Eliminate The Invaders In Your Home With Pest Control In Glen Burnie
Posted in Farming on 02/26/2020 02:05 am by- See More About:
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byAlma Abell
Your home or business can easily become infested with a variety of pests including several types of insects, furry little rodents and even birds, bees and bats. The difficulty with unexpected Pest Control in Glen Burnie isn’t the unusual pests that invade your property, but the unique methods that each pest requires to eliminate the problem. For example, eliminating insects such as the cockroach is usually handled by a series of chemical applications designed to remove successive generations as the young hatch. Rodents on the other hand require the application of baits and traps to properly remove the problem.
Pest problems in your buildings can vary based on several different variables including the location of moisture, a ready source of food and a secure place to build a nest. Consider the termite. This is a small, whitish, pale or lightly colored insect with a social structure similar to the ant. However, the termite is no longer considered as a member of the ant species. Instead, it is considered as the infraorder Isopertera of the cockroach order Blattodea. You rarely see this insect outside of the nest and an experienced Pest Control in Glen Burnie contractor will need to find the nest and apply the proper baits for the termites.
Termites come in literally thousands of species, many of which actually perform a useful function in the wild, the breakdown and removal of dead plant matter, scientifically labeled as cellulose. Unfortunately, much of the material we build our homes with uses wood fibers and the termites aren’t smart enough to know they should find a different food source.
Another home invader that can be difficult to eliminate are rodents such as mice and rats. These pests usually enter your home or business through cracks in the walls or doors or holes that they gnaw away with their sharp front teeth. Once they have entered the building they quickly begin to build their nest in the warmer walls where they will birth their young. Mice and rats breed a lot and those new generations will soon find even more places to nest in the walls of your home which is why you should consider hiring an experienced contractor like Accutech Pest Management for your next pest elimination project.
FBI document reviews symbols used by pedophiles
Posted in Uncategorized on 02/23/2020 03:02 am by
Wednesday, November 14, 2007
File:FBI-pedophile-symbols-416.jpg
In an exclusive report, Wikinews has obtained an internal FBI document from Wikileaks detailing symbols used by organized pedophiles to identify one another.
Wikileaks obtained the document via Spanish “childhood erotica” networks. According to Wikileaks, the unclassified parts of the document were only briefly published by the Ann Arbor, Michigan police department in a newsletter, which was later removed from the internet.
The document, which is titled Symbols and Logos Used by Pedophiles to Identify Sexual Preferences states that “pedophiles, to include those who sexually abuse children as well as those who produce, distribute, and trade child pornography, are using various types of identification logos or symbols to recognize one another and distinguish their sexual preferences.”
According to the FBI, there are at least three groups that pedophiles can use to identify what age and or gender they prefer such as “boylove, girllove and childlove.” Most of the logos have been found to be printed on coins, necklace charms and rings.
The first logo, ‘The BoyLover logo’ (BLogo) “is a small blue spiral-shaped triangle surrounded by a larger triangle, whereby the small triangle represents a small boy and the larger triangle represents an adult man. A variation of the BLogo is the Little Boy Lover logo (LBLogo), which also embodies a small spiral-shaped triangle within a larger triangle; however, the corners of the LBLogo are rounded to resemble a scribbling by a young child,” said the document.
The second logo, ‘The GirlLover logo’ (GLogo) is “a small heart surrounded by a larger heart, which symbolizes a relationship between an adult male or female and minor girl,” the document stated.
The last logo, ‘The ChildLover logo’ (CLogo), “resembles a butterfly and represents non-preferential gender child abusers,” added the document.
It is not known how the document came to be in the hands of Spanish childhood erotica enthusiasts. The logos were found during raids on computers and other items related to pedophile investigations.
Over 900 people dead, 14,000 infected in Haitian cholera outbreak
Posted in Uncategorized on 02/23/2020 02:30 am by
Sunday, November 14, 2010
New figures show an estimated 917 have died and 14,000 more infected with cholera in Haiti’s present outbreak. However, it is suspected that many deaths in mountainous regions far from hospitals are going unreported.
Clinics are rapidly filling up and many deaths are being reported. “The trend is extremely, extremely alarming. We have not reached a peak yet, but it could arrive next week,” said the head of mission for Medecins Sans Frontieres, Stefano Zannini. A health official described the situation in Port-Au-Prince as “[growing] more pathetic each day.” The official also said that hospitals in the capital are not able to cope with all of the patients.
The United Nations has appealed to donor nations for US$164 million in order to import more doctors, medicine, and water purification systems.
According to the US Centers for Disease Control (CDC) “experience from the Peru outbreak in the early 1990s and from other countries in Latin America suggests that we should expect to identify additional cases for many months to several years.”
