Biography of Perelman by Masha Gessen

Masha Gessen first came to my attention because of the controversy caused by her being awarded the Hannah Arendt Prize in 2023. A week before the planned award ceremony Gessen published an essay in the New Yorker with the title ‘In the Shadow of the Holocaust’. In this essay she portrays the Israeli military actions in the Gaza Strip as being comparable to Nazi liquidations of Jewish ghettos. I have written about this issue elsewhere (in German) and I will say no more about it here. While trying to find out more about this person I discovered that she had written a biography of Grigori Perelman with the title ‘Perfect Rigor’. Perelman is one of the most remarkable mathematicians of recent years. He resolved one of the most famous open problems in mathematics, the Poincaré conjecture, formulated in 1904. For this he was offered a Fields medal in 2006, the most prestigious award in mathematics, which he refused. Later, in 2010, he was offered a one million dollar prize by the Clay Foundation, which he also refused, despite living in poverty. As I mentioned in previous posts here and here I had the privilege to hear the first lecture which Perelman gave on his proof of the Poincare conjecture and afterwards I went to a cafe with him together with colleagues, so that I was able to get a further personal impression of him. Masha Gessen was never able to talk to Perelman because by the time she was working on her book he had completely withdrawn from public contacts. She was, however, able to talk to people who had known Perelman very well. She also has special insights into the world in which Perelman grew up in the Soviet Union since she grew up in the same society.

Masha Gessen is not a mathematician although she did apparently have a good school education in mathematics. For that reason her ability to write about the Poincaré conjecture itself is limited. What she does write on that is imprecise in a way which is likely to be a little irritating for people who know the subject fairly well and could be confusing for professional mathematicians with no special knowledge of the subject. However that is only a small part of the book. The main subjects are Perelman himself, the people around him and the society around him. In the previous post where I mentioned Perelman I compared him to another famous mathematician who refused prestigious prizes, Grothendieck. Now I still see similarities between the two men but also major differences. Grothendieck was a very political person and his motivation for refusing prizes probably came mainly from politics. Perelman, as he is portrayed in the book, is very different. He sees it as a disgrace for a mathematician to pay attention to politics. For him mathematics is much more important and valuable than politics. His reasons for refusing prizes are rather personal. He is absolutely convinced of the value of his work and he is not prepared to accept that others (who understand less about the subject than himself) should judge it. The book was written before Perelman had been awarded the Clay prize but at that time it already seemed probable that he would not accept it. At that time his complaint was that it should have been given equally to him and Richard Hamilton, on whose work he had built. However other examples are given where Perelman refuses something for a certain reason, the offer is modified to remove this obstacle and he still refuses. It seems that in a way Perelman was an exceptionally honest person but that he often kept his motives hidden. I notice that I am talking about Perelman here in the past tense and the reason is that he long ago cut off all contact with the rest of the world, with the exception of his mother. It should be mentioned that his mother herself wanted to become a professional mathematician but was prevented from doing so by antisemitism and sexism.

An interesting aspect of the book for me is the picture it gives of mathematics in the Soviet Union, something which was previously just a black box for me. Another is that I know some of the people who play a role in the book personally and I also experienced some aspects of the ICM in Madrid described in the book myself, for instance the lecture of Hamilton, and it is interesting to have some of the background to what I saw revealed. I did not specially like the way the book is written but it certainly kept my attention and I did learn a lot.

Universal deformations of bifurcations

In bifurcation theory the fundamental object is an equation of the form where represents one or more unknowns and one or more parameters. We may also consider the static case . In this post I will only be concerned with the latter case. To what extent these ideas can be extended to more genuinely dynamical phenomena I do not know and I will not try to discuss that question here. Here I will be concerned with local phenomena, i.e. those in small regions close to a point in -space. The meaning of locality here can be formalized using germs but I will not do so here. The discussion here is based on that in the book ‘Singularities in Groups and Bifurcation Theory’ by Golubitsky and Schaeffer. In the theory of dynamical systems the notion of (local) equivalence is often used. I will avoid the issue of the differentiability of the mappings involved but the aim is to work with smooth mappings whenever possible. If we have two bifurcation problems defined by mappings and then equivalence means that there is are invertible transformations , and a positive function such that . Intuitively this means that the two bifurcations are qualitatively the same. A deformation of the bifurcation involves introducing extra parameters. The notational conventions used in the following are not the same as in the book. Consider now an object depending on additional parameters . We think of the previous function as corresponding to in the new notation. This new object is called an unfolding of the original bifurcation. If we have another unfolding we can consider the relation where now , and are not required to be invertible. In this case it is said that factors through . Alternatively it could be said that induces . An unfolding is called versal if every unfolding of the same bifurcation factors through . If in addition depends on the minimum number of parameters it is called universal and this number is called the codimension of the bifurcation. The intuitive idea is that a versal unfolding includes all bifurcations which can be obtained by small deformations of the original one and these can be obtained by fixing the values of the parameters . A universal deformation is in a sense a parametrization of the space of all bifurcations close to a given one and defines the codimension of the space of bifurcations equivalent to the original one in that bigger space.

