Hannah Arendt and the banality of evil

In a previous post I indicated that while I found Hannah Arendt interesting I was not sure whether what I knew about her made a positive or a negative impression on me. I also suggested that I wanted to read something she had written to form an opinion. Now I have read her book ‘Eichmann in Jerusalem. A Report on the Banality of Evil.’ My opinion has been formed and it is clearly positive. I read the original version of the book which is in English. There is an interesting video of an interview with Arendt. There she is speaking German, her native language, and she makes negative comments about her abilities in English. Since she mentions her German accent in English this comment may just refer to the spoken language. In any case, I find her written English excellent.

Adolf Eichmann was tried in Jerusalem for crimes related to the holocaust, after he had been kidnapped in Argentina by the Iraeli secret service. In the end he was sentenced to death by hanging and the sentence was carried out very quickly. Arendt was present live for part of the trial as a representative of the press and had full access to the transcripts of the other parts. The book resulted from articles on the subject she wrote for the New Yorker. One important question the book discusses is how just this procedure was. This is a point I do not want to discuss at all since I have no special expertise in law and it is also not the aspect of the story which interests me most. The aspect that I find most interesting, and the one giving rise to the subtitle of the book, is to try and understand something about the psychology of Adolf Eichmann.

The publication of the book led to attacks on Arendt by many people. What were the causes of this violent criticism? Since Eichmann was involved in the death of millions of innocent people it is easy to think of him as being like a serial killer, with the difference that the number of people killed was much larger. Arendt suggests that this picture is quite wrong. Eichmann did not kill anyone directly and the fact that in some sense he killed so many indirectly was not because he hated Jews and wanted to kill them. Why it happened is more difficult to understand and a central theme of the book. For many readers this idea was difficult to accept. Another cause of the criticism of the book is that Arendt dared to write about the contributions of Jews to the killings of the holocaust and that this subject was taboo. Returning to the first cause, there is a video of a panel discussion where one of the participants was Wolfram Eilenberger, the author of the book I wrote about in the previous post. The subject of the video is the philosopher Karl Jaspers and a book which has now been published on the basis of texts he wrote. The subject of the book is ‘critical thinking’, whereby the point is made that any real thinking is necessarily critical. What is the relation of this to the main subject of this post? Hannah Arendt was a student of Karl Jaspers – he was her PhD supervisor. The book of Jaspers was originally supposed to be a defence of Arendt against the aggressive criticism of her book. As it developed the book came to consist of two parts. The first concerned more general philosophical themes while the second was to concern Arendt. In the end, however, the second part was dropped.There is nevertheless a strong connection to Arendt’s book since for Jaspers Arendt and her book were model examples of what critical thinking means. In the video Eilenberger introduces an interesting idea about why Arendt was attacked so aggressively. Arendt claimed that Eichmann did not think. In more detail what this means is that he did not think about the consequences of his actions. As I understand it the idea of Eilenberg is that many readers of Arendt’s book generally do not think critically about the issues they are confronted with and perhaps are not even able to do so. Thus they may feel at least unconsciously that what Arendt is telling them is that they are not so different from Eichmann. Under other circumstances they could have been Eichmann. They feel this as an attack on them which causes them to fight back.

Let me come back to the psychology of Eichmann. On the basis of what is presented in the book I conclude that he was not driven by a hatred of Jews or a desire to kill. The thing Eichmann wanted most was to appear important. It was very important for him to get promoted, whereby his absolute rank was probably less important to him than his relative rank compared with the people around him. It was very important to him to be taken seriously by people he saw as being important. It was also very important for him to do his duty. The book presents a picture of the mechanism of the holocaust and the roles of notable figures such as Hitler, Himmler, Heydrich and Eichmann. These people, in particular Hitler himself, contributed essentially to initiating the holocaust. However once it had started it ran to a great extent on its own as a dynamical property of the complex network of organizations and individuals comprising the society of Nazi Germany. There was often no clear chain of command and no clear responsibility. Conditions which favoured this process were widespread dishonesty and the use of certain codes to replace clear statements. The frightening message is that the holocaust was not simply the direct effect of the actions of a few evil and more or less insane individuals but an extreme example of how a society can develop from certain initial conditions, a development consisting of the acts of more or less normal people. Coming back to Eichmann, he saw some of the atrocities in the concentration camps with his own eyes but it seems that his reaction was to stick his head in the sand and to see as little of it as possible. He can be seen talking about these things in videos which are publicly available. He talks in a quite unemotional way and seems to be mainly concerned with trying to remember details about where and when certain things happened and who did what. In his testimony at the trial Eichmann lied a lot but he did not lie very consistently. In fact it seemed as if he really had forgotten many things. Sometimes he failed to mention things (and may have forgotten them) which would have proved his innocence to certain charges.

