Trip to Niebüll

Over Easter Eva and I went on a bus trip to the far north of Germany. Our base was a hotel in Niebüll, a place I had never heard of before. We got up very early in the morning and the journey by bus took more than twelve hours, including short breaks. I did not find the trip tiring. The bus driver was doing the work and it was pleasant to observe the surroundings. We passed through Hamburg. Seeing the harbour I was made aware of the huge effort involved in importing all kinds of goods by ship, something I never usually think about. Niebüll itself is some distance from the sea. Nevertheless we could hear groups of Oystercatchers flying around and calling, which reminded me of my childhood. On the first day we visited the dyke with a view onto the Wattenmeer. On the way there we passed through fields with huge flocks of Barnacle Geese. We also saw and heard many other species of birds. Some of these were the sounds which were typical of my childhood, such as Redshanks, Curlews and Meadow Pipits. Thus on this trip I had some experiences which I had hoped to have (and did not) during our trip to Scotland last summer. Other highlights were a Bar-Tailed Godwit and two Avocets.

The people on this trip, organized by Bohr Reisen, were of an older generation, most of them retired. We found their company pleasant. As it happened we always had dinner at the same round table with the same group of people, eight in total. The atmosphere was good and we were able to have good converations with all the others. These days I often have the feeling that it is dangerous to talk about certain topics, in particular political ones, with strangers. In this case I was glad that these constraints were not there. From the first evening on we felt able to talk freely. For this we can be grateful to one woman at the table who did a lot to break the ice. This feeling of freedom is important for a successful holiday. On the first evening there was music after dinner from a DJ but it was not at all our taste. We left very soon, simultaneously with all the others at our table. The next evening there was a group of men singing sea shanties after dinner. They did not sing very well but the performance was reasonable and we stayed to the end. There was one song whose text would probably have been condemned by people who love political correctness. We found it difficult to suppress our laughter, simply due to the stark contrast between this song and many things we experience in daily life. This was a small liberating experience.

On our second full day we crossed the nearby Danish border and the bridge to the island of Rømø. From there we took a ferry to Sylt, which is known as a playground of the rich in Germany. Many of the houses there are owned by people who only spend a couple of weeks a year there. For people with normal incomes it is hard to find affordable accommodation. My impression is that the celebrities who frequent the island are probably not often seen on the street. For instance we were shown the place where a famous restaurant, the Sansibar, is hidden. (It was the first time I had heard of the place but apparently it is a name known to many people.) Recently there was a lot of reporting in the German media about the lavish wedding of Christian Lindner, the leader of the FDP, with the journalist Franca Lehfeldt. Part of the celebrations took place at the Sansibar. Westerland, the main town on Sylt, did not seem to us particularly attractive. We got back to the mainland with a train which can transport cars and buses. On our last day we took a ferry to the island of Föhr, this time without the bus.

To finish this post I want to come back to Franca Lehfeldt. At the time of the publicity about her wedding I knew nothing about her. Now that has changed. Together with Nena Brockhaus she has published a book called ‘Alte Weise Männer’, which has become a bestseller. The title, literal translation ‘old wise men’ is a pun since its title sounds almost identical to ‘Alte Weisse Männer’, literal translation ‘old white men’. In German the second has now become a kind of insult, indicating a class of people regarded as at least out of date and useless and often suggested to be sexist and racist. The idea of the book is that society can learn something valuable from the ‘old white men’. The authors interviewed ten men, all over seventy, who have led interesting and successful lives so as to try and profiit from their wisdom. Up to now I have only read the preface but I intend to read more. I also watched an online presentation of the authors related to the book, which indicated to me that they may be ‘young clever women’ who are worth listening to.

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Grammatical gender and politics in Germany

I find it a little difficult to write about this subject in English and in such a way that it is comprehensible for an international audience. Nevertheless I think it is worthwhile to do so. The content of this post is related to a political theme which is specific to Germany, or at least German-speaking countries, but it is related to political issues of much wider significance. In German a noun belongs to one of three genders, masculine, feminine or neuter. These names have special connotations but fundamentally they are just names for three different classes of nouns, which behave in different ways within the language, such as influencing the form of adjectives which describe them. The English Wikipedia article Grammatical gender mentions that the term ‘noun class’ is sometimes used as a synonym for this. I think that mathematicians in particular will easily understand the logical status of a concept like this which is defined by its logical relations. I am reminded of the famous (and apocryphal?) story about Hilbert saying that in Euclidean geometry instead of points, lines and planes we could say tables, chairs and beer-mugs and it would make no difference. What is important is the relations between the concepts, not their names.

Problems arise from the fact that the names for the genders have strong connotations. Words for male human beings usually belong to the gender ‘masculine’, words for female human beings usually belong to the gender ‘feminine’. In other words, there is a correlation between grammatical and biological gender. This has led some people to give grammatical gender a significance beyond the formal one I have introduced previously. This happens although there are obvious examples where the two notions associated to the word ‘gender’ do not agree. For instance the German word ‘Person’ meaning person is feminine while the word ‘Mensch’ meaning human being is masculine. This exaggeration of the meaning of grammatical gender leads to problems. Let us for instance take the German word ‘Professor’ meaning professor. It can mean a professor of either sex. However if we want to emphasize that a particular professor is female we can use the word ‘Professorin’. The ending ‘in’ indicates a female person. The argument of some people is that if we use the word ‘Professor’ in the inclusive sense, denoting a person who may be female then this can lead to the implicit assumption that the person concerned is a man, due to the fact that the grammatical gender of the word is masculine. Thus they say that this practise leads to women becoming ‘invisible’ and thus discriminates against them. Other people have other opinions on this subject. It is something which could in principle be discussed in a civilised way. In practise this is often not possible. An elaborate system of feminine forms of various words has been developed (sometimes called ‘Gendern’) and anyone who publicly critises the use of this system risks being branded a right-wing extremist. The system is widespread in various areas: politics, state media, universities, public administration, private companies etc. In many cases the system is not just used but imposed, either through official regulations or through peer pressure.

