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Saturday, July 19, 2008

This year’s Leisure Taiwan trade show (a.k.a Taiwan Sport Recreation and Leisure Show) started yesterday, with 131 companies participating including sports media companies such as ESPN and VideoLand Television, businesses selling sports equipment and fitness clubs.

There were also a variety of sports being played in the arena built for the trade show. The events included a 3-on-3 basketball tournament, free style shooting, and bicycle test-riding. In addition, conferences discussed issues related to sports and physical education.

A major topic in the trade show was energy-efficiency and, as a result, bicycles and similar sports equipment were being heavily promoted.

Next Tuesday, companies from the electronics industry plan to promote their industry at “2008 Digital E-Park.” In previous years, organizations from the electronics industry have showcased their products at Leisure Taiwan instead of at the Digital E-Park, so this move has reduced the number of markets covered by Leisure Taiwan.

Friday, July 29, 2011

Today sees the reopening of the National Museum of Scotland following a three-year renovation costing £47.4 million (US$ 77.3 million). Edinburgh’s Chambers Street was closed to traffic for the morning, with the 10am reopening by eleven-year-old Bryony Hare, who took her first steps in the museum, and won a competition organised by the local Evening News paper to be a VIP guest at the event. Prior to the opening, Wikinews toured the renovated museum, viewing the new galleries, and some of the 8,000 objects inside.

Dressed in Victorian attire, Scottish broadcaster Grant Stott acted as master of ceremonies over festivities starting shortly after 9am. The packed street cheered an animatronic Tyrannosaurus Rex created by Millenium FX; onlookers were entertained with a twenty-minute performance by the Mugenkyo Taiko Drummers on the steps of the museum; then, following Bryony Hare knocking three times on the original doors to ask that the museum be opened, the ceremony was heralded with a specially composed fanfare – played on a replica of the museum’s 2,000-year-old carnyx Celtic war-horn. During the fanfare, two abseilers unfurled white pennons down either side of the original entrance.

The completion of the opening to the public was marked with Chinese firecrackers, and fireworks, being set off on the museum roof. As the public crowded into the museum, the Mugenkyo Taiko Drummers resumed their performance; a street theatre group mingled with the large crowd, and the animatronic Tyrannosaurus Rex entertained the thinning crowd of onlookers in the centre of the street.

On Wednesday, the museum welcomed the world’s press for an in depth preview of the new visitor experience. Wikinews was represented by Brian McNeil, who is also Wikimedia UK’s interim liaison with Museum Galleries Scotland.

The new pavement-level Entrance Hall saw journalists mingle with curators. The director, Gordon Rintoul, introduced presentations by Gareth Hoskins and Ralph Applebaum, respective heads of the Architects and Building Design Team; and, the designers responsible for the rejuvenation of the museum.

Describing himself as a “local lad”, Hoskins reminisced about his grandfather regularly bringing him to the museum, and pushing all the buttons on the numerous interactive exhibits throughout the museum. Describing the nearly 150-year-old museum as having become “a little tired”, and a place “only visited on a rainy day”, he commented that many international visitors to Edinburgh did not realise that the building was a public space; explaining the focus was to improve access to the museum – hence the opening of street-level access – and, to “transform the complex”, focus on “opening up the building”, and “creating a number of new spaces […] that would improve facilities and really make this an experience for 21st century museum visitors”.

Hoskins explained that a “rabbit warren” of storage spaces were cleared out to provide street-level access to the museum; the floor in this “crypt-like” space being lowered by 1.5 metres to achieve this goal. Then Hoskins handed over to Applebaum, who expressed his delight to be present at the reopening.

Applebaum commented that one of his first encounters with the museum was seeing “struggling young mothers with two kids in strollers making their way up the steps”, expressing his pleasure at this being made a thing of the past. Applebaum explained that the Victorian age saw the opening of museums for public access, with the National Museum’s earlier incarnation being the “College Museum” – a “first window into this museum’s collection”.

The museum itself is physically connected to the University of Edinburgh’s old college via a bridge which allowed students to move between the two buildings.

Applebaum explained that the museum will, now redeveloped, be used as a social space, with gatherings held in the Grand Gallery, “turning the museum into a social convening space mixed with knowledge”. Continuing, he praised the collections, saying they are “cultural assets [… Scotland is] turning those into real cultural capital”, and the museum is, and museums in general are, providing a sense of “social pride”.

McNeil joined the yellow group on a guided tour round the museum with one of the staff. Climbing the stairs at the rear of the Entrance Hall, the foot of the Window on the World exhibit, the group gained a first chance to see the restored Grand Gallery. This space is flooded with light from the glass ceiling three floors above, supported by 40 cast-iron columns. As may disappoint some visitors, the fish ponds have been removed; these were not an original feature, but originally installed in the 1960s – supposedly to humidify the museum; and failing in this regard. But, several curators joked that they attracted attention as “the only thing that moved” in the museum.

