The Idle Scientist

Not Again

2009-06-05T18:58:00.004+01:00

Continue to invest in the UK's world class science base and develop strategies for commercialising more of that science.

This is what's being tossed around by the Government as the reason for the reorganisation (again) of the departments to give us the shiny new Department for Business, Innovation and Skills which will take over responsibility for science funding. The reaction from those scientists who've commented since the announcement this afternoon? 'We're doomed' seems to sum it up.

It has been pointed out before (I think Carl Sagan once answered a press conference question to this effect, but I can't recall where or when) that if you want commercially useful science, the one thing you should not do is attempt any kind of scheme for developing commercially useful science. You fund research, and new stuff comes along. A lot of it is only good for trivial things like discovering our place in the universe etc etc, but you get fancy spin-offs and everyone's happy.

More worrying, however, is when polititians say they want to fund commercially viable science, what generally happens is that everything without an immediately obvious material benefit gets cut. Short-sighted economically, for the reason above, but disastrous for science as a whole. I know these are times when the Government must try to save money, but there has to be more to life than just profit maximising.

It's not just confined to the current objects of my annoyance, but there does seem something awfully hollow about the present Government. They'll fund some cultural projects, but they don't seem to like them - they're just publicity events. They'll fund some scientific research, but they don't seem interested - it's just potential business capital.

Rant over.

Efficient Area

2009-04-09T10:53:00.002+01:00

Further to my post of units in science, here's a thought:

The efficiency of a car is measured in miles per gallon (or kilometers per litre, or miles per litre or whatever). That is, length travelled per volume of fuel consumed.

We can express this as a length divided by a length cubed - m / m³ if we're using SI. But this works out to be a reciprocal area, 1/m² .

So what's the meaning of this area that somehow describes the fuel efficiency of a car? It's the cross-sectional area of a pipe laid by the road containing stationary fuel such that the amount of fuel you pass is exactly enough to keep the car moving at the present speed.

Hammer Time

2009-04-04T12:51:00.003+01:00

I've been away for a couple of weeks, happily bashing away at rocks in the West Country with my hammer. Spending a fortnight in the company of geologists does odd things to your brain - anyone who thinks the internet has a monopoly on memetic mutation hasn't encountered the running jokes that develop in science departments.

A list of stereotypical traits of geologists that seem to be true a disproportionate amount of the time:

1. Long hair and/or beard
2. Drinks real ale
3. Likes walking and camping
4. Likes folk music
5. Married to another geologist

On a similar subject, almost all the mathematicians I know speak - or are learning - Chinese (none of them actually are Chinese). Why the correlation, I wonder?

The Thagomizer

2009-02-28T23:54:00.000Z

This makes me happy.

That is all.

Die? No!

2009-02-24T16:55:00.003Z

'Early Tertiary dinosaurs' is a fairly controversial phrase to utter in the palaeontological community. It crops up now and again when dinosaur-like fossils crop up in deposits thought to be Cenozoic in age.

[Before I go any further, a word of explanation for those not in the know. The dinosaurs were predominant during the Mesozoic Era which came to an end about 65 million years ago, succeeded by the Cenozoic. The Tertiary refers to everything between then and the beginning of the current Ice Age, after which is the Quaternary. Tertiary and Quaternary are old terms and don't fit neatly into the nice modern hierarchical system of time divisions, but they're pretty convenient]

Now, non-avian dinosaurs are not found - at least, not found definitively - after the end of the Mesozoic, the so-called 'K-T boundary'. However, it's entirely feasible that they hung around for a little while longer; after all, the birds are still going strong and are themselves a variety of dinosaur, hence my use of 'non-avian dinosaurs' at the beginning of this paragraph.

However, we do occasionally find teeth and even sometimes bones in early Tertiary deposits that look dinosaurian. So we are faced with four possibilities:

1. Dinosaurs lasted notably longer than we previously thought.

2. They're not dinosaur remains.

3. They are dinosaur remains, but reworked from previous sediments. That is, they were washed out of older rocks as they eroded and were carried along to be included in younger layers.

4. The rocks are older than we thought.

Which of these is true likely depends on particular deposits of these remains. But I want to look at the problem itself and what it actually means.

Because it depends entirely on what you mean by 'K-T boundary'. We're so used to hearing confident dates for these things that frequently we forget what they mean in practice. And people use 'boundary' in so many ways. Such as:

The Maastrichtian mass extinction event, associated with the disappearance of many forms of life, including the dinosaurs, ammonites, icthyosaurs etc.

A point in the rock record marked by or correlated with a layer of iridium and shocked quartz thought to be the effect of a giant asteroid hitting the Earth at Chixulub. By extension, the point at which this asteroid hit.

A stratigraphic boundary recognisable - though differently formed - in many parts of the world by change of depositional environment and/or fossil assemblage. Presumably associated with the above.

But none of these really mean the same thing. Let us assume for the moment that this asteroid did hit at the date believed - a fairly solid proposal - and that it was what directly caused the mass extinction of the dinosaurs and various other groups. What does this mean for our Tertiary dinosaur hypothesis?

Well, not all of the dinosaurs would have died at once. The fact that some creatures survived is indicative of non-total destruction. Therefore, dinosaurs would almost certainly have struggled on for a little longer. Whether they did so for years or for millions of years; in tiny numbers or as marginal but notable populations we do not know. So if we defined the beginning of the Tertiary as the moment - or even the day or the year - of the impact then yes, there were Tertiary dinosaurs. Maybe not long-lasting, but they were there.

But this is something of a impractical definition. It's pretty obvious that the mass extinction wasn't instantaneous, so why not give the boundary a width as well as a location and define it by the extinction itself, as per the first bullet point above? Now things are more interesting. The presence of Cenozoic dinosaurs in this way of thinking would require one or more populations to survive not only the impact but the associated traumas and extinctions. Only if they then disappeared on their own, after the massive tide of deaths would they truly count as Tertiary. And this is the real nub of the question, because what people actually want to know is not what we call the point that dinosaurs disappeared, but did the dinosaurs actually become extinct as a group, or was it more complex than it might appear? Were they doomed from the moment of impact, or did some of them achieve stability afterwards only to be killed off for some other reason?

Not So Crystal Clear

2008-12-31T11:00:00.009Z

It is exceedingly apparent today that ice defines our world to a great degree. Here I am, about three thousand miles from the North Pole and it's still sub-zero outside my window. Hardly suprising given that we're in the middle of an ice age, although admittedly people tend not to think about it like that.

Ice is a mineral * , and that's something else that seems a little odd, though if you think about it there's no reason why not - it's a crystalline solid with a characteristic composition, it's just that it has a nice low melting point. Actually it's a family of minerals, because all the water molecules can pack together in different ways, giving the different types of ice different physical properties.

The reason snowflakes are hexagonal (unless you break them, obviously) is because pretty much all the ice you'll encounter on Earth is of the hexagonally symmetric variety. What I mean by this is best illustrated by a diagram of how the molecules link to each other:

The hexagonal symmetry is pretty plain looking down this axis. This is going to affect the way the crystal grows and therefore the overall appearance. It's one of the most useful principles for mineralogists that the macroscopic properties of a crystal are indicative of its microscopic structure. In this case, the growth faces of the snowflake have to be arranged with hexagonal symmetry looking down this axis.

(Incidentally, there is no reason why two snowflakes cannot look the same. But given the vast number of possible flakes and the endless variations in initial conditions the chances of finding two identical ones are minimal)

But as I mentioned earlier, there is more than one type of ice and I don't simply mean that in the sense of frost/rime/sheet ice/wrong type of snow. They're all the hexagonal form of ice, ice I-h as it's know. In all, there are fifteen different structures (if one includes amorphous ice - 'ice glass' as it is also known, more on the unconventional use of the word 'glass' another time) with one more predicted but not yet observed definitively. These other forms are only really observed in unusual circumstances or in conditions not encountered on Earth.

Some of them have unexpected properties indeed. Ice XI is 'ferroelectric' - it establishes an electric dipole with a positive end and a negative end, analogous to a magnet with a north and south pole. Ice VI and VII also do odd things with electricity, although in more abstract ways.

This multiplicity of forms masquerading as pure simplicity - for what could appear purer or more regular than clear ice? - is a common theme in mineralogy. It is also a prime example of the importance of interaction in explaining the properties of materials - all the ices have the same chemical formula, the same chemical properties. But the interactions between the identical molecules produce a dazzling variety of possibilities, something mirrored in the infinity of forms of the silica minerals. To drive the point home, over 60% of all the rocks that make up the crust of earth is silica, the same stuff of which glass and quartz are made.

* The Greek for for ice, 'krystallos', gives us our word 'crystal'.

A Colourful Tale

2008-12-06T18:08:00.011Z

Yeah, it's been a long time since the last post. Blame endless piles of work and similar commitments. Anyway, I'm going to talk about light and colour today, via a rather oblique approach. Bear with me.

Here we have two photographs taken down a microscope of a sample of kimberlite, a rock found frequently in South Africa - it's where all those diamonds come from. This sample doesn't have any, though, I chose it to point out the grains of olivine. They're the highly cracked ones in the upper-left, brightly coloured in the right-hand photo.
Now, the coloured photo has not been digitally altered in any way. The colours are not made up - they are there naturally given the right conditions.
What happens is this - a petrographic microscope has two polarising filters, one above the sample which is fixed in place and one above that can be put in and out, called the analyser. A polarising filter, by the way, is a little screen that lets light through only if it is vibrating in the correct orientation.
Any light that's vibrating at the correct orientation (ie. parallel to the grid) goes straight through, any that is perpendicular gets totally blocked and any that is somewhere between the two gets broken down into a parallel component and a perpendicular component. The polarised light then proceeds to travel through the crystals that make up the rock.
As you can probably see, the presence of the analyser creates some possibilities. If it has the same orientation as the polariser, it might as well not be there, as it does nothing that has not already been done. And if it is perpendicular, it'll just block out everything that got through the first time.
As it happens, the analyser is always fixed perpendicular to the polariser. And yet somehow we get an image of the rock, in many bright colours. Something funny must be going on.

What's happening is this: when the newly polarised light passes into a crystal, it encounters obstruction from the atoms, electrons etc. Crystals, by their nature, have internal structure and some directions are going to be more obstructed than others. Without going into the physics of this too deeply, the asymmetrical obstruction creates a twisting effect on the light - the polarisation it has when it goes in is not necessarily the polarisation it has coming out again. So we get some light that's capable of passing through the analyser after all.
What about the colours, though? Well, another effect of the crystal on the light is that some of it gets bent and comes out with a delay:

This means that those rays in the above diagram are going to be out of phase (the peaks and troughs in their vibration will not match up properly). But remember that white light is composed of many different wavelengths (ie colours) of light all mixed up. They won't all match up or fail to match up at the same time - different colours will be transmitted depending on the orientation of the crystal. This is what makes those 'birefringence colours' in the olivine, you're seeing the composite of all the wavelengths that managed to get through without cancelling themselves out.

(The reason you only see the birefringence with the analyser in is that it filters out the component that doesn't get twisted around - in the first picture the birefringence is lost in all the other light that's allowed through to your eyes.)

Colour seems so intuitive a lot of the time - everything has its colour and it's so easy to see how they combine and contrast. But our brains are fooling us, colour isn't as fundamental as we think. Colour is our mind's way of interpreting and representing different wavelength of light. Normally the wavelengths we see coming from an object relate to what that object is good at absorbing - it's colour is the composite of whatever is not absorbed. But not always.
The sky, of course, isn't actually blue. Not really, not in the sense that, say, blue ink is blue. But it looks blue to us because the light from the Sun is scattered differently depending on its colour. Blue light is scattered a lot, red hardly at all. So the red light all seems to be coming from the Sun, while the blue light seems to be coming from all over the sky. Sunsets are often red because the extra air (and smoke etc, this being close to the horizon) scatter the red light enough to dominate the area.

But surely most things do have real colour, barring a few peculiar set-ups like the crossed polars and sky? The photo on the left - that shows how olivine really looks, doesn't it? Well, not really. Remember me saying that certain orientations of the crystal slow down light more than others? Well, they also absorb light more than others. And with polarised light, this means that certain positions of the sample are going to absorb different light than others. If you spin the slide as shown in the first picture around, you would see the colour of the grains twinkling and fading between shades of yellow, brown and colourless.

Colour, I'm afraid, is not truthful. Like so many other things, it tells us things about the world around us. But we have to learn the language it's talking in to understand the tale.

Dialectic and Syllogism

2008-11-16T17:10:00.004Z

Logic and the rational process of deduction can seem to us very dry at times. While we admire and enjoy hearing about clever deductions - the more Holmesian the better - the overwhelming view of logic is that it is cold, unfeeling and boring.
It was not always so. For a period in the Middle Ages, logic was the new intellectual craze. It was seen as exciting, rebellious and even potentially heretical. In the end, though, it was accepted and became the driving force of the scholastic movement that played such a major part in the establishment of the university.
Logical thought of one sort or another has no doubt been around as long as humans ourselves. But formal logical systems - methods of deduction, consideration of what was and was not a valid conclusion - came along much later. The system that was of such influence in the Middle Ages was that of Aristotle. Aristotle's variety of logic was based on syllogisms - two statements, 'premises', leading to a conclusion. The premises take the form of "All x are y", "Some x are y", "No x are y", "Some x are not y" and so on and from these we can construct arguments both valid:

Premise: All cats are animals.
Premise: Some cats are black.
Conclusion: Some animals are black.

And also invalid:

Premise: All cats are animals.
Premise: Some animals are black.
Conclusion: Some cats are black.

(The second syllogism is invalid because it could be that all the animals that are black are not cats. Incidentally, interest in syllogism has been revived lately due to their connection to Venn Diagrams and thence to set theory.)

Now, given only two premises and a conclusion, each of which has a distinct form, there are only a finite number of kinds of syllogisms - some valid and some invalid. Therefore, we can convert a logical argument into a series of syllogisms and judge whether or not the argument holds from whether or not the syllogisms are valid.
When Aristotle's works on logic became reasonably known in Europe around the 12th century, they caused an intellectual revolution. Here was a way to reliably analyse texts and draw precise conclusions. It spurred the current interest in debate and dialectic by providing new weapons for disputants. However, it was highly controversial at first. For one thing, Aristotle had been a pagan and the reading of pagan works - even non-religious ones - roused the ire of the Church. The reading of Aristotle was for a time banned at the nascent University of Paris, one of the more liberal institutions of the time. For another, logical analysis of books was not something to be smiled on by a Church that taught the literal and unquestionable truth of the Bible.
However, the Church eventually did accept Aristotle due largely to the persuasive arguments of Thomas Aquinas and Peter Abelard.
Aquinas wrote that reason could be used to glorify God in discovering the truth and that Greek philosophy was no challenge to the Word. In his Summa Theologica, he drew parallels between the writings of the Greeks and the teachings of the Church. Above all, he made the claim that logic and reason provided evidence for the existence of God and did not threaten people's faith.
Peter Abelard (the same Abelard who was so famously involved with his pupil, Heloise) wrote the Sic et Non, the "Yes and No" in which he considered contrary points of view in the Church's teachings or apparently contradictory passages in Scripture. Using Aristotelian logic, he showed how these could be reconciled, leading to a deeper understanding of the teachings in question. These two books reconciled the Church to rational discourse and to pagan authors. Even then, the exciting freshness of logic, the heady power of deduction and the rebellious spirit of drawing conclusions independent of authority lent logic a popularity it has never enjoyed since.

