Yields from income tax

This post is a tour of income tax and personal national insurance yields, it’s motivated by an interest in seeing how one might pay for a part of the reduction in the deficit through taxation. The reason for focusing particularly on income tax is that it yields a fairly large fraction of the total tax income (28.7% in income tax and 46.6% income tax and national insurance combined), as discussed in a previous post; this means that relatively large amounts of money are raised by relatively small changes when compared to other taxes. Furthermore it’s relatively easy to calculate: I can work out how much income tax I pay in a year but would struggle to tell you how much VAT I pay per year, the impact of a tax on insurance premiums the effect of a change on duty and so forth. Thirdly, it is the tax that is most transparently progressive, in the technical sense that the more you earn the greater the fraction of your income you pay in tax.
This calculation is based on a calculation of personal tax rates from wikipedia, this figure generates the tax rates programmatically and I simply translated the code to my computer language of choice – I thought about doing it in a spreadsheet but that turned out to be a bit brainbending. The second component of the calculation is the number of people in each income bracket: this information along with further information on incomes can also be found on wikipedia. Ultimately the data come from the HMRC. I’ve put these two bits of data together into a program which enables me to fiddle with tax rates, tax thresholds and so forth. It appears to be approximately correct since it matches roughly HMRC’s own figures on the effects of small perturbations to the tax system (pdf). This also tells you it’s possible to look this stuff up – but I find it more fun to calculate it myself! It’s also a good illustration of the general process of how to go about repeating someones calculations from literature sources: try to reproduce their graphs; try to match the summary numbers they produce.
This first figure shows the income and national insurance payable as a fraction of gross (total) pay as a function of pay. The thing I hadn’t appreciated intuitively is that the tax banding system gives quite a smooth increase in percentage tax take, this is because you only pay raised rates on the fraction of your income that lies above the threshold:

Extending the horizontal scale out towards incomes of £1,000,000 and the rate tends to 50%. The next figure shows the distribution of incomes, in the UK:

You can see the same information in text form here. The area under this curve between points on the horizontal axis tells you the number of people in an income band. The median income in the UK is £26k per annum – half the population earn more than this, half less. About 1% of the population earns more than about £100k per annum. This final figure shows the amount that each income band pays according to the latest tax rates.

To summarise this final figure in tax bands, the 20% band accounts for about 57% of tax paid, the 40% band for 26% and the 50% band for 17%. These bands contain respectively 90%, 9% and 1% of the income tax paying population.
In case you’re curious my salary puts me close to the top of the basic rate tax band.
To apply the knowledge embedded in these graphs to some recent problems:
As a rule of thumb: 1p on basic gives about £4bn, 1p on upper rate gives £0.75bn, 1p on the new 50% band gives £0.31bn. The reason for this sharpish dropoff is that relatively few people are effected by the upper rate tax changes so to yield a large tax income the rates have to be changed by a relatively large amount.
Reducing the threshold of the 40% tax band to £40k from £43k yields about £3bn.
The £20billion cut in welfare benefits is equivalent to approximately 5p on the basic rate of income tax, taking it to 24.5% from 20%. This would cost me about £1700 per year.
Tuition fees cost about £7.5billion (based on 1.5 million students each requiring an average £5k tuition fees per year), this is about 2p on basic rate. This would cost me about £800 per year.
The £2.5billion income gained from cutting child benefit from those in the upper tax band could be paid for with an increase in the upper rate to ~43% from 40%. Although it seems the £2.5billion figure is dubious. I can’t help thinking simply increasing the upper rate by this amount, rather than a convoluted attempt at clawback would be simpler. This isn’t to say I support the idea of paying child benefit to all regardless of income, just that implementing withdrawal in this way is technically complicated. This tax rise wouldn’t cost me anything!
I’ve not seen anybody volunteering for these tax increases to support their favoured causes, rather they prefer a range of schemes of dubious value impacting other people to avoid the problem falling upon themselves – a subject for my next post.
Note
This modelling was done using Visual C# running under Windows 7, if you’re interested either in the code or in just the application then let me know in the comments below (or on twitter). There are a couple of minor bits of tidying I’d like to do before release. Please note that the application is “good enough for blogging work” and should not be considered an accurate tool for tax calculations – it’s a toy to help me understand things!

Questions for undergraduates… cabinet edition

Thinking back many years to my first fraught days as an undergraduate, the three questions that came up most frequently as icebreakers between students were:

1. Where are you from?
2. What were your A-level results?
3. What degree are you doing?

In this post I thought I would answer the third question, for members of the cabinet. The data is all culled from wikipedia:

Prime Minister	David Cameron	Politics, Philosophy and Economics (Oxford)
Deputy Prime Minister	Nick Clegg	Social Anthropology (Cambridge), Political Philosophy (Minnesota), MA European affairs(College of Europe)
Foreign and commonwealth affairs	William Hague	Politics, Philosophy and Economics (Oxford), Master of Business Administration (INSEAD)
Chancellor of the Exchequer	George Osborne	History (Oxford)
Justice	Kenneth Clarke	Law (Cambridge)
Home department	Teresa May	Geography (Oxford)
Defence	Liam Fox	Medicine (Glasgow)
Business, Innovation and Skills	Vince Cable	Economics and Natural Sciences (Cambridge), PhD Economics (Glasgow)
Work and Pensions	Iain Duncan Smith	Sandhurst
Energy and Climate Change	Chris Huhne	Certificate in French language and civilisation (Sorbonne); Politics, Philosophy and Economics (Oxford)
Health	Andrew Lansley	Politics (Exeter)
Education	Michael Gove	English (Oxford)
Communities and local government	Eric Pickles	Law (Leeds Polytechnic)
Transport	Philip Hammond	Politics, Philosophy and Economics (Oxford)
Environment, food, rural affairs	Caroline Spelman	European Studies (Queen Mary College)
International Development	Andrew Mitchell	History (Cambridge)
Northern Ireland	Owen Paterson	History (Cambridge)
Scotland	Michael Moore	Politics and Modern History (Cambridge)
Wales	Cheryl Gillian	Law
Culture Olympics Media and sport	Jeremy Hunt	Politics, Philosophy and Economics (Oxford)
First secretary to the treasury	Danny Alexander	Politics, Philosophy and Economics (Oxford)
Leader of the House of Lords	The Lord Strathclyde	Bachelor of Arts (UEA)
Minister without portfolio	The Baroness Warsi	Law (Leeds)

As a scientist this is both depressing and comforting, depressing because of 23 members only 2 has any sort of scientific training: Liam Fox and Vince Cable (the latter of whom only did science in his first year). Comforting because at least we don’t get the blame!

It also highlights once again the dominance of the Politics, philosophy and economics degree at Oxford in providing Cabinet ministers – I haven’t checked but I believe this applies to previous cabinets.

Fun with fluids!

Back to some science stuff again, I’ve been meaning to do a blog post on smoke rings for a while, thinking that a simple description of what’s going on would be rather nice. The image to the right is of a “steam” ring blown by Mount Etna.

The explanation of smoke rings goes into the field of “fluid dynamics”; to a physicist a fluid is a liquid or a gas – some of the examples linked to here are of gas-in-gas rings (like the smoke ring), some are liquid-in-liquid rings and some are gas-in-liquid rings (bubble rings), the underlying physics is always the same.

A smoke ring is an example of a more general phenomena called a “vortex ring”. Scientists aren’t the only ones interested in fluid dynamics: this is a video of a dolphin playing with bubble ring. My fluid dynamics textbook helpfully points out that the velocity field around a vortex ring is equivalent mathematically to the magnetic field lines around a loop of current carrying wire. For a physicist this is a useful statement because it means you can carry across your understanding in one area to another – for non-physicists less so.

