# Talk:British computer scientist's new "nullity" idea provokes reaction from mathematicians

## Original reporting

I have a further communication from Mark C. Chu-Carroll that has yet to be used. I also have a communication from a Professor of Mathematics at the University of Warwick, which I have asked for permission to quote from. I have also requested comments from various other people. Jonathan de Boyne Pollard 02:05, 9 December 2006 (UTC)

There is a reader comment below the BBC news story that purports to have been written by Dr Roy Johnstone, lecturer in the Mathematics department at the University of Reading. It should not be used unless authenticated. I have sent electronic mail to Dr Johnstone, asking whether he did in fact write that comment, but have not yet received any reply. Jonathan de Boyne Pollard 02:35, 9 December 2006 (UTC)

## Mathematical analysis

I'm not sure exactly what it is that commentators have said, but the explanation that 0/x and x/0 have different left/right hand limits is sloppy at best. A more correct summary is that the limit as (x,y)->(0,0) of x/y depends on the angle of approach. 75.6.254.27 12:06, 10 December 2006 (UTC) JB

• I suggest that you read the cited sources and find out what the commentators have said, then. If what they have said is wrong, your argument is with them, not with Wikinews. Your only argument with Wikinews is if this article misrepresents their commentary. Jonathan de Boyne Pollard 12:31, 10 December 2006 (UTC)

The page claims the system is inconsistant. As per the discussion on the Wikipedia talk page, this does not appear to be the case. Rather, the system has changed enough rules from regular algebra to make trivial disproofs invalid. 129.44.17.11 04:50, 12 December 2006 (UTC)

• The commentators claimed that the system is inconsistent. The story is reporting this. Wikinews is a news service. Jonathan de Boyne Pollard 11:17, 13 December 2006 (UTC)

There are three further things that I'd like to add to the piece:

• a BBC Berkshire journalist's reaction to criticism and his defence of the BBC's choice to run the original BBC story.
• a backgrounder on the "Perspex machine", which Anderson appears to have been hawking around (with no takers) for over 4 years, now, in an infobox
• the reaction from the University of Reading Department of Mathematics, to flesh out the section on the university's reputation

However, this is a news service, not an encyclopaedia. We cannot afford to wait indefinitely before publication. Therefore I'm setting a deadline of 16:00 UTC today, at which point I'm going to submit the story to "ready" status. I don't have the time to do the necessary legwork to research the history of Anderson writing about the "Perspex machine" in depth. (Anyone else willing to collaborate by doing the backgrounder, please feel free.) I've contacted the Mathematics department, and I really want to include its opinion on Anderson's work, as a counterpoint in the section on Reading's reputation. But I'm simply getting no responses to my enquiries. I think that I can write up the BBC's defence by that deadline. Jonathan de Boyne Pollard 11:22, 11 December 2006 (UTC)

I've just written to Dr Roy Johnstone, of the University of Reading's Department of Mathematics, again, stressing that I really need confirmation that it really was him that wrote the comment signed with his name on the BBC's web site, and asking for any further comment from the Department of Mathematics because without any comment the Computer Science department is the representative to the world of mathematics at the university, as exemplified by this Reading University press release from this morning.

Perhaps some explanation is in order, as Nyarlathotep appears to be confused.

I've employed a pretty strict policy on what I've selected from web logs here. There are two sets of quotations used, those that specifically analyse the issue and those that merely exemplify the reactions. For the analyses, I've been strict about only selecting postings where, by following hyperlinks from pseudonyms, I've been able to track down people's real names and their (claimed) credentials. (I've cited the curricula vitae used.) I've been less strict about the quotations that simply exemplify reactions, such as the quotations that show the views about the university's reputation, since they are used merely to represent the opinions that people hold in their own words. In contrast, you'll note that the only views about Anderson, specifically, that are quoted are attributed to named people.

