Brief Notes and History Computing in Mexico during 50 years
Genaro J. Martinez, Juan C. Seck-Tuoh-Mora, Sergio V. Chapa-Vergara, Christian Lemaitre
BBrief Notes and History Computing in Mexicoduring 50 years ∗ Genaro J. Mart´ınez , , Juan C. Seck-Tuoh-Mora Sergio V. Chapa-Vergara , Christian Lemaitre May 21, 2019 Escuela Superior de C´omputo, Instituto Polit´ecnico Nacional, M´exico. Unconventional Computing Lab, University of the West of England,Bristol, United Kingdom. ´Area Acad´emica de Ingenier´ıa, Universidad Aut´onoma del Estado deHidalgo, Pachuca, M´exico. Centro de Investigaciones y Estudios Avanzados del Instituto Poli´ecnicoNacional, M´exico, D.F. Universidad Aut´onoma Metropolitona, Unidad Cuajimalpa, M´exico, D.F.Figure 1: McIntosh’s computer museum, Puebla, Mexico. ∗ Genaro J. Mart´ınez, Juan C. Seck-Tuoh-Mora, Sergio V. Chapa-Vergara and ChristianLemaitre (2019) Brief notes and history computing in Mexico during 50 years,
InternationalJournal of Parallel, Emergent and Distributed Systems . DOI https://doi.org/10.1080/17445760.2019.1608990 a r X i v : . [ c s . G L ] M a y he history of computing in Mexico can not be thought without the name ofProf. Harold V. McIntosh (1929-2015) [1, 2, 3]. For almost 50 years, in Mexicohe contributed to the development of computer science with wide internationalrecognition. Approximately in 1964, McIntosh began working in the PhysicsDepartment of the Advanced Studies Center (CIEA) of the National PolytechnicInstitute (IPN), now called CINVESTAV. In 1965, at the National Center ofCalculus (CeNaC), he was a founding member of the Master in Computing,first in Latin America. With the support of Mario Baez Camargo and EnriqueMelrose, McIntosh continues his research of Martin-Baltimore Computer Centerand University of Florida at IBM 709.An excellent quality of McIntosh was his vocation as a professor, whichmeant a great recognition by his students. For this reason, he was strongly sup-ported by Roberto Mendiola, head of the School of Physics and Mathematics(ESFM), where McIntosh was a professor from 1966 to 1975 and coordinatorof the Academy of Applied Mathematics. In the National Institute of NuclearEnergy (INEN) from 1971 to 1975 he research in the Salazar Computer Cen-ter. Under the administration of the physicist Juan Jos´e Ort´ız Amezcua, thecollaboration of Tom’s Brody and a group of young people, programs and soft-ware were developed in a network of computers such as PDP-10, PDP-11 andPDP-15 connected between them. In this way, computer research at the INENrepresented the value of teaching in the ESFM, as one of McIntosh’s greatestlegacies in Mexico.A change of employment of the computer group of the INEN to the Au-tonomous University of Puebla (UAP) coincided with the commercialization ofmicrocomputers. In 1976, Luis Rivera Terrazas, head of the UAP, contractedto McIntosh and a group of 12 INEN researchers to consolidate the Bachelor’sDegree in Computer Science and form a computer research project. Thus arosethe Department of Application of Microcomputers in Puebla, with the inten-tion of building microcomputers with microprocessors such as: Motorola 6800,WD1600, Intel 8080, IMSAID, and others. This was the opportunity to requestthe background of the compiler REC/MARKOV to develop operating systemsfor microcomputers [4].McIntosh’s programming experience earned at the Martin Company in theUS UU. Writing FLT and MBLISP [5] was the antecedent to start a computerproject in Mexico in the IBM 709. LISP was the invention of John McCarthyon a theoretical concept like the Lambda calculus of Church and the conceptof Turing of a universal machine In this way LISP was the representative ofsymbolic computing. In McIntosh’s research in Quantum Chemistry, it was themain motive for the development of MBLISP for symbolic differentiation, thePoisson calculation or the commutator brackets and, in general, computationalgroup-theoretical methods.Mathematical logic was one of the main axes of the courses of the Academy ofApplied Mathematics at the ESFM, offered jointly with CeNaC in the master’sprogram in computer science. The courses were held to alternate between a prac-tical version dedicated to programming in the PDP-8 and a theoretical vision ofBoolean Algebra, the theory of automata and the elements of computability the-2ry. In their two roles, they played the development of programming skills andlearning the fundamentals of computer theory. First, starting with the physi-cal description of the PDP-8, to analyze the editor and the assembler, but thebest of all was the DDT (Dynamic Debugging Technique) program. The DDTprograms in the small DEC computer were very important for the student tohave complete control of the structure