#### Special Honeymoon Transport With Car Service In Dc}

##### August 21, 2017

Special Honeymoon Transport with Car Service in DC

by

MARK JONSH

Your honeymoon trip should be out of the ordinary. It should be exempt from the stress typical to travel, and with car service in DC, you can avoid many transportation related stressors while enjoying the freedom to begin and end your honeymoon with a ride focused on romance.

Erasing and Preventing Stress

Cab service and rentals are often used when catching a plane, but they dont reduce stress, nor do they enhance the experience in the way that a honeymoon deserves. No guarantee of service exists, and driving rather than focusing on your new spouse can get in the way of romance. They simply arent ideal for honeymoon transportation. However, DC car service near me can improve the ride, making the special nature of the trip apparent.

Our company provides a collection of machines that consists of an array of vehicles. Even though all are newer, youll find a plethora of styles and rider capacities. Flamboyance and sophistication all find the answers within our fleet, and we can accommodate the entire family even when its absurdly large. From luxurious limousines, hummers, minibuses, to charters or DC Car service, our fleet is widely varied but standardly high quality. We have full licensure, bonds, and insurance coverage, so ride absent stress. Youll find that mechanical ability is high, and appearance is immaculate. Because all of our machines are worthy of your plans, dont stress about the booking. You can rest assured that your in-laws will be thrilled by the ride and your consideration.

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Concern about punctuality is an obvious joy stealer, which has no role on your wedding day. Escape to your honeymoon should be as carefree as newly joined couples deserve. DC sedan service offers high quality transportation with an emphasis on punctuality. We aim to please our riders, and we realize that the most effective way to achieve this goal is to transport parties quickly and safely. Our drivers have proven abilities, area knowledge, and clear commitment. We check every driver for background problems and substance abuse issues in addition to thorough training and evaluations. We also provide dependable and high-quality vehicles for service from a fleet that is fully insured and ready for your transportation needs.

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Being aware of support available at the touch of a dial goes far to alleviate stress as well. Your accommodation requests, problems, and feedback will all be taken care of quickly when you call our 24-hour customer service center. We intend to personalize each and every ride because we realize that is how to fully satisfy riders. Book Washington sedan service to enjoy a romantic, distraction free ride to your honeymoon that allows for punctual and customized transport.

Securing a remarkable honeymoon ride worthy of the occasion will remove stress and heighten the experience. Opting for professional transportation allows you to fully enjoy a romantic ride that is stress-free and appropriate. Booking this ride is as easy as an Internet reservation and a few moments of communication to customize the experience. From that point, rely on our straightforward chauffeured service in a high quality ride to fully meet your needs as you getaway and begin your marriage in a suitable fashion.

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#### Hydrogen fuel cell cars promoted in various states, but U.S. federal funding cut

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Hydrogen fuel cell cars promoted in various states, but U.S. federal funding cut
##### August 21, 2017

Tuesday, June 2, 2009

American Secretary of Energy Steven Chu is cutting US$100 million dollars from hydrogen fuel cell vehicle research and diverting the remaining$69 million to hydrogen fuel cell research for household current.

#### NASCAR: Edwards wins 2010 Ford 400; Johnson claims championship

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NASCAR: Edwards wins 2010 Ford 400; Johnson claims championship
##### August 21, 2017

Monday, November 22, 2010 Roush Fenway Racing driver Carl Edwards won the NASCAR Sprint Cup Series 2010 Ford 400 held yesterday at Homestead Miami Speedway in Homestead, Florida. Jimmie Johnson claimed the championship after finishing second — his fifth championship in a row. Throughout the course of the race there were 10 cautions and 25 lead changes among 9 different drivers.

Afterward, Edwards commented, “To finish like this is unreal. It’s just these guys didn’t give up. It’s just a great way to end the season.”

Kevin Harvick came in third for Richard Childress Racing, and Aric Almirola finished fourth, after starting 24th. Almirola’s teammate A. J. Allmendinger finished 5th in front of Kasey Kahne. Ryan Newman and Tony Stewart finished behind Kahne in 7th and 8th. Matt Kenseth, and Greg Biffle rounded out the top ten finishers in the race.

In the Drivers’ championship, Johnson claimed his fifth consecutive championship, after being in second prior to the race. Denny Hamlin followed, 39 behind Johnson, and three ahead of Harvick in third. Edwards was scored fourth, Kenseth took fifth , Biffle was sixth, and Stewart was seventh, after finishing eighth. Jeff Gordon and Clint Bowyer was ninth and tenth.

