Frederick Michael Larkin (1936-1982)

F.M. Larkin in a still from the 1967 film Worth a Thousand Words (on which more below).

This is a page devoted to the career of my  father F.M. (Mike) Larkin, a numerical analyst active in England and Canada whose work is attracting increasing scholarly attention now that our world is being taken over by algorithms. (Among the other achievements in his brief career, Dad pioneered non-classical probabilistic approximation techniques while building some of the first graphical calculators.)

I welcome any further information, including the inevitable corrections to the text that follows. If you can provide that or the means to support further research into F.M. Larkin’s career including digitization of his archive, please get in touch.

▽  Brief Chronology
▽  Obituary
▽  The GHOST graphical output system
▽  Advances in probabilistic numerics
▽  The F.M Larkin fonds

Brief Chronology

(Largely transcribed from a Sept 1980 grant application in the Queen’s University archives.)

?-1957: Imperial College, London, England

B.Sc. (Hon) and A.R.S.C., Imperial College, London.

1957-59: U.K.A.E.A., Harwell, Oxfordshire, England

Designs and theoretical assessment of nuclear radiation shielding; extensive use of digital computers.

1960-61: Rolls Royce & Associates, Derby, England

Experimental engineering research on heat transfer characteristics of nuclear reactor fuel elements, using a 5 megawatt heat transfer rig in high pressure hit water.

Design and theoretical assessment of nuclear reactor systems for ship propulsion, particularly transient analysis. Extensive use of analogue computers.

1961-69: U.K.A.E.A., Culham, Berkshire, England

Theoretical and computational work related to the problem of controlled thermonuclear fusion. Design and analysis of unusual magnetic field configurations; invented the “tennis-ball seam conductor” for creating a “magnetic well”, used at the Lawrence Livermore Lab as an experimental plasma containment device.

Research in computer graphics; originated the graphic system now standard at the U.K.A.E.A., the British National Physical Laboratory and a number of British universities.

1969-74:  Computing Centre, Queen’s University, Kingston, Ontario, Canada

Consulting work in Numerical Methods and Applied Mathematics. Research in Approximation Theory. Teaching for Department of Computing and Information Science; originated courses in classical Numerical Analysis, numerical treatment of Partial Differential Equations and numerical techniques in Approximation Theory.

1974-1981: Department of Computing & Information Science, Queen’s U

Teaching of undergraduate courses in Computing and Numerical Analysis, and postgraduate courses in Approximation Theory, and the numerical treatment of Partial Differential Equations. Research in Approximation Theory and Numerical Analysis.


The text below is a transcription of this typescript obituary  likely delivered in Faculty Senate at Queen’s University on February 11 1982.

Michael Larkin was born in England in 1936 and took his B.Sc. in Honours Mathematics at Imperial College, London, England. From 1957 to 1969 Michael worked in government and industry research laboratories in England with stints at the Atomic Energy Labs at Harwell and Culham interrupted by a two year interlude at Rolls Royce. During this period, he worked extensively with digital and analogue computers in modelling theoretical design of nuclear systems. Although most of this work was classified he did publish four papers on topics in numerical computation graphics.

Michael joined the Computing Centre at Queen’s in 1969 as a consultant in Numerical Methods and Applied Mathematics. His role was to help researchers across the campus make effective use of the computing facilities for scientific computing. Through his efforts, Queen’s acquired the state-of-the-art numerical libraries then available and Michael encouraged their use by providing the backup service to users who encountered difficulties. During this period Michael’s interest in research blossomed and he produced five major papers in approximation theory. At the same time his interest in the academic programs at Queen’s grew and he became a part time lecturer in the Department of Computing and Information Science, assisting with curriculum design and teaching in the numerical analysis area.

In 1974, Michael joined the Department on a full time basis as an Associate Professor. He received tenure in 1977 and was promoted to Full Professor in 1980. He taught at all levels of the curriculum and continued his active interest in research. In addition, he took a keen interest in University affairs, serving as a Member of the Senate, as a Member of the Steering Committee of the Graduate School and, briefly, as Vice-Chairman of Graduate Studies. Within the Department he served as Chairman of Graduate Studies and as a member of our Curriculum Committee.