I find ‘Gendern’ unpleasant and avoid it whenever possible. What are my motives for that? The first is an aesthetic one – I love language and ‘Gendern’ makes a mess of the language. German is not my native language but I still do not like seeing it being mistreated. Various surveys show that a majority of Germans are against ‘Gendern’ but it is nevertheless widespread. Its proponents are loud and sometimes also aggressive. Another argument againt ‘Gendern’ is that it not only makes language ugly but it makes it so clumsy as to often make a text difficult to understand and tiring to read. Moving in a language like English where gender in this sense does not exist seems like a luxury in comparison. As I said at the beginning this seems like a very special topic. However I also claimed that it is of wider significance. Why do I say that? I see it as an example of the way in which politics has come to suppress free rational discussion, a phenomenon which occurs in many areas of life and in many countries. Moral convictions are regarded as more important than facts and logic. As yet this has not had much effect on me personally. A mathematician is likely to be less affected than a social scientist. I enjoy using language in different ways, private and professional, and I see ‘Gendern’ as a threat to being able to feel comfortable and at home in the German language. I also see it as an example of the way in which political ideology can have a negative impact on the daily lives of normal people. It is important that the ‘silent majority’ speaks out and does not leave public discourse to vocal minorities.

Visit to Switzerland

Over New Year Eva and I spent some time in Switzerland. It was the first time I had made a private trip there. I have been in Zurich several times for my work and I was once at a conference in Ascona but that was all my experience of the country. We spent three nights in Chur which we found a very pleasant town. The following three nights we were in Lucerne which I liked even better. In some ways visiting Switzerland was like returning to a better past. In what we saw there were no signs of hardship or other problems due to the pandemic or the Ukraine war. The restaurants were full. In the hotels the personnel was plentiful. The complete absence of requirements to wear a mask was refreshing. It was strange at the end of the trip when we reentered Germany on the train and had to put on our masks again. In Switzerland it was easy to forget many of the negative aspects of everyday life at present.

From Chur we took a day trip by train to Arosa, a place I had not heard of before. The town itself is not specially attractive but the scenery on the way there is spectacular. I discovered that the sanatorium in Thomas Mann’s novel The Magic Mountain was based on an institution in Arosa. In the novel the sanatorium is situated in Davos but in fact Mann’s wife stayed for extended periods in both these places. Mann visited her in Arosa. Robert Louis Stevenson also spent time there. In fact I do not like Mann very much. The first book of his I read was Doctor Faustus, in English. While I admired some of the descriptions, particularly that of the music shop, the book as a whole did not appeal to me. Next I read Death in Venice which I did not like better. Finally, after having learned German I read Death in Venice in the original, hoping that this would be an improvement. Unfortunately it was not the case. This is in contrast to my experience with Kafka. When I originally read Kafka’s work in English I liked it a lot and when I later read it in the original I found it even better. In Arosa I saw a lot of Alpine Choughs, the first of many I encountered on the trip.

One thing I liked about Lucerne was its situation on the lake, surrounded by mountains. On one evening the lake provided an impressive variety of colour combinations as the light changed. One striking aspect of the lake is the powerful stream caused by the flow of water being largely held back at one place and confined to a narrow region. (The river Reuss flows into the lake at one end and out again at the other, close to Lucerne.) We took a boat trip on the lake. From there is it possible to see a house where Richard Wagner lived for several years and wrote some of his most famous works. He had a number of famous visitors there, including Nietzsche and Liszt. In Germany it is typical for people to set off fireworks on New Year’s Eve. I do not like that much. Firstly it makes me feel that it is unsafe to go onto the streets at that time. This year it was particularly extreme. On the other hand I do not like being kept awake for much of the night by the noise. In Lucerne they had a variant which I found preferable. Fireworks were forbidden on New Year’s Eve. People did occasionally violate this rule but it was a minor annoyance. Then on the first of January there was a professional firework display over the lake. It was spectacular, it was safe and it did not cost anyone sleep. In Lucerne we visited the Rosengart art collection which only served to show me once again how little I am able to appreciate modern art. The painters represented most there are Picasso and Klee. From what we heard on the guided tour I had the impression that Picasso was a very unpleasant person, in love with himself. I find his paintings ugly and I do not appreciate the paintings of Klee we saw either. Eva has more understanding for such things. The few paintings we saw that I liked were by impressionists, on the side of the border to modern art where I still feel comfortable. I am thinking in particular of paintings of Monet, Renoir and Seurat.

