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Tony Hartin | DESY | Germany

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Murder by Maxwell’s equations – or How I learnt to love the magic bullet

Friday, June 5th, 2009

Science magazines have become pop savvy in recent times. They dress up fairly mundane stories in provocative titles like “Hunks get more sex” (New Scientist) or  “Secrets of the Phallus: Why Is the Penis Shaped Like That?” (Scientific American). So I was only mildly piqued when I stumbled across “Radio-controlled bullets leave no place to hide” on the New Scientist site today.

GI Joe goes room to room

GI Joe goes room to room

Far from this title being a snappy cover for say a new type of flu vaccine its rather banally about, well, radio controlled bullets. The science content of the article is a standard application of Maxwell’s Laws. The said bullets, being rifled, rotate in the earth’s magnetic field. A little loop inside the bullet has an AC current induced which calculates the distance travelled via radio communication with the gun’s ‘smarts’ – that’s the electronic rangefinder – not the grunt who pulled the trigger. It gives the soldier “another tool in his kitbag”. Now all we have to do is find someone capable of pointing it in the right direction or firing it at an appropriate time.

From a scientific point of view it might have been a vaguely interesting article if it had gone on to discuss the effect of turbulence or whether the rotation speed, or pointing it north or south makes much difference to the range accuracy. Instead it read like a boring version of an arms fair advert

“the XM25 rifle to give its troops an alternative to calling in artillery fire or air strikes when an enemy has taken cover and can’t be targeted by direct fire. “This is the first leap-ahead technology for troops that we’ve been able to develop and deploy,” says Douglas Tamilio, the army’s project manager for new weapons for soldiers.”

The “X” stands for Xtremely smart bullet which after passing through the Afghan mudhut window (if it had one) dodges all the kiddies and takes out the wayward father sitting on the couch reading a copy of “Al Qaeda Monthly”. Even if our smart bullet is unable to perform this feat of magic it can simply explode – and since the final range offset is +/- 3 metres – presumably with some force.

Oh did I mention that the bullet explodes? Yes, thats the idea. You cant actually see who is in the room, so better just to cause an explosion, killing or maiming everyone inside. Now the clue as to why this “tool” is any different from the current ones is given in the text:

“You could shoot a Javelin missile, and it would cost $70,000. These rounds will end up costing $25 apiece. They’re relatively cheap,” Tamilio says.”

Now thats a word to the wise in our current economic troubles – carnage on the cheap. The best method (if a little bit of an overkill) would be just to nuke every town in Pak/Afghan/Iraq-istan, but have you seen the price of plutonium recently? That market has gone to the dogs since the North Koreans and Iranians cornered it..

As a little marketing aid, a helpful diagram of how the XM25 carries out its mission is enclosed (and reproduced here for your consideration). killer_rifle_graphic

Our do-gooder marine, outnumbered 2-to-1 by the dastardly foes is wisely prone behind his smart-rifle. Evil-doer number one is taking a rest in his trench after a hard morning studying the suicide bomber manual. Our smart bullet sails over the trench wall and explodes, gently showering our baddie in a black rain (thats the clue that lets you know it actually hurts). Evildoer number two after seeing the fate that has befallen number one flees – in case his uniform also gets wet from the black rain. We then quickly take out the retreater and his cowardly mates with a fuel air or DIME bomb.

As our advertising brochure picture rather gleefully informs us, “trenches arent safe anymore”… because we know how safe they were in WWI where millions of soldiers idled about on banana lounges, sipping cocktails and writing casual postcards home. And the trenches in the first Gulf War were also notably safe. There an older technology was employed – we simply drove giant tractors to the edge of the trenches and buried many tens of thousands of poor Iraqi conscripts alive. But at least they didnt get their uniforms wet from black rain.

From an earlier article in 1999, also strangely from the New Scientist (amazing what 10 years and a change of sub-editors can do) we have a more realistic description of what happens when an exploding bullet strikes flesh

“WHEN Red Cross surgeon Robin Coupland needs to demonstrate the horrific effect of outlawed weapons, he produces a slightly smudged photo of a wounded man on a stretcher. Your eyes widen as you realise what you’re seeing. Like a cartoon character chomped by a shark, there’s a beach-ball sized semicircle where his shoulder used to be. The man’s arm is still attached to his trunk by a perilously thin strip of tissue. The grotesque injury provides ample evidence that an illegal exploding bullet has been used.”