These days, Aristotelian logic has gone out of fashion. Syllogisms are limited by their inability to express things beyond inclusion and exclusion and the ambiguity and mutability of words has always impeded logic and philosophy (Wittgenstein was later to claim that there were no philosophical problems in existence - only appearances of ones due to language). More formal axiomatic systems of mathematic logic have proved more useful to us. And the scholastic movement itself was supplanted by more naturalistic ones drawing their premises from the world, from experience and experiment; rather than from the supposed literal truth of Scripture. But for a time, logic had shaken the foundations of authority and played its part in the origin of the Renaissance.

United Standards

2008-11-14T19:41:00.005Z

For those who want some proof that physicists are human, the proof is in the idiocy of all the different units which they use for measuring energy.

And indeed the many different units devised for this physical quantity are baffling. Joules, ergs, hartrees, electron volts, wavenumbers, calories and the list goes on with each sub-discipline and approach seemingly requiring yet another one. What's the point of them all?
To see why, we need to consider why we have units in the first place and how we choose the standard.

Science involves a lot of measuring things. Usually when we measure something, what we want to find out is how much it undergoes some process in order to compare it with other objects in the same process. That way we can get an idea of the rules behind it all. Obviously, in comparing objects we need a standard.
Standards can be picked for a variety of reasons. Convenience is a good one - the familiar everyday units like inch, kilogram, minute and so on all refer to quantities we are likely to deal with every day. Measurability is an important aspect - think of how the Celcius temperature scale is defined . Tied to these is universality, choosing a basic unit that has some kind of physical analogue. The charge on the electron is the basic measure of charge and is the smallest charge you can get without a big particle accelerator (although the internationally agreed base unit for charge is actually the coulomb, much much larger for reasons of convenience).
Ultimately, we need different units for different purposes, so we all choose different ones. Frequently scientists choose units to make their equations simpler and get rid of loads of constants of proportionality. So if you pick your units such that as many constants as possible are 1, this is much easier. For example, we define volts (the unit of potential difference) in terms of amps (the unit of current) and ohms (the unit of resistance). 'One volt' is 'the potential difference required to push a current of one amp across a resistance of one ohm'.

Eventually, scientists got together and defined a set of base units called the SI (Le Systeme International). These are simple units from which everything else can be defined:

[click to make it big enough to read]

A nice, organised system and like most nice organised systems people ignore it completely whenever is convenient.
It's easier in practice to use whatever comparative standard comes to hand. For particle physics, we use the electron volt, the energy an electron gains when placed in an electric field of one volt. For physical chemistry, the hartree which is the 'absolute value of the electric potential energy of the hydrogen atom in its ground state'. For spectroscopy, the wavenumber, the energy of a photon with a wavelength of one centimetre. Using such things avoids endless prefixes (all that pico-, femto-, micro-), excess constants (the hartree was invented specifically to incorporate a pile of irritating numbers into its value. Now you can make a nice clean calculation and convert back to joules at the end or, more usually, leave the answer in hartress in the confident knowledge that everyone knows what it means) and irrelevant definitions.
But they make learning physics a nightmare.

PS. If you're wondering why SI amps are defined in terms of newtons, an SI-derived unit, I have no idea. For some reason they wanted current to be the base quantity rather than charge. Given that current is a flow of charged particles while charge is a fundamental property of certain particles, I have concluded that the people defining these are being deliberately obtuse.

Similar Similes

2008-11-01T14:13:00.005Z

In a previous post, I wrote about mathematical modelling and in what sense the models constructed can be considered to reflect some aspect of reality. Today I would like to talk more about models and their uses as similes.

Constructing a model for a physical system generally involves some degree of simplification. Perhaps we'll ignore friction for now so we only have one force acting on the system. Perhaps we'll assume that the separation between atoms remains constant while the molecule rotates. This is a very useful thing to do, our thoughts would get very muddles if we kept trying to keep account of every little aspect of a process. Better to try and concentrate on the factors that will significantly affect the aspect we wish to draw conclusions about. Of course, we have to keep our approximations in mind - if we've decided to ignore friction, we have to be prepared to bring it back in if we encounter a situation in which it has a more significant impact.
Now, one of the advantages of simplification in this way is that we can draw parallels between different physical systems with similar forms to their models. It can also give us a starting point for investigating a new phenomenon if we can compare it to one more familiar. For example, if we want to consider the nature of a chemical bond and how it stretches and deforms, we might start by comparing the two atoms linked by a bond to two bodies attracting each other. The physics of the latter situation are well understood with Hooke's and Newton's Laws describing how the attraction between the bodies changes with separation.
Of course, the two systems are not identical. Atoms will attract each other when bonded, but if brought too close together, the repulsion between the nuclei will overcome the attraction between them and the electrons in the bond. If they are too separated, the bond will break. So we have to alter our original model and talk about how the atomic system differs from the bodies under gravity situation. This does not necessarily detract from the usefulness of our original comparison - it will likely hold close to the truth for a certain region of bond lengths. It is also often easier to consider a new phenomenon by comparing it to a more familiar one and then trying to account for the differences than attempting to construct an entirely new picture from scratch.
It is this method that underlies a lot of science. We compare one thing to another, nothing the similarities and differences. A diatomic molecule is like two bodies attracting by gravity, a brick being dropped can be approximated as an entirely rigid object, the Sun-Earth-Moon system can be pictured as the Moon orbiting the Earth which in turn orbits the stationary Sun.

A similar thing happens in mathematics, although in some cases goes deeper. In many ways, mathematical comparisons are more in the order of metaphors rather than similes - we say not that one thing is comparable to another, but that one thing is in some sense the same as another. For example, consider a complex number. A complex number consists of two parts, a real part (a real number being anything on the familiar number line) and an imaginary part (an imaginary number being some multiple of the square root of -1, usually denoted as i). Such things can be difficult to visualise - who, after all, has an imaginary number of horses or a complex amount of potatoes? But a convenient way is the Argand diagram, considering the imaginary numbers to lie on a number line at ninety degrees to the familiar, real, one.

But if you're now thinking about complex numbers as being points on a two dimensional plane, all sorts of new approaches open up. You can start considering addition and multiplication as being analogous to transformations, turning one point into another. Geometry suddenly has something to say about the matter. You realise that in some sense complex numbers can be vectors, and linear algebra gets in on the act. Metaphorically, they are all the same thing.

A Period of Etymology

2008-10-19T21:25:00.004+01:00

The posts are becoming few and far between, I know. This is mainly due to my massively packed life at present.

In a previous post, I compared the history of the Earth to a day. And now, here it is in visual form!

So what are all the names and where do they come from?

Most geological terms, at least for the larger divisions of time, owe their origin to the geologists of the eighteenth and nineteenth century who did so much to get this new science on its feet. Fortunately for those of us in Britain, many of these pioneers were also British and so the periods often relate to easily recognisable divisions in strata as found in Britain. The Americans find the Carboniferous so unweildy and inconvenient for their purposes that they divide it into two, the Mississippian and the Pennsylvanian.
Now, there isn't much going on in the fossil record before the Cambrian, so 'Precambrian' was the term originally used to describe everything up until then. Of course, times have moved on and our methods have improved so we can discover much more in these most ancient of rocks than once we did. There are three eons in the Precambrian, called the Hadean (think Hades), the Archean (think 'archaic') and the Proterozoic ('Early life'). Everything afterwards is lumped into one single era comprising what happens after 9:15 ' - the Phanerozoic.
The Phanerozoic is the part where pretty much all fossils (and most of Britain's rocks) are found.
'Cambrian' is from the Latin name for Wales, because many formations of that age can be seen there. Wales is also the source of the Ordovician and Silurian periods - the Ordovices Silures being ancient tribes from that country. The subdivisions of the Silurian recall the Welsh borders and Shropshire - Pridoli, Ludlow, Wenlock, Llandovery.
'Devonian' surely needs no explanation. Within the Devonian we find the huge formation known as the Old Red Sandstone, mainly of a pinkish colour.
The Industrial Revolution was fuelled by the deposits of coal found in the Coal Measures, part of the Carboniferous period. The name, of course, is Latin for 'coal'. Believe it or not, although Britain was covered in rainforests and hot swamps at the time - hence the fossil fuels - this was actually an ice age with an enormous southern ice cap. Thankfully for the industrialists of Victorian England, we were on the equator at the time and still capable of supporting tropical wetlands.
'Permian' is somewhat more obscure. 'Permia' was a country in the north-west of Russia, near to the border with Finland. It lost its independence from Moscow in the fourteenth century, but the land it once ruled is still called by that name. In Britain, the period is dominated by the New Red Sandstone, a much brighter stone than the Old Red.
Throughout North-West Europe, there is a three-layered rock (red sandstone, chalk and shale) known as the 'trias', hence the 'Triassic'. The 'Liassic', a division of the Jurassic, was named because of the 'Lias', a layered rock of a different sort on the south coast of England. 'Lias' is thought to be a misspelling of the local pronunciation of 'layers'.
The French got 'Jurassic', after the Jura mountains, an offshoot of the Alps. 'Cretaceous' is from the Latin for 'chalk', because the huge expanses of chalk that cover Britain and much of Western Europe were formed here.
Formerly, the time after the Cretaceous was divided into two lumps, the Tertiary, up until the last Ice Age; and the Quaternary, everything during and after it. These names endured even after their companion terms - Primary, for up to and including the Permian and Secondary for the next three periods that we now know as the Mesozoic - dropped out of use. The diagram above still uses them and most geologists too, in an informal sense. Nowadays, the Cenozoic is split into two by the Palaeogene and Neogene. No prizes for guessing what these mean.
Below these periods come a bewildering number of smaller intervals - epochs (fifty odd of them) and ages (well over a hundred). But there are too many to talk about and in any case, it's getting late. Almost into the Permian.

Bottom's Dream

2008-10-10T14:28:00.004+01:00

It's been a while since I last posted, but now much of the beginning-of-term running around chaos has subsided. Time to breathe and time to post again.

I came across this essay, 'The Scientist as Poet'. I'm not particularly going to talk about the subject of it now, I have done so before and will likely do so again. But recently, the historian Richard Holmes published a book, The Age of Wonder, about the relationship between the Romantic poets and the scientists of the Enlightenment, and I want to discuss this topic.
Many people know John Keats' claim that Newton had destroyed the beauty of the rainbow by explaining it - 'Unweaving the Rainbow' was his phrase later adapted by Richard Dawkins for his own book disagreeing with the claim. And this would seem to encapsulate the relations between the scientists of the Enlightenment and the poets of their day - and indeed that between modern scientists and modern poets. But things are not always so simple.
Humphrey Davy, that great chemist, has often been referred to as a poet-scientist, but what is less well-known is his friendship with Coleridge, a scientist-poet. Coleridge was as keen an amateur chemist as any in that day (a day when chemistry was very much the fashionable pastime) and attended many of Davy's lectures not merely to learn but also to, in his words, 'refresh my stock of metaphors'.
And this was not an isolated aberration. The distinction between the sciences and the arts is comparatively recent. In 1800, no-one had ever heard the word 'scientist' ('natural philosopher' was a more common term) and 'artist' was generally used to mean 'craftsman' as well as the more modern definition. Many artists were scientists and the reverse was also true - the poet and author Goethe did much important research into optics, the nature of colour and mineralogy.
And was there a Romantic movement in science, as elsewhere? Indeed there was, although it was more a response to science than a change in the methods of the subject itself. Understanding nature was seen as a spiritual and self-fulfilling pursuit, and by contemplating the world around him, the natural philosopher could gain a greater understanding of himself and his part in it all. Above all was the awe, the grappling with the immensity of the world and its complexity.
Many of the furthest flights of thought in this vein verged on the mystical. Some thought that with enough understanding people could be united with nature, undoing the separation brought about in the Fall and ending all woes. Others believed in a metaphorical nature - everything physical was an allegory on something spiritual.
Ultimately romanticism, both of the mystical and of the appreciative types, went out of fashion in science to be replaced with more useful approaches and science and the arts grew estranged. Perhaps they have both lost something.

I have had a most rare vision. I have had a dream past the wit of man to say what dream it was. Man is but an ass if he go about t'expound this dream. Methought I was—there is no man can tell what. Methought I was, and methought I had—but man is a patched fool if he will offer to say what methought I had. The eye of man hath not heard, the ear of man hath not seen, man's hand is not able to taste, his tongue to conceive, nor his heart to report what my dream was... It shall be called ‘Bottom's Dream', because it hath no bottom. - 'A Midsummer Night's Dream', Shakespeare.

Well Deserved Recognition

2008-10-03T16:19:00.004+01:00

Finally the overly long holiday draws to a close and I return tomorrow to the bubble that is university life. Hooray! So, how to round off this summer? Well, this year's IgNobel prizes have just been announced:

Nutrition: Massimiliano Zampini and Charles Spence for their study showing that food actually tastes better if it sounds crunchier.

Peace: The Swiss Federal Ethics Committee on Non-Human Biotechnology and the citizens of Switzerland for adopting the legal principle that plants have dignity.

Archaeology: Astolfo Gomes de Mello Araujo and Jose Carlos Marcelino for demonstrating that armadillos can turn the contents of an archaeological dig upside down.

Biology: Marie-Christine Cadiergues, Christel Joubert and Michel Franc for showing that fleas on dogs can jump higher than fleas on a cats.

Medicine: Dan Ariely for demonstrating that expensive fake medicine is more effective than cheap fake medicine.

Cognitive Science: Toshiyuki Nakagaki, Hiroyasu Yamada, Ryo Kobayashi, Atsushi Tero, Akio Ishiguro and Agota Toth for demonstrating that slime moulds can solve puzzles.

Economics: Geoffrey Miller, Joshua Tyber and Brent Jordan for discovering that the fertility cycle of a lap dancer affects her tip-earning potential.

