I have just read the book ‘On Democracies and Death Cults’ by Douglas Murray. It is one of the most rewarding reads I have had for a long time and it has my highest recommendation. In recent months I have thought a lot about what is happening in Gaza and Israel but I was missing a lot of background information. I am now much better informed due to reading Murray’s book. One part of the new things I have learned concerns what has happened in Israel and Gaza in the aftermath of 7.10.2023 and this is based on Murray’s extensive research on the ground which in part was done a very short time after the attack on Israel took place. The other part consists of historical information about the conflict between Israel and its neighbours.
A starting point for the book is that while the attack on Israel took place on 7.10 there was already an anti-Israel demonstration in Times Square on 8.10. Murray was there and taking photos. This was at a time when the rape and murder in Israel was still going on. Similar events were observed in other Western countries including Germany, France and Canada. They were out of control of the police. A theme which is central to the book is the paradoxical nature of the reactions to the attack on Israel in the Western world. Instead of the natural reaction of solidarity with Israel there was condemnation of Israel, a particularly blatant example of victim blaming. There was not a single protest against Hamas. All this can be seen as symbolic of a wider trend with Israel playing the role of the Western world. At present many people in the Western world who are publicly visible (such as politicians, intellectuals and journalists) tend to condemn the Western world, its traditions and culture. At the same time they generously pardon the crimes of its enemies to the point of even acting to prevent people from talking about those crimes and their perpetrators by any means possible. Murray feared that people would deny the atrocities that had happened in the attack and he travelled to Israel (and to Gaza) as soon as possible so as to document the events. He was able to view the famous compilation of videos showing the horror of the attack. He was struck by the fact that the terrorists appeared to be enjoying what they were doing and to be proud of it. One of them contacted his parents via WhatsApp and sent them pictures of about ten people he had killed with his own hands. His parents were delighted. Murray quotes the journalist, publisher and diplomat George Weidenfeld as stating that there are people who are worse antisemites than the Nazis. While the Nazis tried to hide their worst crimes from outside observers Hamas publicised their crimes as much as possible. To try to understand this phenomenon better Murray talked to many people, including survivors of the attack, families of those killed and those kidnapped to Gaza, members of the Israeli security forces and Israeli politicians including Benjamin Netanjahu.
Murray explains how the takeover of Iran by Ayatollah Khomeini is at the root of many of the present problems in the Middle East. The enemies surrounding Israel are now like the tentacles of the Iranian regime. The change of government in Iran was praised by many left-wing intellectuals in the West, including Michel Foucault. There may be an exceptional concentration of evil in Hamas but they could not have acted as they have done without weapons, training and other support from Iran. The question of how the disaster of 7.10 could have happened is not one which is answered in the book. However there is one suggestion of something which could have been an important contributing factor: hubris. Israel was known to others and to itself as being a master of defending itself and it seems that the Israeli authorities thought that they had Gaza completely under control, which turned out to be a grave error. A feature of the relations between Israel and Gaza has been the exchanges of huge numbers of Palestinians who were in Israeli prisons (of whom many had committed terrible crimes) for a few hostages. In this context Israel is the perfect target for blackmail. I learned from the book that Yahya Sinwar, the mastermind of the attack on 7.10, was one of more than a thousand Palestinians released in return for just one soldier who had been a hostage. While in prison a doctor discovered that Sinwar was suffering from a brain tumour. He was treated for this in an Israeli hospital. On 7.10 several relatives of that doctor were killed or kidnapped. One of them was an 85 year old holocaust survivor, Yaffa Adar, who had been in the Warsaw Ghetto. She was taken to Gaza and held for 49 days before being released.
Murray was shown around the village of Nir Oz where of about 400 inhabitants about 100 were killed or kidnapped and was told the stories of what had happened to them. There was for instance Bracha Levinson, 74 years old, child of holocaust survivors. The terrorists who came into her house took her cell phone and filmed her murder. Then they took a picture of her lying dead in a pool of blood and uploaded it to her Facebook page so that all her family and friends could see it. Murray visited a bomb shelter where at least 11 Thai workers had been taken and brutally murdered. There was blood everywhere, on the floor, on the walls (including hand prints of the victims) and on the ceiling. He met a young man who had escaped from the Nova festival and who told his story while showing what he had filmed with his phone. He had managed to reach his car but did not dare to drive off. It is important to know that the wave of Hamas terrorists from Gaza was followed by a wave of civilians who went around the scene of the carnage, looting everything they could find. A group of looters was coming closer, going from car to car. Outside the car was another man but he was afraid to get in in case he might be seen. Eventually the group came so close that the man in the car felt he had to drive away, leaving the other man behind. It was possible to escape in the car but the man left behind was lynched by the Palestinians.