“Outlawed”. Yes, thats right, by the St Petersburg Declaration of 1868, the Hague Declaration of 1899 and Article 35 of the Geneva protocols. But the world’s remaining superpower saw fit to dispense with the Geneva convention sometime ago when it became clear that they only faced rag tag foes with nothing else much except for 50 year old kalashnikovs. That shouldnt be good enough for New Scientist though. How about some small disclaimer at the bottom of this banally amoral article saying that editors dont endorse the breaking of international law?

Perhaps I should go further…what the hell is something out of Dr Strangelove’s laboratory notes doing in a science magazine?


Roentgen’s humanitarian machine

Tuesday, June 2nd, 2009
Roentgen's Wurzburg Laboratory

Roentgen's Wurzburg Laboratory

Having the opportunity to do some travelling with my partner in Southern Germany recently, we happened upon the preserved laboratory of Whilhelm Roentgen in Wurzburg. Roentgen discoved what he called x-rays using a Crookes tube cathode to produce a stream of high energy electrons which generated characteristic frequency x-radiation via interactions with the tube anode.

Exhibiting admirable modesty, Roentgen attempted to resist the move to name the new radiation after him (an attempt which failed in at least Germany and Russia). On being awarded the first Nobel prize he declined to make a speech and donated the award money to his university. He was offered the noble appellation “von” from the Prince Regent of Bavaria but turned it down. He accepted honors from his university with a call to new students to focus on the essential joy of research.

“During the time when congratulations and honours were showered upon me […] one thought has always remained lively and fresh, and that is the momenory of the satisfaction which I felt when my work was finally developed and completed.”

Noone could accuse Roentgen’s attitude towards scientific research as being tainted by worldly values. He expressed astonishment at the amount of money available for reearch in the US (even then) and thought that essential physics could be carried out with simple apparatus and  clever thinking. He refused to patent an x-ray machine and endorsed the idea of knowledge for its own sake. This was an attitude that others saw an opportunity in. For instance, Thomas Edison was quoted saying

“Professor Roentgen probably does not draw one dollar profit from his discovery. He belongs to those pure scientists who study for pleasure and love to delve into the secrets of nature. After they have discovered something wonderful someone else must come to look at it from a commercial point of view […] One must see how to use it and how to profit from it financially”

This is either a pragmatic or cynical view depending on how you look at it. I certainly would take a hard line to such pronouncements. Not only should science be persued for the benefit of all (not least because it is funded from the public purse), but one should prevent any individual or corporation from extracting profit from it to the disadvantage of the public generally. 225px-wilhelm_conrad_roentgen

This is particularly an easy case to make for applications related to medical health (as x-rays are). Profits are derived in proportion to the direct cost of medical machines. Without an enlightened public health policy this can only lead to restricted access based on the financial ability of patients. This is a societal disease which we are yet to eradicate.

Apart from his attitude to financial gain, Roentgen does not appear to have particularly left-wing though, expressing a horror of Bolshevism and cheering on the German war effort in WWI. To be fair, one had to have hard left politics to see the ‘Great’ War for what it was, an imperialist adventure in which workers were sent to kill each other.

One wonders what Roentgen thought of the use of poison gas in the trenches (introduced by the Germans but in the end used mostly by the British). Though Roentgen signed the pro-war proclamation of the 93 intellectuals (which Einstein refused to sign) he later expressed embarrassment and claimed he was persuaded to sign without reading it.

On his death, Roentgen ordered his scientific and personal correspondence destroyed. This act of self effacement underlined an earlier speech he gave sayng that scientists must expect their work to be surpassed and forgotten. Roentgen does us a disservice here in my opinion – there is much to be learned from the history of science and the thought processes (and mistakes) of scientists. It is not in the interest of science to obscure the background to significant work.


Bad Science

Friday, April 24th, 2009

Its a lovely sunny Friday afternoon in Hamburg, and the weekend looks equally good weather wise. I should be in a great mood and have a jolly physics tale to tell. I find, however, I’ve been disturbed all week about the release of the CIA torture memos and the subsequent pronouncement that the torturers had no need to fear as there was no intention to prosecute them – “it was a time for reflection”, not justice. This reassurance had to be quickly followed up by a visit to CIA headquarters with the message that they had done a great job.