In the context of the book of Golubitsky and Schaeffer the ideas related to universal deformations are to be applied to a system which is in general obtained by a reduction of dimension. The relevant reduction process is related to centre manifold reduction but because the static problem is being considered it is natural to do it in the context of Lyapunov-Schmidt reduction.

There is a geometrical way of looking at these things which is related to ideas I applied in my PhD thesis very many years ago in a very different context. I already mentioned this in a previous post. One important source for me at that time was the book ‘Stable Mappings and their Singularities’ by Guillemin and Golubitsky. We see that this book has an author in common with the one I cited above. Different types of bifurcation are characterized by algebraic conditions on the derivatives of the vector field defining them at a point. The collection of derivatives up to order is the -jet of the vector field at that point. When the point is varied we get a section of the bundle of -jets of vector fields. There is a bifurcation subset where the first derivative is not invertible. Let us call it for singularity. It can be thought of as a subset of the total space of the bundle of -jets of vector fields which in fact is induced by a subset of the bundle of -jets of vector fields. It is a real algebraic variety. Like all such varieties it is a union of strata, smooth submanifolds which fit together in a nice way. These strata correspond to different types of bifurcations. The jet tranversality theorem implies that any -jet of a vector field can be modified by an arbitrarily small perturbation so as to be transverse to all strata of the variety. In this language a versal deformation of a given bifurcation point is a mapping whose -jet prolongation is transverse at that point to the stratum corresponding to that bifurcation. The codimension of the bifurcation is the codimension of that stratum.

One-dimensional centre manifolds, part 4

In this post I consider the case of the transcritical bifurcation, starting with the case of a one-dimensional dynamical system depending on one parameter . I consider the situation where for structural reasons is always a steady state. Hence for a smooth function . The equation could potentially have a bifurcation at the origin but here I specifically consider the case where it does not. The assumptions are and . Moreover it is assumed that . By the implicit function theorem the zero set of is a function of . By the last assumption made the derivative of this function at zero is non-zero. The graph crosses both axes transversally at the origin. It will be supposed, motivated by intended applications, that . If there exist positive steady states for and if there exist positive steady states with . The conditions which have been required of can be translated to conditions on . Of course and . Since we also have and the origin is a bifurcation point for . The other two conditions on translate to and . It follows from the implicit function theorem, applied to that the bifurcation can be reduced by a coordinate transformation to the standard form . Thus we see how many steady states there are for each value of and what their stability properties are.

My primary motivation for discussing this here is to throw light on the concept of backward bifurcation. At a bifurcation point of this kind there is a one-dimensional centre manifold. I want to explain the relation of general centre manifold theory to Theorem 4 of in the paper of van den Driessche and Watmough. Background for this discussion can be found here. It is explicitly assumed in the discussion leading up to the theorem that the centre manifold at the bifurcation point is one-dimensional. All but one of the non-zero eigenvalues of the linearization have negative real parts close to the bifurcation point. The remaining one changes sign as the bifurcation point is passed. The main idea is to reduce the bifurcation to the two-dimensional extended centre manifold at the bifurcation point. In equations (23) and (24) the key diagnostic quantities and for the bifurcation are defined. They are expressed in invariant form both in terms of the extrinsic dynamical system and in a form intrinsic to the centre manifold. In the coordinate form used above and . Theorem 4 of the paper makes statements about the existence and stability of positive steady states which are essentially equivalent to those made above when it is taken into account that in the situation of the theorem the centre manifold is asymptotically stable with respect to perturbations in the transverse directions. It does not say more than that. The fact, often seen in pictures of backward bifurcation that the unstable branch undergoes a fold bifurcation is not included. In particular the fact that for some parameter values there exists more than one positive steady state is not included.

