Hydrobates

alanrendall.wordpress.com · English

A mathematician thinks aloud

rss2 wordpress content media slash wfw atom dc sy

Open the feed

https://alanrendall.wordpress.com/feed/

Last post: Sep 28, 2026
Posts in 24 h · 7 days · 30 days: 0 · 1 · 4
Our last check: Answering
Served from: United States
Text score at discovery: 5,891
Format: rss2
Features in the feed: content, media, slash, wfw, atom, dc, sy
Community: wordpress

Posts

What our queue read from this feed. Open one to read it here, or go to the site that published it.

Visit to Armenia
Sep 28, 2026 · original
After leaving Tblisi we crossed the border to Armenia. Again we had to walk a certain distance across the border but in this case it was not so far and we did not have to show our passports so often. We spent our first night in Dilijan. This was a place of no special interest in itself but rather a starting point for excursions. After that we continued to Yerevan. I must admit that prior to visiting Armenia my knowledge of the country was essentially zero. My impression now is of a very interesting culture. Our local guide told us a parable. The Armenians are like a swallow building its nest. The swallow invests a great deal of time and effort building the nest, laying eggs, feeding its chicks. Then a predator comes and destroys everything, the nest and its contents. Then the swallow begins again, and again, as long as it takes. The Armenians repeatedly built up their civilisation and we
Visit to Georgia
Sep 24, 2026 · original
After leaving Shaki we crossed the border into Georgia. For this we had to walk several hundred meters uphill with our suitcases but otherwise crossing the border was unspectacular. The land border between Azerbaijan and Georgia can only be crossed in one direction. That between Azerbaijan and Armenia is closed in both directions. This means that if you want to visit all three countries travelling by land and not entering any other country in between the order is fixed uniquely to be the one in which we visited them, namely Azerbaijan, Georgia, Armenia. When we arrived at the Georgian border one of the most prominent things was the national flag. In all three countries the national flag was often to be seen, not only on official buildings. In Baku there is an enormous flag next to the lake which is almost impossible to ignore. This is in stark contrast to the situation in many west Europ
Visit to Azerbaijan
Sep 20, 2026 · original
Eva and I recently visited Azerbaijan. The trip started with a flight from Frankfurt to Baku. Apparently the only European cities which have direct flights to Baku are Frankfurt and Warsaw. In saying this I am not counting Moscow as being in Europe, which is based more on emotional then geographical factors. There are several flights a day between Baku and Moscow and the relationship between Azerbaijan and Russia seems quite good. At the airport in Baku I was surprised that there was a flight coming from Tel Aviv. This is perhaps a reflection of the fact that although the great majority of the inhabitants of Azerbaijan are Muslims there is a strict separation of religion and state. There were less women to be seen wearing obviously Muslim dress in Baku than in Mainz. In Baku there is a large statue representing a woman throwing off her veil. Part of our flight was over the Black Sea and
Biography of Elon Musk by Walter Isaacson
Sep 3, 2026 · original
In the modern world Elon Musk is a very influential person. He receives a lot of hate and envy for what he does and says. In the past my attitude to Musk was rather neutral. This had to do with the fact that I was not well informed about him. Now I set out to change that by reading the book quoted in the title of this post. The book is well written and pleasant to read. It contains a lot of interesting information. I was glad to see that it appeared to be unbiased: the author is neither trying to damn his subject nor to idealise him. What are the most important influences of Musk? One consists of his achievements in new technologies. I was suprised to see how much the ability of the Western world to be active in space is dependent on technologies coming from his company SpaceX. I also learned how great his influence has been in the field of electric cars. These were themes that I had sim
Suicidal Empathy by Gad Saad
Aug 23, 2026 · original
In a previous post I wrote about the book ‘The Parasitic Mind’ by Gad Saad and I mentioned that I saw my reading of that book as a preparation for reading his new book ‘Suicidal Empathy’. I have now finished reading the latter. I found it stylistically more pleasant than the previous book. Either his style has got milder or I have just got used to it. The most significant thing about the book is its contents. I think that it is a very important book and that it should be read by as many people as possible. One aspect of it is that the author presents many examples which are so extreme as to be breathtaking. Incredible extremes of wokeness. The main theme of the book is how Western society is being destroyed by excessive amounts of empathy applied to the wrong targets. The examples are backed up by sources where it is possible to learn details about the cases presented. I made use of this