When reading the book I realized that my own view of the holocaust had been something of a cartoon, consisting of a few ideas and images. Arendt shows how heterogeneous the holocaust was. She explains how the proportion of Jews deported from different European countries or killed in their own country varied extremely between different countries, with Denmark presenting a minimum and Romania a maximum. On one occasion Hitler even complained that Romania was doing ‘better’ in the persecution of the Jews than Germany was. Arendt also explains some of the reasons for these differences.

So what is the meaning of the phrase ‘the banality of evil’? For me it means that the greatest evils in human society (and the holocaust is no exception to this) arise not only due to the influence of a few exceptional evil individuals but also due to negative aspects of the psychology of the majority of human beings which under the wrong circumstances can have catastrophic consequences. Is there any way in which this kind of risk can be reduced? We should do all we can to ensure that such things as truth, honesty, rational arguments and clear formulations (in contrast to coded messages) are as widespread as possible in our communications. Unfortunately it seems that in the recent past the world has been moving in the opposite direction, providing the ideal milieu in which Putin, Trump and many others of a similar kind can flourish.

 

A new branch in my blog: Macronectes

When I started this blog it was intended to cover all subjects I am interested in. In the recent past there have been an increasing number of posts related to politics. Since I live in Germany they have often been concerned with topics in German politics. It was rather inconvenient writing about these themes in English. For this reason I now started a new blog Macronectes. This is intended to house posts on politics and related philosophical themes. The posts there will all be in German. The first post is related to one which I wrote in Hydrobates on grammatical gender in Germany. I will continue to write posts on all other subjects in Hydrobates as before. Anyone curious to know what the name Macronectes means can look here.

Event with Marie-Agnes Strack-Zimmermann

I have a rather poor opinion of most current politicians. An exception is Marie-Agnes Strack-Zimmermann. I have seen her from time to time in short TV appearances and I have also read about her. All this made a positive impression on me. When I saw that she was due to talk at an event at the University of Mainz on Saturday I decided to go there and Eva, who also previously had a positive impression of the speaker, accompanied me. What we experienced at the event strengthened our previous opinion. The speaker came in with a microphone in a very modest way and just started to talk, without any introduction. Strack-Zimmermann is a member of the FDP and is their leading candidate for the coming European elections. This event was certainly part of her campaign for that election and was organized by her party. At the same time it should be emphasized that she did not say ‘vote for me’ but instead ‘go out and vote for a democratic party’, with a particular recommendation not to vote for the AfD or the party of Sahra Wagenknecht who have both explicitly said that they want Germany to leave the EU. I am not a devotee of the FDP. I find some of their policies good and others bad. I went to the event not because Strack-Zimmermann is a member of the FDP but also not in spite of that fact. My motivation was independent of the party she belongs to. We both thought that she made a milder impression than on TV. Probably the reason is that she was in a relatively friendly environment. When she is forced to defend herself against political attacks she is very capable of doing so and then she is less mild. At this event one person did shout out something about peace from the back row. This might have been due to the fact that Strack-Zimmermann is a strong and outspoken supporter of military intervention in the Ukraine by Germany and other Western countries or it might have had to do with Gaza. In any case she was easily able to handle it. In particular she repeated several times, ‘We all want peace’.

Strack-Zimmermann is chair of the defence committee in the German Parliament. Correspondingly her appearances in the media are often related to military themes. She was in the news recently because of her support of providing the Ukraine with the Taurus cruise missile, thus opposing the policy of Chancellor Scholz. She voted in favour of an initiative of the opposition party CDU that Taurus should be provided to the Ukraine. She was the only member of the government to do so. In her presentation yesterday she discussed many political themes and in particular how they all relate to each other. She is qualified to talk about these things because she has been more than once in the Ukraine during the present war, because she has been in other hotspots such as Mali and Niger, because she has spoken personally with one of the Israeli women taken hostage by Hamas and meanwhile released etc. For me it was refreshing to hear a politician talking in a way which struck me as honest, well-informed, experienced, rational and courageous. One thing which surprised me was what she said about the population of Europe compared to that of the world. She gave the figure 5% and I found that very low. In the internet I found the figure 10% which would have surprised me almost as much. Perhaps the explanation for the discrepancy in the figures is that I was not paying enough attention and she mentioned the population of the EU and in that case 5% could be correct. She talked about many political themes, including the Ukraine, China and Taiwan, the US and NATO, the Red Sea and the Houthis and of course Gaza. At the end of her presentation she took questions. An interesting one came from a young woman who identified herself as being in the army. She asked why the German army was not recruiting people from other European countries. Strack-Zimmermann pointed out the following problem. Soldiers in Germany are paid significantly better than soldiers in many other European countries. Thus the danger exists that if Germany tried to recruit in this way this might seriously weaken the armies of allied countries by draining the human resources. She indicated that discussions were underway to find an alternative.

