In the Dark

Archive for 2010

Playfair

Posted in Crosswords with tags Azed, cipher, code, Crossword, Playfair on February 12, 2010 by telescoper

It’s been a while since I’ve blogged about my passion for crosswords, but this Sunday’s Azed puzzle in the Observer was one of my favourite kind so I thought I’d mention it briefly here.

Azed is the pseudonym used by Jonathan Crowther who has been setting the Observer crossword since 1972; this week’s was number 1967. His puzzles are usually standard cryptic crosswords which, though quite difficult as such things go, are nevertheless set in a fairly straightforward style. Every now and again, however, he puts together a different type of puzzle that makes a different set of demands on the solver. To be honest, I don’t always like these “funny” ones as they sometimes seem to me to be contrived and inelegant, but this last one was a type I really like as it combines the normal cryptic crossword style with another interest of mine, which is codes and codebreaking.

The interesting aspect of this particular puzzle, which is laid out on a normal crossword grid, is that it involves a type of code called a Playfair cipher. In fact, this particular scheme was invented by the scientist Charles Wheatstone whom most physicists will have heard of through “Wheatstone Bridge“. It was, however, subsequently popularized by Lord Playfair, whose name stuck rather than its inventor’s.

The Playfair scheme is built around the choice of a code word, which must have the special property that no letter occurs twice within it. Other than that, and the fact that the more letters in the codeword the better the code, there aren’t any real constraints on the choice. The particular example used by Azed to illustrate how it works is ORANGESTICK.

The codeword is used to construct a Playfair square which is a 5×5 arrangement of letters involving the codeword first and then afterwards the rest of the alphabet not used in the codeword, in alphabetical order. Obviously, there are 26 letters altogether and the square only holds 25 characters, so we need to ditch one: the usual choice is to make I stand for both I and J, doing double duty, which rarely causes ambiguity in the deciphering process. The Playfair square formed from ORANGESTICK is thus

This square is then used as the basis of a literal digraph substitution cipher, as follows. To encode a word it must first be split into pairs of letters e.g. CR IT IC AL. Each pair is then seen as forming the diagonally opposite corners of a rectangle within the word square, the other two corner letters being the encoded form. Thus, in the example shown, CR gives SG (not GS, which RC would give).

Where a pair of letters appears in the same row or column in the word square, its encoded form is produced from the letters immediately to the right of or below each respectively. For the last letters in a row or column the first letters in the same row or column become the encoded forms. Thus IC is encoded as CE. When all the pairs are encoded, the word is joined up again, thus CRITICAL is encoded as SGCICEOP.

The advantage of this over simpler methods of encipherment is that a given letter in the plain text is not always rendered as the same letter in the encrypted form: that depends on what other letter is next to it in the digraph.

Obviously, to decipher encrypted text into plain one simply inverts the process.

Now, what does this have to do with a crossword? Well, in a Playfair puzzle like the one I’m talking about a certain number of answers – in this case four – have to be encrypted before they will fit in the diagram. These “special” clues, however, are to the unencrypted form of the answer words. The codeword is not given, but must be deduced. We are, however, told that the answers to these special clues and the codeword are “semantically linked”.

What one has to do, therefore, is to solve the clues for the unencrypted words, then solve all the other clues that intersect with them on the grid. Given a sufficient number of digraphs in both plain text and encrypted form one can infer the codeword and hence encrypt the remaining (unchecked) letters for the special answers.

It probably sounds very convoluted, but in this puzzle it isn’t so bad because the four special clues weren’t so difficult. These are the following “across” clues:

1. Footman having to plough yard (6)

which gives “FLUNKY” – “plough” in university slang, meaning “fail” or “flunk” + y (standard abbreviation for yard).

18. Wallaby No. 2 in penalty infringement, right? (8)

has to be “OFFSIDER”, Australian slang for a deputy and hence Wallaby No. 2, with the cryptic allusion “OFFSIDE” for “penalty infringement” and R for “right”.

19. Staff inadequately blunder – many will conceal this (8)

this is the easiest – straightforward hidden word “UNDERMAN”, meaning “staff inadequately”.

32. Younger mussels one goes for in jar (6)

I think this is the best of this quartet of clues. The answer is “JUNIOR”, with “UNIO” (the genus of mussels) replacing the “a” (i.e. one) in JAR.

This set of answers clearly suggests the common theme that links them to the codeword. Moreover, the geometry of the grid along with the answers to the rest of the clues gives us ten digraphs in plain and encrypted form.

What has to be done then is to try to work out the Playfair square from the letter pairs, work out the codeword and then complete the unchecked letters in the specials in their encrypted form. It isn’t actually all that difficult to find the codeword in this example, by a mixture of induction and deduction. It turns out to be “SUBORDINATELY”, a fine candidate for a Playfair codeword as it is thirteen letters long and doesn’t feature any letter twice.

To enter the monthly Azed competition, however, one generally has to supply a clue as well as solving the puzzle. I’m really not very good at this aspect of crosswords- I much prefer solving the puzzles to setting ones of my own – which is why I’m quite a long way down the annual Azed Honours Table, in 29th place as of this month.