Physics: Dorian Raymer and Douglas Smith for proving that heaps of string or hair or almost anything else will inevitably tangle themselves up in knots.

Chemistry: Sheree Umpierre, Joseph Hill and Deborah Anderson for discovering that Coca-Cola is an effective spermicide (it was shared with C.Y. Hong, C.C. Shieh, P. Wu and B.N. Chiang who showed the opposite).

Literature: David Sims for his passionately written study "You Bastard: A Narrative Exploration of the Experience of Indignation within Organizations."

I shudder to think how some of these projects got started, especially the Coca-Cola one. But some of them raise very interesting question. Why do lap-dancers get tipped more when they're fertile - does the hormone cycle alter their behaviour or somehow that of people around them? If expensive fake medicine is more effective than cheap fake medicine and food tastes better if it sounds crunchier, what can this tell us about the ways our expectations shape our perceptions? I look forward to hearing more from these researchers.

This won a prize a few years ago. Levitating frog, does what it says on the tin.

Paradoxes

2008-09-28T16:04:00.005+01:00

A man is condemned to death. The judge visits him on Sunday and tells him he will be hung this week - Monday to Saturday - but that he won't know what day exactly until the hangman comes to get him at midday precisely. It is to be a suprise. The man considers. If the hanging were on Friday then it would not be a surprise, since he would know by Thursday night that he was to be hanged the following day as it would be the only day left. Therefore it cannot occur on Friday. He then reasons that the hanging cannot be on Thursday either, because that day would also not be a surprise. On Wednesday night he would know that, with two days left (one of which he already knows cannot be execution day), the hanging should be expected on the following day. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. The man rejoices, realising that he will escape death. The hangman turns up on Tuesday, much to his suprise.

Words are 'autological' if they describe themselves ('polysyllabic', 'English', 'vocalised', 'pronounceable' etc) and 'heterological' if they do not. What category does 'heterological' fall into? If it describes itself, it is autological. But then it does not describe itself, so it is heterological. But then it does describe itself.... And so on.

"The smallest number not defineable in under ten words" - defines this number in only nine words.

Is the answer to this question 'no'?

This sentence is false.

Is this disturbing or what? I so need to go see it!

PS. It has come to my attention that the week running from the 27th of September to the 4th of October is Banned Books Week. Why not mark this celebration of free speech and the right to read by opening something that was once banned? There's certainly no shortage.

The Radio Star

2008-09-27T16:19:00.004+01:00

I recently acquired a plasma ball, having wanted one for many years. I know they're supposed to have gone out with lava lamps and the like but I find it exceedingly difficult to get bored of glowing ionised gas.
They were designed - as almost everything seems to have been - by Nikola Tesla. Now, a lot has been said and written about what Tesla may or may not have got up to in his final years when he rather dropped off the radar (something else he was critical to the development of) but even ignoring the more unusual claims it is difficult to play down his radiant level of awesomeness.

Tesla was mainly about two things: alternating current and wireless transmission of energy. The two are closely linked, because it is with an alternating current (that is, a current in which the electrons change direction many times a second) that you can turn the movement of electric charges into electromagnetic radiation and back again, sending it through air, through a vacuum, even through the ground. This is basically how a radio works as well - the currents in the transmitter produce signals in the form of radio waves that travel outwards and produce currents in the aerial, telling the loudspeakers what to do.
I once did a physics experiment in which my lab partner and I had to use an oscilloscope. Never having used one before, we played around with it a bit before we started in the experiment proper. We happened to notice that if you touched the probe, a small flicker appeared on the screen. Zooming in, we saw that it wasn't actually a flicker, not a bit of random interference resulting from, say, the warming of the probe or the change in environment. No, it was a pretty distinct sine wave, a regular alternating current. We measured its frequency and it came out at 50 Hz, fifty changes in direction every second. But what could produce this kind of regular current in my finger?
The mains supply. 50 Hz is the frequency of mains electricity supply. The current in the wires in the walls was sending out EM radiation at this frequency - very low energy radio waves - and our bodies were picking it up and creating currents in response. We were little aerials.

It's a singing Tesla Coil. Nothing needs to be added.

I'm sorry, I just had to include this.

Essential Philosophy

2008-09-21T15:56:00.003+01:00

Imagine a cave. Inside the cave sit three men, facing away from the mouth and the sun, staring at the back wall. The men are shackled and behind these prisoners, other men walk backwards and forwards, holding up a variety of objects. When the sun is out, these objects throw shadows on the wall of the cave, much to the delight of the prisoners. Sometimes the same object throws slightly different shadows, depending on the way in which the guards present it.
The prisoners, of course, do not know this. The shadows are all they have ever seen and they believe them to be the real world. In fact, if you told them that they were mere images caused by actual objects, they would think you mad.

No doubt you recognise Plato's allegory of the cave. He used this parable to illustrate his idea of Forms - that all physical objects we see are mere imperfect reflections of the timeless, unchanging and perfect Form of that object. There's a Form of the Chair, the Form of the Tree and so on.
Now, this belief has rather gone out of fashion in recent centuries, but one aspect of his philosophy has had an enormous impact on the history of science, both positive and negative. This is essentialism.
Put simply, essentialism is the idea that for any particular class of objects there exists a universal set of characteristics, an essence. I don't mean this in a descriptive sense - obviously we use words to class together all objects with certain characteristics for convenience. Essentialism goes further than this and is a prescriptive approach, the belief that there is a 'sheep-ness' or a 'rock-ness' inherent in objects of that type.

Essentialism was of critical importance in the early development of science. If every time you set a flame to alcohol it catches light, you may convince yourself that there is a general rule: Alcohol is capable of combustion. And from this principle you can make a claim about any particular sample of alcohol you encounter in the future: If I touch a flame to this, it will burn. But to extend from the particular occurences to a general rule, you have to assume that in some sense all alcohol conforms to certain properties. If one individual sample fails to catch light because of certain circumstances - maybe it's not pure enough, there's too much water in it - then it becomes an exception to the rule because it deviates from the essential characteristics of alcohol, not because the rule is incorrect. In other words, we have reached the point where we have concieved of an ideal template for alcohol and individual samples are more or less imperfect versions of this.
Science proceeds by making generalisations. Of course, it then has to test and refine them, coming up with explanations for the rules and accounting for any apparent exceptions. But without the assumption that what happens to one object is going to be pretty similar to what happened to all the previous objects of that type, nothing can be done.

However, other applications of essentialism have provided serious obstacles to progress in and understanding of science. Biology suffers from misplaces essentialism quite frequently. The following is a common objection to evolution:
If species A evolves into species B, there must come a point where a mother of species A gives birth to a child of species B. But how then can this child reproduce if it is of a different species to the rest of the population? Surely it is too much to claim that all offspring of that generation have crossed the species barrier at the same time?
The problem here is that 'species' is a misapplied category. They don't really exist in nature, we've just invented them for convenient reference. As Richard Dawkins put it 'real animals are all there ever were'. There are always intermediates, everything is in transition. Each successive generation would be able to breed with the previous generation, and with the next. But it would be subtly different from what came before and what comes after will differ still more. It's the same as happens with language - you can talk to your grandparents and with your grandchildren. But you would be unable to communicate properly with your ancestor of two thousand years ago despite being linked by an unbroken chain of generations capable of speaking fluently together.

Essentialism (and anti-essentialism) continues to influence modern thought. Debates on abortion frequently focus on at what point a foetus can be considered to be human; and whether or not it is actually useful to consider humanity an essential characteristic which something can have in its entirety or not at all. In sociology, the issue of non-binary gender has arisen in recent decades - are our ideas of male/female essentialism adequate? And the constantly-asked question in science is still 'what general rules can we extrapolate from this?'.

Galileo deduced a general rule: the rate at which objects fall depends only on air resistance, not their masses. Here's a good demonstration. You can also do it in a vacuum tube, but it's cooler on the Moon.

Going Ape

2008-09-18T16:21:00.009+01:00

The moment Darwin published his On the Origin of Species, one of the implications was obvious. If all modern animals are descended from common ancestors, then so are we. And if more similar animals are more closely related, then the identity of our closest relatives does not take too long to divine - the great apes.
This print by Thomas Henry Huxley was made in 1863, four years after the Origin was published:(The gibbon skeleton is, of course, enlarged for clarity). But Darwin himself was suprisingly quiet on human origins in the Origin, perhaps afraid of being too revolutionary at once, or perhaps wanting his basic theory to be appreciated alone before he set out its more controversial implications. 'Light will be thrown', was his only comment. His later book, The Descent of Man, finally came out to support the kinship of man to the apes. But how we fit into the ape family continued to be debateable for some time.
The initial approach was to separate ourselves off from the apes. We were like apes, but not apes ourselves.
Homo, of course, are humans, Pan are chimpanzees and bonobos, Gorilla is what it says on the tin, Pongo is the orangutan and Hylobates covers the various types of gibbon. Various types of analysis, including the emerging field of molecular biology, provided evidence that the gibbons were in fact an outgroup. This was something that many had been expecting for some time in any case, so they were shifted away from the others.

Now, what with orangutans being in Asia, people were already suspecting that they might be more distant relatives of the African apes. A bit more research and molecular testing, and the old man of the forest was out on a limb.

You'll see that we are now an ingroup. That is, if you consider chimps, gorillas and orangs to be apes, you have to call us apes too - there's no room to declare that we're 'a bit like' them. Furthermore, chimps are closer to us than to orangs, something that made some people very uncomfortable. Not long after, gorillas went the same way as the orangs.

And you'll notice that the gibbons were judged to be more diverse than perviously. This is the form of evolutionary tree that is still in force today and seems unlikely to be overturned. There's still some room for debate - a minority of specalists think that either the chimp is nearer to us than to the bonobo (also in the Pan genus), or possibly the other way round.
Don't be too fussed about the names of groups or the level they occupy in the classification hierachy. People do argue about them a bit but it's important to remember that they're just a convenient arrangement for reference. The lines connecting species are the important bits.

Here's the great Attenborough on orangs.

A Day to Remember

2008-09-15T15:55:00.004+01:00

The Earth is really absurdly old. Geological time is a a scary, scary thing. It's one of the most difficult things in geology to get your head round - it's not complicated, it's just unimaginable.
Let's take a twenty-four hour day. The Earth will be formed at midnight and the present is the following midnight.
During this day continents will zoom over the planet's surface like pucks on an air hockey table and every few dozen seconds there will be a flash as a giant meteorite smashes into some part of it. You may notice the ocean evaporating a few times during the early hours of the morning.
Life appears pretty soon. 4am is about the earliest we have evidence for, but there might have been some around for a while before. You might as well get out a book, though, because it's going to be single-celled stuff until evening.
At 8:30pm, the sea starts filling up with algae and early plants. Jellyfish begin their blobbing around just before 9:00 along with the rest of the squishy fauna of the Ediacaran. Shortly after nine - five minutes past maybe, the Cambrian Explosion takes place and slimy things with legs do crawl upon the slimy sea. Trilobites scuttle around for a while, looking suprisingly adorable.
Nothing much happens on the land until 10:00, when plants make it, followed shortly after by animals. The marvellously preserved vegetation of the Rhynie Chert is one of the first manifestations of this.
Britain - or what will become Britain - is covered by dense and steaming jungles by half past ten which give way by eleven to endless deserts which will endure for the best part of an hour before sinking beneath the sea not long after the dinosaurs lumber onto the scene. The latter part of the Mesozoic - from 11:15 or so to 11:39 when the dinosaurs are wiped out - is a rather nice time to sit on the beach and enjoy the Bahamas-like climate. But come 11:39, be off the beach and indeed off the planet to watch a giant lump of rock smash into Mexico, obliterating the dinosaurs and many other groups in a few seconds.
There'll be plenty of big birds and mammals to watch for the next twenty minutes until about a minute and a half to midnight when humans appear. The ancient city of Uruk is founded one-tenth of a second before midnight, Jesus Christ is crucified about 40 milliseconds before.
It's a very old planet.

Please let this be a spoof. I cannot bear the possibility that this woman is serious.

Just Having a Look

2008-09-07T20:19:00.006+01:00

For anyone who doesn't recognise the style, this is xkcd (click on the image for a bigger version).
So is this accurate? Is the LHC just going to sit around looking rather embarassed if the Higg's boson turns out not to be there after all?
Well.... no. For one thing, there are a heck of a lot of experiments planned and a large number of projects not connected to the hypothetical Higgs. But the main reason is that the Higgs not being there would be much more interesting than it being as predicted (though a negative outcome will likely annoy many physicists).
The thing is, mass has always been a rather odd aspect of the universe. The inertial mass of an object (its resistance to forces) is the same as its gravitational mass (the degree to which it exerts gravitational attraction) for no adequaely explored reason. There's no reason why it can't vary in certain objects, but it never does (partly explored in this xkcd).
Then there's the incredible weakness of gravity. It may not seem it, but it's a pretty pathetic force. We only feel our lives dominated by it because the Earth beneath our feet is absolutely massive. But every time you hold something, your arm is overcoming the gravitational pull of an entire planet. I tell myself this whenever I feel inadequately male. So mass is rather insignificant when compared to the other major property of matter, charge. (There are some other fundamental properties like strangeness, but we won't worry about those).
Plus there's the whole thing with gravity not squaring up fully with quantum theory. So all in all, we know we're missing big pieces in our understanding of fundamental physics in general and the property of mass in particular. Hopefully the LHC will help fill some of these in, Higgs or no Higgs.

A particulalrly good conspiracy theory. The LHC is going to punch a hole in the van Allen belt and make a gateway for Satan to return.

Particle Physics in Da Club

2008-09-05T15:40:00.000+01:00

Just follow the link.

Just a Theory

2008-09-05T14:36:00.003+01:00

Teach the controversy.
Do you think children should be given only one point of view at school? Or do you think they should be told about both sides of the debate?
You've no doubt heard about the 'Atomic Theory'. It states that all matter is made of tiny discrete components called 'atoms' and it is the combinations of these atoms that give substances their properties. But now, a group of scientists in America is daring to question this long-held assumption.
"What many people don't realise" says Jeremy Johns, a professor at the Kansas Biblical Science Institute, "is that Atomic Theory is just that - a theory. There's still a substantial debate concerning it, but mainstream scientists have until now managed to prevent members of the public hearing the facts".
Johns and his colleagues argue that the evidence for the existence of atoms is poor and ambiguous at best and that a better explanation needs to be found.
"How can a collection of atoms give rise to all these different materials?" he asks. "There are many examples of substances that scientists have not managed to come up with a chemical formula for. They claim that more research is needed, but some of us dare to ask the question is there even a formula to be found? ".
Instead, these critics suggest that properties are conferred upon matter by some external force. This neatly explains the origin and nature of all chemicals and the often confusing changes they can undergo.
The advocates of this new idea (known as EC, or "essential composition") have found unexpected support from religious groups who have long been unhappy about the implications of atomic theory. "If the atom is the smallest unit of matter", says Pastor Robert Hobson, "God would be unable to create a smaller piece. And that is an unacceptable conclusion for a believer in an all-powerful Creator."
Followers of EC have launched a campaign to have it taught in American schools. They say that presenting only one side in an ongoing debate is not science and that children should be allowed to make up their own minds.
Teach the controversy.

