Approaching the Centenary of the 1919 Eclipse Expeditions

Posted in Books, Talks and Reviews, History, The Universe and Stuff on April 4, 2019 by telescoper

Just a brief post to alert my readers – both of them – to the fact that there’s a very big centenary celebration coming up, on May 29th. This is 100 years to the day since a total eclipse of the Sun provided the opportunity to test Albert Einstein’s (then) new theory of general relativity. This was the event that turned Einstein into a cultural icon. I’ll be posting about a number of things to commemorate this important happening – include some new things that I’ve been working on to do with this, and an event here in Maynooth – but for the mean time let me just mention a couple of imminent items.

One is that I am giving a 30-minute talk on the 1919 Eclipse Expeditions at the Ordinary Meeting of the Royal Astronomical Society in Burlington House in London on 12th April 2019 (that’s a week tomorrow). That’s the closest date to the centenary that could be managed, as the May meeting of the RAS is the Annual General Meeting at which there is no scientific programme and there are no meetings after that until October 2019.

The second thing is that I’ve written a review of three books based on the 1919 expeditions for Nature, which I’m told will be the lead piece in their Spring Books supplement, published on April 18th 2019.

Anyway, all this provides me with a good excuse to repost an old item here. I’ve written quite a lot about this in past years, including a little book and a slightly more technical paper. I decided, though, to post this little piece which is based on an article I wrote some years ago for Firstscience.

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The Eclipse that Changed the Universe

A total eclipse of the Sun is a moment of magic: a scant few minutes when our perceptions of the whole Universe are turned on their heads. The Sun’s blinding disc is replaced by ghostly pale tentacles surrounding a black heart – an eerie experience witnessed by hundreds of millions of people throughout Europe and the Near East last August.

But one particular eclipse of the Sun, eighty years ago, challenged not only people’s emotional world. It was set to turn the science of the Universe on its head. For over two centuries, scientists had believed Sir Isaac Newton’s view of the Universe. Now his ideas had been challenged by a young German-Swiss scientist, called Albert Einstein. The showdown – Newton vs Einstein – would be the total eclipse of 29 May 1919.

Newton’s position was set out in his monumental Philosophiae Naturalis Principia Mathematica, published in 1687. The Principia – as it’s familiarly known – laid down a set of mathematical laws that described all forms of motion in the Universe. These rules applied as much to the motion of planets around the Sun as to more mundane objects like apples falling from trees.

At the heart of Newton’s concept of the Universe were his ideas about space and time. Space was inflexible, laid out in a way that had been described by the ancient Greek mathematician Euclid in his laws of geometry. To Newton, space was the immovable and unyielding stage on which bodies acted out their motions. Time was also absolute, ticking away inexorably at the same rate for everyone in the Universe.

Sir Isaac Newton, painted by Sir Godfrey Kneller. Picture Credit: National Portrait Gallery,

For over 200 years, scientists saw the Cosmos through Newton’s eyes. It was a vast clockwork machine, evolving by predetermined rules through regular space, against the beat of an absolute clock. This edifice totally dominated scientific thought, until it was challenged by Albert Einstein.

In 1905, Einstein dispensed with Newton’s absolute nature of space and time. Although born in Germany, during this period of his life he was working as a patent clerk in Berne, Switzerland. He encapsulated his new ideas on motion, space and time in his special theory of relativity. But it took another ten years for Einstein to work out the full consequences of his ideas, including gravity. The general theory of relativity, first aired in 1915, was as complete a description of motion as Newton had prescribed in his Principia. But Einstein’s description of gravity required space to be curved. Whereas for Newton space was an inflexible backdrop, for Einstein it had to bend and flex near massive bodies. This warping of space, in turn, would be responsible for guiding objects such as planets along their orbits.

Albert Einstein (left), pictured with Arthur Stanley Eddington (right). Picture Credit: Royal Greenwich Observatory.

By the time he developed his general theory, Einstein was back in Germany, working in Berlin. But a copy of his general theory of relativity was soon smuggled through war-torn Europe to Cambridge. There it was read by Arthur Stanley Eddington, Britain’s leading astrophysicist. Eddington realised that Einstein’s theory could be tested. If space really was distorted by gravity, then light passing through it would not travel in a straight line, but would follow a curved path. The stronger the force of gravity, the more the light would be bent. The bending would be largest for light passing very close to a very massive body, such as the Sun.