This speech was not recorded but another presentation by Strack-Zimmermann can be found here:

There is quite a lot of overlap in the topics but it was more defiant in tone that what we heard live, as befits an election speech made to politicians.

An evening with Dieter Nuhr

Yesterday Eva and I went to a performance by the comedian Dieter Nuhr in Mainz. It was in a building called Halle 45. According to the ticket it was possible to enter the building 30 minutes before the event. We arrived 40 minutes before the event and most of the people were already inside. The capacity of the building is 2000 people but the chairs are moveable and so this can be varied depending on the event. I do not think that there were so many people there yesterday but it was full and there were many hundreds. Due to the circumstances we ended up sitting quite far back, a long way from the stage. This was a bit disappointing since it meant that there was little sense of intimacy with the performer. We had better experiences with performances we have attended by Lisa Eckhart and Josef Hader (twice) in the past in other (smaller) venues.

In recent years, especially since the pandemic, our society has become more and more polarized in its opinions. It would be an oversimplifcation to think that this is only a polarization along one axis, although there are remarkable correlations between opinions on issues which at first sight are quite unrelated. In fact there are fault lines running in different directions and two people who are on opposite sides in one case may be on the same side in another case. In comedy in Germany (and Austria) there is a clear polarization in the political views expressed. This might be formulated in terms of the words ‘left’ and ‘right’ but this is too simple. Often people with extreme right wing views and those with extreme left wing views seem to agree on many subjects. It seems that the topology of the political spectrum is rather that of a circle than that of the real line. Another word which might be used to characterize one direction on this axis is ‘woke’. That direction is the one often propagated by established political parties and state media in Germany. It is fortunately the case that this bias is not complete. There are two state-run TV companies in Germany, ARD and ZDF and while the principal representative of the ‘woke’ direction among the comedians, Jan Böhmermann, has a show with ZDF Dieter Nuhr, the principal representative of the other direction, has a show on ARD. In his show he performs himself part of the time and he also invites other comedians to take the stage. Recently it was often the case that the last person to appear, and in some sense the highlight, was Lisa Eckhart who I have written about in a previous post.

In the description of the event on the web page of Halle 45 it says ‘Ein Abend mit Dieter Nuhr ist Spaß und Therapie zugleich’ [An evening with Dieter Nuhr is fun and therapy at the same time]. Interestingly, during his performance Nuhr said that he did not consider his performance as therapy, or that he did not like it to be considered in that way. Was this statement sincere or was it intended as a joke? In any case it is worth taking a moment to think about in which sense it might be considered therapy. There are some people who at least some of the time (and I consider myself one of these people) do not feel at home in the public consensus presented by politics and media, which could also be associated with the word ‘woke’. They feel themselves confined by certain barriers in an unpleasant way. The ’therapeutic’ aspect of Dieter Nuhr is that in his texts he breaks through these barriers. (The same is true of Eckhart and Hader in their own ways.) I appreciate Dieter Nuhr because I like his humour. At the same time it is not the only reason I appreciate him. I think he has an important role to play in German politics by contributing to a certain balance and helping to prevent public opinion from becoming too extreme in certain directions. For example, he stepped forward to publicly support Lisa Eckhart when she was attacked in the way I described in a previous post. He also exerts a significant influence by his regular appearances on TV.

There is one point I want to mention before ending this post. In the last post I wrote about Karl Lauterbach. In his programme yesterday Nuhr made jokes about Lauterbach in a rather insulting way. (He has also behaved similarly in other places.) For instance he refers to him as the Sensenmann (‘grim reaper’), referring to his pessimism and his appearance. Now I tend to believe that a comedian should have a lot of freedom in making jokes about public figures, even if they might be unpleasant for the people concerned. Correspondingly, Nuhr’s jokes about Lauterbach do not cross the boundary of what is acceptable for me. At the same time I wonder if Nuhr has a particular grievance against Lauterbach and if so what it is. The jokes about Lauterbach were among the few yesterday I did not laugh at.