Unfortunately, the BBC's web site doesn't provide handy hyperlink-to-the-author features on its postings. (Notice that none of the analyses are sourced from comments on the BBC web site.) So the only way to know that Dr Roy Johnstone wrote what is attributed to him there (rather than someone else just using his name) is to ask him for confirmation that he wrote it. Jonathan de Boyne Pollard 12:32, 11 December 2006 (UTC)

## 'Proof' is not a proof of anything

Although the article correctly explains that Anderson's 'proof' is in fact not a proof that one can divide by zero, it incorrectly claims that it 'proves' that 0^0 = 0/0. In fact, it is not a proof at all. The line 0/1 * 1/0 = 0/0 is meaningless since even in Anderson's 'new system of numbers' 1/0 is undefined. 130.126.108.68 21:06, 15 December 2006 (UTC)

Thank you for the very entertaining article and enjoy. 130.126.108.67 2006-12-13 00:36:22

• the second infobox title and first sentence uses the wor 'proof' without any qualification, while noting later that the 'proof' is in fact, not one. i think the title and lead sentence shld be modified to reflect the "proof"'s status. one not-so-good (which is why i didn't do it already) way is using scare quotes. perhaps some rephrasing will help?  — Doldrums(talk) 04:36, 13 December 2006 (UTC)
• If you look at the second cited source by Ollie Williams, you'll see that Williams describes it as a proof. I did think of a minor clarification yesterday, but hesitated about adding it. You've persuaded me to do so. Jonathan de Boyne Pollard 11:06, 13 December 2006 (UTC)

1/0 is still undefined, even if 0/0 is defined. Of course if 1/0 is defined then 0/0 is because '0*1/0 = 0/0', assuming the system isn't too broken. I took about five minutes to prove to myself that in fact all numbers in this system degenerate into zero, which you can easily verify from the axioms. This is precisely why division by zero is not allowed in general, because it only even begins to make sense in the ring with a single element: {0}. [To see this, consider 0*a = 0 for all a in our system, which is easily provable from say the ring axioms for a ring, such as the integers, or from the field axioms of the reals, or of any field. Then if we can divide by zero we have that a=0/0 for all a in the system, so all numbers are equal to 0/0. Since we already have zero, it must be the case that 0/0=0, as well as every other number in the system.]

So, the 'proof' does nothing but say that 0*0 = 0 repeatedly, and it uses many assumptions that are not initially justified, such as the existence of 1/0. Calling it a proof of anything is ludicrous. 130.126.108.68 21:06, 15 December 2006 (UTC)

• The article points out in a sidebar that many people's mathematical analyses of Anderson's system are fallacious. Several commentators on the various web logs pointed out that a lot of people criticizing Anderson have got their own mathematics wrong.

Ironically, the above is a prime example of such a completely fallacious analysis by someone who has their own mathematics wrong. It conflates the real numbers with the transreal numbers when in fact they are based upon quite different axioms; it assumes that the transreal numbers are a field, when (as this article points out twice) they are not; and it substitutes the wrong value when cancelling zero with its reciprocal when dividing both sides of ${\displaystyle a\times 0=0}$ by zero. If anything is in fact "ludicrous", it is the above.

In the field ${\displaystyle \mathbb {R} ,{\frac {1}{0}}}$ is undefined. But in Anderson's transreal arithmetic, where Anderson's given proof applies, ${\displaystyle {\frac {1}{0}}=\infty }$ is well defined and is a simple consequence of axioms #14, #17, and #20. Similarly, dividing both sides of ${\displaystyle a\times 0=0}$ by zero yields ${\displaystyle {\frac {a\times 0}{0}}={\frac {0}{0}}}$ which by axioms #16, #17 and #20 becomes ${\displaystyle a\times 0\times 0^{-1}=\Phi }$, ${\displaystyle a\times 0\times \infty =\Phi }$, and hence ${\displaystyle a\times \Phi =\Phi }$ (which is axiom #15, incidentally). And the theorem that ${\displaystyle \forall x\neq -\infty :{\frac {0}{x}}\times {\frac {x}{0}}=0\times x^{-1}\times x\times 0^{-1}=0\times 1\times 0^{-1}=0\times 0^{-1}={\frac {0}{0}}}$ is in fact a straightforward application of axioms #14, #17, and #18.

Fortunately, I worked hard, and took more than 130.126.108.68's "five minutes", on the analyses in this article that aren't sourced to a third party, so that they don't contain fallacies such as 130.126.108.68's. Jonathan de Boyne Pollard 10:42, 17 December 2006 (UTC)

## Good work

Enjoyable read. Bawolff 01:52, 13 December 2006 (UTC)

• second that. has this been on lead yet?  — Doldrums(talk) 04:19, 13 December 2006 (UTC)
• Not to my knowledge. Jonathan de Boyne Pollard 11:01, 13 December 2006 (UTC)
• is this synopsis ok: "Reading university teacher Dr. James Anderson's claim that he has devised a number system that handles the "divide by zero" problem has been challenged by academics and bloggers, who have also criticised the BBC for its reporting on the claim." ?