In the “Plain” competition puzzles, one has to supply a clue to replace one which is given as a straight definition. In this case a clue was requested to the codeword, but I think I’ll keep my attempt at “SUBORDINATELY” to myself unless and until I win at least an honourable mention!

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Astronomy Look-alikes, No. 15

Posted in Astronomy Lookalikes with tags James May, Keith Mason, STFC on February 11, 2010 by telescoper

Since it is rumoured that the BBC has decided to axe Top Gear, it’s fortunate that James May has an alternative career as Chief Executive of the Science and Technology Facilities Council. Still, all that experience of things crashing and burning seems to have stood him in good stead..

Professor Keith Mason

James May

14 Comments »

Astronomy Look-alikes, No. 14

Posted in Astronomy Lookalikes with tags Gustav Mahler, Ian Smail on February 10, 2010 by telescoper

Looking at my copy of this month’s Gramophone magazine reminded me that this year, 2010, sees the 150th anniversary of the birth of composer Gustav Mahler (born 7th July 1860). However, the front cover of the special celebratory issue of the esteemed organ that this event inspired features a photograph that reveals something of a likeness to Professor Ian Smail, another noted individual (geddit?) … though, perhaps, one not always known for his harmoniousness.

Gustav Mahler

Professor Ian Smail

Colour in Fourier Space

Posted in The Universe and Stuff with tags Cosmic Web., Cosmology, Fourier Phase, Fourier Transforms, large-scale structure of the Universe, Lung-Yih Chiang on February 9, 2010 by telescoper

As I threatened promised after Anton’s interesting essay on the perception of colour, a couple of days ago, I thought I’d write a quick item about something vaguely relevant that relates to some of my own research. In fact, this ended up as a little paper in Nature written by myself and Lung-Yih Chiang, a former student of mine who’s now based in his homeland of Taiwan.

This is going to be a bit more technical than my usual stuff, but it also relates to a post I did some time ago concerning the cosmic microwave background and to the general idea of the cosmic web, which has also featured in a previous item. You may find it useful to read these contributions first if you’re not au fait with cosmological jargon.

Or you may want to ignore it altogether and come back when I’ve found another look-alike…

The large-scale structure of the Universe – the vast chains of galaxies that spread out over hundreds of millions of light-years and interconnect in a complex network (called the cosmic web) – is thought to have its origin in small fluctuations generated in the early universe by quantum mechnical effects during a bout of cosmic inflation.

These fluctuations in the density of an otherwise homogeneous universe are usually expressed in dimensionless form via the density contrast, defined as $\delta({\bf x})=(\rho({\bf x})-\bar{\rho})/\bar{\rho},$ where $\bar{\rho}$ is the mean density. Because it’s what physicists always do when they can’t think of anything better, we take the Fourier transform of this and write it as $\tilde{\delta}$ , which is a complex function of the wavevector ${\bf k}$ , and can therefore be written

$\tilde{\delta}({\bf k})=A({\bf k}) \exp [i\Phi({\bf k})],$

where $A$ is the amplitude and $\Phi$ is the phase belonging to the wavevector ${\bf k}$ ; the phase is an angle between zero and $2\pi$ radians.

This is a particularly useful thing to do because the simplest versions of inflation predict that the phases of each of the Fourier modes should be randomly distributed. Each is independent of the others and is essentially a random angle designating any point on the unit circle. What this really means is that there is no information content in their distribution, so that the harmonic components are in a state of maximum statistical disorder or entropy. This property also guarantees that fluctuations from place to place have a Gaussian distribution, because the density contrast at any point is formed from a superposition of a large number of independent plane-wave modes to which the central limit theorem applies.

However, this just describes the initial configuration of the density contrast as laid down very early in the Big Bang. As the Universe expands, gravity acts on these fluctuations and alters their properties. Regions with above-average initial density ( $\delta >0$ ) attract material from their surroundings and get denser still. They then attract more material, and get denser. This is an unstable process that eventually ends up producing enormous concentrations of matter ( $\delta>>1$ ) in some locations and huge empty voids everywhere else.

This process of gravitational instability has been studied extensively in a variety of astrophysical settings. There are basically two regimes: the linear regime covering the early stages when $\delta << 1$ and the non-linear regime when large contrasts begin to form. The early stage is pretty well understood; the latter isn’t. Although many approximate analytical methods have been invented which capture certain aspects of the non-linear behaviour, general speaking we have to run N-body simulations that calculate everything numerically by brute force to get anywhere.

The difference between linear and non-linear regimes is directly reflected in the Fourier-space behaviour. In the linear regime, each Fourier mode evolves independently of the others so the initial statistical form is preserved. In the non-linear regime, however, modes couple together and the initial Gaussian distribution begins to distort.

About a decade ago, Lung-Yih and I started to think about whether one might start to understand the non-linear regime a bit better by looking at the phases of the Fourier modes, an aspect of the behaviour that had been largely neglected until then. Our point was that mode-coupling effects must surely generate phase correlations that were absent in the initial random-phase configuration.

In order to explore the phase distribution we hit upon the idea of representing the phase of each Fourier mode using a colour model. Anton’s essay discussed the RGB (red-green-blue) parametrization of colour is used on computer screens as well as the CMY (Cyan-Magenta-Yellow) system preferred for high-quality printing.