Showing his excitement, Johnson said, “I can’t believe this! It’s unbelievable. You guys are the best. I can’t thank you enough,” on his radio. Chevrolet won the Maunfacturers’ championship with 261 points, while Toyota followed with 217.

Afterward, Johnson’s crew chief, Chad Knaus commented, “I think finally, finally after pulling this off Jimmie will get the respect that he deserves. Knowing what we had to do — come down here and beat them — and we beat them.”

“I’m disappointed,” Hamlin said afterward. “Our car was lightning fast until that last wreck. When we hit the 16 (Biffle) that knocked the toe-in out. It wasn’t as fast after that. It’s just circumstances but we had a great year. We won the most races (8) and we contended like we have never contended before but circumstances took us out of this one. I don’t think the 48 (Johnson) showed the strength this year like they did in the past and that opened the door for the rest of us.”

Next, third place finisher, Harvick commented, “We went down swinging and that is what we came here to do. Those guys outran us on that last restart there. All in all I’m proud of all my guys. We did everything we wanted to do today but win the race. This is a great spot to start building for consistent championship runs next year. We had a top three car but they got by us on the restarts. All in all, it was a good day. What can you do?”

#### Affiliate Marketing For Small Businesses}

##### August 16, 2017

Submitted by: Anthony McBride

Affiliate marketing is an internet marketing technique used to bring more visitors to your website. Small businesses and blogs can use affiliate marketing to generate income while driving traffic to partner websites. Chances are that youve already participated in this system if youve visited a website and followed a link that appealed to you.

Affiliate marketing can be a confusing subject because there are many misleading claims about how much money youll make if you participate. While it is a real way to make money from your blog or website, it isnt a magic ticket. It takes significant work and maintenance in order to see financial gain from affiliate marketing programs. But, understanding how it works is a key factor if you want to improve your success online.

What is Affiliate Marketing

Affiliate marketing relies on a series of links on different websites and blogs to drive traffic and sales. Here is how it basically works- You post affiliate links, links to partner websites, on your blog or website. When people visit your site, they sometimes click on those links and visit the websites of your partners. When this happens, you get rewarded by those partners according to your agreement with them.

Affiliate marketing programs work differently, but most give you a small percentage of sales generated by visitors that you send their way. A small percentage of affiliate marketing programs still use the pay per click model, where rewards are calculated off how many people you refer. Either way, the more visitors you get and refer, the more youll make from those referrals.

Is Affiliate Marketing for You?

Affiliate marketing can boost your revenue and increase traffic to your website, but its not a magic ticket to online success. There are several things to consider before signing up with any program. Looking at how they compensate is an important factor in helping you determine if it is worth your time. Though the percent you get back from referrals is small, it can add up if your site gets lots of traffic.

Affiliate marketing is a great way to make money from your online presence. But, be sure that you are aware of the terms of the program before you make any commitment. And, no matter what you do, make sure that your partner sites reflect your ethics and values. Keeping these things in mind can help you turn your average website or blog into a money making gem!

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is dedicated to helping you get the most out of life. Based in the belief that you can change your life through knowledge,

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Source:

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#### Woman killed in house fire in South Yorkshire, England

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Woman killed in house fire in South Yorkshire, England
##### August 16, 2017

Monday, January 25, 2010

An elderly woman has died in a house fire in South Yorkshire, England. The woman, who is currently remaining unidentified, was blind and 93-years-old when her bungalow in Sheffield caught fire as a result of an accident in her kitchen yesterday afternoon.

An internal investigation into the fire has suggested that while the woman was cooking, she dropped a towel onto one of the stovetops while attempting to move a pan on the cooker. The towel then set alight. When she attempted to put out the fire, the towel dropped to the side of the cooker, alongside some plastic bags.

A smoke alarm sounded; a nearby resident heard the alarm and went to assist. The neighbour managed to break into the bedroom window of the bungalow in order to be able to get inside the building. The person made it to the hallway but had to double back upon seeing the fire and the smoke. It is believed that the woman was overwhelmed by the fumes given out from the plastic which was burning.

At around 1350 GMT, fire service workers entered the elderly lady’s residence to find her collapsed inside the kitchen. People investigating the incident have come to the conclusion that this particular fire was an accidental one. A spokesperson for the South Yorkshire Fire and Rescue Service noted: “Neighbours who tried to enter the property were fought back by smoke and flames.”

