@article {DeMoltoappear, title = {Formalism. The success(es) of a failure}, year = {In Press}, institution = {College publications}, author = {De Mol, Liesbeth}, editor = {Moktefi, A. and Moretti, A. and Schang, Fabian} } @article {de2013haskell, title = {Haskell before Haskell: an alternative lesson in practical logics of the ENIAC}, journal = {Journal of Logic and Computation}, year = {In Press}, abstract = {

This article expands on Curry{\textquoteright}s work on how to implement the problem of inverse interpolation on the ENIAC (1946) and his subsequent work on developing a theory of program composition (1948–1950). It is shown that Curry{\textquoteright}s hands-on experience with the ENIAC on the one side and his acquaintance with systems of formal logic on the other, were conductive to conceive a compact ‘notation for program construction’ which in turn would be instrumental to a mechanical synthesis of programs. Since Curry{\textquoteright}s systematic programming technique pronounces a critique of the Goldstine-von Neumann style of coding, his ‘calculus of program composition’ not only anticipates automatic programming but also proposes explicit hardware optimizations largely unperceived by computer history until Backus{\textquoteright} famous ACM Turing Award lecture (1977). The cohesion of these findings asks for an integrative historiographical approach. An appendix gives, for the first time, a full description of Curry{\textquoteright}s arithmetic compiler.

}, doi = {10.1093/logcom/exs072}, author = {De Mol, Liesbeth and Carl{\'e}, Martin and Bullynck, Maarten} } @incollection {de2014proof, title = {The Proof Is in the Process: A Preamble for a Philosophy of Computer-Assisted Mathematics}, booktitle = {New Directions in the Philosophy of Science}, series = {The Philosophy of Science in a European Perspective}, volume = {5}, year = {2014}, pages = {15{\textendash}33}, publisher = {Springer}, abstract = {

According to some well-known mathematicians well-versed in computer-assisted mathematics (CaM), “Computers are changing the way we are doing mathematics”. To what extent this is really true is still an open question. Indeed, even though some philosophers of math have taken up the challenge to think about CaM, it is unclear in what sense exactly a machine (can) affect(s) the so-called “queen of the sciences”. In fact, some have concluded that issues raised by the use of the computer in mathematics are not specific to the use of the computer per se. However, such findings seem precarious since a systematic study of computer-assisted mathematics is still lacking. In this paper I argue that in order to understand the impact of CaM, it is necessary to take more seriously the computer itself and how it is actually used in the process of doing mathematics. Within such an approach, one searches for characteristics that are specific to the use of the computer in mathematics. I will focus on a feature that is beyond any doubt inherently connected to the use of computing machinery, viz. mathematician-computer interactions. I will show how such interactions are fundamentally different from the usual interactions between mathematicians and non-human aids (a piece of paper, a blackboard etc) and how such interactions determine at least two more characteristics of CaM, viz. the significance of time and processes and the steady process of internalization of mathematical tools and knowledge into the machine. I will restrict myself to the use of the computer within so-called experimental mathematics since this is the main object of CaM within the philosophical literature.

}, doi = {10.1007/978-3-319-04382-1_2}, author = {De Mol, Liesbeth}, editor = {Galavotti, Maria Carla and Dieks, Dennis and Gonzalez, Wenceslao J. and Hartmann, Stephan and Uebel, Thomas and Weber, Marcel} } @incollection {de2013generating, title = {Generating, solving and the mathematics of {H}omo {S}apiens. {E}mil {P}ost’s views on computation}, booktitle = {A Computable Universe: Understanding and Exploring Nature as Computation}, year = {2013}, pages = {45{\textendash}62}, publisher = {World Scientific Publishers}, author = {De Mol, Liesbeth}, editor = {Zenil, H.} } @proceedings {dereasoning, title = {Reasoning with computer-assisted experiments in mathematics}, journal = {Third Workshop in the Philosophy of Information}, year = {2012}, pages = {80-92}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e} door Wetenschappen en Kunsten}, author = {De Mol, Liesbeth}, editor = {Primiero, Giuseppe and Allo, Patrick} } @article {DeMol2012, title = {Report {\textquoteright}International Conference on History and Philosophy of Computing{\textquoteright} (HAPOC)}, journal = {The Reasoner}, volume = {6}, number = {1}, year = {2012}, pages = {7-8}, author = {De Mol, Liesbeth and Primiero, Giuseppe} } @article {de2012short, title = {A short history of small machines}, year = {2012}, abstract = {

