Slashdot Mirror
Professor Comes Up With a Way to Divide by Zero
54mc writes "The BBC reports that Dr. James Anderson, of the University of Reading, has finally conquered the problem of dividing by zero. His new number, which he calls "nullity" solves the 1200 year old problem that niether Newton nor Pythagoras could solve, the problem of zero to the zero power. Story features video (Real Player only) of Dr. Anderson explaining the "simple" concept."
Wow, since this guy is a computer science prof, maybe he can come up with some value or symbol to represent "nullity." I suggest "NaN" for "not a number." (ducks to avoid rotten tomatoes)
Dividing by zero is not a "problem". It's just IMPOSSIBLE due to the way we structure our species' math. If you want to restructure our math as we know it (which he basically does by inventing his own false reality, so to speak), then you're not solving any problems. You're just being clever, and designing another system.. which has been done hundreds of times.
As I heard at one math forumn at the local university years ago, generations of mathematicians will be rising up from their graves, wracking their ancient canes against the tombstones, all screaming: "How dare you defy hundreds of years of tradition with this gabarage!"
(These old folks know how to scream!)
This is computer programming ABC: you DONT allow undefined behavious to occur in your program! (especially if your doing MIL-STD Ada for avionics etc.) This guys 'method' is just a form of exception handling that any programmer with half-a-brain could implement.
www.tribalnetworks.org - helping tribal people around the world to own their own means of high-tech communications
Needless to say people working with computers in the 1950s identified this problem and made sure that it would not happen in their programs but people who do not understand basic high school mathematics have managed to recreate it many times since. Next up - fifty years of people forgetiing about buffer overflows and race conditions.
Not really. NaN is: Not a Number.
He proposes to define a new number that doesn't exist (or fit for that matter) in the current system.
But still it's useless, or at least I think it is.
100/0 != 10/0 != 1/0 != 0/0
but he uses the same identifier for all of them, so that would mean:
(100/0) / (1/0) = 1
That goes against the principle of:
infinity / (infinity - 1) != 1
Seriously, in elementary school a teacher of mine tried to tell us that 1/0 = infinity
Read up on the definition of division. If for a moment we ignore the "and the divisor is not 0" part of the definition, one of the basic principles of division is:
if a * b = c
then a / c = b, and b / c = a
A fundamental part of his explanation pivots on the following being true:
1/0 = infinity
-1/0 = -infinity
So, according to that, the following would hold:
if 1/0 = infinity
then infinity * 0 = 1
which does not work, for obvious reasons. This I told my teacher in 6th grade.
The real idea is that, for an equation 1/x = y, y approaches infinity as x approaches 0. At x=0, y is undefined, and that's all there is to it.
Secondly, the story promises one thing, and "delivers" another. It promises to tell you how to divide by 0, and instead tells you how to get 0^0 (which is based on the previously mentioned false premises). And the answer he gives on how to divide by 0 is that the answer is infinity, which it isn't! I'd fire the professor that has the gall of teaching this to kids (after probably being laughed out by his colleagues).
Because mathematics doesn't deal with the real world. Physics does.
People take mathematical tools and models and apply them to the real world because they are useful. However, that usefulness is a lucky accident.
"Software is too expensive to build cheaply"
That behavior is a good thing. NULL is not 0 or an empty string -- it means "undefined". If you want 0, write 0. If you want "", write "".
If you add a regular number and an undefined number, the result can't be defined. That's why 1 + NULL causes the entire operation to reduce to NULL. Makes perfect sense and is an important part of relational design.
My other car is first.
Hmmm, that's different from my answer.
0*infinity=nullity
0 * infinitity becomes:
(0)*(1/0) becomes:
(0*1)/0 becomes:
0/0 = nullity
If Mr. Edison had thought smarter he wouldn't sweat as much. --Nikola Tesla
... where you can actually determine meaningful values for 0/0 in specific cases via calculus?e
I.e., it may well be that 0/0=a where a has a definite value? After all, any derivative is dy/dx=0/0.
That means to me that 0/0 is *really* undefined - may be this or that, depending on the circumstances; more information is needed, and assigning a specific symbol to it doesn't make much sense in the general case.
http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rul
thegodmovie.com - watch it
ALL Mathematics is COMPLETELY synthetic. That's the whole point -- that's the power of mathematics. You can define any set of rules, any set of axioms, any set of symbols, and start deducing. If the tools you need don't exist, you make them up. Nothing is more valuable in mathematics than a nice, clean, clear definition that increases the expressivity of math. Since math has no independent existence anyway, you can get away with pretty much anything so long as your new system has useful properties. Mathematicians with the guts to make things up as they go along end up with their names in textbooks and attached to great theorems, assuming what they made is conceptually useful (whether nullity is conceptually useful remains to be seen; a written description of the definitions would be nice).
