Archive for April, 2019

The Arthritic Cosmological Principle

Posted in Biographical with tags , on April 7, 2019 by telescoper

When I attended a meeting recently quite a few people expressed concern about my health given that I turned up with a walking-stick. I’ve actually been using one on occasions for quite a few months now, and it may well become a regular accessory, so to avoid anyone else I meet wondering what’s going on I thought I’d post a brief explanation.

Over the past six months or so I’ve had an increasing problem with swelling and stiffness in my knees. This is worst in the morning when I’ve just got out of bed, in which situation my knees are invariably bright red.

You can see what I mean in the picture here (viewer discretion advised). The stiffness sometimes makes me a bit wobbly on my pins and makes it a bit tricky dealing with stairs. I use the stick more for balance than anything else, and once I get going I can walk quite comfortably. I spent most of a day walking around Copenhagen without ill effects when I visited there in February.

I’ve been to the doctor several times about this and, although I’m still waiting for various test results, it’s clear that I have some form of arthritis. For the time being I’m just taking an anti-inflammatory drug which is quite effective at reducing the swelling. In due course I may be put on other medication, possibly involving a course of injections, and maybe even surgery. I’ll just have to wait and see about that.

The important thing is that, although I’m not exactly thrilled to have arthritis, I’m not in any real pain. It’s just a bit uncomfortable, that’s all, though that does make it hard to concentrate sometimes and it has impacted on my capacity to work long hours. I am sorry that I have missed some deadlines as a result.

You may or may not know that I used to run a lot when I was younger, including a few marathons and half-marathons. This has caused me some problems with my knees before, and I had minor surgery (arthroscopy) about 15 years ago to help with this. That procedure went pretty well, but I was warned that I was a relatively high risk for arthritis. It looks like the doctor wasn’t wrong! My running days are well and truly over, that’s for sure.

One other thing worth mentioning is that this condition does seem to be highly temperature-dependent. This last week the weather suddenly turned a lot colder and the arthritis definitely got worse. Perhaps in future I could learn to use the colour of my knees as some kind of forecasting method?

Der Englische Patient

Posted in Politics with tags , , on April 7, 2019 by telescoper

I couldn’t resist sharing this brilliant cartoon by Jürgen Tomicek

A challenge in the dark

Posted in Uncategorized on April 6, 2019 by telescoper

Answers through the Comments Box please..

Cherokee – Clifford Brown

Posted in Jazz with tags , , , , on April 6, 2019 by telescoper

Well, I’ve been on duty all day so far at the Open Day I mentioned yesterday and am about to knock off and go home for a rest but first I thought I’d share this wonderful version of Cherokee, a tune that because of its complex chord changes is generally regarded as a test piece for jazz musicians. You’d never guess that from the ease that Clifford Brown shows as he tackles the 64-bar harmonic labyrinth at a breakneck tempo. If you want an example of jazz as a white knuckle ride, this is it!

Clifford Brown was a phenomenal virtuoso on the trumpet and it’s so sad that he died so young, at the age of 25, in a car accident. This performance was recorded in August 1953 and features an extended solo by Clifford Brown followed by a series of four-bar exchanges with the great drummer Art Blakey. Other principals are Percy Heath on bass and John Lewis on piano; Gigi Gryce (alto) and Charlie Rouse (tenor) also participate on the intro and outro. Enjoy!

Theoretical Physics at Maynooth University Open Day!

Posted in Education, Maynooth with tags , on April 5, 2019 by telescoper

Well, tomorrow (Saturday 6th April)  is an Open Day at Maynooth University. If you want to find out more about it you can look here where you will find this video which has some nice views of the campus:

I used to give Open Day talks quite frequently in a previous existence as Head of School of Mathematical and Physical Sciences at the University of Sussex and now I’m at it again, giving a talk on behalf of the Department of Theoretical Physics this Open Day. If you come along, please come along to my talk (at 14.10 on Saturday)!

We also have a stall in the Iontas Building from 10.30, where you can meet staff and students and talk to them about the course, or anything else vaguely related to Theoretical Physics. There are other stalls, of course, but the Theoretical Physics one is obviously way more interesting than the others!

Looking for fun pictures to put in my talk I stumbled across this:

I think that’s the only one I need, really!

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.