Hartman’s theorem on conjugacy of saddles in two dimensions
Aug 10, 2026 · original
In a previous post I discussed the topic of conjugacy of vector fields on , concentrating on the case where the vector field and the conjugation are smooth, i.e. . In what follows I will continue to consider smooth vector fields but allow the conjugations to have only finite differentiability. In the last post I showed that in the case all vector fields are smoothly conjugate near a non-degenerate zero. In particular in this case each vector field is conjugate to its linearization at a steady state. Consider now the case . The theorem of Hartman mentioned in the title of this post concerns a hyperbolic saddle in two dimensions. (The reference is ‘On local homeomorphisms of Euclidean space’, Bol. Soc. Mat. Mex. 5 (1960) 220–241.) In other words we consider the case that the linearization of a vector field at a steady state has one positive and one negative eigenvalue. The theorem says tha
Conjugacy of one-dimensional vector fields near a zero
Aug 6, 2026 · original
A vector field on the real line can be written in the form and in this sense it is equivalent to a function. From a geometrical point of view it is different from a function because it has a different transformation behaviour under diffeomorphisms. If a function is transformed using a diffeomorphism to get a function then . This is a pull-back operation, transforming a function on the range to one the domain. By contrast the transformation of a vector field goes in the opposite direction with the vector field written above being transformed to a vector field represented by a function with . If is the inverse of then this is equivalent to . Suppose now that has a zero at zero, i.e. . The zero is called non-degenerate if . This is an invariant statement since , where the last equality holds at a zero of . If we have two vector fields of this kind does there exist a local diffeomorphism def
Definitions and politics
Jul 28, 2026 · original
In mathematics definitions play a central role. Before starting a mathematical discussion it is necessary to fix necessary definitions. When mathematicians discuss other subjects they also often want to know the definitions of the terms being used and this is often difficult. It can already be difficult in physics and of course it is much more difficult in areas such as law or politics. A definition involves explaining something in terms of something else which is already known and already defined. In many areas this becomes difficult because so many terms used are poorly defined. The extreme case is that where terms are not defined at all but at just phrases connected to an emotion or a value judgement. In law or politics it is often hard for people to agree on a definition since different individuals may have concrete advantages or disadvantages depending on what definition is chosen.
Normal forms of dynamical systems
Jun 22, 2026 · original
Here I consider a system of ODE or equivalently a vector field on an open subset of Euclidean space. The question is in what way it can be simplified by a coordinate transformation. This leads to the theory of normal forms. My main source for what follows is the book ‘Qualitative Theory of Planar Differential Systems’ by Dumortier, Llibre and Artes. I will mainly concentrate on the two-dimensional case, as that book does. The aim is to simplify the vector field in the neighbourhood of a steady state, which is placed at the origin. Then we can write it in the form where is a matrix and vanishes faster than linearly at the origin. To avoid any subtleties with differentiability let us suppose that is smooth ( ). We want to apply a diffeomorphism to bring the vector field into the form where is in some sense as simple as possible. Let be the set of vector fields which are homogeneous of degr
A conflict of visions by Thomas Sowell
Jun 20, 2026 · original
These days people often talk about how society is divided when it somes to various political issues. What is remarkable is a certain correlation. People who are on the same side in the case of one political issue often find themselves on the same side in the case of an apparently unrelated issue. This is a phenomenon I have thought about a lot and also discussed with other people. Recently I talked about it with Samuel Blotiu and he recommended me a book which is concerned with this subject and offerred to lend it to me. It is the book which is the title of this post. I was not immediately enthusiastic about reading the book but I was a little intrigued and I accepted his offer. I knew the name of Sowell only through some quotes I had seen on X but I usually liked them. When I started reading the book it immediately made a positive impression on me. The first sentence is ‘One of the curi

Discovered by the rss-feed-index crawler, which checks each feed at most once a month.

Same record as JSON: https://api.agentalog.com/api/feeds/fd_alanrendall_wordpress_com_aa850d9ea85afb1e. More from this site: alanrendall.wordpress.com in the Feeds tab.