The museum’s original architect was Captain Francis Fowke, also responsible for the design of London’s Royal Albert Hall; his design for the then-Industrial Museum apparently inspired by Joseph Paxton’s Crystal Palace.

The group moved from the Grand Gallery into the Discoveries Gallery to the south side of the museum. The old red staircase is gone, and the Millennium Clock stands to the right of a newly-installed escalator, giving easier access to the upper galleries than the original staircases at each end of the Grand Gallery. Two glass elevators have also been installed, flanking the opening into the Discoveries Gallery and, providing disabled access from top-to-bottom of the museum.

The National Museum of Scotland’s origins can be traced back to 1780 when the 11th Earl of Buchan, David Stuart Erskine, formed the Society of Antiquaries of Scotland; the Society being tasked with the collection and preservation of archaeological artefacts for Scotland. In 1858, control of this was passed to the government of the day and the National Museum of Antiquities of Scotland came into being. Items in the collection at that time were housed at various locations around the city.

On Wednesday, October 28, 1861, during a royal visit to Edinburgh by Queen Victoria, Prince-Consort Albert laid the foundation-stone for what was then intended to be the Industrial Museum. Nearly five years later, it was the second son of Victoria and Albert, Prince Alfred, the then-Duke of Edinburgh, who opened the building which was then known as the Scottish Museum of Science and Art. A full-page feature, published in the following Monday’s issue of The Scotsman covered the history leading up to the opening of the museum, those who had championed its establishment, the building of the collection which it was to house, and Edinburgh University’s donation of their Natural History collection to augment the exhibits put on public display.

Closed for a little over three years, today’s reopening of the museum is seen as the “centrepiece” of National Museums Scotland’s fifteen-year plan to dramatically improve accessibility and better present their collections. Sir Andrew Grossard, chair of the Board of Trustees, said: “The reopening of the National Museum of Scotland, on time and within budget is a tremendous achievement […] Our collections tell great stories about the world, how Scots saw that world, and the disproportionate impact they had upon it. The intellectual and collecting impact of the Scottish diaspora has been profound. It is an inspiring story which has captured the imagination of our many supporters who have helped us achieve our aspirations and to whom we are profoundly grateful.“

The extensive work, carried out with a view to expand publicly accessible space and display more of the museums collections, carried a £47.4 million pricetag. This was jointly funded with £16 million from the Scottish Government, and £17.8 million from the Heritage Lottery Fund. Further funds towards the work came from private sources and totalled £13.6 million. Subsequent development, as part of the longer-term £70 million “Masterplan”, is expected to be completed by 2020 and see an additional eleven galleries opened.

The funding by the Scottish Government can be seen as a ‘canny‘ investment; a report commissioned by National Museums Scotland, and produced by consultancy firm Biggar Economics, suggest the work carried out could be worth £58.1 million per year, compared with an estimated value to the economy of £48.8 prior to the 2008 closure. Visitor figures are expected to rise by over 20%; use of function facilities are predicted to increase, alongside other increases in local hospitality-sector spending.

Proudly commenting on the Scottish Government’s involvement Fiona Hyslop, Cabinet Secretary for Culture and External Affairs, described the reopening as, “one of the nation’s cultural highlights of 2011” and says the rejuvenated museum is, “[a] must-see attraction for local and international visitors alike“. Continuing to extol the museum’s virtues, Hyslop states that it “promotes the best of Scotland and our contributions to the world.“

So-far, the work carried out is estimated to have increased the public space within the museum complex by 50%. Street-level storage rooms, never before seen by the public, have been transformed into new exhibit space, and pavement-level access to the buildings provided which include a new set of visitor facilities. Architectural firm Gareth Hoskins have retained the original Grand Gallery – now the first floor of the museum – described as a “birdcage” structure and originally inspired by The Crystal Palace built in Hyde Park, London for the 1851 Great Exhibition.

The centrepiece in the Grand Gallery is the “Window on the World” exhibit, which stands around 20 metres tall and is currently one of the largest installations in any UK museum. This showcases numerous items from the museum’s collections, rising through four storeys in the centre of the museum. Alexander Hayward, the museums Keeper of Science and Technology, challenged attending journalists to imagine installing “teapots at thirty feet”.

The redeveloped museum includes the opening of sixteen brand new galleries. Housed within, are over 8,000 objects, only 20% of which have been previously seen.

The Window on the World rises through the four floors of the museum and contains over 800 objects. This includes a gyrocopter from the 1930s, the world’s largest scrimshaw – made from the jaws of a sperm whale which the University of Edinburgh requested for their collection, a number of Buddha figures, spearheads, antique tools, an old gramophone and record, a selection of old local signage, and a girder from the doomed Tay Bridge.

The arrangement of galleries around the Grand Gallery’s “birdcage” structure is organised into themes across multiple floors. The World Cultures Galleries allow visitors to explore the culture of the entire planet; Living Lands explains the ways in which our natural environment influences the way we live our lives, and the beliefs that grow out of the places we live – from the Arctic cold of North America to Australia’s deserts.