A vortex ring is made by pushing a pulse of fluid through a hole, friction slows down the fluid close to the edges of the hole whilst the fluid in the centre of the hole continues to move more quickly. On leaving the hole, fluid at the edges is rotating around the perimeter of the ring. Push the air to fast and the vortex ring won’t form, it’ll be destroyed by turbulence. You can see how this works in the image below (or, perhaps better, this video). The smoke in a smoke ring is only there to highlight what the air is up to – in liquids dyes can be used to reveal the patterns of liquid flow, or small particles. In the laboratory, small particles suspended in liquid can be illuminated by sheets of laser light to provide cross-sections through the flow patterns.

The first surprising thing about smoke rings is their persistence – for a gassy disturbance they maintain their shape for a remarkably long time. The smoke is actually trapped inside the vortex, and can only diffuse away slowly. By their very nature vortex rings are obliged to travel along in the direction of their axis, as the core of the vortex ring gets larger the forward motion of the ring slows.

Beyond simple vortex rings: we can also see vortex rings colliding and breaking up into rings of rings, and vortex rings overtaking – a faster vortex ring forces a slower one to expand whilst it passes through. These behaviours are all understandable using fluid dynamics, and can be simulated in a computer.

Vortices can also be found in lines, a vortex ring is simply a vortex line with the two loose ends tied together. Tornados and the whirlpool of water going down the plughole in the bath are examples of vortex lines.

Vortex rings are simply one facet of fluid behaviour arising from “vorticity”, that’s to say the behaviour of spinning packets of fluid. The “packets” being a handy conceptual device of breaking up a body of fluid into little pieces for further consideration. From a historical point of view, vortex lines were first understood by Helmholtz (1858), with some details added later by Kelvin (1867). What’s interesting about the Kelvin paper is that it was written at a time when the existence and understanding of atoms was in it’s infancy and there was some thought that atoms may be made from vortex rings (this turns out not to be true).

More generally fluids are understood using the Navier-Stokes equations which are a combination of Newton’s laws for fluids (forces make things move), viscosity (friction for liquids) and pressure. Beyond this the effects of surface tension, chemical reactions and magnet and electric fields to introduce ever more complexity. Even with the equations in hand, there is a large difficulty in solving them to produce useful results – just how fast can I pump liquid through this complicated shape?

Research into fluid dynamics is important for practical reasons (like making aeroplanes fly, simulating the weather and understanding how liquids move through all manner of mechanical devices from aerosol sprays to hydroelectric power plants) but it’s also just plain fun.

These videos of vortex rings are well worth a look:

1. Dolphins playing with vortex rings
2. Vortex ring collision
3. Vortex ring, overtaking manoeuvre
4. Computer simulation of a vortex ring

There’s many more like this, try searching You Tube for “vortex rings”.

Book review: God’s Philosophers

I seem to be on a run of book reviewing at the moment, as I’ve indicated before these are as much for me as they are for you! This weeks contribution is on “God’s Philosophers: How the Medieval World laid the foundations of Modern Science“ by James Hannam. This book looks at the development of science, or at least a precursor to modern science, during the Middle Ages (5th-15th century). This fits in with my previous book reviewing which has gone back to the founding of the Royal Society (1662), and a little earlier with Gerard Mercator (1512-1594).

To my mind the book makes a poor start in the introduction by telling me how everything I believe about the Middle (or Dark) Ages is wrong, and so is everyone else. I’m prepared to accept that my visualisation of the Dark Ages, as being quite literally Dark with peasants fumbling around in a permanent twilight may be wrong, however this type of introduction generally leaves me believing that the writer is a conspiracy theorist!

A recurring theme of the book is how those studying natural philosophy (a convenient term for the proto-science) continually ran the risk of being accused of heresy. Hannam seems to portray the treatment of heresy as not really so bad: only 1 in 20 trials resulted in burning at the stake, there wasn’t much torture, the victim was asking for it, the church handed over the heretics to the secular authorities who carried out the most terrible punishment. This seems to treat lightly the death, by burning at the stake, of people who simply believed something different. Perhaps more insidiously anyone studying natural philosophy had to have an eye to what the church believed in case what they studied was considered to be heretical. Later Hannam’s defence turns out to be more narrowly defined: he sees himself as defending the Catholic Church against Protestants. He reserves a special ire for humanists, those in the Renaissance who had a particular fondness for studying the ancient classics.

This said, the book is a nice overview of the development of the academic life after the fall of the Roman Empire, with the early universities in Italy and France growing up as offshoots from the great cathedrals. The very earliest of these institutions taught law, and sometime later medicine although the core of early teaching was in theology. A great deal of effort was expended in recovering the work of the Ancients (Greek philosophers) this was made difficult by the absence of much knowledge of Greek in Western Europe. The Arabs had picked up much of this material in an earlier period but translated it into Arabic rather than Greek whilst Western Europe had Latin as a common scholarly language. Interest was primarily in Aristotle, although later the works of Plato were re-discovered. In some ways it’s this aspect of the Middle Age and Renaissance enterprise which is so confusing to a modern scientist. It just looks like it would be far easier, and quicker, to make a fresh start and discover things for yourself rather than dredge through ancient, partial manuscripts in ill-known languages for clues.

There are various places in the book where I can feel myself trying to shout back through the ages “Yes, yes, you’re on the right track, keep going!”. Only to see the protagonist draw back at the last minute or for their work to be subsequently ignored. Examples include Nicole Oresme (1323-1382) and his use of graphs in understanding physical ideas. Or the theory of impetus developed by Jean Buridan (~1300-1358), which is a very direct precursor of modern theories of mechanical motion. Similarly isolated sparks spoke of doing controlled experiments to test theories, and the idea that mathematics could be used to describe physical processes. However these ideas did not seem to start drawing together until the period in which Galileo lived (1564-1642).

The part that astrology played in the development of astronomy is rather illuminating, as part of their programme the astrologers wanted to known exactly where heavenly bodies would be at some point in time in the past or future therefore they expended considerable, skilled effort in measuring the locations of these bodies and building models from these measurements. This was the work that lead Copernicus to propose a heliocentric solar system, and would have fed into Newton’s work on gravity, and all done for completely ridiculous reasons. This also highlights some of the oddities in the thinking of the early pioneers of the modern period, for example William Gilbert, who did excellent work on magnetism did it in a distinctly odd framework – he believed the magnet was the soul of a planet, similarly William Harvey’s work on the circulation of blood and Isaac Newton’s obsessive alchemy and bible study.

During the Middle Ages there were various technological developments: the mechanical clock (Norwich, 1273), spectacles (Venice, 1300), modern printing (by Gutenberg around 1439). Paper making had been brought to Europe at some time before 1276 when the first paper mill is recorded in central Italy. Gunpowder was first mentioned in Europe by Roger Bacon (1267), having been invented in China in around the 9th century. These inventions largely arose outside of the university system.

The book ends with the death of Galileo in 1642, who had been subjected to a trial for heresy following which he was held under house arrest for the remainder of his life. The book makes clear, that in common with Newton, Galileo was “standing on the shoulders of giants” drawing heavily on work in the Middle Ages – although synthesising into a coherent whole, making his own additions and also covering a large range of topics over his lifetime.

Finally there is a timeline, a cast of characters and a nice, manageable set of further readings.

