Abstracts

A Heavenly Calculator at the Princely Court: The Digital Re-animation of a War-Damaged Renaissance Equatorium

Dr. Michael Korey Mathematisch-Physikalischer Salon, Dresden (Curator)

Ptolemy’s theory to predict the motion of the planets was received and refined over many centuries by successive generations of mathematicians and astronomers writing in Greek, Arabic, and Latin, for whom the theoretical models largely served for the computation of tables to predict planetary positions. At least since the eleventh century, a class of specialized, analog mathematical instruments known as equatoria emerged alongside these tables. They consisted of rotatable graduated disks and radially turnable arms or threads (volvelles), with which planetary positions could readily be found.... Such instruments offered a visual representation of Ptolemy's geometric models and a means for approximate calculation of the planets’ positions. Certain of these instruments used metal gears to realize interconnected components of the desired motion. Next to nothing of these early geared mechanisms survives, so that the rediscovery or re-analysis of each such instrument is a cause for interest. One such geared equatorium made of brass, with a simultaneous display of the ‘true’ zodiacal position of all seven classical planets, was sent to the Saxon court by the Coburg mathematician Nicolaus Valerius in 1564. After it was caught up in the bombing of Dresden in 1945, it survives only as a disfigured, molten fragment, but even before World War II it was never subject to a comprehensive analysis. The richly illustrated talk describes the many steps undertaken using digital means to analyze and reconstruct what this equatorium once showed – and thereby to suggest for what purpose it was made.

Modern Calculating Instruments: How to Preserve Microprocessors for the Future?

Professor Dr. Stephan Held Research Institute for Discrete Mathematics, Bonn

To be announced.

„WAN ICH BIN EIN GESCHENCKH VOL. SO ZAIG ICH DIE STUNDT GOR WOL. BIN ABER LEHR. SO DUE ICHS NIT MEHR“ – Markus Purmann’s scaphe dial at the Germanisches Nationalmuseum

Dr. Susanne Thürigen Germanisches Nationalmuseum, Nuremberg (Head of Collection: Scientific Instruments etc.)

Among a number of remarkable concave sundials in the collection of scientific instruments at the Germanisches Nationalmuseum – including scaphe dials by Georg Hartmann, Christian Heyden, and Johannes Praetorius – one later example, dated 1590, is noteworthy for its chalice-like form. It was signed and dated by the instrument maker Markus Purmann, who is mentioned in the Munich court chamber records of July 7, 1588, as a maker of clocks and scientific instruments.... Purmann’s scaphe dial claims to operate only when “filled” with liquid taking into account the refraction light at the intersection of air and water. Although Purmann provides no explicit reference, the sundial may allude to the well-known Old Testament miracle in Isaiah 38:8, imitating the backward-moving shadow of the “Horologium Achaz.” Beyond this, however, we may ask whether Purmann also recognized that the refraction of light was “in the air” as a mathematical problem around 1600, being studied in various parts of Europe. The scaphe dial was certainly intended for courtly conversation and entertainment, and it cannot be ruled out that such optical experiments were occasionally conducted with wine instead of water. It will be displayed in a studio exhibition on science and drinking culture in the early modern period, featuring drinking vessels that simultaneously served as scientific instruments and/or conveyed scientific knowledge – while also inviting convivial drinking. The exhibition will take place in 2027 to mark the 175th anniversary of the Germanisches Nationalmuseum (a research museum of the Leibniz Association) – as a toast to science.

Between Cultural Objects and Scientific Instruments: Timekeepers at the Beyer Clock and Watch Museum

Thierry Jaquemet Beyer Clock and Watch Museum, Zurich

Founded in 1971, the Beyer Zurich Clock and Watch Museum holds one of the most important private watch collections. Far more than a collection of luxurious wristwatches, the variety of objects allows it to cover large parts of the history of timekeeping from the antiquity to today. Though the development of mechanical clockworks is emphasised, their cultural-historical context is considered, too.... Therefore, modern watches are displayed just as well as marine chronometers used for navigation or planetariums and elementary clocks used for and based on natural scientific observations. This contribution presents timekeepers as instruments on the edge between cultural objects and scientific tools. After a few examples on how mathematical knowledge, artistic spirit, gifted handcraft, and socio-cultural environment combine in timekeepers, the focus is drawn to the oldest original object in the collection: a sun quadrant from 1510. Its appearance and use is described, and symposium participants will be invited to discuss the scientific base needed to produce such a piece and contemplate the term «time» from different angles.

