Is Zero Divided by Zero Really Solved After 1200 Years?

[neutrino]

...or so says Dr.James Anderson from the University of Reading. The school students to whom this was shown feel "cool" to have understood 'nullity' - the result of dividing zero by zero - for the first time in 1200 years.

http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml

There's a video where the Dr.Anderson demonstrates this, but I'm not able to view it at the moment.

Decide for yourself. :tongue2:

 

[dontdisturbmycircles]

Holy crap, screw L'Hospital's rule, this limit approaches nullity!


I will be tempted to use this new theorem on my next exam.

 

[dontdisturbmycircles]

I like UK Anonymous's answer, I think I will put it in my signature.

 

[kesh]

this isn't mathematics, it's just error detection

 

[Rach3]

If your heart pacemaker divides by zero, you're dead."

Wonder who programmed in that feature...

 

[Rach3]

http://www.cs.reading.ac.uk/people/J.Anderson.htm

From his official webpage, he links to his personal webpage, where he links to his , err, "original research":

Two papers have been released. The first paper, Perspex Machine VIII: Axioms of Transreal Arithmetic describes how to divide by zero consistently in a non-trivial way. This shows that division by zero is no longer an error. Amongst other things, the paper explains why the standard model of arithmetic is not valid. The second paper, Perspex Machine IX: Transreal Analysis explains how to extend calculus so that it works with transreal numbers. This paper disposes of various counter "proofs" that attempt to show that division by zero is impossible. The paper ends with a very simple equation demonstrating the possibility of division by zero and challenges the reader to accept it.

http://www.bookofparagon.com/News/News_00012.htm

Typical crackpottery. This "Reading University" must be some dirthole indeed, to be hiring loons like this.

 

[neutrino]

If you're really bored, you could while away time by counting the number of times he's used the word 'Arithmetic(s)' in his first paper.

 

[kesh]

This "Reading University" must be some dirthole indeed, to be hiring loons like this.

though it's not a top class institution it's by no means a dirthole either. very hard to sack academics in the uk when they go bonkers though

 

[Rach3]

though it's not a top class institution it's by no means a dirthole either. very hard to sack academics in the uk when they go bonkers though

I'm not familiar with any research there, the only thing I've heard about this Reading is this crackpot guy. Certainly they have an image problem now.

 

[kesh]

judging from a quick glance at one of the papers, he's just put a symbol to the notion of undefined

 

[kesh]

reading's computer science department got a 4 in the independent, uk wide, research assessment exercise 2001 (the most recent). the scale runs 1, 2, 3b, 3a, 4, 5, 5*; 5* being the highest.

his research group specialises in fault tolerance, and as i suggested above, i think he's just mathematically formalised division by zero errors, then presented it as some new mathematical discovery

i wonder if he knows about non-standard analysis

 

[Hurkyl]

Division by zero is undefined in nonstandard analysis too.

 

[kesh]

Division by zero is undefined in nonstandard analysis too.

sure, but i wonder if he's rediscovering division by infinitesimals, his strange historical reference an'all

 

[Kurdt]

"Imagine you're landing on an aeroplane and the automatic pilot's working,"

The chances of me landing on an aeroplane are as close to nullity as you can get.

 

[FrogPad]

"...heart pace maker divides by zero, you're dead..."

:rofl:

 

[Anttech]

I thought this comment was particularly funny:

If the airplane divides by zero, my pacemaker crashes :-) or, the pilot has to deal with "we are nullity meters from the ground. Press any key to crash now, or wait for nullity minutes for an auto-crash" How I wish my bank divided my $1 balance by zero and told me that I have infinite money ;-)

:rofl:

 

[radou]

'...proclaims Dr Anderson having demonstrated his solution on a whiteboard at Highdown School, in Emmer Green.'

:tongue2:

 

[Alkatran]

BREAKING NEWS: Professor comes up with new word for "indeterminate"!

Ridiculous. How can people get away with news stories like this? Also hilarious: he defined 1/0 to be infinity and -1/0 to be -infinity. No word on 1/-0 though! It's like that monthly division by 0 post, but on an international scale.

 

[neutrino]

Don't forget the symbol! :P

 

[0rthodontist]

There's something (well, more than 1 thing) amusing in the PDF he has for that. One of his axioms in there is that $$0^{-1} = \infty$$. I wonder what distinction he makes between 1/0 and 0^-1.

 

[mattmns]

LMAO! That is one of the funniest things I have ever read, especially the comments about it :rofl:

 

[dontdisturbmycircles]

This guy must be starting to feel pretty dumb (Although if he has a phd he can't be that dumb can he??). I think he made a post on that site in the comments just recently, but who knows if its him.

 

[kesh]

we should email him for an explanation

j.anderson@reading.ac.uk

the important things to ask are is his arithmetic internally consistent? maybe

is it new? i highly doubt it

 

[Rach3]

the important things to ask are is his arithmetic internally consistent? maybe

is it new? i highly doubt it

It's obviously inconsistent. The problems are elementary, things like (-1)(1/0) = 1/(-0) = 1/0 and such, ugly stuff. It's not new either, we get lots of junk threads in the PF math forums, about 1/0, 0/0, infinity^(-0), etc.

There are good reasons why the real algebra is the way it is.