Now I’m not an ethicist or a lawyer. I will not attempt to understand the apparent contradiction between something which is morally repugnant and illegal (as well as ineffective) on one hand, and a “good job, well done” on the other. Likewise I’m sure I dont understand the legal subtleties in the position that torture under direction from the previous administration was legal, and, say, the Nuremberg defence of the Nazis – that they were only following orders.

No what my concern properly should be is the “science of torture”. For make no mistake, a lot of research time and effort has been spent in trying to understand how to break a person. A lot of the modern research was based on CIA funded studies from the 1950s and “experimented” on in places like Vietnam and Central America. One conclusion was that medieval type tortures (of which waterboarding is one) fail consistently to produce reliable information. As a case in point, we learn from the recent memos that one victim was water tortured 288 times. Presumably there were still one or two items he forgot to mention after the first couple of dozen sessions. Or perhaps he successfully managed to endure 287 successive boardings and then suddenly gave in on the 288th out of sheer boredom.

What was discovered, in the ever refining art of torture, was that other methods may be preferable

“Guantanamo Bay turned into a de-facto behavioral science laboratory,” McCoy told LiveScience, where sensory deprivation and self-inflicted pain—allowing a detainee who had stood for hours to sit if he would only “cooperate”—regularly took place. […] Though captives are less resentful when tortured psychologically, it doesn’t make their statements any more trustworthy

Now that sounds like my sort of torture. Anyone who has stood in a bank queue in the UK knows that they could put up with that almost indefinitely if pressed. A point complained upon by one Washington bureaucrat privy to the memos, who himself “had to stand for 8 hours behind his desk all day” (why?) – couldn’t they find something tougher? Its not all fun and games however

You simply make somebody stand for a day or two. And as they stand – okay, you’re not beating them, they have no resentment – you tell them, “You’re doing this to yourself. Cooperate with us, and you can sit down.” And so, as they stand, what happens is the fluids flow down to the legs, the legs swell, lesions form, they erupt, they separate, hallucinations start, the kidneys shutdown.”

I dont want to go on at length about how torture – psychological as well as physical – hasn’t helped. How almost all released prisoners from Guantanamo have had no charges filed against them or have been found not guilty. How after 8 years of war we are further away from an end to terrorism than ever.

Presumably if a whole swathe of people have a grievance against you because they perceive that they have been mistreated in the past, then torturing some of their innocent number wont help soothe them. You can’t torture or kill everyone with a grievance. Even the most hardened hawk must get sick of infinite war sooner or later.

What my real concern, as a scientist, is what sort of people carry our ‘research’ like this? I like to think of myself as a person engaged in science because I see the value in knowledge for its own sake. What can we say of ‘scientists’ with stop watches and notebooks who try to find out the quickest method for dehumanising a person? Could we excuse Josef Mengele as being primarily concerned with advancing medical science?

Of course not. The conclusion I come to is that you can’t separate Science from Society, or indeed Politics, Law or Morality. This must be because, as a human endeavour Science is related to all other fields of human activity. As a physicist I know who went for an interview at a well known multinational arms manufacturer and who was asked whether he minded doing research on things that killed people, I can state that there is such a thing as Bad Science.



Friday, April 17th, 2009

Ahh summer – those long lazy days on holiday by the sea…with the peace… and quiet.. and… well boredom, which can be relieved by finding a good read in the local library. Now call me weird, but when I drop into the library in those sleepy far off towns I usually pass by the physics shelf in the science section for a bit of a squiz. The shelf’s contents are almost always desultory and mercifully I’m usually forced to pass those long afternoons with some pulp fiction.

Journal shelf in DESY library

Journal shelf in DESY library

In contrast, imagine my excitement to discover how absolutely well stocked with fabulous physics books is the DESY library. And those long shelves full of (actually not) dusty old journals like Soviet Physics JETP (journal of experimental and theoretical physics). Now to come across even such a journal title, as I did when I was an undergraduate in the still cold war world of the 80’s, was exciting enough. It seemed like a little bit of a communist 5th column in our bourgeois decadent science library. And that journal is jammed pack full of very intelligent theoretical work – no doubt drummed out of proletarian scientists as they were forced to think away in some Siberian institute that was bound to be a state secret.