The adjacent Patterns of Life gallery shows objects ranging from the everyday, to the unusual from all over the world. The functions different objects serve at different periods in peoples’ lives are explored, and complement the contents of the Living Lands gallery.

Performance & Lives houses musical instruments from around the world, alongside masks and costumes; both rooted in long-established traditions and rituals, this displayed alongside contemporary items showing the interpretation of tradition by contemporary artists and instrument-creators.

The museum proudly bills the Facing the Sea gallery as the only one in the UK which is specifically based on the cultures of the South Pacific. It explores the rich diversity of the communities in the region, how the sea shapes the islanders’ lives – describing how their lives are shaped as much by the sea as the land.

Both the Facing the Sea and Performance & Lives galleries are on the second floor, next to the new exhibition shop and foyer which leads to one of the new exhibition galleries, expected to house the visiting Amazing Mummies exhibit in February, coming from Leiden in the Netherlands.

The Inspired by Nature, Artistic Legacies, and Traditions in Sculpture galleries take up most of the east side of the upper floor of the museum. The latter of these shows the sculptors from diverse cultures have, through history, explored the possibilities in expressing oneself using metal, wood, or stone. The Inspired by Nature gallery shows how many artists, including contemporary ones, draw their influence from the world around us – often commenting on our own human impact on that natural world.

Contrastingly, the Artistic Legacies gallery compares more traditional art and the work of modern artists. The displayed exhibits attempt to show how people, in creating specific art objects, attempt to illustrate the human spirit, the cultures they are familiar with, and the imaginative input of the objects’ creators.

The easternmost side of the museum, adjacent to Edinburgh University’s Old College, will bring back memories for many regular visitors to the museum; but, with an extensive array of new items. The museum’s dedicated taxidermy staff have produced a wide variety of fresh examples from the natural world.

At ground level, the Animal World and Wildlife Panorama’s most imposing exhibit is probably the lifesize reproduction of a Tyrannosaurus Rex skeleton. This rubs shoulders with other examples from around the world, including one of a pair of elephants. The on-display elephant could not be removed whilst renovation work was underway, and lurked in a corner of the gallery as work went on around it.

Above, in the Animal Senses gallery, are examples of how we experience the world through our senses, and contrasting examples of wildly differing senses, or extremes of such, present in the natural world. This gallery also has giant screens, suspended in the free space, which show footage ranging from the most tranquil and peaceful life in the sea to the tooth-and-claw bloody savagery of nature.

The Survival gallery gives visitors a look into the ever-ongoing nature of evolution; the causes of some species dying out while others thrive, and the ability of any species to adapt as a method of avoiding extinction.

Earth in Space puts our place in the universe in perspective. Housing Europe’s oldest surviving Astrolabe, dating from the eleventh century, this gallery gives an opportunity to see the technology invented to allow us to look into the big questions about what lies beyond Earth, and probe the origins of the universe and life.

In contrast, the Restless Earth gallery shows examples of the rocks and minerals formed through geological processes here on earth. The continual processes of the planet are explored alongside their impact on human life. An impressive collection of geological specimens are complemented with educational multimedia presentations.

Beyond working on new galleries, and the main redevelopment, the transformation team have revamped galleries that will be familiar to regular past visitors to the museum.

Formerly known as the Ivy Wu Gallery of East Asian Art, the Looking East gallery showcases National Museums Scotland’s extensive collection of Korean, Chinese, and Japanese material. The gallery’s creation was originally sponsored by Sir Gordon Wu, and named after his wife Ivy. It contains items from the last dynasty, the Manchu, and examples of traditional ceramic work. Japan is represented through artefacts from ordinary people’s lives, expositions on the role of the Samurai, and early trade with the West. Korean objects also show the country’s ceramic work, clothing, and traditional accessories used, and worn, by the indigenous people.

The Ancient Egypt gallery has always been a favourite of visitors to the museum. A great many of the exhibits in this space were returned to Scotland from late 19th century excavations; and, are arranged to take visitors through the rituals, and objects associated with, life, death, and the afterlife, as viewed from an Egyptian perspective.

The Art and Industry and European Styles galleries, respectively, show how designs are arrived at and turned into manufactured objects, and the evolution of European style – financed and sponsored by a wide range of artists and patrons. A large number of the objects on display, often purchased or commissioned, by Scots, are now on display for the first time ever.

Shaping our World encourages visitors to take a fresh look at technological objects developed over the last 200 years, many of which are so integrated into our lives that they are taken for granted. Radio, transportation, and modern medicines are covered, with a retrospective on the people who developed many of the items we rely on daily.

What was known as the Museum of Scotland, a modern addition to the classical Victorian-era museum, is now known as the Scottish Galleries following the renovation of the main building.

This dedicated newer wing to the now-integrated National Museum of Scotland covers the history of Scotland from a time before there were people living in the country. The geological timescale is covered in the Beginnings gallery, showing continents arranging themselves into what people today see as familiar outlines on modern-day maps.