Talks about malaria

I recently heard two talks about malaria at the Mainzer Medizinische Gesellschaft. The first, by Michael Schulte, was historical in nature and the main theme was the role of quinine as a treatment. The second, by Martin Dennebaum, was about malaria and its therapy today. Both talks were not only useful sources of information about malaria but also contained more general insights about medicine and its relations to society. In German the tree which is the natural source of quinine is called Chinarinde (i.e. China bark, in English it is called cinchona) and this had left me with the impression that the tree was from China. The first thing I learned from the first talk is that this is false. The tree comes from the Americas and was first used for medicinal purposes in Peru. A few weeks ago Eva and I visited a botanical garden in Frankfurt (Palmengarten) and saw a lot of those tropical plants which are the sources of things we are familiar with in everyday life (e.g. chocolate, cocoa, tobacco) and we in particular saw a cinchona tree. However I did not pay enough attention to realise its geographical origin at that time. There were men in Peru who had to cross a river to get to work and shivered a lot after they came out of the water. The idea came up that the bark of this tree could be used to reduce the shivering. At that time there were Jesuit missionaries in Peru. The Jesuits had been instructed by their leader Ignatius Loyola to bring back interesting things such as animals and plants from the exotic places they visited. One of the Jesuits in Peru, knowing that malaria is often accompanied by intense shivering, thought that cinchona bark might also help against malaria. This quite random analogy turned out to lead to a great success. Cinchona bark was sent to Rome and used there to treat malaria. It is remarkable how successfully this was done although the doctors knew nothing about the mechanisms at work in malaria. Without knowing about the existence of quinine they developed a way of extracting it very effectively using alcohol. They determined the right time to give the drug in the cycle of symptoms. In order for the treatment to be successful the drug must be given just after the infected red blood cells burst and the organisms are in the open in the blood and not protected. Quinine, the element of the cinchona bark most active against malaria was isolated around 1820. The first industrial production took place in Oppenheim, a town on the Rhein not far from Mainz. At one time Oppenheim was reponsible for 60 per cent of the world production of the substance. Malaria was a big public health problem in that region at the time and that was what stimulated the development of the industry. There is a story that the British colonists in India used to drink gin and tonic because tonic water contains quinine and thus provides protection against malaria. The speaker left it until the end of his talk to say that while the colonists did use quinine in other forms the concentration in tonic water is too low to be useful against malaria.

The second talk started with an interesting case history. A flight attendant flew from Frankfurt to Equatorial Guinea. Ten days after she got back she developed fever. Her husband had fever at that time due to influenza and she assumed she had the same thing. For this reason she did not seek medical advice until three days later. That was a public holiday and she was told she should come back the next day so that all the necessary tests could be done. The next day she landed as an emergency in the University Hospital in Mainz. A blood test showed that 25 per cent of her blood cells were infected with the organism causing malaria. The amount which is considered life-threatening is 5 per cent. The speaker said that if she had waited longer she would probably not have lived another day. Fortunately she did get there on time and could be cured. There are very effective drugs to treat malaria, namely those based on artemisinin. These drugs have their origin in traditional Chinese medicine. During the Vietnam war malaria was a big problem for those on both sides of the conflict. On the US side four or five times as many soldiers died of malaria than in combat. Both sides were looking for a drug to help with this problem and both looked to herbal sources, at first with little success. In the case of the Vietnamese they had enlisted the help of the Chinese to do this work for them. In China a secret ‘Project 523’ was set up for this purpose. As a part of this project Tu Youyou led the search for a malaria drug based on traditional Chinese medicine. She was successful and eventually got a Nobel Prize in 2015 for the discovery of artemisinin. From traditional literature she obtained a list of candidate plants and then subjected them to modern scientific analysis, in particular using experiments on mice. Her first attempts with the plant which produces artemisinin were not successful and it was another hint from ancient literature which helped her to overcome that difficulty. In fact the active substance was being destroyed by an extraction process at high temperature and once she had developed an alternative process at lower temperature positive results were obtained. Once the right candidate drug had been obtained the further analysis proceeded using all the tools of modern (non-alternative) medicine. I am no friend of ‘alternative medicine’ and I cannot help comparing the phrase to ‘alternative facts’. One of the things I have against ‘alternative medicine’ is that I think that if some part of it was really effective then it would quickly be adopted by real medicine and thus leave the alternative region. Nevertheless the story of artemisinin shows how in exceptional cases there can be a valuable flow information from traditional to real medicine and that this may require a great amount of effort. The type of malaria which is sometimes deadly is that caused by Plasmodium falciparum. Other types, caused by other Plasmodium species are less deadly but can become chronic. I think of novels where a typical figure was an army officer who suffered from malaria because he had served in India. From the talk I learned that the other types of malaria can be prevented from becoming chronic – it is just necessary to give the right treatment. To emphasize that malaria should be taken seriously in a country like Germany today he mentioned that at that moment there was again a malaria patient in intensive care in the University Hospital in Mainz although that case had not been so critical as that of the flight attendant.