Fighting homeopathy

Most health systems in the world have financial problems and Germany is no exception to this. As a scientifically educated person it seems to me outrageous that the public health system here in Germany should spend money on homeopathic treatments. There is hardly anything in the area of ‘alternative medicine’ which is based on ideas which so blatantly contradict scientific reasoning. I was thus very glad to see that the health minister Karl Lauterbach has announced that he wants to ban the public health system from paying for homeopathic treatments. It is not the first time that a politician has tried this and suggestions of this type are usually greeted by a storm of opposition. I am not very optimistic that the idea of stopping public funds being used to finance homeopathy will actually find a sufficiently strong political consensus so as to result in legislation. If the idea actually succeeded I would be very happy. Of course the loudest opposition comes from those who earn money with homeopathy. One argument used is that the money involved is a small part of the total costs of the public health system. Of course it is the duty of those responsible to make sure that government money spent on health is well spent. The standards are usually very high. Often people cannot get treatments paid which are probably valuable but where the level of evidence required has not been reached. Thus I see the issue of homeopathy is one of principle. It is an insult to someone who is seriously ill and has to accept that the health insurance cannot pay for a treatment which would probably be effective (but is not yet provably so) while it pays for quackery. Germany has made a lot of important contributions to medicine but it should not be forgotten that although the disease homeopathy (as I see it) is widespread in the world it had its origin in Germany.

Karl Lauterbach is quite open about the fact that it is not the amount of money which is the central point. He is a scientist and qualified as a medical doctor and acts according to the ethical principles of these disciplines. He became publicly known through his role in the COVID-19 pandemic. (His academic speciality is epidemiology and public health.) During the pandemic he tended towards recommending strict measures and in this way he made himself unpopular with many people. At the same time his role was appreciated by many others (including myself) and this led to his appointment as health minister. He is a member of the SPD, having switched a long time ago from the CDU. Some politicians of other parties have accused him of using the issue of homeopathy to direct people’s attention away from other parts of his health policy which are seen as unsuccessful. I feel sure that this is not true. It is typical of Lauterbach, during the pandemic and otherwise, that he publicly says what he believes to be the truth, even when that results in unpopularity and attacks on him in the media. Although there are many aspects of Lauterbach’s politics I do not agree with I tend to identify with him as a person. I see him as a representative of honesty and rationalism in the public domain. The fact that many of the attacks on him involve personal antipathy and making fun of his appearance only tend to strengthen my feeling of solidarity with him.

It might be said that politicians have more important things which they should concentrate on than homeopathy but I am not prepared to accept that. I think that in the long term the struggle between science and superstition is a matter of key importance for the future of our civilization.

The Fountainhead

In a recent post I mentioned the novel ‘The Fountainhead’ by Ayn Rand. This motivated me to read the book and I have now done so. I found it enjoyable and compulsive reading. The plot does have something of a TV thriller and this may have to do with the fact that the author had a considerable involvement with Hollywood. This is something which leads the reader on but the book also has interesting aspects of a quite different kind. Probably the most important feature of the central character, Howard Roark, is his uncompromising nature. He is clear about his aims and does everything to achieve them. I have met a few people in real life who are extremely uncompromising and I found that an attractive quality. I will not name them here. Of course it is important to mention that these were people where their uncompromising nature was not linked to a desire to harm, or even destroy, other people. People of the latter kind are only too common and the opposite of heroes for me. The thing which is most foreign to me in ‘The Fountainhead’ is that most of the main characters seem to be sadists, masochists or both. It is not just that they behave in a way I would condemn in many cases but it is often incomprehensible to me why anyone should behave in that way.

One of the central ideas in the book is the importance for the individual of a goal which he really wants to achieve. In contrast, the behaviour of most people is controlled by their desire for recognition by others. I am reminded of the story of Grothendieck who developed integration theory on his own as a student and was not dismayed when he learned that the problem had been solved many years previously by Lebesgue. He was satisfied that he had done it and was not concerned with questions of priority. If I compare this ideal with my own life then I see a mixed picture. Of course what you can do in life, or in a particular field of endeavour, is limited by your talents. However that it not the point here. The most important thing is not the final achievement but the commitment. Howard Roark is not able to change many aspects of the world he lives in which he sees as undesirable but he is able to achieve certain specific goals (while failing to achieve others). In my case I feel that I have spent too little of my life working to achieve elevated goals. At the same time I did often go in those directions I felt to be important, while being little influenced by scientific fashions. This was probably unfavourable for my career but favourable for my happiness. It is enough to allow me to feel myself very far from Peter Keating, the negative example in the novel and the antithesis of Roark.