Just next door, the history of the earliest occupants of Scotland are on display; hunters and gatherers from around 4,000 B.C give way to farmers in the Early People exhibits.

The Kingdom of the Scots follows Scotland becoming a recognisable nation, and a kingdom ruled over by the Stewart dynasty. Moving closer to modern-times, the Scotland Transformed gallery looks at the country’s history post-union in 1707.

Industry and Empire showcases Scotland’s significant place in the world as a source of heavy engineering work in the form of rail engineering and shipbuilding – key components in the building of the British Empire. Naturally, whisky was another globally-recognised export introduced to the world during empire-building.

Lastly, Scotland: A Changing Nation collects less-tangible items, including personal accounts, from the country’s journey through the 20th century; the social history of Scots, and progress towards being a multicultural nation, is explored through heavy use of multimedia exhibits.

Monday, December 11, 2006

On December 7, BBC News reported a story about Dr James Anderson, a teacher in the Computer Science department at the University of Reading in the United Kingdom. In the report it was stated that Anderson had “solved a very important problem” that was 1200 years old, the problem of division by zero. According to the BBC, Anderson had created a new number, that he had named “nullity”, that lay outside of the real number line. Anderson terms this number a “transreal number”, and denotes it with the Greek letter ? {\displaystyle \Phi } . He had taught this number to pupils at Highdown School, in Emmer Green, Reading.

The BBC report provoked many reactions from mathematicians and others.

In reaction to the story, Mark C. Chu-Carroll, a computer scientist and researcher, posted a web log entry describing Anderson as an “idiot math teacher”, and describing the BBC’s story as “absolutely infuriating” and a story that “does an excellent job of demonstrating what total innumerate idiots reporters are”. Chu-Carroll stated that there was, in fact, no actual problem to be solved in the first place. “There is no number that meaningfully expresses the concept of what it means to divide by zero.”, he wrote, stating that all that Anderson had done was “assign a name to the concept of ‘not a number'”, something which was “not new” in that the IEEE floating-point standard, which describes how computers represent floating-point numbers, had included a concept of “not a number”, termed “NaN“, since 1985. Chu-Carroll further continued:

“Basically, he’s defined a non-solution to a non-problem. And by teaching it to his students, he’s doing them a great disservice. They’re going to leave his class believing that he’s a great genius who’s solved a supposed fundamental problem of math, and believing in this silly nullity thing as a valid mathematical concept.

“It’s not like there isn’t already enough stuff in basic math for kids to learn; there’s no excuse for taking advantage of a passive audience to shove this nonsense down their throats as an exercise in self-aggrandizement.

“To make matters worse, this idiot is a computer science professor! No one who’s studied CS should be able to get away with believing that re-inventing the concept of NaN is something noteworthy or profound; and no one who’s studied CS should think that defining meaningless values can somehow magically make invalid computations produce meaningful results. I’m ashamed for my field.”

There have been a wide range of other reactions from other people to the BBC news story. Comments range from the humorous and the ironic, such as the B1FF-style observation that “DIVIDION^[sic] BY ZERO IS IMPOSSIBLE BECAUSE MY CALCULATOR SAYS SO AND IT IS THE TRUTH” and the Chuck Norris Fact that “Only Chuck Norris can divide by zero.” (to which another reader replied “Chuck Norris just looks at zero, and it divides itself.”); through vigourous defences of Dr Anderson, with several people quoting the lyrics to Ira Gershwin‘s song “They All Laughed (At Christopher Columbus)”; to detailed mathematical discussions of Anderson’s proposed axioms of transfinite numbers.

Several readers have commented that they consider this to have damaged the reputation of the Computer Science department, and even the reputation of the University of Reading as a whole. “By publishing his childish nonsense the BBC actively harms the reputation of Reading University.” wrote one reader. “Looking forward to seeing Reading University maths application plummit.” wrote another. “Ignore all research papers from the University of Reading.” wrote a third. “I’m not sure why you refer to Reading as a ‘university’. This is a place the BBC reports as closing down its physics department because it’s too hard. Lecturers at Reading should stick to folk dancing and knitting, leaving academic subjects to grown ups.” wrote a fourth. Steve Kramarsky lamented that Dr Anderson is not from the “University of ‘Rithmetic“.

Several readers criticised the journalists at the BBC who ran the story for not apparently contacting any mathematicians about Dr Anderson’s idea. “Journalists are meant to check facts, not just accept whatever they are told by a self-interested third party and publish it without question.” wrote one reader on the BBC’s web site. However, on Slashdot another reader countered “The report is from Berkshire local news. Berkshire! Do you really expect a local news team to have a maths specialist? Finding a newsworthy story in Berkshire probably isn’t that easy, so local journalists have to cover any piece of fluff that comes up. Your attitude to the journalist should be sympathy, not scorn.”