The autobiography of Andrew Carnegie

The last post made some statements about Andrew Carnegie, with my main source of information about him being his autobiography, which was published posthumously. I just finished reading that book for the second time and here I want to mention some further things about him which I find interesting. Carnegie’s life after he arrived in the US is an exemplary rags to riches story corresponding to the American dream. His first job in a factory was for one dollar and 25 cents a week, working long hours. He writes that his first week’s earnings made him happier than any of the millions he made later, for they meant that he was contributing to the subsistence of his family. He was thirteen years old. After this he moved to a job which was even harder but it already brought him two dollars a week and after that his income rose steadily. He became a messenger boy and used this to start to build up a network of contacts. He was always ready to grab any opportunity that came along and to make any efforts which he thought might help him to improve his situation in life. He made himself useful in the office and managed to get a position as a telegraph operator. With the contacts he made there he was able to move to a job as clerk and telegraph operator to an important railway employee, Thomas Scott. At this time a serious incident took place. Carnegie had the duty of fetching the pay for the employees working under Scott. Once he was bringing it, travelling by train. It was quite a new thing at that time and he travelled on the engine because he found it exciting. While he was not paying attention the packet containing the pay, which he had under his jacket, fell out of the train. Some time later he noticed the loss. It could have meant losing his job and suddenly having huge debts. He was able to persuade his companions to drive the train back and eventually saw the packet lying on the bank of a river. If it had rolled a little further it would have ended in the river and been lost. In fact it stopped soon enough, he found it and the disaster was averted. The fact that Carnegie was so successful in his life no doubt had a lot to do with luck, with this being a notable example. What would have happened if the packet had landed in the river? It would have been a big setback for him but I think he would soon have overcome it. He certainly had luck but I think that played much less of a role in his success than his character.

A big step forward in Carnegie’s career involved taking a big risk. His boss was responsible for organizing the railway traffic in a big network. In particular, if there was some problem such as an accident (and these were not so rare) he was the one who had to sort it out and get the trains running again. For this purpose he prepared telegraph messages and Carnegie sent them out. In this way he learned how Scott carried out these tasks. One morning many trains were standing still due to previous problems. The situation was such that they could have started running again and this would have been beneficial for the company. Scott was not in the office. He decided to take the decisions needed to start up traffic again and send them out in Scott’s name. Of course he had no authority to do that. When Scott came back Carnegie was very apprehensive but immediately said what he had done. Scott looked through the documentation of the measures taken and then simply returned to his desk without a word. Carnegie’s explanation for this behaviour was as follows. Scott could not praise him for what he had done since he had broken all the rules. On the other hand he could not scold him since he had done everything right. So he just said nothing. Now Carnegie could relax concerning the consequences of that incident but he almost decided to never do such a thing again. Then he heard from an acquaintance how Scott had talked to someone else about the matter and this allowed him to judge the impression his daring action had made on Scott. After that he had no hesitation about carrying out such actions. Since Scott liked coming in late he had plenty of opportunities for that. Eventually this put Carnegie in the position to take over the job of his boss and thus take a big step to a higher level of status and pay.

Carnegie later got involved in the production of iron and things constructed out of it, such as rails and bridges. He got an advantage over his competitors by employing a chemist. The iron ore from some mines was unpopular and correspondingly relatively cheap. There had been problems with smelting it. A chemical analysis revealed the source of the problem – that ore contained too much iron for the smelting process to work well. The solution was to modify the process (with the help of scientific considerations) and then it was possible to buy the high quality ore at a cheap price while others continued to buy low quality ore at a high price. Previously nobody really knew what they were buying. Carnegie believed in the value of real knowledge. Carnegie did not like the stock exchange and emphasized that except for once at the beginning of his career he never speculated. It was always his policy to buy and sell things on the basis of their real value. Carnegie was no friend of unions and often fought them hard. On the other hand he was, or claimed to be, a friend of the working man. His idea was not to give people money just like that but to give them the opportunity to improve their own situation. In later years he gave a huge amount of money, about 300 million dollars in total for various causes. He gave money for libraries (more than two hundred), for scientific research, for church organs and of course for the Carnegie Hall. These were all things which he believed would do people good.

Carnegie was committed to the goal of world peace. He had a lot of influence with powerful politicians and it seems that in at least one case he used it to prevent the US becoming involved in a war. He got into contact with Kaiser Wilhelm II. It turned out that both of them were admirers of Robert the Bruce. He had great hopes for the Kaiser as someone who could help to bring peace and he must have been bitterly disappointed in 1914 when things went a very different way. Then he transferred his hopes to President Wilson. At that point his autobiography breaks off. Here I have only been able to present a few selected things from a fascinating book which I thoroughly recommend. I find Carnegie an admirable character.

Andrew Carnegie and me

At the moment I am rereading the autobiography of Andrew Carnegie. For me he is a leading example of a ‘good capitalist’. I see some parallels between my early life and that of Carnegie and I have been thinking about similarities and differences. We were both born in Scotland to parents who were not rich. His father was a weaver. At some stage advances in technology meant that his form of industry was no longer viable. The family had difficulty earning their living and decided to emigrate to America. While still in Scotland Carnegie’s mother started a business to supplement the income of her husband.

My father was a farmer. When he began the size of the farm (70 acres) was sufficient. (I recently noticed the coincidence that the father of Robert Burns, Scotland’s national poet, also had a farm of 70 acres.) Later there was a trend where the size of farms increased and the machinery used to work them became more advanced. In order to do this the farmers, who were mostly not rich, had to borrow money to buy more land and better machines. The banks were eager to lend them that money. Of course this meant a certain risk but many of the people concerned were prepared to take that risk. My father, on the other hand, never borrowed any money in his life and so he missed taking part in this development. This meant that under the new conditions the farm was too small (and in fact some of it was not very good land – it was too wet) to support our family (my parents, my grandmother and myself) very easily. My mother did everything she could to supplement the income of my father. In particular she took in bed and breakfast guests during the summer. I should point out that we were not poor. We did not lack anything essential, living in part from our own produce such as milk, butter, cheese, eggs, potatoes and meat. My grandmother kept a pig and hens. The school I attended, Kirkwall Grammar School, was the school for all children in the area – there was no alternative. The parents of many of the other children I went to school with were better off financially than my parents. As a sign of this, I mention an exchange between our school and one in Canada. Many of the other pupils took part in that. My parents could not afford to finance it for me. At a time when many people were getting their first colour TV we still had a very old black and white device where with time ‘black’ and ‘white’ were becoming ever more similar. I did not feel disadvantaged but I just mention these things to avoid anyone claiming that I grew up in particularly fortunate economic circumstances.

