Teun Koetsier

Mechanism and Machine Science: its History and its Identity

This paper contains an outline of the pre-twentieth century history of the investigation of the topologic-kinematic aspect of machines. Moreover, the paper contains an attempt to define the identity of mechanism and machine science.

The Archimedean Screw-Pump: A Note on Its Invention and the Development of the Theory

Following Drachmann and others the authors argue that it is reasonable to assume that Archimedes invented both the infinite screw and the screw-pump. They argue that these inventions can be related to Archimedes’ interest in the problem of the quadrature of the circle. Moreover, they discuss aspects of the development of the theory of the screw-pump.

On the prehistory of programmable machines: musical automata, looms, calculators

An important characteristic of modern automation is the programmability of the machinery involved. Concentrating on the aspect of programmability, in this paper an attempt is made to study the following three kinds of machines in their pre-twentieth century development: computers, weaving looms and music automata.

Burmester and Allievi: A Theory and Its Application for Mechanism Design at the End of 19th Century

The second half of 19th century can be considered as the Golden Age of TMM for the achieved theoretical and practical results that led to enhancements of machinery during the second Industrial Revolution. Burmester and Allievi can be considered as significant examples of that time for their personalities and careers as well as for their work on kinematics of mechanisms. In this paper, a survey is presented on their curricula and main scientific works on mechanism design with the aim also to stress similarities and differences in the life of kinematicians and in developments in mechanism design at the end of 19th century.

Lakatos’ Mitigated Scepticism in the Philosophy of Mathematics

Lakatos liked to view his work in the philosophy of mathematics against the background of the traditional epistemological battle between dogmatists and sceptics. Dogmatists are those who hold A) that we can attain truth and B) that we can know that we have attained truth. Sceptics are those who hold A) that we cannot attain truth, or at least B) that we cannot know that we have attained truth. Lakatos himself represented a form of mitigated scepticism (often called critical fallibilism). Like the sceptics, he held A) that we cannot attain truth, or at least B) that we cannot know that we have attained truth, but he held in addition — and in this respect he distinguished himself from extreme sceptics — C) that we can improve our knowledge and know that we have improved it.

General Topology, in Particular Dimension Theory, in the Netherlands: The Decisive Influence of Brouwer’s Intuitionism

Dutch work in dimension theory can be very naturally divided into two periods. The first period encompasses the contributions of Luitzen Egbertus Jan Brouwer (1881–1966), whose work brought about a revolution: modern topology was born and with it dimension theory. The second period concerns the work of other Dutch mathematicians who worked in topology after Brouwer, when topology had become an established discipline.

Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity

Lakoff and Nunez have argued that all of mathematics is a conceptual system created through metaphors on the basis of the ideas and modes of reasoning grounded in the sensory motor system. This paper explores this view by means of a Lakatosian reconstruction of the history and prehistory of the intermediate-value theorem, in which the notion of continuity plays an essential role. I conclude that in order to give an acceptable description of the actual development of mathematics, Lakoff’s and Nunez’s view must be amended: Mathematics can be viewed as a system of conceptual metaphors; however, it is permanently refined through proofs and refutations.

On the IFToMM Permanent Commission for History of MMS

In this paper we have outlined the historical development of the IFToMM Permanent Commission for History of MMS (Mechanism and Machine Science) by also looking at the recently established field of History of MMS with technical perspectives. The activity of the PC for History of MMS has been overviewed thought facts and efforts of the many members over the time. Subjects of History of MMS have been presented by using published results of historical investigations with modern technical reformulation.

By their fruits ye shall know them: some remarks on the interaction of general topology with other areas of mathematics

In his letter of invitation to contribute to this “Handbook of the History of Topology”, Professor James asked us to discuss the role of general topology in other areas of topology. So this paper is not a paper on the history of general topology, it is a paper on the history of its interactions with other fields of mathematics. Of the many possibilities, we decided to report on the one hand on the genesis of general topology and on the other hand on infinite-dimensional topology and set theoretic topology. For a much more comprehensive desciption of (parts of) the history of general topology, we refer the reader to [15]. The primary goal in general topology, also sometimes called point set topology, is the investigation and comparison of different classes of topological spaces. This primary goal continues to yield interesting problems and results, which derive their significance from their relevance with respect to this primary goal and from the need of applications. In the history of general topology we distinguish three periods. The first period is the prehistory of the subject. It led to the work of Hausdorff, Brouwer, Urysohn, Menger and Alexandroff. The prehistory resulted in a definition of general topology, but it left many questions unanswered. The second period, roughly from the 1920s until the 1960s was general topology’s golden age. Many fundamental theorems were proved. Many of the results from that period can be viewed as a necessary consequence of the genesis of the subject. However, much work from the golden age was also an investment in the future, an investment that started to yield fruit in the third period lasting from the 1960s until the present. That is why we will call this period the period of harvesting. In this paper we concentrate on the first and the last period: the prehistory and on the period of harvesting. In §2, which deals with the prehistory, we describe in particular the historical background of the concept of an abstract topological space. We discuss the contributions of Georg Cantor, Maurice Frechet and Felix Hausdorff. That

CHAPTER 30 – Arthur Schopenhauer and L.E.J. Brouwer: A Comparison

Luitzen Egbertus Jan Brouwer 1 (1881–1966) is one of the few truly great Dutch mathematicians. 2 Brouwers intellectual development is full of surprises. In 1905 he published a controversial booklet, Leven, Kunst en Mystiek ( Life, Art and Mysticism , [ 2 , 26 ]), in which science and technology are attacked; the human intellect and everything it brought about are depicted as evil. Yet this did not stop Brouwer from exploiting his own intellectual capacities and pursuing an academic career. In 1907 he defended his doctoral dissertation, Over de grondslagen van de wiskunde (On the Foundation of Mathematics , [ 3 ]). Moreover, after proving in the period 1908–1912 a number of topological theorems that made him famous, Brouwer became in 1912 professor of mathematics at the University of Amsterdam. At the end of World War I, Brouwers work once more radically changed course. In 1917 he started developing mathematics without use of the principle of the excluded third, the unreliability of which he had already shown in 1908. The consequences were dramatic: in so-called intuitionistic mathematics considerable parts of classical mathematics—including Brouwers topological results—do not in fact occur.