However, there are other systems that use parameters different to those representing basic tones in these schemes. In particular, there are colour models that involve a parameter called the hue, which represents the position of a particular colour on the colour wheel shown left. In terms of the usual RGB framework you can see that red has a hue of zero, green is 120 degrees, and blue is 240. The complementary colours cyan, magenta and yellow lie 180 degrees opposite their RGB counterparts.

This representation is handy because it can be employed in a scheme that uses colour to represent Fourier phase information. Our idea was simple. The phases of the initial conditions should be random, so in this representation the Fourier transform should just look like a random jumble of colours with equal amounts of, say, red green and blue. As non-linear mode coupling takes hold of the distribution, however, a pattern should emerge in the phases in a manner which is characteristic of gravitational instability.

I won’t go too much further into the details here, but I will show a picture that proves that it works!

What you see here are four columns. The leftmost shows (from top to bottom) the evolution of a two-dimensional simulation of gravitational clustering. You can see the structure develops hierarchically, with an increasing characteristic scale of structure as time goes on.

The second column shows a time sequence of (part of) the Fourier transform of the distribution seen in the first; for the aficianados I should say that this is only one quadrant of the transform and that the rest is omitted for reasons of symmetry. Amplitude information is omitted here and the phase at each position is represented by an appropriate hue. To represent on this screen, however, we had to convert back to the RGB system.

The pattern is hard to see on this low resolution plot but two facts are noticeable. One is that a definite texture emerges, a bit like Harris Tweed, which gets stronger as the clustering develops. The other is that the relative amount of red green and blue does not change down the column.

The reason for the second property is that although clustering develops and the distribution of density fluctuations becomes non-Gaussian, the distribution of phases remains uniform in the sense that binning the phases of the entire Fourier transform would give a flat histogram. This is a consequence of the fact that the statistical properties of the fluctuations remain invariant under spatial translations even when they are non-linear.

Although the one-point distribuition of phases stays uniform even into the strongly non-linear regime, they phases do start to learn about each other, i.e. phase correlations emerge. Columns 3 and 4 illustrate this in the simplest possible way; instead of plotting the phases of each wavemode we plot the differences between the phases of neighbouring modes in the x and y directions respectively.

If the phases are random then the phase differences are also random. In the initial state, therefore, columns 3 and 4 look just like column 2. However, as time goes on you should be able to see the emergence of a preferred colour in both columns, showing that the distribution of phase differences is no longer random.

The hard work is to describe what’s going on mathematically. I’ll spare you the details of that! But I hope I’ve at least made the point that this is a useful way of demonstrating that phase correlations exist and of visualizing some of their properties.

It’s also – I think – quite a lot of fun!

P.S. If you’re interested in the original paper, you will find it in Nature, Vol. 406 (27 July 2000), pp. 376-8.

11 Comments »

Astronomy Look-alikes, No. 13

Posted in Astronomy Lookalikes with tags Ian Roxburgh, Last of the Summer Wine on February 8, 2010 by telescoper

Some of you may previously have been unaware that Professor Ian Roxburgh of Queen Mary, University of London had an extremely successful career playing Compo in the longrunning television series Last of the Summer Wine. Sadly, I’ve been unable to find a look-alike for Nora Batty.

Compo

Ian Roxburgh

3 Comments »

RIP Sir John Dankworth

Posted in Jazz with tags Cleo Laine, Johnny Dankworth on February 7, 2010 by telescoper

I awoke this morning to news of the death of Sir John Dankworth (on Saturday 6th February) at the age of 82. I won’t write a long post about him today as the newspapers and television have been filled with glowing detailed tributes that do greater justice to his many achievements than I could possibly do. However, there is a special place in my heart for Jazz musicians, do I couldn’t let this sad event pass without paying a small tribute here.

John Dankworth was born in 1927 and started playing Jazz clarinet as a teenager in the 1940s, largely inspired by Benny Goodman. However, he soon came under the spell of Charlie Parker who was leading the way towards a new, “modern” kind of Jazz called bebop. In the early 1950s, the British jazz scene was split in two hostile camps, the traditionalists (exemplified at that time by Humphrey Lyttelton‘s band) and the modernists (exemplified by the lovely band that John Dankworth put together in 1952). The mutual loathing of the fans of these two kinds of music often erupted in the form of pitched battles which prefigured the fights between “mods” and “rockers” in the 1960s. You can find a fine example of John Dankworth with his 7-piece band (vintage 1950) here, playing a Charlie Parker tune called Marmaduke and showing the Parker influence clearly during his alto sax solo.

As I’ve often mentioned on this blog, my Dad played the drums with various jazz bands over the years but was firmly rooted in the traditionalist camp. I remember him telling me how furious he and his friends were when Humphrey Lyttelton’s marvellous trombonist Keith Christie defected to John Dankworth’s band in the 50s. It was like a Newcastle player signing for Sunderland. However, despite this treason, even diehard traddies like my Dad never had personal animosity towards John Dankworth, who was universally admired for his technical playing ability, encyclopedic knowledge of music and, above all, kindly and warm personality. But then musicians rarely think the same way that their fans do. Humph was a great admirer of John Dankworth’s music as, incidentally, was Benny Goodman of Charlie Parker’s…

Everyone who got to meet John Dankworth – which I did only once, and only very briefly – immediately came to the conclusion that he was a class act. A few days ago I quipped about how few remaining National Treasures we have in Britain. How could I have forgotten John Dankworth? Now he’s gone too.

