Archive for June, 2009

First Digits and Electoral Fraud in Iran

Posted in Bad Statistics with tags , , on June 22, 2009 by telescoper

An interesting issue has arisen recently about the possibility that the counting of the recent hotly contested Iranian election results might have been fraudulent. I mention it here because it involves  Benford’s Law – otherwise known as the First Digit Phenomenon – which I’ve blogged about before.

Apparently what started this off was a post on the ArXiv by the cosmologist Boudewijn Roukema, but I first heard about it myself via a pingback from another wordpress blog.  The same blogger has written a subsequent analysis here.

I’m not going to go into this in more detail here: the others involved have an enormous headstart and in any case I wouldn’t want to try to steal their thunder.  Suffice to say that there is at least a suspicion that the distribution of first digits in the published results is more uniform than would be expected by chance, given the that the general behaviour under Benford’s Law is to have more digits beginning with the digit “1” than any other. This apparently paradoxical result is quite easily explained. It also provides a way to check for fraud in, for example, tax returns.  How it applies to election results is, however, not so clear and the analysis is a bit controversial.

I’m sure some of you out there will have time to look at this in more detail so I encourage you to do so…

 

Oh. The story is gathering momentum elsewhere too. See here.

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Mabel’s Dream

Posted in Biographical, Jazz with tags , , , on June 22, 2009 by telescoper

I could attempt to make a cheesy Radio 2 kind of link between my previous post and this one, along the lines of “From one dream to another..” but I don’t think I’ll bother.

Years ago my mum told me that she heard the tune Mabel’s Dream played on the piano by a friend of the family by the name of Johnny Handle. Best known as a folk musician (and founder member of a well-known band called The High Level Ranters) he is also a music teacher and musicologist with a wide range of interests in music.  I read somewhere that this lovely tune was originally written by Jelly Roll Morton and performed by him on solo piano, but I’ve never managed to locate a solo version. However, every time I try looking for it (which I did this evening) I seem to come across something really nice. Today was no exception.

By far the most famous recording of Mabel’s Dream was made by King Oliver and his Creole Jazz Band in Chicago in 1923. This was the band that the young Louis Armstrong belonged to before going on to make the classic Hot Fives and Hot Sevens, one of which I posted a bit ago. It’s interesting how different the earlier band sounds:  with two cornets (King Oliver and Louis Armstrong), clarinet (Johnny Dodds), and trombone (Honore Dutrey) playing  together virtually all the time except for short improvised solo breaks. King Oliver usually played lead cornet, at least in their earlier recordings, with Louis Armstrong playing a decorative counterpoint around him rather like a clarinettist might. Later on, they swapped leads freely and completely intuitively producing a sound that was entirely unique.

The ensemble playing is intricate, but the band had no written music preferring to work exclusively from “head” arrangements. Their music is consistently delightful to listen to, even though the recordings are very low-fi, with a succession of marchy themes that makes it impossible not to want to tap your feet when you listen to them. You can find their version of Mabel’s Dream here.

Over time, this classic type of polyphonic Jazz- derived from its New Orleans roots – gradually morphed  into musical form dominated by much simpler arrangements and a succession of virtuoso solos. This change was also reflected in the differing fortunes of Louis Armstrong and King Oliver. The former went on to become an international celebrity, while the latter lost all his savings when his bank went bust during the Wall Street Crash. He ended his days working as a janitor, and died in poverty in a dingy rooming house in Savannah, Georgia in 1938.

When the traditional Jazz revival happened after the Second Wold War, many fans turned against the Hot Sevens because they weren’t genuine “Noo Awlins” meaning that they hankered after music that was made more collectively and had less emphasis on the soloists. Across Europe in particular, many bands tried to recreate the sound of the earlier era of American Jazz, with varying degrees of success. 

Looking around for a version of Mabel’s Dream, I came across the following clip from a French band called The High Society Jazz Band which I think is just gorgeous. The recording was made at a live performance in 1960, at the height of the “trad” revival. The lineup of the band is just like King Oliver’s many years earlier, complete with the front line of two cornets, clarinet and trombone as well as piano, drums, banjo and sousaphone. Mostly it’s a deliberate note-for-note copy of the King Oliver version, but at a slightly slower tempo. Normally I don’t really go for deliberate copies like this, even if they’re meant as a tribute, but any two cornettists willing and able to copy Louis Armstrong and King Oliver deserve the greatest respect! Hats off , then, to Pierre Merlin and Claude Rabanit (two names quite new to me) for doing such a great job. In fact, I also like Pierre Atlan’s take on Johnny Dodd’s clarinet breaks, and the trombonist (Mowgli Jospin) deserves a mention for his name alone!

