On the Shanghai metro yesterday, we saw a man with a T-shirt bearing the caption


Do I smell a trace of Cantor’s diagonal argument here? Perhaps even Russell’s paradox? Suppose that every social club is named after a person, and a person X is antisocial if X is not a member of the X club. Then let the club of antisocial people be the Y club, and ask: Is Y social or antisocial?

Perhaps you would like to formalise this …

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Xu Guangqi

Xu Guangxi

Our hotel in Shanghai is very close to the tomb of Xu Guangqi (1562-1633), Chinese Renaissance man: mathematician, first Chinese translator of Euclid, astronomer, calendar reformer, military strategist, agronomist, and more.

Just across the road from our hotel is the site of his observatory, and outside is a fine statue of him (pictured above). Along at the next corner is a tiny park which contains more statues, his tomb (with a sacred road to it from the entrance gate), more statues (including other facets of his life: one with a telescope, one with a European cannon, one planting sweet potatoes), and a small museum about him (which contains his Euclid translation, apparently, though it was closed when we visited the park). The trees are full of singing birds, quite extraordinary in this busy built-up part of the huge city, and the pond contains turtles and huge goldfish. In the park, people play cards (very many of these), do tai chi exercises, or stroll around photographing the memorials on their phones.

Xu was converted, both to a belief in the superiority of Western science, and to Christianity, by the Jesuit scholar Matteo Ricci, and gave the land on which the Catholic cathedral is built, also across the street from our hotel. Around here there were many monasteries. Indeed, we dined in a very good restaurant called “Ye Olde Station Restaurant” which, despite its name, was previously a nunnery, and also contains many old artefacts such as sewing machines and cameras.

You can read the St Andrews MacTutor account of Xu’s life and work here.

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In Shanghai


On Friday afternoon, at the LMS meeting, I received from the outgoing President Simon Tavaré the certificate for the Senior Whitehead Prize. Simon gave a delightful Presidential Address, but now is not the moment to describe it. Then a very pleasant occasion at dinner after the meeting.

On Saturday we packed and went to the airport to catch a China Eastern Airlines flight to Shanghai, as guests of Yaokun Wu at Shanghai Jiao Tong University.

So this morning we woke up in a hotel in Shanghai.

Reports may be intermittent for a while. Last night I discovered that some things work and others don’t; was it the conspiracy theory (blocked by the great Chinese firewall) or the cockup theory (the rather pathetic hotel wi-fi)? As I would expect, it was the latter. So I can connect to WordPress, but it is rather slow and painful.

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Shrikhande 100

Professor S. S. Shrikhande is 100. I offer him my warmest congratulations and birthday greetings.

Among much else in his distinguished career, he was one of the three who showed that a pair of orthogonal Latin squares exists for every order except 2 and 6, thus disproving a conjecture of Euler (who thought they would not exist for orders congruent to 2 mod 4). These three (Bose, Shrikhande and Parker) were dubbed the “Euler spoilers”. He also characterised the line graphs of regular complete bipartite graphs by their parameters as strongly regular graphs, apart from a unique exception on 16 vertices now called the Shrikhande graph. This led on to the work of Seidel and others on strongly regular graphs, and in particular to my own work with Goethals, Seidel and Shult on graphs with least eigenvalue −2 and their connection with root systems.

I discussed these two things and their relationship here.

You can find a tribute and account of the celebrations here.

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Around All Hallows Eve

A few things to note, at this very autumnal time of year.

On Saturday we went to a concert, part of the St Andrews Voices festival. The concert was given by Dowland Works (five singers including Emma Kirkby, and two lutenists) and four St Andrews students. They performed the music in St Andrews church, as it might have been done in Dowland’s time (around 1600), with singers and lutenist sitting at a table. Indeed, the pieces in Dowland’s First Booke of Songs and Aires were printed one per double page spread, with the parts angled so that each performer could see his or her own part the right way up.

Dowland is one of my all-time favourite musicians. Although reports say he knew how to be jolly, his music is filled with melancholy, appropriate for the season perhaps. His motto was Semper Dowland, semper dolens, and indeed the song titles such as “Flow my teares” (the most famous), “Alas, what a wretched life this is”, or “In darkness let me dwell” are uniformly gloomy. (My favourite Dowland song, which they didn’t perform, is “Come heavy sleepe”, a song about insomnia, the singer lying awake and thinking thoughts of death. Benjamin Britten used a single phrase from the lute part as the basis of a set of variations for guitar depicting a night of disturbed sleep.) The concert included Italian madrigals, but for me the best bits were the songs with a single singer accompanied by a single lute.