I feel ambivalent about this book, the historical aspects of it I found very interesting, the proselytising less so. It seems evident that there was progress in proto-science during the Middle Ages, and also in technology. Hannam claims that the Catholic Church facilitated this progress; the evidence he presents is mixed – they supported scholarship and the founding of universities but simultaneously ran a system of Inquisition to detect heresy which made free academic enquiry difficult.

Image: Frontspiece of Bible Moralisee, God the Geometer.

Early reports of the Royal Society

In an earlier post I wrote about Thomas Sprat’s “History of the Royal Society of London, for the improving of Natural Knowledge“. Published in 1667, under the direction of the Royal Society which had first met in 1660, receiving their royal charter in 1662. In that post I deferred discussion of a selection of the early reports of the Society that were embedded in the History, for reasons of space.

The reports by title are these:

• Answers returned by Sir Philberto Vernatti (Resident of Batavia in Java Major)
• A Method for making a History of the Weather by Mr Hook
• Directions for the Observations of the Eclipses of the Moon by Mr Rooke
• A Proposal for Making Wine by Dr. Goddard
• A Relation of the Pico Teneriffe
• Experiments of the Weight of Bodies increased in the Fire by Lord Brouncker
• Experiments of a Stone called Oculus Mundi by Dr Goddard
• An account of a Dog dissected by Mr Hook
• Experiments of the Recoiling of Guns by Lord Brouncker
• The History of the Making of Salt-Peter and The History of Making Gunpowder by Mr Henshaw
• An Apparatus to the History of the Common Practices of Dy[e]ing by Sir William Petty
• The History of the Generation and ordering of Green Oysters Commonly called Colchester-Oysters

Interspersed amongst them Sprat adds in various brief comments on other work of the Society along with what amounts to a personal eulogy to Christopher Wren, who seems to have been involved in pretty much everything although Sprat seems to have been generous in attributing to Wren work which was largely done by other people.

Looking first at the authors: of Sir Philberto Vernatti I can find little, he appears to have been Governor of Batavia (now Jakarta) for the Dutch East India Company whilst most references I’ve found to him arise from this report to the Royal Society; Mr Hook was the first curator of experiments for the Royal Society and paid an important role in keeping the Society with interesting things to see, he was an outstanding scientist in his own right; Lord Brouncker was the first President of the Royal Society; Mr Rooke appears to have been Lawrence Rooke, who died in 1662; Dr Goddard is Dr Jonathan Goddard the early Society met in his lodgings at Gresham College, physician to Charles I and present at the death of Cromwell; Mr Henshaw is Thomas Henshaw an early Biological Sciences Secretary to the Royal Society; Sir William Petty was amongst other things an economist and a Parliamentarian in the Civil War. On the whole these reports look like they have been selected on political grounds, they are from the movers and shakers of the Society.

The contributions vary considerably in length and content, Dr Goddard’s proposal on making wine amounts to: “Do it in the West Indies using sugar cane”, similarly Mr Hooks account of dissecting a dog is very brief (it’s also pretty horrifying).

The reports on dyeing, oysters and the making of Salt-peter and gunpowder are quite detailed reviews of the current “state-of-the-art” in important trades, involving both references to previous literature and reports of current practice which read very much as if the authors had gone and observed the processes described. The answers returned by men in distant places: Sir Philoberto Vernatti in Batavia, Java and the report on the scaling of Pico Teneriffe are also very much directed to trade: does this wood grow well there? These are quite lengthy and range over quite a range of topics. From this it’s clear that the Royal Society wanted to be seen as contributing to the national wealth.

The reports by Hooke (on recording the weather), Rooke, Brouncker and Goddard (on Oculus mundi) are those which most closely resemble modern scientific papers. They report methods for conducting measurements, or the results of those measurements, unlike modern papers they do not draw strong conclusions from those measurements. In a sense they are following the scheme laid out by Sprat in which empirical measurement is important and theorising comes later. Oculus Mundi is a form of opal now known as hydrophane which goes transparent when it absorbs water, the OED reports that Sir Kenelme Digby had brought some of this material to the Society in 1661.

In sum it looks like the early Society was very busy. Much of what they wrote was very practical and aside from a comment on making insects from cheese and sack it largely looks quite sensible. In these reports I can see the origins of the primary scientific literature that I access as part of my work.

Children and numbers

One of this mornings news items is on government plans to limit benefit to a family to the average wage, apparently regardless of the size of the family. This seems to be built around the idea that there are families out there with vast numbers of children who are milking the system to the cost of the rest of us. We can check this idea with numbers. The graph below shows the number of claimants broken down by number of children in the household, the final category is for families containing 8 or more children.

The heights of the columns are a lower bound on the fraction of benefit going to each group, an upper bound would be to multiply each column by the number of children but this would be an over-estimate since benefits don’t increase linearly with number of children. There are a little under 1000 families with 8 children or more. 90% of claimant families have less than four children.
These data tell us nothing about the circumstances of each of the families represented which will include the loss of parents, illness, job loss and all the other small disasters which can befall a family.
The data shown here are from Department of Work and Pensions via The Spectator (here).

Book review: The History of the Royal Society of London by Thomas Sprat

In which I venture into original material, in the form of Thomas Sprat’s “History of the Royal Society of London, for the improving of Natural Knowledge“. Published in 1667, under the direction of the Royal Society which had first met in 1660, receiving their royal charter in 1662. I must admit to having attempted to read this book a couple of times before and failed; the copy I have is a facsimile of the original therefore written in early modern English with heavy use of the “long s” inevitably leading to an internal voice with a pronounced lisp! It’s probably useful to replace “History” with “Prospectus” in the title, to satisfy modern tastes. Despite it’s age the writing style is surprisingly readable to my modern eyes.

Unlike any other book I have read the book starts with a dedication to the King, followed by a poem praising Francis Bacon (1561-1626). Bacon’s presence recurs throughout the book, Sprat clearly sees him as the intellectual godfather of the organisation. The book is divided into three sections; the first is a prehistory describing the state of natural knowledge before the Royal Society, the second section details the founding of the Society and the final section discusses the value of the knowledge the Society seeks.

The tour of prehistory is rapid; starting with the ancient priests who held knowledge to themselves, followed by the Greek philosophers (described as the Ancients) who Sprat feels were too fond of rhetoric in determining questions of knowledge and who he accuses of “hastiness”. The Romans receive relatively short shrift. Following the Roman Empire, Sprat sees the rise of the Church of Rome and a relatively barren period dominated by war, he cites here William of Malmsbury (1080-1143), an early English historian in support of this. He then bemoans the time spent by the Scholastics in what he considers pointless theology in the later period, presumably 1000-1500, William of Ockham falls into this group. Finally he comes to the recent era where he lists five groups involved in natural philosophising. Francis Bacon is cited reverentially once again, those taking on the philosophy of the ancients – tidying it up after it’s release from the abbeys in the Reformation, are less venerated. “Chymists” receive a mixed review with the more pedestrian welcomed but the alchemists, often seeking eternal life or some other fancy, are scorned. Isaac Newton, a later president of the Royal Society was a keen alchemist but by this time it was seen as not quite proper. He also comments on the coming of specialisation to different areas of science.

The founding fathers of the Royal Society started meeting in Doctor Wilkins lodgings in Wadham College, Oxford – it’s not stated explicitly when this started but it ended in around 1638 when the meetings moved to Gresham College in London. Sprat skims over the Civil War (1642-1651), although this period was clearly much on his mind in writing the book, then happily reports: “For the Royal Society had its beginning in the wonderful pacifick year of 1660”, the year of the Restoration when Charles II returned to the English throne. Sprat goes on to describe in some detail the guiding principles of the society, explicitly ruling out a teaching organisation citing the time required to do this and the potentially unhealthy Master-pupil relationship as damaging to the purposes of the Society. It is a principle of the new organisation that men of all religions and nations are welcome. This internationalism is a hallmark of modern science. Also highlighted is the idea that the Royal Society becomes a central repository for written information, the first of its kind. The Royal Society was funded from the subscriptions of it’s fellows, although they were open to public funding.