and operation of this program, reason forthe REC/DDT projects for the PDP-8, PDP-15, PDP-12 and PDP-11. On theother hand, the teaching of infinite machines and the theory of computability,the Turing machine, the Post systems and the Markov algorithms [6].REC (Regular Expression Compiler) was a relevant programming languagein the history of the Academy of Applied Mathematics of the ESFM [8]. With apedagogical desire, it was used as a language model of a finite state machine toprocess four control symbols based on regular expressions. REC has the char-acteristic of dealing with recursively defined data structures, typical of manysymbol manipulation tasks and, characteristic of REC compiler writing. Theparticular version of REC arises from the choice of collections of arithmetic oper-ators with the REC / arithmetic version similar to APL. However, the flexibilityto create other compilers results in REC for special purposes: REC/DDT fordebugging programs, REC/MA for controlling the multichannel analyzer andREC/Visual for visual control [9]. Indeed, REC and CONVERT [7] were citednotoriously by Marvin Minsky in his historic book “Computation: Finite andInfinite Machines” [8].In the direction of processing the Markov algorithms, McIntosh proposedthe development of REC/Markov for the PDP-10 [9]. An imitation text editinglanguage or as a supplement to TECO; editor, available on the PDP-10’s time-share system. Originally, seven operators were provided, enough to programMarkov algorithms studied in symbolic logic courses. Markov algorithms arevery fundamental for the theory of computation, but they are not practical fortext editing because they only allow the substitution of fixed character stringsafter a search from the beginning of the text. By allowing additional operationsand the handling capabilities of adjacent files, a highly useful and efficient texteditor emerges. In the Nuclear Center of Salazar (INEN) it was used for severalyears as a partner of TECO and calling routines of Fortran.By tradition, the numerical analysis in the Academy of Applied Mathemat-ics had as courses the diagonalization of matrices and numerical integration ofordinary differential equations, with emphasis on systems of linear differentialequations. The important thing was the research in theoretical-computationalmethods for groups applied to the solution of the wave equation of quantum me-chanics. When many of the students were connected to the Mexican PetroleumInstitute, there was a lot of interest in numerical analysis with physical-chemicalapplications. From the point of view of programming, Mc developed in the IBM1130 and PDP-10, gradually a family of matrix arithmetic packages: MATRIX,PENTA and TRI, together with the integration of Runge-Kutta SERO andSECO and, TWOC for Hamiltonian mechanics. From the theoretical point ofview, they dealt with the matrizante, its factorization and, the behavior of itseigenvalues and its eigenvectors. For the application in quantum mechanics,3pectral density and Weyl’s theory of singular equations [10].In the INEN, one of the main objectives of the purchase of its PDP-10 wasto carry out a radiological study of mineral deposits in Mexico, for which itwas possible to convince the administration to start a new computer graphicsproject. The fulfillment of this obligation led mainly to initiate programs ofdata reduction and contour graphics. PLOT was a collection of subroutinesfor the CalCom tracer, which consists of most contour programs and hiddenline subroutines. The design programs were divided into several more specificareas, reaching a wide range of applications. In this way, PLOT [11] was verysuccessful in the INEN, promoting a wide dissemination by students of theESFM with its installation in a great majority of the computers in Mexico City,especially in Petroleos Mexicanos (PEMEX). Aside from developing an abstractplotter program, McIntosh paid considerable attention to applications, such asthe collection of programs to draw spheres GEOM. In this way, advances in thePLOT package allowed the Academy of Applied Mathematics to advance in thefield of projective geometry, with a package such as PHOC (Plane HomogeneousCoordinates) and SHOC (Space Homogeneous Coordinates). The first electronic computer in Mexico was an IBM 650 installed in theNational Autonomous University of Mexico (UNAM), in June 1958. The teamresponsible of this project was a selected group of researchers in Engineering,Physics and Mathematics working in key roles at UNAM: Nabor Carrillo (Rec-tor); Alberto Barajas (Sciences Provost); Carlos Graef (Dean of the Faculty ofScience); and Sergio Beltran, leader of a research group at the Faculty of Engi-neering, who was named the first director