One of the most famous results of Alan M. Turing is the so-called universal Tur- ing machine (UTM). Its in uence on (theoretical) computer science can hardly be overestimated. The operations of this machine are of a most elementary na- ture but nonetheless considered to capture all the (human) processes that can be carried out in computing a number. This kind of elementary machine ts into a tradition of {\textquoteleft}logical minimalism{\textquoteright} that looks for simplest sets of operations or axioms. It is part of the more general research programme into the foundations of mathematics and logic that was carried out in the beginning of the 20th cen- tury. In the 1940s and 1950s, however, this tradition was rede ned in the context of {\textquoteleft}computer science{\textquoteright} when computer engineers, logicians and mathematicians re-considered the problem of small(est) and/or simple(st) machines in the con- text of actual engineering practices. This paper looks into this early history of research on small symbolic and physical machines and tie it to this older tradi- tion of logical minimalism. Focus will be on how the transition and translation of symbolic machines into real computers integrates minimalist philosophies as parts of more complex computer design strategies. This contextualizes Turing{\textquoteright}s machines at the turn from logic to machines.

}, author = {De Mol, Liesbeth and Bullynck, Maarten} } @article {de2011complex, title = {On the complex behavior of simple tag systems — An experimental approach}, journal = {Theoretical Computer Science}, volume = {412}, number = {1}, year = {2011}, pages = {97{\textendash}112}, abstract = {

It is a well-know fact that apparently simple systems can give rise to complex behavior. But why exactly does a given system behave in a complex manner? There are two main approaches to tackle this and other related questions. One can take on a more theoretical approach or start from a more experimental study of the behavior of such systems with the help of the computer. In this paper, the experimental approach will be applied to very small tag systems. After a discussion of some of the main theoretical results on tag systems, several results from a computer-assisted and experimental study on tag systems will be analyzed. Special attention will be given to the well-known example Post provided and studied with only 2 symbols and a deletion number v = 3. These results will be combined with some theoretical results on tag systems in order to gain more insight into the computational power of simple tag systems.

}, author = {De Mol, Liesbeth} } @incollection {de2011looking, title = {Looking for busy beavers. A socio-philosophical study of a computer-assisted proof}, booktitle = {Foundations of the Formal Sciences}, year = {2011}, pages = {61{\textendash}90}, publisher = {College Publications}, abstract = {

"Young man, in mathematics you don{\textquoteright}t understand things, you just get used to them" John von Neumann

}, author = {De Mol, Liesbeth}, editor = {Fran{\c c}ois, Karen and L{\"o}we, Benedikt and M{\"u}ller, Thomas and Van Kerkhove, Bart} } @article {934535, title = {Setting-up early computer programs: D. H. {L}ehmer{\textquoteright}s ENIAC computation}, journal = {Archive for Mathematical Logic}, volume = {49}, number = {2}, year = {2010}, pages = {123{\textendash}146}, abstract = {

A complete reconstruction of Lehmer{\textquoteright}s ENIAC set-up for computing the exponents of p modulo two is given. This program served as an early test program for the ENIAC (1946). The reconstruction illustrates the difficulties of early programmers to find a way between a man operated and a machine operated computation. These difficulties concern both the content level (the algorithm) and the formal level (the logic of sequencing operations).

}, issn = {1432-0665}, url = {http://dx.doi.org/10.1007/s00153-009-0169-8}, author = {Bullynck, Maarten and De Mol, Liesbeth}, editor = {Beckmann, Arnold and Dimitracopoulos, Costas and L{\"o}we, Benedikt} } @article {de2010solvability, title = {Solvability of the halting and reachability problem for binary 2-tag systems}, journal = {Fundamenta Informaticae}, volume = {99}, number = {4}, year = {2010}, pages = {435{\textendash}471}, abstract = {

In this report we will provide a detailed proof of the solvability of the halting and reachability problem for 2-symbolic tag systems with a shiftnumber v = 2.

}, doi = {10.3233/FI-2010-257}, author = {De Mol, Liesbeth} } @conference {678341, title = {Doing mathematics on the ENIAC. {V}on {N}eumann{\textquoteright}s and {L}ehmer{\textquoteright}s different visions}, booktitle = {Mathematical Practice and Development throughout History. Proceedings of the 18th Novembertagung on the History, Philosophy and Didactics of Mathematics}, year = {2009}, publisher = {Logos Verlag Berlin}, organization = {Logos Verlag Berlin}, abstract = {

In this paper we will study the impact of the computer on math- ematics and its practice from a historical point of view. We will look at what kind of mathematical problems were implemented on early electronic computing machines and how these implementations were perceived. By doing so, we want to stress that the computer was in fact, from its very beginning, conceived as a mathematical instru- ment per se, thus situating the contemporary usage of the computer in mathematics in its proper historical background. We will focus on the work by two computer pioneers: Derrick H. Lehmer and John von Neumann. They were both involved with the ENIAC and had strong opinions about how these new machines might influence (theoretical and applied) mathematics.