The concert provoked a couple of thoughts. First, in this performance, and every other that I have heard, the singer and lutenist are different people. Did Dowland sing his songs and accompany himself on the lute? It seems very natural that he would have done so.

The other was inspired by three of a set of six pieces composed by John Cooper (or Giovanni Coprario as he called himself, being a lover of all things Italian) on the death of Prince Henry, eldest son of James VI (or James I of England). Henry died at the age of 17, and subsequently his younger brother Charles came to the throne (and to a bloody end). Charles was never punished for anything; he had a whipping boy, as I reported earlier. Did this contribute to Charles’ belief in the Divine Right of Kings (i.e. that everything he did was right in God’s eyes)? Was Henry brought up in the same way? Would he have been a better king than Charles had he survived?

On Sunday, a cold but clear day, we went for a walk, from St Andrews to Cupar via Craigtoun Park and Cameron Reservoir. In Craigtoun park they were preparing for Halloween, with ghosts hanging in the branches of the trees and various other scary things in evidence. I’ll say a bit more about Halloween shortly. It was also a time when the best of the autumn leaves had gone but some good displays remained. There was also a lot of evidence of trees and plants fooled by the very mild autumn into budding and even flowering; several wild roses had flowers as well as soggy rosehips.

Autumn scene

Last night, we went to the 90th Andrew Lang Memorial Lecture. The lectures series was established by Scott Lang, Regius Professor of Mathematics at the University of St Andrews for 42 years (and, we were told, no relation to Andrew Lang, despite being born in the same town, Selkirk in the Scottish Borders).

Andrew Lang was many things: “novelist, literary critic, […] contributor to the field of anthropology [, …] collector of folk and fairy tales” [Wikipedia]. It was as the last of these that he was discussed by the lecturer, Dr Lizanne Henderson, University of Glasgow. The lecture was entitled Andrew Lang and the Folkloristic Legacy of “The Forest”. “The Forest” denoted both Ettrick Forest, around his birthplace Selkirk, or more metaphorically the source of folklore about fairies, witches, etc. Appropriate stuff for Halloween.

Lizanne Henderson’s research involved (among other things) reading accounts of Scottish witch trials. It seems that the women who were accused of witchcraft were imprisoned and tortured; unsurprisingly, they told their interlocutors what they thought they wanted to hear, which was stories of witches which they may have heard in their childhood; so a lot of folklore is recorded there, some of it almost worthy of inclusion in one of Andrew Lang’s Fairy Books.

Nowdays, Halloween involves plastic figures of ghosts and bats bought from the supermarket; this is driven by commerce and in some people’s view is an American import. But it is clear that this time of year was traditionally regarded as one where the barrier between this world and the other was low, and supernatural manifestations were to be expected. The Celtic pagan festival of Samhain occurs around now; it was a time when surplus cattle were slaughtered for winter supplies, bonfires built, and cleansing rituals undertaken.

But back to Lang. He argued against the “diffusion” theory of folklore propounded by Max Müller, which apparently stated that it originated in north India and had been brought here (along with Indo-European languages) by movement of peoples. Lang claimed that folk stories were indigenous to the cultures in which they are found, and are survivals which if studied carefully can give information about our ancestors’ beliefs.

Fittingly, today’s news reported the reconstruction, using forensic software, of the face of Lilias Adie, who was accused of witchcraft and died in prison in 1704 before she could be sentenced. Her skull was in the St Andrews University Museum until it “disappeared” in around 1930, and the face was reconstructed from photographs; she was buried under a stone slab on the Fife coast and the burial spot was only recently rediscovered.

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Untangling academic publishing

Most academics would agree that academic publishing is in a period of rapid change, even upheaval; some would even argue that it is not acting in our interests. We produce the primary product, typeset it, act as editors or referees for journals, and then have to buy it back from publishers who have profit margins of 37% in at least one case.

Aileen Fyfe, a professor of history at the University of St Andrews, headed a panel who wrote a report entitled “Untangling Academic Publishing”, available from the doi 10.5281/zenodo.546100. (I hadn’t come across Zenodo before; it seems to be a bit like the arXiv with some extra features.) This week we went to the Scottish launch of the report. Aileen spoke for nearly an hour, and then was joined by a biochemist and a lawyer for a question-and-answer session.