The Bell Jar by Sylvia Plath

I recently bought the novel ‘The Bell Jar’ by Sylvia Plath. This came about as follows. I have now lived in Mainz for over ten years. Bookshops exert a strong attraction on me. It is therefore strange that I had never entered the shop ‘Shakespeare and so …’ which I must have passed very many times. Now I have done so. I had nothing special in mind and I had no definite plan to buy anything. I spent quite some time looking around the shelves and in the end I did buy a book, ‘The Bell Jar’ by Sylvia Plath. I knew the title of the book and the name of the author but not much more than that. So why did I feel attracted to it? I guess that it is due to the fact that forty years ago Ali Smith talked to me positively about the author. I do not know if this is really the case but it seems to me plausible. I suppose that the recommendation has slumbered in my unconscious all the time and was brought out again by the chance encounter with the book. I did once have a flat-mate who was writing a PhD on Ted Hughes, the husband of Sylvia Plath, but I do not think that the recommendation came from him. In fact I must have read at least one poem by Plath at that time since on the way home the following fragment which must have been lodged in my memory came into my mind: ‘ebon in the hedges fat’. After I got home I was able to find out that it comes from a poem called ‘Blackberrying’, which must have impressed me as a student. On the way home in the tram I read the first few pages of the novel and it became clear to me that it was a piece of luck that I had bought the book. I had the delicious experience of beginning to read a book and immediately feeling at home.

Reading the book was a positive experience for me from beginning to end, although it includes things I experienced as frightening perspectives. I had warm feelings towards both the protagonist and the author. The book has now been given a place of honour on the bookshelf containing those books I esteem most. I do not feel that I have to provide a justification for the feelings I have just expressed but I will at least mention a couple of aspects of the book which have played a role in producing these. One is the remarkable objectivity with which Plath describes all kinds of things which in principle could have a strong emotional impact. Here I think of Jünger although the authors’ subjects are so different. A second is the way I experience many of Plath’s sentences. When the sentence starts you think it is going in a certain direction and then it suddenly turns and goes in quite a different one. A third is the fact that the book presents a picture of mental illness as seen from the inside. Here I think of the shell-shocked veteran in Mrs Dalloway who I see as portraying some part of Virginia Woolf’s illness. A fourth is that I was struck by the fact that the main character assesses the attractiveness of men by the sound of their names. I never proceeded in this way when deciding how attractive I found women but in this point, where in a sense language overrules reality, and in several others in the book I felt ‘This could be me’. As a last point I simply mention the great originality of the book which is quite different from any other book I have read. This originality is not just an effect of the book as a whole but instead impregnates the whole text.

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.

 

One dimensional centre manifolds, part 3

I now want to generalize the discussion relating the case that the leading order term in the dynamics on a centre manifold is quadratic and the generic fold bifurcation to a related case where one more derivative has been taken. So the aim is to relate the case that the leading order term in the dynamics on the centre manifold is cubic and the generic cusp bifurcation. To do this we express in terms of derivatives of . In fact we will only write out those terms explicitly which do not always vanish at the bifurcation point. The result is .
In this way it is possible to express the condition for the non-vanishing of the cubic term in the dynamics on the centre manifold by . Note, however, that the expression is not intrinsic to the centre manifold. Because of the vanishing of the first derivatives the second order derivatives and define tensors in the full dimension of the dynamical system. Hence we can write invariantly in the form . It remains to compute . The invariance of the centre manifold implies that . Hence . This equation has a unique solution for . In this way one of the conditions for a generic cusp bifurcation can be expressed in an invariant way. This corresponds to (8.128) in the book of Kuznetsov. In trying to understand these things better I was confused by equation (5.28) in the book which should be almost the same as (8.128) but in fact contains a typo. There is a repetition of . For a generic cusp bifurcation we need two parameters and . The genericity condition involving derivatives with respect to parameters can easily translated into an invariant form. The result is
Formulae similar to those just given were used in a paper I wrote with Juliette Hell some years ago (Nonlin. Analysis: RWA. 24, 175). Looking back at that I have the feeling that we must have been doing some sleepwalking when writing that paper. Or maybe I was sleepwalking and Juliette was paying attention. In any case, the final result was correct.

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.

One-dimensional centre manifolds, part 2

I continue with the discussion of the previous post. There I mentioned a preliminary transformation of the coordinates. I will discuss this in more detail here. Suppose we have a two-dimensional dynamical system for unknowns and a steady state . The usual aim is to understand systems up to certain transformations. One type of transformation is of the form . A second is of the form . A third is of the form . With the assumptions which have been made we can do a translation to achieve . Assume now that the linearization of the system at the origin is diagonalizable with rank one. Then it has one eigenvalue zero and one non-zero eigenvalue. It can be diagonalized by a linear transformation of the coordinates. After these transformations the system has almost been reduced to the form in the last post, except that there is a non-zero constant in front of the first summand in the evolution equation for which might not be . It can be reduced to the latter case by rescaling the time coordinate. A similar process can be carried out when the centre manifold is of higher codimension. Then the variable becomes vector-valued and the first summand in the evolution equation for is if the form for an invertible matrix . The function defining the centre manifold is then also vector-valued. The centre manifold analysis can be done in a manner very similar to what we have seen already.