Sprat then provides a rather detailed description of how the Royal Society is constituted including how they go about their business in terms of doing and reporting experiments, I must admit to finding this a bit dull. It has the air of an organisational fanatic describing his perfect organisation, it’s questionable how closely the Royal Society managed to keep to this ideal. However, in his description of the processes of the Society we can see the genesis of the still used scientific literature, with the primary literature comprised of relatively short papers containing experimental results and theoretical developments based on those results. Charles II makes several appearances here, unsurprising given the recent granting of the Royal charter, but he also seems to have been moderately involved in the Society and had his own chemistry laboratory.

A substantial portion of the middle of the book is taken by a compilation of reports by the early Royal Society, these include:

• Answers returned by Sir Philberto Vernatti (Resident of Batavia in Java Major)
  
• A Method for making a History of the Weather by Mr Hook
  
• Directions for the Observations of the Eclipses of the Moon by Mr Rooke
  
• A Proposal for Making Wine by Dr. Goddard
  
• A Relation of the Pico Teneriffe
  
• Experiments of the Weight of Bodies increased in the Fire by Lord Brouncker
  
• Experiments of a Stone called Oculus Mundi by Dr Goddard
  
• An account of a Dog dissected by Mr Hook
  
• Experiments of the Recoiling of Guns by Lord Brouncker
  
• The History of the Making of Salt-Peter by Mr Henshaw
  
• The History of Making Gunpowder
  
• An Apparatus to the History of the Common Practices of Dy[e]ing by Sir William Petty
  
• The History of the Generation and ordering of Green Oysters Commonly called Colchester-Oysters

I shall write on these reports in a separate post.
The book ends with a lengthy rebuttal of various criticisms of the Royal Society, including how “experimenting” is entirely compatible with the Christian religion and specifically the Church of England; this is perhaps unsurprising given Sprat’s occupation as a churchman. In addition to this there is the appeal that experimental philosophy as demonstrated by the Royal Society can benefit the nation by improving its industry and trade, including such things as importing plants across the emire. It also defends the interest of the nobility in this area, claiming that their country estates are the ideal places to conduct such studies, whilst the lower orders go off to fight wars!

Reading this book was an unusual experience for me. In contrast to the modern histories I more usually read I felt much more obliged to ask questions like: Why is this person writing this book? Why was Bacon so important? Is this some reverence to a politically important forbearer? Why the need for the book at all? A book length defence of such an organisation only 5 years after its formation seems a bit odd.

Reading this has given me a taste for contemporary material, I think I might have to look into Pepys and some original scientific publications.

Further Reading

1. Google Books version of the History of the Royal Society of London, for the improving of Natural Knowledge.
   
2. My earlier blog posts on the Royal Society
   
3. Image from the National Portrait Gallery

Regulation and reward

This post is stimulated by an exchange on twitter as to why we are bothered about bankers being paid stacks, whilst seemingly less worried about football players and entertainers being paid similar amounts. This post fails to address that specific question.

Banks are rich because they handle money and take a little charge at each transaction, also they rent out money which attracts few overheads. Footballers and entertainers are rich because wealthy organisations realise that to sell a football team or a film requires a star. Doctors and lawyers are rich because they have rare skills that people are willing to pay well for, the costs of poor legal advice or poor medical advice are loss of wealth or life, respectively, and their lack becomes rapidly obvious.

Pay does not measure a person’s value. Pay measures how much money an employer believes an employee is worth to them, if the employer is also the employee this judgement may be flawed. In some cases this is easy to determine, in other cases it is not. If I look at the company I work in, higher salary goes with greater responsibility for people and greater budgets. In the case of patent attorneys, who are relatively well paid, then it goes with a marketable skill. Scientists doing science are paid acceptably, the company is clear that they are not paid more because there are not local jobs for scientists which pay better.

We’ve recently gone through repeated rounds of “How much are  you paid compared to the Prime Minister”, exclusively directed at other public sector workers. This is ridiculous. It’s usually inaccurate as well: the typical figure quoted for the Prime Ministers salary is £142,500; however he will also receive an MP’s salary of £65,738. In addition to this he has use of an apartment in central London at Number 10 and a country house, Chequers. As Tony Blair has demonstrated, the Prime Minister can also expect substantial financial rewards on leaving the position, through speaking fees, directorships and so forth that are based largely on their position of former prime minister (see here and here). The Prime Minister is also entitled to receive half of his salary as pension after he has left office, although Gordon Brown waived this payment.

People make the money they can under the situations they find themselves. I’m sure we’ll all argue that that’s not we’d do personally but let’s assume that we’re all special. Do you own up if you’re under-charged or you receive more change than you deserve or if the electrician offers you a lower price for cash? Viewed in this light the MP’s expenses scandal is nothing unexceptional. Looking at what they were up to I can easily imagine that we’d find exactly the same distribution of abuses if the expenses scheme where I work were regulated in the same way. A whole bunch of people would claim to the limit in an entirely “legal” way; a few would claim less through incompetence in milking the system and a few would act in ways that were basically fraudulent.

What’s the message of this post?

In terms of regulation: don’t rely on the goodwill of man to obtain a favourable societal outcome. Although that might work for some chunk of the population it won’t for a substantial fraction and so the scheme will fail.

Book review: The Map that Changed the World

These are some notes on “The Map that changed the World: The Tale of William Smith and The Birth of a Science” by Simon Winchester. It is the story of the creation, by William Smith, of the first geological map of England and Wales, and the first such map on this scale in the world. A geological map shows the distribution of different rock types on the earth’s surface. Sedimentary rocks are laid down in horizontal layers, known as strata, subsequently these layers may be deformed and distorted. Therefore the distribution of rock types on the surface is a slice this distorted underground structure. William Smith’s work went beyond simple mapping the surface by recording what went on under the surface.

William Smith was born in 1769, as the industrial revolution was getting under way. Enclosures, coal mining, canal building and drainage work were building blocks to Smith’s maps; as a young man he became involved in surveying as a result of enclosures around his birthplace of Churchill, near Oxford. Following this experience in surveying he became involved in coal mining in Somerset. Here he saw directly the strata beneath the surface and learnt their individual character. Then he was involved in surveying for a canal to link the Somerset coal mines to the main canal system. This combines surveying with geology, since the type of rock the canal goes over determines how easy it is to dig the canal and whether it leaks.

A key insight was that the fossils found within a strata could be used to exactly correlate two distinct outcrops – in the absence of fossils two outcrops might look very similar but actually belong to different strata. Secondly, strata always appeared in the same order: A always comes below B, which comes below C. In places, because subsequent distortion of the rock, this ordering may not be obvious. It was Smith who was responsible for “” which identified the order of strata occurring in England.

Fossils had become collectors items around the time of Smith’s birth. As a result of the increasing awareness of the fossils in the surroundings, sea animals many miles from the sea and fossils with no living counterparts, the biblical account of the creation of the earth was becoming increasingly shaky. In a sense it is geology that brought Darwin to his theory of evolution, the study of rocks makes it increasingly clear that the world is unimaginably old and that in this vast space of time there is room for evolution. In common with Darwin, Smith’s great work was a long time in preparation.

