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lmnk

Nullity

9 posts in this topic

So we were talking about this on IRC, and I thought I'd bring it here becuase I have strong feelings on this issue (this is math related, but I don't know if it should be somewhere else, please move out of hacking if I'm an idiot).

A solution to divide by zero

Long story short x/0 = nullity. Nullity = "sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)"

Does this solve anything? It just gives a new new name to what I previously knew as 'undefined'. Knowing that something equals nullity will not help anything.

In the BBC article the guy who came up with this says that this solves the divide by zero "problem". He goes on to say that "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."

I hope to god that a computer program I have to trust with my life has a try/catch to handle a DivideByZeroException. If nullity is going to be implemented into a programming language it would do nothing. At best nullity will be handled by anything checking for a divide by zero and at worst will just create another set of bugs.

"The theory of nullity is set to make all kinds of sums possible that, previously, scientists and computers couldn't work around."

We know that the limit as x->0 of (n/x) = infinity. So how is nullity going to help?

If someone could explain to me how this could be used practically, please, please, please let me know otherwise I'm just going to give myself an aneurysm trying to figure it out.

Edited by lmnk
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Inventing a new number if you have a maths problem is almost never a solution.

I doubt this one is too.

1/nullity = ??

there are so many things he will need to define before this can be accepted as a serious 'extra' number.

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if($denominator==0){$result=int null;}else{$result=$numerator/$denominator}

:roll:-_-

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It should make your head hurt; cos it's complete nonsense. Giving something a name doesn't make it real or useful. It solves absolutely nothing. It's quite possibly also meant as a joke ...

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We know that the limit as x->0 of (n/x) = infinity. So how is nullity going to help?

And if n is 0?

Inventing a new number if you have a maths problem is almost never a solution.

To hell with imaginary numbers!

Giving something a name doesn't make it real

Have you even bothered to read his paper? Do you have any training in abstract mathematics?

The guy's making division a closed operation over the reals (well, over the 'transreals' as he calls them), it's nothing really spectacular. All he's doing is defining division by reciprocals instead of multiplicative inverses and comes out with a consistent system given some axioms. Is it useful? For most things, not really.

Don't worry, 0/0 still is an indeterminate form.

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Have you even bothered to read his paper? Do you have any training in abstract mathematics?

I had not read his papers at the time of writing (I didn't know they were available). Although I have taken some courses in abstract mathematics at university level, I don't find that these courses should be necessary in order to draw the conclusion that giving something a name does not make it real or useful. I will however agree that this argument does not in itself disprove the hypothetical usefulness of allowing division by zero.

Having read the papers (available for download here: http://www.bookofparagon.com/News/News_00012.htm ) I will have to say that the BBC article does not at all explain what 'nullity' is supposed to be good for. The way it's presented I will indeed call it nonsense. As for the actual publication, although unorthodox, there might perhaps be some valid reasoning in the madness.

For those who have not read it; the publication is about what the author calls transreal arithmetic as a proposed, more flexible, alternative to traditional arithmetic (which he finds much too restrictive). He treats nullity as an actual number with specific mathematical properties. To make a long story short, he postulates that by implementing his transreal arithmetic one can overcome possible barriers that traditional arithmetic imposes on mathematical fields such as computing and abstract physics.

I see one major flaw in his reasoning. He argues that transreal arithmetic is better because it's more flexible, but he demonstrates no actual implementation in which this flexibility proves useful or more versatile than what we currently have.

Edited by snow
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I agree the BBC article is fluff, but jumping to the conclusion "oh this is bullshit!" is absurd. There were hardly any details.

I see one major flaw in his reasoning. He argues that transreal arithmetic is better because it's more flexible, but he demonstrates no actual implementation in which this flexibility proves useful or more versatile than what we currently have.

Just because it has no apparent use does not mean it's invalid mathematics (I guess that is what you mean by flaw in his reasoning?). His main argument is that it's useful for computer arithmetic since you won't encounter any NaN's. So there's your "use". Unfortunately it's rife with edge cases, so don't expect to see it adopted. Not to mention the word "nullity" is already used to indicate the dimension of a null space, so the name is a bit confusing.

giving something a name does not make it real or useful

He didn't just give 0/0 a name-- he has provided a superset of axioms for the reals. Whether these axioms are useful in a pure mathematical sense is a value judgement.

You keep on using the word "real". Could you please provide a rigorous mathematical definition? I'd like to hear it!

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Aren't real numbers just the rational and irrational numbers?

[ basically the numbers less ethereal than the complex (imaginary) numbers? ]

I don't know but that's what I always thought (I'm not deep into mathematics though...but hoping to learn).

If not, can someone supply some linkage where i can read up about it?

thanks muchly!

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I agree the BBC article is fluff, but jumping to the conclusion "oh this is bullshit!" is absurd. There were hardly any details.

Just because it has no apparent use does not mean it's invalid mathematics (I guess that is what you mean by flaw in his reasoning?). His main argument is that it's useful for computer arithmetic since you won't encounter any NaN's. So there's your "use". Unfortunately it's rife with edge cases, so don't expect to see it adopted. Not to mention the word "nullity" is already used to indicate the dimension of a null space, so the name is a bit confusing.

He didn't just give 0/0 a name-- he has provided a superset of axioms for the reals. Whether these axioms are useful in a pure mathematical sense is a value judgement.

You keep on using the word "real". Could you please provide a rigorous mathematical definition? I'd like to hear it!

Personally I don't find it absurd to assume that an article I read at least captures the essence of what it's actually about. In this case, however, I will say that the article explains nothing. After reading his paper it's no longer my understanding that what he's done is just giving 0/0 a name.

I do in fact not think his work is invalid mathematics. However his reasoning appears to be that because it's less restrictive it is also superior to what we currently have. This may perhaps be true, but not automatically so. It is quite possible that the entire concept, although probably mathematically valid, is useless. I'm not saying he should abandon his ideas though. I wouldn't expect it, but perhaps they will prove useful (in the ways he proposes) some day.

It was not my intention to give the impression that I was using the word 'real' in a rigorous mathematical way. A perhaps more formally correct way to express my opinion would be that by what the BBC article presented I could not see what more he did but giving something, that has always been regarded as undefined, a name. And like I've said I see now that this was not at all what he meant. My conclusion was hasty.

So you see my original opinion was based on a false understanding and has changed.

Edited by snow
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