}, author = {De Mol, Liesbeth}, editor = {Witzke, Ingo and Wilhelmus, E.} } @conference {678298, title = {Mathematics through man-computer interaction. A study of the early years of computing.}, booktitle = {Logic, Philosophy and History of Science in Belgium. Proceedings of the Young Researcher Days 2008}, year = {2009}, publisher = {Koninklijke Vlaamse Academie van Belgi{\"e} voor Wetenschappen en Kunsten}, organization = {Koninklijke Vlaamse Academie van Belgi{\"e} voor Wetenschappen en Kunsten}, isbn = {9789065690432}, author = {De Mol, Liesbeth}, editor = {Weber, Erik and Libert, Thierry and Marage, Pierre and Vanpaemel, Geert} } @conference {678254, title = {On the boundaries of solvability and unsolvability in tag systems. {T}heoretical and experimental results.}, booktitle = {The complexity of simple programs}, year = {2008}, publisher = {Cork University Press}, organization = {Cork University Press}, abstract = {

Several older and more recent results on the boundaries of solvability and unsolvability in tag systems are surveyed. Emphasis will be put on the significance of computer experiments in research on very small tag systems.

}, author = {De Mol, Liesbeth}, editor = {Woods, Damien and Neary, Turlough and Seda, Tony} } @article {678369, title = {How to talk with a computer: an essay on computability and man-computer conversations}, journal = {Off Topic: {U}bersetzen. {Z}eitschrift f{\"u}r Medienkunst der KHM}, volume = {1}, year = {2008}, pages = {80{\textendash}89}, issn = {1867-5948}, author = {De Mol, Liesbeth} } @article {436211, title = {Tag systems and Collatz-like functions}, journal = {Theoretical Computer Science}, volume = {390}, number = {1}, year = {2008}, pages = {92{\textendash}101}, abstract = {

Tag systems were invented by Emil Leon Post and proven recursively unsolvable by Marvin Minsky. These production systems have shown very useful in constructing small universal (Turing complete) systems for several different classes of computational systems, including Turing machines, and are thus important instruments for studying limits or boundaries of solvability and unsolvability. Although there are some results on tag systems and their limits of solvability and unsolvability, there are hardly any that consider both the shift number n, as well as the number of symbols {\textmu}. This paper aims to contribute to research on limits of solvability and unsolvability for tag systems, taking into account these two parameters. The main result is the reduction of the 3n + 1-problem to a surprisingly small tag system. It indicates that the present unsolvability line – defined in terms of {\textmu} and v – for tag systems might be significantly decreased.

}, issn = {0304-3975}, url = {http://dx.doi.org/1854/12954}, author = {De Mol, Liesbeth} } @conference {430672, title = {A week-end off: the first extensive number-theoretical computation on the ENIAC}, booktitle = {Logic and Theory of Algorithms}, year = {2008}, publisher = {Springer Verlag}, organization = {Springer Verlag}, abstract = {

The first extensive number-theoretical computation run on the ENIAC, is reconstructed. The problem, computing the exponent of 2 modulo a prime, was set up on the ENIAC during a week-end in July 1946 by the number-theorist D.H. Lehmer, with help from his wife Emma and John Mauchly. Important aspects of the ENIAC{\textquoteright}s design are presented-and the reconstruction of the implementation of the problem on the ENIAC is discussed in its salient points.

}, isbn = {978-3-540-69405-2}, doi = {10.1007/978-3-540-69407-6_19}, author = {De Mol, Liesbeth and Bullynck, Maarten}, editor = {Beckmann, Arnold and Dimitracopoulos, Costas and L{\"o}we, Benedikt} } @conference {384497, title = {Study of limits of solvability in tag systems}, booktitle = {Lecture Notes in Computer Science}, year = {2007}, publisher = {Springer}, organization = {Springer}, abstract = {

In this paper we will give an outline of the proof of the solvability of the halting and reachability problem for 2-symbolic tag systems with a deletion number v = 2. This result will be situated in a more general context of research on limits of solvability in tag systems.

}, isbn = {978-3-540-74592-1}, author = {De Mol, Liesbeth}, editor = {Durand Lose, J and Margenstern, M} } @phdthesis {PhD_Liesbeth, title = {Tracing Unsolvability. A Mathematical, Historical and Philosophical Analysis with a Special Focus on Tag Systems}, year = {2007}, month = {May 23}, publisher = {Ghent University}, type = {phd}, author = {De Mol, Liesbeth} } @article {340414, title = {Closing the circle: An analysis of {E}mil {P}ost{\textquoteright}s early work}, journal = {Bulletin of symbolic logic}, volume = {12}, number = {2}, year = {2006}, pages = {267{\textendash}289}, abstract = {

In 1931 Kurt G{\"o}del published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post’s approach and method differs substantially from those offered by G{\"o}del, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.