 

[kesh]

It's obviously inconsistent. The problems are elementary, things like (-1)(1/0) = 1/(-0) = 1/0 and such, ugly stuff. It's not new either, we get lots of junk threads in the PF math forums, about 1/0, 0/0, infinity^(-0), etc.

There are good reasons why the real algebra is the way it is.

but I'm not sure he's claiming it's a field. okay I've not actually read his paper, I'm just giving him the benefit of the doubt on this and my hunch is he's talking about the extended reals or the real projective line, plus some 'point' for undefined he calls nullity

ie nothing new

wikipedia has labelled anderson's nullity as nothing more than a neologism and wikipedia is always right

 

[AKG]

His axioms are consistent, he's used a computer to check it. The question is whether his new system is useful or interesting. Defining i such that i² = -1 could be considered just a neologism, in fact we don't really need the symbol i, we could just talk about the set of ordered pairs of real numbers, with addition and multiplication defined in such a way as to mimic the addition and multiplication of the complex numbers. Whether we use the symbol i or not, the thing we get is an algebraically closed field. Now the transreals aren't even a field, but maybe they're useful or interesting in some other way. Whether they are or not, I can't tell. What I don't like is how in his second paper, he's supposed to be extending real analysis to the transreals, but instead of doing things like defining a topology, a metric, limits, etc. pretty much all he does is extend the definition of functions like exp, log, sin, etc. to the three strictly transreal numbers, and then talk more about transreal arithmetic.

 

[DaveC426913]

http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml

There's a video where the Dr.Anderson demonstrates this, but I'm not able to view it at the moment.

Any links to the lecture in a format I can view without exposing my computer to RealRape?

 

[AKG]

There's no lecture really. All he does is define $\infty = \frac{1}{0},\ -\infty = \frac{-1}{0},\ \Phi = \frac{0}{0}$, then "solves" the "problem" of what 0⁰ is as follows:

0⁰
= 0^1+(-1)
= 0¹ x 0^-1
= 0 x 0^-1
= $\left (\frac{0}{1}\right ) \times \left (\frac{1}{0} \right )$
= $\frac{0 \times 1}{1 \times 0}$
= $\frac{0}{0}$
= $\Phi$

 

[moose]

He's WRONG!
It is actually "DIVIDE BY 0" (according to my Ti-83) which is equal to undefined (according to my Ti-89) which equals "Result of function is undefined." (according to windows xp calculator)

Geez, what kind of moron doesn't even check his work on a calculator before having it published

 

[Hurkyl]

What I don't like is how in his second paper, he's supposed to be extending real analysis to the transreals, but instead of doing things like defining a topology, a metric, limits, etc. pretty much all he does is extend the definition of functions like exp, log, sin, etc. to the three strictly transreal numbers, and then talk more about transreal arithmetic.

That worries me too. I don't really have confidence that he understands the analytical issues here! (or, at least, hasn't given it the thought it deserves)

Extended real arithmetic is defined as it is because continuty is of prime importance to analysis. In particular, 1/0 is left undefined because both of the limits

$$\lim_{x \rightarrow 0} \frac{1}{|x|} = +\infty$$
$$\lim_{x \rightarrow 0} \frac{1}{-|x|} = -\infty$$

have the form 1/0. It almost looks like he made the freshman mistake of thinking of 1/0 as +infinity when he selected his axioms. His surprise that he computes $1^{+\infty} = \Phi$ makes things worse, since that's one of the basic indeterminate limit forms. (Though, it does indicate that maybe the arithmetic is doing something reasonable)

 

[kesh]

this just in

from the same page as the article

"Given the, er, light-hearted mathematical debate Dr Anderson's theory has generated, we're delighted to announce he will join us on Tuesday 12 December to answer questions and discuss some of the criticisms levelled against his theory of 'nullity'.
You will be able to hear in more detail from Dr Anderson on this page later on Tuesday."

http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml"

 

[chronon]

I've a feeling that nullity is just the start in his promotion of his 'Perspex machine' http://www.bookofparagon.com/Mathematics/SPIE.2002.Perspex.pdf which he claims is 'more powerful that a Turing machine'. Essentially he's pointing out that a computer which could manipulate exact real numbers in a single operation would be infinitely more powerful than current computers - nothing particularly new.

The most encouraging thing about this is the number of comments about it on http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml . About half a megabyte - the content of a small book - from people who know enough mathematics to realize what nonsense this is.

 

[DeadWolfe]

There is now a section of him responding to objections:

http://www.bbc.co.uk/berkshire/content/articles/2006/12/12/nullity_061212_feature.shtml

 

[EmilK]

This entire thing seem quite useless in fact. You can't just go define new sets of principles. I agree with the fact that it only seems to be a euphemism with no real value in mathematics. 0⁰ is still not solved satisfactory.

The work was developed over ten years, it's been peer reviewed and reported in seminars in mathematics and computing departments in the UK, and it's been reported at a learned society.

Is it just me or does this seem to be plain out ridiculous? How is it possible to develop this over a period of 10 years, even if it was periodically meant. Even a student in Junior High could think of this.

Although I can appreciate his quest for simplification and definition, it can only go so far before it becomes nonsensical. I would like to see his "proof" and the work that has lead to this discovery. Let's see if he can actually get his ideas published in a respectable journal.

 

[DeadWolfe]

Indeed. If it took ten years, I would really like to see the hundreds of pages of ideas he threw away before he came up with this one.