William Smith was dogged by financial problems, he had taken up a mortgage to buy a substantial estate whilst surveying for a canal and was then promptly sacked. Throughout his life he appears to have spent rather enthusiastically, sometimes simply to be seen as having an address in the right place. Ultimately William Smith went to debtor's prison for a short period in 1819, a few years after his map had first been published. On his release he moved to Yorkshire where he worked on various minor projects in obscurity. He was later returned to the public eye to receive the first Wollaston Medal from the Geological Society of London, along with the recognition he deserved. 

Earlier the Geological Society, under the presidency of George Greenough treated Smith shamefully: plagiarising a substantial chunk of his work on the geological map to produce their own version which was published not long after his, at lower cost. Furthermore they refused him admission to the society largely, it seems, on the basis of class. Smith had some previous experience of being plagiarised whilst in working in Bath, by a reverend! Although the subject of class arises a number of times through the book it doesn’t seem to have caused Smith huge impediment, aside from his initial contact with the Geological Society, throughout his life he worked with the landed gentry on various projects and it seems he was valued for this work. In addition he was apparently quite well known to Sir Joseph Banks – long time President of the Royal Society.

It’s striking that in addition to the Royal Society in London, the rest of the country was apparently riddled with philosophical societies, Bath is mentioned in particular in this regard but what really brought it home to me was mention of the Scarborough Philosophical Society, somewhere one wouldn’t now associate with such things.

The book is written in something of a docu-drama style with some sections reading a little like a novel, this is a mixed blessing to my mind – it enhances readability however it always leaves me with the fear that I’m being tricked into believing detail that doesn’t exist. I feel something of a connection to this work; I grew up on the Jurassic coast in Dorset (although this in a time before the marketing term had stuck) and did geology AO level whilst at school. It’s tempting to believe that England was the perfect spot for William Smith to be born: the geology of England is very varied and the industrial revolution provided a perfect excuse for detailed rummaging around in the rocks.

You can see the modern, interactive version of the geological map of Britain here.

Wallpaper paste and the giant death ray

Nature is good a growing fancy structures. It takes air and water and turns them into sugar, a small molecule, which it then stitches together in chains to form starch and these starch chains arrange themselves into starch granules: organised structures with a diameter about that of hair, found in plants. The electron micrograph to the right* shows one that has been eroded to show some of its internal structure.
I have my name on a couple of pieces of work on starch. I played a small part in the piece of work described here:

Waigh, T. A., I. Hopkinson, A. M. Donald, M. F. Butler, F. Heidelbach, and C. Riekel. “Analysis of the native structure of starch granules with X-ray microfocus diffraction.” MACROMOLECULES 30, no. 13 (June 30, 1997): 3813-3820. (pdf)

Tom Waigh was a PhD. student in the group I worked in, he was studying starch granule structure. This meant visits to the ESRF in Grenoble; source of mighty x-rays and a micro-focus beam-line, to do experiments. Tom had several days of beam-time, with experiments which essentially required continuous attention (a starch granule in the x-ray beam lasted 15 seconds), therefore a collection of warm bodies were required to press buttons and stuff through the night. Mike Butler and I stayed up late and pressed buttons. Florian Heidelbach and Christian Riekel designed and built the beam-line, and Athene Donald was the boss – supervising Tom’s PhD. and raising money to do the work.
Starch granule structure is interesting and funding-worthy for several reasons: we eat lots of starch based things both natural like potatoes and not so natural, like Cheesy Wotsits; it’s used in processing paper and fabric and as a glue. There’s also work going to make plastics from starch, little extruded starch worms can also be found as a replacement for expanded polystyrene packing. Understanding starch granule structure is useful to people who run industrial processes, better knowledge of the granule structure leads to a better understanding of its processing properties which might lead to seeking out or breeding plants, which produce different sorts of starch granule, with different or better properties.
There are two types of starch: amylose and amylopectin. Amylose makes shorter, less branched chains, whilst amylopectin makes longer branched chains. Starch granules are onion-like structures with alternating crystalline and amorphous regions. (Crystalline means nicely ordered, amorphous means not nicely ordered). Crystallisation in polymers is one of those puzzling things, how does all that long stringy polymer get folded up into such a nice neat structure. Blind physics is the answer, it’s broadly understandable but when I was active in the field it still wasn’t clear how it got started; once the nucleus of a crystal had formed, its growth was understandable but the formation of the nucleus was not so clear. X-rays tell us about the structure of things on very small length scales, since we’re interested in the variations in structure of an object only 0.1mm across we need to use an x-ray beam much smaller than this. The beam at the ESRF is only 0.002mm across so we can get a very detailed picture of the crystalline and amorphous regions of the starch granule. If you want to find the structure of a car by poking it with a stick, then you need a stick which is much smaller in diameter than the car. All we know of starch granule structure is summarised below:

Schematic illustration of the starch granule structure*

The experimental procedure was entertaining: the starch granules were deposited on an electron microscope grid – a very fine wire mesh with numbers and letters allowing you to identify where you were on the grid. The starch granules were visible under a low power optical microscope, as were the numbers and letters. The numbers and letters were visible under the harsh stare of the x-ray beam but not the starch granules. So we would print out an optical micrograph, and take it off to the instrument hutch where we would get a shadowograph of the grid from the x-ray beam (sans starch granules). Then there would be a process of half-blind navigation, this was far from leisurely since once the x-ray beam was shining on the starch granule it lasted a few seconds before becoming irreversibly damaged. Once we’d found a starch granule we would take sets of closely spaced scattering patterns in a quest to discover the structure of the crystalline and amorphous bits of the granule.  It was like Battleships but rather more sophisticated expensive.
To make a microfocus beam line you take the output of a synchrotron – a big wide beam of x-rays and direct it down a cone – known as a capillary. At some point we decided to be cunning and reduce the power of the micro-focused x-ray beam by offsetting the capillary so that the incoming x-ray beam didn’t hit the open end fully. This failed, because it turns out the beam wobbles up and down very slightly. What we should have done was put the attenuators in, but we were a bit tired.
These experiments didn’t solve the structure of the starch granule, they filled in another little corner of the big picture. This is how much of science works. The story of the starch granule structure is one of a repeating theme in nature: it can do subtle things with structure without a large machinery to make it happen.
Update: Athene Donald has written on her side of this story -"Am I having impact?" some nice detail on the origins of the work and the problem of impact.*Images from Braukaiser.com

Science is Vital - history repeating 1667

I'm reading Thomas Sprat's "History of the Royal Society of London, for the improving of Natural Knowledge"* published in 1667. He's just mentioned that following the return of Charles II much spending has been made on public works and goes on to say:

This general Temper being well weigh'd; it cannot be imagin'd that the Nation will withdraw its Assistance from the Royal Society alone; which does not intend to stop at some particular Benefit but goes to the Root of all noble Inventions, and proposes an infallible Course to make England the Glory of the Western World.

This seems terribly relevant to current circumstances, he does spoil it slightly by going on to say:

There is scarce any Thing has more hindered the true Philosophy than a Vain Opinion, that men have taken up, that Nothing could be done in it, to any purpose, but upon a vast Charge, and a mighty Revenue.

 Old Sprat had a fine way with words!

*Quotes are from p78-79

Book Review: The Fellowship

I’ve written previously about the Royal Society via the medium of book reviews: Seeing Further, Joseph Banks and Age of Wonder, and also in a data mangling exercise. This post is about “The Fellowship: The Story of the Royal Society and a Scientific Revolution” by John Gribbin, it describes the scientific world before the Society and the founding of the Royal Society. As with many books about this period, the front cover of my copy features “An experiment on a bird in the Air pump” by Joseph Wright of Derby and so that is the image I use to decorate this post. Following my usual scheme this review is really an aide memoire as much as a review.