For those of you who are still being close-minded and think chemistry is real, here's a dichromate volcano.

Gothic Me, Gothic You

2008-09-01T16:21:00.007+01:00

I am in a good mood today. I have done my working for this summer and can now sleep late in the mornings again. Because of this, I decided that I would write about something beautiful and nice. I chose Gothic architecture.
The arch itself - a simple round-topped arch, with no embellishments - is a work of genius.

Because of the way the pieces are cut and positioned, the more you push down on it, the more it resists the push (until you push really hard, but that takes some doing). Engineers say that the arch converts tensile stresses into compressive stresses. That is, forces that might otherwise try to make the materials bend (think of the way a plank bridge dips in the middle when you stand on it) get turned into ones that try to squash them. Stone is pretty damn resistant to squashing, so it's an excellent solution to the problem of carrying weight. However, a sideways force can still do quite a bit of damage, so you need to make the sides bulky or support them with buttresses.

Now, the gothic arch has some advantages over the circular arch. Firstly, it is steeper. This means that a greater proportion of the forces are directed downwards. Therefore you don't need so bulky a buttress to hold the thing up against sideways forces. Secondly, the peak of the arch is higher for a given amount of masonry. Together, these two refinements of the arch enabled medieval builders to construct buildings that were higher and lighter than previously. Windows became easier to make, collonades became lighter and airier. With some careful considerations, architectural marvels can be raised.

This is San Zanipolo in Venice. Notice how the high vaulted roof is supported by thin columns. The weight of the roof is distributed by buttresses to the outside of the church. This allows the inside to escape the restrictions on height, window size and column thickness and closeness that circular-arched buildings suffer from. We tend to think of the Gothic style as being dark and brooding, but compared to earlier forms, they are flooded with light. A fine example of aesthetic appeal being married to practical purpose.

A video showing the intricate decoration used in the Gothic style. Chartres Cathedral is one of the masterpieces of the form.

(PS. Bonus points for anyone with the kind of weird musical interests to get the reference in the title)

Unsolved Puzzles

2008-08-30T16:17:00.003+01:00

One of the most common reasons people give for being turned off science is dull lessons which require them simply to learn facts. Little attention is given to the scientific process of discovery and where the action is (this is even worse in mathematics, with many people being of the opinion that there are no new discoveries to make). I thought I'd present here a few problems that need solving and some questions that need answering.

Why is there more matter than antimatter in the visible universe? Is antimatter more prevalent in other areas, or is the whole universe predominately material?

Why did the universe begin with such low entropy?

Are there more dimensions than the four familiar ones? (including time)

What are the chemical origins of life?

What is the structure of liquid water? (Believe it or not, we don't actually properly understand how the water molecules interact with each other)

What caused the Cambrian explosion? Or is it just an illusion caused by an increase in fossilisation?

Why do we sleep?

How are memories stored?

How do proteins fold so damnably fast?

As for mathematics, could someone please find me a pattern to connect the prime numbers? It's been bugging me since I was seven.

This is an rather good video I found. Never thought of the Fifth Symphony that way before.

Food, Glorious Food

2008-08-24T13:21:00.002+01:00

Many of you will have read recently of Prince Charles' objections to genetically modified crops. Published in various newspapers, they have produced much discussion, both in favour of his views and opposed to them. And as with every time the issue of genetic modification crops up, the opinions have been expressed with more than usual forcefulness. I'd like to examine some of the objections to GM.

GM crops are bad for the environment
Not a good argument this, although in a way it's also the strongest and most important to consider. With the introduction of any new crop, GM or not, environmental considerations must be carefully weighed. There are countless examples of occasions when a new or foreign organism has been introduced into an ecosystem only for things to turn nasty. I'm thinking specifically of the bullfrog plagues in Australia or the decimation of the native European Crayfish in English waters by their American cousins. Will GM wheat cause similar problems? Possibly. But here's the weakness of the argument - the effect an organism has on its environment depends on both the organism and environment. Is there something magical about genetic modification that automatically causes it to become malevolent? Of course, the possibility is there. But it's an argument against specific strains, against certain varieties of GM, not an argument against GM itself. You might as well ban frogs on the basis that one variety of frog has damaged one specific environment.

Genetic modification is unnatural
Well of course it is. But is this really a good argument against using it? Central heating isn't natural but we still use it. Naturalness should not be a criterion for deciding whether or not to do something. I quote from The Fifth Elephant by Terry Pratchett:
"Colon drew himself to attention. 'Not natural in my view, sah. Not in favour of unnatural things.'
Vetinari looked perplexed. 'You mean you eat your meat raw and sleep in a tree?' "
Besides, we've been genetically modifying animals and plants for thousands of years. Wheat is a GM grass, dogs GM wolves. All the fruit varieties we're familiar with have been modified to produce more and better food for us - bananas have been so extensively altered from their wild forms that their seeds are almost entirely eradicated and they can only breed by farmers taking cuttings and growing them. All that has changed in recent years is the method.

Companies will patent GM organisms and use them to extract money from farmers
Yes, they probably will. When it comes to world-enhancing technologies, you can bet that someone's going to be trying to make money off them. This is why we need legislation now, to prevent corporations doing this. Of course, we also need incentives for people to invent better crops. Many scientists are pushing for compulsory patent purchase, whereby any company inventing a GM organism with potential for improving some aspect of food supply will be required to sell it to the UN World Food Programme on request. They will then make it freely available. Whatever approach is taken, it is important to regulate this technology properly. But that's not an argument against GM, it's an argument against unrestrained capitalism.

GM won't solve the problem of feeding everyone
Not on it's own it won't. But combined with other approaches, GM has the power to become our major weapon against hunger. The possibilities are endless. Wheat that can grow with half the water, beans that fix extra nitrogen into the soil, chickpeas that produce vitamins to combat deficiencies. We'll need more than just new types of crop to feed to world. But to do it only with what we have now is going to be much, much harder.

I don't know about you, but I find Sam Neill's voice rather soothing - third place only to David Attenborough and Morgan Freeman. It's probably something to do with Jurassic Park, I loved that film far too much.

The Value of the Useless

2008-08-16T10:35:00.003+01:00

My apologies for the recent scarcity of new posts, I have been otherwise engaged. Unfortunately the exigencies of a student life have caught up with me and I found myself with only one option - regular paid employment. Fortunately the horrors of commuting daily to an office shall not last beyond the end of this month but until then I shall be a notably less idle scientist than is my normal wont.
Funding is a perennial source of concern for scientists. It has been particularly so of late - most of all in the field of physics - with the government's budget for funding research being greatly slashed. In the currently uncertain economic situation, scientists are being increasingly pressed to justify why they should receive government grants for their research.
The most common argument used - and certainly the most common trotted out to the politicians holding the purse strings - is that science brings with it economic benefits in the form of patents and innovations in technology. It is for this reasons that the CBI regularly calls for more science graduates. But this doesn't really explain why we should fund pure research rather than targeted development. What tangible benefits do we expect to gain from contributing to the construction of the Large Hadron Collider?
The normal rejoinder to this is that it is impossible to know what might be useful in the future and that new discoveries open up new opportunities for development and invention. If someone had tried to invent television in 1800 it would have been utterly impossible. It was only with a century of research into electricity, magnetism and optics that it was possible.
But there is another, much better, reason to do scientific research. It's fascinating. We don't do it because it's useful, we do it because it's wonderful and exciting and knowlege gives our civilisation value. It's a very similar argument to that used to justify giving money to the arts - life would be so much worse without it, not through any easily calculable material loss, but through a much more significant loss of purpose and quality. There has to be more to life than just making and spending money. Discovery - the realm of the sciences - and creation - the realm of the arts - provide us this.
'All art', said Oscar Wilde, 'is quite useless'. It's not for anything except itself and that's part of why we have it. Science cannot quite claim the same, it has many more profitable spin-offs. But there is something of a similarity present and it remains difficult for many scientists to answer the question 'What use is your research?'.

Some of the history of electromagnetism. They really should have made that substation out of glass, it would have been so cool!

U-Turn if You Want

2008-08-10T10:30:00.003+01:00

In many ways, polititians and scientists are exact opposites. One of the main differences between them is their attitude to people changing their minds. We've all seen debates in which one polititian has accused another of flip-flopping, or doing a U-turn. This is presented as a bad thing, to alter your beliefs. Scientists, on the other hand, are condemned if they do not change their minds in the face of new evidence.
I'm not saying this to lampoon polititians - many have pointed out how essential it is for a good leader to stick to his course of action even when it becomes unpopular if he knws that course of action to be right for the country. Instead, I'm saying it to criticise one of the criticisms of a sceptical outlook.
"Scientists are always changing their minds!" often comes up as an argument against the power of science. An alternative is "Scientists didn't believe X, but X turned out to be true!", used to support whatever dubious theory the speaker is defending.
Both claims are true. Scientists always are changing their minds, and there are many examples of ideas that were widely disbelieved at first but later became accepted - continental drift, for example (albeit in the modified form of plate tectonics).
The first criticism is a virtue, not a vice. If new evidence comes up which tilts the balance in favour of a previously-disregarded theory, it is only sensible to alter your beliefs to accomodate the new advances. The Science of Discworld put this across best: "Sometimes scientists cahnge their minds. New developments cause a rethink. If this bothers you, consider how much damage is being done to the world by people for whom new evidence does not cause a rethink."
Of course, not all scientists can live up to this lofty ideal. If you've spent fifteen years researching the implications of and teaching a particular theory, and this theory is then demonstrated to be false, it's difficult to let go. But some people manage this, and provide an inspiration for us all. Richard Dawkins recalls a professor he once knew who had believed and vociferously taught that a microscopic structure in cells called the Golgi Apparatus was not in fact there, that it was merely an illusion caused by various other cellular artefacts. Dawkins was witness to a lecture in which a visiting lecturer demonstrated conclusively that it did exist. The professor got up at the end of the lecture, walked to the front of the hall and shook the lecturer's hand. "My dear fellow, I want to thank you. I have been wrong these fifteen years". The hall erupted in applause.
The second criticism is one which can only be used with the benefit of hindsight. Yes, people did not believe in the movement of the continents when it was first proposed and it later turned out to be true. But that was because when it was first suggested, there wasn't a huge amount of evidence for it. But as the evidence mounted up, more and more people were convinced until it became generally accepted. It was the evidence that provided this conclusion, and that evidence had to be discovered. I've heard this 'you may not believe this, but they didn't use to believe in X either' advanced in favour of all sorts of nonsense. As Carl Sagan put it, "They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown."

You may have heard about a project to beam a message to a recently discovered Earth-like planet. Here's Carl Sagan on contacting our neighbours.

Blogger Weirdness

2008-08-08T09:18:00.002+01:00

It's come to my attention that sometimes when I click on the blogs in the Blogroll, I get the feeds rather than the actual blogs themselves, which is what I want to link to. This appears to happen randomly and I can't find how to sort it out. Do bear with the links.
That is all.

Be Cause?

2008-08-05T13:54:00.006+01:00

What is a mathematical model of a physical system? At what kind of level is it really there? Is it actually there at all, or is it simply an aid to calculation?
These questions are of great importance in the philosophy of science and also to science itself, especially in the light of quantum physics and the Schrodinger Equation.
Let us take a simple model of a system - for example, Newton's Law of Gravitation:

We know it works. We know it gives true predictions. So is this an accurate representation of what is actually there? Or is this equation simply a machine that will give us a prediction but not an explanation? After all, we could represent this gravitational force in many ways. We could imagine particles - 'gravitons' that move from one body to the other. We could think of space as deformed like a rubber sheet by massive bodies, causing other bodies to roll inwards. Or perhaps there is a field created by mass, much like the one generated by charge. All of these realities could be represented by the same equation.
There may not be any way to tell apart these differing stories. After all, if they all produce the same effect, what can we possibly do to distinguish them? Are we doomed to know nothing more than our models which may turn out to be absolutely accurate in terms of effect but hopelessly lost in terms of cause?
There is a debate in computer science about algorithms, sets of instructions for the computer to follow. If two algorithms give exactly the same results in the same circumstances, are they the same algorithm? I would say 'yes'. Think about all the different ways and shortcuts there are to do multiplication. The exact same process is actually taking place here, there are simply different ways to represent it.
So perhaps all those little stories we might tell ourselves are all true at the same time. If they have the same effect, if there is no way to tell them apart, are they different at all? They may turn out to be like all the dozens of proofs of Pythagoras' Theorem - they are all exactly equivalent.
But this leaves open the question of causality. If the three ideas I have given about the origin of gravity are all true at once, what is actually causing it? Our law tells us that gravitational attraction occurs between two masses, but is that actually an explanation? Or is it just a statement of prediction - that when two masses exist, they will attract each other?
Of course, any answer to this would require us to define causality properly. We all know that just because two things are correlated, it does not mean that one causes the other. But on the other hand, if two things correlate absolutely perfectly (A always preceeds B, B is always preceeded by A), isn't that enough? If we had a perfect mathematical model (and of course we don't), doesn't that provide all the explanation we need? Or is it merely a description of the effects of the real cause?

My head is starting to hurt, so here's a cute and unrelated video.

Not Having to Think Originally

2008-07-31T16:11:00.003+01:00

You know, I might as well rename this blog 'The Idle Mathematician' and have done with it. I seem to be talking about maths more than anything else recently. I found this (pdf) essay online today and rather liked it. I'm not sure it's necessarily a good thing to dispense entirely with rote learning in maths - after all, even English lessons require a certain amount of rote memorisation of spellings and punctuation before reading is possible. But it's a nice piece, I like the analogies it draws.

But to move on. I can't talk about maths all the time. I want to quote Robert Heinlein, author of Starship Troopers, Stranger in a Strange Land and dozens of other works of science fiction. I wasn't actually familiar with his work until yesterday, I don't read much sci-fi (oddly). But I came across his page on Wikiquote (oh, that wonderful invention that is the internet!) and have resolved to find and read some of his as soon as possible.

It may be better to be a live jackal than a dead lion, but it is better still to be a live lion. And usually easier.