One month after the attack on Israel Murray went into Gaza with the IDF. They passed through the hole in the fence where most Gazans had crossed into Israel on the day of the attack. Then they proceeded until they reached the main road from north to south where Gazans were following the Israeli orders to leave the north. Many of them were shot by Hamas to prevent them doing so. Murray saw them queueing up to pass the control post. The fact that he was deep inside Gaza makes his account more authoritative than those of people giving their opinions from Israel or from thousands of miles away from Gaza.
The book discusses the antisemitic activities in Ivy League Universities. This is a development which I had followed on my own from a distance but here I learned some more things. It is discussed how the German left moved from supporting Israel to supporting the ‘Palestinians’. This had to do with always wanting to be on the side of the oppressed. It has parallels with what has happened in the US and elsewhere in the West in the last two years. There is a description of the highjacking of a plane by Germans and Palestinians in 1976. The hostages were separated by the Germans into Jews, who were to be held, and non-Jews, who were to be released. The criterion was not being Israeli but being Jewish. One of the hostages showed the terrorists the number tattooed on his arm which showed that he had been in a concentration camp. He told them in German that he thought that something had changed in Germany since the time of the Nazis but that he suspected from the behaviour of these people that he had been mistaken. There is a discussion of antisemitism which contains two interesting quotes. The first, due to Vasily Grossman, is ‘Tell me what you accuse the Jews of – I’ll tell you what you’re guilty of’. The second is an adaptation of this to the present, due to Murray, ‘Tell me what you accuse the Jews of – I’ll tell you what you believe you are guilty of.
Murray talks about how impressed he was by some young women he met in Israel. One of them, nineteen years old, was an army recruit and was helping in an operation to collect the last human remains from vehicles which had been destroyed in the attack on the Nova Festival. Another, twenty-three years old, was working as an intelligence expert on Yemen. He was very impressed by these and other young women he met and contrasted them with women of the same age he had met in other Western countries and who often seemed to him like spoiled children. Being in a war can sometimes bring out the best in people. It is easy to see parallels between the Nazis and Hamas but it is not so well known that there is a direct connection. This connection is explained in the book. The Grand Mufti of Jerusalem was an ally of Hitler and collaborated with him in the annihilation of Jews. The Mufti was the one war criminal of the Second World War of this caliber who was able to live openly and without being brought to trial after the war. He was given a warm welcome in his home country of Egypt and praised in the highest terms by the leader of the Muslim Brotherhood, an organisation of which Hamas is one of the descendants.
Murray visited some of the Palestinians who had been taken prisoner during the attack on 7.10. He was able to see them in their cells. He recognised some of them as the killers he had seen in the horrific videos. They looked surprisingly like normal human beings. When Sinwar was finally killed Murray heard about it and immediately travelled to the place in Rafah where it had happened. When Sinwar was shot (by a nineteen year old soldier) without his identity being known he was able to escape, badly wounded, into a building and sit in an armchair. There he bled to death. Murray saw the traces of blood Sinwar had left during his escape and sat in the bloodstained chair where his life had ended. He looked out at the ruins of Rafah and speculated about what thoughts might have gone through Sinwar’s mind as he sat there.
This book reports on many horrors but the author found something positive at the end. He was encouraged by seeing the heroism of young men and women in Israel who had risen to the occasion and shown what is possible. Anyone interested in Gaza should read this book.
. When I asked the lecturer who was teaching us a course on thermodynamics he was not able to give me an explanation which I found satisfactory. As a schoolboy physics was the subject which interested me most. After my second year at university I had to decide between doing a degree in physics, a degree in mathematics or a joint degree in both. My decision for the second alternative was strongly influenced by that thermodynamics conundrum. Another experience which contributed to my decision was that at one time I happened to have two courses on the same topic, Fourier series, in the same term, one in physics and one in mathematics. The second was quite transparent to me, the first obscure. The fact that I had
or open subsets thereof. The considerations are local, i.e. whenever necessary the functions will be restricted to arbitrarily small neighbourhoods of the origin. A relatively simple case is 
. Suppose that 
for a smooth function 
. Then the derivatives 
vanish for all 
. The question whether the converse holds is the simplest example of the type of questions to be considered here. In fact it does hold but the proof is not quite trivial. It is easy to construct an inductive proof once the case 
is known. That case can be treated using the fundamental theorem of calculus and a change of variables. This leads to the formula 
.