The book opens with a set of brief biographies, starting with William Gilbert of Colchester (1544-1603), and his scientific study of magnetism: de Magnete (1600). This work on magnetism was unusual for it’s time in that it was very explicitly based on experimental observation, rather than the “philosophising” of Aristotelian school which imputed that the world could be understood simply by thinking. William Gilbert is relatively little known (ok – I didn’t know about him!), perhaps because his work was in a relatively narrow field and was superseded in the 18th century by work of people like Michael Faraday furthermore Gilbert seems to have spent most of his life practicing as a doctor with his scientific work playing only a small part of his life.

Next step is Galileo Galilei (1564-1642). He continued in the tradition of William Gilbert, eschewing the philosophical approach for experiment. In contrast to Gilbert, Galileo made contributions across a wide range of science for a long period – promulgating technology such as telescopes, microscopes and computing devices. This likely explains his greater fame. A detail that caught my eye was that as a professor of mathematics at the University of Pisa he was paid 60 crowns per year, whilst the Professor of Medicine gained 2000 crowns. For many early scientists, medical training appears to be the major scientific training available.

Francis Bacon (1561-1626) was more important as a parliamentarian, lawyer and courtier than a scientist. I link reluctantly to wikipedia in this instance, since in the opening paragraph they seem to be repeating the myth that he met his end through stuffing snow into a chicken to see if this helped preservation. His fame as a founding father of modern science is based largely on a book he didn’t write in which he intended to describe how a scientist should work – a scientific method. Perhaps more notably he had a vision as to how science might function in society at a time when there was no such thing as a scientist. It is apparently from Bacon that Isaac Asimov got his “Foundation”; it is the name of an organisation of scientific Fellows found in Bacon’s fictional work New Atlantis. Finally we are introduced to William Harvey (1578-1657), who identified the circulatory system for blood in the human body by a process of observation and experiment (published in De Motu Cordis (1628)) he was primarily a physician.

The point of this preamble is to say that, as the founding of the Royal Society approached, a number of people had started doing or proposing to do a new kind of science (or rather natural philosophy as it would have been called). The new natural philosophy involved doing experiments, and thinking about them – it was experimental science in contrast to the “received wisdom” from the ancient Greeks which was certainly interpreted to mean at the time that thinking was all that was required to establish true facts about the physical world. It’s not really accurate to say that one person did this and everything changed: rather that a shift had started to take place in the middle years of the 16th century. The foundation of the Royal Society can be seen as the culmination of that shift.

The Royal Society was founded at Gresham College in London on 28th November 1660, although it’s origins lay in Oxford where many of the group that would go on to form the Society had been meeting since the 1640’s. The Royal charter of the Society was agreed a couple of years later. The central figure in the Oxford group was John Wilkins (~1614-1672). The original Society included Christopher Wren, Robert Boyle and Robert Hooke amongst others. What striking is the political astuteness of the founding fathers as the monarchy returned to England in the form of Charles II, the first President, Viscount Brouncker, was a Royalist and the Society clearly identified that a Royal seal of approval was what they required from the very beginning. The Society had an air of purposefulness about it, not of airy philosophising for the amusement of gentlemen. The Society started publishing the worlds first scientific journal, “Philosophical Transactions”, and commissioning a history of their founding by Thomas Sprat only a few years later.  As a scientist I have picked out those names that mean most to me, however it’s very clear that the Royal Society was more than a group of scientists meeting to talk about science and the other less scientifically feted Fellows were equally important in the success of the Society.

Gribbin’s book then goes on to consider three men important in the early life of the Royal Society. Firstly: Robert Hooke (1636-1703), originally scientific assistant to Robert Boyle (1627-1691) who became the Society’s first “Curator of Experiments”. Prior to his appointment the Fellows appeared to be poorly organised in terms of providing weekly demonstration experiments for the Society’s education. Hooke was a really outstanding scientist, a skilled draftsman and maker of scientific equipment. The reason Hooke is not better known is largely down to Isaac Newton, with whom he had a longstanding feud and who outlived him. Newton (1643-1727) does not need further introduction as a scientist, his role in the Royal Society was to provide scientific gravitas (after Hooke had died) he was also President of the Society for the period 1703-27. Edmond Halley (1656-1742) was more important to the Society on the administrative side, he is chiefly remembered from the scientific point of view for his prediction of the return of a comet calculated using Newton’s theory of gravitation. He also spent a great deal of time persuading Newton to publish and trying to extract data from Flamsteed (the Astronomer Royal). In addition to this he invented a diving bell, wrote the first article on life annuities, published on the trade winds and monsoons, made observations of the stars of the Southern hemisphere and went on several scientific expeditions.

Some miscellaneous thoughts that arose as I read:

• Royal patronage, in this instance by Charles II, was important for the Society in this period and later by George III – as described a little in Age of Wonder.
• On the face of it astronomy is blue-skies research, but at the time the precise measurement of the position of the stars was seen as a route to determining the longitude - an important practical problem.
• It’s notable that the persistent anecdotes about the scientists mentioned here i.e. Francis Bacon and the frozen chicken, Newton and the apple falling from the tree and Galileo dropping things from towers, originate from the earliest biographies often written by people who knew them personally. These anecdotes have later been found to be rather fanciful, but nevertheless have persisted.
• There was serious feuding going between scientists in the early years of the Society!

Overall I enjoyed this book, although it does sometimes have the air of a collection of short biographies of men who are already relatively well known. The most interesting part to me was the core part around the founding of the Society, bringing in some of the lesser known members and also highlighting the importance of the non-scientific aspects of the Society in it’s success.

In terms of scientific history reading, where next? “God’s Philosophers” by James Hannam seems relevant to understanding scientific activities prior to those covered in this book. A deeper investigation into Edmond Halley seems worthwhile, and I should also make another attempt at the Thomas Sprat history of the Royal Society.

Further reading

1. “Joseph Banks” by Patrick O’Brian.
2. “Seeing Further” edited by Bill Bryson.
3. “God’s Philosophers” by James Hannam.
4. “Age of Wonder” by Richard Holmes.
5. “The Curious Life of Robert Hooke” by Lisa Jardine.
6. “Hostage to fortune” by Lisa Jardine and Alan Stewart, which is a biography of Francis Bacon.
7. “The History of the Royal Society of London, for the Improving of Natural Knowledge” by Thomas Sprat.
8. “Isaac Newton: The Last Sorcerer” by Michael White.

God and the scientist

Recently I observed that Stephen Hawking* had introduced God into his book “The Grand Design” as a way of gaining sales. Last weeks story on Hawking and God irritated me for two reasons. Firstly, the idea that a new idea that Stephen Hawking has introduced in his forthcoming book either proves or disproves the existence of God is fatuous nonsense. Secondly, revealing some intellectual snobbery on my part, this is a popular science book – such an important idea would have been published in peer-reviewed literature first – most likely Nature! On the first point Mary Warnock covers the philosophical side of this well in a short article in The Observer this week, in summary: proof / not proof of the existence of God is a hoary old chestnut.

As an atheist and scientist, I’m quite clear that my demand for evidence for the existence of God is what makes me an atheist. You don’t need evidence if you have faith. Although many scientists are atheists, this is by no means a pre-requisite. Many scientists in the past have been professed strong religious beliefs, no doubt in large part because of the spirit of the time they lived in. It’s only for particular variants of theism and particular topics that the two things are in direct collision: Creationism and the study of evolutionary biology are not happy bedfellows. The degree of cognitive dissonance required to accommodate a religious view of the world and a scientific view is really rather minor. Many scientists in the past have seen their scientific work as revealing the mechanism that God has created.