Kunstcamera, St Petersburg - original site of the Science Library

I based a lot of my research on papers from that journal – in the 80’s it felt like I was the only person in the West who even knew of their existence! Not true of course. They had obviously been translated into english quite sometime before and I was being naieve – but its nice to daydream sometimes. In any case during the process of my research I ran into a mathematical problem (see my previous blog entry) and I found, tucked away in a little corner of one of those JETP papers, a delicious reference to a soviet maths book – that hadn’t been translated and in fact wasn’t in our library’s catalogue. Or indeed in any library catalogue in the country. Eventually my brave inter-library loans librarian established that it could be obtained from the Leningrad library itself!

Obtained? Obtained!?? Would such a thing be possible? Even if the Apparatchiks allowed it out of the country, could it make it past the Iron Curtain? Even then, wouldn’t some US blockade (like the one around Cuba) stop my precious Leningrad maths book in its tracks? Somehow my intrepid book found its way into my eager hands some satisfyingly long 6 weeks later. And it was satisfyingly jammed pack full of mathematical identities, none of which, sadly, helped me to solve my maths problem. So I sent my brave little book back from whence it came.

To its doom. Horrifyingly, just a few months later the Leningrad National Academy of Sciences library burnt to the ground – destroying some 400,000 precious books and damaging millions of others. As this was really before the whole OCR, electronic library thing, perhaps many were lost forever – a veritable chernobyl of the soviet library world. The only thin silver lining was that it wasn’t the gorgeous Kunstkammer – built by Peter the Great to house the science collection and the original home of the Science Library – that was destroyed, but a faceless brown cubish building, which cant have been as nice to work in in any case.

The Russian Academy of Science Library

The Russian Academy of Science Library

These days the internet has brought us the means to better preserve our collective science knowledge. Many physics text books are now available online and the academic papers likewise – though more work needs to be done to digitize the older papers in journals like the JETP. And its still the case that this information has to be made free. I mean it not now in an iron curtain sense but a financial one. Subscription rates to academic journals are prohibitively high meaning that you have to be an employee of a large university or laboratory to get access to it. The international science community however thrives on the free exchange of information and to that end set up the freely accessible preprint server ArXiv. Here you will find academic papers in electronic form before they get locked away in the journals. There are high hopes for ArXiv

“Its existence was one of the precipitating factors that led to the current revolution in scientific publishing, known as the open access movement, with the possibility of the eventual disappearance of traditional scientific journals.”

One advantage of the journals are that the work that appears in them is peer (or if you like) quality reviewed. However mechanisms exist for the endorsement of ArXiv material – in general the quality of the work is very high, and its a great resource.

To finish with an adage then, information wants to be free and Science thrives on openness, cooperativeness and the absence of a profit motive!


Physics and Mathematics

Tuesday, April 7th, 2009
Airy pattern

Airy pattern

When I was an undergraduate I enjoyed both my mathematics and physics subjects. Pure maths was an exercise in precision, when in proving a simple enough looking theorem, you should be concerned about the minutest detail. Physics I enjoyed because it was mysterious, it was about the world and it involved maths. That seemed like a compelling combination – that a whole class of physical phenomena could be encapsulated in a single mathematical expression. However, there is always the question lurking in the background, what exactly is the relationship of physics to maths?

There are of course many different attitudes and indeed deeply philosophical attitudes. A mathematician might think something like this:

In mathematics, the pure notions of numbers and other structures do not need physics to exist or explain or even justify them. But the surprising thing is that often some newly discovered abstract formulation in mathematics turns out, years later, to describe physical phenomena which we hadn’t known about earlier. The only conclusion I can bring myself to is that mathematics is not just a tool of physics; it must be much, much more.

Conversely, mathematics alone is not enough to determine a physical system. For instance in studying magnetism historically, the English physicist Michael Faraday invisioned lines of forces in an invisible medium stretching between, say, your fridge magnet and your fridge as you bring the former towards the latter. Continental physicsts like Laplace and Poisson envisaged centres of force acting over a distance across empty space. James Maxwell showed that the two different visions were identical mathematically. However physically they were completely different systems giving rise to long debates and experiments about the existence of a universal aether which may transmit Faraday’s lines of force

George Airy

George Airy

One concept which occurs often in physics – and which gives rise to interesting mathematical expressions is that of symmetry. For instance the image above is caused by focusing light onto a circular hole and resulting in a centrally symmetric diffraction pattern. The mathematical function which describes how the brightness of the pattern varies is called after its creator – the Airy function.