He broke up his small group around 1952 or so to concentrate on running a big band, which gave him the opportunity to develop his talents as an arranger. During the 60s and 70s he became a prolific writer of TV and film music, including the original theme tune for Tomorrow’s World. However, it’s his partnership with Cleo Laine that I guess people will remember best. He hired her as a singer for his small band in 1951. . They married in 1958 and remained together for over 50 years, until separated by John’s death. She was (and is) a feisty lady, but you could tell whenever you saw them together at any time that John loved her very much.

Anyway, let’s go out on a high note with this lovely version of George Gershwin’s great tune Lady be Good. John Dankworth takes a back seat – as he often did when Cleo was singing – but the band is in great form. And if you didn’t realise what a terrific vocalist Cleo Laine was, then pin back your lugholes around 2 minutes in where she demonstrates a range and level of control that would put many opera singers to shame.

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(Guest Post) What is Colour?

Posted in Art, The Universe and Stuff with tags colour, Encaustic Painting, Goethe, Light, Newton, Olive Chedburn on February 7, 2010 by telescoper

As often happens on this blog, the comments following an item a few days ago went off in unexpected directions, one of which related to optics and vision. This led to my old friend, and regular commenter on this blog, Anthony Garrett (“Anton”), sending me an essay on the subject of colour perception and some very fine examples of abstract art. There thus appeared a perfect opportunity for another Guest Post, so for the rest of this item I’m handing over to Anton…

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Some years ago I was privileged to get to know, toward the end of her life, a retired teacher from Durham called Olive Chedburn. She made wonderful greeting cards which she sent to her friends, using a technique known as encaustic art. This employs heated beeswax with coloured pigment added, and a hot iron; you can read more about it at Wikipedia.

Here are the three pieces that she sent to me:

Although I am in general not a fan of abstract art, I think these are lovely. One friend said that they resembled underwater coral scenes. To me they look more like the inside of caves or chasms, perhaps with a waterfall. One of their beauties is that they definitely look like something – but you can never quite catch what.

Olive wrote a meditation on light and colour, in nature and in the Christian Bible, which I enjoyed reading very much. The main thing she left out was the science of light and colour, of which she had no knowledge. I wrote and sent her a complementary essay about this. Peter clearly likes her art and my essay, because he kindly offered to reproduce both on his blog, as you see. Olive died two years ago and her art now stands as her memorial. I hope you enjoy it as much as I did.

My essay now follows; if you want to look into the subject in greater depth then I recommend this website, which was designed to inform artists.

Colour perception is often said to be subjective. It is less clear what that means, however. The relevant scientific notion is wavelength. Light is a wave – although, remarkably, no physical medium oscillates (unlike sound waves in air, for instance); in the language of a century ago there is no ‘aether’.

Strictly speaking it would be better to talk about the frequency of light waves, because the wavelength changes with the density of the medium through which the light passes, but the frequency is unchanged. (The product of the wavelength and the frequency is the speed of light, which is a staggering 300,000 kilometers per second in empty space.) But the change in wavelength of light passing from a vacuum into air is so small that it can be ignored for present purposes. The change in wavelength (and in wave speed) is much greater when light passes into glass, or into the transparent fluids inside the eye, is much greater (25% reduction in water), since these media are much denser than air.

Light that consists of a single wavelength is called monochromatic light. Monochromatic light is not divided (further) by a prism, or by anything else that is done to it – a fact discovered by Isaac Newton in the 17th century. (Newton also reassembled the various colours back into white light.) One may superimpose differing amounts (intensities) of light of various wavelengths and look at the result. ‘White light’ is a superposition having roughly the same intensity in each colour band, as we confirm by putting it through a prism. (A prism splits light, because differing wavelengths of light entering the prism are shortened by differing amounts. The same effect creates rainbows as light passes through water droplets in the atmosphere.) In analysing colour, physics deals only the notion of how much light of each wavelength reaches the eye – the ‘spectrum’ (formally, the spectral density function) of the light. The distribution of the light across the retina – the screen at the back of the eye – also counts; a single object may appear to be coloured somewhat differently when viewed against differing backgrounds. Light has further characteristics (such as coherence, which is significant in lasers), but they make no difference to the perception of colour. A property of light known as its polarisation may change upon reflection from – or transmission through – a medium, but polarisation of light is not itself detected by the eye. (This raises the question: Are we interested in the object we are looking upon, or the light entering our eye?)

Wavelength is precisely defined, but colours – such as ‘blue’ – relate to a (fairly narrow) band of wavelengths, such that any monochromatic beam within that band will be perceived as blue. Moreover, if I add a low intensity of white light into blue, the result will still be perceived as blue. And if, in a spectrum that is generally agreed to be white, I make a small change in the amount of one particular wavelength, the result will still generally be agreed to be white. Only black is unambiguous: it is the absence of any light, of any wavelength. (Even then, it is the perceived absence, for light that is below the sensitivity threshold of the eye does not count; we shall consider perception below.)