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#### Suspected serial killer appears in British court

">
Suspected serial killer appears in British court
##### August 16, 2017

Friday, May 28, 2010

A man accused of being a serial killer has appeared in Bradford magistrates court in West Yorkshire today charged with three counts of murder. 40-year-old Stephen Griffiths is accused of killing Suzanne Blamires, 36, Susan Rushworth, 43, and Shelley Armitage, 31, all prostitutes.

Griffiths, a former van driver with a degree in psychology and studying for a PhD in criminology, gave his name as “Crossbow Cannibal” when asked. He has been in police custody since Monday when police were alerted to a CCTV recording that appeared to show a murder.

A caretaker had been reviewing footage from the flats where Griffiths lives when he saw footage of a woman and a man enter a flat early on Saturday morning. Two minutes later, she ran out and was followed by the man, who beat her to the ground and shot her in the head with a crossbow. Over the course of the weekend, the man was seen several times with bin bags and a rucksack.

On Tuesday, the day after the arrest of Griffiths, Blamires’ remains were found in the River Aire in nearby Shipley. She had been cut into several pieces and her head was located in a rucksack. Police continue to search for the other two alleged victims; Rushworth has been missing since June last year and Armitage vanished in April.

Police have searched much of Bradford’s red-light district, where Griffiths’ third-floor flat is located. Forensic investigations at the flat are expected to last around three weeks. There are plans to search landfill sites for bodies, and police may yet expand the inquiry to cover three more cold cases, although at present they have not been linked to the current inquiry.

Sniffer dogs have been used throughout the city, and police have been taking away plastic evidence bags. Some alleyways remain closed off. Police charged their suspect yesterday.

Griffiths was known as “the lizard man” in his block of flats owing to his habit of walking his two pet monitor lizards in the area. One neighbour is reported to have quoted him as saying he was studying for “a PhD in murder and Jack the Ripper,” and he has spent time in a high-security psychiatric hospital. During his five-minute court appearance he did not enter a plea, kept his head bowed and fidgeted with his cuffed hands. He said “Here, I guess,” when asked for his address.

As he stood in the glass-fronted dock, guarded by three security officers, he was watched by the families of Rushworth and Armitage, who were accompanied by police family liaison officers. Blamires’ family chose not to be present, but the victim’s mother Nicky Blamires, 54, has told the press that Suzanne was a “much-loved” family member even though she “went down the wrong path and did not have the life she was meant to have.” “Nobody deserves this,” she said. “All these girls were human beings and people’s daughters.”

Griffiths’ morning court appearance was followed by a second one this afternoon, at Bradford Crown Court. This time, he confirmed his name without incident. He was remanded into custody until next month, when he will appear in court again.

British media has been quick to compare the case to Peter Sutcliffe, dubbed the “Yorkshire Ripper”. Sutcliffe was a Bradford killer responsible for thirteen murders and seven attempted murders, including several prostitutes. Since his 1981 conviction he has spent most of the last three decades in Broadmoor high-security psychiatric hospital near London.

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#### Ancient Strip Dancing And Its Modern Version}

##### August 14, 2017

Ancient strip dancing and its modern version

by

The ancient form of exotic dancing or erotic dancing was meant for the satisfaction of the gods. Erotic dancing originated thousands of years ago, it was seen even the Egyptian civilization. The priestesses of the temples used to act as the goddesses they were praying for and danced naked. The priests of the temples slept with those priestesses and considered it as sleeping with the goddess. Erotic dancing is still practiced nowadays, but in a different way and having a different purpose. The modern version of erotic dancing started in the strip clubs during the early 20th century. The modern erotic dancing was considered as a matter of perversion at that time. Only the men of the lower class of the society used to visit the strip clubs to watch the naked girls dancing. However, common people started accepting strip dancing gradually and nowadays it is practiced in several countries all over the world and often considered as the best form of entertainment. When a person wants to hang out with friends or with his partner he heads for the strip club or gentlemens club to spend the evening. Strip dancing has become popular all over the world and men and women of various age groups visit the strip clubs.

