Alan Kenneth Head 1925–2010
This memoir was originally published in Historical Records of Australian Science, vol.21, no.2, 2010.
Numbers in brackets refer to the bibliography at the end of the text.
Alan Head had many scientific interests. He was a mathematical physicist but was so widely read that he could turn his hand to almost anything that had a scientific basis. His contributions ranged from a design for a giant radio telescope to writing a computer program to simulate the diffraction of electrons as they pass through a crystalline specimen containing defects on an atomic scale and to calculate the images produced by these defects; from the elastic properties of engineering materials to the aberrations in aplanatic, non-spherical lens systems; from the causes of fracture in solid state materials to the patented design for a refrigerator that obtains its cooling power by selectively radiating electromagnetic radiation through a ‘window’ in the earth’s atmosphere to outer space; from Galois theory to quantum computers. Perhaps his greatest success was the theory of fatigue in aluminium alloys used in the construction of jet aeroplanes. Not only was he able to establish the micro-mechanisms involved, his analysis was such that the time that the processes would take to produce a complete failure could be estimated. Without this analysis, commercial aviation as we know it today would have been totally unsafe, whereas knowing the effective lifetime of components and replacing them before the end of their lifetime meant that, provided the relevant maintenance was carried out diligently, travel by air could be safe. The project that gave Alan most pleasure was his understanding of Galois theory and his being the first person to apply it to a practical case concerning the elastic anisotropy of crystalline materials. These two examples epitomise the value Alan put on ‘theory’. Theory was only good if it led to a practical, useful result. Alan Head had a brilliant career but his feet were always firmly on the ground. He was modest, quietly spoken and very approachable. He was a friend and mentor to many. There are more than ten scientific topics (including those mentioned above) described in this memoir and he made significant contributions to all of them.
Alan Kenneth Head was the first child of Elsie May (née Burrell) and Rowland Henry Jack Head. Elsie and Jack had grown up together in Surrey Hills (an eastern suburb of Melbourne). After their marriage, they moved to Bairnsdale in Victoria to run the newsagency there. Within a few years they moved back to Melbourne to take over the Toorak newsagency. Alan was born on 10 August 1925. The family lived in residential accommodation above the shop. Two more children, Margaret and Keith were born but then, when Alan was about seven, his father died suddenly. His mother was left to look after three young children (with another, Sybil, on the way) and to carry on running the newsagency. This was the early 1930s and there was a deep depression in Australia as in most parts of the world. To make matters worse, the newspaper companies were reluctant to accept that a woman could run the business. Moreover, the usual protocol for running a newsagency was that next week’s papers had to be paid for in advance. More than once Elsie had to rely on the generosity of friends to help her meet her obligations.
However, they all survived and, indeed, there were some perks and advantages for the children of a newsagency proprietor. For instance, they were allowed two comics a week. Rather than comics, Alan chose Scientific American and Practical Mechanics; possibly a sign of things to come! Also, newsagencies carried a range of other goods for sale and on special occasions, such as birthdays and Christmas, the children could choose toys from the stock in the shop. Alan and Keith each had a collection of Dinky toys acquired in this way. Keith played with his, but Alan kept his in their original boxes and put them on display on a side table. Keith also recalls that Alan was irritatingly unbeatable at Monopoly and other board games: ‘Our excuse was that he was older than we three, but, in truth, we knew that he was simply thinking at a different level to us’.
Keith was about three or four when his father died, but later, probably when Alan had started school, he remembers Alan helping to run the newsagency, doing the ordering and banking and keeping the books. It seems likely that Alan earned money from his mother for doing this because when his youngest sister, Sybil, fell in love with a brown coat that mother could not afford, Alan bought it for her.
Alan’s school education was mainly in church schools, but at first he was sent to the Toorak State School. That was very short-term because he ‘came home with swear words’ and was removed immediately. He then went to Christ Church School in South Yarra. When Alan was about ten or eleven it was decided to send him to Ballarat Grammar School on the strength of a recommendation that there was a particularly fine Housemaster there. Alan won a boarding scholarship, which no doubt eased the financial burden on the family. Keith said ‘So that we didn’t lose touch with Alan, some weekends mother would pack a picnic lunch, bundle us three into the car and go and visit Alan’.
The Housemaster was indeed ‘fine’ and liked to play bridge on Saturday afternoons. Alan discovered that pupils who were invited to make up a four also received afternoon tea and scones with jam and cream. So Alan went to the library and learned how to play contract bridge from books. In fact, all through his life, libraries, self-education and books played a major role. Alan was Dux of Ballarat Grammar School in 1940.
Because the education at Ballarat Grammar School only went to ‘Leaving’ level (year 11), Alan had to change schools to do his two ‘honours’ years, which would qualify him to go on to higher education. He won a boarding scholarship to Scotch College in Melbourne and was Dux of Scotch in 1942.
There is a coincidental connection here. The Head family’s great-great-grandparents arrived in Sydney in 1838, fifty years after the First Fleet. They decided to move to the Melbourne area, which had just been settled (illegally) by John Batman and others arriving from Van Diemen’s Land (Tasmania) in 1835. The Heads arrived in the Melbourne region in 1839 and decided to settle on the land on which Scotch College stands today. In 1939 the collective Head family decided to celebrate their centenary by having a large gathering, a party and a Big Raffle. The prize for the Big Raffle was a tailored suit. Alan won the Raffle, but since it was obvious that at the age of thirteen he had no real use for a suit, it was decided that he should be given the very best Malvern Star bicycle instead. Sixty years later, when the Head family held another reunion, Alan donated the money for the Raffle.
On the basis of his academic results at Scotch, Alan was awarded a scholarship to Ormond College to study at the University of Melbourne. In his final year at school Alan’s subjects were Mathematics 1, Mathematics 2, Mathematics 3, Mathematics 4, Physics and Chemistry. At university, he embarked on a double course of Mathematics and Physics. Towards the end of his time at Ormond, Alan met his future wife, Gwen, at dancing classes held at the College. Reports have it that Alan was quite a good dancer and during their ensuing five-year courtship, dancing seems to have been their main social pastime. After the dance, usually on Saturday night, Alan took Gwen home, as a good escort should. But apparently Gwen never knew where he lived. She explained this to me as ‘Alan didn’t talk much’!