Midsummer Madness

Posted in Biographical, Music, Poetry with tags , , on June 21, 2009 by telescoper

I’ve just realised that the Summer Solstice happened this morning at about 6.47am British Summer Time (5h 46m 45s UTC). Astronomy buffs will know that’s the time when the Sun reaches its most northerly position in the sky, leading to the longest day in the northern hemisphere.

Since it’s also the bicentennial year of Felix Mendelssohn it was a no-brainer to decide to celebrate by picking one of the beautiful pieces he wrote as music for the play A Midsummer Night’s Dream by William Shakespeare.

Whenever anyone mentions that play I can’t help remembering the version of it we did at School. I only got to act in two plays when I was a schoolboy, but they were both authentically Shakespearean in the sense that all the parts, including the female ones, were played by boys. It was an all-boys school, you see. My best role was undoubtedly as Lady Macbeth in the Scottish play – a much more interesting part than her husband, if you ask me. The only other attempt at acting I ever engaged in was in A Midsummer Night’s Dream. Although I say so myself, my Bottom was the talk of the sixth form.

(I was going to say “and thereby hangs a tail”, but decided not to…)

I should also mention that I also saw Andy Lawrence playing the same part in the Queen Mary Players production of The Dream. I wonder if he remembers doing that?

Curiously, the phrase from which I got the title of this post (“this is very midsummer madness”) is not from this play but from Twelfth Night, a play whose title refers to winter time. I think it might have been a joke.

Anyway, I’m rambling. This clip is a plug for a new recording which sounds pretty good to me. I’ve picked the wonderful Notturno:

Postscript: I’m aware that some people might have been offended by some of the clerihews recently posted on this site. Sometimes the lure of a rhyme can take these into areas best left unvisited. I’d therefore like to offer these, the closing lines of A Midsummer Night’s Dream, by way of an apology. I’ve also now taken the Clerihews themselves offline, owing to a number of attempts to post  abusive and/or threatening comments on that page (none of which came from anyone actually named there).

If we shadows have offended,
Think but this, and all is mended,
That you have but slumber’d here
While these visions did appear.
And this weak and idle theme,
No more yielding but a dream,
Gentles, do not reprehend:
if you pardon, we will mend:
And, as I am an honest Puck,
If we have unearned luck
Now to ‘scape the serpent’s tongue,
We will make amends ere long;
Else the Puck a liar call;
So, good night unto you all.
Give me your hands, if we be friends,
And Robin shall restore amends.

I’m glad at least that nobody tried to do a clerihew about Puck. I mean, how could you possible find a rhyme for “Robin Goodfellow”?

Preview from Herschel

Posted in The Universe and Stuff with tags , , on June 20, 2009 by telescoper

I thought you might like to see this image from Herschel, which I got from the ESA website. The Spitzer/MIPS and the Herschel/PACS images of M51 at 160 µm are shown above. The advantage of the larger size of the Herschel telescope is clearly reflected in the much higher resolution of the image: Herschel reveals structures that cannot be discerned in the Spitzer image.

By golly, it seems to work!

Multiversalism

Posted in The Universe and Stuff with tags , , on June 17, 2009 by telescoper

The word “cosmology” is derived from the Greek κόσμος (“cosmos”) which means, roughly speaking, “the world as considered as an orderly system”. The other side of the coin to “cosmos” is Χάος (“chaos”). In one world-view the Universe comprised two competing aspects: the orderly part that was governed by laws and which could (at least in principle) be predicted, and the “random” part which was disordered and unpredictable. To make progress in scientific cosmology we do need to assume that the Universe obeys laws. We also assume that these laws apply everywhere and for all time or, if they vary, then they vary in accordance with another law.  This is the cosmos that makes cosmology possible.  However, with the rise of quantum theory, and its applications to the theory of subatomic particles and their interactions, the field of cosmology has gradually ceded some of its territory to chaos.

In the early twentieth century, the first mathematical world models were constructed based on Einstein’s general theory of relativity. This is a classical theory, meaning that it describes a system that evolves smoothly with time. It is also entirely deterministic. Given sufficient information to specify the state of the Universe at a particular epoch, it is possible to calculate with certainty what its state will be at some point in the future. In a sense the entire evolutionary history described by these models is not a succession of events laid out in time, but an entity in itself. Every point along the space-time path of a particle is connected to past and future in an unbreakable chain. If ever the word cosmos applied to anything, this is it.