Men rarely (if ever) manage to dream up a god superior to themselves. Most gods have the manners and morals of a spoiled child.

Moving parts in rubbing contact require lubrication to avoid excessive wear. Honorifics and formal politeness provide lubrication where people rub together.

Never underestimate the power of human stupidity.

One man's "magic" is another man's engineering. "Supernatural" is a null word.

If we blow ourselves up we will do it by misapplication of science; if we manage to keep from blowing ourselves up, it will be through intelligent application of science.

Being intelligent is not a felony. But most societies evaluate it as at least a misdemeanor.

I wonder why it is that cynical quotations are always so much more memorable - and true - than idealistic ones? Even Oscar Wilde, who affected to despise cynicism, comes across as remarkably jaded in many of his comments on society. I suppose we should be thankful. Quotation - as Dorothy Parker said - saves us having to think originally.

Instead of the normal video, here is why physical theories are like past girlfriends.

Odd Decision by Birmingham Council

2008-07-30T09:13:00.003+01:00

I am annoyed.
I've got no problem with the council blocking various websites, they need to keep their employees on track after all. But either ban the religious sites along with the atheist and occultist ones, or let those through. I accept there might be a case for blocking websites relating to certain religious positions - I'm thinking Satanism - since the filter also blocks sites promoting criminal activity and Satanists aren't all friendly and cheerful (though apparently, some are. I can't help but feel these ones missed the point). But you can't include atheism among these, it doesn't have any violent or illegal beliefs. It is an absence of religion, not a religion itself.
I'm very much in favour of freedom of religion and treating them all the same. But that doesn't mean giving them a privileged position and exalting faith above lack of faith in the eyes of the law.

The Geeks Shall Inherit the Earth

2008-07-28T11:53:00.002+01:00

I would like today to celebrate the nerd and the geek.
How ironic it is that in youth culture, where everyone seems constantly to be striving to avoid being considered 'mainstream', those who have truly different tastes are considered weird.
How odd that so many people spend so long trying to appear as if they care nothing for the opinions of others when those who are truly unconcerned with social norms are rejected.
How pitiful that those who have great creative talents in the arts are praised for this, where those who have equally great creative talents in maths and the sciences are mocked for this.
How sad that those who sincerely believe that people should not be judged on appearances nevertheless throw nerds into the basket marked 'boring' or 'unimaginative' despite the likelihood of said nerd having more going on in their head than anyone else in the room.

Dr. Roger Spain: Wow, I thought you'd be the last person to have a problem with nonconformity.
Dr. House: Nonconformity; right... I can't remember the last time I saw a twenty-something kid with a tattoo of an Asian letter on his wrist. You are one wicked free thinker! You want to be a rebel; stop being cool. Wear a pocket protector like he does, and get a hair cut. Like the Asian kids that don't leave the library for a twenty hours stretch. They're the ones that don't care what you think.

That's from House, a television series which I enjoy to a completely unreasonable degree. This quotation is a particular favourite of mine, though not because I dislike long hair or tattoos (I'm rather protective of my own long hair). The point is that nerds possess rare and desirable traits - deep and passionate interests (ok, so one of those might be comic books. Is that any worse than modern art?), a refreshing orginality of mind, lack of concern for the opinions of others, their own dress sense (or lack of dress sense, which comes under the previous point).
So be nice to nerds. Not because you'll end up working for one (though you may well do so), but because they are fascinating people in their own right.

Geeks can love too.

Pi in the Sky

2008-07-25T10:15:00.004+01:00

Ok, I found this image up at Good Math, Bad Math:

I'm not going to bother ranting about it to any great extent, MarkCC has done that rather well himself. Instead I'm going to focus in on one of the points he makes against it, one that I'm suprised more people don't see in this and similar claims of mystic digits.
Pretty much all of those connections in the 'proof' are in Base 10. As I have pointed out beforehand, there's nothing privileged (to steal a sociological buzzword) about Base 10. Here's pi in the common form we all know and love:
3.141592653589....
Here it is in binary:
11.0010010000...
How about hexadecimal?
3.243F6A8885A...
So you can't just take digits from a random base system and expect them to have significance (oh, I suppose you could claim that God knew we'd use Base 10 and therefore encoded a message in that base, but given that this chap is trying to prove God, that would be assuming the conclusion as part of the proof).
The take-home message here is that pi is not defined by its decimal expansion - or any other explansion, for that matter. I once had a discussion with a chap who seemed somewhat confused over the digits of pi. He wondered why people kept changing it and making it longer. Didn't that make the pi of the past different to the pi of the present? Of course, where he was getting confused here was between pi itself -unchanging, a fundamental constant of the universe - and our best approximation to pi - increasing in accuracy as mathematical methods improve and the need for greater precision in engineering continues.
There is a group in America (considered somewhat nutty even by the lunatic fringe) which wants pi to be officially redefined as 3. The justification for this is the verse in the Second Book of Kings "he made a circular vessel ten cubits across and a wall of thirty cubits encompassed it". You simply can't do that. It is impossible to make a circle where the circumference is three times the diameter, no matter how many laws you pass saying you can. Pi is not something we have invented - it is something we have discovered. It is only our represntations and appriximations to it that are invented.

I'd also like to quote this from one of the comments to MarkCC's post, submitted by someone else known as Josh:

Theorem: All whole numbers are interesting.
Proof. Suppose that there are some uninteresting numbers. By the fact that the whole numbers are well-ordered, there is a smallest uninteresting number n. But hey, that's pretty interesting! Thus, n is interesting, a contradiction.

It's time for Euler's Identity! Cue ethereal music!

Arabic Words in the Sciences

2008-07-22T16:32:00.003+01:00

The Arabs came up with many important ideas in the sciences, and these origins are often preserved in the words we use for them. Here are some examples:

Alchemy - The art of transmutation.

Alcohol - The essence of a substance.

Alembic - A still.

Algebra - The restoration of missing parts.

Algorithm - The Kwarizmiam, which was the epithet of the scientist Muhammed ibn Musa.

Amalgam - Amalgam, suprisingly enough.

Azimuth - The path.

Cipher - Zero.

Elixir - Medicine.

Realgar - Realgar.

Zero - Zero.

The Arabic nations were historically very good with architecture. This is, of course, bound up with their knowledge of geometry and algebra.

Gratuitous Quotation

2008-07-21T18:58:00.002+01:00

I quote from Zero Divides:

Spelling is to writing as arithmetic is to mathematics.

That is all.

All Your Base

2008-07-21T15:21:00.003+01:00

A second post in one day, you cry? Yes, your eyes tell you the truth. I have been lax of late and updates have been sparse. Need to catch up!

Numbers are not the symbols with which we represent them.
What a number is is a matter for philosophy and logic and I may return to it on a later date. But today I'm going to talk about the ways in which we represent these entities.
There are two basic ways you can represent a number. You can have an additional system, whereby each symbol stands for a certain amount and you can combine these symbols by addition to represent the number that they sum to. (I suppose if you gave each prime a symbol, you could also do it by multiplication) Of this type are Roman numerals where I represents one, V five and so on to give numbers of the form MMCCCLV. This particular system has alternative forms: IV instead of IIII which can cause confusion. But the main problem is that it is somewhat unwieldy.
A better system is place values. We come up with a few symbols to represent small numbers and then construct bigger numbers by multiplying by a common factor. Our decimal system is like this: 123 means 1x100, 2x10 and 3x1 all added together. The advantage of this is that it breaks up the number into pieces that fall in the same ratio as all other numbers. This makes sums easier to do, since we can add the components or whatever.
This system - ours we call Arabic numerals although they are Indian in origin - took some time to catch on in Europe because it needs a placeholder ie. something to represent 0 and distinguish between 100, 10 and 1, for example.
Of course, there's nothing special about ten. The Babylonians used base sixty - that is, they had symbols for the numbers one to fifty-nine and after that they moved once place to the left to express sixty as '10'. We still preserve a relic of this - that's why there are 60 minutes in an hour and 360 degrees in a circle.
Binary is base two so only has two symbols to give numbers like 11010 (which is twenty-six). Hexadecimal is often used in computing because it provides a convenient shortcut for converting between our conventional decimal system and the binary used by computers. The numerals are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F and 0.
So why is the base ten system so common? Well, the obvious answer is that we have ten fingers and it's therefore natural to count in tens. In one African language, the word for six literally means 'skip' ie. to skip to the next hand.
This is why when we send out messages into space in the hope of reaching an audience, we never do it in decimal. The odds of any listeners using decimal is low and they may therefore miss the message. Binary is a better choice, since it's the smallest possible place value system and is therefore the easiest to programme machines with. They'll probably think of looking for communications encoded in binary.

The Monty-Hall Problem. Interestingly, when an article appeared in a newspaper (I think it was the New York Times) that mentioned this and how switching your choice makes you more likely to win, thousands of people wrote in to criticise the paper and its apparent inability to calculate odds. But the paper was right.

Pretty Little Physics

2008-07-21T10:24:00.002+01:00

Is a qualitative understanding of science actually possible? I have made the suggestion in previous posts that people might try to gain an understanding of science without necessarily having to learn the principles necessary for practising it themselves. For some things this is clearly easy - anyone can picture the Earth moving around the Sun in an ellipse. It's very easy to visualise Kepler's Second Law without performing any calculations, too. But can something similar be done for everything?
Quantum physics is a good example of a field which is very difficult for practitioners to explain in a public-friensly manner (To be fair to them, it's damnably difficult to explain even in a public-unfriendly manner too). Would it ever be possible to get across the ideas inherent in it in an accurate but easily visualised way?
Now, I'm entirely the wrong person to consider that particular example since I'm not a physicist any further than first-year undergraduate level and have hardly begun to scratch the surface of this field. But I do think there's hope.
Einstein's theories of relativity (the Special and the General) have a reputation for being massively difficult to understand. The General Theory has some nasty mathematics in it - Einstein joked that once the mathematicians had got hold of it, even he didn't understand it any more. It's also exeedingly counter-intuitive. But there exist oft-used ways of visualising its effects ('rubber-sheet' spacetime and of course the omnipresent clocks-and-trains demonstrations). I don't say it's possible to appreciate every nuance in this way, but people can read or watch an explanation and have a reasonable idea of the theory's outline and consequences.
Perhaps this is in large part due to the way Einstein seems to have constructed his theories - he visualised them first and then built up the rigorous and mathematical descriptions of them. Feynman, too, used to say that he tried to get a qualitative idea of what was going on in a system before applying mathematics to it.
So I think there is hope. Science is mathematical, there's no way to escape from that. And to be a scientist - especially a physicist - you'll need a heck of a lot of it under your belt. But for the public, I don't think it's absolutely necessary. It helps to be able to appreciate the technical form of the theory and I would encourage everyone to study some maths if they want to gain a deeper understanding of the natural world. But sooner or later we all have to settle for qualitative explanations.

I never get tired of this.

Ripple Tank Simulator

2008-07-16T19:10:00.000+01:00

Play and Enjoy.

The Deadly Mrs A.

2008-07-15T13:45:00.003+01:00

Buzzwords are a double-edged sword for scientists (as, I suspect, for everyone else).
One the one hand, they provide an easy reference to concepts that might be otherwise difficult to explain. Many people these days have heard of, for example, the Human Genome Project. Pretty much every media article will use something along the line of "cracking the code" or "the blueprint for life". It's quite catchy and conveys a general sense of what's going on.
But on the other hand, there is a danger that people focus on the buzzwords and cliches to the detriment of the science behind it. In the former example, this is of little more than annoyance to scientists. DNA isn't like a blueprint that explains everything, nor does it provide a cast-iron description of your fate (there seems to be an assumption that if something is 'in your genes', it's unavoidable. Bear in mind that many cases of short-sightedness are genetic. But we've invented glasses, clever us.). This is the kind of thing that gets on the nerves of those who study genetics, but it doesn't really have an effect on people's everyday lives. Regrettable, but not dangerous.
What is dangerous is when the media uses buzzwords and popular cliches that lead people to make potentially hazardous decisions. 'Superbugs' is a current one. Words like this are, I think, irresponsible. If we take the example of MRSA, the most famous one, most people will tell you that you're most likely to catch it in a hospital and that it's a killer. They may also say that, in effect, our modern medical system has created 'superbugs'.
Like most misunderstandings, the facts are true, but the interpretation leads people astray. MRSA stands for 'methicillin resistant staphylococcus aureus'. That is, it's a strain of the bacterium staphylococcus aureus that cannot be killed by methicillin, a common antibiotic. That's why it's only really found in hospitals! Staphylococcus aureus is a common bacterium that causes a whole host of diseases (including pneumonia, meningitis and septicaemia). It hasn't been created by hospitals, it's just got used to them to the extent where one medicine used there won't kill it. In other words, it's just normal SA that can't be treated so easily which is why it's so dangerous.
Now here's the danger. People hear the name, they hear 'superbug'. They know it's mainly found in hospitals. So many people choose not to go to hospital if they fall ill. Maybe they see an alternative practitioner. And in attempting to avoid an untreatable disease, they do not treat their disease. To put it bluntly, MRSA in a hospital is just the same as untreated SA at home.
So we must be careful when we use buzzwords. The opportunities for interesting and informing people are there, to be sure. But they go hand in hand with the opportunity to scare and misinform.

Sorry, but I'm a chemist writing a science blog. I had to post this sooner or later.

With, After and Beyond

2008-07-10T10:53:00.004+01:00

This comes from an episode of that most witty television programme, Yes Minister:

Concerned woman: Listen, I've heard that this factory will be making the chemical that poisoned Seveso.
Jim Hacker: Now that's not true. The chemical in Seveso was dioxin. This is metadioxin.
Woman: Well that must be virtually the same thing.
Hacker: No, it's just a similar name.
Woman: It's the same name, only with 'meta' stuck on the front.
Hacker: And that makes all the difference.
Woman: Why, what does 'meta' mean?
Hacker: baffled What does 'meta' mean, Humphrey?
Sir Humphrey: It's quite simple. It means 'with' or 'after', sometimes 'beyond'. It's from the Greek. In other words, with or after dioxin, sometimes beyond dioxin. It depends whether it's the accusative or the genitive. With the accusative it's beyond or after, with the genitive it's with. As in Latin, of course, as you no doubt obviously recall, where the ablative is used for words needing a sense of 'with' to preceed them.
Bernard: But of course there isn't an ablative in Greek, is there Sir Humphrey?
Sir Humphrey: Well done, Bernard, well done.
Hacker: You see?
Woman: Not really, no.

