## Hair from Bayeux

Posted in Beards, History with tags , , , , on January 18, 2018 by telescoper

Since the Bayeux Tapestry (which, being stitched rather than woven, is an embroidery rather than a tapestry) is in the news I thought I’d share some important information about the insight this article gives us into 11th century hairstyles.

As you know the Bayeux Tapestry Embroidery concerns the events leading up to the Battle of Hastings between the Saxons (who originated in what is now a part of Germany) led by Harold Godwinson (who had relatives from Denmark and Sweden) and the Normans (who lived at the time in what is now France, but who came originally from Scandinavia).

Most chronicles of this episode leave out the important matter of the hair of the protagonists, and I feel that it is important to correct this imbalance here.

Throughout the Bayeux Untapestry, the Saxons are shown with splendid handlebar moustaches, exemplified by Harold Godwinson himself:

This style of facial hair was obviously de rigueur among Saxons. The Normans on the other hand appeared to be clean-shaven, not only on their front of their heads but also on the back:

This style of coiffure looks like it must have been somewhat difficult to maintain, but during the Battle of Hastings would mostly have been hidden under helmets.

With a decisive advantage in facial hair one wonders how the Saxons managed to lose the battle, but I can’t help thinking the outcome would have been different had they had proper beards.

## Planes, Trains and Quaternions

Posted in Biographical, History, mathematics, Maynooth with tags , , , , , , , , on January 4, 2018 by telescoper

Well, here I am in Maynooth for the first time in 2018. I flew over from Cardiff yesterday. The flight was rather bumpy owing to the strong winds following Storm Eleanor, and it was rather chilly waiting for the bus to Maynooth from Dublin Airport; nevertheless I got to my flat safely and on time and found everything in order after the Christmas break.

This morning I had to make a trip by train to Dublin city  to keep an appointment at the Intreo Centre in Parnell Street, which is about 15 minutes walk from Dublin Connolly train station. I bought an Adult Day Return which costs the princely sum of €8.80. Trains, stations and track in Ireland are maintained and operated by Irish Rail (Iarnród Éireann), which is publicly owned. Just saying.

The distance between Maynooth and Dublin about 25 km, which takes about 40 minutes on the local stopping train or about 25 minutes on the longer distance trains which run nonstop from Maynooth to Dublin. As it happens I took one of the fast trains this morning, which arrived on schedule, as did the return journey on a commuter train. My first experience of the Irish railway system was therefore rather positive.

I had thought of having a bit of a wander around the city on my way to Parnell Street but it was raining and very cold so I headed straight there. I arrived about 20 minutes ahead of my scheduled appointment, but was seen straight away.

The reason for the interview was to acquire a Personal Public Services Number (PPSN), which is the equivalent of the National Insurance Number we have in the United Kingdom. This number is needed to be registered properly on the tax and benefit system in Ireland and is the key to access a host of public services, the electoral roll, and so on. You have to present yourself in person to get a PPSN, presumably to reduce the opportunity for fraud, and I was told the interview would take 15 minutes. In fact, it only took about 5 minutes and at the end a photograph was taken to go on the ID card that is issued with the number on it.

So there I was, all finished before I was even due to start. The staff were very friendly and it all seems rather easy. Fingers crossed that the letter informing me of my number will arrive soon. It should take a week or so, so I’m told. After that I should be able to access as many personal services as I want whenever I want them. (Are you sure you have the right idea? Ed.)

For  the return trip  to Maynooth I got one of the slower commuter trains, stopping at intermediate stations and running right next to the Royal Canal, which runs from Dublin for 90 miles through  Counties Dublin, Kildare, Meath and Westmeath before entering County Longford, where it joins the River Shannon. One of the intermediate stations along the route next to the canal is Broombridge, the name of which stirred a distant memory.

A quick application of Google reminded me that the town of Broombridge is the site of the bridge (Broom Bridge) beside which William Rowan Hamilton first wrote down the fundamental result of quaternions (on 16th October 1843). Apparently he was walking from Dunsink Observatory into town when he had a sudden flash of inspiration  and wrote the result down on the spot, now marked by a plaque:

Picture Credit: Brian Dolan

This episode  is commemorated on 16th October each year by an annual Hamilton Walk. I look forward to reporting from the 2018 walk in due course!