We perceive some objects because they emit light into our eyes, such as a LED (light-emitting diode). Light of a particular frequency/wavelength/colour is emitted is when a (negatively charged) electron within an atom falls from one orbit around the positively charged atomic nucleus to another orbit around it; quantum theory tells us that only certain orbits are possible. (The difference in energy between the two orbits goes into the light that is emitted when the electron shifts orbit, and is proportional to the frequency of the light.) We see non-emitting objects because they reflect some of the light that falls on them, into our eyes. The colour that we say such an object is depends on the light that passes from the object to our eyes. This depends in turn on two factors: the combination of wavelengths falling on it; and how much of each particular wavelength the object reflects. (All light that is not reflected is absorbed, warming the object in the same way as sunbathing.) Intrinsic to the object is not its ‘colour’ but the proportion of each wavelength hitting it that it reflects. ‘Red paint’ means paint containing pigment that reflects only red light and absorbs all other colours (likewise for blue paint, etc); so that if ‘red paint’ is illuminated by a uniform mixture of light colours (i.e., white light) then only the red bounces back off it, and it looks red. But if the same object is illuminated by blue light, it absorbs the blue light so that (virtually) nothing comes off by way of reflection, and the object is perceived as black. We say that objects ‘are’ a particular colour because we generally view them in daylight or artificial white light, which contains all colours. ‘White paint’ is paint that reflects all colours and absorbs none. It looks whatever colour is shone at it – red in red light, blue in blue light, white in white light, and so on. Black paint absorbs all colours, and (uniquely) looks the same in any light.

A ‘red filter’ is something designed to let only red wavelengths through (and similarly for other filters). Something that lets all wavelengths through – the analogue of ‘white paint’ – is called transparent. (Air is virtually transparent, although it lets slightly more blue light through than other wavelengths – that is why the sky, which is lit by the many wavelengths emitted by the sun, looks blue.) Something that lets no light through – the analogue of black paint – is called a barrier. On its far side from the light source it looks black.

Also important is the texture of a surface. A perfectly reflecting material is colloquially called a white surface if it is rough enough to disperse incoming light in all directions, but if it is smooth on the scale of the incoming wavelengths then it is called a mirror. Texture is also responsible for the difference between matt and gloss paint. As for the scales involved, wavelengths of light visible to humans vary from red, which is around wavelength 0.7 micrometers (a micrometer is one thousandth of a millimetre) to blue/violet, which is about half that wavelength. In contrast, radio waves, which are of the same family and speed as light, have wavelengths of hundreds of metres.

Biological science can translate the physical specification of what lands on the retina into a specific pattern of nerve impulses passing from the eye to the visual cortex. That can in turn be correlated with the person saying “it’s green” or “it’s red” (or whatever). The names of colours are learned by tradition. As a child, each of us shared with an adult the experience of perceiving light of a particular wavelength; the adult named the colour and we learned the name. If children were not taught the names of colours then a consensus would emerge among them of what to call the colours, based on the similarity of their experiences. This consensus arises in turn from the common features of their perceptive systems (eye plus visual cortex).

Every colour to which humans give a name corresponds to a characteristic shape of the spectrum of wavelengths entering the eye. Lodged in the human retina are different types of colour receptor cells, known as cones. Each type of cone contains a different light-sensitive pigment, which absorbs and reacts most strongly to light of a particular wavelength. If you fire monochromatic light at a particular cone cell and then gradually decrease the wavelength (starting from red), the cell will transmit an increasingly strong signal to the brain until its own wavelength of peak sensitivity is reached; after that the signal will fall away on the other side the peak. Humans have three working types of cone cell, having distinct wavelengths of peak sensitivity. (The three sensitivity curves overlap to some extent.) This is why we can reasonably accurately simulate all colours that humans perceive by mixing just three colours, known as the primary colours.

People who are said to be colour-blind may have only two types of working cone, rather than three. They perceive the world differently, although they learn this only by observing that their reactions to certain wavelengths of light differ from the reactions of the majority. A man who was not colour-blind and whose cones of one particular type were suddenly switched off would see the world tinted, but a colour-blind man whose retinal cells had identical firing responses would say that things looked normal – because his brain would have trained itself from birth to regard this as the norm. Some species of animals have sensitivity spectra very different from the normal human one. Some animals see in black-and-white only (like humans at low light levels – see below); others have cone combinations with a less or a more uniform response than humans to light that is equally intense across the visual spectrum.

The mixing of primary colours of light to generate any colour known to human experience is a conceptually different problem from mixing paints to do the same. When you mix (‘add’) together light beams of the primary colours (Red, Green, Blue, roughly corresponding to the responses of the differing pigments in the three types of cone cells), you get white light. (Colour monitors and televisions have a multitude of ‘RGB’ dots.) These three are known as the ‘additive primary colours’. If you mix pigments of the three primary colours then the result is black paint, since each primary reflects only one colour, which the other primary pigments in the mixture suppress. Colour printers in fact mix cyan (which is blueish), yellow and magenta (pink-purple) in order to create all the colours known to man when the printer output is viewed in white light. These are the ‘subtractive’ primary colours, so named because if we subtract one of the additive primary colours from white light, leaving a mixture of the other two, we obtain the three subtractive primary colours. Whereas the mixing of light to obtain a desired colour is systematic, the mixing of pigment to do likewise is based on a library of knowledge gained by trial and error. Similarly, prediction of the colour of light that passes through consecutive glass jars of coloured translucent liquid (i.e., filters) is systematic, but the result of mixing the fluids is not.