Example for Multiplication in Analogue Electronics – as Common as Tricky

Dipl.-Ing. Luise Allendorf-Hoefer Deutsches Museum, Munich (Curator: Collection of Communication Technology and Electronics)

Since the introduction of radio at the beginning of the 20th century, amplitude modulation (AM) has been the standard radio transmission method. Medium frequency (MF) radio (in Germany until ist decommissioning in 2015), many longwave (LF) and shortwave (HF) radio services such as aeronautical radio and radio navigation were and still are transmitted via AM. Even analogue TV channels (video only) were generated in this way.... The multiple use of telephone cables and frequency conversion processes were also implemented using carrier frequency technology in amplitude modulation, as were certain sound effects that play an important role in music production. Essentially, amplitude modulation, in which the amplitude of a high-frequency carrier wave is changed by a low-frequency signal (e.g. speech, music), is generated by multiplying these sinusoidal voltages. Let's take a look at analogue electronic components that were used to implement this basic calculation in a technically sophisticated way. A prominent example of this is the ring modulator, which has a wide range of applications.

Hidden Protagonists: A Pascaline Replica and its Makers in 1960s Italy

Simona Casonato Museo Nazionale Scienza e Tecnologia Leonardo da Vinci, Milan (Curator: Collections Media, ICT and Digital Culture)

The Museo Nazionale Scienza e Tecnologia Leonardo da Vinci in Milan preserves in its collections a 1960s working replica of the famed Blaise Pascal’s 17th Century adder, the so-called “Pascaline, that at the moment is not on display. It belongs to a larger collection of similar artefacts, provided in the 1970s by the Italian IBM Company.... Within the context of a larger program of reflexive research undertaken by the Museum, about its historical identity and approaches (Canadelli, Beretta, Ronzon, 2019; Paoloni, Reali, Ronzon, 2018), this artefact has been considered for a study aimed at assessing its meaning and scope. Furthermore, in 2020-2022 the Museum was involved in the “Circuits of Practice” research project, carried out by the Loughborough University (with the participation of other universities and museums in the world) and aimed at studying how narratives about the history of computing have been established and circulated throughout museums (Natale, Parry & Foti, 2022).

Slonimski Adding Device – One Object, Many Stories

Dr. Maciej Kluza Jagiellonian University Museum, Collegium Maius, Kraków (Curator)

The subject of this presentation is a small brass adding and subtracting device. The object bears the signature of Jakub Pik (1806-1897), a Warsaw optician and maker of scientific instruments, as well as the emblem of the Russian Empire, the double-headed eagle. Therefore, the first part of the talk will focus on the production of scientific instruments in Warsaw in the nineteenth century, with particular attention to Pik’s role. However, Pik was not the inventor of this device.... Its creator was Chaim Zelig Slonimski (1810–1904), a mathematician and inventor from Białystok, and one of the pioneers of calculating machines, alongside Abraham Stern and Izrael Abraham Staffel. The second part of the presentation will address the history of Polish inventors of calculating machines in the nineteenth century. The subsequent fate of this particular instrument led to the Kraków Museum of Technology and Industry (1868–1950), the second technical museum on Polish land and the first public museum in Kraków. This story highlights the reception of scientific and technical heritage in Poland and the role of museums in its dissemination. Slonimski’s adding device is, in a sense, also the reason for my participation in this symposium. Until 2024, mathematical instruments represented only a small fraction of the historical scientific collections in our museum. This changed last year, when we received more than 500 objects from the collection assembled by Walter Szrek (1951–2024). His first contact with us, over a decade ago, was, in fact, connected with this very device. While preparing an article on Slonimski’s calculating machines, Szrek identified our instrument as the Slonimski invention. The museum provided access to the object and its photographs for his research, and the collaboration that followed ultimately led to the donation of his entire collection. The story of Walter Szrek and his assemblage will thus form the final narrative inspired by this one small device. Thus, a single small device offers four distinct stories: Warsaw instrument makers, Polish inventors of calculating machines, institutional preservation of technical heritage, and contemporary collecting.

