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.
Yeah - thanks - I figured out the computer language point a little too late...
OK, OK.
Ah know you jest loooooooooove math, so ....
Ya gotta believe!
b.
Making up a word is not solving a problem!
Doing something appropriate is not crashing and instead giving me a useable number that's effectively rounded to infinity. It's wasteful to make the code do it, and it causes issues then the programmer forgets.
The value 0.1 cannot be represented in floating point, and this doesn't cause anyone any greef when I use a rounded value instead. I'm of the opinion that computer hardware should do the same for divide by zero exceptions, and return a rounded value of infinity that operates in succeding calculations. Returning a NAN merely trashes everything afterward, and it's not a useable option.
Me either. When "i" refers to thee not me ;)
All numbers are abstractions, even the ordinary counting numbers. It took a while for mankind to accept fractions, then gradually irrational numbers, then transcendental numbers, like pi, that are not the root of any algebraic equation with a finite number of terms and then negative numbers and "finally" complex numbers. If you accept all the others, you're five-sixths of the way there!
Complex numbers are useful, in that they complete the algebra of real numbers. The interesting thing is that solutions involving complex numbers are surprisingly useful in solving real world problems.
As others have pointed out, they can represent voltages, or for that matter, any time vary quantity. The complex notation falls naturally from the solution of linear differential equations, and they represent a very convenient notation for representing the phase and amplitude of real time or spatially varying quantities.
It occurs to me that I never see debates like this over at DU. And they are the self-professed "Intelligent Progressives"...
DU = Nullity!
You'd be testing for the "nullity" value in your computer programs if you had your theoretical new hardware anyhow, so what's the difference? Is a little precondition checking or exception handling too hard for you? We need new computer hardware to solve this horrendous problem that plagues the software development community!!
I think you've got it! You implied that it was confusing in some way to you to "divide something by nothing." All I'm saying to you is that it's confusing to you because it makes no sense; i.e., you've got very good intuition! :-)
No.
Excel already deals with division by zero:
#DIV/0!
Yeah. The programmer had to put in manual exception handling. That's a cheezy solution when the divide could merely return a useable value. Other operations round to the nearest value that can be stored, such as the 1/10 floating point issue. What's so sacred about divide by zero that mathmaticians think they need to crash my software instead of returning a rounded value of infinity?
Yeah, it's infinity^2! Of whatever.
>> 1/0
Warning: Divide by zero.
(Type "warning off MATLAB:divideByZero" to suppress this warning.)
ans =
Inf
>> Inf/0
Warning: Divide by zero.
(Type "warning off MATLAB:divideByZero" to suppress this warning.)
ans =
Inf
>> 1/Inf
ans =
0
>> Inf*0
ans =
NaN
So there! I performed the experiment, rather than speculate.
Why? A "nullity", would merely be infinity rounded down to the nearest value that can be stored in the machine. No need to test for it. The whole point of the "nullity" is to avoid having to bother to test for it.
We've established that mathmaticians have no problems with rounded values, such as the 1/10 rounding error in floating point. It's just rounding infinity into a storable value that they can't tolerate.
Maybe the problem is the fact that most mathematicians are teachers, and they teach the issue of *why* you can't divide by zero, so when the hardware designers tackled the problem the math guys ran screaming NO, NO, NO, YOU CAN'T DIVIDE BY ZERO. So they crash the computer instead. Often actually crashing the machine, if the OS doesn't handle the divide by zero interrupt. Now there's an intelligent solution.
Zero is not a number in a real world sense compared to practical numbers that can be ascribed to an object as conveying a meaningful attribute of the object. Consider, 1 could be described as a count attribute at a given state-time for an object, an apple let's say. If the apple is removed, there are not only zero apples, but also zero bananas, zero pairs and zero elephants, etc. The connection of the count attribute to any object is broken at zero. As attributes convey meaning and information, the dissociation of an attribute from an object renders the attribute meaningless. Dividing by zero, a meaningless attribute, therefore can convey no real world meaning. In reality, it is an answer for a question never asked.
Philosophically, an optimist would say that zero is not a number but a 100% probability of anything. Nature abhors a vacuum.
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