Both Carnegie and I benefitted from the good educational system in Scotland. School was already free and compulsory in his time. My university education was mostly financed by the state, although I did win a couple of bursaries in competitions which helped to make my life more comfortable. In my time parents had to pay a part of the expenses for their childrens’ university education, depending on their incomes. My parents did not have to pay anything. Some of the people I studied with should have got a contribution from their parents but did not get as much as they should have. Thus I actually had an advantage compared to them. Carnegie’s father was involved in politics and had quite a few connections. My parents had nothing like that. It might be thought that since my parents did not have very much money or connections and since there were very few books in our house I started life with some major disadvantages. I would never make this complaint since I know that my parents gave me some things which were much more important than that and which helped me to build a good life. I grew up in a family where I felt secure. My parents taught me to behave in certain ways, not by command but by their example. They taught me the qualities of honesty, reliability, hard work and humility. Carnegie received the same gifts from his parents.

Let me now come back to the question of books. As a child I was hungry for them. We had a good school library which included some unusual things which I suppose not all parents would have been happy about if they had known the library as well as I did. For instance there was a copy of the ‘Malleus Maleficarum’. What was important for my future was that there were current and back issues of Scientific American and New Scientist. There was also a public library from which I benefitted a lot. Apparently this was the first public library in Scotland, founded in 1683. In the beginning it was by subscription. It became free due to a gift of money from Andrew Carnegie in 1889. He spent a huge amount of time and effort in supporting public libraries in many places. In 1903 Carnegie also gave the money to construct a building for the library and that is the building it was still in when I was using it. He visited Kirkwall to open the library in 1909. Thus it can be said that I personally received a gift of huge value from Carnegie, the privilege of using that library. His activity in this area was his way of returning the gift which he received as a young boy when someone in Pittsburgh opened his private library to working boys.

Is mathematics being driven out by computers?

In the past two weeks I attended two conferences. The first was the annual meeting of the Deutsche Mathematikervereinigung (DMV, the German mathematical society) in Berlin. The second was the joint annual meeting of the ESMTB (European Society for Mathematical and Theoretical Biology) and the SMB (Society for Mathematical Biology) in Heidelberg. I had the impression that the participation of the SMB was relatively small compared to previous years. (Was this mainly due to the pandemic or due to other problems in international travel?) There were about 500 participants in total who were present in person and about another 100 online. I was disappointed with the plenary talks at both conferences. The only one which I found reasonably good was that of Benoit Perthame. One reason I did not like them was the dominance of topics like machine learning and artificial intelligence. This brings me to the title of this post. I have the impression that mathematics (at least in applied areas) is becoming ever weaker and being replaced by the procedure of developing computer programmes which could be applied (and sometimes are) to the masses of data which our society produces these days. This was very noticeable in these two conferences. I would prefer if we human beings would continue to learn something and not just leave it to the machines. The idea that some day the work of mathematicians might be replaced by computers is an old one. Perhaps it is now happening, but in a different way from that which I would have expected. Computers are replacing humans but not because they are doing everything better. There is no doubt there are some things they can do better but I think there are many things which they cannot. The plenary talks at the DMV conference on topics of this kind were partly critical. There occurred examples of a type I had not encountered before. A computer is presented with a picture of a pig and recognizes it as a pig. Then the picture is changed in a very specific way. The change is quantitatively small and is hardly noticeable to the human eye. The computer identifies the modified picture as an aeroplane. In another similar example the starting picture is easily recognizable as a somewhat irregular seven and is recognized by the computer as such. After modification the computer recognizes it as an eight. This seems to provide a huge potential for mistakes and wonderful opportunities for criminals. I feel that the trend to machine learning and related topics in mathematics is driven by fashion. It reminds me a little of the ‘successes’ of string theory in physics some years ago. Another aspect of the plenary talks at these conferences I did not like was that the speakers seemed to be showing off with how much they had done instead of presenting something simple and fascinating. At the conference in Heidelberg there were three talks by young prizewinners which were shorter than the plenaries. I found that they were on average of better quality and I know that I was not the only one who was of that opinion.

In the end there were not many talks at these conferences I liked much but let me now mention some that I did. Amber Smith gave a talk on the behaviour of the immune system in situations where bacterial infections of the lung arise during influenza. In that talk I really enjoyed how connections were made all the way from simple mathematical models to insights for clinical practise. This is mathematical biology of the kind I love. In a similar vein Stanca Ciupe gave a talk about aspects of COVID-19 beyond those which are common knowledge. In particular she discussed experiments on hamsters which can be used to study the infectiousness of droplets in the air. A talk of Harsh Chhajer gave me a new perspective on the intracellular machinery for virus production used by hepatitis C, which is of relevance to my research. I saw this as something which is special for HCV and what I learned is that it is a feature of many positive strand RNA viruses. I obtained another useful insight on in-host models for virus dynamics from a talk of James Watmough.