But as the field of relativistic cosmology matured it was realised that these simple classical models could not be regarded as complete, and consequently that the Universe was unlikely to be as predictable as was first thought. The Big Bang model gradually emerged as the favoured cosmological theory during the middle of the last century, between the 1940s and the 1960s. It was not until the 1960s, with the work of Hawking and Penrose, that it was realised that expanding world models based on general relativity inevitably involve a break-down of known physics at their very beginning. The so-called singularity theorems demonstrate that in any plausible version of the Big Bang model, all physical parameters describing the Universe (such as its density, pressure and temperature) all become infinite at the instant of the Big Bang. The existence of this “singularity” means that we do not know what laws if any apply at that instant. The Big Bang contains the seeds of its own destruction as a complete theory of the Universe. Although we might be able to explain how the Universe subsequently evolves, we have no idea how to describe the instant of its birth. This is a major embarrassment. Lacking any knowledge of the laws we don’t even have any rational basis to assign probabilities. We are marooned with a theory that lets in water.

The second important development was the rise of quantum theory and its incorporation into the description of the matter and energy contained within the Universe. Quantum mechanics (and its development into quantum field theory) entails elements of unpredictability. Although we do not know how to interpret this feature of the theory, it seems that any cosmological theory based on quantum theory must include things that can’t be predicted with certainty.

As particle physicists built ever more complete descriptions of the microscopic world using quantum field theory, they also realised that the approaches they had been using for other interactions just wouldn’t work for gravity. Mathematically speaking, general relativity and quantum field theory just don’t fit together. It might have been hoped that quantum gravity theory would help us plug the gap at the very beginning of the Universe, but that has not happened yet because there isn’t such a theory. What we can say about the origin of the Universe is correspondingly extremely limited and mostly speculative, but some of these speculations have had a powerful impact on the subject.

One thing that has changed radically since the early twentieth century is the possibility that our Universe may actually be part of a much larger “collection” of Universes. The potential for semantic confusion here is enormous. The Universe is, by definition, everything that exists. Obviously, therefore, there can only be one Universe. The name given to a Universe that consists of bits and pieces like this is the multiverse.

 There are various ways a multiverse can be realised. In the “Many Worlds” interpretation of quantum mechanics there is supposed to be a plurality of versions of our Universe, but their ontological status is far from clear (at least to me). Do we really have to accept that each of the many worlds is “out there”, or can we get away with using them as inventions to help our calculations?

 On the other hand, some plausible models based on quantum field theory do admit the possibility that our observable Universe is part of collection of mini-universes, each of which “really” exists. It’s hard to explain precisely what I mean by that, but I hope you get my drift. These mini-universes form a classical ensemble in different domains of a single-space time, which is not what happens in quantum multiverses.

According to the Big Bang model, the Universe (or at least the part of it we know about) began about fourteen billion years ago. We do not know whether the Universe is finite or infinite, but we do know that if it has only existed for a finite time we can only observe a finite part of it. We can’t possibly see light from further away than fourteen billion light years because any light signal travelling further than this distance would have to have set out before the Universe began. Roughly speaking, this defines our “horizon”: the maximum distance we are in principle able to see. But the fact that we can’t observe anything beyond our horizon does not mean that such remote things do not exist at all. Our observable “patch” of the Universe might be a tiny part of a colossal structure that extends much further than we can ever hope to see. And this structure might be not at all homogeneous: distant parts of the Universe might be very different from ours, even if our local piece is well described by the Cosmological Principle.

Some astronomers regard this idea as pure metaphysics, but it is motivated by plausible physical theories. The key idea was provided by the theory of cosmic inflation, which I have blogged about already. In the simplest versions of inflation the Universe expands by an enormous factor, perhaps 1060, in a tiny fraction of a second. This may seem ridiculous, but the energy available to drive this expansion is inconceivably large. Given this phenomenal energy reservoir, it is straightforward to show that such a boost is not at all unreasonable. With inflation, our entire observable Universe could thus have grown from a truly microscopic pre-inflationary region. It is sobering to think that everything galaxy, star, and planet we can see might from a seed that was smaller than an atom. But the point I am trying to make is that the idea of inflation opens up ones mind to the idea that the Universe as a whole may be a landscape of unimaginably immense proportions within which our little world may be little more than a pebble. If this is the case then we might plausibly imagine that this landscape varies haphazardly from place to place, producing what may amount to an ensemble of mini-universes. I say “may” because there is yet no theory that tells us precisely what determines the properties of each hill and valley or the relative probabilities of the different types of terrain.