Photography is conceptually more complicated than painting. What you see depends on further factors: the light that originally hit the photosensitive recorder; the response of the photosensitive recorder; the printing of the photograph (which may compensate for deficiencies in the response); and the light that the photograph is viewed in. Furthermore, negative film followed by printing and viewing; slide film viewing; digital photography viewed onscreen; and viewing a printout of a digital photograph each provide distinct re-creations at the eye of the light coming into the viewfinder.

Human perception of colour is actually more complex than I have stated. There are other cells in the retina called rods. These are more sensitive to light than cones but do not distinguish between colours. They come into their own at low levels of illumination; as a result, human vision under dimly lit conditions is essentially black-and-white. When the light intensity increases, beginning from darkness, the cones ‘kick in’ roughly when the rods become ‘saturated’ and send out no stronger signal as the brightness increases further. The brain also appears to take into account differences between the signals coming from the three types of cone, and differences between these and the rods.

A century after Newton, Goethe wrote on colour in an apparently opposing (and highly critical) way. Although what Newton had said was correct, hindsight makes it clear that Goethe was more concerned with the perception of colour than with the physics of light. We glimpse here two different philosophies: the ‘modern’ view espoused by the Enlightenment (no pun is intended on the name) that a world exists ‘out there’ to be explained (Newton), and the ‘post-modern’ view that our sensory impressions are all we have, and are therefore the most fundamental (Goethe). Goethe took the view that colour arises from the interplay between light and dark. Nowadays we have learned that humans perceive colours when they look at a spinning disc with a particular black-and-white pattern printed on it, for instance – presenting a challenge to theories of colour perception. Although Goethe’s explanations have been superseded, he was an acute observer of colour phenomena more complex than those analysed by Newton. There is still plenty to learn about the perception of colour.

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Results and Transfer Gossip

Posted in Finance, Football, Science Politics, Uncategorized with tags Cardiff City, Cardiff University, Newcastle United on February 6, 2010 by telescoper

I had to skip the usual trip to the Poet’s Corner last night and go home early because the general state of fatigue I’ve been in suddenly morphed into a fever. I went home at 5, went straight to bed, and it was only Columbo’s frantic pawing that woke me up several hours later. I had not only missed a leaving party for Kate Isaak, who is now off to work for the European Space Agency, but also slept all the way through Newcastle United’s splendid 5-1 hammering of Cardiff City in last night’s Coca Cola Championship match at St James’ Park.

Despite home advantage, and the fact that Newcastle won the corresponding away fixture here in Cardiff, I thought this tie would be pretty difficult for Newcastle so I was overjoyed to see the result when I finally roused myself from feverish slumbers. It seems that Newcastle’s recent signings in the January transfer window actually came good, especially Wayne Routledge who gives the side a much-needed injection of pace down the wing. Cardiff City, on the other hand, didn’t buy any players at all because they need all the cash they’ve got to pay off an outstanding tax bill and thwart various winding-up orders that have been served on them. The turbulence behind the scenes seems to have worked its way onto the pitch: the blues are definitely the most erratic team in the division, winning 6-0 only a week or so ago and then getting thrashed 5-1 yesterday.

And just to make my allegiances clear, I do have a soft spot for Cardiff City and do want to see them do well – except when they’re playing Newcastle. Once a Geordie, always a Geordie…

Results of a different kind were the topic of discussion around the School of Physics & Astronomy yesterday, as it was the official day for tutors to hand the results of the 1st semester exams to their tutees. It’s always great to see students leaving their tutor’s office with a big smile on their face, which happened rather a lot yesterday. Some, of course, got more disappointing news, but to them I’d just say that it’s only half way through the year so there’s plenty of time to recover. Stick at it, and don’t let setbacks get you down. I hope to see even more happy faces in June than I did yesterday….

Football teams like Cardiff City aren’t the only things to be enduring financial uncertainty these days, either. Even the Premiership clubs of the university sector are feeling the pinch. Many institutions around the country are planning departmental closures and redundancies, but you know it’s serious when it hits the big colleges in London. Last week University College (UCL) and Imperial both announced plans for large-scale layoffs, and this week they were joined by King’s College which plans to sack 205 academics, including 30 in the School of Physical Sciences and Engineering.

The background to all this is that the cuts announced by Lord Mandelson in December have now been officially passed on to English universities by HEFCE, but one suspects also that in some cases this is being used as a cover for other management decisions. Imperial, for example, is going ahead with the purchase of new property in Wood Lane for a cool £28 million at the same time as cutting academic positions costing a fraction of that.