I like that conversation, not least because it seems to have become fashionable recently to stick 'meta' in from of anything to make it sound cooler. I was privileged some months ago to have someone try to explain the concept of 'meta-irony' to me. As far as I can see, it's just like irony, except you're being ironical about it (to be fair, I don't think she really gave the term much credit either).
'Meta' in this case is a chemical term. Take a substituted benzene ring:
When you add in an extra group, it goes on one of those three sites (the other two are, of course, ortho and meta as well). Hence you can distinguish two chemicals with the same formula and similar structure. Ortho is from the same root as orthogonal, it's Greek for 'straight'. Meta in this case is accusative, as it's 'after' ortho. Para is damned confusing word since it can also mean 'beyond'. But an alternative meaning 'contrary' is the root since it's opposite the primary group.
There isn't actually any such thing as metadioxin, dioxin has the wrong geometry to apply these terms to it. Happily for the Prime Minister in that episode, it turns out that 'metadioxin' is indeed perfectly safe. It's an inert chemical ie. it's unreactive. There is a later section in that episode where Sir Humphrey explains that inert chemicals are not 'ert', although he uncharacteristically doesn't know to what the 'ert' refers to. It's from the same root as exert, to put out work. Inert chemicals do very little, if anything.

Everyone likes a good bit of spontaneous combustion.

Censored. Heavily.

2008-07-07T20:48:00.004+01:00

Today’s topic was suggested to me to a friend after our conversation had somehow wandered into it from a starting point of cannibalism across the world (just don’t ask).
Carl von Linne is one of the most recognisable names in biology, though most will be more familiar with him from the Latinised version of his name, Carolus Linnaeus. The self-named “Prince of Naturalists” founded the modern science of taxonomy and organised much of biology into a comprehensible and organised form. But he also had something of a mischievous side. Others would describe it as downright filthy.
Because he had an almost pathological obsession with sex. He named species after it (even now the slipper limpet is crepidula fornicata). One genus of plants ended up as clitoria. Parts of plants were given suggestive names (anus, hymen, vulva, pubes to name just a few). All in all it dismayed many of his readers.
Perhaps fortunately for biology teachers who have to take teenagers through the parts of flowers, most of these terms were removed in the nineteenth century so as not to offend those of sensitive dispositions.
Linnaeus was, it must be admitted, massively arrogant. Is it too much to suggest that maybe this apparent obsession was nothing of the sort? That maybe what he was doing was imposing these entirely arbitrary terms on the world for nothing more than the sheer joy of seeing his word accepted no matter how obscene? I’d like to think so, taxonomists don’t have much of a reputation for fun and games. It would be nice to redress the balance.

Someday, as Randall Monroe at xkcd once commented, physics will get over its huge collective crush on Richard Feynman. But speaking for myself, I don't see that happening any time soon. Here's the man himself.

Short and Simple

2008-07-05T15:19:00.004+01:00

There was a couple of programmes on Radio 4 some time ago concerning the Two Cultures debate (see a couple of posts ago). It had the idea of sending an art student and a physics student around each other's department and much interesting discussion was had. Listen to the programmes here.
But what I want to talk about today is related to something the art student said in the first episode. She describes the bafflement she felt in a physics lecture - mirrored interestingly in the similar lack of understanding when the physicist attended one of hers - and her feeling that somehow the meaning of the lecture was 'hidden in the equations on the board'.
In a sense, she was right. The equations contained the exact and precise meaning of what the lecturer was discussing. However, it seems to me that here are two different approaches to an equation - on the one hand the artist looking on in confusion as the meaning is 'hidden' within the symbols; and on the other the lecturer and (hopefully) the physicists seeing the distilled meaning cleared of all dross and ambiguity. This is perhaps the same as the two-fold impression that any kind of technical description has on people, as those who understand the language see so much clearer and those who do not feel excluded.
A good equation is, many would contend, beautiful. There's a certain elegance to some special formulae. The benefit of an equation is that the ideas are set out independent of the syntax of language or the irrelevant need for explanation - there's no need because the idea is already expressed in its simplest form. Consider:

(which is perhaps a massively over-used formula but it's nice and simple). Let's not worry about the meanings of the symbols for now, just treat them as quantities. That formula describes everything in a stunningly succint manner. You can see it all - increase m and you increase E. The same goes for c, only more so. You can analyse it more and in many different ways, pages and pages of words would be needed to express what these five symbols mean. It may seem that the meaning is hidden. But if you know the language - and it's not that hard to learn with a good teacher - the simple Platonic beauty of the idea shines through.

This is cool.

PS. I hear Oxford University's Physics department has appointed an Artist-in-Residence. Good news for healing the divide!

A Stone by Any Other Name

2008-07-03T18:38:00.004+01:00

He who with pocket hammer smites the edge
Of luckless rock and prominent stone,
... detaching by the stroke
A chip or splinter to resolve his doubts:
And with that ready answer satisfied,
The substance classes by some barbarous name,
And hurries on...

William Wordsworth there, on the superficiaility of names. Richard Feynman once spoke about how his father taught him about the world. But one day, a friend pointed to a bird and asked if the young Richard knew what it was. The boy replied that he didn't. 'Your father', responded the friend, 'doesn't teach you anything'. The point Feynman was making was that the boy was wrong. His father had taught him a lot of things. He knew much about the bird, but not it's name. Knowing something's name doesn't actually tell you anything about it.
This was a good point to make. So why do we bother giving things generic names in the first place?
The obvious answer is that things are similar. If you want to refer to all of a particular kind of tree, you invent a name for that type. Oak, maybe, or Common Oak for a subdivision. The name acts as a key - once you have identified something that has the characterisitics of an oak, we can assign it the name of 'oak' and extrapolate that it possesses all the properties of this kind of object. You can look up the tree in reference books, speak to people who know about them and get more information. Much more useful than if you either had to show the individual tree to an expert or start over from knowing nothing of it. So generic names are an indexing system, a way to classify knowledge so we know to what kind of objects it refers.
This is the reason people studying a subject have to learn lots of lots of names. Geologists have to know what we mean by 'sandstone', chemists the definition of 'acid'. Philosophers need to know what is considered 'modernism' or 'Platonism', else discussion between them bog down into cross-purposes. And so on. But knowing those names is, as Wordsworth pointed out, nothing like knowing what something is.

Here's another key to meaning. The book.

Science and Technology - an Important Difference

2008-07-02T16:43:00.006+01:00

I was reading earlier an article on feminist perspectives on science. I have a bone to pick with something it said. Not that this was one of those nutty postmodernist 'thinkers' who reckon that if you dress up any old nonsense with words like 'hermeneutics' or 'hegemony' it automatically qualifies as advanced thought (and for those of you who may think I'm being overly harsh on the postmodern and poststructuralist movements, may I remind you of the Sokal Affair).
No, this article was pretty well thought-out, discussing the effects that the societal exclusion of women for the past few millenia has had on the progress of science. As regards this, I have no problem. No doubt all of history, not only science, would have been radically different if half the population had actually been given the chance to participate in activities other than home life. But then I came across this: "A feminist science may not, for example, have chosen to build Stealth Bombers".
Now, it could be a defensible position that a more egalitarian society would not place so much emphasis on having the biggest war planes. It can also be argued that the increased inclusion of women in society could have resulted in a more peaceful path to history (I'm not sure this would stand up, but it could be argued without the speaker being considered slightly delusional).
But the building of Stealth Bombers isn't an integral part of science. It has no bearing on the argument that science would be different if women had more of a history of involvement with it. Granted, you can't build such weapons without a deep understanding of electronics, acoustics etc. But the bomber isn't science. It's technology. What I mean is this: that if, for whatever reason, no one had ever built a warplane, it would not make a jot of difference to the nature of our science. The laws that govern our universe are exactly the same whether or not we choose to build any particular technology. Claiming that science is bad because the atomic bomb can only be built with scientific understanding is as absurd as claiming that books are bad because Stalin could only have massacred so many people because of Karl Marx's Das Kapital.
I just happened to be sparked off on this tangent by the article, but this is not a viewpoint held exlusively by feminists (It's not even the main theme of the article). Indeed, it's a common idea now that science is inherently linked to death, destruction and the will to dominate.
Someone once said that "Sociology of science is as useful to scientists as ornithology is to birds". I disagree with this, people should always be aware of the greater impact of their work. No man is an island and all that. But it's important to remember that what people do with science is not a part of the science itself (even if it's done by scientists). We have an understanding of nuclear physics. That understanding is science. What we do with it is technology, politics and sociology.

I love this video.

One More Contribution to the Debate

2008-06-29T13:21:00.016+01:00

It has been some time (it was 1959, to be exact) since the author C. P. Snow gave his influential and exceedingly controversial lecture ‘The Two Cultures’.

The basic thesis of this lecture (I wasn’t able to find the whole text online, unfortunately) was that there existed a huge gulf between the arts and humanities on one side and the sciences on the other. Neither side was capable of understanding the other; they had practically ceased to communicate. Snow also suggested that perhaps the artists were somewhat falling behind:

"A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of Have you read a work of Shakespeare. I now believe that if I had asked an even simpler question -- such as "What do you mean by acceleration, which is the scientific equivalet of saying, Can you read? -- not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern goes up, and the majority of the cleverest people in the western world have about as much insight into it as their neolithic ancestors would have had.

So are artists utterly irredeemable snobs? No, I think not. What we have here, I believe, are two closely linked problems.

The first is lack of breadth in knowledge, not something that is new. This affects all people and is perhaps an inevitable consequence of the growth in academia and research. This does not mean, however, that it is a good thing. Communication between people in different fields is essential and to limit oneself to knowledge, expertise or skills in a highly specific area (whether it be quantum chemistry of metal oxides, the early sonnets of Shakespeare or dogme films) is to produce a narrow minded person. Someone once commented that ‘you know more and more about less and less until eventually you know everything about nothing’.

The second problem is specific to the sciences. They are all too often not communicated well. So many people say their involvement with science ended after school and that they found the lessons dull and unimaginative. Indeed, the major complaint was that they were taught as a set of facts to be learned off by rote and as if everything were already known. Lots of them say they couldn't understand what was being taught - no suprise when you consider how the examination system requires rote learning with few principles, less justification and often hardly any practical experience. I have expressed my distaste for this bastardisation of science before and won't bore you by ranting further.

Much controversy was sparked off by Snow’s suggestion that those in the fields of the arts and humanities were somehow putting less effort in. In this, I think he was wrong. But a nerve had been touched and the screams have scarcely died down since then. James Watson (not exactly known for staying out of controversial issues) ranted about how any literary work was seen to be superior to any scientific work (as a writer of scientific work himself, I cannot help but feel that he had something of a vested interest).

A good objection came from many academics in non-scientific fields. They pointed out that, actually, their subjects were not well-understood by scientists or the public. The public may feel that having read a work of Shakespeare is some kind of qualification, but there’s a lot more to literature than simply reading. To appreciate art is not the same as to create it and there is a heck of a lot going on behind the scenes. All everyone else has is an appreciation of the subject, not the knowledge or expertise of the practitioners. Why demand that lay people suddenly learn to become scientists?

But of course, Snow was demanding nothing of the sort. An appreciation of science and understanding of the basic principles that underlie it is not the same as to become a scientist. There is a world of difference, for example, between knowing that in an electric circuit electrons flow through the conducting wires and the friction they create within the lightbulb causes it to glow brightly; and to gain a full understanding to the processes happening at all stages. The former is a qualitative approach – an appreciation of what happens. The latter is a quantitative approach – the expertise of a practitioner.

Richard Dawkins, in one of his own pleas for greater public appreciation of science, used the analogy of music. One can listen to music as an active practitioner within that field – as a musician or a composer. Alternatively, one can simply know a bit about it, be able to talk with reasonable knowledge about Beethoven and gain a qualitative understanding. It may not be as complete as the understanding of the musician, but it’s a lot better than nothing. The music will be all the more beautiful for it.

Something of this sort is already true of literary, historical and artistic pursuits, though I think it needs to be more so. Perhaps it could become true for science also? I hope so.

Here is discussed the importance of scientific understanding for everyday life, in addition to its intellectual and aesthetic pleasures.

An L of a Time

2008-06-27T19:39:00.005+01:00

Let's look at an ancient riddle today, one of my favourites. It is known as the Riddle of Diophantus, and the riddle is to find the age of this man when he died (Diophantus of Alexandria was a third-century Greek mathematician, but the puzzle is only recorded in a 5th century puzzle book).

'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.'

So how old was he? Let us use algebra, where his life-span is represented by L:

He was a boy for one-sixth of his life, so that's L/6.
'While whiskers grew rife' - he was a young man for one-twelfth of his life, ie. L/12.
One-seventh as an unmarried adult - L/7.
He was married for five years before the birth of his son.
This son lived for half his father's life - L/2.
He lived four years after this.

Now, the total of these segments of his life make up his life, quite obviously. So we can form an equation from this:

(L/6) + (L/12) + (L/7) + 5 + (L/2) + 4 = L

Adding together the fractions of L and the numbers:

(25/28)L + 9 = L

Multiplying by 28 to get rid of the fraction:

25L + 252 = 28L

Rearranging to collect the L's:

252 = 3L

And therefore finding the answer:

L = 84.

So, according to this riddle, Diophantus was 84 years old when he died. Whether or not this was in any way connected to the man, it is very apt. Diophantus is regarded by many to be the inventor of much of our algebra, although he had no notation with which to express it. It was all in words, which makes it much harder to do.

Here's Bronowski on Pythagoras' Theorem, from his series The Ascent of Man.

Grandeur in this View of Life

2008-06-25T20:51:00.004+01:00

There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

That was Charles Darwin, from Origin of Species.

Poets say science takes away from the beauty of the stars — mere globs of gas atoms. Nothing is "mere". I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination — stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern — of which I am a part... What is the pattern or the meaning or the why? It does not do harm to the mystery to know a little more about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

Richard Feynman, from The Feynman Lectures on Physics

It is sometimes said that scientists are unromantic, that their passion to figure out robs the world of beauty and mystery. But is it not stirring to understand how the world actually works — that white light is made of colors, that color is the way we perceive the wavelengths of light, that transparent air reflects light, that in so doing it discriminates among the waves, and that the sky is blue for the same reason that the sunset is red? It does no harm to the romance of the sunset to know a little bit about it.

Carl Sagan, Pale Blue Dot

You could give Aristotle a tutorial. And you could thrill him to the core of his being. Aristotle was an encyclopedic polymath, an all time intellect. Yet not only can you know more than him about the world. You also can have a deeper understanding of how everything works. Such is the privilege of living after Newton, Darwin, Einstein, Planck, Watson, Crick and their colleagues.

You don't have to be a scientist – you don't have to play the Bunsen burner – in order to understand enough science to overtake your imagined need and fill that fancied gap. Science needs to be released from the lab into the culture.