Another central element in the book is the role of the press in society. The poor quality popular newspaper The Banner and its founder and editor Gail Wynand are key. A question which goes through my head is what analogies exist between the popular press of that time (and its portrait in the book) and the social media of today. I cannot judge this well since I myself hardly have any contact with social media. I nevertheless do seem to detect some similarities. There are evil tendencies out there which come into existence through the collective behaviour of the masses. Often this evil is not being directly caused by some individual. What an individual does is to spread an evil influence which is then absorbed by the masses, develops autonomously and causes damage. This is the method of the journalist Toohey in the novel. He himself compares his activity to applying weedkiller, which is much more effective than tearing out individual plants. He uses this metaphor in the context of destroying the integrity of individuals.

As a last observation I note that one of the jurors in Roarke’s trial at the end of the book, largely chosen by himself, is a mathematician.

Four female philosophers

I have just read the book ‘Feuer der Freiheit’ by Wolfram Eilenberger. It has been translated into English under the title ‘The Visionaries’. It describes aspects of the life of four women in the years 1933-1943. They are Simone Weil, Simone de Beauvoir, Ayn Rand and Hannah Arendt. It seems that the author considers all four to have been philosophers although I am not sure to what extent they themselves would have agreed with the description. Before reading the book I knew Simone Weil only as the sister of the mathematician André Weil. I read his autobiography ‘The Apprenticeship of a Mathematician’ many years ago. All I knew about Simone de Beauvoir was that she was a famous feminist and a couple of the titles of her books (Mémoires d’une jeune fille rangée, Le deuxième sexe). I had seen some parts of documentaries about Hannah Arendt and associated her above all with the trial of Eichmann. I had not read anything by any of those three. The exception is Ayn Rand, who I wrote about in a previous post. I came across the book by seeing advertising for a reading by the author and then realizing that it was long past. The theme seemed to me interesting enough to motivate me to have a look at the book.

Simone Weil was a very extreme person and I am tempted to use the word ‘crazy’ to describe her. She had an extreme, not to say pathological, feeling for the suffering of others. At one time she was a dedicated and active communist and later she turned to religious mysticism. At one time she went to work on an industrial production line, living from the money she earned from that job. She wanted to learn what it was really like to be a worker. She wanted to experience for herself things which Marx, Lenin and Trotsky had not experienced. She only managed to get the job by personal contacts. She was not able to work with the necessary speed or to survive the long hours. She damaged the machines by her carelessness. Thus she made no positive contribution to the company she worked for. She also did not really live on the money she earned since she was supported by her parents. At one time she invited Trotsky to live in an appartment belonging to her parents. He did live there for some time although his relationship with her was not at all harmonious. Another adventure was her participation in the Spanish civil war. She was determined to carry a gun although she was so short-sighted that she probably could not have used it in a reasonable way. While she was taking part in a campaign she walked into a bowl of hot oil which had been covered to avoid producing smoke which might have been seen by the enemy. This resulted in very serious burns to her legs and she was brought back to France by her parents. During the mid 1940s she was in England and was determined to parachute into France to take part in the resistance. She informed herself in detail about parachuting but since she was clearly not capable of such a mission she was not allowed to do so. She died in 1943 through a combination of tuberculosis and her own refusal to eat enough, the latter being once again a kind of solidarity. Of course the book contains not only these adventures but also material on her philosophical ideas. There are parts of the book where I feel that the philosophy is getting detached from reality and degenerating into a game with words. I think that these parts are less the production of Eilenberger than those of his subjects. Passages of this kind are quite common in the descriptions of Weil’s ideas, particularly in those relating to her later mystical phase.

A central role in the description of Simone de Beauvoir in the book and also in her life was played by her relationship to Jean-Paul Sartre. This was long and intimate. On the other hand it was an ‘open’ relationship where they had sex with other partners, often with the same partners, leading to triangular relationships. Both of them worked as schoolteachers and seduced several of their pupils. Simone de Beauvoir was eventually tried for corrupting minors and lost her teaching job as a consequence. I found a lot of these matters rather repulsive. It seems that a high priority for both of them was to avoid conforming to (bourgeois) society. Both of them were influenced by certain German thinkers, Hegel, Marx and Heidegger, who I personally see as very negative influences. They lived in Paris during the German occupation and an interesting anecdote is how they reacted to the experience of being approached by German soldiers, who asked them the way very politely and in French. They felt embarassed by this. The problem was the conflict between the nature of these men as representatives of evil (the Nazi regime) and their normal and pleasant behaviour at that time. Sartre, who was determined not to help Nazis in any way, adopted the strategy of pretending not to know the way to the place they were asking about. It was interesting to see a picture of this period complementary to those I know from the writings of Jünger and Banine.

