Marshall Hall Research Articles

Was It for This the Clay Grew Tall?

Irresolute Clay: Shaping the Foundations of Modern Environmental Law. By RICHARD MACRORY [Oxford: Hart Publishing, 2020, ISBN 9781509928118, hardback, 189 pp, £25] When I was a law student at Cambridge in the 1970s, I developed the habit of browsing second-hand bookshops, of which there was then no shortage in Cambridge, for legal biographies, autobiographies and memoirs. This pastime continued through to my early years as a Cambridge lecturer. I amassed quite a collection, almost all of which have over the years found their way back into the charity shops which had become the successors to the second-hand book shops. In truth, their value was pretty limited. They were often rather sycophantic portraits of legal luminaries or judicial monsters such as Norman Birkett, Marshall Hall, Lord Goddard, etc, depicting a legal landscape that had already largely passed into history by the time I acquired them. The least valuable by far tended to be the autobiographies or memoirs, which were generally of much less interest to the reader than to the author. I recall one rather dire read entitled Jottings of an Old Solicitor, which was essentially a catalogue of less than interesting cases and anecdotes.1 A much more engaging biography was that of Sir George Lewis, the Victorian and Edwardian celebrity solicitor who practiced from Ely Place in Holborn and numbered royalty among his clients.2 There, however, more of the interest lay in his extra-legal life. At Ely Place, Sir George and Lady Lewis met ‘tout le monde’ as described by his biographer, his house thronged with painters, sculptors, musicians, actors, writers, lawyers, politicians, where the establishment and Bohemia were thrown together. Lewis was depicted in a fine portrait of 1892 by John Singer Sargent, one of his regular guests.

First-order model theory of free projective planes

We prove that the theory of open projective planes is complete and strictly stable, and infer from this that Marshall Hall's free projective planes (πn:4⩽n⩽ω) are all elementary equivalent and that their common theory is strictly stable and decidable, being in fact the theory of open projective planes. We further characterize the elementary substructure relation in the class of open projective planes, and show in particular that (πn:4⩽n⩽ω) is an elementary chain. We then prove that the theory of open projective planes does not have a prime model, that it has elimination of quantifiers down to Boolean combinations of existential formulas, and that it is not model complete. Finally, we characterize the forking independence relation in models of the theory and prove that the πn's (4⩽n⩽ω) are strongly type-homogeneous.

Robert Graves, Marshall Hall, and reflex action in 1837

ABSTRACTIn several issues of the London Medical Gazette during June–July of 1837 there was an interchange of letters between Robert Graves, Regius Professor of the Institutes of Medicine at Trinity College, Dublin, and the London physician and experimental physiologist Marshall Hall, often considered the discoverer of the phenomenon of reflex activity. Graves asserted that he, rather than Hall, was the originator of the idea of reflex action as a disease mechanism. Hall rejected that assertion and, after exchange of some verbal “pleasantries,” began a tirade about a somewhat different, although not unrelated issue into which the journal editor interjected some not exactly dispassionate comments. Graves soon let the matter of priority lapse, and Hall continued his war with the Council of the Royal Society, but examination of the contemporary and earlier literature suggests that Graves probably was correct, by a narrow time margin, in relation of his claim for priority in using the concept of reflex action in explaining neurological disease mechanisms (not a claim for discovering reflex action), that Hall had used the phrase “reflex action” earlier than Graves, and that others before Hall had gone a long way in studying reflex mechanisms, although Hall’s writings had familiarized the medical profession with the concept.

Helen Brooke Taussig: preserver of babies’ hearts and limbs

As a paediatric cardiologist in Depression-era America, Helen Brooke Taussig (1898–1986) saw many “blue” babies, their blood starved of oxygen as it failed to circulate properly through the lungs. The infants gasped for breath after the least exertion and usually died at an early age. After studying the condition, which was caused by a cluster of congenital heart defects, Taussig proposed to her surgical colleague at Johns Hopkins University, Alfred Blalock (1899–1964), that it might be alleviated by a procedure to divert another artery to the lungs. They first did the Blalock–Taussig shunt on a baby in 1944, and since then many parents have had the joy of seeing their babies turn pink and healthy almost overnight. Women making medical history: introducing A Woman's PlaceIn December, 2017, The Lancet issued a call for papers for its special theme issue on women in science, medicine, and global health .1 The Comment outlined the gender inequalities in medicine that still persist, long after many overt barriers to women's participation have fallen. While that theme issue will be forward-looking, I believe we can also gain insights from looking to the past for examples of women who have made their mark against the odds, and by asking what it was about their particular circumstances that enabled them to do so. Full-Text PDF Marie Boivin: from midwife to gynaecologistThe authoritative Traité pratique des maladies de l'uterus et de ses annexes, published in Paris in 1833, was one of the most forward-thinking gynaecological texts of 19th-century Europe. It was more specific than previous texts, such as the British physician Marshall Hall's Commentaries on Some of the More Important of the Diseases of Females of 1827, and it focused on the reproductive organs as a system rather than simply in relation to childbirth. This textbook was based not on previous authorities but on first-hand case studies and autopsies, including the first account of the surgical removal of a cancerous cervix. Full-Text PDF