Many theorists believe that such an ensemble is required if we are to understand how to deal probabilistically with the fundamentally uncertain aspects of modern cosmology. I don’t think this is the case. It is, at least in principle, perfectly possible to apply probabilistic arguments to unique events like the Big Bang using Bayesian inference. If there is an ensemble, of course, then we can discuss proportions within it, and relate these to probabilities too. Bayesians can use frequencies if they are available but do not require them. It is one of the greatest fallacies in science that probabilities need to be interpreted as frequencies.

At the crux of many related arguments is the question of why the Universe appears to be so well suited to our existence within it. This fine-tuning appears surprising based on what (little) we know about the origin of the Universe and the many other ways it might apparently have turned out. Does this suggest that it was designed to be so or do we just happen to live in a bit of the multiverse nice enough for us to have evolved and survived in?  

Views on this issue are often boiled down into a choice between a theistic argument and some form of anthropic selection.  A while ago I gave a talk at a meeting in Cambridge called God or Multiverse? that was an attempt to construct a dialogue between theologians and cosmologists. I found it interesting, but it didn’t alter my view that science and religion don’t really overlap very much at all on this, in the sense that if you believe in God it doesn’t mean you have to reject the multiverse, or vice-versa. If God can create a Universe, he could create a multiverse to0. As it happens, I’m agnostic about both.

So having, I hope, opened up your mind to the possibility that the Universe may be amenable to a frequentist interpretation, I should confess that I think one can actually get along quite nicely without it.  In any case, you will probably have worked out that I don’t really like the multiverse. One reason I don’t like it is that it accepts that some things have no fundamental explanation. We just happen to live in a domain where that’s the way things are. Of course, the Universe may turn out to be like that –  there definitely will be some point at which our puny monkey brains  can’t learn anything more – but if we accept that then we certainly won’t find out if there is really a better answer, i.e. an explanation that isn’t accompanied by an infinite amount of untestable metaphysical baggage. My other objection is that I think it’s cheating to introduce an infinite thing to provide an explanation of fine tuning. Infinity is bad.

Old Talk

Posted in Books, Talks and Reviews, The Universe and Stuff with tags on June 16, 2009 by telescoper

I just stumbled upon a post about a talk I did last year at the Multi-Faith centre at the University of Derby. I’ll let you follow the link to see how the talk and discussion went, but here’s a copy of a photograph of me trying to talk with my mouth full.

The Cat and the Rat

Posted in Columbo on June 16, 2009 by telescoper

I was just about to go to work this morning when I heard a screaming sound from the garden. Thinking that Columbo had suffered another funny turn, I raced back into the house. There he was, sitting in the kitchen, pleased as punch, with a small wriggling animal in his mouth. He dropped it at my feet and it tried to escape by running up my leg. That took me a bit my surprise and I kicked out, sending the furry thing flying against the wall. Stunned, it fell to the ground and Columbo got hold of it again.

A few seconds later he let it go and, using my forensic skills to establish that it was dead (separation of the head from the body is quite a good indicator of death), I took it away before he could dismember it any further. This could have been the small creature that led him a merry dance under the decking some time ago. However, it wasn’t a mouse. The scaly tail proved beyond all doubt that what he’d caught was in fact a baby rat.

I hope its mother doesn’t come looking for it.

Anyway, this is the second remarkable thing that Columbo has experienced in the last few days. The other is that he seems to have acquired a girlfriend. A very pretty lady cat has started calling for him and, unlike all other cats that have entered his domain, Columbo doesn’t mind her at all. There’s not going to be any rumpy-pumpy of course – Columbo was “done” when he was a youngster – but they hang out together quite comfortably, and he cries when she goes away. She can easily jump up and climb over the fence at the back of the garden, whereas Columbo is too old. Still, it’s nice for him to have some company. She’s been here most days. Perhaps he was hoping to impress her with the rat he caught.

The cat that visits Columbo wears a collar and is friendly enough to let me look for her name on it, but there isn’t one there. I’ve decided to call her Maud, because she comes into the garden.