Unfortunately, the most massive objects known to astronomers at the time were also very bright. This was before black holes were seriously considered, and stars provided the strongest gravitational fields known. The Sun was particularly useful, being a star right on our doorstep. But it is impossible to see how the light from faint background stars might be bent by the Sun’s gravity, because the Sun’s light is so bright it completely swamps the light from objects beyond it.

A scientific sketch of the path of totality for the 1919 eclipse. Picture Credit: Royal Greenwich Observatory.

Eddington realised the solution. Observe during a total eclipse, when the Sun’s light is blotted out for a few minutes, and you can see distant stars that appear close to the Sun in the sky. If Einstein was right, the Sun’s gravity would shift these stars to slightly different positions, compared to where they are seen in the night sky at other times of the year when the Sun far away from them. The closer the star appears to the Sun during totality, the bigger the shift would be.

Eddington began to put pressure on the British scientific establishment to organise an experiment. The Astronomer Royal of the time, Sir Frank Watson Dyson, realised that the 1919 eclipse was ideal. Not only was totality unusually long (around six minutes, compared with the two minutes we experienced in 1999) but during totality the Sun would be right in front of the Hyades, a cluster of bright stars.

But at this point the story took a twist. Eddington was a Quaker and, as such, a pacifist. In 1917, after disastrous losses during the Somme offensive, the British government introduced conscription to the armed forces. Eddington refused the draft and was threatened with imprisonment. In the end, Dyson’s intervention was crucial persuading the government to spare Eddington. His conscription was postponed under the condition that, if the war had finished by 1919, Eddington himself would lead an expedition to measure the bending of light by the Sun. The rest, as they say, is history.

The path of totality of the 1919 eclipse passed from northern Brazil, across the Atlantic Ocean to West Africa. In case of bad weather (amongst other reasons) two expeditions were organised: one to Sobral, in Brazil, and the other to the island of Principe, in the Gulf of Guinea close to the West African coast. Eddington himself went to Principe; the expedition to Sobral was led by Andrew Crommelin from the Royal Observatory at Greenwich.

British scientists in the field at their observing site in Sobral in 1919. Picture Credit: Royal Greenwich Observatory

The expeditions did not go entirely according to plan. When the day of the eclipse (29 May) dawned on Principe, Eddington was greeted with a thunderstorm and torrential rain. By mid-afternoon the skies had partly cleared and he took some pictures through cloud.

Meanwhile, at Sobral, Crommelin had much better weather – but he had made serious errors in setting up his equipment. He focused his main telescope the night before the eclipse, but did not allow for the distortions that would take place as the temperature climbed during the day. Luckily, he had taken a backup telescope along, and this in the end provided the best results of all.

After the eclipse, Eddington himself carefully measured the positions of the stars that appeared near the Sun’s eclipsed image, on the photographic plates exposed at both Sobral and Principe. He then compared them with reference positions taken previously when the Hyades were visible in the night sky. The measurements had to be incredibly accurate, not only because the expected deflections were small. The images of the stars were also quite blurred, because of problems with the telescopes and because they were seen through the light of the Sun’s glowing atmosphere, the solar corona.

Before long the results were ready. Britain’s premier scientific body, the Royal Society, called a special meeting in London on 6 November. Dyson, as Astronomer Royal took the floor, and announced that the measurements did not support Newton’s long-accepted theory of gravity. Instead, they agreed with the predictions of Einstein’s new theory.

The final proof: the small red line shows how far the position of the star has been shifted by the Sun’s gravity. Each star experiences a tiny deflection, but averaged over many exposures the results definitely support Einstein’s theory. Picture Credit: Royal Greenwich Observatory.

The press reaction was extraordinary. Einstein was immediately propelled onto the front pages of the world’s media and, almost overnight, became a household name. There was more to this than purely the scientific content of his theory. After years of war, the public embraced a moment that moved mankind from the horrors of destruction to the sublimity of the human mind laying bare the secrets of the Cosmos. The two pacifists in the limelight – the British Eddington and the German-born Einstein – were particularly pleased at the reconciliation between their nations brought about by the results.

But the popular perception of the eclipse results differed quite significantly from the way they were viewed in the scientific establishment. Physicists of the day were justifiably cautious. Eddington had needed to make significant corrections to some of the measurements, for various technical reasons, and in the end decided to leave some of the Sobral data out of the calculation entirely. Many scientists were suspicious that he had cooked the books. Although the suspicion lingered for years in some quarters, in the end the results were confirmed at eclipse after eclipse with higher and higher precision.