Amid all the gloom, however, it is nice to be able to report some good news. Cardiff University was almost declared bankrupt in the 1980s when it failed to get to grips with the cuts imposed by Margaret Thatcher’s Conservative government which were similar in scale to those being implemented by New Labour. It was brought back from the brink, however, and since then has managed its finances with almost excessive caution. Other universities have scored spectacular successes in the League tables by spending money freely on fancy research initiatives and overseas campuses, but in the new reality of austerity Britain these may turn out to have been risky ventures.

By contrast, “Safe and Steady” has long been the motto in Cardiff. We might not have done brilliantly in the RAE but the insitution has an extremely sound financial base that should put it in as good position as any to withstand these difficult times. Moreover, we’ve just heard that the University management has agreed that the School of Physics & Astronomy can go ahead and make four new academic appointments, and that these will be accompanied by substantial startup packages with which the new appointees can begin to equip their own laboratories. This involves a considerable investment in the School from the University’s central coffers and I think it’s fantastic news. I doubt if many UK universities are going to be investing so heavily in physics at this time, so this is an extremely welcome development. It’s always nice to buck the trend.

The adverts will be going out pretty soon, so the transfer window is about to open. I look forward to meeting our new signings in due course, and I’m confident that they’ll help us climb up the League.

If only I could say the same for Cardiff City…

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Of the Last Verses in the Book

Posted in Biographical, Columbo, Poetry with tags Edmund Waller, Leonard Cohen, Of the Last verses in the Book, Poetry on February 5, 2010 by telescoper

I was having some quality Columbo time last night, giving my old moggy a good going-over with his favourite brush while watching a DVD featuring the detective with the same name. Columbo (the cat) loves being brushed with a metal brush, especially on his head and his face. If I stop he grabs hold of it and pulls it back onto his muzzle as if to say “All right then, I’ll do it myself.” He likes such a firm application of the brush that it seems incredible to me that it doesn’t hurt him, but he clearly enjoys it, so what the hell…

When I’d finished he looked even more handsome than usual, but as he sat next to me on the sofa I reflected on the fact that he is starting to show his age a bit especially around the face – possibly owing to his penchant for the brush! Nowadays his purring sounds more like snoring, his kittenish moments are rarer and crotchety episodes a bit more common. He also gets stiffness in his legs from time to time, which the vet attributes to rheumatism and, although it doesn’t cause him actual pain, this problem makes him a lot less active than he used to be. Still, he has a right to take things easy. He’ll be 16 next month, which is quite a venerable age for a Tom cat.

I’ve been feeling pretty old myself this week, probably caused by fatigue associated with the onset of lecturing. All that walking up and down and waving your arms about can be quite tiring, I can tell you. Not sleeping much might have something to do with it too. I’m also feeling miserable because I need new spectacles, another sign of ongoing physical deterioration. I’ve got less excuse for feeling my age than Columbo, however, as I’m only 46. I think that’s only about 6 in cat years!

However, getting older definitely has its good points too. Twenty years ago I would never have envisaged myself sitting at home reading dusty old poetry books rather than going out to some sleazy nightclub, but the cardigan, carpet slippers and Columbo are suiting me just fine these days. Next week I’m going to go wild and have a night at the Opera, something that always makes me feel young. I may be no chicken, but I’m still younger than the average opera-goer!

I haven’t posted any poems for a few days, so here’s one that seems to fit. It’s by a relatively obscure poet and politician called Edmund Waller. The wikipedia page about him isn’t very complimetary about his talents as a poet, but he is at least credited with having pioneered the use of heroic couplets in English verse. His biography is interesting too. He narrowly escaped being executed in 1643, during the English Civil War, and was instead imprisoned in the Tower of London. He was only released after paying a fine of £10,000 – a truly enormous amount of money for the time. Although banished on his release, he subsequently returned to politics and lived to the ripe old age of 81.

Although his poetry is very unfashionable, this one is quite well known and – I think – rather marvellous, especially the last verse which puts me in mind of the lines from Leonard Cohen‘s great song Anthem:

There is a crack in everything
That’s how the light gets in.

The poem is called Of the Last Verses in the Book.

When we for age could neither read nor write,
The subject made us able to indite.
The soul, with nobler resolutions deckt,
The body stooping, does herself erect:
No mortal parts are requisite to raise
Her, that unbodied can her Maker praise.

The seas are quiet, when the winds give o’er,
So calm are we, when passions are no more:
For then we know how vain it was to boast
Of fleeting things, so certain to be lost.
Clouds of affection from our younger eyes
Conceal that emptiness, which age descries.

The soul’s dark cottage, batter’d and decay’d,
Lets in new light through chinks that time has made;
Stronger by weakness, wiser men become
As they draw near to their eternal home:
Leaving the old, both worlds at once they view,
That stand upon the threshold of the new

(And, please, no jokes about “cottages”….)

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Value for Money?

Posted in Art, Biographical, Finance, Science Politics with tags Alberto Giacometti, Chateau Petrus, L'Homme qui Marche, Sotheby's, STFC, Wine on February 4, 2010 by telescoper

Looking at the BBC website at lunchtime while I munched a sandwich I’d bought for £1.40, the item that really caught my eye was a story about the sale of a sculpture at Sotheby’s for £65 million. The starting price for this particular work (L’Homme qui Marche by Alberto Giacometti) was set at £12 million, but only took a few minutes for the bidding to reach its final level. An anonymous bidder now gets to keep the sculpture, which will probably now be kept in a private location, or possibly even a bank vault.