of the UNAM Computer Center. Inthose days, very few people were aware of how to run an electronic computer,only some few researchers in Physics and astronomy had some experience usingcomputer programs to do part of their PhD work in US Universities.Beltran showed a great creativity and enthusiasm organizing the ComputingCenter with students of engineering and physics, training them with the sup-port of IBM, and organizing an annual colloquium for researchers and studentswith some of the top researchers at the time. From 1959 to 1962, Beltran or-ganized four international colloquiums of Computer Science, among the invitedkey speakers we find, Alan Perlis, McCarthy, Minsky, McIntosh and NiklausWirth [12].During the 60s years, other Universities like the IPN, and the private insti-tution, the Technological Institute of Monterrey (ITESM), installed their owncomputer centers. The training programs of the academic computing centersadded to those of the computer industry, allowed the first government institu-tions and some few private enterprises to install their own computer centers.By 1968, the first generation of Mexican students with a PhD in computerSciences came back to Mexico: Renato Iturriaga, Adolfo Guzm´an, EnriqueCalder´on, and Mario Magidin. They were the result of a successful policy indeveloping scientific infrastructure in many third world countries at the time, Some of these original papers can be found in McIntosh’s webpage http://delta.cs.cinvestav.mx/~mcintosh/cellularautomata/Welcome.html , the Natural Computing journal , the IEEE Transactions on EvolutionaryComputation and the ACM journal on Emerging Technologies in Computing. .Indeed several of these models developed in unconventional computing are de-signed with cellular automata [21, 13, 14, 15].From von Neumann era, the idea of supercomputing in non-linear media wasa central problem in cellular automata theory [16]. This concept and proposalare explored on diverse ways, such as: irreducible signals, gliders, self-mobilelocalizations, particles, waves, or molecules [17, 18]. The power of computa-tion in cellular automata has been researched mainly on the name of ‘complexrules’ [20, 22]. McIntosh had discusses several times in his classroom which vonNeumann have captured the essence of massive computation and the cellularautomata is a natural consequence to understand the power of computationboth conventional and unconventional. Recurrently, it is a very long discussionabout of von Neumann architecture versus non-von Neumann architectures intocomputer science community. McIntosh condense all his contribution in cellularautomata with his book “One-Dimensional Cellular Automata” published atUnited Kingdom for the 2009 year [23]. An excellent book applying several ofMcIntosh’s analysis was wrote by Burton Voorhees in “Computational Analy-sis of One-dimensional Cellular Automata” [24]. In this history, McIntosh hadsome personal meetings in his office with Fredkin and in other time with Moritaand Wuensche both in 2011 year.One of the most relevant subjects which McIntosh dedicated in his last yearswas to the problem of reversible cellular automata, a classical research fieldbecause these systems can conserve the initial information of the automata.This property has been of great interest for theoretical reasons to understandhow information is conserved and can be recovered in the evolution of a discretesystem, and for its computational implications.McIntosh began his studies in reversible cellular automata in the early ’90s,in these studies had the vision to include undergraduate and graduate studentsthrough the Research Summers organized by the Mexican Academy of Sciences(AMS). In these summers, the group of students in charge of McIntosh hadthe opportunity to assimilate the knowledge about the graphical tools usedto analyze the one-dimensional cellular automata, such as: de Bruijn, pair, andsubset diagrams. So, observe which properties of reversibility were characterizedwith these tools. These studies were enriched with the revision of the works of Gustav Hed- https://link.springer.com/journal/11047 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4235 https://jetc.acm.org Research Summer guided by McIntosh at UAP. http://uncomp.uwe.ac.uk/genaro/Papers/Veranos_McIntosh.html This work in the investigationof the calculation of reversible automata allowed to have direct contact withinternational professors such as Wolfram, David Hillman who were also workingon similar algorithms [28].Another important point that was studied with McIntosh was the question ofgiving a limit for the maximum length of the minimum neighborhood required tohave a reversible behavior in evolution rule of one-dimensional cellular automata.Czeizler and Kari solved this problem [30] [29], which allowed to have directcommunication with them that was reflected in a visit to Finland as part of a