Alan obtained his BA in Mathematics in 1945 and his BSc in Physics in 1946. He spent most of 1947 tutoring in mathematics at Trinity, another College of the University of Melbourne. In late 1947 or early 1948 he obtained a position as Research Officer at the CSIR Division of Aeronautics (the Council for Scientific and Industrial Research [CSIR] being the forerunner of CSIRO – the Commonwealth Scientific and Industrial Research Organisation).
The Division of Aeronautics had established a large experimental programme on the fatigue of metals and they were gathering data on full-size specimens such as the wings of Mustangs. These were single-seat, long-range fighter aircraft built in large numbers during the Second World War. Alan was recruited to try to assess the data and extract useful information from it. Alan did this in a seminal paper entitled ‘The Growth of Fatigue Cracks’ published in the Philosophical Magazine in 1953 (6). This paper was the first in a book entitled Top Ten Papers 1907–2007 published by the Defence Science and Technology Organisation. Interestingly, the second paper in this book is by D. R. Warren concerning his invention of the flight recorder (black box), first published in 1954. The invention was a success, but the development was not taken up by Australia.
Soon after Alan joined the Division of Aeronautics it was decided that the Division should come under the umbrella of the Commonwealth Department of Supply and it was renamed the Aeronautical Research Laboratories. In the early 1950s the Department of Supply was keen to bring their staff up to date with work going on in other parts of the world. To this end, they were awarding studentships for scientists to go overseas for up to two years. Alan obtained one of these in 1951. On 8 March 1951 he married Gwenneth Nancy Barlow (Gwen) and a month later they left Melbourne for England.
Alan and Gwen spent some time in London while Alan visited UK Government laboratories, some of which offered him a job. But Alan politely declined all offers. Although the studentships were not supposed to be used to further the recipient’s formal education, Alan was keen to be part of the Physics Department at the University of Bristol. This was the place to be in Solid State Defect Physics, because it was at the forefront of the new science concerning dislocations in crystals.
A dislocation is a line defect in a crystal where a plane of atoms in the lattice is incomplete. Dislocations can be moved about inside the crystal by external stresses, and they are necessary for the permanent (plastic) deformation of all crystalline materials. They can multiply if stresses greater than the yield stress are applied and they can tangle, whereupon they become difficult to move and produce the phenomenon known as work hardening. Work hardening can increase the load that the material can support, but it can also produce a higher degree of brittleness, which can lead to failure. It seems that Alan had assimilated this knowledge and recognised that it was crucial to the problem of fatigue.
In 1951 Alan got his wish and enrolled as a PhD student at the H. H. Wills Physics Laboratory at the University of Bristol.
It is interesting that the paper referred to earlier concerning the growth of fatigue cracks (6) contains no reference at all to dislocations. It is a paper based on ordinary elasticity/plasticity theory applied to a material which is elastically and plastically inhomogeneous. The inhomogeneous regions are, of course, the result of varying numbers, different types of dislocation arrays and varying densities of dislocations. As mentioned in the abstract, not only did the paper explain the processes in detail, but it was also capable of predicting the life span of a part or component, so that it could be taken out of service before a catastrophic failure occurred.
The paper was received by Philosophical Magazine on 20 May 1953. This was just eighteen days after the first fatal crash of the De Havilland Comet aircraft. Unfortunately two more fatal Comet crashes occurred in 1954. Wreckage of Comet G-ALYY was recovered and examined and it was concluded that the crash was due to metal fatigue initiated at the corners of the rectangular shape of the cabin hatches and windows acting as local stress raisers. Other contributing factors were the punching, rather than the drilling of smooth holes for rivets and the omission of Redux glue (to spread the load between rivets, and therefore reduce the stress-raising effect) in the construction of the fuselage. The Comet was one of the first airliners to use jet engines. Jet engines were more fuel efficient at high altitudes and enabled aeroplanes to fly above most of the weather. But at high altitudes it was necessary to pressurize the cabins for the well-being of the passengers. This pressurization and de-pressurization provided the cyclical stress conditions under which fatigue occurred. It is no exaggeration to say that without Alan’s pioneering work, a safe commercial aviation industry could not have been developed.
One of the main influences of this period on his life in the Physics Department of the University of Bristol were the sessions at morning and afternoon tea when senior scientists discussed and explored their topic freely with each other. Alan adopted this practice with enthusiasm and introduced similar informal discussions in all the places in which he subsequently worked. For instance, Steven Celotto, a PhD student from the University of Queensland who came to our Division to do his research, remembers that the best time was going to morning and afternoon tea with the rest of the group: ‘It was fun and I learned so much. Alan was the best to learn from; he never talked down to me, but he never spoon fed me. He tried to get me to work it out and if I got stuck he would get me moving again. He tailored his explanations to the person. I learned my physics and chemistry not at the University of Queensland, but at the CSIRO coffee table’.
Alan took less than two years to finish his PhD work. His thesis was on two topics, ‘The Interaction of Dislocations and Boundaries’ and ‘The Growth of Fatigue Cracks’. He was back in Australia when he was awarded a PhD in absentia at a ceremony on 7 July 1954.
In 1955 the CSIRO Division of Radio-physics was giving a lot of consideration to the construction of a large radio telescope, of the order of 300 feet in diameter, to be installed somewhere in Australia to view the southern skies. The large dish at Jodrell Bank near Manchester was under construction at the time and it was considered that these telescopes would complement each other. In the early months of 1956, the Chief of Radiophysics, E. G. Bowen, and the assistant chief, J. L. Pawsey, got in touch with Alan to enquire if the ‘new’ stronger aluminium alloys used in aeroplanes would be suitable to construct a large, rigid, steer-able dish. The main problem was that it was likely that the dish would sag under its own weight and thus change shape as it was pointed in different directions and elevations. They wanted a dish that was able to pick up the 21-centimetre hydrogen line and any distortions in the shape of the dish of the order of a centimetre or so would compromise its performance. Alan’s reaction was that it would be better to have a two-component ‘mirror-arrangement’ in which the large dish is set rigidly into the ground and points vertically upwards and a second, much smaller, mirror of a barrel-type shape is sited near the focus of the large dish to collect the reflected radiation. Different areas of the sky could be examined by steering the smaller mirror to point at different regions of the dish. There followed a year or so of meetings and discussions on the pros and cons and several detailed technical reports on the suitability of a steerable dish versus a stationary one. Among Alan’s personal papers there was a very thick file containing correspondence and calculations of likely performance parameters for each of the telescopes. However, in late 1956 it was decided to construct the radio telescope with a steer-able dish and locate it at Parkes in New South Wales. Alan wrote up his novel design and it was published in Nature in 1957 (16). Several telescopes have been constructed to Alan’s design in the former USSR and the USA. Perhaps the best-known radio telescope that is based on Alan’s design is the 305-metre dish at Aricebo in Puerto Rico operated by Cornell University. Alan’s work on the geometrical optics of a two-mirror system for the telescope led to a series of five papers on aplanatic mirror and lens systems (17), (19), (21), (22) and (66).