An Astonishing Object still in Private Hands: The Sundial Quadrant and Trient signed by Christoph Schissler (Augsburg, 1569)

Professor Dr. Patrick Rocca Arithmeum, Bonn (Chief Curator)

In 1569, Christoph Schissler (c.1531-1608), one of the most renowned scientific instrument makers from Augsburg, made a remarkable instrument for measuring time: the sundial quadrant and trient. This extremely refined copper gilded and finely engraved instrument is only the second one known of this type and was called ‘Sonnenquadrant und Triens’ in the book by Maximilian Bobinger in 1954.... It combines two instruments that were described separately by Peter Apian (1495-1552). One is the quadrant published in 1532 in Quadrans Apiani astronomicus (Ingolstadt, 1532). The other is the so-called Trient, or in German Triens, a solar quadrant created by Peter Apian, but published posthumously by his son Philipp Apian (1531-1589), a mathematician and mapmaker, in De utilitate trientis, instrumenti astronomici novi (Tübingen, 1586). Using this instrument as an example, we can not only highlight the rediscovery of an exceptional maker and the exploration of a little-known mathematical cultural treasure, but also show an aspect that is still underdeveloped: the relationship between private collectors and the museum world with the aim of studying, preserving and exhibiting to the public exceptional works, which are most often kept within the same family for generations and never shown. This sundial quadrant and trient was certainly intended for conversation and entertainment at court, but also to demonstrate its owner's interest in the latest scientific developments. It will be featured in an exhibition devoted to exceptional scientific instruments, mainly German from the 16th and 17th centuries, never shown in public before. This exhibition will feature sundials, mathematical instruments including compendiums, armillary spheres, table clocks, astronomic clocks and astrolabes. It will open in spring 2026 and will follow on from the exhibition devoted to sectors.

Constructing Order: Neumann’s Proportional Sector and his Architecture

Teresa Novy Museum für Franken, Staatliches Museum für Kunst- und Kulturgeschichte, Würzburg (Curator and Head of Collection: Middle Ages and Early Modern Era)

In 1713, at the very beginning of his career, Balthasar Neumann designed and crafted a brass proportional sector he called Instrumentum Architecturae. This instrument, now preserved in the Museum für Franken Würzburg, is signed Inv. et Fe. Bal. Neumann 1713, testifying to his early engagement with questions of calculations and architectural design. Far more than a generic calculating device, the compass reflects Neumann’s architectural ambitions: its most distinctive feature is a set of engraved lines dedicated to the classical column orders – Tuscan, Doric, Ionic, Corinthian, and Composite.... These scales reflect a baroque concern with symmetry, harmony, and rhythmic proportion – qualities grounded in mathematical ratio. The instrument demonstrates how such principles could be operationalized in design practice: modular measurements could be transferred directly to the drawing board, ensuring coherence in the relation of shafts, pedestals, and entablatures. Neumann’s need to construct his own mathematical design tools at an early stage of his career helps explain how he later developed an architectural language of striking clarity, balance and complexity. Rather than situating the compass within the history of other proportional instruments, the talk will contextualize it within Neumann’s career as architect and engineer, linking this early invention to his later monumental projects such as the Würzburg Residence. The instrument thus emerges as both a personal experiment and a practical tool – illuminating how Neumann combined mathematical thinking and architectural creativity at a formative stage of his work.

The Calculation Globe of Landgraf Wilhelm IV. of Hesse-Kassel (1532-1592) – A Most Unique Analogue Computer to Convert Spherical Angles in Ecliptical and Equatorial Coordinates without any Calculation

Dr. Karsten Gaulke Astronomisch-Physikalisches Kabinett, Kassel (Curator)

In the 1560s Landgrave Wilhelm IV, one of the most important astronomers of the 16th century, repeatedly measured the brightest stars in the sky using various angle-measuring instruments and different methods of observation.... During the same years, he commissioned coppersmiths and his instrument maker, Eberhard Baldewein, to create a 72-centimeter-diameter copper sphere, which he then fitted with extremely carefully spaced great circles. This lecture will describe the tasks Wilhelm and his astronomers performed with this instrument (which is still in the collection, but not on display) and its value for the workflow at the first Kassel Observatory (1560-1597).