Returning to the issue of mathematics and computers another aspect I want to mention is arXiv. For many years I have put copies of all my papers in preprint form on that online archive and I have monitored the parts of it which are relevant for my research interests for papers by other people. When I was working on gravitational physics it was gr-qc and since I have been working on mathematical biology it has been q-bio (quantitative biology) which I saw as the natural place for papers in that area. q-bio stands for ‘quantitative biology’ and I interpreted the word ‘quantitative’ as relating to mathematics. Now the nature of the papers on that archive has changed and it is also dominated by topics strongly related to computers such as machine learning. I no longer feel at home there. (To be fair I should say there are still quite a lot of papers there which are on stochastic topics which are mathematics in the classical sense, just in a part of mathematics which is not my speciality.) In the past I often cross-listed my papers to dynamical systems and maybe I should exchange the roles of these two in future – post to dynamical systems and cross-list to q-bio. If I succeed in moving further towards biology in my research, which I would like to I might consider sending things to bioRxiv instead of arXiv.

In this post I have written a lot which is negative. I feel the danger of falling into the role of a ‘grumpy old man’. Nevertheless I think it is good that I have done so. Talking openly about what you are unsatisfied with is a good starting point for going out and starting in new positive directions.

Trip to Scotland with some obstacles

Recently Eva and I travelled to Scotland. It was an organized tourist trip although I was also able to meet my sister and some other family for dinner on one evening. We flew from Frankfurt to Edinburgh via Brussels. We had heard a lot about chaos at airports in the recent past and were pleasantly surprised when everything went smoothly in Frankfurt. This did not last long. Our flight to Brussels was late and we had to run as fast as we could and jump the queue for immigration to just get to the gate in time for boarding. Our luggage was not so successful as we were. When we arrived in Edinburgh we waited a long time for our luggage to come and it did not. There was no information on the display and the information office was closed. There were no airport employees visible. Eventually we had no choice but to leave the baggage area and file a lost baggage claim. During the trip we were moving from one hotel to another and it was not possible to leave more than one forwarding address. We had to make several calls about this matter in the days that followed and often got the information that the person we were calling was not responsible and that we should call another number. The people I talked to often had strong Indian accents and I suppose that they were all sitting in call centres in India. We arrived in Edinburgh on a Sunday and in the end we got a message the following Saturday that our luggage would be delivered to our hotel in Aberdeen that day at a certain time. This was later revised to say that it would arrive on the Sunday between 00.02 and 02.22. It did arrive and was received by the hotel. Of course we had to buy various things during the week to replace those sitting in our suitcases. This whole business cost us a lot of time and nerves. On the way back we had to cross the EU border in Brussels.The only problem was that there was nobody there, only a written message that it was not possible to call anyone. In the end, fearing that we would miss our flight I spoke to a security guard who was buying a sandwich. He was very helpful. He made several phone calls. Then he took us through a security gate and passed us on to an immigration official who checked our passports. Again we just managed to reach the gate in time. In fact the flight was late so that we would have had a bit more time. The flight was almost empty. In Frankfurt there was a message that the luggage would arrive in thirty minutes. Then thirty suddenly changed to eight and the luggage came even faster than that. Thus positive surprises are also possible.

What conclusions do I draw from this? Firstly, I do not believe that we had specially bad luck but rather that this is the usual state of affairs at the moment. (The luggage of several other members of our group, arriving from different airports with different airlines, also took many days to arrive, in one case even a day longer than ours.) We also experienced a number of other things while in Scotland, such as lifts or coffee machines in hotels which were not working and had been waiting for months to be repaired. Many hotels in Scotland, especially in rural areas, have closed, at least for the season and maybe for ever. For these reasons we had to stay in some cases at hotels much further away from the points we wanted to visit than planned and there were long drives. The situation with logistics is dire. We were not organizing the trip alone. The organization was being done by a company which has many years of experience organizing trips of this kind in Scotland and all over the world. We know from previous experience that this company is very good. Thus things are very difficult even for the experts. If things do not change quickly this type of tourism is threatened. In future I will think very carefully about flying anywhere. This has nothing to do with the frequently discussed environmental issues but simply with the doubt that I will arrive successfully with my luggage and without an excessive amount of stress. If I do fly anywhere then I will be prepared to pay a higher price to get a direct flight. This is then the analogue of my present practise with train trips where I try to minimize the number of connections which have to be reached since the trains cannot be expected to be on time. It seems that these days the most reasonable thing is to expect that everything that can go wrong will go wrong. Travelling has become an adventure again. Will this change soon? I do not expect it will.