P.S. Maynooth is home to the Hamilton Institute which promotes and facilitates research links between mathematics and other fields.

## Finlandia!

Posted in History, Music with tags , , , , on December 6, 2017 by telescoper

Today marks the 100th anniversary of Finland’s Declaration of Independence from Russia, which took place on 6th December 1917.

To celebrate the occasion here is  Finlandia by Jean Sibelius from this year’s Proms, performed by the BBC Singers, BBC Symphony Chorus and the BBC Symphony Orchestra, under the direction of Finnish conductor Sakari Oramo.

Happy Independence Day to Finns everywhere, and especially to my friends and colleagues in the world of physics and astronomy!

Posted in History with tags , on December 3, 2017 by telescoper

This is the book I brought with me to read while I stay here in St Patrick’s College, a Roman Catholic seminary…

## Historical References

Posted in Biographical, History, Maynooth with tags , , , , , , , on December 2, 2017 by telescoper

This morning, having a few hours free after breakfast before some househunting activities, I took a stroll to buy a newspaper and decided to take a few snaps.

First, here are a couple of pictures of St Patrick’s College, where I am staying. My room is on the top floor, to the left in the wing that juts forward from the main building. The chapel (with the spire) is on the other side.

The building I’m in forms the most impressive side of a quadrangle, one other part of which you can see in the second photograph.

St Patrick’s College was founded in 1795, and its style could best be described as Gothic Revival. It was in fact built as a theological college with funds supplied by King George III. There was a political reason for his largesse. Roman Catholicism was brutally suppressed in Ireland during and after the Eleven Years War in the mid-17th Century, culminating in the vicious subjugation of Ireland by Oliver Cromwell. In effect, the Catholic Church in Ireland was outlawed. Starting from about 1766 some of the restrictions on Catholics began to be removed, but there were no institutions in Ireland capable of training priests so all of those wishing to join the priesthood had to study abroad, primarily in France. George was worried that this would lead to an influx of priests whose heads were filled with revolutionary ideas from the continent, so he decided to fund a place where they could be taught in Ireland, where at least there could be some control over their education.

The old theological college of St Patrick (the `Pontifical University’) forms the core of what is now the South Campus of Maynooth University. Some of the old buildings here seem to take their names from the components of the old Liberal Arts degree: there is a Music House, Logic House, Rhetoric House and so on.

Next the entrance to the South Campus you can see this:

These are the remains of Maynooth Castle (or Geraldine Castle, after the Fitzgerald family), built around 1200. It was a huge and imposing fortress but now only the gatehouse and solar tower remain. It has violent history: heavily damaged in 1535 by siege cannons, its garrison surrendered only to be summarily executed. Rebuilt in the 1630s, it was destroyed completely in the 1640s during – you guessed it – the Eleven Years War. It has been a ruin ever since, but provides an intriguing entrance to the campus!

I’m by no means an architectural expert but I had a hunch that the Church (above) that stands opposite the Castle on the other side of the road leading into campus might also be quite old. Indeed it is. It was built in 1248 as the chapel to Geraldine Castle. It is now an Anglican Church, still used for regular worship.

The South Campus is separated from the North Campus (where the Science Building and other modern facilities are) by a main road. The North Campus is very new, most of the buildings are less than 20 years old. Here’s a picture showing the splendid library, with the spire of the chapel of St Patrick’s College in the background.  This is one of the few newer buildings on the South Campus: the pedestrian path you see leads to the main road that splits North and South Campuses.

Posted in History, The Universe and Stuff with tags , , , on November 29, 2017 by telescoper

I stumbled across a little video on Youtube (via Twitter, which is where I get most of my leads these days) with the title Why is it Dark at Night? Here it is:

As a popular science exposition I think this is not bad at all, apart from one or two baffling statements, e.g. “..the Universe had a beginning, so there aren’t stars in every direction”.  A while  ago I posted a short piece about the history of cosmology which got some interesting comments, so I thought I’d try again with a little article I wrote a while ago on the subject of Olbers’ Paradox. This is discussed in almost every astronomy or cosmology textbook, but the resolution isn’t always made as clear as it might be.  Here is my discussion.