}, issn = {1079-8986}, author = {De Mol, Liesbeth} } @conference {DeMol2006, title = {Facing the Computer. Some techniques to understand technique.}, booktitle = {Computers and Philosophy, an International Conference}, year = {2006}, month = {May}, publisher = {EOARD}, organization = {EOARD}, author = {De Mol, Liesbeth}, editor = {Schmidt, C. T. A.} } @article {demathematics, title = {Mathematics and Pictures. Some popular examples}, year = {2006}, abstract = {

Mathematics is a science that is traditionally known as a highly abstract discipline. Due to its apparent possibility of deducing abstract formulas without the necessity of back-linking to the outside reality, pure mathematics’ status is often experienced as being isolated from and superior to the dubious reality and our evenly ambiguous perception of it. Despite this attitude, several examples can be given of the usefulness of this back-linking. Moreover, since the commercialisation of the computer, new possibilities for mathematical research became available. These possibilities though can only be reached through experimenting. One of the aspects of this experimental approach to mathematics is the use of computer generated images. On the one hand they are used as testing instruments, on the other hand they are necessary tools for certain mathematical theories to be possible - as the outside reality is the object of observation of a physicist, computer generated images are the reality to be observed and perceived by the mathematician.

}, author = {De Mol, Liesbeth} } @booklet {de2006post, title = {Post{\textquoteright}’s machine}, year = {2006}, abstract = {

In 1936 Turing gave his answer to the question ”What is a computable number?” by constructing his now well-known Turing machines as formalisations of the actions of a human computor. Less well-known is the almost synchronously published result by Emil Leon Post, in which a quasi-identical mechanism was developed for similar purposes. In 1979 these Post ”toy” machines were described in a little booklet, called ”Post’s machine” by the Russian mathematician Uspensky. The purpose of this text was to advance abstract concepts as algorithm and programming for school children. In discussing this booklet in relation to the historical text it is based on, the author wants to show how this kind of ideas cannot only help to teach school children some of the basics of computer science, but furthermore contribute to a training in formal thinking.

}, author = {De Mol, Liesbeth} } @article {detheory, title = {Theory and Experiment in the work of {A}lonzo {C}hurch and {E}mil {P}ost}, journal = {unpublished}, year = {2006}, abstract = {

While most mathematicians would probably agree that ‘experimentation’ together with an ‘empirical’ attitude – both understood in their most general sense – can be important methods of mathematical discovery, this is often obscured in the final presentation of the results for the sake of mathematical elegance. In this paper it will be shown how this “method” has played a significant role in the work of two major contributors to the rather abstract discipline called mathematical logic, namely Alonzo Church and Emil Post.

}, author = {De Mol, Liesbeth} } @article {332160, title = {Study of fractals derived from {I}{F}{S}-fractals by metric procedures}, journal = {Fractals. {C}omplex Geometry, Patterns, and Scaling in Nature and Society}, volume = {13}, number = {3}, year = {2005}, pages = {237{\textendash}244}, abstract = {

It is a well-known fact that when visualizing an IFS-attractor through the chaos game, it is possible that the first points mapped will come closer to but stay visibly different from the attractor. This simple fact will be analyzed in more detail, through visualizations of different aspects of this convergence process. It will be shown that, in applying on every point in a 2D-plane the same sequence of mappings and coloring each point according to convergence distance, neighboring points form structures which resemble the attractor itself. Further, it is in this way possible to generate boundaries of the attractor that vary between small and coarse-grained. Using these results, it will be shown that it is possible to, starting with an IFS-attractor, construct fractals of which this IFS-attractor is a subset.

}, issn = {0218-348X}, doi = {10.1142/S0218348X05002878}, url = {http://www.worldscientific.com/doi/abs/10.1142/S0218348X05002878}, author = {De Mol, Liesbeth} } @conference {383110, title = {Computer Generated Images as Mathematical Tools}, booktitle = {Proceedings of the 7th International Conference and Exhibition on Generative Art}, year = {2004}, abstract = {

Since the commercialisation of the computer, it became possible to visualise certain aspects of mathematics that were not possible to visualise before because of the complexity or the size of the datasets involved. Some of these computer generated images even have become the icons of certain mathematical theories like for example fractal geometry. One of the advantages of these visualisations is the fact that in using them, certain properties that involve complexity can be immediately shown. This possibility will be discussed through experiments done by the author.

}, author = {De Mol, Liesbeth} }