A further element to this is the degree to which modern cosmology requires a degree of faith. As an experimental soft condensed matter physicist the world of cosmologists is very far away. The things I study are essentially testable in the lab, you can put your hands on them, prod and poke them. Modern cosmology has a large degree of internal logical consistency and mathematical beauty, but it has close to zero contact with observations. At times it feels like any experimental test is wilfully pushed into timescales, or size scales that are simply impossible to observe (and not just impossible in practice, but impossible in principle). This is not to say they are wrong, but simply that their correctness must be taken on faith.

*Pointless name dropping/anecdotage: I had dinner with Stephen Hawking at Gonville and Caius College, he’s not very dynamic.

Sunlight

Some time ago we installed “solar thermal” on our roof, as described in: “The Dorothy Hopkinson Memorial Solar Panel”. This heats water, it’s significantly reduced our gas usage over the summer when the central heating is not on but during the winter when most of our gas is consumed the effect is minimal.

Next step on the renewable energy list is solar photovoltaic (PV) – this converts light to electricity directly. Solar PV systems are rather more expensive than solar thermal systems, until recently the economics of this were a bit questionable - £10,000 is a lot to spend to reduce your electricity consumption by half. However, the feed-in tariff scheme was introduced in the UK in April 2010. This scheme pays a generous tariff based on the total amount of renewable electricity generated by an installation in an effort to increase the uptake of such systems. A similar scheme has been in place in Germany since 2000, where it has been pretty successful in reaching this goal.

We have a medium-sized 3 bed semi-detached house with East-West facing roof elements which are relatively small. Two of us live in the house, our annual electricity consumption is typically 6.5 kWh  per day or 2400kWh per year (*see below for a comment on units). When we first moved into the house our consumption was around 11kWh per day (4000kWh per year). We reduced this by replacing all our light bulbs with low energy versions; switching off a second fridge/freezer; almost entirely stopping using a tumble drier and on replacing fridges and washing machines we bought the lowest energy versions we could find. So these measure achieved roughly 40% reduction. I know all this because I’ve been recording our electricity and gas consumption once a week for the last 3 years!

A colleague at work has recently installed both solar thermal and solar PV, and he gave a talk describing his experiences. After some delay we arranged for a survey by The Green Electrician, who were the installers recommended locally by Segen. The surveyor did a few measurements of our roof and then went through sample power generation calculations and costings based on those measurements. The calculation is described in “The Government’s Standard Assessment Procedure for Energy Rating of Dwellings” (SAP 2005 page 69). Beforehand I was under the impression that this wasn’t going to be worthwhile since only our East-facing roof is available for installation and this is always described as ‘non-ideal’. However, the calculations show that the penalty for an East-facing roof compared to a south-facing one is only about 15%. Unlike solar thermal, direct sunlight is not required – useful energy is still generated on a cloudy day or when the panel is in shadow.

Slight diversion: we were original quoted for an 8 panel system, however once on the roof the installers found they could fit two more panels. I’ve redone the calculations to allow for this – they may be a little bit inaccurate but not much.

The system recommended was a 1.85kWp Suntech system (ten 1580 x 808mm panels = 12.64m²) limited by the size of our roof. The calculated output of this system is 1393kWh per year i.e. about 60% of our annual usage. The price quoted for this system is ~£8,600 (excluding cost of scaffolding which was just over £400). The feed-in tariff is £575 per year based on 1393kwH per year production at a price of 41.3p per kWh. The savings on our electricity bill should be £98 per year (based on 50% of generated electricity being used by us at 14p per Kwh) and £21 based on selling the other 50% back to the grid at 3p per kWh. The feed-in tariff is inflation linked, and it’s reasonable to assume that the buy and sell prices of electricity will go up in the future. As you can see the feed-in tariff is what makes this financially sensible. In theory we will be getting £694 back on the system every year, so it will pay for itself in 13 years or less, mainly due to the feed-in tariff. The tariff is paid for 25 years so at the end of 25 years we will have been “re-paid” at least £8350 more than we spent. This is an embarrassingly high “middle-class benefit”. There are companies who will install renewable systems, paying the upfront costs, providing significantly cheaper electricity and taking the tariff (see Guardian article here): in summary this could work for you but the companies aren’t doing you a favour.

Installation is pretty straightforward: we needed substantial scaffolding across the front of the house to provide roof access; there’s some electrical gear to go in the loft (this is a panel about 1m²) and there’s a cable run from there down to our consumer unit under the stairs where there is a further small meter the size of a central heating controller. In our house this is fairly straightforward: the cable runs up to the loft via ducting up the stairwell – we’ll bury this in the wall when we next decorate. Three chaps were working for a substantial fraction of two days but they also cleaned out my gutter and re-pointed the ridge-tiles. At this point I’d like to commend Ian, Danny and John: the installers, who did a fine job and were most polite.  

There’s still some paperwork for us to do, but essentially the power companies are obliged to pay the feed-in tariff and accept energy back from us onto the grid.

At the moment I’m going up and down the loft stairs to look at my power generation at 30 minute intervals! Overall I’m very pleased with the system: survey to installation was a day under 3 weeks and on a not particularly sunny day I’ve been generating 1000W since 10:30am and peaked at around 1500W. As of 3pm I’ve generated 4.4Kwh which is nearly 70% of our average daily usage. We expect to get less electricity from the system as we head into the shorter days of winter with a sun lower in the sky, but it’s not a bad start.

As an additional bonus we can now electrocute unsuspecting electricians in a sustainable fashion – unlike a normal house you need to switch off supply from the grid and from the solar panel before sticking your screwdriver anywhere electrical. There are big signs to this effect next to the consumer unit.

*Note on units: Power is the rate at which something consumes energy, and the units for this are Watts (W), 1000 Watts is known as 1kiloWatt (kW) – a kettle uses about 2kW when it is running, the PC I’m using about 300W and the electric shower about 9kW. Ultimately what you buy from the electricity company is an amount of energy. For domestic electricity consumption we talk about “kWh” or “kilowatt-hours” this is a power multiplied by a time which in physical terms is “energy” which physicists would normally quote in units of “Joules” however, we’re not in physics at the moment. The quoted output of our system is in “kWp” or “Kilowatt-hours (peak)” – this is the maximum power we could possibly obtain from the system.


Some pictures of the system, including a graph of gas and electricity consumption over the last three years.

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More colours than the rainbow

This post is about making the bridge between how a physicist understands colour, and something a bit more useful.

Light is a collection of electromagnetic waves; for a physicist the most important property of a wave is its wavelength, its "size". The wavelengths of visible light fall roughly in the range 1/1000 of a millimetre to 1/2000 of a millimetre. (1/1000 of a millimetre is a micron). Blue light has a shorter wavelength than red light.

Things have colour either because they generate light or because of the way they interact with light that falls upon them. The light we see is made of many different wavelengths, the visible spectrum. Each wavelength has a colour, and the colour we perceive is a result of adding all of these colours together.

The diagram to the right summarises this: it’s called a chromaticity diagram, the numbers around the edge are wavelengths in nanometres (a millionths of a millimetre), pure, single wavelength light falls on this line; any point inside the line is formed from the mixture of wavelengths. The line represents "all the colours of the rainbow"; colours inside the line are not in the rainbow. The chromaticity diagram is the “periodic table” for colour scientists, it’s iconic and it summarises the world of colour.
This chromaticity diagram is just a slice through a volume, we could draw another one a little bit dimmer, and a little bit dimmer than that until we reached black.