Two from Richard Dawkins

The wonderful thing about science is that it's alive.

Feynman again, that most excellent of speakers.

I think you can see what I'm getting at here.

Endless Rain

2008-06-23T18:48:00.005+01:00

I like rocks. This makes many friends fear for my sanity. Today I'm going to talk about chalk, because it's very nice.
Most of the chalk in this country (including that which makes up the White Cliffs of Dover, the Downs and the Chilterns) comes from the Cretaceous period, between about 150 and 65 million years ago. Indeed, this period is named because of this - the Latin for chalk is creta.
The primary question that faces a geologist in the field is 'how did this rock form?'. This may not be immediately obvious when it comes to chalk. After all, it doesn't really look like anything except itself. Sandstone is clearly made of sand, and mudstone often appears... well, muddy. But we don't see unlithified chalk lying around every day, so where did it come from?
Fossils are the geologist's friend here. There are various ones to be found in the chalk, and they indicate a marine environment (thus going a long way to explain why we don't see raw chalk everywhere). One of my favourites is Micraster, a common little burrowing sea urchin [I like sea urchins. I think they're cute. And Micraster is heart-shaped. I'm sorry for my weirdness].

So if the chalk was formed in the sea, what is it made from? We now turn to two tools - chemical and microscopic analysis. Chemical tests tell us that the rock is made up mainly - almost exclusively - of calcium carbonate, calcite to be specific. This is a reasonably common material, many animals use it to build their shells. Others use aragonite, another form of calcium carbonate, but this usually alters to the more stable calcite after death. Under the microscope, we see the structure of the chalk. Largely, it's made of a calcareous mud - that is, very small calcite particles. But we see also little circular plates sometimes, in various states of decay. What are these? Well, they look like the plates that cover the bodies of microscopic organisms called coccoliths. They look in life like this:

They swarm in huge numbers where conditions are right. And when they die, they come apart, unravelling, and the little plates rain down as snow with all the other debris of the ocean. What actually reaches the bottom depends on the conditions. Different minerals dissolve at different temperatures, at different depth and with different limiting concentrations. But at the time the chalk was formed, the conditions were perfect for a ceaseless rain of little shields.
There are over 200 vertical metres of chalk (correcting for the way it's been tilted by subsequent events), and they originall covered an area rather larger than Britain (although not actually covering all of Britain, the old sea bore no resemblance to the modern landscape). Billions upon billions of miniscule animals died year upon year to slowly build up the shining white walls.

Here's another rock forming. In this case it's basalt, solidifying from lava in Hawaii.

PS. There never will be 'bluebirds over the White Cliffs of Dover'. The bluebird is exclusively American.

To See Through a Scanner Darkly

2008-06-19T13:06:00.004+01:00

Browsing through the skepticism-themed Bronze Blog, I came across the words "Science isn't just a collection of scanners, despite what Hollywood will tell you", which I thought was a good way of summing up what many people feel science to be.
You might be forgiven for believing that scientists are so because of factual knowledge, that science itself is merely a miscellaneous collection of facts. This could not be further from the truth. Science is a method, a way of thinking and a route to finding the truth. I forget who it was that said 'The scientist is soon bored by what is known. It is the unknown that motivates him', but it's largely true.
Perhaps that is why so many feel disenchanted with science - it is too often portrayed by the media as an immovable collection of frequently abstruse facts. Where is the interest in that? It also leads to the impression that there is a fixed scientific world view and that anything outside of it is 'not science', even if it is true.
To explain what I mean by that, consider a TV programme or film dealing with some kind of unexplained occurence. Usually, there's a skeptic and a believer as characters (think Mulder and Scully etc). How many times have we heard the skeptic say, confronted with something unsual "there must be a scientific explanation!" or their foil say the reverse "this is outside the realm of science".
I think this betrays a lack of understanding about science. What does it mean to say that something is 'outside the realm of science'? Science concerns itself with observing something, devising an explanation and suggesting relationships and then testing those ideas to refine (or sometimes entirely replace) them. Granted, there are things that lie outside science - I'm thinking ethics, art and the like. But to state that, for example, ley lines 'do not have a rational explanation' is nonsense. If they exist, they can be detected (or else how would we know about them?). If they exist, they can be studied. To be sure, the study may throw up new facts, create new theories and very likely require the alteration and replacement of many old ones. But this is no more of a challenge to science than a new movement in art is a challenge to art itself.
As it stands, the scientific community does not believe ley lines exist because there is absolutely no evidence for them. But this is not due to their 'lying outside of science' or 'transcending rational explanation', nor is it because they 'do not fit into the scientist's world view'.
Science is there to discover the truth, no matter what the truth turns out to be. It's not a collection of scanners, finding only the things it expects to. Science is what we do to see the world in its true glory.

Here's a good talk on the strangeness of science by Richard Dawkins. I've always thought that it's a shame that his excellent writings on science have been somewhat eclipsed by his (in my opinion almost as good, though far more controversial) writings on religion.

Passing the Buck

2008-06-18T16:35:00.003+01:00

A full blog post will appear when I have time off from the partying of May Week, but I thought I'd share with you an excellent post I found on the notable blog Science After Sunclipse.

Distilled Wisdom

2008-06-15T14:44:00.001+01:00

My apologies for the lack of posts this last week, exams got in the way and were inevitably followed by post-exam celebrations.
Alcohol. If an alien civilisation comes to visit, one of the things I am sure they will be impressed by is the sheer number of ways we have come up with to priduce it and get it into our bodies. We make it from pretty much everything (I don't think any has ever been made from oats, at least not on a large scale, but I was once privileged to try porridge flavour vodka).
Making alcohol in the first place is quite easy and was likely first discovered by accident (although some animals do eat overripe fruit for the same effect, and it is possible that controlled fermentation by humans followed the fortuitous discovery of pleasantly fermented fruits). Basically, you take something with sugar in. Fruit is good but cereal grains can be used and even less tradtional substrates like beans and peas. Then, you infuse it into a liquid. Again, fruits come up trumps here because their juice already is a perfectly acceptable liquid.
Next, it must be left to go off in the absence of too much oxygen. Our good friend yeast is responsible for this, in the same chemical reaction that makes bread rise (unbaked bread contains alcohol but this is destroyed in the oven). The sugars in the liquid are broken down as food for the fungus, producing alcohol. (If the fermentation continues too long with too much oxygen, or if the produced alcohol is exposed to the air for too long, it is oxidised and produces vinegar.)
Wine, beer (later flavoured by infusing hops into the product), cider etc are all made this way, but a problem comes if we want strong drink. The yeast dies once the concentration of alcohol becomes much higher than in wine. Spare a thought for the poor fungus, it has to live in its own refuse. However, chemistry comes to the rescue. Alcohol and water have different boiling points, 78 degrees and 100 degrees respectively. So if you heat a mixture to between those two temperatures, only the alcohol will come up. Cool the vapour down, and the resulting liquid will have a much higher concentration than before.
Here we see chemical distillation apparatus. The mixture is heated in the flask (15), a vapour passes up the tubing to 3 and is forced into the condenser (5). This is where it cools (the type shown is a Leibig which has a water jacket around the tube to cool the gas) and runs down as liquid to be collected at 8.
Of course, the final product will not be pure alcohol. As you will have observed on seeing a steaming hot bath, water will vaporise partially before its boiling point. But this isn't a problem, most people don't want to drink 100% ABV whisky. In the transfer between flasks, not all of the flavourings get passed along, which is why strong drinks are a lot more similar to each other than undistilled ones (the large amount of alcohol also masks some of the taste).
Distillation has many other forms - here it is used to purify dirty water. With a bike.

Just Deserts

2008-06-06T11:52:00.005+01:00

After several mathematical posts in a row, I think it is time for something with a less quantitative approach. Rocks would be appropriate, given that I did my geology practical exam yesterday and can now think about them without shuddering.
Rocks can be very pleasant. Many of them are pretty. Many of them, unfortunately for geology students, look very similar to one another. But all of them are filled with interest for they all preserve in their structure the story of the Earth's past.
I have, for instance, a small red pebble on my desk, souvenir of a field trip to the Isle of Arran in Scotland. It is not especially dramatic. I can scratch at it with my nail and rub off a few grains. Those grains reveal themselves to be sand. Indeed, the whole pebble is sand, cemented together by (perhaps unimaginatively) silica, recrystallised from more sand that broke down under pressure and with a little help from water. I picked this pebble up from what is now a beach. A natural place for sand, you might think. But this sandstone did not form in a beach. No, the rounding of the grains, their small size and the microscopic traces of rusty iron oxide that give it the characteristic red colour came from a desert. Indeed, the deposit I took it from still preserves huge 'cross-bedding', the traces of sand dunes left behind. This sand was once part of a desert.
It was over two hundred and fifty million years ago that the land that would one day be Britain lay not far north of the equator in the midst of the supercontinent called Pangaea. A great desert covered this part of the continent for a very long time. The New Red Sandstone, as the formation it left behind is called, was deposited over a period of forty million years.
Forty million years of desert. In some places, you can see shallow U-shaped deposits of pebbles much larger than the surrounding sand. The pebbles are the same stuff as the sand, but not eroded small enough. How did they come to occupy these positions? They are the cross-sections of seasonal flood channels, wadis, that brought with them the stuff of the mountains far away.
Much has happened to Britain since this sand was layed down. it has been tilted, uplifted and drowned. It has been eroded, and more sediment layed down on top, and that itself has been eroded. It has been in the middle of the sea, in subtropical islands, on the edges of a sea the same latitude as the Mediterranean. Ice sheets have covered it and melted only for another to come and freeze the land again. Huge amounts of new rocks have been formed, hundreds of metres of limestone and chalk, reminders of the shallow seas that once covered all that is around you and rained down upon it an endless snow of shell fragments and mud.
Eventually, we walked on its surface. The geology of Britain is not merely varied, but quite remarkable in that it preserves, somewhere in these islands, a record of the Earth for over five hundred million years. And in my hand I hold a chunk of desert so old that the four and a half thousand years since the building of the Great Pyramid is but the blink of an eyelid in comparison.

In this video of Bryce Canyon, we see an example of an ancient, lithified desert eroding to provide the sand that litters a modern one.

Endless fields, as far as the eye can see...

2008-06-04T11:25:00.009+01:00

Let's talk about something nice today to cheer us all up. Maxwell's Equations are really quite lovely. Readers of Physics World magazine, the publication of the Institute of Physics, voted them the most beautiful set of equations ever derived. So here they are:

OK, they probably look very confusing right now and not very elegant. Well, let's go through them and see how they work.
Right, the first one. That triangle followed by a dot is called the divergence operator. When you apply it to E, which is the electrical field, it gives you a number describing a property of the field - its divergence, hence the name. It basically means 'how much is coming out' (and here I'm simplifying a bit). So the right-hand-side of the equation tells you how strong the electric field coming from an area of space is. And it's ρ, the electric charge density divided by ε_o, the permittivity of free space. The permittivity is a fundamental physical constant, so basically this equation states that the electric field coming from a region of space is proportional to the total electric charge in that region.
Number Two is pretty much the same. There's the same divergence operator, this time acting on B, the magnetic field. And the divergence is zero. What does this mean? Well, that there must be no net magnetic field coming from anywhere. If this sounds odd, remember the word 'net'. You can envisage a magnetic field line coming out of an area of space so long as another one comes in. This means there's no net divergence. Magnetic field lines go round in loops with no beginning or ending. Every north pole has a corresponding south pole and we've never observed one without the other.
We've got a new operator for the third equation, that of curl. This does more or less what it says on the tin. It's a measure of how curly the field is. Zero curl would imply a uniform field of parallel field lines. So the bit on the right? The fraction with the B and the curly ds means 'the rate of change of B - the magnetic field, remember - with time'. So if the magnetic field doesn't change, the rate of change is zero and so is the curl. Conversely, any change in the magnetic field will alter the curliness of the electric field. Why is this significant, I hear you cry (go on, cry it)? Let's think about it. A curly E will push charged particles around in loops. In loops. Isn't that an electric circuit, charges moving along a looped path? Why yes, I believe it is. Changing magnetic fields generate electric current.
Only one left! This one should be all right for you to read now. Curl of a magnetic field equals some multiple of J (this is the 'current density', how much electric current is flowing in a particular region) plus a multiple of the rate of change of E. We know ε_o from above, μ_o is a similar fundamental constant, the permeability of free space. Now, we know from above that magnetic field lines are always loops. So how can the curliness vary? Well, if the lines are tighter together, it's more curly, isn't it? Smaller circles have to curve more. So the curl of a magnetic field is basically a measure of its strength. This means that the strength of a magnetic field varies with current flowing and with a changing electric field.
So we now have a complete description of electric and magnetic fields and the interactions between them. These are quite profound results, we have layed out the rules governing one of the fundamental forces, electromagnetism. Just one last point, a nice little addendum:
Imagine an electric field that wobbles a bit. This makes a magnetic field that also wobbles a bit, a little out of time with the electric field. But the magnetic field will produce more E, wobbling again and a little more out of time with the first. How fast would this chain of interlinked fields move forward? If you do the maths, you get an answer of:

So let's measure the values of those constants (we've already done so to get the other equations, as a matter of fact) and find v. It's 300,000,000 metres per second. It's the speed of light. Light is a chain of electric and magnetic fields oscillating through space. Isn't that wondeful?