The central element in the description of Ayn Rand in the book is her work on her novel ‘The Fountainhead’. It is her portrait of the ultimate egoist Howard Roark. It has had a strong influence on right wing politics in the US. It is said that Donald Trump has praised it but somehow Donald Trump and reading long books are two things that just do not seem to fit. When the book was published there was little or no advertising done. At the beginning the sales were very low and Rand was discouraged. Later the book became known by word of mouth recommendations and became a bestseller. In the meantime it has sold more than nine million copies. The film rights were sold to Hollywood for a sum which justifiably made the author feel rich.

What I have read in the book about the first three women on the list leads me to a clear verdict, negative for both Simones (whereby in the case of Simone de Beauvoir my negative reaction is perhaps due more to Sartre than to her) and positive for Ayn Rand. Perhaps the most interesting case for me is that of Hannah Arendt, since in her case I feel undecided. She was a student of Heidegger and also had an affair with him at that time. The fact that Heidegger later aligned himself with the Nazis would have been a good reason for Arendt, as a Jew, to cut off all contact with him. However I read that they were still friends after the second world war. Arendt fled from Germany to Paris. There is a story about how she crossed the border to Czechoslovakia in the Ore Mountains (Erzgebirge) through a house whose front door was in the one country and whose back door was in the other. From there she went to Karlsbad. I have seen this story in several places but I was not able to find out where this house was, or a reliable source for the story. It seems as if people just repeat the same story. I was interested to find out more about this since my wife grew up on that border (cf. this post). We spent some time in Karlsbad a few months ago and from there we could see the Erzgebirge. The reference in the book of Eilenberger for this story is the biography of Arendt by Elisabeth Young-Bruehl. She does not give a precise reference but does refer vaguely to the book ‘Erlebte Judenfrage’ by Kurt Blumenfeld. I found no further information on the matter there. After the Germans invaded France Arendt had to escape again. There is an interesting portrait of the situation of Jewish intellectuals coming from Germany and trying to reach the US. When she reached America Arendt was not very happy there. One problem was that she got into controversies with the Jewish community in the US. She had ideas different from the ruling consensus and she was not afraid to present these ideas publicly. As a result of reading this book I now have an interest in reading something of Arendt myself, perhaps ‘Eichmann in Jerusalem: a report on the banality of evil’ or ‘The Origins of Totalitarianism’.

In the book of Eilenberger the stories of the four women are not told one after another but instead interwoven in a way which makes them more interesting. The book contains a lot of interesting things about philosophy, politics, history and other subjects.

The Schauder fixed point theorem and Leray-Schauder theory

The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to the infinite-dimensional case. I already discussed the former topic in a previous post on degree theory. One good source for the topics of the present post is the book ‘Nonlinear Functional Analysis and its Applications’ by Eberhard Zeidler. When I start reading this book I automatically think of its author, who I experienced as an exceptionally pleasant human being who was very kind to me on several occasions. I first met him in 1991 when I gave a talk at a conference in Leipzig. Some time later he invited me to give talks aimed at students in the DFG project he had at the University of Leipzig at that time. I remember that at one point he stood up spontaneously and talked enthusiastically about the importance of the Brouwer fixed point theorem. He seemed impressed by the fact that I used so many German words (instead of English ones) when lecturing in German. This was not due to my achievements in collecting or inventing German words for mathematical (or physical) concepts but due to the influence of Jürgen Ehlers, who was always careful about the use of language in scientific discussions. While living in East Germany Zeidler had problems with the political system. He was not free to travel and his possibilities of doing research were restricted. Thus he concentrated his efforts on writing textbooks. After German reunification he had more freedom. He was the founding director of the Max Planck Institute for Mathematics in the Sciences in Leipzig in 1996. He then vacated his professorship at the University of Leipzig and suggested to me that I should apply for the position of his successor. I did not do so since I was in a health crisis at that time and I did not dare to take such a big step. If I had decided differently and I had been succesful with that application it would have changed my life in a way which I cannot imagine but would certainly have been fundamental. In particular I would not have met my wife. Zeidler died in 2016.

