Signal Codes and Machine Codes

Codes: Mathematical Objects for Transmitting Messages

Signal Codes

Signals enable communication between people via machines. They make it possible to exchange messages, thereby conveying information. Every signal has technical, material, and mathematical abstract components. For example, each Morse signal that is transmitted from a sender to a recipient is comprised of a series of states of electrical energy that can also be expressed mathematically as the dots and dashes of the Morse alphabet. The Morse code is the essential part of the exchange of messages. The electrically generated signal executes and transmits the Morse code via the technological apparatus available. Certain technical, physical devices are necessary in order to generate signals and to transmit, save, and receive them. The technical means used for optical, acoustic, mechanical, magnetic, and electrical signals can be generated by means of physics, optics, acoustics, mechanics, magnetism, electricity, and electromagnetic waves. In principle, all of these types of signals can be used to display one and the same signal code.

The assignment of code symbols belonging to a signal is called encoding. The transformation of one signal into another is known as signal conversion. Analogue signals are those for which the associated mathematical description requires the use of a system of real numbers. Analogue signals are found predominantly in the measurement of physical states. The signals that are generated by musical instruments or by human voices are also examples of analogue signals. Digital signals are those that can be expressed mathematically through a system of whole numbers. Together with their associated digital codes, digital signals currently make the effective exchange of messages possible by means of microelectronics, computer technology, and information technology. They also provide the basis for data to be processed by computers.

Codes: Mathematical Objects to Generate Dynamic Processes

Machine Codes

In everyday life and the workplace, we are constantly confronted with dynamic processes. We designate processes as dynamic that take on different states over the course of time. For example, consider the dynamic process that takes place in connection with the purchase of a ticket from a ticket machine. This begins with the initial state; the ticket machine is directed toward an end state in temporal succession through incremental signals that are sent by clicking, which culminates in the issue of a ticket after payment has been made. Another example of a dynamic process is the weather forecast shown on television, in which the weather conditions in geographic areas are shown in chronological order for successive days of the week. The implementation of work plans, in which the state of the work at given times is shown, can also be considered an example of a dynamic process. We live in a world in which we are surrounded by a multitude of dynamic processes. Ultimately, one can even see oneself as a dynamic process – albeit a highly complex one.

Generally speaking, every dynamic process is a conglomerate of parts: material, energy, and information. Dynamic processes that primarily relate to information, however, are the focus of the »Open Codes« exhibition. This is a matter of dealing with the mathematical foundations, the mathematical system that is essential for the generation of dynamic processes. The machine codes are responsible for this at the exhibition. Machine codes in this sense lead us into the world of the mathematical analysis devised by Isaac Newton and Gottfried Wilhelm Leibniz; the world of mechanics from Leonhard Euler to Joseph-Louis de Lagrange and Pierre-Simon Laplace; and also the world of automata, calculators, and computers created in the modern era, plus the world of algorithms created through programming. Charles Babbage, Alan Turing, Kurt Gödel, Konrad Zuse, Howard Aiken, John von Neumann, Claude E. Shannon, and Gustav Knuth are all significant here, to name some important pioneers. Mathematically, the machine codes at the exhibition have to do with areas such as differential equations, difference equations, mathematical logic, Boolean algebra, finite automata, cellular automata, Petri nets, and algorithms. For all of these areas there are associated mathematical theories, which can be used in dealing with dynamic processes and the associated machine codes. The programming systems for social networks such as Facebook, as well as operating systems for personal computers (such as smartphones) and the application systems for them (e.g. Google) are current practical examples of machine codes. Because of the business models associated with them, in many ways these represent counterexamples to the concept of »open codes« in an information technology sense. They are, however, addressed in the »Open Codes« exhibition.

Codes: Historical Technical Components and Writings

Building blocks for »open codes«

Besides its focus on art, science, and society, the »Open Codes« exhibition also addresses the historical development of the technical components and systems necessary to generate, transmit, and process codes. These are: mechanical or electrical counting mechanisms; memory modules created by mechanical, magnetic, or electronic technology; and combinatorial circuits ranging from simple routers with plug contacts to the microelectronic gates and microprocessors in use today. Because of the historical significance of Morse code, the exhibition devotes particular attention to this system. With regard to the development of computers, various forms and models of calculating machines are exhibited in the exhibition. The technical and mathematical development of codes and their use as signal codes or machine codes is presented through seminal texts, from Ramon Llull’s Ars Magna and Friedrich von Knaus’s book on the miraculous writing automata he constructed to the mathematical works of George Boole, Claude E. Shannon, and John von Neumann.

Franz Pichler


In the »Open Codes« exhibition around eighty objects from the Pichler Collection are on show. Large parts of this collection were added to the ZKM | Collection in 2011.