One of the most basic astronomical observations one can make, without even requiring a telescope, is that the night sky is dark. This fact is so familiar to us that we don’t imagine that it is difficult to explain, or that anything important can be deduced from it. But quite the reverse is true. The observed darkness of the sky at night was regarded for centuries by many outstanding intellects as a paradox that defied explanation: the so-called Olbers’ Paradox.

The starting point from which this paradox is developed is the assumption that the Universe is static, infinite, homogeneous, and Euclidean. Prior to twentieth century developments in observation (e.g. Hubble’s Law) and theory  (Cosmological Models based on General Relativity), all these assumptions would have appeared quite reasonable to most scientists. In such a Universe, the intensity of light received by an observer from a source falls off as the inverse square of the distance between the two. Consequently, more distant stars or galaxies appear fainter than nearby ones. A star infinitely far away would appear infinitely faint, which suggests that Olbers’ Paradox is avoided by the fact that distant stars (or galaxies) are simply too faint to be seen. But one has to be more careful than this.

Imagine, for simplicity, that all stars shine with the same brightness. Now divide the Universe into a series of narrow concentric spherical shells, in the manner of an onion. The light from each source within a shell of radius $r$  falls off as $r^{-2}$, but the number of sources increases as $r^{+2}$. Multiplying these together we find that every shell produces the same amount of light at the observer, regardless of the value of $r$.  Adding up the total light received from all the shells, therefore, produces an infinite answer.

In mathematical form, this is

$I = \int_{0}^{\infty} I(r) n dV = \int_{0}^{\infty} \frac{L}{4\pi r^2} 4\pi r^{2} n dr \rightarrow \infty$

where $L$ is the luminosity of a source, $n$ is the number density of sources and $I(r)$ is the intensity of radiation received from a source at distance $r$.

In fact the answer is not going to be infinite in practice because nearby stars will block out some of the light from stars behind them. But in any case the sky should be as bright as the surface of a star like the Sun, as each line of sight will eventually end on a star. This is emphatically not what is observed.

It might help to think of this in another way, by imagining yourself in a very large forest. You may be able to see some way through the gaps in the nearby trees, but if the forest is infinite every possible line of sight will end with a tree.

As is the case with many other famous names, this puzzle was not actually first discussed by Olbers. His discussion was published relatively recently, in 1826. In fact, Thomas Digges struggled with this problem as early as 1576. At that time, however, the mathematical technique of adding up the light from an infinite set of narrow shells, which relies on the differential calculus, was not known. Digges therefore simply concluded that distant sources must just be too faint to be seen and did not worry about the problem of the number of sources. Johannes Kepler was also interested in this problem, and in 1610 he suggested that the Universe must be finite in spatial extent. Edmund Halley (of cometary fame) also addressed the  issue about a century later, in 1720, but did not make significant progress. The first discussion which would nowadays be regarded as a  correct formulation of the problem was published in 1744, by Loys de Chéseaux. Unfortunately, his resolution was not correct either: he imagined that intervening space somehow absorbed the energy carried by light on its path from source to observer. Olbers himself came to a similar conclusion in the piece that forever associated his name with this cosmological conundrum.

Later students of this puzzle included Lord Kelvin, who speculated that the extra light may be absorbed by dust. This is no solution to the problem either because, while dust may initially simply absorb optical light, it would soon heat up and re-radiate the energy at infra-red wavelengths. There would still be a problem with the total amount of electromagnetic radiation reaching an observer. To be fair to Kelvin, however, at the time of his writing it was not known that heat and light were both forms of the same kind of energy and it was not obvious that they could be transformed into each other in this way.

To show how widely Olbers’ paradox was known in the nineteenth Century, it is worth also mentioning that Friedrich Engels, owner of a factory owner in Manchester (in the Midlands) and co-author with Karl Marx of the Communist Manifesto also considered it in his book The Dialectics of Nature, though the discussion is not particularly illuminating from a scientific point of view.