We arrived in Edinburgh in the midst of the Festival. The streets were full of people and the atmosphere good. On the evening of the second day we went to the Edinburgh Military Tattoo. The spectacle was impressive as was the way the arrival and departure of the mass of spectators was coordinated. The weather was dry and not too cold and so we were in luck. We heard that at the corresponding performance one week later it rained the whole time. Since almost all the spectators are sitting out in the open the weather makes a big difference. After leaving Edinburgh we crossed into Fife over the old road bridge which was only open for buses due to repairs. We briefly visited St. Andrews where I had not been before and then continued to Pitlochry where we spent a couple of nights. While there we had an excursion to visit the house of Walter Scott. I am not an admirer of Scott. One time years ago I felt the duty to read at least something by him and I read ‘Heart of Midlothian’. It did not leave a lasting impression on me. The main thing I remember about Scott is how the father in ‘To the Lighthouse’ often talks about his novels. From Pitlochry we drove to Braemar and then down Deeside to Aberdeen. We also made an extra little excursion to Dunnottar Castle. I had never been there before although it is so close to Aberdeen where I lived for seven years. The excursions I made from there were generally to the north or to the west. In Aberdeen we had a guided tour from a local which was quite entertaining.We then went into the Machar Bar (a place where I spent many hours as a student), ate stovies (which I had forgotten about for many years) and drank whisky. The guide recited some Burns and we did some singing. Together with him I sang ‘The Northern Lights of Old Aberdeen’. Up to that time we had almost only warm weather and sun (apart from a little coastal fog). After that we crossed over to the west coast. A rear view mirror of our bus was destroyed by another passing bus and this lead to some delays. In the end we took the most direct route from Inverness to Gairloch where our next hotel was. Perhaps we actually profited from the accident since the landscape on that route was spectacular. After the stress with our luggage I felt a great relaxation in Gairloch. The impression it made on me was of somewhere which is really far away and isolated from my usual everyday world. From our hotel room we could see Gannets fishing in the bay and in the night I heard Ringed Plovers calling on the beach. This is nature in the form I appreciate it most. The next day we crossed to Skye. It was rather foggy but what else can be expected from Skye? Our next hotel was in Tyndrum. From there we made a day trip to Iona via Oban and Mull. The general impression of the participants (and it was also my impression) was that the day was too hectic in order to enjoy it properly. For reasons already indicated the hotel was too far away and as a consequence the time was too short. I did not really get a feeling about what it might have been like for St. Columba to arrive on Iona and do what he did there. Another religious figure I would like to know more about after this trip is John Knox. Knowing very little about him I had the feeling that he was a bigot and an extremist. Now I wonder if he might not be responsible for some of most positive aspects of Scottish culture, aspects which I have profited from in my life. We spent our last night in Stirling, where we visited the castle.

The Prime of Miss Jean Brodie

The novel ‘The Prime of Miss Jean Brodie’ by Muriel Spark has been on my bookshelf at home for many years. I bought it and read it when I was a student. I suppose I did so because I heard friends of mine who were studying English (including Ali Smith – see here for my relations with her) praising it. I do not know how much I liked it at the time. Now, for reasons not worth relating here, I took it off the shelf and opened it. I started reading a little and then could not stop until I had finished it. I had the strange impression that I liked the book much better and laughed a lot more than than the first time. Is this true or is it just my memory failing with increasing age? Now I am considering the possibility that among all novels by Scottish writers it is the one I like the best. What are other possible contenders for this role? The one which occurs to me is ‘Lanark’ by Alasdair Gray. I read it with admiration as a student. In a way Gray is to Glasgow as Joyce is to Dublin although I would not think of regarding Gray as being on the same level as Joyce. I once met Gray personally. The Aberdeen University Creative Writing Group invited him and Jim Kelman (who years later won the Booker Prize) to Aberdeen to give a reading. They came on the train from Glasgow and presumably consumed alcohol continuously during the whole journey. At any rate they were both very drunk when they arrived, whereby Gray appeared a bit less intoxicated than Kelman. I had no particular interest in Kelman; Gray was the one who interested me. I cannot remember much about our conversation, except that he pronounced ‘Proust’ incorrectly. I am not sure if that was ignorance or provocation. It was probably the latter. I have not read Lanark again since then and I think my copy did not survive my moves since then. I do not know what my impression would be if I started reading Lanark again but my intuition tells me that it would not captivate me like Miss Jean Brodie. This is because of the way I have changed over the past almost forty years.

As the title suggests the novel ‘The prime of Miss Jean Brodie’ is dominated by one character. She is strong and fascinating but it is wise to be cautious of having too much admiration for her. This is made clear at the latest by her professed admiration for Mussolini. (The novel is set in the years leading up to the Second World War.) She is a teacher at a private school, her pupils being girls of under the age of twelve. A group of these girls from one year come together to form ‘the Brodie set’. They are brought together not by any similarities between them but by their bond to Jean Brodie. This also keeps them together for the rest of their time at school. She is regarded by most of the teachers at the conventional school as too progressive and the headmistress is keen to find a reason to get rid of her. Eventually she succeeds in doing so. I cannot see Jean Brodie as a model for a teacher. She hatches out schemes to allow her pupils to avoid the work they should be doing and to listen to the stories she tells them. She has very definite ideas, for instance as to the relative importance of subjects: art first, philosophy second, science third. My ordering would be: science first, art second, philosophy third. The book is often very funny but I think there is also a lot in it which is very serious. Apart from the content, the use of language is very impressive. I enjoyed trying to imagine what it means for a jersey to be ‘a dark forbidding green’. There is even a little mathematics, although that is a subject which Jean Brodie has little liking for. Concerning the conflict of Miss Brodie with the Kerr sisters we read, ‘Miss Brodie was easily the equal of both sisters together, she was the square on the hypotenuse of a right-angled triangle and they were only the squares on the other two sides’. For me this is one of those few books which is able to bring some movement into my usual routine. I watched a documentary about Muriel Spark herself, which is also very interesting. Maybe I will soon read another of her novels. ‘Aiding and Abetting’ has also found its way from my distant past onto my bookshelf but I am not sure it will be the next one I read.