The discussion of the fold bifurcation also generalizes in a straighforward way to the case of higher codimension. There is, however, one thing about that discussion which is unsatisfactory. The bifurcation conditions are expressed in terms of the transformed coordinates. It would be more satisfactory, because more invariant, if they could be expressed in terms of the original coordinates. This leads to considering the way in which these conditions are affected by the three types of coordinate transformations previously discussed. The first type of transformation leaves the conditions involving only and its derivatives with respect to unchanged. The derivative of with respect to is rescaled by the non-zero factor and so the fact of its being non-zero is unchanged. The third type of transformation just scales all the relevant quantities by the non-zero factor and so also does not change whether these are zero or not. It remains to consider the second type of transformation. At this point a more geometrical point of view will be adopted. We change the notation for the right hand side of the equations to . These are the components of a parameter-dependent vector field which satisfies . Because of this condition the derivative defines a vector at the origin independently of the transformation of the second type. The linearization of the vector field at the origin defines a tensor. We suppose as before that it is diagonalizable and of rank one. Let be a vector spanning the kernel of , Thus using the Einstein summation convention we have . Similarly there is a one-form with . It is unique up to rescaling and we choose it to satisfy . With these notations the condition previously written in the form can be written in the invariant form . The condition previously written in the form can be written in the invariant form . Here we use the notation . It is because the vector field vanishes at the origin and is in the kernel of its first derivative that the expression involving the second derivative is invariant. These considerations may be compared with those in section 5.4 in the book of Kuznetsov.

One-dimensional centre manifolds

I have used one-dimensional centre manifolds in my research on several occasions. I now see that I always did this in quite an ad hoc way. I did not exercise due diligence in the sense that I did not take the time to get a general picture of what was going on, so as to be able to use this technique more efficiently in the future. Now I want to do so. I start with the two ODE and . This example is general enough to illustrate several important ideas. Here and are supposed to be smooth and vanish at least quadratically near the origin. The linearization of this system has the eigenvalues and zero. Its kernel is spanned by the vector with components . It follows that there exists a centre manifold of the form , where has any desired finite degree of differentiability. By definition this manifold is invariant under the flow of the system, it passes through the origin and its tangent space there is the axis. Consider the Taylor expansion . Substituting this into the evolution equation for gives . This is a leading order approximation to the flow on the centre manifold. If we can use it to read off the stability of the origin within the centre manifold. This argument uses no information about the way the centre manifold deviates from the centre subspace, i.e. how fast grows near zero. If we need to go further.

Differentiating the defining equation with respect to time and substituting the evolution equations into the result gives . Call this equation (*). It can be analysed with the help of the Taylor expansions and . Substituting these into (*) we see that the left hand side is of order three. Thus the same must be true of the right hand side and we get and . Substituting this back into the evolution equation for gives . Thus if the stability of the origin is determined by the sign of . If it is zero we can do another loop of the same kind. Looking at the third order terms in the equation (*) we get . This allows the fourth order term in the evolution equation for to be determined. This procedure can be repeated as often as desired to get higher order approximations for the centre manifold and the restriction of the system to that manifold.

We can now sum up the steps involved in doing a stability analysis. First look at the coefficient of in the equation for . If it is non-zero we are done. If it is zero use the equation (*) to determine the leading term in the expansion of the centre manifold. Put this information into the equation for . If the leading term is non-zero we are done. If it is zero we can repeat the process as long as is necessary to get a case in which the leading order coefficient is non-zero. As long as this point has not been reached we cycle between using (*) and the equation for . The system I have discussed here was special. The codimension of the centre manifold was one and the system was in a form which usually could only be achieved by a preliminary linear transformation of the coordinates. The special case nevertheless exhibits the essential structure of the general case and can serve as a compass when treating examples.

These ideas can be extended to give information about bifurcations. The equations are replaced by and , where is a parameter. This can be made into a three-dimensional extended system by adding the equation . The origin is a steady state of the extended system and the centre manifold at that point is of dimension two. It is of the form . Suppose that we are in the case . Then this looks very much like the case of a generic fold bifurcation. We are just missing one condition on the parameter dependence. The dynamics on the centre manifold is given by . Of course the equation remains unchanged. We can now check the conditions for a generic fold bifurcation in the system reduced to the centre manifold. The first is . The second is . Hence is equivalent to . The third involves . We see that is equivalent to . The fourth involves . We see that is equivalent to . The first three conditions for a generic fold bifurcation of the system on the centre manifold are already satisfied and the fourth is equivalent to . In this way the bifurcation conditions can be expressed directly in terms of the coefficients of the original system. This is an illustration in a relatively simple example of a relationship discussed in much more general cases in the book of Kuznetsov.

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.