In this cosmic ‘gravitational lens,’ a huge cluster of galaxies distorts the light from more distant galaxies into a pattern of giant arcs. Picture Credit: NASA

Nowadays astronomers are so confident of Einstein’s theory that they rely on the bending of light by gravity to make telescopes almost as big as the Universe. When the conditions are right, gravity can shift an object’s position by far more than a microscopic amount. The ideal situation is when we look far out into space, and centre our view not on an individual star like the Sun, but on a cluster of hundreds of galaxies – with a total mass of perhaps 100 million million suns. The space-curvature of this immense ‘gravitational lens’ can gather the light from more remote objects, and focus them into brilliant curved arcs in the sky. From the size of the arcs, astronomers can ‘weigh’ the cluster of galaxies.

Einstein didn’t live long enough to see through a gravitational lens, but if he had he would definitely have approved….

Bad Statistics and the Gender Gap

Posted in Bad Statistics with tags , , , on April 3, 2019 by telescoper

So there’s an article in Scientific American called How to Close the Gender Gap in the Labo(u)r Force (I’ve added a `u’ to `Labour’ so that it can be understood in the UK).

I was just thinking the other day that it’s been a while since I added any posts to the `Bad Statistics’ folder, but this Scientific American article offers a corker:

That parabola is a  `Regression line’? Seriously? Someone needs to a lesson in how not to over-fit data! It’s plausible that the orange curve might be the best-fitting parabola to the blue points, but that doesn’t mean that it provides a sensible description of the data…

I can see a man walking a dog in the pattern of points to the top right: can I get this observation published in Scientific American?

 

 

Poisson (d’Avril) Point Processes

Posted in Uncategorized with tags , , , on April 2, 2019 by telescoper

I was very unimpressed by yesterday’s batch of April Fool jokes. Some of them were just too obvious:

I’m glad I didn’t try to do one.

Anyway, I noticed that an old post of mine was getting some traffic and when I investigated I found that some of the links to pictures were dead. So I’ve decided to refresh it and post again.

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I’ve got a thing about randomness. For a start I don’t like the word, because it covers such a multitude of sins. People talk about there being randomness in nature when what they really mean is that they don’t know how to predict outcomes perfectly. That’s not quite the same thing as things being inherently unpredictable; statements about the nature of reality are ontological, whereas I think randomness is only a useful concept in an epistemological sense. It describes our lack of knowledge: just because we don’t know how to predict doesn’t mean that it can’t be predicted.

Nevertheless there are useful mathematical definitions of randomness and it is also (somtimes) useful to make mathematical models that display random behaviour in a well-defined sense, especially in situations where one has to take into account the effects of noise.

I thought it would be fun to illustrate one such model. In a point process, the random element is a “dot” that occurs at some location in time or space. Such processes occur in wide range of contexts: arrivals of buses at a bus stop, photons in a detector, darts on a dartboard, and so on.

Let us suppose that we think of such a process happening in time, although what follows can straightforwardly be generalised to things happening over an area (such a dartboard) or within some higher-dimensional region. It is also possible to invest the points with some other attributes; processes like this are sometimes called marked point processes, but I won’t discuss them here.

The “most” random way of constructing a simple point process is to assume that each event happens independently of every other event, and that there is a constant probability per unit time of an event happening. This type of process is called a Poisson process, after the French mathematician Siméon-Denis Poisson, who was born in 1781. He was one of the most creative and original physicists of all time: besides fundamental work on electrostatics and the theory of magnetism for which he is famous, he also built greatly upon Laplace’s work in probability theory. His principal result was to derive a formula giving the number of random events if the probability of each one is very low. The Poisson distribution, as it is now known and which I will come to shortly, is related to this original calculation; it was subsequently shown that this distribution amounts to a limiting of the binomial distribution. Just to add to the connections between probability theory and astronomy, it is worth mentioning that in 1833 Poisson wrote an important paper on the motion of the Moon.

In a finite interval of duration T the mean (or expected) number of events for a Poisson process will obviously just be proportional to the product of the rate per unit time and T itself; call this product λ.