The report had grown out of an AHRC-funded project on the history of the Philosophical Transactions of the Royal Society, which claims to be the world’s oldest-surviving scholarly journal. At a certain point in its lifetime, this project spun off a new initiative to look more broadly at academic publishing.

As befits a talk by a historian, the emphasis of the lecture was on how we got to where we are now. In short, in the nineteenth century, academic journals were given away to interested parties; Aileen showed a remarkable map showing the distribution of Phil. Trans. Roy. Soc. at the beginning of the twentienth century, including two dots in the middle of Siberia. Of course, this was expensive for learned societies, and unsurprisingly they began to sell subscriptions to provide an income to defray the costs.

The revolution occurred in the mid-twentieth century. In Britain, partly as a result of the Cold War and partly because of wider social changes, university education began to be greatly expanded; many new universities were founded at this time, and some colleges were upgraded to universities. The generous funding allowed these universities to appoint staff, and to equip their libraries with the books and journals these staff required. (The number of staff at UK universities rose from 4000 in the 1930s to 200000 in 2015.) Probably a similar story is true of other countries.

Entrepreneurs, including Robert Maxwell (does anyone remember Pergamon Press?), were quick to spot the chance to make money. They were able to set up journals with editorial boards and refereeing systems which could compete with the journals published by learned societies. The number of journals worldwide rose from 10000 in 1950 to 62000 in 1980.

It was inevitable that the Golden Age would end; firstly, money became tighter, and second, the rise in the number of journals led to a “serials crisis” where no university could afford to subscribe to all the journals its staff needed.

The advent of the World Wide Web in the 1990s brought in the possibility of electronic publishing. (The Electronic Journal of Combinatorics, one of the first journals free to authors and readers in the modern age, was founded by Herb Wilf and Neil Calkin in 1994.) By this time, the publishers had become addicted to high profit margins and were very reluctant to give them up; so, along with page charges and subscription bundling, they tried to keep control of metadata such as citation indices.

This, of course, is related to the other use of academic publishing, in judging our research for the purposes of appointments, grant applications, and so forth. The use of publication records in academic appointments has been traced back to Prussia in the late eighteenth century, and of course is in full flow now. Appointment panels routinely filter candidates by the “quality” of the journals in which they publish, judged by one (extremely dodgy) number.

This brings us to where we are now. What can we do to take back control of academic publishing? I have discussed this on many previous occasions. I believe we should do all we can to encourage genuinely free journals such as Electron. J. Combin., by publishing our best papers in them, refereeing, and joining editorial boards. But we must also use what influence we have to persuade university administrators and grant-awarding bodies that the quality of a publication cannot be reliably inferred from the impact factor of the journal in which it appears, and that it is in their interest as well as ours to take these journals seriously.

I found myself quite strongly in agreement with almost everything that was said. In particular, it is up to established academics to take the lead on this. (I am old enough that I no longer have anything to lose, but I cannot say the same for young colleagues.)

The one exception was the question of impact. As I have said before ad nauseam, the current rules for impact are not fair to academics. However, one panel member defended impact, as the best way to persuade politicians and others of the importance of what we do. Clearly I am not a politician!

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Charles Sims

This morning I received the news that Charles Sims died on Monday.

Sims was one of the most influential figures in computational group theory, but was much more besides. His name is attached to two sporadic simple groups; the one I know best, the Higman–Sims group, was found without any recourse to computation at all. It is a subgroup of index 2 in the automorphism group of a graph on 100 vertices, constructed from the 22-point Witt design. The graph had been constructed earlier by Dale Mesner, as I described here. By coincidence it happened that the paper by Misha Klin and Andrew Woldar on this has just been published here.

Indeed, from my point of view, Higman and Sims were the two people who introduced graph theory into the study of permutation groups. I was lucky enough to be in on the ground floor, beginning my doctoral studies in 1968 (the year after the Higman–Sims group was found, though I wasn’t yet in Oxford on that memorable occasion).

Also it happened that Michael Giudici was here last week, and gave a colloquium talk about his work on extending the work of Sims and others from graphs to digraphs, and reminded me that in my thesis I extended a result of Sims on paired subconstituents of a finite transitive permutation group.

I first met Sims in the early 1970s, when he came to a miniconference on permutation groups organised by Peter Neumann. One thing that I recall is that, at Peter’s house, we were discussing perfect pitch; Charles pulled out his watch and asked me to put my ear to it and tell him the pitch of the tone. (As I recall, the mechanism cauused it to vibrate at 360 hertz.)

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