After Alan’s success in producing a theory of fatigue that was able to predict the safe life of a structure and a busy but largely fruitless year spent detailing his new design for a giant radio telescope, it seems that he considered moving on from the Aeronautical Research Laboratories. Word got around and in early 1957 Walter Boas, Chief of the CSIRO Division of Tribophysics (‘Tribo’) invited him to the Division for a talk. Walter was a researcher of the old school and agreed with the maxim of Sir Ian Clunies Ross, Chairman of CSIRO, that the way to run a research organization was to appoint top-quality scientists in the relevant field and let them decide the topics to study. The job of the Chief was to ensure that they had sufficient resources to carry out their studies. Alan was pleased to be asked to join Tribo, but not even he knew what path his career might take. He called his appointment ‘an experiment’. On a later occasion, in 1980, when Alan was moving from the Division of Materials Science (the old Tribophysics re-named) he wrote in reply to an invitation from Lew Chadderton, Chief of Chemical Physics to join his Division: ‘What would I be doing? The same sort of things I have been doing, whatever that means. I always have been a bit difficult to fit into grand organisational charts, programs and subprograms etc. I suppose because I tend to “redeploy” myself at unpredictable times and in unexpected directions. For the last few years I have been classed as an “overhead”, which at least provided some general mirth’.
Alan commenced duty at Tribophysics on 8 July 1957. His period at the University of Bristol had equipped him with a knowledge of dislocations to last him for the rest of his career. With a few exceptions, the science of single dislocations and simple interactions of two or three dislocations was either known or calculable. But in the case of ductile metals it was obvious from experiment that extremely large numbers of dislocations are generated and moved by the external applied stresses, and interact not only with each other in huge crowds and entanglements but also with the internal crystal boundaries. So further work on dislocations consisted of examining the stability of arrays and their mobility as a group under applied stresses. Eventually this led to what could be termed continuum theories of dislocations. For instance, from 1972 to 1973Alan produced six papers (55), (56), (57), (58), (59) and (60) on ‘Dislocation Group Dynamics’. (Two of these (58) and (59) were co-authored by W. W. Wood.) Towards the end of his career he, with colleagues from the Mathematical Institute at the University of Oxford, produced another series of papers, this time on continuum modelling of dislocations and associated plasticity, (79), (82), (83) and (85).
However, his next ‘off-track’ activity occurred in 1959, after Alan and Gwen had taken a holiday in Queensland. They were travelling by car on a hot day in the region of the Glasshouse Mountains. They had some tomatoes in the boot that were getting hotter and riper by the minute. Thoughts turned to how to keep them cool. Here the story becomes unclear, but what is certain is that Alan took the problem of how to keep things cool in the Outback seriously. He came up with a design for a refrigerator that required no power. Described like that, it sounds as if he had invented a device for perpetual motion (or at least perpetual cooling) and this led to difficulties when he lodged the patent (28). The device consists of a sheet of a good thermal conductor (for example, aluminium) coated with a substance that selectively radiates and absorbs electromagnetic radiation at a wavelength of about 10 microns. It so happens that, providing there are no clouds in the sky, there is a ‘window’ in the atmosphere between the absorption band for carbon dioxide on one side and an absorption band for water vapour on the other. This window lies between 8 and 13 microns, so that if a radiator emits radiation at 10 microns it escapes to outer space, the radiator loses heat and cools down. Thus the design of the refrigerator consists of a lid made of a good thermal conductor coated with a selective emitter. This is fitted to an insulated box containing, for example, the tomatoes. The device is placed so that it can see clear sky, but it has to be shaded from direct sunlight. This is because the power of sunlight falling on the surface of the earth when there is a cloudless sky is approximately 1,000 watts/m2 compared to the power of the refrigerator which is about 100 watts/m2. Thus the heating power is ten times greater than the cooling power. This is a difficult hurdle to overcome without high-quality insulation. The lack of cooling power may be one reason why this invention has not been taken up commercially. Another way of enhancing the cooling performance could be to find a selective coating material for the conductor that has a much narrower band of radiation, so that it fits through the window at 8 to 13 microns without any being absorbed at the edges. The refrigerator works day and night as long as the skies are clear.
In Australia, peak loads for electricity occur in the summer because of the widespread use of air conditioning. If such a device were perfected and fitted to every house and building in Australia it would make an enormous difference to the amount of fuel used to produce electricity and would reduce the production of carbon dioxide dramatically.
In 1962 Alan received the degree of Doctor of Science from the University of Melbourne for a thesis on three topics— Fatigue of Metals; Dislocation Theory; and Geometrical Optics of Aspherical Systems.
Also in that year Alan accepted an invitation to Brown University in Rhode Island to work with John Gilman and his group for a year. At the time of Gwen and Alan’s visit to Rhode Island, the Americas Cup Challenge yacht races between Weatherly (USA) and Gretel (Australia) were being staged. By a circuitous route, involving a cocktail party given by the Australian Ambassador and an American friend with connections with the US Navy, Gwen and Alan were invited to watch one of the races at close range from a US destroyer. This happened to be the second race of the series, in which Gretel beat Weatherly. Unfortunately from an Australian point of view, Weatherly won the series by four races to one.
On his return from Rhode Island, Alan became interested in anisotropic elasticity. It is a difficult concept to explain, but dislocations, which are the individual elements of plasticity (that is, permanent deformation), are described mathematically by linear elasticity (Hooke’s Law; stress is proportional to strain), implying that if a stress is applied and then removed the strain returns to zero. Usually the type of elasticity used to make these calculations was isotropic; that is, the material has the same elastic properties in all directions. But crystals are generally anisotropic elastically and Alan began to apply the theory of anisotropic elasticity to dislocations and dislocation groups.
