Archive for February, 2020

R.I.P. Freeman Dyson (1923-2020)

Posted in The Universe and Stuff with tags , on February 29, 2020 by telescoper

I was just about to leave work last night when I heard via social media the sad news of the death at the age of 96 of the theoretical physicist Freeman Dyson.

Overnight the regular media have been running tributes to him, and various friends and colleagues have been posting their own personal recollections of a remarkable scientist who also seems to have been a kind and generous human being.

I never had the opportunity to meet, or even correspond with, Freeman Dyson myself but I do recall from Nottingham times being told that both Dyson and Julian Schwinger visited and gave lectures for the bicentennial celebrations of the birth of George Green. People there remembered him with fondness.

Please feel free to share any personal reminiscences through the Comments Box below.

Freeman Dyson was an original and creative thinker who was by no means always right but I’ve always felt that scientists should be judged by their best work rather that their worst, and Dyson was a wonderful generator of ideas and made important and influential contributions across a wide range of fields from Quantum Electrodynamics and Solid State Physics to Astronomy and Cosmology.

Rest in peace, Freeman Dyson (1923-2020).

Maynooth University Library Cat Update

Posted in Maynooth with tags on February 28, 2020 by telescoper

This morning I was proceeding in a Northerly direction when I spied the local celebrity feline on post near the library. As I prepared to take a picture he turned to wash his rear parts. If he sits there when it’s raining or snowing it’s because he wants to be fed, so I duly opened a small serving of luxury cat food. Before I could get it into his bowl, however, he legged it over the wall and and hid in the bushes. Turning round, I saw that a person was approaching with a dog on a lead. As soon as they passed, he was back on the wall scoffing the vitacat salmon terrine.

Yesterday the Library hosted a visit from the President of Ireland, Michael D. Higgins, but he likes dogs rather than cats so I won’t dwell on the matter.


Booming Stats

Posted in Biographical on February 27, 2020 by telescoper

I really don’t understand the internet at all. After months in the doldrums the traffic to this blog suddenly went into overdrive yesterday as a result of a little post about W.K. Clifford. It’s not often that I get more than 2,000 visitors per day but so far today I have already had 2,500, and it’s not even 6pm!

I have never been able to predict which posts will  generate interest and which won’t, so I gave up trying to do that a long time ago. In any case I’ve written pieces that I thought were much more interesting only to watch them sink without trace. This time I can only assume that Clifford’s magnificent beard is responsible for the factor of ten increase in traffic.

On the subject of not really understanding the internet, I saw the other day I saw an incoming link from Phil Moriarty’s blog and followed it back to see what he disagreed with me about.

It turns out he was answering a question I have often been asked but have never really answered (because I really don’t know): why write a blog? If I ever had a reason then eleven years after I started I’ve definitely forgotten. There probably never was `a’ reason…

Part of it is that I actually quite like writing. Another is that writing about something is often quite a good way of working out what you actually think (this is basically the same as one of Phil’s points). Another is that, perhaps, it is quite useful to pass on little snippets of information that might be useful to various people. Another (that applies especially to music, poetry, etc) is that I like the idea that sharing things here might introduce someone – perhaps a total stranger – to something that they go on to enjoy.

So you see there are lots of reasons to write a blog, but none of them has anything to do with traffic statistics. It’s nice when posts prove popular, of course, but it’s not as if my livelihood depends on how many visitors I get (which is the case for people who write for commercial sites). I wouldn’t enjoy this blogging lark half as much if I felt I had to produce content that I thought would be popular!

Clifford’s `Space-Theory of Matter’

Posted in Beards, History, mathematics, The Universe and Stuff with tags , , , on February 26, 2020 by telescoper

Well, here’s another thing I didn’t know until I was informed by Twitter.

Way back in 1876 –  forty years before Einstein presented his Theory of General Relativity – the mathematician W.K. Clifford (who is most famous nowadays for the Clifford Algebra) presented a short paper in the Proceedings of the Cambridge Philosophical Society in which he speculated that space might be described by Riemannian rather than Euclidean Geometry.

Here are a couple of excerpts:


The paper does not contain any actual equations, and his concentration on small scales rather than large was misguided, but it is quite remarkable that he was thinking about such matters such a long time ago!

Unfortunately Clifford died very young, in 1879, at the age of 33, tuberculosis. Had he lived longer he might have been able to develop these ideas a bit further.

