Posted on 12/08/2006 12:20:06 PM PST by LibWhacker
Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - 'nullity'. But the suggestion has left many mathematicians cold.
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.
"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."
Computers simply cannot divide by zero. Try it on your calculator and you'll get an error message.
But Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity).
'Quite cool'
The theory of nullity is set to make all kinds of sums possible that, previously, scientists and computers couldn't work around.
"We've just solved a problem that hasn't been solved for twelve hundred years - and it's that easy," proclaims Dr Anderson having demonstrated his solution on a whiteboard at Highdown School, in Emmer Green.
"It was confusing at first, but I think I've got it. Just about," said one pupil.
"We're the first schoolkids to be able to do it - that's quite cool," added another.
Despite being a problem tackled by the famous mathematicians Newton and Pythagoras without success, it seems the Year 10 children at Highdown now know their nullity.
This is the kind of stuff that you get when you do not teach because you do not want to hurt someones feelings. I suppose that the flat earth society will come back next.
Shoot! I woulda thought a dumbass idea like that woulda come from UC Berkeley.........so your calculator spits out "nullity" instead of "error." whassupwidat?
It doesn't really matter, as long as the number you divide by is small enough that the result is within a tolerance of precision you're looking for. And/or you just specify the result as being large enough for the precision.
I like the idea that this guy might force chip makers to do the special case handling internally so that I don't have to waste code on it. Perhaps there could be an option in the chip to turn it on/off, in case you needed the old method.
sin (X) / X = 1 as X approaches X=0 ......apparently not....
"...Grabel's law still prevails; 2 is not equal to 3, not even for large values of 2."
"One cannot say of something that it is and that it is not in the same respect and at the same time" - Aristotle
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned." - Avicenna
It's not as bad as you think. In fact, it's not even original. Dividing by zero is a much bigger deal in the computer world where it's often the start of unrecoverable errors if not properly trapped.
And the trapping of said error has traditionally been assigning a value of null (which is not zero, not positive, not negative) which typically begins a control-break function.
What this educator is doing is essentially laying the groundwork for this in his elementary students. It's IMHO a recognition that we live in the 21st century, nothing more.
See my comment #145. He's not just dumbing down his poor students a little bit, he's making them truly stupid.
I hope this moron gets some relief in knowing that pacemakers don't do arithmetic.
LMAO!
But earlier you said: It would be given an arbitrary value that wouldn't be used in any other fashion in that software. So it sounds like you're backing away from that idea now.
Exception handling is usually all that's needed unless for some reason you need to retain the fact that you divided by zero later in the code. That's not too common, but not unheard of either.
So why don't you just use a boolean variable - set the value to true when you divide by zero? Why do you need a pointer for that?
If you do need to retain a divide by zero in memory, pointers in most programming languages help you out. In most languages, pointers can be set to null (with 'null' being a reserve word). I don't know what the binary code behind this is, but it doesn't matter. What matters is that I can set a pointer to null if I divide by zero, and that's a special case that works no matter what. Most languages that do this also overload the '=' operator so you can test if a pointer's value is null.
The value "null" is equal to zero. A pointer contains the address of a location in memory. If the pointer value is 0, that means it's pointing to address 0 in memory. The '=' (or '==') operator is not overloaded - it's doing a normal arithmetic comparison to see if the pointer's value is 0.
The mathematicians I have known aren't looking to model the real world with their math. They are trying to make intellectual discoveries and leaps in math. And if they eventually lead to something that models the real world, great. But it's not their raison d'etre.
Nothing really new here.
He's just giving a name to an imaginary number. I don't know why people are giving this guy this much attention.
That's all dividing by 0 gets you, an imaginary number.
It's use prevents misleading mathematical notation: For every real number, (a^-2)*(a^-2) =a.
But (-1)^-2 * (-1)^-2 is not equal to (-1*-1)^-2;
i*i equals -1! The use of i reminds the problem-solver that even though we can treat (-1)^-2 like a number to help us perform algebra, it is not, in fact, a real number. So rather than write an unreal number, such as (-6)^-2, the reader writes 6i, thus enabling him to continue to manipulate that term as if it represented a real number, even though it doesn't. This is vital, because by multiplying a negative radical by another negative radical, you can arrive at a real number, even though the negative radical is not real!
Nullity, on the other hand, is useless. If the term is eventually multiplied by zero, the entire term can be eliminated. If not, the presence of the nullity makes for an unsolvable equation.
i does not exist. It is, however, a useful concept. Nullity is useless.
In the real world, dividing by zero can in fact yield a real value.
Example:
The democrats were able to divide the electorate and have positive results (make gains) with 0 ideas.
Democrats = no ideas = 0
Voters/0 ideas = 16 more seats for the democrats
Thus, dividing by zero yields a positive result (net gain) of some 15 or 16 seats for the democrats
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