for models in pristine condition with notable serial numbers. The Curta's design

5916-426: The principle of pre-established harmony , each monad follows a pre-programmed set of "instructions" peculiar to itself, so that a monad "knows" what to do at each moment. By virtue of these intrinsic instructions, each monad is like a little mirror of the universe. Monads need not be "small"; e.g., each human being constitutes a monad, in which case free will is problematic. Monads are purported to have gotten rid of

6003-531: The problematic: The Theodicy tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds . It must be the best possible and most balanced world, because it was created by an all powerful and all knowing God, who would not choose to create an imperfect world if a better world could be known to him or possible to exist. In effect, apparent flaws that can be identified in this world must exist in every possible world, because otherwise God would have chosen to create

6090-406: The reports of the army about the precision-production of the firm and especially about the technical expertise of Herzstark led the Nazis to treat him as an "intelligence-slave". His imprisonment at Buchenwald seriously threatened his health, but his condition improved when he was called to work in the factory linked to the camp, which was named after Wilhelm Gustloff . There, he was ordered to make

6177-511: The significant mechanical complexity created when "borrowing" during subtraction. This drum was the key to miniaturizing the Curta. His work on the pocket calculator stopped in 1938 when the Nazis forced him and his company to concentrate on manufacturing precision instruments for the German army. Herzstark, the son of a Catholic mother and Jewish father, was taken into custody in 1943 and eventually sent to Buchenwald concentration camp , where he

6264-527: The term " possible world " to define modal notions. Gottfried Leibniz was born on July 1 [ OS : June 21], 1646, in Leipzig , Saxony, to Friedrich Leibniz (1597–1652) and Catharina Schmuck (1621–1664). He was baptized two days later at St. Nicholas Church, Leipzig ; his godfather was the Lutheran theologian Martin Geier  [ de ] . His father died when he was six years old, and Leibniz

6351-602: The view of Leibniz, because reason and faith must be entirely reconciled, any tenet of faith which could not be defended by reason must be rejected. Leibniz then approached one of the central criticisms of Christian theism: if God is all good , all wise , and all powerful , then how did evil come into the world ? The answer (according to Leibniz) is that, while God is indeed unlimited in wisdom and power, his human creations, as creations, are limited both in their wisdom and in their will (power to act). This predisposes humans to false beliefs, wrong decisions, and ineffective actions in

6438-423: The world must be perfect. Leibniz also comforts readers, stating that because he has done everything to the most perfect degree; those who love him cannot be injured. However, to love God is a subject of difficulty as Leibniz believes that we are "not disposed to wish for that which God desires" because we have the ability to alter our disposition (IV). In accordance with this, many act as rebels, but Leibniz says that

6525-406: The world that excluded those flaws. Leibniz asserted that the truths of theology (religion) and philosophy cannot contradict each other, since reason and faith are both "gifts of God" so that their conflict would imply God contending against himself. The Theodicy is Leibniz's attempt to reconcile his personal philosophical system with his interpretation of the tenets of Christianity. This project

6612-651: Was liberated by U.S. troops on 11 April 1945, and by November Herzstark had located a factory in Sommertal, near Weimar , whose machinists were skilled enough to produce three working prototypes. Soviet forces had arrived in July, and Herzstark feared being sent to Russia, so, later that same month, he fled to Austria. He began to look for financial backers, at the same time filing continuing patents as well as several additional patents to protect his work. Franz Joseph II, Prince of Liechtenstein eventually showed interest in

6699-770: Was a life member of the Royal Society and the Berlin Academy of Sciences , neither organization saw fit to honor his death. His grave went unmarked for more than 50 years. He was, however, eulogized by Fontenelle , before the French Academy of Sciences in Paris, which had admitted him as a foreign member in 1700. The eulogy was composed at the behest of the Duchess of Orleans , a niece of the Electress Sophia. Leibniz never married. He proposed to an unknown woman at age 50, but changed his mind when she took too long to decide. He complained on occasion about money, but

6786-593: Was as a salaried secretary to an alchemical society in Nuremberg . He knew fairly little about the subject at that time but presented himself as deeply learned. He soon met Johann Christian von Boyneburg (1622–1672), the dismissed chief minister of the Elector of Mainz , Johann Philipp von Schönborn . Von Boyneburg hired Leibniz as an assistant, and shortly thereafter reconciled with the Elector and introduced Leibniz to him. Leibniz then dedicated an essay on law to

6873-558: Was considered that there were already enough foreigners there and so no invitation came. He left Paris in October 1676. Leibniz managed to delay his arrival in Hanover until the end of 1676 after making one more short journey to London, where Newton accused him of having seen his unpublished work on calculus in advance. This was alleged to be evidence supporting the accusation, made decades later, that he had stolen calculus from Newton. On

6960-466: Was educated influenced his view of their work. Leibniz variously invoked one or another of seven fundamental philosophical Principles: Leibniz would on occasion give a rational defense of a specific principle, but more often took them for granted. Leibniz's best known contribution to metaphysics is his theory of monads , as exposited in Monadologie . He proposes his theory that the universe

7047-420: Was encouraged to continue his earlier research: While I was imprisoned inside Buchenwald I had, after a few days, told the [people] in the work production scheduling department of my ideas. The head of the department, Mr. Munich said, 'See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it

7134-661: Was guided, among others, by Jakob Thomasius , previously a student of Friedrich. Leibniz completed his bachelor's degree in Philosophy in December 1662. He defended his Disputatio Metaphysica de Principio Individui ( Metaphysical Disputation on the Principle of Individuation ), which addressed the principle of individuation , on 9 June 1663 [ O.S. 30 May], presenting an early version of monadic substance theory. Leibniz earned his master's degree in Philosophy on 7 February 1664. In December 1664 he published and defended

7221-438: Was identified as a Protestant and a philosophical theist . Leibniz remained committed to Trinitarian Christianity throughout his life. Leibniz's philosophical thinking appears fragmented because his philosophical writings consist mainly of a multitude of short pieces: journal articles, manuscripts published long after his death, and letters to correspondents. He wrote two book-length philosophical treatises, of which only

7308-668: Was motivated in part by Leibniz's belief, shared by many philosophers and theologians during the Enlightenment , in the rational and enlightened nature of the Christian religion. It was also shaped by Leibniz's belief in the perfectibility of human nature (if humanity relied on correct philosophy and religion as a guide), and by his belief that metaphysical necessity must have a rational or logical foundation, even if this metaphysical causality seemed inexplicable in terms of physical necessity (the natural laws identified by science). In

7395-403: Was one of the three influential early modern rationalists . His philosophy also assimilates elements of the scholastic tradition, notably the assumption that some substantive knowledge of reality can be achieved by reasoning from first principles or prior definitions. The work of Leibniz anticipated modern logic and still influences contemporary analytic philosophy , such as its adopted use of

7482-556: Was quite an honor, especially in light of the meteoric rise in the prestige of that House during Leibniz's association with it. In 1692, the Duke of Brunswick became a hereditary Elector of the Holy Roman Empire . The British Act of Settlement 1701 designated the Electress Sophia and her descent as the royal family of England, once both King William III and his sister-in-law and successor, Queen Anne , were dead. Leibniz played

7569-437: Was raised by his mother. Leibniz's father had been a Professor of Moral Philosophy at the University of Leipzig , where he also served as dean of philosophy. The boy inherited his father's personal library. He was given free access to it from the age of seven, shortly after his father's death. While Leibniz's schoolwork was largely confined to the study of a small canon of authorities, his father's library enabled him to study

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