Let me make it clear at the start that I’m not going to embark on a rant about modern art in general or Giacometti in particular. A couple of years ago I went to an exhibition of his work at the Museum of Modern Art in Louisiana, just north of Copenhagen (in Denmark) and I found his strange elongated figures really fascinating. He started out making small ones that he stretched and scratched obsessively to get the shape he wanted. Over time the figures got larger, but he didn’t make many of them. I suppose the rarity of his work has something to do with why they are so valuable, which they obviously are.

But when I say they’re fascinating, I don’t necessarily mean £65 million worth of fascinating….

The point that has always really fascinated me about this sort of thing is exactly how something can acquire such an absurdly high commercial value and what it is that makes any collector decide to pay such a huge price. A work of art obviously has some intrinsic worth, but there doesn’t seem to me to be any simple relation between aesthetic, technical or historical considerations and the market value. That’s not just the case for modern art, either. Go to the Louvre in Paris and you’ll see hordes of people clamouring around a small, drab and frankly rather uninteresting painting called the Mona Lisa – and ignoring the dozens of wonderful things all around them in the same room, and even in the corridor leading to it. Some process – I don’t know what – has assigned a particular status to this painting and not to others which seem to me to have at least as much value, in an artistic sense. Not that I’ve any right claim my judgement is any better than anyone else’s, of course.

A similarly mysterious process goes on with other collectible things. Take wine, for example. I like a glass of wine now and then – or rather more often than that, if truth be told. I am, however, very fortunate that I don’t have a particularly discerning palate. I can tell the difference between cheap-and-nasty stuff and pretty good stuff but, generally speaking, my taste has saturated by the time the price reaches about £25 a bottle, and often long before that. That’s great because it means I can have a perfectly enjoyable evening drinking a bottle costing £15 when if I’d been an expert I would be unsatisfied unless I spent a lot more.

Years ago I went with a friend of mine to a house clearance in rural Sussex. He was an interior designer and he liked to buy old furniture from country houses and do it up to sell on. It’s a good plan, actually – old furniture is far better made than the modern stuff. Anyway in the middle of a whole load of junk was a case of vintage wine. Not just any wine, either. It was, in fact, Chateau Petrus – one of the finest Pomerols. It wasn’t a specialist auction, however, and nobody seemed to think it had any value. Bidding was slow when it came up in front of the auctioneer so I bid for it. In the end I bought the case (12 bottles) for about £300. When I got it home I realised what I had got. It turned out £300 per bottle would have been cheap. I was scared to open any of the bottles in case the wine was off or I didn’t like it, so I put it away. I sold the case some years later for about £6500.

Having told that story though, my main point is to wonder out loud about those wines that cost thousands of pounds per bottle. There is a roaring trade in these things – even ones that are two hundred years old – but I don’t think their value has anything to do with how they are likely to taste. In the local wine merchant – conveniently located about 20 yards from my house – price is a good indicator of taste, but the scaling doesn’t apply at the extreme end of the fine wine market. Some other process is involved.

A house also has a value that doesn’t have anything to do with anything other than what someone will pay to buy it. But what sets this price? The market, obviously, but that is guided and controlled by Estate Agents who influence values in strange and subtle ways.

I suppose this all just goes to show I don’t know anything about economics, a point I’m now no doubt going to reinforce.

Governments also have to decide how much to spend on different things: health, education, defence, and so on. You can argue with the way their priorities work out at any given time, but the thing that baffles me is what the process is that leads to a decision to spend X on hospitals and Y on education. How can anyone possibly decide the relative value of £1 spent on health versus £1 spent on education?

I strongly support the notion that the government should support the performing arts, such as the Opera. But how much it should spend is an unfathomable question to me. Some will say nothing, some would say more. Who decides? Clearly someone does.

And that brings us back home to science. The ongoing ructions about the financial crisis at the Science and Technology Facilities Council – unfolding in front of a parliamentary select committee – seem to me to be really about the process by which value is assigned different bits of science by the people who hold the purse strings but probably don’t know much at all about science. I place a high value on astronomical research and, within that field, on cosmology. But that’s a personal judgement. Others will disagree. We all end up working in those areas we find more interesting than the others so we can’t really be unbiased, but I think I’m more even-handed than many when it comes to the scientific merits of other fields. Having said that, it would take a lot of doing to convince me that the scientific value for money involved in sending, say, another probe to the Moon was anything like as high as, say, exploiting the full potential of the Herschel observatory.

Worse still, all spending on blue skies research looks like to be cut back severely at the expense of shorter-term activity that leads to immediate commercial spinoffs. Commerce clearly trumps curiosity in the value game. If the STFC debacle was – as certainly seems likely to me – the result of a deliberate high-level decision, then who was it and what were their reasons for placing so little value on the quest to understand the most fundamental properties of the Universe?

And why doesn’t science have patrons like the anonymous buyer of the Giacometti figure? £65 million would solve an awful lot of STFC’s problems, as long as we stop certain people from wasting it on silly moon missions….

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