Ben Goldacre, author of the Bad Science column in The Guardian, wrote on his web log that “what is odd is a reporter, editor, producer, newsroom, team, cameraman, soundman, TV channel, web editor, web copy writer, and so on, all thinking it’s a good idea to cover a brilliant new scientific breakthrough whilst clearly knowing nothing about the context. Maths isn’t that hard, you could even make a call to a mathematician about it.”, continuing that “it’s all very well for the BBC to think they’re being balanced and clever getting Dr Anderson back in to answer queries about his theory on Tuesday, but that rather skips the issue, and shines the spotlight quite unfairly on him (he looks like a very alright bloke to me).”.

From reading comments on his own web log as well as elsewhere, Goldacre concluded that he thought that “a lot of people might feel it’s reporter Ben Moore, and the rest of his doubtless extensive team, the people who drove the story, who we’d want to see answering the questions from the mathematicians.”.

Andrej Bauer, a professional mathematician from Slovenia writing on the Bad Science web log, stated that “whoever reported on this failed to call a university professor to check whether it was really new. Any university professor would have told this reporter that there are many ways of dealing with division by zero, and that Mr. Anderson’s was just one of known ones.”

Ollie Williams, one of the BBC Radio Berkshire reporters who wrote the BBC story, initially stated that “It seems odd to me that his theory would get as far as television if it’s so easily blown out of the water by visitors to our site, so there must be something more to it.” and directly responded to criticisms of BBC journalism on several points on his web log.

He pointed out that people should remember that his target audience was local people in Berkshire with no mathematical knowledge, and that he was “not writing for a global audience of mathematicians”. “Some people have had a go at Dr Anderson for using simplified terminology too,” he continued, “but he knows we’re playing to a mainstream audience, and at the time we filmed him, he was showing his theory to a class of schoolchildren. Those circumstances were never going to breed an in-depth half-hour scientific discussion, and none of our regular readers would want that.”.

On the matter of fact checking, he replied that “if you only want us to report scientific news once it’s appeared, peer-reviewed, in a recognised journal, it’s going to be very dry, and it probably won’t be news.”, adding that “It’s not for the BBC to become a journal of mathematics — that’s the job of journals of mathematics. It’s for the BBC to provide lively science reporting that engages and involves people. And if you look at the original page, you’ll find a list as long as your arm of engaged and involved people.”.

Williams pointed out that “We did not present Dr Anderson’s theory as gospel, although with hindsight it could have been made clearer that this is very much a theory and by no means universally accepted. But we certainly weren’t shouting a mathematical revolution from the rooftops. Dr Anderson has, in one or two places, been chastised for coming to the media with his theory instead of his peers — a sure sign of a quack, boffin and/or crank according to one blogger. Actually, one of our reporters happened to meet him during a demonstration against the closure of the university’s physics department a couple of weeks ago, got chatting, and discovered Dr Anderson reckoned he was onto something. He certainly didn’t break the door down looking for media coverage.”.

Some commentators, at the BBC web page and at Slashdot, have attempted serious mathematical descriptions of what Anderson has done, and subjected it to analysis. One description was that Anderson has taken the field of real numbers and given it complete closure so that all six of the common arithmetic operators were surjective functions, resulting in “an object which is barely a commutative ring (with operators with tons of funky corner cases)” and no actual gain “in terms of new theorems or strong relation statements from the extra axioms he has to tack on”.

Jamie Sawyer, a mathematics undergraduate at the University of Warwick writing in the Warwick Maths Society discussion forum, describes what Anderson has done as deciding that R ? { ? ? , + ? } {\displaystyle \mathbb {R} \cup \lbrace -\infty ,+\infty \rbrace } , the so-called extended real number line, is “not good enough […] because of the wonderful issue of what 0 0 {\displaystyle {\frac {0}{0}}} is equal to” and therefore creating a number system R ? { ? ? , ? , + ? } {\displaystyle \mathbb {R} \cup \lbrace -\infty ,\Phi ,+\infty \rbrace } .

Andrej Bauer stated that Anderson’s axioms of transreal arithmetic “are far from being original. First, you can adjoin + ? {\displaystyle +\infty } and ? ? {\displaystyle -\infty } to obtain something called the extended real line. Then you can adjoin a bottom element to represent an undefined value. This is all standard and quite old. In fact, it is well known in domain theory, which deals with how to represent things we compute with, that adjoining just bottom to the reals is not a good idea. It is better to adjoin many so-called partial elements, which denote approximations to reals. Bottom is then just the trivial approximation which means something like ‘any real’ or ‘undefined real’.”