After this personal excursion I now return to the mathematics. One valuable thing which Zeidler does in the discussion of degree theory in the book and which I had failed to do is to look carefully at the one-dimensional case. This gives an intuition for the meaning of the concept of degree. Consider a continuous mapping from to the real line which is non-zero at both endpoints. If its values at both endpoints have the same sign the degree is zero. If and then the degree is one. If and then it is minus one. In this situation it is clear that the degree is unchanged by continuous deformations of within the class of functions being considered. The actual definition of the degree in the generic case where the zeroes of are non-degenerate is the sum of the signs of at the zeroes of . One version of the Brouwer fixed point theorem says that any continuous mapping from the closed unit ball in to itself has a fixed point. Another replaces the ball by an arbitrary non-empty compact convex set. I will not discuss here how the second, apparently stronger, version follows from the first. It is the second version which is extended in the Schauder fixed point theorem. That theorem says that a compact mapping of a non-empty closed, bounded, convex subset of a Banach space to itself has a fixed point. Here a compact mapping is a continuous one which maps bounded sets to compact sets. In an alternative version of the theorem it is only assumed that the mapping is continuous but it is assumed that the set is compact. This fixed point theorem can be used to develop Leray-Schauder theory. One version of this, discussed in Zeidler’s book, is as follows. Let be a Banach space and a compact mapping. If all solutions of the equation with satisfy for a constant then has a fixed point. Another nice discussion of these topics can be found in the standard textbook on elliptic equations by Gilbarg and Trudinger. They also discuss a more general version of the Leray-Schauder theory where the mapping is replaced by a more general one. In other words the requirement of the linear dependence of the mapping on the parameter is dropped. Here we see the relation to degree theory. They present quite self-contained proofs of these results, modulo the Brouwer fixed point theorem. In fact they do not need that theorem for a general compact convex subset, but only the case of the convex hull of a finite set. The theory can be used to obtain existence theorems for boundary value problems for nonlinear elliptic equations (or initial boundary value problems for nonlinear parabolic equations). The necessary input is a priori estimates together with some compactness. The latter comes from the regularizing properties of solving equations of these kinds. The idea then is to deform the problem to be solved continuously to one which is easier to solve, or even trivial.

The Frankfurt book fair and Ahmad Mansour

Yesterday I went to the Frankfurt book fair. It was the first time I had been to an event of that kind. It was the last day of the fair and I only visited the stands of some of the important scientific publishers in the afternoon. A lot of the companies I am involved with in my own work were there: Springer, Wiley, Taylor and Francis, Princeton University Press, Cambridge University Press, Oxford University Press, World Scientific. Many smaller companies were also represented, including many I did not know. Most of the stands were already more or less empty. I do not know if this would have been different on Saturday, or on Sunday morning. A lot of people seemed to have packed up and gone home. This was not only true for the scientific exhibits. A visit to the part of the fair related to French literature was similarly disappointing. The only thing which appeared to me to be extremely active was the area of children’s books. The cynical idea crossed my mind that perhaps there are many parents who feel that it is their duty to try to make their children read books but that the adults are not so interested in reading books themselves. In any case, if more children read more books I am happy about that. This aspect of the fair, the exhibits, brought me no benefit.

My main motivation for going to the fair this time was to experience the live recording of a discussion by the TV channel Phoenix, where the central participant was Ahmad Mansour, someone who I have mentioned in a previous post. When he came onto the podium Mansour looked a bit nervous to me and in fact my wife made the same comment independently. However his contribution soon became not only competent but also confident. This discussion was related to a series by Diana Kinnert und Harald Welzer which is usually a podcast. This time, exceptionally, they had a guest, Mansour, and a video was produced, which can be seen here. Of course the attack on Israel by Hamas and the reactions to it in Germany were a central theme in the discussion. Welzer quoted a policeman concerning the recent demonstrations in Neukölln who said [my translation] ‘we cannot do more than to try to pick up the pieces which are the result of the failure to integrate these people’. Mansour said that he has repeatedly experienced the following scenario. In response to a certain event mainstream politicians say the right things in public but when he, Mansour, says the same things a few months later people call him a racist for doing so. Mansour said that there is antisemitism on the right, the left and in the centre of politics as well as among Muslims. It is important for him to talk about Muslim antisemitism and about that on the left. Mansour then went on to talk about matters related to cancel culture and mentioned, without naming the organizer, what happened with the workshop of Susanne Schröter, something I discussed in a previous post. Then he went on to discuss post-truth, which he said is destroying political culture, where truth is no longer important but only emotions. At this point I have to remark that scientists and especially mathematicians should have a particular duty and motivation to combat post-truth. Mansour said that he is not interested in being praised for his courage by people who talk to him or send him e-mail. He wants to see these people becoming active themselves and becoming loud. I take the point. The participants in the discussion were looking forward to a pro-Israel demonstration to take place in Berlin later in the day. It did take place. The police estimated ten thousand participants, the organizers a bit more. There were reactions in the media, which I agree with, saying that it was good that a demonstration with this many people took place but that it would have been more appropriate if ten times as many people had attended.