Workshop on Discrete Models for Complex Systems held in 2004.Derived from the studies on de Bruijn diagrams and subsets, and in talkswith McIntosh about its possible applications, the conceptualization and ap-plication of an algorithm for the calculation of preimages in one-dimensionalcellular automata [31] was reached. The study of the properties of reversiblecellular automata using graphical tools such as de Bruijn diagrams and Welchdiagrams gave rise to new ways of calculating several systems using symbolicdynamics tools, such as the use of full-shift partitions reported in [32]The work of McIntosh continues to have a relevant influence in later studiesbeyond the understanding of the properties of reversible automata and the useof various graphical tools. This influence has generated other types of results,such as the classification of behaviors in elementary cellular automata [33], thecalculation of reversible automatons applying random block permutations [34],a direct use of the Welch indices for the random generation of reversible rules[35] and applications of cellular automata to simulate manufacturing systemsbased on de Bruijn diagrams [36].In 2011 a cellular automata collider was presented in the paper titled “Cel-lular automaton supercolliders” [37] where a virtual cellular automata collidercan simply a computation. Derived as a large research started at Department ofApplication of Microcomputers of the UAP lead by McIntosh from 1998. In thistime a relevant result in cellular automata theory was done. In 1998, MathewCook proofed which the elementary cellular automaton rule 110 is universal, theresult was presented in a special workshop organized by the Santa Fe Institutein New Mexico, USA. Cook invented a novel finite machine, a cyclic tag systemadapted to work on millions of millions of cells with dozens of particles coded,controlled and synchronized in the evolution of the one-dimensional cellular au-tomata rule 110 [38]. Two years later this result was published by Wolfram inhis book “A New Kind of Science” [39]. By the way, McIntosh and students Special issue dedicated to McIntosh in the Journal of Cellular Automata at 2008. Dis-crete Tools in Cellular Automata This cellular automata collider was developed during two years in collabora-tion with the Nuclear Science Institute (ICN) of the UNAM, the Department ofApplication of Microcomputers of the UAP, and the Unconventional Comput-ing Lab (UCL) at UWE in Bristol, United Kingdom. So, outstanding by theMassachussets Institute of Technology publication with the article titled “Com-puter Scientists Build Cellular Automaton Supercollider”. In this stage, sixyears later finally a full simulation of this virtual collider was published the lastyear in a specialized book “Advances in Unconventional Computing: Volume ITheory” with the paper “A Computation in a Cellular Automaton Collider Rule110” [41, 42]. At the same time, this reference was aggregated to the EuropeanOrganization for Nuclear Research (CERN) digital library. A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. The infinite computation which was designedoriginally by Cook is compressed in a circular machine coding package of parti-cles by regular expressions.In the late 70s Edward Fredkin and Tommaso Toffoli proposed a conceptof computation based on ballistic interactions between quanta of informationthat are represented by abstract particles [43]. The Boolean states of logicalvariables are represented by balls or atoms, which preserve their identity whenthey collide with each other. Fredkin, Toffoli and Norman Margolus developeda billiard-ball model of computation, with underpinning mechanics of elasticallycolliding balls and mirrors reflecting the balls’ trajectories. Margolus proposed aspecial class of cellular automata which implements the billiard-ball model [44]named partitioned cellular automata exhibited computational universality be-cause they simulated Fredkin gates via collision of soft spheres [18]. Also, theconstruction of this cellular automata collider consider previous results aboutcircular machines designed by Michael Arbib, Manfred Kudlek, and Yurii Ro-gozhin.Cellular automata collider use cyclotrons to explore large computationalspaces where exact structures of particles are not relevant but only the inter-actions between the particles. There we can represent the particles as pointsand trains of particles as sequences of points. The cellular automata collider isa viable prototype of a collision-based computing device. It well complimentsexisting