any ideas for what image to be used on the lead?  — Doldrums(talk) 11:10, 13 December 2006 (UTC)

• That synopsis seems all right to me. It doesn't take sides. As for an image, I don't have any. We cannot use any of the BBC images, as that would not be fair use, and those are the only images that exist. I suggest putting ${\displaystyle 0^{0}={\frac {0}{0}}=\Phi }$ where you would normally have an image. Jonathan de Boyne Pollard 11:27, 13 December 2006 (UTC)
! and a laugh... really laughing now after reading more closely! :}
Second the motion. Someone really did some work and it shows. My compliments for making a rather abstract feeling mathematical story quite readable! 68.39.174.238 21:53, 17 December 2006 (UTC)

## Quotes

Well, to be honest, when I got to the quote about the "idiot math teacher" I had to wonder if this article is about a crank, or if the crank was the one being quoted, because the phrase "idiot math teacher" sounds so much like the juvenile spouting-off one can hardly avoid in forums and blogs all over the net. No offense intended, but I think this kind of thing detracts from the credibility of the article.

• It only does so if one cannot tell the difference between an article itself saying that someone is an "idiot math teacher" and an article reporting Mark C. Chu-Carroll writing that someone is "idiot math teacher". Quotation marks indicate reported speech, you know. Jonathan de Boyne Pollard 21:05, 13 December 2006 (UTC)

Calling someone an idiot is an exersize in juvenile bad behavior, and in my personal opinion the fact that the article quotes extensively from this man, who later is quoted as calling reporters "innumerative idiots," gives the opening passages of the article a rather tabloid flavor. This is compounded by later passages quoting "readers" who say, among other things, that the lecturers at the University of Reading should "stick to folk dancing and knitting." My apologies if I'm out of line, but when I clicked on the link for Wikinews I did not expect "Chuck Norris Facts."

• You are out of line. This is not "tabloid flavour". This is balance, in accordance with the Wikinews:Neutral point of view. To report only the mathematical analyses would have been to ignore by far the largest group of responses, and to not properly report the actual discussions that occured, which, as the article says, quoting examples, included all of humour, criticism, insults, and defence. Jonathan de Boyne Pollard 13:30, 15 December 2006 (UTC)

## Proof commentary

It is not even a proof that ${\displaystyle 0^{0}=\Phi }$. To justify the equation ${\displaystyle 0^{0}=0^{1-1}=0^{1}\times 0^{-1}}$ in his system you need first to DEFINE ${\displaystyle 0^{0}=\Phi }$ so that what it states is that ${\displaystyle \Phi =0\times \infty }$. His other proof that ${\displaystyle 0^{0}=\Phi }$ again is not a proof for the same reason.

I removed the above from the commentary on the proof because, like so much of the commentary that there has been, it is wrong. The first two lines of Anderson's proof are, as far as I can tell, in accordance with Anderson's axioms, and don't require ${\displaystyle 0^{0}}$ to be defined. ${\displaystyle 1-1=0}$, required for the first equation, is a straightforward deduction from one of the transreal number axioms, for example. Jonathan de Boyne Pollard 20:05, 15 December 2006 (UTC) Why is the equation ${\displaystyle 0^{1-1}=0^{1}\times 0^{-1}}$ a consequence of Anderson's axioms? Can anyone please supply a proof?

I don't know another place to mention this thought, but if i is interval, i:-1->1 !< i: x->(x+2) -> = !0 >= 0 theoretically. Also i feel you can't explain 0, using negative numbers, since without a definition of 0 (smallest unmeasurable amount) you will never be sure of the distance between 1 and it's theoretical negative counterpart.That is because 0 is a filosofical nr. x=0 x=1-1 not (some)0/0=0/0. although with positive numbers they are i think.80.57.243.100 09:48, 24 December 2006 (UTC)

## Similar theory?

The nullity idea is incomplete. It seems a, primitive, reinvention of wikipedia: Non_standard_analysis. Or, possibly an attempt an providing a finite encoding of one manifestation of NSA's infinitesimal.

## Typo

{{editprotected}}
'humourous' => 'humorous' ('humourous' is always incorrect, even in British English) Van der Hoorn (talk) 14:03, 26 February 2009 (UTC)

DoneGopher65talk 21:29, 12 March 2009 (UTC)

Mark Chu Carroll is a fool who knows nothing about anything.