The full distribution is then of the form:

This gives the probability that a finite interval contains exactly x events. It can be neatly derived from the binomial distribution by dividing the interval into a very large number of very tiny pieces, each one of which becomes a Bernoulli trial. The probability of success (i.e. of an event occurring) in each trial is extremely small, but the number of trials becomes extremely large in such a way that the mean number of successes is l. In this limit the binomial distribution takes the form of the above expression. The variance of this distribution is interesting: it is alsol.  This means that the typical fluctuations within the interval are of order the square root of l on a mean level of l, so the fractional variation is of the famous “one over root n” form that is a useful estimate of the expected variation in point processes.  Indeed, it’s a useful rule-of-thumb for estimating likely fluctuation levels in a host of statistical situations.

If football were a Poisson process with a mean number of goals per game of, say, 2 then would expect must games to have 2 plus or minus 1.4 (the square root of 2)  goals, i.e. between about 0.6 and 3.4. That is actually not far from what is observed and the distribution of goals per game in football matches is actually quite close to a Poisson distribution.

This idea can be straightforwardly extended to higher dimensional processes. If points are scattered over an area with a constant probability per unit area then the mean number in a finite area will also be some number l and the same formula applies.

As a matter of fact I first learned about the Poisson distribution when I was at school, doing A-level mathematics (which in those days actually included some mathematics). The example used by the teacher to illustrate this particular bit of probability theory was a two-dimensional one from biology. The skin of a fish was divided into little squares of equal area, and the number of parasites found in each square was counted. A histogram of these numbers accurately follows the Poisson form. For years I laboured under the delusion that it was given this name because it was something to do with fish, but then I never was very quick on the uptake.

This is all very well, but point processes are not always of this Poisson form. Points can be clustered, so that having one point at a given position increases the conditional probability of having others nearby. For example, galaxies like those shown in the nice picture are distributed throughout space in a clustered pattern that is very far from the Poisson form. But it’s very difficult to tell from just looking at the picture. What is needed is a rigorous statistical analysis.

 

The statistical description of clustered point patterns is a fascinating subject, because it makes contact with the way in which our eyes and brain perceive pattern. I’ve spent a large part of my research career trying to figure out efficient ways of quantifying pattern in an objective way and I can tell you it’s not easy, especially when the data are prone to systematic errors and glitches. I can only touch on the subject here, but to see what I am talking about look at the two patterns below:

pointbpointa

You will have to take my word for it that one of these is a realization of a two-dimensional Poisson point process and the other contains correlations between the points. One therefore has a real pattern to it, and one is a realization of a completely unstructured random process.

I show this example in popular talks and get the audience to vote on which one is the random one. The vast majority usually think that the top  is the one that is random and the bottom one is the one with structure to it. It is not hard to see why. The top pattern is very smooth (what one would naively expect for a constant probability of finding a point at any position in the two-dimensional space) , whereas the bottom one seems to offer a profusion of linear, filamentary features and densely concentrated clusters.

In fact, it’s the bottom  picture that was generated by a Poisson process using a  Monte Carlo random number generator. All the structure that is visually apparent is imposed by our own sensory apparatus, which has evolved to be so good at discerning patterns that it finds them when they’re not even there!

The top  process is also generated by a Monte Carlo technique, but the algorithm is more complicated. In this case the presence of a point at some location suppresses the probability of having other points in the vicinity. Each event has a zone of avoidance around it; the points are therefore anticorrelated. The result of this is that the pattern is much smoother than a truly random process should be. In fact, this simulation has nothing to do with galaxy clustering really. The algorithm used to generate it was meant to mimic the behaviour of glow-worms which tend to eat each other if they get  too close. That’s why they spread themselves out in space more uniformly than in the random pattern.

Incidentally, I got both pictures from Stephen Jay Gould’s collection of essays Bully for Brontosaurus and used them, with appropriate credit and copyright permission, in my own book From Cosmos to Chaos. I forgot to say this in earlier versions of this post.

The tendency to find things that are not there is quite well known to astronomers. The constellations which we all recognize so easily are not physical associations of stars, but are just chance alignments on the sky of things at vastly different distances in space. That is not to say that they are random, but the pattern they form is not caused by direct correlations between the stars. Galaxies form real three-dimensional physical associations through their direct gravitational effect on one another.

People are actually pretty hopeless at understanding what “really” random processes look like, probably because the word random is used so often in very imprecise ways and they don’t know what it means in a specific context like this.  The point about random processes, even simpler ones like repeated tossing of a coin, is that coincidences happen much more frequently than one might suppose.

I suppose there is an evolutionary reason why our brains like to impose order on things in a general way. More specifically scientists often use perceived patterns in order to construct hypotheses. However these hypotheses must be tested objectively and often the initial impressions turn out to be figments of the imagination, like the canals on Mars.