Because a dislocation is a defect in the lattice of a crystal, the crystal is not in its state of minimum energy as there is an amount of energy per unit length associated with the dislocation. In order to minimize this as much as possible, dislocations usually run straight from surface to surface or from pinning point to pinning point. Alan found that using anisotropic elasticity, the energy per unit length could be very different—so much so that it would be quite possible for a segment of the dislocation pinned at each end to assume an angular elbow shape so that, although it had increased its length, the two new directions it was lying in were low energy directions and the overall energy of the dislocation was decreased. Alan asked a colleague, Mike Loretto, to use the transmission electron microscope to look for dislocations in a piece of lightly deformed beta brass. Beta brass is quite anisotropic elastically and Alan had calculated the angles of the bends for different types of dislocations lying on different slip planes and different Burgers vectors (37). Mike found the bent dislocations but was unable to determine their Burgers vector using the usual invisibility criteria. In fact, these criteria rely on isotropic elasticity and arise from the physical condition that, for pure screw and pure edge dislocations, some diffracting planes remain flat and in these cases, therefore, the diffraction of the electrons is as if from a perfect crystal and there is no image. For elastically anisotropic crystals, in general (except for some special cases of symmetry) no plane remains flat and one obtains an image of the dislocation for all diffracting conditions. This was the phenomenon that Mike had been observing.
(Biographer’s note: Dislocations are line defects in a crystal that can be present because of ‘mistakes’ in the packing of atoms as the crystal grows or can be formed when the crystal is deformed plastically. The Burgers vector of a dislocation is determined by comparing a clockwise circuit taken around the dislocation line in the imperfect crystal with a similar circuit in a perfect crystal. The lack of closure of the circuit in the good crystal (measured from finish to start) is the Burgers vector. The magnitude of the Burgers vector, its direction in the crystal and the direction of the dislocation line in the crystal determine the detailed displacements of the atoms in the vicinity of the dislocation. These displacements can be detected and imaged in the transmission electron microscope by electrons diffracting through the crystal and forming an image on the microscope screen (or on film).)
Alan decided that the thing to do was to simulate the two-beam operation of the electron microscope in a computer and to calculate the images of the dislocations corresponding to the different diffraction conditions used experimentally. Computation of images was not new. Peter Hirsch’s group at the University of Cambridge had been doing it for several years. They produced graphs of intensity of the image across the dislocation line. But Alan realised that because the differential equations to be integrated were a pair of first-order linear differential equations, the numerical integration of these could be speeded up considerably. At first this produced some consternation because so much information was produced that it became difficult to assimilate. So it was decided to transform each calculated intensity into a pixel and form a half-tone image that could be directly compared with the actual electron micrograph image. Using this comparison, Burgers vectors were determined and it was found that the dislocation angles were as predicted by Alan’s theory. The immediate result of this work was the production of four papers (37), (40), (41) and (42). The long-term consequence was the production of a monograph that explained the technique of image matching in detail and provided the computer program (61).
In the space of about eight months, starting with an odd prediction based on anisotropic elasticity, Alan had created a new field of defect identification using image matching. In the next few years it was taken up by other groups around the world as a standard method of defect identification.
In 1966 Australia changed to decimal currency and by 1968 the Reserve Bank was becoming increasingly aware of large-scale counterfeiting of $10 notes. The Governor of the Reserve Bank, Dr H. C. ‘Nugget’ Coombs, convened a meeting on 9 April 1968 to which seven wise men of science were invited. Alan was one of them. There were several follow-up meetings, but after that only one of the group, Sefton Hamann, Chief of the CSIRO Division of Applied Chemistry, stayed with the project to the end. The result was the introduction of plastic ‘paper’ to print the notes on (suggested by polymer scientist David Solomon), the inclusion of a clear window and an upgrading of the apparently chaotic line markings on the notes.
Also in 1968 Alan developed an interest in earthquakes. Many earthquakes demonstrate a pattern of behaviour reminiscent of dislocation movement, in which many small movements occur along the slip line, building up the stress so that eventually this is relieved by the fracture of the rock, producing a very large relative movement on opposite sides of the fault line. Alan chose to study the San Andreas Fault in California because this had by far the largest amount of instrumentation on it and the records were detailed and covered a long period of time. He found it was possible in some cases and at some times to describe the movements as analogous to dislocations. But there were other times when the behaviour seemed to be random and chaotic. I believe that Alan had hoped that he could analyse the data in the same way as he had done for fatigue of metals and be able to predict when failure would occur. Bearing in mind that any prediction had to be given in time to evacuate the population, yet could not be too far into the future so that the people would be away from home for weeks or months, this seems to have been a very ambitious aim. After a year or two, he shelved the idea and went on to other things.
Throughout his career, Alan liked to promote the myth that all he needed to do his work was a pile of paper and some 2B pencils. In fact he embraced computers from their first inception. During 1956 when the Giant Telescope design and its performance parameters were being determined, Australia’s first—and the world’s fourth—stored-memory electronic computer CSIRAC (Council for Scientific and Industrial Research Automatic Computer), was commissioned. It was about 1,000 times faster than the best mechanical calculators. It was built at the CSIRO Division of Radiophysics by a team led by Maston Beard and Trevor Pearcey. Trevor Pearcey had improved the analysis of the performance parameters for the design of Alan’s telescope by extending Alan’s geometric optical calculations to take into account diffraction effects as well. Initially CSIRAC was located in Sydney, but in the late 1950s it was moved to the University of Melbourne and Alan started using it for his work on anisotropy elasticity.
In the early 1960s, CSIRO set up a computing network with one large machine based in Canberra and smaller satellite machines in Adelaide, Melbourne and Sydney. This phase lasted for about ten years until ‘supercomputers’ began to appear and the rest of us had our very own, very powerful personal computers. Alan now became interested, not so much in number crunching, but in using symbolic languages (such as MuMATH and LISP) to do algebra, to solve equations and even to delve into fairly exotic manipulations using Lie Groups, Lie Algebras and Galois Theory. Both Lie and Galois are classified as abstract algebras. Lie Groups were initially introduced as a tool to solve or simplify ordinary differential equations or partial differential equations or combinations of the two. The model for this seems to have been Galois Theory. Originally, Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other. Galois theory was originally motivated by the question, ‘Why is there no formula for the roots of a fifth (or higher) degree polynomial equation in terms of the coefficients of the polynomial, using only the usual algebraic operators (addition, subtraction, multiplication and division) and application of radicals (square roots, cube roots etc.)?’ Apparently, Galois Theory not only provides a beautiful answer to this question, it also explains in detail why, on the other hand, it is possible to solve equations of degree four or lower in the above manner. ‘Beautiful’ it may be, but it has also been described as ‘refined and inaccessible’ by Professor J. R. Ockendon.