Marie Boivin: from midwife to gynaecologist

The authoritative Traité pratique des maladies de l'uterus et de ses annexes, published in Paris in 1833, was one of the most forward-thinking gynaecological texts of 19th-century Europe. It was more specific than previous texts, such as the British physician Marshall Hall's Commentaries on Some of the More Important of the Diseases of Females of 1827, and it focused on the reproductive organs as a system rather than simply in relation to childbirth. This textbook was based not on previous authorities but on first-hand case studies and autopsies, including the first account of the surgical removal of a cancerous cervix. And its principal author was a woman, Marie Boivin. Susan La Flesche Picotte: a doctor who spanned two culturesAs a child, she accompanied her father and the Omaha people on buffalo hunts. As an adult, she saw their traditional way of life disappearing, provided medical care to her community, and acted as an advocate for the Omaha people's rights over land. Susan La Flesche Picotte, the first Native American woman to qualify as a doctor in the USA, learned the ways of the dominant white population while never rejecting her Omaha identity. Full-Text PDF Women making medical history: introducing A Woman's PlaceIn December, 2017, The Lancet issued a call for papers for its special theme issue on women in science, medicine, and global health .1 The Comment outlined the gender inequalities in medicine that still persist, long after many overt barriers to women's participation have fallen. While that theme issue will be forward-looking, I believe we can also gain insights from looking to the past for examples of women who have made their mark against the odds, and by asking what it was about their particular circumstances that enabled them to do so. Full-Text PDF

Differences of Bijections

When is a function from an abelian group to itself expressible as a difference of two bijections? Answering this question for finite cyclic groups solves a problem about juggling. A theorem of Marshall Hall settles the question for finite abelian groups, and a forgotten theorem of László Fuchs settles the question for infinite abelian groups. After explicating these theorems, we extend the problem by examining expressibility as a difference of injections or surjections. We also extend the question beyond the realm of group theory, where the expressibility of a function translates to questions about partial transversals in Latin squares.

Aligning JN-25 messages in depth using weights when the code groups scan

By the end of 1943, US Navy mathematician/codebreaker Marshall Hall Jr. had developed a system of statistical weights to align JN-25 messages in depth. Although then-current methods of aligning JN-25 messages in depth were working satisfactorily, Hall developed his method “just in case.” On 1 December 1943, the Japanese changed the method of numbering the lines and columns of additives on pages of the JN-25 additive book, and Hall’s weights, which had been developed “just in case,” were needed immediately. This paper discusses both the mathematical idea that was the foundation of Hall’s weights and the construction of the weights. It also explores the navy’s use of the weights as well as their use at Bletchley Park. At the same time, the navy was exploring the use of two other systems of weights to align JN-25 messages in depth, and those systems of weights are also described.

Susan La Flesche Picotte: a doctor who spanned two cultures

As a child, she accompanied her father and the Omaha people on buffalo hunts. As an adult, she saw their traditional way of life disappearing, provided medical care to her community, and acted as an advocate for the Omaha people's rights over land. Susan La Flesche Picotte, the first Native American woman to qualify as a doctor in the USA, learned the ways of the dominant white population while never rejecting her Omaha identity. Dorothy Stopford Price and the control of tuberculosis in IrelandDuring the 1930s, tuberculosis was a leading cause of death in Irish children. By then, Albert Calmette and Camille Guérin had demonstrated their Bacillus Calmette–Guérin (BCG) vaccine in France and it was beginning to be used elsewhere, but the British and Irish medical establishments were not convinced. Against this background, a young Anglo-Irish paediatrician, Dorothy Price, decided to do her own studies in Dublin. Her persistence was instrumental in the introduction of a national tuberculosis vaccination schedule for Ireland in 1949, ahead of the UK's in 1954. Full-Text PDF Women making medical history: introducing A Woman's PlaceIn December, 2017, The Lancet issued a call for papers for its special theme issue on women in science, medicine, and global health .1 The Comment outlined the gender inequalities in medicine that still persist, long after many overt barriers to women's participation have fallen. While that theme issue will be forward-looking, I believe we can also gain insights from looking to the past for examples of women who have made their mark against the odds, and by asking what it was about their particular circumstances that enabled them to do so. Full-Text PDF Marie Boivin: from midwife to gynaecologistThe authoritative Traité pratique des maladies de l'uterus et de ses annexes, published in Paris in 1833, was one of the most forward-thinking gynaecological texts of 19th-century Europe. It was more specific than previous texts, such as the British physician Marshall Hall's Commentaries on Some of the More Important of the Diseases of Females of 1827, and it focused on the reproductive organs as a system rather than simply in relation to childbirth. This textbook was based not on previous authorities but on first-hand case studies and autopsies, including the first account of the surgical removal of a cancerous cervix. Full-Text PDF