Commentators have pointed out that in the field of mathematical analysis, 0 0 {\displaystyle {\frac {0}{0}}} (which Anderson has defined axiomatically to be ? {\displaystyle \Phi } ) is the limit of several functions, each of which tends to a different value at its limit:

• lim x ? 0 x 0 {\displaystyle \lim _{x\to 0}{\frac {x}{0}}} has two different limits, depending from whether x {\displaystyle x} approaches zero from a positive or from a negative direction.
• lim x ? 0 0 x {\displaystyle \lim _{x\to 0}{\frac {0}{x}}} also has two different limits. (This is the argument that commentators gave. In fact, 0 x {\displaystyle {\frac {0}{x}}} has the value 0 {\displaystyle 0} for all x ? 0 {\displaystyle x\neq 0} , and thus only one limit. It is simply discontinuous for x = 0 {\displaystyle x=0} . However, that limit is different to the two limits for lim x ? 0 x 0 {\displaystyle \lim _{x\to 0}{\frac {x}{0}}} , supporting the commentators’ main point that the values of the various limits are all different.)
• Whilst sin ? 0 = 0 {\displaystyle \sin 0=0} , the limit lim x ? 0 sin ? x x {\displaystyle \lim _{x\to 0}{\frac {\sin x}{x}}} can be shown to be 1, by expanding the sine function as an infinite Taylor series, dividing the series by x {\displaystyle x} , and then taking the limit of the result, which is 1.
• Whilst 1 ? cos ? 0 = 0 {\displaystyle 1-\cos 0=0} , the limit lim x ? 0 1 ? cos ? x x {\displaystyle \lim _{x\to 0}{\frac {1-\cos x}{x}}} can be shown to be 0, by expanding the cosine function as an infinite Taylor series, dividing the series subtracted from 1 by x {\displaystyle x} , and then taking the limit of the result, which is 0.

Commentators have also noted l’Hôpital’s rule.

It has been pointed out that Anderson’s set of transreal numbers is not, unlike the set of real numbers, a mathematical field. Simon Tatham, author of PuTTY, stated that Anderson’s system “doesn’t even think about the field axioms: addition is no longer invertible, multiplication isn’t invertible on nullity or infinity (or zero, but that’s expected!). So if you’re working in the transreals or transrationals, you can’t do simple algebraic transformations such as cancelling x {\displaystyle x} and ? x {\displaystyle -x} when both occur in the same expression, because that transformation becomes invalid if x {\displaystyle x} is nullity or infinity. So even the simplest exercises of ordinary algebra spew off a constant stream of ‘unless x is nullity’ special cases which you have to deal with separately — in much the same way that the occasional division spews off an ‘unless x is zero’ special case, only much more often.”

Tatham stated that “It’s telling that this monstrosity has been dreamed up by a computer scientist: persistent error indicators and universal absorbing states can often be good computer science, but he’s stepped way outside his field of competence if he thinks that that also makes them good maths.”, continuing that Anderson has “also totally missed the point when he tries to compute things like 0 0 {\displaystyle 0^{0}} using his arithmetic. The reason why things like that are generally considered to be ill-defined is not because of a lack of facile ‘proofs’ showing them to have one value or another; it’s because of a surfeit of such ‘proofs’ all of which disagree! Adding another one does not (as he appears to believe) solve any problem at all.” (In other words: 0 0 {\displaystyle 0^{0}} is what is known in mathematical analysis as an indeterminate form.)

To many observers, it appears that Anderson has done nothing more than re-invent the idea of “NaN“, a special value that computers have been using in floating-point calculations to represent undefined results for over two decades. In the various international standards for computing, including the IEEE floating-point standard and IBM’s standard for decimal arithmetic, a division of any non-zero number by zero results in one of two special infinity values, “+Inf” or “-Inf”, the sign of the infinity determined by the signs of the two operands (Negative zero exists in floating-point representations.); and a division of zero by zero results in NaN.

Anderson himself denies that he has re-invented NaN, and in fact claims that there are problems with NaN that are not shared by nullity. According to Anderson, “mathematical arithmetic is sociologically invalid” and IEEE floating-point arithmetic, with NaN, is also faulty. In one of his papers on a “perspex machine” dealing with “The Axioms of Transreal Arithmetic” (Jamie Sawyer writes that he has “worries about something which appears to be named after a plastic” — “Perspex” being a trade name for polymethyl methacrylate in the U.K..) Anderson writes:

We cannot accept an arithmetic in which a number is not equal to itself (NaN != NaN), or in which there are three kinds of numbers: plain numbers, silent numbers, and signalling numbers; because, on writing such a number down, in daily discourse, we can not always distinguish which kind of number it is and, even if we adopt some notational convention to make the distinction clear, we cannot know how the signalling numbers are to be used in the absence of having the whole program and computer that computed them available. So whilst IEEE floating-point arithmetic is an improvement on real arithmetic, in so far as it is total, not partial, both arithmetics are invalid models of arithmetic.

In fact, the standard convention for distinguishing the two types of NaNs when writing them down can be seen in ISO/IEC 10967, another international standard for how computers deal with numbers, which uses “qNaN” for non-signalling (“quiet”) NaNs and “sNaN” for signalling NaNs. Anderson continues:

[NaN’s] semantics are not defined, except by a long list of special cases in the IEEE standard.

“In other words,” writes Scott Lamb, a BSc. in Computer Science from the University of Idaho, “they are defined, but he doesn’t like the definition.”.