Nevertheless, Alan needed it to see if the sextic equation that is central to the theory of anisotropic elasticity has any rational roots, either in general or for specific orientations in the crystal. In pursuing this goal, he found that 2B pencils let him down. The process was just too long and intricate. So he wrote computer programs suitable for personal computers for the manipulation of both Lie and Galois algebras so that he could obtain answers in a shorter time (67), (69), (77), (78), (81), (84) and (86).
Among Alan’s files, I found some correspondence, dated August 1985, between Professor H. M. Edwards and Alan concerning a book that Edwards had recently published. The first exchange of letters goes thus:
Alan to Prof. Edwards:
Congratulations! I have just come across your book on Galois Theory. It is beautiful and my regret is that you did not write it ten years ago. At that stage I was silly enough to actually want to apply Galois theory to a real physical problem, not knowing anything about it except that it existed. It took me several years of perplexity before I realised that no one actually applied it but only admired its beauty. Books on the subject seem to be written with someone else other than me in mind and it wasn’t until I got back to the original Galois that I started to see the light ….
Reply form Prof. Edwards to Alan:
Thank you for your kind letter and for the reprints. It looks to me like you didn’t need me at all. You seem to have mastered Galois theory by reading Galois on your own. A great achievement.
But perhaps I need you. There is one point in Galois’s memoir that I have not succeeded in understanding. It is at the bottom of p. 112 in the translation in my book where it describes ‘the method one must use in practice’ to determine whether a given equation is solvable by radicals ….
(Biographer’s note: It seems that not only was Alan working from the original French, but also he was probably the first person to use Galois Theory to solve a practical problem. As far as I could understand the correspondence, the two never did quite agree on the ‘point on p. 112’.)
Alan developed a strong interest in the emerging, but extremely popular, concept of Quantum Computers. With conventional silicon chips, the memory elements are becoming smaller and smaller and are being packed closer and closer together until ultimately they will be limited by the size of the atoms themselves. Quantum Computers may present a potential solution for this problem. They do involve atoms, but the concept is more to do with the quantum states of the atom (or ion) and the zeros and ones of today’s technology (bits) would be replaced by different quantum states of the atom (qubits) and mixtures of these quantum states. It would be a requirement that the atoms stay in their given state or mixture of states for a period of time and are not affected by outside disturbances. Work by Peter Hannaford and Tim Bastow was going on in our laboratory that was relevant to the possible development of a quantum computer. Peter Hannaford attended a conference in June 1995 at which there was a talk about quantum computing and on his return to the laboratory he asked Alan to give a talk on the subject. The talk was well attended—standing room only. Alan was invited to repeat the talk at La Trobe University and at the University of Melbourne. Alan encouraged Peter Hannaford to approach the Defence Science and Technology Organisation (DSTO) at Salisbury near Adelaide about funding a joint project to develop quantum computing. Nothing came of this; again, Alan was too far ahead of his time.
Throughout his career, Alan’s emphasis was always on research. On many occasions this was achieved alone but he was also keen to collaborate. No matter how esoteric his research may have appeared to others, for him it always had to have a useful result. He spent periods abroad collaborating with people who had (at that specific time) similar interests to his own. He spent a year at Brown University working with John Gilman; six months in 1971 at the University of Florida with John Hren’s group; a year at the Department of Materials Science at Oxford University in 1968 with Peter Hirsch’s group. Later he had several, almost yearly visits to the Mathematical Institute at Oxford University to collaborate with John Ockendon and his colleagues.
It was during one of his visits to the Mathematical Institute that Alan observed in action a scheme whereby people from industry could bring problems along to be considered, and hopefully have them taken on and solved, by a panel of mathematicians. The scheme was MISG, which stands for Mathematics in Industry Study Group. Alan was so impressed that he imported the idea to Australia and pulled a few strings to get it going. Initially it was organized by CSIRO’s Division of Mathematics and Statistics. It is still going, now under the wing of the Australia and New Zealand Institute of Applied Mathematics, and recently had its 26th birthday. Noel Barton, who was heavily involved with MISG in Australia, including being the director for seven years, recalls that ‘Alan was an influential participant. He had deep knowledge in areas where many of the mathematical participants were weak, especially in chemistry and physics and was therefore useful on topics with origins in chemical engineering. These included development of new mathematical models for phenomena involving chemistry coupled with aspects such as coating, droplets, bubbles and phase change. Alan had a dry and easy-going style. Allied with his obvious intelligence and special knowledge, his style enabled him to work well in the group dynamics required in the MISG. He was a valuable contributor on numerous occasions and we were always pleased to have him as a delegate’.
Alan was offered Chairs at overseas universities but always turned them down. The administration involved would interfere with his research and working in Australia was far enough away not to be interrupted by too many visitors. But there were several instances when he did take on an administrative role. When Walter Boas retired, Alan was appointed Acting Chief of Tribophysics until a new Chief was found. He was also appointed interim Chief when the Division of Materials Science joined the Division of Chemical Physics and was renamed the Division of Materials Science and Technology. He was invited to become the founding Director of the Institute of Physical Sciences when CSIRO was grouping divisions into an Institute structure. He declined the offer. He sat on review boards for the Division of Radiophysics and for the Division of Mathematics and Statistics. He served for many years on the Australian Aeronautical Research Committee. In 1968 Alan was one of the founding members of the International Congress on Fracture. In the same year he became one of the editors of the International Journal of Fracture and he only resigned when he retired in 1990. He was one of the organizers of a meeting held on 8–9 October 1996 under the auspices of the Royal Society of London on ‘Vortices, Dislocations and Line Singularities in Partial Differential Equations’. The meeting is recorded in Phil. Trans. of the Roy. Soc. Lond., 355, 1945–2072 (Number 1731).