models of computing circuits based on particle collisions. Thus, thesimulated collider have just thousands of cells not millions. A Way to Construct Complex Configurations in Rule 110. Computer Scientists Build Cellular Automaton Su-percollider. http://cds.cern.ch/record/2216884 By the way, in 2018 we celebrate the 60 anniversary of computationin Mexico. In 2018 year, it was done the construction of the first Turing machine inMexico, the first robotic Turing machine internationally: the Cubelet-LEGOTuring machine (CULET) [45]. This Turing machine define its constructionwith Cubelets robots and helped with LEGO pieces. The machine works ona fixed type and the head is controlled by the concatenation of several robots.This way, you can program any 2-symbol Turing machine in CULET. Actually,the machine can simulate the behaviour of a universal Turing machine sim-ulating the universal elementary cellular automaton rule 110 and a Turingmachine which double the number of ones. The machine was constructed inthe Artificial Life Robotics Lab (ALIROB) and the Computer Science Lab-oratory (LCCOMP) at the Escuela Superior de C´omputo (ESCOM) of theIPN in collaboration with the Unconventional Computing Lab (UCL) of UWE.The robotic Turing machine was presented this year in the “2019 InternationalConference on Artificial Life and Robotics” (ICAROB2019), Oita in Japan. Bythe way, the founder of Cubelets robots, Eric Schweikardt, comments about thismaquine in the forum of Modular Robotics with a post titled “Can you makea computer out of Cubelets?” The machine was an old project which wasworked during more than two years in an international cooperation betweenIPN and UWE.
References [1] Gerardo Cisneros (2015) Harold V. McIntosh, Physics Today, People &History. DOI:10.1063/PT.5.6193[2] Paul McJones (2015) Harold V. McIntosh, 1929-2015. https://mcjones.org/dustydecks/archives/2015/12/02/845/ . http://uncomp.uwe.ac.uk/HVM/
60 a˜nos de la computaci´on en M´exico y la influencia de Harold V. McIntosh. https://youtu.be/GIQDA5Gnxkc https://youtu.be/CrUrKtIw34w ALIROB LCCOMP http://uncomp.uwe.ac.uk/LCCOMP/
93] Genaro. J. Mart´ınez (2016) Obituary: Prof. Harold V. McIntosh,
Journalof Cellular Automata
The Fundamental Logic Translator I. A Schemefor the Automatic Programming of Large Electronic Computers , RIAS, Bal-timore, Technical Report 62-2;
The Fundamental Logic Translator II. ListProcessor , RIAS, Baltimore, Technical Report 62-9. MBLISP was neverproperly documented, although some of its features were the subject of aseries of Program Notes from the Quantum Chemistry Group of the Uni-versity of Florida. One, ”Operators for MBLISP”, Program Note no. 9, hassome importance as a precursor of the REC.[6] Harold V. McIntosh (1967) The mathematical theory of machines, Booleanalgebra, combinatorial and sequential circuits, semigroups. Escuela Supe-rior de F´ısica y Matem´aticas, Instituto Polit´ecnico Nacional, M´exico.[7] Adolfo Guzm´an & Harold V. McIntosh (1966) CONVERT,
Commun. ACM
Computation: Finite and Infinite Machines , Pren-tice Hall.[9] Carlos Garc´ıa-Jurado Mart´ınez (1975)
REC/SM , Instituto Nacional de En-erg´ıa Nuclear, Centro Nuclear, Salazar, Estado de M´exico, M´exico.[10] Sergio V. Chapa-Vergara, Amilcar Men´eses & Harold V. McIntosh (2015)
Ecuaciones Diferenciales y Teor´ıa de Weyl Sistemas Lineales de Ecua-ciones Diferenciales con un enfoque geom´etrico-matricial , Porra Print,M´exico.[11] Harold V. McIntosh (1974)
PLOT74 , Departamento de Computaci´on, Cen-tro Nuclear en Salazar (INEN). PLOT74 was distributed with the number10-228A of the DECUS program library (user group DEC). A derivative ofthis package, PLOT79 was distributed by N.H.F. Beebe (School of Com-puter Science, Department of Physics and Chemistry, University of Utah).[12] Miguel M. Soriano & Christian Lemaitre (1985). Primera d´ecada de la com-putaci´on en Mxico: 1958-1968,
Ciencia y Desarrollo , Vol 60-61. CONA-CyT.[13] Andrew Adamatzky (Ed.) (2017)
Advances in Unconventional Computing(Volume 1: Theory) , Springer International Publishing.1014] Andrew Adamatzky (Ed.) (2017)
Advances in Unconventional Computing(Volume 2: Prototypes, Models and Algorithms) , Springer InternationalPublishing.[15] H´ector Zenil (2012)
A Computable Universe , World Scientific Press.[16] John von Neumann (1966)
Theory of Self-reproducing Automata (editedand completed by A. W. Burks), University of Illinois Press, Urbana andLondon.[17] Tommaso Toffoli (1998) Non-Conventional Computers, In:
Encyclopedia ofElectrical and Electronics Engineering , J. Webster (Ed.) Collision-Based Computing , Springer.[19] Salvador E. Venegas Andraca (2018) Difusi´on y Divulgaci´on de la Com-putaci´on Cu´antica en M´exico y allende sus Fronteras.