things become more complicated. If 
is a function of two variables then there is no condition on the derivatives of 
at the origin which will ensure the existence of a function 
. This can be seen by choosing 
. All derivatives of this function at the origin are zero. However there is no smooth function 
. For setting 
in a relation of this form gives a contradiction. There are true analogues of the theorem in one dimension for 
with 
. This can be formulated in algebraic language as follows. In the ring of germs of smooth functions at the origin the ideal of functions which vanish at the origin is generated by the monomials 
. The proof is very similar to that in the one-dimensional case. More generally, if for a given 
the function 
vanish at the origin there exist functions 
such that 
. Here 
is a multi-index.
, to play a special role. It is now assumed that the restriction 
is divisible by 
, i.e. 
for a smooth function 
. The conclusion is that under this assumption it is possible to multiply 
in such a way that the result is a polynomial of degree 
. Another related result is the Mather division theorem. In that case we start with any smooth function 
such that 
and 
with coefficients which are smooth functions of 
in the second and rearrange the result. For the converse first multiply by a positive function to make 
. The Malgrange preparation theorem is an analogue for smooth functions of the Weierstrass preparation theorem for analytic functions of complex variables. The big difference is that the analytic theorem includes a uniqueness statement while the smooth one does not. It seems that the Malgrange theorem cannot simply be got by approximating the smooth functions by analytic ones and using the Weierstrass theorem. Instead it is proved by decomposing the Fourier transform using a partition of unity.
, where 
and 
denote the first and second order derivatives of 
, respectively. The boundary condition is an inhomogeneous Dirichlet condition 
. Now replace 
to get the equation 
. Suppose that this equation has a unique solution for a given function 
between suitable function spaces by 
. A solution of the problem we want to solve is then a fixed point of 
. Since the equation which defines 
. A priori estimates for the elliptic problem then give the bound needed to apply the theorem to this problem and obtain an existence theorem for the boundary value problem for the nonlinear equation.
be the open unit ball in a Banach space 
and let 
into 
is contained in 
. They involve both scaling the argument and modifying the parameter. A fixed point is obtained for each 
and then 
. It is supposed that any fixed point of the latter with 
satisfies the inequality 
. Now 
which satisfies 
for 
and 
for 
. Let 
be the closed ball of radius 
about the origin. Then 
at this point then it is also a fixed point of 
then 
is proportional to 
with a factor 
. Applying the assumption of the theorem we see that the norm of 
is no greater than 
is less than one and there nevertheless exists a positive steady state. The bifurcation which occurs in the proof is a transcritical bifurcation. Intuitively this means that as a parameter is varied a steady state moves across another steady state which is fixed. There is a sign involved in a bifurcation of this type. One value of the sign corresponds to a backward bifurcation while the other corresponds to the forward bifurcations more familiar in epidemiology. The steady state which arises in a backward bifurcation is unstable. In simulations of models with backward bifurcations it is often seen that the steady state can be continued to larger values of the parameter until it reaches a point where a fold bifurcation takes place. There it changes from unstable to stable. This phenomenon cannot be captured by the analysis of the transcritical bifurcation since in general it occurs far away from the bifurcation point. We have now found an extension of that analysis which allows the fold bifurcation to be treated. The idea is to replace the transcritical bifurcation by one whose codimension is one higher. This is similar to passing from a fold to a cusp. The transcritical bifurcation could be given the intuitive name ‘moving hyperbolic steady state’ and by analogy with this we give the bifurcation studied in the paper the name ‘moving fold’. In this type of bifurcation two positive steady states arise, one stable and one unstable. This is a tool which may be used to prove the existence of more than one positive steady state in epidemiological models. The general theorem we prove applies to both the cases 
and 
but up to now we have only found interesting examples for the first of these cases. Our original model for hepatitis C is one such example. We were not able to decide whether in that example there exist parameters which would allow the second case of the theorem to be applied. We proved the relative statement that if parameters with this property exist there actually exist three positive steady states. An interesting side effect of this work is that we found a limiting case of that model (where two parameters are set to zero) where there can exist a continuum of steady states.
Hydrobates 