1200-year-old problem 'easy' [dividing by zero]

BBC ^ | 12/8/06

[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.

[Fierce Allegiance]

LOL! Circuits class was almost as bad as thermodynamics.

[Professional Engineer]

pICKY, PICKY.

oH WAIT, THAT'S WHAT i DID TOO.

lol

[GoLightly]

I have to admit, though, "nullity" is exactly the WRONG word for this value continuum, because "null" is nothing, and therefore "nullity" cannot be defined rationally to mean "anything".

Ah ha, someone else who rejects the name. I think it should be called a pixie...

[gb63]

When I was writing accounting software, one of the areas I had to foresee was dividing by zero. The Windows core routines will 'throw an exception' when encountering a divide-by-zero. The software program must 'catch' the 'thrown exception' and handle it in some way. I wrote elaborate error functions to catch every error we could think of, but of course, some user would always manage within 30 seconds to do something stupid. However, almost all modern software handles divide-by-zero problems gracefully.

[avacado]

"Don't see it as anymore ridiculous than i. Square root of negative -1. What sort of math is that?"

That's actually valid in the real world. Doing transforms and then reverse transforms if you have "i". We use it all the time with Fourier transforms.

[paulat]

Jack Bauer doesn't count to infinity, but his cell phone battery does carry an infinite charge.

LOLOLOL!!!

[Slings and Arrows]

Thanks! In the words of Rodney Dangerfield, this guy tells it like it ain't.

[CharlesWayneCT]

The problem with thinking about it as "approaching infinity" is that it implies that, as n approaches infinity, 0*n approaches every number.

Because if X/0 approaches infinity, then 0*infinity would be X, where X is any number.

But in fact 0*n as n approaches infinity is ZERO.

Which is why we don't usually say that X/0=> infinity, but rather than you can't divide X by zero.

[CharlesWayneCT]

sssshhhh.


That's how you tell if the person you are talking to has any practical use; if they use "i", the answer is probably not, if the use "j" then you can be pretty sure they actually have a POINT to their math.


:-)

[RFEngineer]

"Don't see it as anymore ridiculous than i. Square root of negative -1."


The number you have reached is imaginary. Please rotate your phone 90 degrees and try again.

[Right Wing Assault]

I wonder what the log of "nullity" is.

[Tinian]

In my code, I have to pre-test any division to ensure that it's not attempting a divide-by-zero. If it is, I often substitute a really-tiny-number, and procede with the division.

Sounds like the most realistic real-world work around to me. What's the difference between the sine and tanget of .01^th seconds of arc?

[quikdrw]

Jack Bauer is a fictional character based on the real-life Chuck Norris.

[HarmlessLovableFuzzball]

And did you ? (you can prove it to some degree with lab equipment.)

[I see my hands]

"Only Chuck Norris can divide by zero. Plus, Chuck Norris has counted to infinity.....twice."

Big deal. Jack Bauer can do that on one hand.

[Slings and Arrows]

That pretty much nails it.

[AndrewC]

Of course it is easy... The answer is

[vrwc1]

I don't think there's much to the "mathematics" of renamed infinity (nullity) at all. If you hit the link to the story and watch the video of the guy explaining it, he is clearly a doofus, and his "proof" is nonsensical.

[lepton]

In signal processing code, they often use the NaN for this

Shouldn't that be NaNO2, decomposing to NaNO3? :-P

[JamesP81]

How are you going to now represent "nullity" with "an arbitrary value" that will be returned when you divide by zero?

Declare the pointer to the value to be null after exception handling the divide by zero error. Either that, or we determine that the lowest value for a given variable or its highest possible value (either –2,147,483,648 or 2,147,483,647 since we're using 32 bit signed integers) to be a divide by zero condition. This is only if you need to look back later in the code to see if a divide by zero occurred. Normally, exception handling at the time of the error is sufficient and such methods aren't necessary, but they are available if needed and I've used them on more than one occasion.