Now, I think I’ll complain to wordpress about the widget that links pages to a “random blog post”. I’m sure it’s not really random….

 

 

Time-Varying Constants

Posted in The Universe and Stuff with tags , , , on April 1, 2019 by telescoper

Two serious questions crossed my mind during Friday’s very interesting talk about the redefinition of SI units. One is that the changeover to the new system takes place on 20th May, which is right in the middle of the examination period at Maynooth University. We will therefore have to supply two differents set of physical constants, one to go with examination papers taken before 20th May and the other for those taken afterwards. This will even affect those of us who like to use natural units in which, for example, Planck’s Constant is set equal to unity: after the redefinition of Planck’s constant on 20th May 2019, we will have to set its value in natural units to be equal to 0.99999999987.

The other question is that the new system of SI units presupposes that the constants of physics are actually constant and can therefore provide a stable framework. Many theories have been suggested in which the fundamental constants change with time. In the present context I feel obliged also to point out as an example the classic paper of Scherrer (2009) (PDF available here) the abstract of which reads:

We examine the time variation of a previously-uninvestigated fundamental dimensionless constant. Constraints are placed on this time variation using historical measurements. A model is presented for the time variation, and it is shown to lead to an accelerated expansion for the universe. Directions for future research are discussed.

This casts grave doubt on the motivation for the new system of SI units, at least until 12 noon.

Singular Shenanigans

Posted in Pedantry with tags , , , , , on March 31, 2019 by telescoper

I used the word `shenanigans’ in a recent post, after which I wondered to myself whether there’s such a thing as a single `Shenanigan’. The Oxford English Dictionary says yes, defining it thusly:

I was a little surprised by this as I’ve only ever heard this word in the plural, shenanigans, but there we are. Another thing that surprised me is the `Origin obscure’; even the One True Chambers says `Origin unknown’. I’d always assumed that this was a word of Irish origin like, e.g., `slogan’. The oldest uses given in the OED are all American, from the mid-19th Century which does not refute the possibility that it is based on an Irish word because of the huge Irish diaspora in the United States, especially after the Great Famine of the 1840s, but I’m surprised the main English dictionaries have been unable to locate the connection.

The best I’ve been able to do using Google is the Irish word sionnachulghim,meaning `to play tricks, to be foxy’ (from sionnach, `fox’). That seems to me to be a plausible idea, but not it’s conclusive. If anyone has any further thoughts on the origin of shenanigans I’d be very interested to hear them through the comments box below.

To return to my original thought that shenanigans was a noun that that only exists in the plural, if it were so it would belong to the class of Plurale Tantum (which I blogged about a long time ago, here in the context about whether `data’ is singular or plural). Other examples of English nouns that exist in the `plural only’ include: suds, entrails, outskirts, odds, tropics, riches, surroundings, thanks, heroics, faeces and genitalia.

To my mind you should treat your data the same way you treat your genitalia. Grammatically speaking, I mean.

160 Years of the Irish Times

Posted in Biographical, Crosswords, Politics with tags , , on March 30, 2019 by telescoper

With all the shenanigans surrounding yesterday’s non-Brexit Day I quite missed the news that March 29th 2019 was an important for my newspaper of choice, The Irish Times, which was first published on March 29th 1859, the front page of which is reproduced above. Initially The Irish Times was only published on Tuesdays, Thursdays and Saturdays but it became a daily paper a few months after its launch, in June 1859.

The first edition promised to

make a first-rate Irish newspaper, complete in its details, sagacious and consistent in its policy and faithfully reflecting the opinions of the most independent, intelligent and truly progressive portion of Irish society.

That pretty much applies to it now, I’d say. Interestingly, though, it started out as a staunchly Unionist paper and every one of its editors until 1986 was a Protestant.

I don’t buy a paper every day but I do always get the Weekend Edition, which is full of excellent writing (even if often disagree with its take on various things).

It’s interesting to note that the front page of the first edition was dominated by goings-on in the House of Commons in Westminster, as is today’s edition. Plus ça change..

The only real drawback to the Irish Times is that it doesn’t have a very good cryptic crossword. Fortunately, the UK papers give theirs away for free so I now do the Financial Times, Guardian and Observer Prize Crosswords without buying them.