Michael had many outside interests as well. He was an avid downhill skier in winter and a sailor in the summer. He had a deep interest in music, which he passed on to his son, Matthew, and his harmonica and tin flute playing entertained us at many department gatherings. Michael exhibited a zest for life that we all admired.

I would like to finish by saying something about Michael’s research work. He worked in isolation at Queen’s in that few graduate students and fewer faculty members were aware of the nature of his research contributions to the field.

Essentially, all numerical methods rely on the use of local approximation of functions to achieve their goals. The classical approximation techniques, based on Taylor series expansions, are the foundation of almost all present day practical methods. Michael pioneered the idea of using a probabilistic approach to give an alternative local approximation technique. In some cases this leads to the classical methods, but in many others leads to new algorithms that appear to have practical advantages over more classical methods. This work has finally begun to attract attention and I expect that the importance of his contributions will grow in time. Michael was a self made researcher. He had no formal mathematics beyond the B.Sc. level, yet he was able to make fundamental contributions at the highest levels of applied mathematics. His curiosity about how the world around him worked was evident to all who knew him well.

The Faculty and the Department have lost a true scholar and are the poorer for his passing.

The GHOST graphical output system

Dad helped develop the GHOST graphical output system during his time at the UKAEA Culham Laboratory, which can be seen here in early photos. Here’s a film that largely explains the mechanics of making film-based animations of computer-drawn images.

As I note in the more extensive description of the film here, it was produced in 1967 by members of the Computing and Applied Mathematics Group at the UKAEA Culham Lab. It explains the uses of automated computers graphical output and describes a system developed at Culham Lab for achieving it. A number of examples of computer-produced ciné film output are included, drawn from the fields of astronomy, geometry and plasma physics. The same year Larkin published the User’s guide to the Culham Computer Graphical Output System.

Alan Sykes recalls that “Mike was developing the graphics system when I started at Culham in July 1965. It was called ‘GHOST’ later, when the graphics programme became too large for the KDF9 computer — which I think had just 64K of memory — so the system had to be split into two parts. GHOST was in widespread use for many years — and may still be.” (Email correspondence with author.)

Why GHOST? As Larkin explains in a 1968 publication “the acronym Ghoul has been coined, by an obvious choice of letters from the phrase graphical output language, to denote the hardware independent set of users’ commands, while the term Ghost has been reserved for the … implementation of Ghoul in the form of a graphical output system.”

Advances in probabilistic numerics

As noted by J. Oates and T. J. Sullivan in “A Modern Retrospective on Probabilistic Numerics” (2019; PDF),

The field of probabilistic numerics (PN), loosely speaking, attempts to provide a *statistical* treatment of the errors and/or approximations that are made en route to the output of a deterministic numerical method, e.g. the approximation of an integral by quadrature, or the discretised solution of an ordinary or partial differential equation.


The perspective developed by Larkin was fundamentally statistical and, in modern terminology, the probabilistic numerical methods he developed would be described as *Bayesian* … . Neverthe-less, the pioneering nature of this research motivated Larkin to focus on specific numerical tasks, as opposed to establishing a unified framework. In particular, he considered in detail the problems of approximating a non-negative function (Larkin 1969), quadrature (Larkin 1972,1974), and estimating the zeros of a complex function (Larkin 1979a,b).

The authors go on to explain that Larkin made great strides in the development of PN beginning in the late 1950s, as did the Russian A. V. Sul′din (1924–1996) although at the time they seem to have been unaware of each others’ essential advances in this domain.

The F.M Larkin fonds, Queen’s University Archives

In January 2019 I looked through the  2.2 m of textual records of his correspondence, articles, reports, notes, lectures and publications on mathematics in the archives at Queen’s University, Kingston, Ontario, Canada. Here are a few tweets with photos from that day of exploration. I plan to share more photos in future blog posts, and I welcome any funding that could help with further digitization.