Is Zero Divided by Zero Really Solved After 1200 Years?

[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.

 

[Alkatran]

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

That changes the way you do mathematics - that statement is revolutionary. It remains to be seen whether it is correct or not, whether people accept it or not, but that's my position.

Wait, he's not sure if it's correct or not?! How can you be teaching mathematical ideas when you're not sure they're correct??

 

[cristo]

Wait, he's not sure if it's correct or not?! How can you be teaching mathematical ideas when you're not sure they're correct??

Let alone teaching them to school kids!

 

[Rach3]

Wait, he's not sure if it's correct or not?! How can you be teaching mathematical ideas when you're not sure they're correct??

Well, it's "only a theory". You know, like evolutionary theory, intelligent design theory, algebraic topology theory, or TimeCube.

 

[EmilK]

Well, it's "only a theory". You know, like evolutionary theory, intelligent design theory, algebraic topology theory, or TimeCube.

I'd like to refer you to an excellent entry by ZapperZ that can be found here :)

 

[Alkatran]

What really, really bothers me about this story is the comments.

People giving obviously wrong inconsistency proofs, people saying "yeah, well people said imaginary numbers didn't exist", people saying 1/0 is equal to infinity, just people making it clear they don't understand division in general.

How hard is it people? a/b = c if and only c is the unique solution to a = bc.

I also wonder why the sets {x | 1 = 0*x} (the empty set) and the set {x | 0 = 0*x} (the set of all real numbers, given that we're working with the reals). They pretty clearly show why you can't divide by 0. Sort of hard to justify giving the empty set or the set of all reals numeric values!

 

[unit_circle]

Well, it's "only a theory". You know, like evolutionary theory, intelligent design theory, algebraic topology theory, or TimeCube.

I'd like to refer you to an excellent entry by ZapperZ that can be found ot.com/2006/10/imagination-without-knowledge-is_16.html]here[/url] :)

I think you forgot to turn on your saracasm detector, EmilK. Rach3 was jesting when he compared evolution to the TimeCube (at least I hope so, Rach3). It's funny the TimeCube was mentioned, because when I told my brother about this Anderson crackpot, he said "Division by 0? Isn't that TimeCube territory?"

 

[Hurkyl]

How hard is it people? a/b = c if and only c is the unique solution to a = bc.

It's easy to prove someone wrong if you define all the symbols to mean something different than the other person intends. "Transreal" division is not the same thing as division in a field.

 

[Alkatran]

It's easy to prove someone wrong if you define all the symbols to mean something different than the other person intends. "Transreal" division is not the same thing as division in a field.

I wasn't making a point against his system in that post, I was complaining about the public's lack of knowledge on how division is defined. Otherwise, excellent point.

 

[Sleek]

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

Hurray to exception handling :P.

 

[Karlisbad]

This seems to me a big nonsense similar to the "hoax" by Peter Lynds and his "supposed" phylosophical solution to Zeno Paradoxes..

By the way i think that the problem with 0/0 was studied and made rigorous with infinitesimals and so on, although i would like to know what "impact" this would have with derivatives since for h-->0 the quotient:

\frac{f(x+h)-f(x)}{h} is just 0/0 and hence a "nullity" , if this can be applied to some math derivatives and integral could benefit from this number.

 

[AKG]

This seems to me a big nonsense similar to the "hoax" by Peter Lynds and his "supposed" phylosophical solution to Zeno Paradoxes..

By the way i think that the problem with 0/0 was studied and made rigorous with infinitesimals and so on, although i would like to know what "impact" this would have with derivatives since for h-->0 the quotient:

\frac{f(x+h)-f(x)}{h} is just 0/0 and hence a "nullity" , if this can be applied to some math derivatives and integral could benefit from this number.

This isn't true. For h-->0, this is the L such that for all e > 0, there exist d > 0 such that, well, you know the rest. There's a specific meaning for "h-->0" which is different from h=0.

 

[Hurkyl]

On a related note, division is discontinuous anywhere where the denominator is zero. So, even if you use the transreals, you still cannot do any of the naïve things you would like to do with the limit of f/g when g goes to zero.

 

[Cyrus]

I don't know about what he is doing mathematically, but he says in the BBC audio clip that his use of nullity helps solve computer problems and that he has a working chip that does math with this concept that is not easily done without it.

He says very clearly that his concept of nullity is not mathematical, but computer science related, something to do with NaN not= NaN.

That being said, maybe we should wait and see if this actually does provide any use before bashing him in the head? Because I read a lot of people here complaining about his use of Nulity for MATHEMATICAL concepts, which he clearly says is NOT what nullity is for.

 

[FrogPad]

I don't know about what he is doing mathematically, but he says in the BBC audio clip that his use of nullity helps solve computer problems and that he has a working chip that does math with this concept that is not easily done without it.

He says very clearly that his concept of nullity is not mathematical, but computer science related, something to do with NaN not= NaN.