XXII Congreso Na-cional de Divulgaci´on de la Ciencia y la T´ecnica , Universidad de Guana-juato, Guanajuato, Mxico.[20] Stephen Wolfram (1988) Cellular Automata Supercomputing, In:
HighSpeed Computing: Scientific Applications and Algorithm Design , R. B. Wil-helmson (Ed.), University of Illinois Press, pages 40–48.[21] Anthony J.G. Hey (1998)
Feynman and computation: exploring the limitsof computers , Perseus Books.[22] Genaro J. Mart´ınez, Juan C. Seck-Tuoh-Mora & H´ector Zenil (2013) Com-putation and Universality: Class IV versus Class III Cellular Automata,
Journal of Cellular Automata
One Dimensional Cellular Automata , LuniverPress, Bristol, UK.[24] Burton Voorhees (1996)
Computational Analysis of One-dimensional Cel-lular Automata , World Scientific Press.[25] Gustav A. Hedlund (1969) Endomorphisms and Automorphism of the ShiftDynamical System,
Math. S. Theory
Math. S. Theory
Math. S. Theory
Physica D: Nonlinear Phenomena
International Colloquium on Automata,Languages, and Programming Springer
Theoretical computer science
InternationalJournal of Modern Physics C
Journal of Cel-lular Automata Communications inNonlinear Science and Numerical Simulation , 941–966.[34] Juan C. Seck-Tuoh-Mora, Sergio V. Chapa-Vergara, Genaro J. Mart´ınez& Harold V. McIntosh (2005) Procedures for calculating reversible one-dimensional cellular automata,
Physica D: Nonlinear Phenomena
Information Sciences , 81–95.[36] Irving Barragan-Vite, Juan C. Seck-Tuoh-Mora, Norberto Hern´andez-Romero, Joselito Medina-Mar´ın & Eva S. Hern´andez-Gress (2018) Dis-tributed Control of a Manufacturing System with One-Dimensional Cel-lular Automata,
Complexity .[37] Genaro J. Mart´ınez, Andrew Adamatzky, Christopher R. Stephens & Ale-jandro F. Hoeflich (2011) Cellular automaton supercolliders,
InternationalJournal of Modern Physics C
Com-plex Systems
A New Kind of Science , Wolfram Media, Inc.,Champaign, Illinois.[40] Harold V. McIntosh (1999) Rule 110 as it relates to the presence ofgliders, http://delta.cs.cinvestav.mx/~mcintosh/comun/RULE110W/rule110.pdf
Advancesin Unconventional Computing: Volume I Theory , A. Adamatzky (Ed.),Springer, chapter 9, 199–220.[42] Genaro J. Mart´ınez, Andrew Adamatzky, & Harold V. McIntosh (2017)Computing with virtual cellular automata collider, In:
Proceedings of the2015 Science and Information Conference (SAI) , London, UK, pages 62–68. DOI: 10.1109/SAI.2015.7237127.[43] Edward Fredkin & Tommaso Toffoli (1982) Conservative logic,
Int. J. The-oret. Phys. Physical ReviewLetters
Journal of Robotics, Networking and Artificial Life5(4)