A Change of Units

Posted in The Universe and Stuff with tags , , , , on March 29, 2019 by telescoper

To round off a very strange week I’ve just been to an interesting talk by Dr Bajram Zeqiri of the National Physical Laboratory in Teddington (UK) about imminent changes to the International System of Units (usually known as SI units). In a nutshell, what is to happen is that the current seven base units are to be redefined in terms of fundamental constants. In effect this means that the these constants will fix the standard units rather than the other way round. For more details, see here. The change is due to come into effect on 20th May 2019.

Our speaker Dr Zeqiri is nearing the end of a short tour of Ireland speaking about these changes. Before giving the third talk on this subject talk today, 29th March 2019, thought to be the date on which the United Kingdom would leave the European Union, he wondered whether he might be able to claim political asylum in Ireland. Fortunately, today is not Brexit Day and following today’s events in Westminster it is by no means certain when that might be or indeed whether Brexit will even happen at all…

Machine Learning in the Physical Sciences

Posted in The Universe and Stuff with tags , , , , , on March 29, 2019 by telescoper

If, like me, you feel a bit left behind by goings-on in the field of Machine Learning and how it impacts on physics then there’s now a very comprehensive review by Carleo et al on the arXiv.

Here is a picture from the paper, which I have included so that this post has a picture in it:

The abstract reads:

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences.This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges.

The next step after Machine Learning will of course be Machine Teaching…

BICEP2: Is the Signal Cosmological?

Posted in Astrohype, The Universe and Stuff with tags , , on March 28, 2019 by telescoper

An article in Physics Today just reminded me just now that I have missed the fifth anniversary of the BICEP2 announcement of `the detection of primordial gravitational waves’. I know I’m a week but I thought I’d reblog the post I wrote on March 19th 2014.You will see that I was sceptical…

..and it subsequently turned out that I was right to be so.

telescoper's avatarIn the Dark

I have a short gap in my schedule today so I thought I would use it to post a short note about the BICEP2 results announced to great excitement on Monday.

There has been a great deal of coverage in the popular media about a “Spectacular Cosmic Discovery” and this is mirrored by excitement at a more technical level about the theoretical implications of the BICEP2 results. Having taken a bit of time out last night to go through the discovery paper, I think I should say that I think all this excitement is very premature. In that respect I agree with the result of my straw poll.

First of all let me make it clear that the BICEP2 experiment is absolutely superb. It was designed and built by top-class scientists and has clearly functioned brilliantly to improve its sensitivity so much that it has gone so…

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Brexit: What’s the Indicative Mood?

Posted in Pedantry, Politics with tags , , , , , on March 27, 2019 by telescoper

If you are confused about today’s `Indicative Votes’ in Parliament on Brexit let me provide some helpful information about the indicative mood, and how it relates to Brexit.

The English word “exit” is derived from the third person singular of the present tense in the indicative mood in the active voice of the Latin verb “exire” (“to go out”) i.e. it means “he/she/it leaves”, though the noun form it usually has in English derives from the supine form “exitus”. I feel it is important that we all get used to the grammar of Brexit, so here is a fairly complete list of the parts of the verb `Brexire’ in the active voice of the indicative mood, some or all of which may be relevant in the forthcoming debates, complete with accents to assist punctuation. At least these may prove useful in following any contributions from Jacob Rees-Mogg.

First let’s start with the basics:

Infinitive: Brexīre
Present participle: Brexiēns; Brexiéntis
Future participle: Brexītúrus
Gerund: Brexeúndum
Gerundive: Brexeúndus

And now here are representative examples of the conjugation of the verb Brexire in various tenses of the Indicative Mood in the order: first, second and third person singular followed by first, second and third person plural:

Present:

Brexeō,
Brexīs
Brexit
Brexīmus
Brexītis
Brexeunt

Past Imperfect

Brexībam
Brexībās
Brexībat
Brexībāmus
Brexībātis
Brexībant

Past Perfect

Brexiī
Brexīstī
Brexiit
Brexíimus
Brexīstis
Brexiḗrunt

Pluperfect

Brexíeram
Brexierās
Brexíerat
Brexierāmus
Brexierātis
Brexierant

Future Simple

Brexībō
Brexībis
Brexībit
Brexībimus
Brexībitis
Brexībunt

Future Perfect

Brexíerō
Brexíeris
Brexíerit
Brexiérimus
Brexieritis
Brexierint

The last tense here is not really relevant, but I’ve included it anyway.

No doubt when the Indicative votes are over, the House of Commons will proceed to the Subjunctive Mood – or even directly to the Imperative – but I shall leave these to a future post.