Advances in the treatment of lung cancer

I enjoy going to meetings of the Mainzer Medizinische Gesellschaft [Mainz Medical Society] but they have have been in digital form for a long time now due to the pandemic. Recently I attended one of these (digital) events on the subject of the development of the treatment of lung cancer. There was a talk by Roland Buhl about general aspects of the treatment of lung cancer and one by Eric Roessner on surgery in lung cancer. Before going further I want to say something about my own relation to cancer. When I was a schoolchild my mother got cancer. In Orkney, where we lived, there was no specialist care available and for that reason my mother spent a lot of time in the nearest larger hospital, Foresterhill in Aberdeen. During my first year as a student in Aberdeen there was an extended period where I visited my mother in hospital once a week. I was not intellectually engaged in this issue and I do not even know what type of cancer my mother had. I seem to remember that at one point her spleen was removed, which suggests to me that it was a cancer of the immune system, lymphoma or leukemia. After some months my mother had reached the point where no useful further therapy was possible. She returned to Orkney and died a few months later. I must admit that at that time I was also not very emotionally involved and that I was not a big help to my mother in those troubled times for her. While I was a student I was friends with two other students, Lynn Drever and Sheila Noble. At one time I frequently heard them talking about a book called the ‘The Women’s Room’ by Marilyn French. I was curious to find out more but they did not seem keen to talk about the book. After the end of my studies I read the book myself. It is a feminist book and I think a good and interesting one. The reason I mention Marilyn French here is another good and interesting book she wrote. It is called ‘A Season in Hell’, which is a translation of the Rimbaud title ‘Une saison en enfer’. In the book she gives a vivid inside view of her own fight with a cancer of the oesophagus. After very aggressive treatments she was eventually cured of her cancer but the side effects had caused extensive damage to her body (collapse of the spine, kidney failure etc.). Parallel to the story of her own illness she portrays that of a friend who had lung cancer and died from it quite quickly. This book gave me essential insights into what cancer means, objectively and subjectively, and what lung cancer means. My own most intensive contact with cancer was in 2013 when my wife was diagnosed with colon cancer. I do not want to give any details here except the essential fact that she was cured by an operation and that the disease has shown no signs of returning. Motivated by this history I recently did something which I would probably otherwise not have done, namely to have a coloscopy. I believe that this is really a valuable examination for identifying and preventing colon cancer and that it was my responsibility to do it, although I was anxious about how it would be. In fact I found the examination and the preparations for it less unpleasant than I expected and it was nice to have a positive result. It is also nice to know that according to present recommendations I only need to repeat the examination ten years from now. A few years ago in the month of November my then secretary got a persistent cough. After some time she went to the doctor and was very soon diagnosed with lung cancer. She only survived until February. I attended a small meeting organised by her family in her memory and there I learned some more details of the way her disease progressed.

Now let me come back to the lectures. The first important message is nothing new: most cases of lung cancer are caused by smoking. Incidentally, the secretary I mentioned above smoked a lot when she was young but gave up smoking very many years ago. The message is: if you smoke then from the point of view of lung cancer it is good to stop. However it may not be enough. In the first lecture it was emphasized that the first step these days when treating lung cancer is to do a genetic analysis to look for particular mutations since this can help to decide what treatments have a chance of success. In the case of the secretary the doctors did look for mutations but unfortunately she belonged to the majority where there were no mutations which would have been favourable for her prognosis under a suitable treatment. In the most favourable cases there are possibilities available such as targeted therapies (e.g. kinase inhibitors) and immunotherapies. These lectures are intended to be kept understandable for a general audience and accordingly the speaker did not provide many details. This means that since I have spent time on these things in the past I did not learn very much from that lecture. The contents of the second lecture, on surgical techniques, were quite unfamiliar to me. The main theme was minimally invasive surgery which is used in about 30% of operations for lung cancer in Germany. It is rather restricted to specialized centres due to the special expertise and sophisticated technical equipment required. It was explained how a small potential tumour in the lung can be examined and removed. In general the tumour will be found by imaging techniques and the big problem in a operation is to find it physically. We saw a film where an anaesthetised patient is lying on an operating table while the huge arms of a mobile imaging device do a kind of dance around them. The whole thing looks very futuristic. After this dance the device knows where the tumour is. It then computes the path to be taken by a needle to reach the tumour from outside. A laser projects a red point on the skin where the needle is to be inserted. The surgeon puts the point of the needle there and then rotates it until another red point coincides with the other end. This fixes the correct direction and he can then insert the needle. At the end of the needle there is a microsurgical device which can be steered from a computer. Of course there is also a camera which provides a picture of the situation on the computer screen. The movements of the surgeon’s hands are translated into movements of the device at the end of the needle. These are scaled but also subject to noise filtering. In other words, if the surgeon’s hands shake the computer will filter it out. There is also a further refinement of this where a robot arm connected to the imagining device automatically inserts the needle in the right way. The result of all this technology is that, for instance, a single small metastasis in the lung can be removed very effectively. One of the most interesting things the surgeon said concerned the effects of the pandemic. One effect has been that people have been more reluctant to go to the doctor and that it has taken longer than it otherwise would have for lung cancer patients to go into hospital. The concrete effect of this on the work of the surgeon is that he sees that the tumours he has to treat are on average in a more advanced state than they were than before the pandemic. Putting this together with other facts leads to the following stark conclusion which it is worth to state clearly, even if it is sufficiently well known to anyone who is wiling to listen. The reluctance of people to get vaccinated against COVID-19 has led to a considerable increase in the number of people dying of cancer.