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Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano.
Hartree attended St Faith's School in Cambridge, then Bedales School, returning to Cambridge for his degree studies at St John's College, Cambridge, which the first World War interrupted. He (and his father and brother) joined a group working on anti-aircraft ballistics under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods for differential equations, executing most of his own work with pencil and paper.Van der Kloot(2011). "Mirrors and smoke: A. V. Hill, his brigands, and the science of anti-aircraft gunnery in world war I. ." Notes Rec. R. Soc. Lond. 65: 393–410. According to Hill, writing in Hartree's obituary, ‘Quietly one day he improvised a long-base height-finder out of some wires, posts, and a steel tape’. This became known as the Hartree height-finder and was used extensively by British Anti-Aircraft troops until better optical height-finders were introduced. Its advantage was said to be that the height can be calculated from the observed quantities ‘very rapidly by the use of nothing but simple arithmetic’. It was also cheap to manufacture and easy to use.
After the end of World War I, Hartree returned to Cambridge graduating in 1922 with a Second Class degree in natural sciences.
In 1933, he visited Vannevar Bush at the Massachusetts Institute of Technology and learned first hand about his differential analyser. Immediately on his return to Manchester, he set about building his own analyser from Meccano. Seeing the potential for further exploiting his numerical methods using the machine, he persuaded Sir Robert McDougall to fund a more robust machine, which was built in collaboration with Metropolitan-Vickers.
The first application of the machine, reflecting Hartree's enthusiasm for railways, was calculating timetables for the London, Midland and Scottish Railway. He spent the rest of the decade applying the differential analyser to find solutions of differential equations arising in physics, including control theory and laminar boundary layer theory in fluid dynamics, making significant contributions to each of the fields.
The differential analyser was not suitable for the solution of equations with exchange. When Vladimir Fock publication pre-empted Hartree's work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton–Hartree equation. In 1935, his father, William Hartree, offered to do calculations for him. Results with exchange soon followed. Douglas recognised the importance of configuration interaction that he referred to as "superposition of configurations". The first multiconfiguration Hartree–Fock results were published by father, son, and Bertha Swirles (later Lady Jeffreys) in 1939.
At Hartree's suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation in 1935. With Hartree's advice, the first relativistic calculations (without exchange) were reported in 1940 by A. O. Williams, a student of R. B. Lindsay.
In April 1944 a committee which included Hartree recommended that a mathematical section be set up within the National Physical Laboratory (NPL). In October this recommendation was put into effect with its first two objectives being the investigation of the possible adaptation of automatic telephone equipment to scientific equipment and the development of electronic computing devices suitable for rapid computing. One suspects that some members already knew of the Colossus computer. John R. Womersley (Alan Turing bête noire) was the first Director. In February 1945 he went on a two-month tour of computing installations in the US, including visiting ENIAC (still not complete). He became acquainted with drafts of von Neumann's famous June 1945 EDVAC report. About two months later Hartree also went over to see ENIAC, not then publicly known.
Hartree did further work in and was involved in the early application of , advising the US military on the use of ENIAC for calculating ballistics tables. In the summer of 1946 Hartree made his second trip to ENIAC as an evaluation of its applicability to a broad range of science, when he became the first civilian to program it. For this he selected a problem involving the flow of a compressible fluid over a surface, such as air over the surface of a wing travelling faster than the speed of sound.
At the end of 1945 or very early in 1946 Hartree briefed Maurice Wilkes of the University of Cambridge on the comparative developments in computing in the USA which he had seen. Wilkes, then received an invitation from the Moore School of Electrical Engineering (the builders of ENIAC) to attend a course on electronic computers. Before leaving for this, Hartree was able to brief him more fully on ENIAC. It was on the boat home that Wilkes planned the original design of EDSAC, which was to become operational in May 1949. Hartree worked closely with Wilkes in developing use of the machine for a wide range of problems and, most importantly, showed users from a number of areas in the university how they could use it in their research work.
Hartree returned to Cambridge to take up the post of Plummer professor of mathematical physics in 1946. In October he gave an inaugural lecture entitled "Calculating Machines: Recent and Prospective Developments and their impact on Mathematical Physics". This described ENIAC and the work that Hartree had done on it. Even in 1946, two years before stored programming electronic computing became a reality, Hartree saw the need for the use of sub-routines. His inaugural lecture ended with a look at what computers might do. He said: "..there are, I understand many problems of economic, medical and sociological interest and importance awaiting study which at present cannot be undertaken because of the formidable load of computing involved."
On 7 November 1946 The Daily Telegraph, having interviewed Hartree, quoted him as saying: "The implications of the machine are so vast that we cannot conceive how they will affect our civilisation. Here you have something which is making one field of human activity 1,000 times faster. In the field of transportation, the equivalent to ACE would be the ability to travel from London to Cambridge ... in five seconds as a regular thing. It is almost unimaginable."
Hartree's fourth and final major contribution to British computing started in early 1947 when the catering firm of J. Lyons & Co. in London heard of the ENIAC and sent a small team in the summer of that year to study what was happening in the US, because they felt that these new computers might be of assistance in the huge amount of administrative and accounting work which the firm had to do. The team met with Col. Herman Goldstine at the Institute for Advanced Study in Princeton who wrote to Hartree telling him of their search. As soon as he received this letter, Hartree wrote and invited representatives of Lyons to come to Cambridge for a meeting with him and Wilkes. This led to the development of a commercial version of EDSAC developed by Lyons, called LEO, the first computer used for commercial business applications. After Hartree's death, the headquarters of LEO Computers was renamed Hartree House. This illustrates the extent to which Lyons felt that Hartree had contributed to their new venture.
Hartree's last famous contribution to computing was an estimate in 1950 of the potential demand for computers, which was much lower than turned out to be the case: "We have a computer here in Cambridge, one in Manchester and one at the NPL. I suppose there ought to be one in Scotland, but that's about all." Such underestimates of the number of computers that would be required were common at the time.
Hartree's last PhD student at Cambridge, Charlotte Froese Fischer, became known for the development and implementation of the multi-configuration Hartree–Fock (MCHF) approach to atomic structure calculations and for her theoretical prediction concerning the existence of the negative calcium ion.
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