As a postscript I should mention that Clifford had an impressive beard.

Ash Wednesday Observance

Posted in Uncategorized on February 26, 2020 by telescoper

So today is post-Pancake Day, or Ash Wednesday as it is sometimes known. I remember this time two years ago when I was very much a newcomer to Maynooth being quite surprised to see some folk wearing a cross marked in ash on their forehead as in the picture above. I think this practice is a tradition within the Roman Catholic Church with which Maynooth has long historical associations, so it’s not really surprising to see it here. Having been brought up in Protestant England I had never seen this before moving to Ireland, but it has become a familiar sight to me to see people with crosses on their foreheads.

Apparently the tradition used to be for ashes to be sprinkled on the top of the head of a male worshipper but a cross to be made on the forehead of a woman because she would be expected to be wearing a hat. Based on a small sample of those I have observed it seems both genders wear the cross on the forehead nowadays.

Anyway, although I’m not a Christian myself, respect to all those observing the season of Lent (Quadragesima), whether that means fasting, devotional prayer, or just giving up luxuries, such as reading this blog perhaps.

P.S. I’m told that the normal rule for Lent is `One meal and two collations’. The word collation, in the sense of ‘light meal,’ comes from the title of John Cassian‘s early fifth-century work Collationes patrum in scetica eremo (Conferences with the Egyptian hermits), which was read in Benedictine communities before a light meal. I haven’t heard that English word for a while, but it has the same origin as the Italian colazione, used in prima colazione (breakfast).

A Problem of Snooker

Posted in Cute Problems, The Universe and Stuff with tags , , , on February 25, 2020 by telescoper

I came across the following question in a first-year physics examination from Cambridge (Part 1A Natural Sciences) and, since I have posted anything in the Cute Problems folder for a while I thought I would share it here:

Answers through the comments box please! And please show your working!

P.S. The preamble does not say whether you can also assume irrelevant formulae without proof…


A Statistical Solution to the Chaotic, Non-Hierarchical Three-Body Problem

Posted in The Universe and Stuff with tags , , , on February 24, 2020 by telescoper

I’m a bit late passing this on but I think some of my readers might find this interesting, as I did when I came across it a week or so ago. There’s a paper on the arXiv by Nicholas Stone and Nathan Leigh with the title A Statistical Solution to the Chaotic, Non-Hierarchical Three-Body Problem and the following abstract:

The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but only where hierarchies of masses or separations exist. Numerical integrations show that bound, non-hierarchical triples of Newtonian point particles will almost always disintegrate into a single escaping star and a stable, bound binary, but the chaotic nature of the three-body problem prevents the derivation of tractable analytic formulae deterministically mapping initial conditions to final outcomes. However, chaos also motivates the assumption of ergodicity, suggesting that the distribution of outcomes is uniform across the accessible phase volume. Here, we use the ergodic hypothesis to derive a complete statistical solution to the non-hierarchical three-body problem, one which provides closed-form distributions of outcomes (e.g. binary orbital elements) given the conserved integrals of motion. We compare our outcome distributions to large ensembles of numerical three-body integrations, and find good agreement, so long as we restrict ourselves to “resonant” encounters (the ~50% of scatterings that undergo chaotic evolution). In analyzing our scattering experiments, we identify “scrambles” (periods in time where no pairwise binaries exist) as the key dynamical state that ergodicizes a non-hierarchical triple. The generally super-thermal distributions of survivor binary eccentricity that we predict have notable applications to many astrophysical scenarios. For example, non-hierarchical triples produced dynamically in globular clusters are a primary formation channel for black hole mergers, but the rates and properties of the resulting gravitational waves depend on the distribution of post-disintegration eccentricities.

The full paper can be downloaded here. The abstract is very clear but you might want to read the wikipedia entry for the three-body problem for general background. Here’s a fun figure from the paper:

Let me just add a note of explanation of the word `hierarchical’ as applied here: it means when the mass of one body is very different from the other two, or that two of the bodies have a much smaller separation from each other than they do from the third.

This paper does not present an analytic solution of the unrestricted three-body problem (which is known to be intractable) but does provide some very useful statistical insights into the long-term evolution of three-body systems, for example confirming the generally held opinion that most such systems evolve into a state in which one body is ejected and the other two form a tight binary.