These Airy functions (written Ai(z)) occur whenever we try to describe any physical system with the same type of symmetry. And indeed I have an ulterior purpose in making such a long-winded introduction – I study a particular physical system with such a symmetry – in fact an interaction between particles embedded in a strong centrally symmetric field. So naturally in my study I obtain Airy’s functions – and not just one or two, but an awkward combination of Airy’s and other functions.

To be frank this “awkward combination” has been driving me nuts for quite sometime – with me wishing that my undergraduate maths lectures hadn’t occurred so long ago. You didn’t think I was going to spare you the gory details did you?

Maths conundrum

Maths conundrum

There are two ways of simplifying this little bit of maths. Firstly, the squiggly, almost vertical line on the left – the integration – can be done analytically. That is we can perhaps find an algebraic expression exactly equivalent to the above, but without the integration. This is usually the preferred result – to be able to see a physical system described in assimple mathematics as possible is not only asthetically pleasing, but leads to deep insights about the physical system in question. For instance the formula describing the entropy S (or amount of disorder) of a gas, developed by physicist Lugwig Boltzmann, was considered so important that it is engraved on his grave.

Boltzmann's Tomb

Boltzmann's Tomb

In the second method of simplification, my problem integration could be done numerically by using a computer to plot the functions to the right of the integration sign and then calculating the area under the plot. This is the “brute force” method and not very satisfactory if you expect a physical system to be written simply in the language of mathematics. On the other hand, since all simple functions like the Airy function are themselves written in terms of integrations over other functions, then it may be the case that I’m dealing with a new type of function that deserves to be “fundamental” in some sense.

This goes to a deeper question – what is more important, the abstract formulae that describe a physical system, or a the real numbers that arise from calculating such formulae and which are compared with real experiments on the system in question? I suspect the answer is that both are equally important and it is the interplay between the numbers and the formulae – the experiment and the theory – that leads to a deeper understanding.


Kaos (theory) on Wall Street

Wednesday, April 1st, 2009
Hey Broker no need to jump, come down here and learn how to saw

"Hey Broker dont despair, come here and learn to saw and build"

Is it really true that lapsed physicists who work in financial institutions applying physics to stock market modelling have caused the current world economic turmoil? This idea has been raised in a NYT opinion piece and has been discussed in other blogs.

The idea is that physicist influenced modelling became so esoteric that no one else could understand it or the now toxic packages of debt. Since no one understands where or exactly what the debt is, no bank wants to lend any more, ergo the crisis.

You see its just the packaging of debt that’s the problem, not the shyster 100+% housing loans and the insane housing price bubble it produced. Nor the wholesale privatisation or the government approval of banking excesses. Its not really surprising that bankers are trying to spread the heat around. Not when the public sentiment towards bankers is something like,

“I’ll tell you what we should do, spray them with wildebeest odour and make them run through the Serengeti, with a commentary by Attenborough”

But an investment bank cant be a very nice place to work at the best of times. One former physicist who works on Wall Street

“termed the market a wild beast that cannot be controlled, […] There are a thousand physicists on Wall Street, she estimated, and many, she said, talk nostalgically about science. ‘They sold their souls to the devil’.”

Now thats a sad story. Though it is true, in some of my darkest moments, in the face of some crazy research grant cut, I entertained the thought of taking up the devil’s offer. But my motives were noble you understand. I saw myself as a latter day Parvus who would expose the system for what it was. But since Parvus’ scheme ended in disaster and that the bank interviewers would more than likely see through me to my bad attitude, I thought better of it.

Benoit Mandelbrot gave a lecture recently in which he railed against the prevailing economic models as (clearly) wrong. Attempts to model data as “random walks which assume that the price at any given moment depends on what it was the moment before” ignored the fact that stock prices were often discontinuous – jumping wildly from time to time. In fact, Mandelbrot went on the say, economists often ignore “outliers” – data from extreme events (like the one we are going through at the moment). But its the wild swings which constitute the reality

[Mandelbrot] contends that more realistic models of economics—including, naturally, models based on fractals—are driven by “wild randomness,” wherein things don’t average out and individual freak occurrences matter. This wildness, he said, “imitates real phenomena in a very strong way.”