How do we get to this diagram? The central issue to understanding perceived colour is that although the light in the environment comes as a mixture of a multitude of wavelengths, our eyes are limited by the light sensitive cells they contain, known as “cones”. In humans cones come in three types, which are sensitive in three different ranges of the spectrum. Roughly there are red-, blue- and green sensitive cones. So the eye gives just three readings in terms of colour description. The chromaticity diagram comes from a calculation trying to predict these three values and combining them to fit on a flat page (which only gives you two dimensions to play with).

Some other animals don’t have three sorts of cones. Birds, for example, have four – this is known as tetrachromacy which sounds to me like some sort of wizardry involving chairs (I’m reading Terry Pratchett at the moment). Birds have an extra type of cone in the ultra-violet part of the spectrum – so they are sensitive to wavelengths which we are not. Most mammals are dichromatic, but other primates, like humans, are also trichromatic. Dichromatic animals will be able to perceive a smaller range of colours than us. The evolutionary implication here is that earlier mammals lost some colour sensing ability, possibly for a gain in low light sensitivity but some mammals subsequently regained the ability.

The chromaticity diagram is still something of a physicists play-thing, it’s useful for doing calculations. There are other ways of describing colour which are related to human perception, they are developments based on the first steps used in constructing the chromaticity diagram. The aim of these methods is to similar numbers to colours that look similar; make those numbers reasonably easy to explain from a conceptual standpoint and try to give numbers twice as big to colours that are twice as bright. My favoured system in this respect is the CIE LAB system. The colours are expressed as three numbers L, a and b: L tells you something about overall brightness, a tells you the point on a scale between red and green and b tells you a point on the scale between yellow and blue.

But all of this is a bit of a fraud, because actually the colours you’re seeing on your monitor aren’t the real colours I’m trying to show you. The problem is that display devices contain red, green and blue elements but they don’t fall anywhere near the extremes of the chromaticity diagram and we can only get colours inside the the triangle defined by the red, green and blue elements in the monitor. A typical monitor gamut is shown here.

All this is based on the study of ideal colour stimuli (little square patches) on grey backgrounds, things get an awful lot more complicated if we start to worry about context. This is best illustrated with an image:

As far as my computer is concerned squares A and B have the same colour, my brain and your brain are interpreting the scene context and giving them different colours. This is called Adelson’s checker shadow illusion.

“Intimidating equations”

Taking lessons from Goldacregate, I’ve removed all the rant and sarcasm from this post.
In this article in today’s Observer, we’re advised that this:
P^A = gU_G + min(k - g, (1 - g)(1 - r))
is an “intimidating" equation”. Only if we’re easily scared! It relates the profit gained from dynamically priced airline tickets to some variables. This equation really is a very straightforward it says:
“profit equals two things multiplied together plus the smallest of two other things”
Using a Greek letter (capital pi) with a superscript following is a bit of showmanship, P would have done perfectly well in this instance. You can read the paper from which it is drawn here. It is written in the style of a paper in pure mathematics, which might explain the intimidation of the journalists in question.
I wrote a little bit about maths a while back: maths is the language of much of the science I do, but its a convenient tool – it’s not an end in itself. The seed of “Goldacregate” was a query by a journalist as to how to read out an equation, the thing is that practitioners rarely speak equations out loud: they scribble them on the nearest available surface (often illegibly, and incorrectly) or fight endless battles with machines to get them into electronic documents. Furthermore there is a long and dishonourable history of public relations companies using essentially meaningless equations to promote products and services.
For non-users of equations they are simply a cloak, a cloud of chaff thrown up to hide the truth beneath. For users, they are a compact and exact way of writing down the truth.
The next time you see an equation, don’t be scared beneath it there is something simple which can be said.
Unexpurgated version: Ah, bless, the economists are playing at being scientists by using an equation and the journalists have got the vapours at the impossible complexity of it all. Nasty equation: please, don’t hurt me.

100 days later: A Lib Dem view

I woke this morning to the sound of a bandwagon rolling past, grabbing my keyboard I jumped aboard. It is 100 days since the Coalition formed following the General Election. For people wedded to the decimal system of counting 100 is a nice round number, for programmers of a certain generation 128 is preferable. Perversely the Marquis de Sade chose 120 days, but I can't wait 20 days.

As a member of the Liberal Democrats for 20 years, I thought my opinions on a 100 days of partly Liberal Democrat government might be interesting to at least a few people. You can see my previous political postings here, to get a bit more context.

Things I'm pleased about:
Pupil premium; a rising lower tax threshold; increased capital gains tax; Ken Clarke sounding like a liberal on prison policy, an end to ID cards and over-enthusiastic lawmaking for every occasion; some hope of constitutional reform both in the Lords and for general elections;  no changes to the married tax allowance;

I'm also pleased by the very existence of a coalition government, it seems far more healthy to me that government is composed of members from two parties representing a majority of voters in the country, rather than one party who through a quirk of the electoral system has scraped in with a majority of seats based on a minority of votes. Far better coalition than more opposition where our influence is minimal.

I see my vote as delegating my views to the Liberal Democrats based on their manifesto, if they were in government alone I'd expect them to attempt to implement the entire manifesto (even if I didn't like all of it). In coalition I expect them to negotiate using that manifesto as a basis, the fact that the entire manifesto is not being implemented is a result of them not achieving an overall majority. The inability to implement the entire manifesto is a fact of electoral arithmetic.

Things I'm not so pleased about:
fatuous comparisons of civil servant pay with the Prime Ministers pay; ostentatious "dipping of hands in blood" following the Budget, at times it felt like the only people cabinet ministers defending it were Liberal Democrats; David Laws' rapid exit from government; Trident - I'm not particularly anti-nuclear but now was the perfect time to get shot of a piece of Cold War willy-waving.

As far as the economy is concerned, I believe we'd be in approximately the same place as we are now regardless of which party was in government prior to the election. The logic of this is also that regardless of who would have won the election they would have ended up doing approximately the same thing now (or in the near future): cutting government spending fairly dramatically. Arguments about timing are largely political; economics, it seems to me, is a "science" too imprecise to tell us much about the future and the fervent calls for cuts now, or cuts later are largely political. There is some marginal argument about the scale of the cuts, but given a Labour government we would be facing cuts of broadly the same magnitude.

I suspect there is a lot of departmental spinning going on at the moment: they've been asked to make fairly large cuts and they're leaking the ideas for cuts that they know will be politically the most unpalatable in order to give themselves some leverage for the spending review.

There's much enthusiasm about the LibDem's apparent problems in the polls, however they're generally at levels comparable with the last 10 years or so (see the Guardian Datablog). They are only low if you compare them to the heady heights of the election campaign which were quite evidently wildly inaccurate - the only accurate poll was the exit poll. I suspect a LibDem party in coalition with Labour would find itself in very much the same position.

It's worth highlighting again the inequity of first past the post system: plug the latest opinion poll into the BBC's calculator: (Lab:37% Con: 37% LibDem: 18%) and you get (Lab: 336 Con: 244 LibDem: 42). Labour get a 92 seat advantage over the Tories for an identical percentage of the vote and they get  8 times the number of seats as the Liberal Democrats for twice the vote. The Electoral Reform Society did a report for "Conservative Action for Electoral Reform", on this subject - interesting conclusion is that equalising constituency size doesn't really address the problem.

After the General Election the Liberal Democrats had three options: one it seems was unworkable, one was simply lazy, we chose to do the other thing. The only principle the Liberal Democrats have given up is the principle of not being a party of government.