That being said, maybe we should wait and see if this actually does provide any use before bashing him in the head? Because I read a lot of people here complaining about his use of Nulity for MATHEMATICAL concepts, which he clearly says is NOT what nullity is for.

So were those children computer science students?

 

[Cyrus]

What does that have to do with anything?

 

[FrogPad]

Because I read a lot of people here complaining about his use of Nulity for MATHEMATICAL concepts, which he clearly says is NOT what nullity is for.

All I'm saying is his presentation (probably more for the BBC) was in a MATHEMATICAL environment.

 

[NoTime]

I don't know about what he is doing mathematically, but he says in the BBC audio clip that his use of nullity helps solve computer problems and that he has a working chip that does math with this concept that is not easily done without it.

He says very clearly that his concept of nullity is not mathematical, but computer science related, something to do with NaN not= NaN.

That being said, maybe we should wait and see if this actually does provide any use before bashing him in the head? Because I read a lot of people here complaining about his use of Nulity for MATHEMATICAL concepts, which he clearly says is NOT what nullity is for.

He discovered the database NULL field?
Or the NULL pointer?

 

[Cyrus]

How should I know? I am just repeating what he said on the radio interview. Someone linked it, you can listen to it for yourself.

I said something about NaN not = NaN. I don't know if this has to due with the database Null field or the Null pointer. He said he got it to work on a chip, and that it solves formulas that are otherwise more difficult using standard algorithms.

No where, did he say this concept was to be used for mathematical proofs.

 

[FrogPad]

How should I know? I am just repeating what he said on the radio interview. Someone linked it, you can listen to it for yourself.

I said something about NaN not = NaN. I don't know if this has to due with the database Null field or the Null pointer. He said he got it to work on a chip, and that it solves formulas that are otherwise more difficult using standard algorithms.

No where, did he say this concept was to be used for mathematical proofs.

Here's a video:
http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml

Here's a quote:
"That changes the way you do mathematics - that statement is revolutionary. It remains to be seen whether it is correct or not, whether people accept it or not, but that's my position."
-http://www.bbc.co.uk/berkshire/content/articles/2006/12/12/nullity_061212_feature.shtml"

 

[Hurkyl]

Because I read a lot of people here complaining about his use of Nulity for MATHEMATICAL concepts, which he clearly says is NOT what nullity is for.

Very few people are criticizing his technical work; it's almost entirely directed at the comments he makes. And some of them are mathematical. For example, taken from the link in the OP:

Dr James Anderson, from the University of Reading's computer science department, says his new theorem solves an extremely important problem - the problem of nothing.​

For example, take this quote from Perspex Machine VIII: Axioms of Transreal Arithmetic

For example, contemporary real analysis recognizes two special limits \infty = 1/0 = k/0 when k > 0 and -\infty = -1/0 = -k/0 when k < 0.​

where he makes one of the classic freshman mistakes. (he goes on to say he finds it disturbing that it doesn't include a number for k/0 when k=0)


And his problems aren't limited to the mathematical domain. Again, going back to the link in the original thread:

"Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in big trouble. If your heart pacemaker divides by zero, you're dead."​

which is, of course, absurd. Computers divide by zero all the time. (I just did it on my computer in the course of writing this message, just to prove a point) And it demonstrates an utter lack of understanding of fault-tolerant programming.


In summary, (almost) nobody's complaining about his arithmetic system -- everyone's criticising his remarks about other things. Even if we assume he's doing good work with his Perspex machine, that doesn't mean he's not a crackpot.

 

[Kurdt]

I'm sure a similar stink was kicked up when Dirac found it useful to use his delta function in quantum mechanics. Perhaps if this is useful in the field of computer science then its implication and justification in a purely mathematical sense will have to be investigated as was Dirac's delta function. I suppose this strikes a chord because it is portrayed clumsily by the media.

 

[DeadWolfe]

But what on Eath IS the use of this concept supposed to be (aside from the obvious application to pacemakers)?

 

[Hurkyl]

I'm sure a similar stink was kicked up when Dirac found it useful to use his delta function in quantum mechanics. Perhaps if this is useful in the field of computer science then its implication and justification in a purely mathematical sense will have to be investigated as was Dirac's delta function. I suppose this strikes a chord because it is portrayed clumsily by the media.

I would be surprised. TMK, when Dirac introduced the delta function, he solved problems with it. And, TMK, Dirac demonstrated that he had a grasp of his subject.

Dr. Anderson, on the other hand, doesn't seem to have used transreal arithmetic to do anything. But that hasn't stopped him deeming his own work revolutionary, and contacting the media so that the whole world will know how smart he his. (And, in the process, making plenty of very basic mistakes about other fields... and his own)

 

[Hurkyl]

Comapre Dr. Anderson's work with, say,

http://www.math.su.se/~jesper/research/wheels/wheels.pdf

or, if you just want the arithmetic,

http://www.math.su.se/~jesper/research/wheels/wheelsshort/wheelsshort.pdf

 

[Kurdt]

I haven't had a proper look at his work as I've been busy but I do like to keep an open mind. I'll save my opinion for then.