CDC says cholera is “an acute, diarrheal illness caused by infection of the intestine with the bacterium Vibrio cholerae. The infection is often mild or without symptoms, but sometimes it can be severe… In severe cases, the infected person may experience profuse watery diarrhea, vomiting, and leg cramps, which can cause rapid loss of body fluids and lead to dehydration and shock. Without treatment, death can occur within hours.”
Affordable Houses For Sale
Posted in Wordpress Developers on 02/23/2020 02:09 am bySee More About:
byadmin
Looking to move to a new place in Missouri? Why not consider some of the fine houses for sale in Lake of the Ozarks?
Lakeside Life
Having your home by a lakeside can be quite an enjoyable experience. First, there is the beautiful view of the lakeside and the activities revolving around it. Housing areas by lakesides are often quite tranquil compared to housing areas near cities. It is sure to do your mind some good. Also, if you are up for it, having lakeside property also allows for an easily accessible boating experience. Those reasons and more spurred on the development of housing areas around the Lake of the Ozarks, where many houses are currently up for sale.
A Potential Investment
Buying property on good locations can also turn out to be quite an investment later on, especially if you add to the value through good remodeling work because the value of property typically rides on an upward trend since everyone needs a place to live. While getting a house on prime real estate can oftentimes turn out to be very costly, there are houses for sale in Lake of the Ozarks region that won’t break the bank, should you know where to look. Houses for sale in Lake of the Ozarks range from modest dwellings to decently-sized ones that can comfortably house a growing family.
For the full listing of the many lakeside houses for sale, one can drop by their website at www.janekelly.com. If you are in need of further assistance, you can chat live with a member of the team.
Family sues CNN’s Nancy Grace after ‘heated debate’
Posted in Uncategorized on 02/22/2020 02:31 am by
Thursday, November 23, 2006
The family of a woman who committed suicide recently after appearing on CNN Headline News Nancy Grace’s self titled show said Tuesday that they will be taking her to court.
Melinda Duckett, the mother of an infant son, Trenton Duckett, reported him missing on August 27, and fatally shot herself in her grandparents’ retirement home on September 8. Shortly before her death, she had appeared on Grace’s show, where she engaged in debate with the former Georgia prosecutor regarding her perceived lack of transparency regarding the disappearance. A suicide note was later found at the scene. The case made national headlines after her appearance.
“Nancy Grace and the others, they just bashed her to the end,” said Duckett’s grandfather, Bill Eubanks, during an interview with The Orlando Sentinel. “She wasn’t one anyone ever would have thought of to do something like this. She and that baby just loved each other, couldn’t get away from each other. She wouldn’t hurt a bug.”
Grace’s spokeswoman called the suicide “a sad development,” and Grace herself issued a statement saying, “I do not feel that our show is to blame for what happened to Melinda Duckett.”
“The truth,” said Grace, “is not always nice or polite or easy to go down. Sometimes it’s harsh, and it hurts.”
However, thesmokinggun.com, a true crime website run by Court TV (where Grace also hosts a show), revealed pending litigation by the family on the behalf of Melinda Duckett’s estate. Duckett’s family is issuing a wrongful death claim against both CNN and Nancy Grace.
After the murder of Grace’s fiancee in 1979, she became a prosecutor in her native Georgia and later hosted her own show on Court TV, followed later by her CNN tenure. Grace, however, has been criticized for her sense of ethics and allegedly playing fast and loose with the facts, both in the courtroom and on the air.
Grace’s heated interview, however, was not without proper motive. The police had long suspected Melinda Duckett of involvement in her son’s disappearance, due to her behavior and contradictory statements. After Duckett’s suicide, police named her as a prime suspect in her son’s disappearance. Recently, they have announced that they have reason to believe that Trenton Duckett is still alive.
News briefs:July 26, 2010
Posted in Uncategorized on 02/22/2020 02:26 am by
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Hardwood Floor Installations And How They Delight Buyers And Owner}
Posted in Timber on 02/19/2020 02:25 am bySee More About:
Hardwood Floor Installations and How They Delight Buyers and owner
by
Steve Evans
As your complete flooring resource, the HWF web site ‘How To’ helps determine which flooring is right for you and your home. Browse product many articles for hardwood, carpet, laminate and floor refinishing, ideas of selectors to quickly narrow down the choices.
Your choice of hardwood flooring is a decision that can dramatically impact the very essence of your home’s character. That’s why there’s no finer choice than HomerWood’s exclusive Character Grade flooring.
Because all people are unique, the best flooring suppliers do offer a diverse selection of hard wood flooring styles produced in a wide range of wood species and colors. Award Hardwood Floors are one make of these floors which say that they are sure to satisfy even the most discriminate consumer.
Commitment to high quality products and state of the art manufacturing advances is only a feature of the very best suppliers and can easily be seen from product to product, board to board.