Mandelbrot leaves open the possibility that the stock markets could be modelled using fractals. As a guide I point out one feature of fractals – that they display the same level of complexity at all scales. To that end I took the liberty of posting here a plot of US GNP since 1950.us_gnp_1950

Now I would say, that plot shows a regularity that is simply missing from say, daily currency fluctuations (which I look up sometimes to watch my modest savings in UK pounds become ever more modest). The regularity is indicated by the grey vertical bands – the recessions. If you allow for the special case of the mid-70s “oil-shock” recession and the (relatively mild) mid-50s recessions, then there is a recession every, ooh lets say, 10 years:

since 1825, when the first general crisis broke out, the whole industrial and commercial world, production and exchange […] are thrown out of joint about once every ten years. Commerce is at a standstill, the markets are glutted, products accumulate, as multitudinous as they are unsaleable, hard cash disappears, credit vanishes, factories are closed
Fredrich Engels 1877 Anti-Duhring Part 3, Chapter 2

If referring to Engels(and Marx) makes you uncomfortable, then you can take a respectable bourgeois economist like Ricardo who recognised these cycles even before Marx and Engels. Or German chancellor Angela Merkel – herself a former physicist – a couple of days ago, “The world stands at a watershed. We cannot afford crises like this every 10 years”.

Indeed. And to make a value judgement, why should we listen to our “leaders” when they spent the last 10 years encouraging greed, speculation and debt, and now we are suposed to trust them that they’ve seen the light? Actually I dont think they have any real idea about how the economic system works.

So that brings me to my point. We should bemoan the fact, not that so many physicists attempt to understand the economy, but that so much effort is wasted on daily stock fluctuations in order to make the rich richer. The system shows regularity at larger scales and its these fluctuations that really need to be studied and prevented – even if the system has to be stood on its head as Marx and Engels argued.



Friday, March 27th, 2009
DESY back entrance

DESY back entrance

Welcome all to this round of quantum diaries and to my blog in particular! I view this as rather an interesting experiment as I’m not really sure what I will write about. So lets say it will be an emergent phenomenon.

Since I am still a relative newcomer at DESY (I have actually been here over 6 months, but it still feels new to me) then DESY will be my first subject. It seems appropriate as snow flakes drift past the window to put up a wintry picture of the “back” entrance. Opposite DESY is the refreshing Altonaer Volkspark and DESY itself has a surprising amount of wildlife including pheasants, heron and tortoises!

This is my first time working long term at a Laboratory (as opposed to a university without accelerators) and its a real joy to be able to walk from my desk and computer simulations, next door to the test beam and real experiments. But more on the testbeam in a forthcoming entry.

We just began a series of events marking the 50th anniversary of the founding of DESY, and so its seems appropriate to mention one noteworthy physics event that happened here. DESY is where the gluon was discovered by the Mark-J experiment in PETRA (Positron-Electron Tandem-Ring Facility) in 1979. I’ve reproduced a plot shown by Symmetry magazine (who acknowledged physicist Sau Lan Wu). It shows the three jet signature of the two quarks and a gluon, and the question for the day is, can we say which jet is the gluon?

TASSO 3-Jet event

TASSO 3-Jet event

In 1990 PETRA went on to serve as a pre-accelerator for the HERA (Hadron-Electron Ring Facility) accelerator which stands sadly quiet now since its shutdown in 2007 after a distinguished 17 years of operation (though data analysis is still ongoing). However there is actually a lot of construction going on for the exciting XFEL (European X-ray Free Electron Laser) project.

The PETRA ring itself is being converted into a synchrotron and this time lapse footage shows the inner construction of the experimental hall. I love that footage – its like something out of Aliens. I particularly feel for the guy at the end rolling out the top layer of the floor by himself! I’m reminded of the quote:

“Who built Thebes of the seven gates? In the books you will find the names of kings. Did the kings haul up the lumps of rock?”
Brecht, Questions from a Worker who Reads, 1935

My work at DESY is within the Lepton Collider Research (FLC in German) group. FLC is involved in research towards the International Linear Collider (ILC). The group is busy preparing a bid for one of the future detectors for this facility. Within FLC, I work in quite a few areas including polarimetry, detector background studies and theoretical topics in Supersymmetry and Quantum Electrodynamics. I plan to describe each of these, in time and in more detail, in upcoming posts.