Alan was awarded several honours during his career. He was awarded the Syme Medal by the University of Melbourne in 1969 for the best original research in physics produced in Australia in the previous two years. He was elected to the Australian Academy of Science in 1971 and to the Royal Society of London in 1988. He was appointed an Officer of the Order of Australia in 1991 and was awarded the John Shearer Medal in 1976 for a paper entitled ‘Earthquakes and Dislocations’ as the best paper for that year presented to the Australian Mineral Foundation. He received a Centenary Medal in 2003 (instigated in 2001 to mark the centenary of Federation in Australia) from the Australian Government for his service to research and science.
Alan retired in 1990 from CSIRO at the mandatory age of 65, but was given an Honorary Research Fellowship so that he could stay in the laboratory and do what he did best: encourage, mentor, advise and interact generally with the other researchers. In March 2001 he was made an Adjunct Professor at Swinburne University of Technology for three years.
Alan was a quiet man, generally of few words. He was an avid reader. His evening routine was to go home, have dinner, put on some favourite classical music and read a book; usually he read one book a night. All his books were borrowed from libraries and when he ran out of books of interest at one library he went to another library in another suburb. I believe he changed libraries four times. As Gwen told me several times, ‘He didn’t talk much’.
Despite all this success he kept his feet on the ground. He was a quietly spoken, unassuming, approachable man. I never saw him get angry. When he was annoyed, he simply opted out of the conversation. There was one occasion, however, when he did lose his temper. In 2005 the laboratory was being extensively rebuilt and refurbished. As a result of this, Alan lost his office of which he had been the sole occupant since 1980 and in which he had done all his thinking. He was offered a desk in a communal office for about eight people as a replacement. He reportedly became very angry, left the building immediately and never went back. The circumstances surrounding the office change are not clear, but I think that Alan believed he would be unable to work in such surroundings. He may also have considered that he was being hounded out and was considered by the management to be of no further use. He became very with-drawn. Apart from his work, his interactions with others in the laboratory and his reading, he had few other interests so he stayed at home. Occasionally he did have some ex-colleagues call at his home to discuss their work and obtain advice.
Alan died in a nursing home in Melbourne on 9 January 2010 from cardiopulmonary degeneration. Since his passing, messages of appreciation have been arriving from all over the scientific world. Needless to say, all these messages were glowing in their assessment of Alan, both as a scientist of extraordinary ability and as a friend and colleague who was always willing to talk to and help others without any sign of pomposity or pretentiousness.
Alan is survived by his wife, Gwen, and his siblings, Margaret Boston, Keith Head and Sybil Kent. Alan and Gwen had no children.
It has been an honour, a privilege and a very pleasing experience to write about the life and career of Alan Head, my friend and colleague of some forty years.
During the process I drew on many sources and received help from many people. I should like to thank the following for their time and effort: Tim Bastow, Rob Birtles, Steve Celotto, Leo Clarebrough, Richard Donelson, Chris Forwood, Peter Hannaford, Gwen Head, Keith Head, Anita Hill, Cassandra Humble, Tien Kieu, Dimitria Kyriacopoulos, Julie McInerny, Allan Morton, Hilary Ockendon, John Ockendon, Ian Polmear, Rosanne Walker and Geoff West.
- Head, A. K., ‘Statistical Properties of Fatigue Data on 24ST’, A. S. T. M. Bull., 169 (1950),51.
- Wood, W. A. and Head, A. K., ‘Some New Observations on the Mechanism of Fatigue in Metals’, J. Inst. Metals, 79 (1951), 89–102.
- Head, A. K., ‘The Interaction of Dislocations and Boundaries’, Phil. Mag., 44 (1953),92–94.
- Head, A. K., ‘The Mechanism of Fatigue in Metals’, J. Mech. Phys. Solids, 1 (1953), 134–141.
- Bullen, F. P., Head, A. K. and Wood, W. A., ‘Structural Changes during the Fatigue of Metals’, Proc. Roy. Soc., A, 216 (1953), 332–343.
- Head, A. K., ‘The Growth of Fatigue Cracks’, Phil. Mag., 44 (1953), 925–938.
- Head, A. K., ‘Edge Dislocations in Inhomogeneous Media’, Proc. Phys. Soc., B, 66 (1953),793–801.
- Head, A. K. and Louat, N. P., ‘The Distribution of Dislocations in Linear Arrays’, Aust. J.Phys., 8 (1954), 1–7.
- Head, A. K., ‘The Growth of Fatigue Cracks’, A. R. L. Metals Report, 5 (1954).
- Clarebrough, L. M., Hargreaves, M. E., Head, A. K. and West, G.W., ‘Energy Stored During the Fatigue of Copper’, J. Metals, 7 (1955),99–100.
- Head, A. K., ‘The Effect of Frequency on the Fatigue of Metals’, J. Phys. Soc Jap., 11 (1956),468–469.
- Head, A. K. and Hooke, F. H., ‘Fatigue of Metals under Random Loads’, Nature, 177 (1956),1176–1177.
- Head, A. K., ‘The Propagation of Fatigue Cracks’, J. Appl. Mech., 23 (1956), 407–410.
- Head, A. K. and Hooke, F. H., ‘Random Noise Fatigue Testing’, Int. Cong. Fatigue of Metals(1956), Session 3, Paper 9, 3–5.
- Head, A. K., ‘Fatigue’, J. Aust. Inst. Metals, 1(1956), 148–154.
- Head, A. K., ‘A New Form for a Giant Radio Telescope’, Nature, 179 (1957), 692–693.
- Head, A. K., ‘The Two Mirror Aplanat’, Proc.Phys. Soc. B, 70 (1957), 945–949.
- Clarebrough, L. M., Hargreaves, M. E., West, G. W. and Head, A. K., ‘The Energy Storedin Fatigued Materials’, Proc. Roy. Soc. A, 242(1957), 160–166.
- Head, A. K., ‘A Class of Aplanatic Optical Systems’, Proc. Phys. Soc., 71 (1958),546–551.
- Head, A. K., ‘The Position of Dislocations in Arrays’, Phil. Mag., 4 (1959), 295–302.
- Head, A. K., ‘Aplanatic Lenses’, Proc. Phys.Soc., 74 (1959), 731–736.
- Head, A. K., ‘Aplanatic Lenses of High Refractive Index’, J. Op. Soc. Am., 50 (1960), 922.