Since 1998, thousands of home-owners and various home decorating publications have looked to the top flooring web sites for helpful flooring information for all types of floors, including: hardwood flooring, laminate flooring, carpet, cork, bamboo floors and ceramic tile. Our consumer reviews cover all types of floors for both for new home construction as well as remodeling projects.
Hardwood flooring suppliers offer a wider selection of sizes, colors and species and finishes than ever before.
While wood flooring has been much in vogue in recent years, it has received little if any exceptional treatment from do-it-yourself writers. Bollinger, an experienced flooring contractor, states that he has produced what has to be the definitive guide to installing and finishing wood floors. He writes about the three types of flooring: strip, plank, and parquet covering such topics as estimating costs; selecting wood types and grades; preparing the underlay; planning the layout; sanding; and applying various finishes.
Bollinger says he brings in many tricks of the trade, such refinements as wood and metal inlays, and ideas for dealing with the irregularities that invariably crop up in the repair or layout of floors as part of renovation projects. Nicely illustrated with photos and drawings. For most public libraries with active how-to collections. A companion video is also available; contact the publisher.
Using crisp photos and drawings, Bollinger says he gives you step by step instructions through the process. You will learn how to estimate materials, select the right kind of wood, prepare the subfloor and achieve a blemish-free finish for an old or new floor. This supplier says he also provides numerous tips and tricks, and sources of supply. The book is indexed for easy reference.
Nothing gives a home an air of timelessness and quiet elegance like a quality hardwood floor. At one supplier they carry a wide range of prefinished engineered, solid and floating floor systems designed to suit almost every need. They say that they have carefully selected their lines based on their reputation, quality and value for money, and to continually be on the look out for fresh, exciting flooring solutions to bring to you.
We recommend you use a full service hardwood flooring company providing expert sales and installation for your home. Plenty of suppliers offer knowledgeable service from initial design consultation to final installation and maintenance programs.
When you enter a room, your first impression of it is made from the floor upwards. It is essential to get this right, and by fitting hardwood flooring, you have usually at a stroke, solved the most difficult and important part of making an impact. Wood flooring gives you the ultimate in timeless elegance, flexibility and durability. Its hard wearing qualities and range of styles make it perfect for any room in the house.
Most suppliers provide hardwood flooring in Ash, Beech, Cherry, Hevea, Jatoba, Kempas, Maple, Merbau, Oak, Red Oak and Walnut, allowing you to create the ambience and mood to suit the design qualities of your home.
Regular care of your wood floor is simple and practical, and involves merely vacuuming and wiping your hardwood floor with a damp cloth. It helps to attach felt pads to the bottom of furniture, and bear in mind that any spilt liquid should immediately be dried of from hardwood floors.
Add the warmth and beauty of ready-to-install hardwood to almost any room in the house. Engineered Hardwood floors can be installed below grade in basements and on concrete. Hand-sculpted and exotics available.
Enjoy the luxury of solid hardwood with ready-to-install selections of beautiful wood flooring in a wide variety of domestic and exotic species. A hand-sculpted type may also available. Select from a broad palette of species and grades. Choose from traditional domestic species or exotic foreign hardwoods. Finish it with your choice of stain and sealants.
Inviting, familiar, and stable. Your home will be your refuge, your castle! By all means, make it beautiful, starting with the floors.
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Hardwood Floor Installations and How They Delight Buyers and owner}
White House press center evacuated after bomb scare
Posted in Uncategorized on 02/19/2020 02:19 am by
Monday, June 18, 2007
A press room across the street of the White House was evacuated after a bomb sniffing dog had a reaction to a van it was searching. The van was believed to be a transport vehicle for Israeli Prime Minster Ehud Olmert, but some reports also say that it is not known to whom the van belongs.
The evacuated space is where the press gathers before they enter the Press Briefing Room in the West Wing of the White House. It is around the corner from Blair House.
“Police were called, they are on the scene currently attempting to clear the vehicle. The vehicle is part of the delegation that is staying at the Blair House,” said Darrin Blackford, a spokesman for the Secret Service.
Police searched the van using a robot and blocked off streets around the area to vehicle traffic, but at 4:30 p.m. (eastern time), authorities gave the “all-clear” for personnel to be allowed back into the building.
The “suspicious” van was parked in front of Lafayette Park. Other areas near the White House were also evacuated including Pennsylvania Avenue, on which the White House is located, and the Jackson Square Press Center, because “of an abundance of caution.”
Olmert is currently a guest in the Blair House which is located across the street from the White House. Olmert is expected to meet with United States President George W. Bush to discuss the Palestinian government and other issues. It is not known if Olmert was inside the house at the time of the incident.
It is not known why the dog reacted to the van, but nothing was found inside it after the Secret Service searched it.
British computer scientist’s new “nullity” idea provokes reaction from mathematicians
Posted in Uncategorized on 02/18/2020 03:05 am by
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.”.