Pseudo Sylow Numbers

One part of Sylow’s famous theorem in group theory states that the number of Sylow p-subgroups of a finite group is always congruent to 1 modulo p. Conversely, Marshall Hall has shown that not every positive integer occurs as the number of Sylow p-subgroups of some finite group. While Hall’s proof relies on deep knowledge of modular representation theory, we show by elementary means that no finite group has exactly 35 Sylow 17-subgroups.

Conditions for the Parameters of the Block Graph of Quasi-Symmetric Designs

A quasi-symmetric design (QSD) is a 2-$(v,k,\lambda)$ design with intersection numbers $x$ and $y$ with $x< y$. The block graph of such a design is formed on its blocks with two distinct blocks being adjacent if they intersect in $y$ points. It is well known that the block graph of a QSD is a strongly regular graph (SRG) with parameters $(b,a,c,d)$ with smallest eigenvalue $ -m =-\frac{k-x}{y-x}$.The classification result of SRGs with smallest eigenvalue $-m$, is used to prove that for a fixed pair $(\lambda\ge 2,m\ge 2)$, there are only finitely many QSDs. This gives partial support towards Marshall Hall Jr.'s conjecture, that for a fixed $\lambda\ge 2$, there exist finitely many symmetric $(v, k, \lambda)$-designs.We classify QSDs with $m=2$ and characterize QSDs whose block graph is the complete multipartite graph with $s$ classes of size $3$. We rule out the possibility of a QSD whose block graph is the Latin square graph $LS_m (n)$ or complement of $LS_m (n)$, for $m=3,4$.SRGs with no triangles have long been studied and are of current research interest. The characterization of QSDs with triangle-free block graph for $x=1$ and $y=x+1$ is obtained and the non-existence of such designs with $x=0$ or $\lambda > 2(x+2)$ or if it is a $3$-design is proven. The computer algebra system Mathematica is used to find parameters of QSDs with triangle-free block graph for $2\le m \le 100$. We also give the parameters of QSDs whose block graph parameters are $(b,a,c,d)$ listed in Brouwer's table of SRGs.

Water Best Paper Award 2015

To better recognize the outstanding papers in the area of water sciences and technology published in Water, we announce the institution of an annual award.[...]

Alan Turing, Marshall Hall, and the Alignment of WW2 Japanese Naval Intercepts

M arshall Hall Jr. (1910–1990) is deservedly well remembered for his role in constructing the simple group of order 604800 = 27 × 33 × 52 × 7 as well as numerous advances in combinatorics. A brief autobiography is on pages 367–374 of Duran, Askey, and Merzbach [5]. Hall notes that Howard Engstrom (1902–1962) gave him much help with his Ph.D. thesis at Yale in 1934–1936 and later urged him to work in Naval Intelligence (actually in the foreign communications unit Op-20-G). I was in a research division and got to see work in all areas, from the Japanese codes to the German Enigma machine which Alan Turing had begun to attack in England. I made significant results on both of these areas. During 1944 I spent six months at the British Headquarters in Bletchley. Here there was a galaxy of mathematical talent including Hugh Alexander the chess champion and Henry Whitehead the eminent topologist... Burroughs, Lieberman, and Reeds [2] clarified the work of Op-20-G on the Enigma in a contribution to the obituary of Andrew Gleason (1921–2008). Unfortunately the surviving records scarcely allocate credit to individuals. Hall was one of about ten core members of a team of about thirty not far from being another galaxy of mathematical talent. See Christenson [3].