Another person who I had hoped to hear live was Michel Friedman. According to the online programme of the fair, even in the form it is in at present, he should have been talking immediately before Mansour, on the same stage. However that event had been replaced by a quite different one. Maybe I can see him another time. According to the programme he was to give three different presentations at the fair, two of them on Saturday. At least one of them must have taken place, since there are corresponding videos in the internet. One of the videos is here and I can strongly recommend it.

Rereading Atlas Shrugged

A few years ago I read the novel ‘Atlas Shrugged’ by Ayn Rand. I came across this book by chance in a shop in Regensburg. My main reason for being there was to have a pleasant place to keep out of the rain for a couple of hours. I got hooked and ended up buying the book and reading the more than a thousand pages of relatively small print in a fairly short time. It is an unusual book. The story is a fantasy which is far from being realistic. It is an ideological work. The characters are divided very sharply into good and bad. There are some long monologues. The longest one, by the key character John Galt, is more than 60 pages long and is at least in part the type of philosophy which consists of words without meaning. Despite this I found the book rewarding to read. Now I am reading it a second time. I am not sure how I got started this time but I was once again drawn in. When I read the book the first time I experienced the content in a rather abstract way. This time it is different. The book is a dystopia, a portrait of a decaying society. Now I see that many of the processes described in the book are happening around me in everyday life. For instance the quality of goods and services is getting poorer, businesses are closing down, there are shortages of various commodities and qualified labour. The causes of these processes are very different from those in the novel in many cases. In the novel there is no pandemic and no dictator like Putin. The similarity of the processes themselves is nevertheless striking.

It seems that the book is very well known in the US and rather unknown in Europe. It seems that many people are enthusiastic about it as adolescents and then reject it when they are ‘grown up’. They like to think they are mature and can now criticize the book strongly. I was already quite old when I encountered it and so this narrative does not apply to me. In any case, I am liking it at least as much on the second reading as on the first. Perhaps in certain ways I have stayed young and I do not feel the need to reject things which some people see as signs of immaturity. Other examples which occur to me is that I still like the music of Abba and the novels of Aldous Huxley more than forty years after my first enthusiasm for them. I have encountered people who either seem ashamed to act in this way or proud to show that they do not do so.

A key aspect of the book is how it reverses notions widely accepted in our society. It was written in the 1950’s but has not lost its relevance. At this point I am reminded of the Marquis de Sade, who also liked to reverse all the moral ideas of his time. In ‘Justine’, the only one of his books I have read, passages of pornography alternate with passages of philosophy. Pornographic writing is naturally very boring since it is limited to variations on an extremely small number of themes. There Sade is very inventive. The philosophical parts, on the other hand, are extremely boring. Returning to ‘Atlas Shrugged’, there the heroes are industrialists, an idea not very popular these days. The villains, who make up the great majority, are the collectivists and those who submit to their influence. So can industrialists reasonably be considered as admirable? I think there were some in the past who could. In reading autobiographical texts of Andrew Carnegie and Henry Ford these people made a positive impression on me. What I later read about Ford’s antisemitism took away any desire I might have had to admire him. In any case, in principle these people were like the positive figures in the novel in that their primary desire was to provide a good product or service. I wonder to what extent that still exists today. The main things left in my memory by a biography of Bill Gates which I read were not at all positive. The one idea is that when a smaller company came up with a good idea that company should be taken over and closed down. The second is that promises were made to develop products on unreasonably short time scales so that they were put on the market in half-finished form. At least Gates had a definite product even if I might not like it. In contrast a lot of modern big business seems to be just a kind of game which is far away from real goods or services. It deals with the abstract entities which are companies and money. Somehow it bears a resemblance to the villains in the book. My first insight into that kind of world came through an autobiography of Jean-Marie Messier. His career crashed in 2002 and it is interesting to see that his friend Thomas Middelhoff later went to prison. The stock exchange seems to play no role in the world of Atlas Shrugged although Ayn Rand is known for her close friendship with, and influence on, Alan Greenspan.

What I find important about the positive characters in the book is their attachment to truth and honesty. The background I grew up in was protestant with a strong emphasis on the idea that each person should act according to their conscience. Although I became an atheist during my teens I inherited some of these ideals from my mother. This also connects to the theme of the conflict between individualism and collectivism which is central to ‘Atlas Shrugged’.