The increasing popularity of strip dancing has also led several women to take it as a profession. Thousands of strip clubs have grown up all over the world and millions of people visit these clubs to watch the seductive dance performance of the erotic dancers every night. The well-known strip clubs recruit new strip dancers every year and they organize strip dancing competition to get new faces. The increasing popularity of strip dancing has created job opportunities for numerous young women. Young women from different family and job backgrounds are trying their luck in strip dancing. If you want to work as an exotic dancer in any well-known strip club, you should gather all the necessary information and participate in the exotic dancer competition arranged by the strip dance clubs. You can get the necessary information about the strip dance competition in any online adult community over the internet. Every strip dancers wants to get a job in any of the best strip clubs as these clubs pay quite well.

Winning the exotic dancer competition arranged by the best strip clubs is not quite easy as thousands of girls and young women from all over United States participate in these competitions and the participants must have several qualities to satisfy the judges. The best erotic dancers are chosen by the judges and placed in the famous strip clubs of the metropolitan cities. Learning the dance steps of strip dancing and presenting them in front of the judges during audition is very important. Several clubs provide lessons on strip dancing and taking these classes is very important to make mark in the exotic dancer competition. Strip dancing gained its popularity in the past few years and mass media should be thanked as it was because of them that erotic dancing became such popular worldwide.

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Ancient strip dancing and its modern version }

#### Billy West, voice of Ren and Stimpy, Futurama, on the rough start that shaped his life

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Billy West, voice of Ren and Stimpy, Futurama, on the rough start that shaped his life
##### August 14, 2017
 This article mentions the Wikimedia Foundation, one of its projects, or people related to it. Wikinews is a project of the Wikimedia Foundation.

Wednesday, February 13, 2008

Ren and Stimpy. Bugs Bunny. Philip J. Fry and Professor Hubert Farnsworth on Futurama. Sparx. Bi-Polar Bear. Popeye the Sailor Man. Woody Woodpecker. You may not think you have ever heard Billy West, but chances are on a television program, a movie, a commercial, or as Howard Stern’s voice guru in the 1990’s, you have heard him. West’s talent for creating personalities by twisting his voice has made him one of a handful of voice actors—Hank Azaria and the late Mel Blanc come to mind—who have achieved celebrity for their talent. Indeed, West is one of the few voice actors who can impersonate Blanc in his prime, including characterizations of Bugs Bunny, Daffy Duck, Elmer Fudd and other characters from Warner Bros. cartoons.

What is the fulcrum in Mr. West’s life that led him to realize a talent to shape personalities with his voice, and how did the discovery of that gift shape him? Wikinews reporter David Shankbone found that like many great comedians, West faced more sour early in life than he did sweet. The sour came from a physically and emotionally abusive alcoholic father (“I could tell you the kind of night I was going to have from the sound of the key in the door or the way the car pulled up.”), to his own problems with drug and alcohol use (“There is a point that you can reach in your life where you don’t want to live, but you haven’t made the decision to die.”).

 I’m telling you stuff that I never said to anybody…

If sin, suffering and redemption feel like the stages of an endless cycle of American existence, West’s own redemption from his brutalized childhood is what helped shape his gift. He performed little bits to cheer up his cowed mother, ravaged by the fact she could not stop her husband’s abuse of young West. “I was the whipping boy and she would just be reduced to tears a lot of times, and I would come in and say stuff, and I would put out little bits just to pull her out of it.”

But West has also enjoyed the sweet. His career blossomed as his talent for creating entire histories behind fictional characters and creatures simply by exploring nuance in his voice landed him at the top of his craft. You may never again be able to forget that behind the voice of your favorite character, there is often an extraordinary life.

Below is David Shankbone’s interview with renowned voice actor Billy West, who for the first time publicly talks about the horrors he faced in his childhood; his misguided search for answers in anger, drugs and alcohol; and the peace he has achieved as one of America’s most recognizable voice actors.

## Contents

• 1 The use of celebrities for voiceovers
• 2 Iconic characters and choosing projects
• 3 Discovering his talent
• 4 “It was a horror chamber where I grew up”
• 5 West moves to Boston after his parents divorce
• 6 How West dealt with his father’s abuse
• 7 Rehabilitation and sobriety
• 9 West on his career
• 10 West on politics
• 11 Billy West on modern American society
• 12 Billy West on telling it like it is
• 13 Source

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#### British computer scientist’s new “nullity” idea provokes reaction from mathematicians

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British computer scientist’s new “nullity” idea provokes reaction from mathematicians
##### August 14, 2017

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 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.”

• “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.”.

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