Topographies of amusement: the evolving terrain of Glen Echo Park, Maryland

Click to increase image sizeClick to decrease image size Notes 1. Lange, Deborah (date unknown), Glen Echo Park: A Walking Tour, brochure prepared by National Park Service, US Department of the Interior in cooperation with the Glen Echo Partnership for Arts and Culture, Inc. Montgomery County, Maryland and the Maryland Heritage Area Authority, p. 1. 2. Levy, Benjamin, Glen Echo: Chautauqua on the Potomac (Washington, DC: Government Printing Office, for the National Park Service, US Department of the Interior, June 1967), pp. 1–6; Unrau, Harlan D., Historic Structures Report: Glen Echo Park (Denver, Colorado: Denver Service Center, Branch of Cultural Resources, Northeast Team, George Washington Memorial Parkway, Maryland–Virginia, Historical Data Section, National Park Service, US Department of the Interior, May 1986), pp. 1–4. 3. Unrau, pp. 1–3. 4. Baltzley, Edwin, Glen Echo-on-the-Potomac: The Washington Rhine (Philadelphia: H. Gutekunst, 1891), p. 39. 5. Baltzley, pp. 3, 17–22. 6. Levy, pp. 5–6; Unrau, pp. 2–8. 7. Levy, pp. 7–8; Unrau, pp. 9–12. 8. Simpson, Jeffrey, ‘Utopia by the Lake’, American Heritage, 23/5, August 1972, pp. 76–88; Unrau, p. 180. 9. Levy, p. 7; Unrau, p. 14. 10. Baltzley, pp. 41–42. 11. Unrau, pp. 15–18. 12. Levy, pp. 9–16; Unrau, pp. 17–18. 13. Levy, pp. 17–19; Unrau, pp. 14, 20–30, 36–44. 14. Simpson, pp. 82–88. 15. National Park Service, Glen Echo Park: Then and Now, author unknown, brochure prepared by National Park Service, US Department of the Interior in cooperation with the Glen Echo Partnership for Arts and Culture, Inc., and Montgomery County, Maryland, 2006; Unrau, pp. 45–62. 16. National Park Service, 2006; Nye, David E, Electrifying America: Social Meanings of a New Technology, 1880–1940 (Cambridge, MA: MIT Press, 1999), pp. 4–10, 82–89, 140–154; Scott, Gary, and Bill Brabham, Glen Echo Amusement Park National Register of Historic Places Inventory — Nomination Form, Washington, DC: National Park Service, US Department of the Interior, 1984. 17. Deanwood History Committee, Washington, D. C.’s Deanwood (Mount Pleasant, SC: Arcadia Publishing, 2008), pp. 12–18; National Park Service, 2006; Rose, C. B., Jr., Arlington County Virginia: A History (Arlington, VA: Arlington Historical Society, 1976), pp. 140–166; Templeman, Eleanor Lee, Arlington Heritage: Vignettes of a Virginia County (privately published, 1959, in collection of Arlington County Library), pp. 35–40; Unrau, p. 55–61. 18. National Park Service, 2006; Unrau, pp. 58–132. 19. Lange, pp. 1–2; Unrau, pp. 63–104. 20. Lange, pp. 1–2; Unrau, pp. 102–130. 21. Unrau, pp. 63–65, 90–94, 113–130; Washington Evening Star, newspaper advertisement, 17 May 1911, p. 3. 22. Lowenthal, David, Possessed by the Past: The Heritage Crusade and the Spoils of History (New York: Free Press, 1996), pp. 55–75, 182–191; Rose, pp. 140–166; Young, Terrance, and Riley, Robert, Theme Park Landscapes: Antecedents and Variations (Washington, DC: Dumbarton Oaks Research Library and Collection, 2002), pp. 1–24, 119–156, 235–268. 23. Nelson, Peter D., Fighting Traffic: The Dawn of the Motor Age in the American City (Cambridge, MA: MIT Press, 2008), pp. 207–261. 24. National Park Service, 2006; Unrau, pp. 131–150. 25. Unrau, pp. 125–158. 26. Deanwood, pp. 12–18; Unrau, pp. 141–158; Washington Bee, newspaper advertisement, 16 August 1902, p. 5; Washington Bee, newspaper advertisement, 20 March 1920, p. 3. 27. National Park Service, 2006; Schulte, Brigid, ‘Protest on a Sculpted Horse’, The Washington Post, 29 June 2004, p. B01. 28. Ibid. 29. National Park Service, 2006; Schulte, Brigid, ‘Protest on a Sculpted Horse’, The Washington Post, 29 June 2004, p. B01; US Supreme Court decision, Griffin v. Maryland (1964), 378 US 130. 30. Nelson, Peter D., pp. 207–261; Unrau, pp. 141–159. 31. Unrau, pp. 146–162. 32. National Park Service, 2006; Unrau, pp. 162–177. 33. Long, Susan, Historic Structure Report: Architectural Data Section for Marshall Hall, Piscataway Park (Denver, CO: Denver Service Center, National Park Service, US Department of the Interior, 1983). 34. Unrau, p. 175. 35. National Park Service, 2006; Lange, pp. 1–2.

