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.
Great background for my first real job as a pencil on velum draftsman.
Except i works out beautifully with e.
Nah. inf * 0 = 0
IOWs 0 infs is zero, or inf 0s is 0.
Reboot the calculator and try again.
Your own words refute you. You complained in a previous post that MAX_INT wasn't a very good approximation of infinity! If you're putting the result of your division into an integer that is what you would get! Even if you were using a double, I fail to see how 1.7976931348623158e+308 could be considered a good approximation of infinity! It's not even close!
Besides, what's so sacred about your software that an invalid operation (like divide by zero) shouldn't make it crash? There are plenty of other conditions that will make that happen and you have to guard against them too...why pick on divide by zero?
As long as you don't care what order they are in, or when they occur after the oceanic lights are on.
The same way you represent the square root of -1 as i.
Or the same way you represent the perimeter of a circle divided by the radius as p.
Thanks - I didn't click through.
The sqr(-1) or "i" has utility in places you might not imagine. Electrical Engineers use it to analyze Alternating Current circuits. Works great there. It allows Ohm's law to work for both AC and DC circuits by using "imaginary" numbers to describe things.
I'm not convinced that "nullity" is going anywhere, but maybe it'll prove a useful concept.
Glad I'm a civil!
You're welcome! :-)
It means the limit is taken from the positive direction. Otherwise, the result is imaginary.
After looking over them, I can see they are far from trivial, and this is someone who clearly understands the problem, not someone who is obviously a crackpot as I originally thought.
Whether or not he is correct is another question. I'd have to study it carefully to come to any conclusion in that regard (which I have no intention of doing).
He defines the "transreals," which include the reals, plus and minus infinity, and this "nullity" number of his, and then "proves" a number of theorems and properties for the transreals.
So, while I'm not eating crow exactly, right now... Perhaps we should try to find out what the peer reviewers, if any, have to say about all this. For now, I'm remaining skeptical but guarded in any further comments I make about it!
Just from a common sense perspective, if the "transreals" include nullity, then shouldn't nullity be on the numberline with all the other transreals? Why is it that in the video in the linked article he shows the nullity value floating off the number line by itself? That alone is enough to convince me that he is a crackpot. Perhaps a very intelligent one, but a crackpot nonetheless.
You are partly correct. But there is a problem in the way you phrased it. Mathematics has the concept of infinity and a symbol for it, but it isn't a value or a number. Think of it as a direction on the real number line. Or you can think of it a process that goes on forever. But we don't really have a good understanding of forever.
15 divided by 5 = 3.
That means that 3 times 5 = 15.
If we say that 15 divided by 0 = infinity,
then infinity times 0 = 15
If 10 divided by 0 = infinity,
then infinity times 0 = 10
So now infinity times 0 can equal any number you like. But any number times 0 is 0. Do you see the problem? We have now introduced an inconsistency. So division by zero is is undefined.
We have a glimpse of it in pi.
+/- xi is used to characterize the frequency response of an AC circuit. If you were to sit down with a pencil and calculator and think yourself into a stupor like in your first AC circuit class.
i is simalarly used in microwave. Sweep a range of frequencies using a network analyzer looking into the waveguide device of your choice. Mark a few points using the log mag display and note the frequency and amplitude. Switch to polar display and note the impedence values of those same points.
Now, grab an X-Y plotter and manually sweep that band on a Smith chart. That's the most primitive and will give you your reactance, resistance and phase. If you know basic electronics, you can relate to microwave with a Smith chart.
When you get to the polar plot, an LED will turn on and you will want to get the Agilent 50 GHz network analyzer (~$200K) so you can tune things fast without the slightest thought about the math; listen to talk radio and BS with buddies and the gals. Then go out and prove that what you built actually performs to spec!!!
huh?
You complained in a previous post that MAX_INT wasn't a very good approximation of infinity!
That's my subjective opinion! Many processors I work with would have MAX_INT = 32767! Not very close to infinity I think!
Even if you were using a double, I fail to see how 1.7976931348623158e+308 could be considered a good approximation of infinity!
It is a bit closer than 32767!!!
Besides, what's so sacred about your software that an invalid operation (like divide by zero) shouldn't make it crash?
Because it's driving around many tons of steel with humans in it that might die when my software crashes.
There are plenty of other conditions that will make that happen and you have to guard against them too...why pick on divide by zero?
If my software has no errors in it, then it won't crash. But a divide by zero can occur merely because the vehicle is in the wrong place, or pointed the wrong direction. There are innumerable inaccuracies and approximations all over the math functions, and it amazes me that divide by zero deserves an actual hardware interrupt, often at a higher priority than clock interrupts, merely because the concept that dividing by zero returns an approximate result at the edges of computer number representation drives mathematicians loopy.
pi is an irrational number. So is e. So is the square root of 2. These are not infinite numbers. What you are referring to is that we can't write those numbers in a base-10 number system with a finite number of digits. That is why we have symbols for them.
Draw a right triangle with the two arms one inch long. How long is the hypotenuse? It has exactly of length of the square root of two. Does the hypotenuse have an infinite length? No, it has a finite length. Irrational numbers are finite numbers.
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