The main difference between nullity and NaN, according to both Anderson and commentators, is that nullity compares equal to nullity, whereas NaN does not compare equal to NaN. Commentators have pointed out that in very short order this difference leads to contradictory results. They stated that it requires only a few lines of proof, for example, to demonstrate that in Anderson’s system of “transreal arithmetic” both 1 = 2 {\displaystyle 1=2} and 1 ? 2 {\displaystyle 1\neq 2} , after which, in one commentator’s words, one can “prove anything that you like”. In aiming to provide a complete system of arithmetic, by adding extra axioms defining the results of the division of zero by zero and of the consequent operations on that result, half as many again as the number of axioms of real-number arithmetic, Anderson has produced a self-contradictory system of arithmetic, in accordance with Gödel’s incompleteness theorems.

One reader-submitted comment appended to the BBC news article read “Step 1. Create solution 2. Create problem 3. PROFIT!”, an allusion to the business plan employed by the underpants gnomes of the comedy television series South Park. In fact, Anderson does plan to profit from nullity, having registered on the 27th of July, 2006 a private limited company named Transreal Computing Ltd, whose mission statement is “to develop hardware and software to bring you fast and safe computation that does not fail on division by zero” and to “promote education and training in transreal computing”. The company is currently “in the research and development phase prior to trading in hardware and software”.

In a presentation given to potential investors in his company at the ANGLE plc showcase on the 28th of November, 2006, held at the University of Reading, Anderson stated his aims for the company as being:

• To build a transreal computer.
• To derive Maxwell’s equations and classical gravitation in transreal numbers so that they have no naked singularities (infinities affecting a neighbourhood of space).
• To collaborate with anyone who wants to unify Quantum Electro-Dynamics with gravitation.

To investors, Anderson makes the following promises:

• “I will help you develop a curriculum for transreal arithmetic if you want me to.”
• “I will help you unify QED and gravitation if you want me to.”
• “I will build a transreal supercomputer.”

He asks potential investors:

• “How much would you pay to know that the engine in your ship, car, aeroplane, or heart pacemaker won’t just stop dead?”
• “How much would you pay to know that your Government’s computer controlled military hardware won’t just stop or misfire?”

The current models of computer arithmetic are, in fact, already designed to allow programmers to write programs that will continue in the event of a division by zero. The IEEE’s Frequently Asked Questions document for the floating-point standard gives this reply to the question “Why doesn’t division by zero (or overflow, or underflow) stop the program or trigger an error?”:

“The [IEEE] 754 model encourages robust programs. It is intended not only for numerical analysts but also for spreadsheet users, database systems, or even coffee pots. The propagation rules for NaNs and infinities allow inconsequential exceptions to vanish. Similarly, gradual underflow maintains error properties over a precision’s range.

“When exceptional situations need attention, they can be examined immediately via traps or at a convenient time via status flags. Traps can be used to stop a program, but unrecoverable situations are extremely rare. Simply stopping a program is not an option for embedded systems or network agents. More often, traps log diagnostic information or substitute valid results.”

Simon Tatham stated that there is a basic problem with Anderson’s ideas, and thus with the idea of building a transreal supercomputer: “It’s a category error. The Anderson transrationals and transreals are theoretical algebraic structures, capable of representing arbitrarily big and arbitrarily precise numbers. So the question of their error-propagation semantics is totally meaningless: you don’t use them for down-and-dirty error-prone real computation, you use them for proving theorems. If you want to use this sort of thing in a computer, you have to think up some concrete representation of Anderson transfoos in bits and bytes, which will (if only by the limits of available memory) be unable to encompass the entire range of the structure. And the point at which you make this transition from theoretical abstract algebra to concrete bits and bytes is precisely where you should also be putting in error handling, because it’s where errors start to become possible. We define our theoretical algebraic structures to obey lots of axioms (like the field axioms, and total ordering) which make it possible to reason about them efficiently in the proving of theorems. We define our practical number representations in a computer to make it easy to detect errors. The Anderson transfoos are a consequence of fundamentally confusing the one with the other, and that by itself ought to be sufficient reason to hurl them aside with great force.”

Geomerics, a start-up company specializing in simulation software for physics and lighting and funded by ANGLE plc, had been asked to look into Anderson’s work by an unnamed client. Rich Wareham, a Senior Research and Development Engineer at Geomerics and a MEng. from the University of Cambridge, stated that Anderson’s system “might be a more interesting set of axioms for dealing with arithmetic exceptions but it isn’t the first attempt at just defining away the problem. Indeed it doesn’t fundamentally change anything. The reason computer programs crash when they divide by zero is not that the hardware can produce no result, merely that the programmer has not dealt with NaNs as they propagate through. Not dealing with nullities will similarly lead to program crashes.”