Alternating quotients of free groups

We strengthen Marshall Hall's theorem to show that free groups are locally extended residually alternating. Let F be any free group of rank at least two, let H be a finitely generated subgroup of infinite index in F and let \{\gamma_1,\ldots,\gamma_n\}\subseteq F\smallsetminus H be a finite subset. Then there is a surjection f from F to a finite alternating group such that f(\gamma_i)\notin f(H) for any i . The techniques of this paper can also provide symmetric quotients.

William Gowers’ interpretation of epileptogenic mechanisms: 1880-1906

In the 1870s, early in his neurologic career, William Gowers (1845-1911) was exposed to three main schools of thought concerning epileptogenesis, namely, that seizures resulted from (1) excessive neural activity in the medulla oblongata or pons (Marshall Hall, John Russell Reynolds, and Brown-Séquard), (2) excessive local cerebral cortical activity (Hughlings Jackson), or (3) suddenly decreased cerebral activity that released the intrinsic contractibility of skeletal muscle (Radcliffe). By 1881, Gowers had reasoned his way to the idea that epileptogenesis was best accounted for by local cortical overactivity. This overactivity might at times be initiated by local loss of inhibition. The overactivity in turn then might inhibit other parts of the central nervous system to explain loss of consciousness in seizures and postseizure temporary hemiparesis. The possibilities of the idea of inhibition, at first often called "resistance," continued to interest Gowers over the following 25 years. He settled on the synaptic gap as its likely site. However, the inhibition mechanism that he proposed, namely, retraction of dendrites, was rather extraordinary in the light of subsequent knowledge.

Near-automorphisms of Latin squares

We define a near-automorphism α of a Latin square L to be an isomorphism such that L and αL differ only within a 2 × 2 subsquare. We prove that for all n≥2 except n∈{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if α has the cycle structure (2, n − 2), then L exists if and only if n≡2 (mod 4), and can be constructed from a special type of partial orthomorphism. Along the way, we generalize a theorem by Marshall Hall, which states that any Latin rectangle can be extended to a Latin square. We also show that if α has at least 2 fixed points, then L must contain two disjoint non-trivial subsquares. Copyright © 2011 John Wiley & Sons, Ltd. 19:365-377, 2011

Transhumane Physiologie. Bilder und Praktiken des Reflexes (Thomas Willis, Robert Whytt, Marshall Hall)

The essay examines the function of visualizations and practices in the formation of the reflex concept from Thomas Willis to Marshall Hall. It focuses on the specific form of reflex knowledge that images and practices can contain. In addition, the essay argues that it is through visual representations and experimental practices that technical knowledge is transferred to the field of human reflex physiology. When using technical metaphors in human physiology authors often seem to feel obliged to draw distinctions between humans, machines and animals. On closer scrutiny, these distinctions sometimes fail to establish firm borders between the human and the technical.

Hall’s Theorem for Limit Groups

A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela.

On Some Finiteness Properties in Infinite Groups

We consider some questions concerning finiteness properties in infinite groups which are related to Marshall Hall's theorem. We call these properties Property S and Property R, and they are trivially true in finite groups. We give several elementary proofs using these properties for results on finitely generated subgroups of free groups as well as a new elementary proof of Hall's basic result. Finally, we consider these properties within surface groups and prove an analog of Hall's theorem in that context.

Silvester's technique of artificial respiration

The widespread acceptance of manual methods of artificial respiration followed upon the introduction of a simple technique published in 1856 by Marshall Hall, a senior and widely respected London physician.1,2 In essence Hall’s technique involved alternate rotation of the patient’s body from a prone position to the side. As a later modification he added expiratory pressure to the thorax when the patient was in the prone position.3 About the same time in London a young recently qualified physician, Henry Robert Silvester, turned his attention to the technique of artificial respiration. He was prompted to do so when Hall’s technique was used on a stillborn male infant without success. He changed the position of the infant, put him on his back and raised both arms upward to cause expansion of the chest and inspiration, after which he folded the arms on the chest and applied expiratory pressure. The infant recovered.4 He referred to this technique as the ‘‘natural method’’ and outlined the rationale in a more detailed publication in the British Medical Journal in 1858.5 (Figure 1) In this paper he pointed out that the current methods of artificial respiration involved alternate compression and relaxation of the chest. He felt this was inadequate because ‘‘there is no elevation of the