In fact, probably the first inklings of a correct resolution of the Olbers’ Paradox were contained not in a dry scientific paper, but in a prose poem entitled Eureka published in 1848 by Edgar Allan Poe. Poe’s astonishingly prescient argument is based on the realization that light travels with a finite speed. This in itself was not a new idea, as it was certainly known to Newton almost two centuries earlier. But Poe did understand its relevance to Olbers’ Paradox.  Light just arriving from distant sources must have set out a very long time ago; in order to receive light from them now, therefore, they had to be burning in the distant past. If the Universe has only lasted for a finite time then one can’t add shells out to infinite distances, but only as far as the distance given by the speed of light multiplied by the age of the Universe. In the days before scientific cosmology, many believed that the Universe had to be very young: the biblical account of the creation made it only a few thousand years old, so the problem was definitely avoided.

Of course, we are now familiar with the ideas that the Universe is expanding (and that light is consequently redshifted), that it may not be infinite, and that space may not be Euclidean. All these factors have to be taken into account when one calculates the brightness of the sky in different cosmological models. But the fundamental reason why the paradox is not a paradox does boil down to the finite lifetime, not necessarily of the Universe, but of the individual structures that can produce light. According to the theory Special Relativity, mass and energy are equivalent. If the density of matter is finite, so therefore is the amount of energy it can produce by nuclear reactions. Any object that burns matter to produce light can therefore only burn for a finite time before it fizzles out.

Imagine that the Universe really is infinite. For all the light from all the sources to arrive at an observer at the same time (i.e now) they would have to have been switched on at different times – those furthest away sending their light towards us long before those nearby had switched on. To make this work we would have to be in the centre of a carefully orchestrated series of luminous shells switching on an off in sequence in such a way that their light all reached us at the same time. This would not only put us  in a very special place in the Universe but also require the whole complicated scheme to be contrived to make our past light cone behave in this peculiar way.

With the advent of the Big Bang theory, cosmologists got used to the idea that all of matter was created at a finite time in the past anyway, so  Olber’s Paradox receives a decisive knockout blow, but it was already on the ropes long before the Big Bang came on the scene.

As a final remark, it is worth mentioning that although Olbers’ Paradox no longer stands as a paradox, the ideas behind it still form the basis of important cosmological tests. The brightness of the night sky may no longer be feared infinite, but there is still expected to be a measurable glow of background light produced by distant sources too faint to be seen individually. In principle,  in a given cosmological model and for given assumptions about how structure formation proceeded, one can calculate the integrated flux of light from all the sources that can be observed at the present time, taking into account the effects of redshift, spatial geometry and the formation history of sources. Once this is done, one can compare predicted light levels with observational limits on the background glow in certain wavebands which are now quite strict .

## Friends at War

Posted in History, Politics with tags , , , on November 27, 2017 by telescoper

I found this letter by accident yesterday while I was searching for something else. Apparently, it’s very famous but I had never seen it before, and it struck me as unbearably moving. It was written by Sir William Waller to his friend Sir Ralph Hopton on 16th June 1643, during the (First) English Civil War and it is the last known communication between the two men. The former was a General in the Parliamentarian army, the latter held the same rank in the Royalist army.

This one heartbreaking letter reveals the tragedy that was unfolding all over the country at the time, as friends and families were torn apart by  forces not of their making but that proved impossible to to resist. It seems that countries are doomed to do this from time to time.

To my noble friend Sir Ralph Hopton at Wells

Sir,

The experience I have of your worth and the happiness I have enjoyed in your friendship are wounding considerations when I look at this present distance between us. Certainly my affection to you is so unchangeable that hostility itself cannot violate my friendship, but I must be true wherein the cause I serve. That great God, which is the searcher of my heart, knows with what a sad sense I go about this service, and with what a perfect hatred I detest this war without an enemy; but I look upon it as an Opus Domini and that is enough to silence all passion in me. The God of peace in his good time will send us peace. In the meantime, we are upon the stage and must act those parts that are assigned to us in this tragedy. Let us do so in a way of honour and without personal animosities.

Whatever the outcome I will never willingly relinquish the title of Your most affectionated friend.

William Waller

Following the eventual defeat of the Royalist cause Sir Ralph Hopton fled to the Continent with the young Prince Charles. He died of fever in Bruges in 1651. Sir William Waller served as a Member of Parliament but became increasingly disillusioned with the new Commonwealth and subsequently worked for the Restoration of the Monarchy, which began in 1660 with Charles II. Waller died in 1668.