- Head, A. K., ‘The Interaction of Dislocations with Boundaries and Surface Films’, Aust. J.Phys. 13 (1960), 278–283.
- Head, A. K., ‘The Stress Fields Around Some Dislocation Arrays’, Aust. J. Phys., 13 (1960),613–615.
- Mitchell, L. H. and Head, A. K., ‘The Buckling of a Dislocated Plate’, J. Mech. Phys. Solids, 9(1961), 131–139.
- Clarebrough, L. M., Hargreaves, M. E., Head, A. K. and Loretto, M. H., ‘Stored Energy and Flow Stress in Deformed Metals’, Phil. Mag.,6 (1961), 819–822.
- Head, A. K. and Thomson, P. F., ‘On the Method of Eshelby, Frank, and Nabarro for Calculating the Equilibrium Positions of Dislocations’, Phil. Mag., 7 (1962), 439–449.
- Head, A. K., ‘Method and Means for Producing Refrigeration by Selective Radiation’, lodged9/2/1959; issued 1962. U.S. Patent 3,043,112, Australian Patent 239364 issued 1962.
- Head, A. K., ‘The Energy of a Screw Dislocation in a Cubic Crystal’, Phys. Stat. Sol., 5(1964), 51–54.
- Head, A. K., ‘The  Dislocation in a Cubic Crystal’, Phys. Stat. Sol., 6 (1964), 461–465.
- Chen, H. S., Gilman, J. J. and Head, A. K., ‘Equilibrium of Extended Dislocations within Edge Dislocation Dipoles’, Phil. Mag., 10(1964), 35–42.
- Chen, H. S., Gilman, J. J. and Head, A. K., ‘Dislocation Multipoles and their role in Strain Hardening’, J. Appl. Phys., 35 (1964),2502–2514.
- Armstrong, R. W. and Head, A. K., ‘Dislocation Queuing and Fracture in an Elastically Anisotropic Medium’, Acta Met., 13 (1965),759–764.
- Head, A. K., ‘The Dislocation Image Force in Cubic Polycrystals’, Phys. Stat. Sol. (1964),481–484.
- Head, A. K., ‘The Equilibrium and Stability of Dislocations in a Non-Uniform Stress Field’, International Conference on Electron Diffraction and the Nature of Defects in Crystals, Melbourne, 1965.Vol. 2: The Nature of Defects in Crystals (Canberra: Australian Academy of Science, 1965).
- Atkinson, C. and Head, A. K., ‘The Influence of Elastic Anisotropy on the Propagation of Fracture’, Int. J. Frac. Mech., 2 (1966),489–505.
- Head, A. K., ‘Unstable Dislocations in Anisotropic Crystals’, Phys. Stat. Sol., 19(1967), 185–192.
- Humble, P., Segall, R. L. and Head, A. K., With an Appendix by Gottlieb, H. P.W., ‘The Energy of Dissociated Triangular Frank Loops in F. C.C. Metals’, Phil. Mag., 15 (1967), 281–296.
- Head, A. K., ‘Abnormal Damping by Unstable Dislocations in Anisotropic Crystals’, Phys.Rev. Lets., 18 (1967), 484–485.
- Head, A. K., Loretto, M. H. and Humble, P., ‘The Influence of Large Elastic Anisotropy on the Determination of Burgers Vectors of Dislocations in Beta-Brass’, Phys. Stat. Sol., 20(1967), 505–519.
- Head, A. K., Loretto, M. H. and Humble, P., ‘The Identification of Burgers Vectors and Unstable Directions of Dislocations in Beta-Brass’, Phys. Stat. Sol., 20 (1967), 521–536.
- Head, A. K., ‘The Computer Generation of Electron Microscope Pictures of Dislocations’, Aust. J. Phys., 20 (1967), 557–566.
- Head, A. K., ‘HALFTONE’, Technical Note21, CSIRO Computing Section (1967).
- Baker, B. G. and Head, A. K., ‘Computed Adsorption on Heterogeneous Surfaces’, Trans. Farad. Soc., 64 (1968), 485.
- Head, A. K., ‘The Reconstruction of Displacement Fields of Defects in Crystals from Electron Micrographs, I: Analytic Fields’, Aust. J.Phys., 22 (1969), 43–50.
- Head, A. K., ‘The Reconstruction of Displacement Fields of Defects in Crystals from Electron Micrographs, II: Discontinuous Fields and Many Beams’, Aust J. Phys., 22 (1969),345–350.
- Clarebrough, L. M. and Head. A. K., ‘Unstable Directions of Shockley Partial Dislocations’, Phys. Stat. Sol., 33 (1969), 431–434.
- Head, A. K., ‘The Outer Fringe of a Stacking Fault’, Aust. J. Phys., 22 (1969), 569–571.
- Head, A. K., ‘The Invisibility of Dislocations’, in Physics and Strength and Plasticity, Ed. A. S. Argon (Cambridge, Mass.: M.I.T. Press,1969), 65–73.
- Morton, A. J. and Head, A. K., ‘The Elastic Anisotropy of CuZn as Determined by an Electron Microscopy Study of Unstable Dislocations’, Phys. Stat. Sol., 37 (1970), 317–324.
- Head, A. K., ‘Dislocation Energies in Cubic Solids with C12=−C44’, Phys. Stat. Sol., 38(1970), K119–K122.
- Head, A. K., ‘The Recursive Evaluation of Functions’, Decuscope, 9, No. 3 (1970), 4.
- Head, A. K., ‘Dislocation Theories of the Plastic Properties of Metals and the Transition to Continuum Mechanics’, in Inelastic Behaviour of Solids, Eds M. F. Kanninen, W. F. Adler, A. R. Rosenfield and R. I. Joffe (New York: McGraw Hill, 1970), 45.
- Head, A. K., ‘Discrete Dislocations in Continuum Elasticity’, in Fundamental Aspects of Dislocation Theory, Eds J. A. Simmonds, R. DeWit and R. Bullough (Washington: National Bureau of Standards, 1970)(National Bureau of Standards Publication,317), Vol. 1, 5.
- Head, A. K., ‘Dislocation Group Dynamics, I:Similarity Solutions of the n-body Problem’, Phil. Mag., 26 (1972), 43–53.