The Planimeter and Other Instruments of the Strange Mr. Ernst

Dr. Cyrille Foasso Musée des Arts et Métiers, Paris (Curator)

A mathematical instrument for the graphic calculation of plans, whose builder presented himself as a mechanical engineer from - and received a prize for mechanics from the Paris Academy of Sciences in 1836, Mr. Ernst's planimeter takes us on an investigation into an astonishing character at the crossroads of different disciplines, cultures, industries and markets.

Egnazio Danti’s Instrumentum primi mobilis and the Sinical Quadrant

Giorgio Strano / Gaia Cugini Museo Galileo, Florence (Curator)

In 1568, Egnazio Danti, cosmographer of the Duke of Tuscany Cosimo I de’ Medici, made a specimen of the device called Instrumentum primi mobilis. This was not conceived by Danti, but by the German cosmographer Peter Bienewitz (Apianus), who specifically wrote a book titled Instrumentum primi mobilis (Nuremberg, 1534).... Apianus also suggested that the particular shape of the device was intended to honor the Bishop of Augsburg Christoph von Stadion, whose coat of arms included three axe heads. Actually, the particular shape of the instrument has nothing to do with axe heads; it’s the geometrical outcome of the sine and cosine trigonometric relations. By examining a number of the so-called sinical quadrants, the same combination of circular segments of the instrumentum primi mobilis in relatively frequent from the fourteenth century onward. Such quadrants allow the user to perform the same trigonometric calculations than Apianus’s and Danti’s device, i.e. to obtain the sine and cosine of an angle, and vice-versa. However, sinical quadrants also help to determine other trigonometric relations, to perform the same proportional calculations than a “shadow square”, and to allow the user to increase (at least theoretically) the precision of angular measurements. Such an increase was the holy grail of astronomers and surveyors who, from antiquity, tried to determine not only the degrees of an angle, but their minute fractions too.

Johann Jacob Sauter – Clockmaker and Calculating Machine Inventor: The Appeal of the Original Object versus Preserving its Function - a Contrast?

Professor Dr. Ina Prinz Arithmeum, Bonn (Director)

In 1796, Johann Jacob Sauter produced a calculating machine for all four basic arithmetic operations - it was the most compact and most elegant calculating machine of the 18th century. Its existence and whereabouts were unknown for a long time until it was rediscovered 2005 by chance in the Gothenburg City Museum.... This calculating machine is not only extremely aesthetic, it is also mechanically unique, as it is the only surviving calculating machine with a repeating mechanism and it is the first calculating machine with a reset mechanism. In addition, the functioning of the Sauter calculating machine allows conclusions to be drawn about the function of a lost calculating machine by Hahn and Schaudt. Using this machine as an example, we can shed light on several fascinating aspects of our work: The rediscovery of an inventor, the exploration of an unknown mathematical cultural treasure, the physical restoration, the construction of a faithful, functional replica, the creation of a real model, a digital twin and an emulator. Finally, this example can be used to discuss the appeal of a unique original and the importance of preserving it for the future and giving access to its fascinating mechanics.

To be announced

Christel Schollaardt / Tiemen Cocquyt Rijksmuseumborhaeve Museum, Leiden (Manager Collections and Research / Curator)

To be announced.

Restaurierungs- und Dokumentationsprojekt zu Konrad Zuses Nachbau der Z1

Eva Kudraß Deutsches Technik Museum, Berlin (Exhibition Curator: Mathematics and Informatics)

To be announced.

Toward an ethical stewardship of instrument collections: exploring practice in a scientific heritage collection

Joshua Gorman Collection of Historical Scientific Instruments, Harvard University, Harvard (Executive Director)

Throughout the west, ethical stewardship has emerged as a cluster of practices relating to the care, exhibition, and ownership of collections emerging from colonial interactions and moments of community destruction. This talk explores the deployment of those practices in an instrument collection seeking to understand the utility of these tools to our community of users and how they might shape understanding of and access to the collections in our care.

Historical Books and Original Objects

Johannes Kaminski Arithmeum, Bonn (Curator ArithmeumLibrary)

To be announced.