“Do the Anderson transrational semantics give any advantage over the IEEE ones?”, Wareham asked, answering “Well one assumes they have been thought out to be useful in themselves rather than to just propagate errors but I’m not sure that seeing a nullity pop out of your code would lead you to do anything other than what would happen if a NaN or Inf popped out, namely signal an error.”.

Thursday, February 10, 2011

Calgary city council voted 10 to 3 on Wednesday to stop fluoridating their water supply. This overturns a previous plebiscite from 1989 to add the fluoride in an attempt to reduce tooth decay.

Opponents of water fluoridation claim that there could be unknown health effects of fluoride, and question its effectiveness in preventing tooth decay. They also claim that individuals should be able to decide for themselves whether or not to use fluoride. However, Alberta Health Services maintains that current evidence shows that fluoride is both safe, and beneficial to dental health.

It is estimated that no longer fluoridating the water supply could save Calgary’s city council C$750 thousand (€550 thousand) annually, as well as cutting a C$6 million (€4.3 million) upgrade to the fluoridation system.

Tuesday, February 23, 2010

Toyota has been accused by a U.S. House of Representatives committee with misleading the public and investigators over its recent recalls.

The accusations, in a statement from the House Energy and Commerce Committee, claim that Toyota both relied on a flawed study in its assessment of the issue of sticking accelerator pedals at the heart of the recalls, and then made misleading statements about its response. According to the authors of the letter, Henry Waxman and Bart Stupak, Toyota dismissed, rather than investigated, the idea that the cars’ computers were at fault. In a statement, James Lentz, the president of Toyota’s American division, claimed that hardware issues were to blame, and that dealers were repairing the faulty part. Toyota also released a study commissioned from the research firm Exponent that said electronic systems were not to blame.

According to the House committee, however, the study involved only six vehicles, none of which had problems with their electrical systems, and was insufficient to produce an accurate result. “Our preliminary assessment is that Toyota resisted the possibility that electronic defects could cause safety concerns, relied on a flawed engineering report and made misleading public statements concerning the adequacy of recent recalls to address the risk of sudden unintended acceleration.”

The company is under a criminal investigation, and has received two subpoenas for documents from two House committees relating to the recalls, although whether they are directly related to the letter is unclear. The documents are related to accelerator issues in several models, as well as brake problems with the Prius hybrid car, and were served earlier in in February by a federal grand jury and the Securities and Exchange Commission. Toyota has released upwards of 75,000 pages of documents under the requests.

In a separate, though related, development, it has emerged that Toyota last year negotiated a limited recall for two models, the Toyota Camry and Lexus ES, that were affected by the accelerator recalls, saving the company an estimated $100 million. A confidential internal presentation in July 2009 made the claim, and a month later, a Lexus ES, one of the models under the limited recall crashed in California, killing four people. The claims apparently referenced a September, 2007 recall of floor mats that could trap gas pedals, the same problem that triggered a full recall of numerous Toyota cars to fix the same problem. In the same presentation, the company claimed to have avoided recalls of another model related to rust, as well as delaying new federal safety regulations.

Friday, November 20, 2009

Ten passengers on board a British Airways jet that crashed in London’s Heathrow Airport are suing the manufacturer of the aircraft. Documents filed before a court in Chicago, Illinois claim that Boeing were responsible for design flaws with the fuel system.

The Boeing 777 crash-landed early in 2008 after engine power was lost on final approach, coming down short of the runway. The aircraft was severely damaged. The United Kingdom’s Air Accidents Investigation Branch is still investigating, but interim reports have indicated that engine components became clogged with ice developing in the fuel.

The crew of the aircraft were praised for their handling of the emergency, avoiding the perimeter fence and nearby houses. None of the 136 passengers and 16 crew were killed but some of those suffered serious injuries, including broken bones and facial injuries. Some were left unable to fly and there were cases of Post Traumatic Stress Disorder.

The case, run by London firm Stewarts Law, is that Boeing are liable for the design of the engine component upon which the ice settled during the accident. “Our clients are not critical of BA and feel that the pilots performed heroically in guiding the aircraft down in exceptionally difficult circumstances,” said the partner in charge of the case, Stuart Dench. “However the two interim reports from the Air Accident Investigation Branch suggest design defects in the aircraft’s fuel system and in particular its limitations in the prevention of dangerous ice build-up. The passengers we represent are therefore prepared to take on Boeing in its home court in Chicago, which is undoubtedly the most appropriate jurisdiction for this case.”

Boeing may seek to have the case heard in London before the High Court. If successful, the claimants are estimated by the media to be able to claim US$1 million (£600,000).

Sunday, December 10, 2006

Space shuttle mission STS-116 began today with its successful launch at 8:48pm EST (01:47 GMT). Liftoff was uneventful with no immediate problems. Last Thursday’s launch attempt was scrubbed due to low, dense cloud cover. It is the first Space Shuttle night launch in over four years and the last mission planned for pad 39b.

In the complex mission Discovery will first dock with the International Space Station. In three spacewalks the astronauts will install a segment of the station’s integrated truss and replace the orbital laboratory’s power wiring system.