- Head, A. K., ‘Dislocation Group Dynamics, II: General Solutions of the n-body Problem’, Phil. Mag., 26 (1972), 55–63.
- Head, A. K., ‘Dislocation Group Dynamics III: Similarity Solutions of the Continuum Approximation’, Phil. Mag., 26 (1972), 65–72.
- Head, A. K. and Wood, W. W., ‘Dislocation Group Dynamics, IV: General Solutions of the Continuum Approximation’, Phil.Mag., 27(1973) 505.
- Head, A. K. and Wood, W. W., ‘Dislocation Group Dynamics, V: Equilibrium Revisited’, Phil. Mag., 27 (1973), 519–530.
- Head, A. K., ‘Dislocation Group Dynamics, VI: The Release of a Pile-up’, Phil. Mag., 27(1973), 531–539.
- Head, A. K., Humble, P., Clarebrough, L. M., Morton, A. J. and Forwood, C. T., Computed Electron Micrographs and Defect Identification(Amsterdam: North–Holland Publishing,1973), pp. 400.
- Wood, W.W. and Head, A. K., ‘The Motion of Dislocations’, Proc. Roy. Soc., 336A (1974),191–209.
- Head, A. K. and Sanders, J. W., ‘The Uniqueness of Electron Micrographs of Crystal Defects’, in Eighth International Congress on Electron Microscopy, Canberra, 1974, vol. 1(Australian Academy of Science, 1974),p. 302.
- Clarebrough, L. M. and Head, A. K., ‘On the Width of Stacking Faults’, Phil. Mag., 33(1976), 557.
- Head, A. K., ‘The Identification of Crystal Defects by Computer Simulated Electron Micrographs’, in Proceedings of the 1976International Conference on Computer Simulation for Materials Applications, Eds R. J. Arsenault, J. R. Beeler and J. A. Simmonds, Nuclear Metallurgy, 20 (1976), 1179–1183.
- Head, A. K., ‘Aplanatic Mirror Pairs’, Applied Optics, 15 (1976), 2621.
- Head, A. K., ‘The Galois Insolvability of the Sextic Equation in Anisotropic Elasticity’, J. Elasticity, 9 (1979), 9–20.
- Head, A. K., ‘The Elastic Anisotropy of Metals’, in Physics of Materials: a Festschrift for Dr Walter Boas on the Occasion of his 75thBirthday, 10 February 1979, Eds D. W. Borland, L. M. Clarebrough and A. J. W. Moore(Melbourne: CSIRO, 1979), pp. 105–110.
- Head, A. K., ‘The Monodromic Galois Groups of the Sextic Equation of Anisotropic Elasticity’, J. Elasticity, 9 (1979), 321–324.
- Head, A. K., ‘Multiplication modulo n’, BIT,20 (1980), 115–116.
- Head, A. K., ‘Table Errata 568’, Mathematics of Computation, 34 (1980), 331.
- Head, A. K., ‘Why Materials Behave as they do’, in Materials for the Future, Ed. P. M. Kelly (Canberra: Aust. Acad. Science, 1981),pp. 1–8.
- Head, A. K., ‘The Explicit Solution of the Howie – Whelan Differential Equations of Electron Microscopy’, Phil. Mag. 44 (1981),827–833.
- Head, A. K., ‘Partial Fractions and other Goodies’, The Softwarehouse Newsletter, 9 (1983),7–10.
- Wood, W. W. and Head, A. K., ‘Dislocation Pile-ups and Stress Intensity Factors’, Q. J. Mech. Appl. Math., 37 (1984),161–178.
- Head, A. K., ‘Polynomial Addition Speedup’, The Softwarehouse Newsletter, 13 (1985),6–8.
- Head, A. K., ‘The Sextic Polynomial of Crystal Elasticity’, Phys. Stat. Sol., 132 (1985),117–123.
- Hurley, A. C. and Head, A. K., ‘Explicit Galois Resolvents for Sextic Equations’, Int. J. Quantum Chem., 31 (1987), 345–359.
- Head, A. K., Howison, S. D., Ockendon, J. R., Titchner, J. B. and Wilmott, P., ‘Continuum Model for Two-Dimensional Dislocation Distributions’, Phil. Mag., 55 (1987), 617–629.
- Clarebrough, L. M. and Head, A. K., ‘Walter Boas, 1904–1982’, Historical Records of Australian Science, 6 (1987), 507–517.
- Head, A. K., ‘Explicit Galoisian Solutions in Anisotropic Elasticity’, Euro. J. Appl. Math., 2(1991), 191–197.
- Head, A. K., Howison, S. D., Ockendon, J. R., and Tighe, S. P., ‘Mathematical Modelling of Dislocation Plasticity’, Festschrift in Honour of Jens Lothe on his Sixtieth Birthday, 25thNovember 1991, pp. 317–321.
- Head, A. K., Howison, S. D., Ockendon, J. R. and Tighe, S. P., ‘Mathematical Modelling of Dislocation Plasticity’, Physica Scripta, T44(1992), 135–136.
- Head, A. K., ‘LIE, a PC Program for Lie Analysis of Differential Equations’, Computer Physics Communications, 77 (1993),241–248.
- Head, A. K., Howison, S. D., Ockendon, J. R. and Tighe, S. P., ‘An Equilibrium Theory of Dislocation Continua’, S. I. A. M. Review, 35(1993), 580–609.
- Head, A. K., ‘LIE, a PC Program for Lie Analysis of Differential Equations’, Computer Physics Communications, 96 (1996),311–313.
- Sherring, J., Head, A. K. and Prince, G. E., ‘Dimsym, and LIE; Symmetry Determination Packages’, Mathematical and Computer Modelling, 25 (1997), 153–164.
- Chapman, S. J., Elliott, C. M., Head, A. K., Howison, S. D., Leslie, F. M. and Ockendon, J. R., ‘Vortices, Dislocations and Line Singularities in Partial Differential Equations’, Discussion Held 8th and 9th October 1996,Phil. Trans. Roy. Soc., A355 (1997), 1947.
- Head, A. K., ‘Some Echoes of CSIRAC: Using CSIRAC for Scientific Computing’, in The Last of the First: CSIRAC, Australia’s First Computer, Eds D. McCann and P. Thorne (Melbourne: U. Melbourne, 2000), p. 176.
Peter Humble. email@example.com