This is how excited some people get about the equations.
(There is an error in the video's expression for curl of E)

Number Theory

2008-06-03T13:27:00.005+01:00

In the news today, a report from think-tank Reform that the standards of mathematics education in theis country have fallen drastically in the last forty years. Though stories of this kind are very common these days and though it seems that every generation laments the apparent decline in the quality of the country since their own day, this particular conclusion is of no suprise to many in the scientific community.
There is much discussion in scientific journals and magazines about the fall in people studying science and maths. The subject suffering most seems to be physics. Rountinely, the point is made that students do not have the mathematical skills to adequately cope with the sciences. This goes hand in hand with their unwillingness to study these subjects to higher levels. Why is maths so disregarded?
A geeky image, maybe? Well, that certainly isn't helping. But I don't think this can be the whole story. It would certainly put off some people, but wouldn't actually force them to loose their interest. Bad teachers? Perhaps. But if there are enough bad teachers to have such an effect, then this itself needs an explanantion. So maybe it's the curriculum and the knowledge required for exams that's at fault. Many believe modern maths GCSEs are inferior to their older counterparts, demanding less of pupils. This seems, at least from the examples given by Reform, to have some basis. The questions seem more fragmented, concentrating on getting the students to go through routines learnt by rote.
And this, I think, is the heart of the matter. Maths is being taught as a collection of unconnected methods designed to get the right answer. It's like teaching English as nothing but a collection of quotations without reading the book they come from (and I am aware that some English teachers do take this approach and that many students are put off reading as a result). Maths is a process and a way of thinking, not some reasonless set of rules.
Also, too, there is the lack of interest in mathematics, an assumption that it can be left to those odd people who seem to take pleasure in it. The average person's connection to maths is no more than adding 10% into a bill in a restaurant. It is one of the only subjects people can express their ignorance of without being considered ignorant. Imagine someone confessing that they couldn't read. This is regarded as a problem, which clearly needs to be fixed. Not so with maths. You can shrug your shoulders and it no longer matters.
Not that people are necessarily to blame for lack of mathematical ability. The aformentioned bad curriculum has no doubt done enormous damage in hiding from them the true unity and satisfaction of the subject as well as destroying any enthusiasm they may have had. And of course, not all of us are mathematicians in waiting. But I think there should be wider appreciation of what the subject is and what it can do. Physics has its Carl Sagans and Steven Hawkings, biology its Stephen Jay Goulds and Matt Ridleys. But no one seems to speak on mathematics for the general public. I am reminded of Doctor Who: 'Doesn't anyone do recreational mathematics any more?'
Here are some nice aspects of maths. If you like them, don't be afraid to find out more. It's not scary.
Moebius Tranformations.
Some lovely equations. I'm very fond of Euler's Identity.
Some topology.

Lies and Damn Lies

2008-05-31T16:33:00.003+01:00

Statistics are unpleasant. I've never liked them, I find them complicated and arbitrary. Nevertheless, they are useful as they help us understand what our data mean. Unfortunately, statistics are too easily misunderstood.
There are a number of polititians who have lamented that half their country/constituency is below avergae in some aspect or other. A variant on this is the worries some have over half the population having an IQ lower than 100. It used to be the case (and for all I know, may still be) that the poorest one-third of the British population was classed as deprived. Opposition parties have managed to score points against the government by pointing out that the proportion of families considered deprived has not changed at all in the years said government was in office.
You may be familiar with adverts claiming 'eight out of ten women agreed...' or 'seven out of ten dog owners preferred...'. They're rather cunningly done. Like all manipulative statistics, they are absolutely true. 500 women/dog owners/insurance customers were brought in and divided into random groups of ten. With fifty groups to give fifty results, there was almost certain to be one in which eight out of ten preferred the product in question.
There are good news headlines along these lines as well. Immigrants take four out of five jobs, screamed the Daily Mail once last year. The logic ran as follows: x jobs were created, immigrants took y jobs. y was four-fifths of x, therefore immigrants took four-fifths of all new jobs. QED. The error here was that it didn't take into account all the variables. Those who died, retired, moved out of the country or into retraining thus leaving their jobs open. They weren't new jobs, so they weren't taken into account.
Remember the MMR controversy? Parents were afraid that the triple injection would cause autism in their children due to a paper published by a Dr Wakefield in 1998. The paper contained details of twelve children who developed autism in the weeks following their vaccinations. This is the same kind of error as in the 'eight out of ten...' adverts. The sample size was too small - especially when the doctor had chosen the sample from children admitted to his hospital with developmental disorders. In other words, he picked those for whom the vaccination had shortly preceded appearance of autistic symptoms and ignored all those for whom it had not.
Studies both before and since have concluded that there is no link between the triple vaccine and autism. There is a rise in reported cases of autism, likely due to increased awareness of the condition and it does often appear around that age. So taking the vaccine almost certainly poses no risk to children. Not taking it, however, it exceedingly dangerous - measles is a killer. There were 449 cases in children in 2006 compared to 56 in 1998.
Draw your own conclusions from those numbers.
Again, no particularly nice videos could be found on this and in retrospect, the video I posted last time would actually have gone better here. So here's some more Carl Sagan instead, on experimentation.

A Quantum of Idiocy

2008-05-28T16:29:00.005+01:00

Quantum mechanics is appreciably weird. Neils Bohr used to say that if you were not shocked when you first came across it, you hadn't understood it. It is perhaps this weirdness and counter-intuitive nature of the theory that allows it to be the source of much insanity in the New Age movement (notably by Deepak Chopra who won an IgNobel Prize for "his unique interpretation of quantum physics as it applies to life, liberty, and the pursuit of economic happiness")
It seems everyone is using quantum these days. Just put the word in and it makes everything sound scientific (and admit it - it's a damn good word, isn't it? It's got that technical, slightly unusual feel to it). And the strange consequences leave lots of room for hand-waving and wooly thinking. There's quantum mysticism, quantum healing, even quantum happiness. To those of us who have had to study some of the mechanics, we can't help but feel left out. When was the quantum happiness lecture? Why didn't I know about it?
This came to a head recently with the release of the film What the #$*! Do We Know? (Official title, not censorship. I am perfectly OK with the entirely gratuitous use of 'fuck' in my blog). It purports that quantum physics leads to the conclusion that we 'create our own realities' and that 'everything is consciousness'. There is little physics in the film and what is there is misused.
And I find this rather sad. There is so much excitement and wonder in science and perhaps especially in physics. Quantum physics is genuinely exciting, of great fundamental importance and fascinating to study. But for some reason - perhaps due to the mathematics integral to it, perhaps even out of a belief that the lack of scented candles is the Uncertainty Principle's major flaw - great swathes of the public aren't interested. They ignore the real world in all its beauty, wonder and bafflement and instead opt for opaque and misleading platitudes that make them feel good for no effort. It's a shame to think what they're missing.
These mystics need to be more open-minded, I think.
Couldn't find a decent video on this, so here's A Bit of Fry and Laurie on gullibility.

An Ongoing Battle with the Walls

2008-05-25T12:06:00.003+01:00

"The wallpaper and I are fighting a battle to the death. One or other of us has to go" were reputedly the last words of Oscar Wilde. They seem particularly apt now, with the rather miserable cloudy light that fills my room now bringing out the really quite unpleasant shade of light blue that my college has seen fit to paint my room with. One day, that wall will drive me mad.
Stories of people being poisoned by wallpaper are suprisingly common. Before synthetic chemistry really took off and lots of nice dyes were created (the first was a pleasant shade of purple the inventor named 'mauve') most included tranistion metals from that nice long block in the middle of the periodic table. Some paint names still preserve the connection although alternative pigments are usually found these days - cadmium yellow, for example.
Green dyes often contained arsenic - Scheele's Green was copper arsenite, Emerald Green was copper acetoarsenite. For years it was rumoured that Napoleon had been poisoned by his green wallpaper, the damp climate of St Helena leached it from the walls and wafting around the room. This has recently been shown to be unlikely, but there is no doubt that the clear green so beloved of van Gogh and Cezanne (Paris Green is thought to have been his favourite pigment) was deadly.
Lead compounds are often a bright and clear yellow. They, too have been frequently used as paints. You might know the short story 'The Yellow Wallpaper' by Charlotte Gilman. The tale of a woman kept in a yellow room by her husband slowly going mad and believing the wallpaper to be inhabited by a woman is a rather good one. But the little chemist inside my head notes that the colour that rubs of on her hands and clothing from it is a bright, sulphorous yellow - it is chock full of lead. All over her hands, it would get into her mouth and allow the lead to poison her brain.
I doubt this is actually what the author intended, but it is an odd, quite appropriate coincidence.
This is a neat little demonstration of the nice colours produced by transition elements. All the shades in the flask are due to manganese in different oxidation states.

Sounds Nice!

2008-05-22T16:40:00.006+01:00

It's all looking very depressing today. Oil prices are up, sharks are endangered and everyone's run out of money (especially me). I think we need something to cheer ourselves up. Music is always nice.
Perhaps oddly, music is very mathematical. I say 'oddly' because many people think maths is dull and ugly which, perhaps tellingly, is the opposite view held by those who actually participate in it.
Take a guitar, for instance. Pluck a middle C. That corresponds to a particular frequency of sound wave. Play the C one octave higher and you've doubled the frequency you're hearing. This is why they're both C, the waveform of one is a multiple of the waveform of another.
And the other notes? Well, there are conventionally twelve notes in an octave. Yes, I know 'octave' suggests there are eight, but we name twelve, four of which are suffixed - B flat, F sharp. Conveniently, they are spaced with an exact ratio - the frequency of the next note is the twelfth root of two times the previous one. (The twelfth root of two being the number which, if multiplied by itself twelve times, produces an answer of two). So twelve of these fit nicely together.
(Actually, you can have as many notes as you like in an octave - so long as the beginning note of one is twice the frequency of the beginning note of the last and all the notes you've included are in the same ratio, it's fine. Being radical, you can even establish a nice ratio like the one above and then insert extra notes with different ratios to really make things interesting. But we'll stick to the conventional scale to make things easier)
Now, this leads to an understanding of why some notes go harmoniously together and some clash. If the two notes have a ratio of frequencies that is rational (can be expressed as a fratio of whole numbers) they combine together to make a new harmonious sound. But if they don't, then the new sound is mucked up. Why? Because there will be no periodicity to the sound wave produced, there isn't a repeating pattern. And this makes it sound awful.
Exactly why the brain percieves mathematical patterns as pleasant and non-mathematical ones as unpleasant is not known. Some people think it means the human brain is set-up to appreciate mathematics intrinsically and that people who are 'bad at maths' only lack a good teacher. Perhaps, then, the best way to teach children is to show them the true beauty and import of what they do.
Here's a cool use of sound waves. It's done by sending waves through the sheet from different places. Where the waves interfere constructively (they push the sheet in the same direction), the resultant wave is big enough to shake the grains loose into positions of destructive interference (the waves cancel each other out).

The Fall of the Phoenix

2008-05-20T11:20:00.001+01:00

Fortunately I am feeling rather more at peace with the world than yesterday, when a link to the DHMO Hoax reminded me of the story and produced some fulmination.
Browsing through today's news I notice that on Monday, the next NASA probe will be landing on Mars. It is quite odd that I can write this in complete calm. After all, space exploration is still very much in its infancy and any mission to another world is a huge undertaking. If Phoenix is successful, it will be only the sixth spacecraft to touch down on the Red Planet. Like the rovers currently in place, the main job of the lander is to research the geology and climate of the planet's surface. Since it will touch down in the north polar region, it will have an unparalelled opportunity to investigate the water ice locked in the permafrost.
There is a huge amount of water on Mars. NASA estimate that if the southern polar cap were melted - assuming that it is all water - the whole surface of the planet could be covered with over ten metres of water. But Mars is too cold today for liquid water and the atmosphere too thin to allow any that formed to stay as liquid on its surface. Gone are the days when it existed in such volumes as to carve out the great river valleys and flood plains still visible today.
Even so, the landing of a human-made object on a rock over 45 million miles away is a huge achievement. It has been just over a century since we first gained the ability to fly, fifty years since we (to borrow a phrase from Carl Sagan) 'emancipated ourselves' and sent one of our creations into orbit, up to a place no one had ever even come close to before. Forty years ago, men stood on the surface of the Moon, on that silver disc hanging in the sky. And on Monday, we come a step closer to walking on our next-door neighbour's soil.
I apologise for being dramatic, but there are times when you have to be.
Hear Carl Sagan speak rather more eloquently than me on space exploration here.

A Chemical-Free Death

2008-05-19T14:52:00.001+01:00

Sometimes one is afraid for the continued survival of the human species.
You may have heard of the Dihydrogen Monoxide Hoax, one of the more worrying of the many recent reports concerning scientific education in the general public.
It went like this. Dihydrogen monoxide, also known as 'hydroxyl acid' is a major component of acid rain. It contributes to the greenhouse effect. It can cause severe burns in its gaseous form. It corrodes metals and erodes the natural environment. Too much can kill you. And yet companies pump this stuff into the sea by the gallon load. It's added to food, used as a fire retardent and a solvent. Even after washing, it remains.
That last claim shoud set alarm bells ringing, if they haven't already. Dihydrogen monoxide is water. But suprising numbers of people did not recognise this. A member of the New Zealand Parliament, Jacqui Dean wrote a letter to the Minister of Health Jim Anderton asking if the government had a 'view on the banning of this drug'.
So why did this happen? Surely if someone wanted your support to help ban something you'd never heard of, would you not try to find out what it is? We would hope so. But when that thing is a chemical, well. Everyone knows chemicals are bad and unnatural things. They must harm you, it stands to reason.
It's worth pointing out at this point that arsenic is perfectly natural.
A chemical is a substance with a definitite chemical composition - that is, it is made of a particular combination of certain atoms. That is all it is. Water is a chemical, made of two atoms of hydrogen joined to one atom of oxygen. Air is not a chemical, but oxygen, one of its constituents, is. Alcohol is a more complex chemical, being two carbon atoms, one oxygen and six hydrogen atoms linked in a particular way. That something is chemical says nothing about its naturalness (whatever that means - even artificial chemicals are made up of naturally occuring atoms).
This all strikes us as something of a joke, a laugh at those uninformed. But this is symptomatic of a greater problem - the lack of scientific education amongst the public. If this is the level of ignorance concerning water, what must it be in regard to everything else?

The Arrival of the Information Age

2008-05-19T14:29:00.001+01:00

With the opening of this blog, I have perhaps completed my arrival into the modern world. It was something I resisted for a long time, acquiring a mobile phone less than a year ago and a Facebook account at about the same time. But some things are just inevitable. They are particularly inevitable when the looming spectre of exams brings into my life the endless joys of an afternoon spent attempting to say something meaningful about the Maxwell-Boltzmann distribution. It says something about my feelings towards this exact model that two of Beethoven's symphonies have played since my pen last made its mark on the paper.
I confess to feelings of bitterness concerning James Clerk Maxwell. One of the many disadvantages to letting a man discover more or less everything is that the same name crops up all over the place. Maxwell's equations, the aformentioned distribution (with which he at least had the dignity to merely co-author), Maxwell's Demon, Maxwell's Theorum. When it comes to incorporating his name into seemingly unconnected titles, only McDonalds and their inexplicable habit of placing 'Mc' in front of every foodstuff lest you forget in what establishment you are eating lunch comes close.
But the purpose of this blog is not to abuse long-dead Scots. No, it has two purposes. A friend, unacquainated with the myriad of odd little diagrams on my work (only marginally more comprehensible to me than to him) asked me the killer question 'what is it you're actually doing?'. In the weeks that followed, I came to the conclusion that what the world needed, what it really needed, was for me to tell it what I do all day. Clearly this was the missing piece of the puzzle, that essential element without which humanity has been suffering all these millenia.
The second purpose of this is that by writing something vaguely connected to science, I am technically engaged in a productive activity.