Mathematicians that only do calculations that we already know about and are comfortable with? They're called accountants, and they have no friends. Seriously though -- since when did making up new ideas become a bad thing? I was under the (apparently mistaken) view that creativity was a praiseworthy trait.
Parent is correct. It is truly mind boggling how terrible his reasoning is. You simply don't define infinity and -infinity as numbers. That is not what they are. Add this guy to the list of cranks http://www.amazon.com/Mathematical-Cranks-Spectrum -Underwood-Dudley/dp/0883855070
I say this report is Bullshit. What professor, after making a huge discovery, proceeds to teach it to children before presenting it at a seminar of his peers? If these children are his peers, then I suggest he merely drew a symbol and named it 0/0.
A Good Troll is better than a Bad Human.
How did this type of crank bullshit get on the BBC ? What's next, an article on the timecube ?!
In Soviet America the banks rob you!
0/0 should be a special case where dividing by zero actually yields a valid real number, and all other divisions by 0 are undefined.
Wrong.
0/x gives 0. Always. And x/x gives 1. Always. Now, try for x=0... That gives 0/0 = 0 and 1 at the same time. That's why it's undefined, usually called NaN (Not a Number).
Anything else divided by zero can be defined as giving infinity or -infinity, which can be used in further calculations just fine, even coming to the correct result.
Example: The angle of the vector (1,0): arctan(1/0)*180/pi = 90 degrees. Works just fine. Not so for NaN, any calculation involving NaN will continue giving NaN.
Umm... you're obviously looking at only half the picture.
You said that 2 = 2*0*infinity = (2*0)*infinity = 0*infinity = 1
You could also say that 3 = 3*0*infinity = (3*0)*infinity = 0*infinity = 1 and so on
If you apply this formula enough times you'll notice that anything = anything*0*infinity = (anything*0)*infinity = 0*infinity = anything
This man is clearly a genius... he discovered that anything = anything!! Imagine the philosophical implications! For example, the universe can be whatever you want it to be (shit in a bottle of vodka) and visa versa!
Unfortunately, that explanation seems to have been replaced by gibberish in the copy I just downloaded. Check it out:
So basically, the two NaNs have subtle semantics (much like his nullity) and don't have a catchy name or reuse a symbol that already means the golden ratio, therefore they're broken. In other words, they are defined, but he doesn't like the definition.Right. Now my airplane won't drop out of the sky, because the thrust calculation that used nullity as an input produced nullity as an output, in a way completely different from the one that produced NaN from NaN before. This new name and slightly different semantics magically mean the right amount of fuel will go into the engine.
Only Chuck Norris can divide by zero.
Chuck Norris just looks at zero, and it divides itself.
Soylent Green is peoplicious!
Wow. Looking over the guy's axioms, as soon as you introduce "nullity" the result of all of your computations is nullity:
- the sum of anything and nullity is nullity (his axiom A4)
- the product of nullity and anything is nullity (his axiom A15)
- the reprical of nullity is nullity (his axiom A22)
So, his arithmetic is normal arithmetic, but as soon as you hit nullity anywhere, it's a black hole you can never get out of. All he's essentially done is take the "error state" and add it into the system as an object. You still can't compute anything you couldn't compute before. So yes, he has truly discovered NaN.
The projective line is neat and all but what he is doing is just stupid and fucking up his kids.
He reasons thusly 1/0=+inf -1/0=-inf (already see the problem that +inf=-inf) and 0/0=nullity (hence nullity = +inf)
He then reasons that 0^0=0^(-1)*0^(1)=1/0*0 = 0/0 = nullity.
Now let's try that another way.
nullity*0=0/0*0=0/0=nullity.
But also if 0^0 is a number then 0^0*0^1 = 0^1 = 0 Thus nullity*0=0 hence nullity*0=nullity=0. This is a pretty clear contradiction.
In other words it's just dumb. Mathematicians are not idiots. We haven't missed something like this for thousands of years.
If you liked this thought maybe you would find my blog nice too:
Computers can't deal with imaginary numbers natively....why would nullity be any different?
I fear the Y2038 bug
What's so amusing about that? Nah, what's amusing is the fact that exactly zero (0) slashdot nerds know that this is in fact the correct answer, and that the professor is wrong.
The answer to a / 0 is defined as the limit for a / x when x approaches 0. Some examples:
23 / 0 = lim x->0 (23 / x) = inf
-5 / 0 = lim x->0 (-5 / x) = -inf
0 / 0 = lim x->0 (0 / x) = 0
Simple as that.
Disclaimer: I haven't read the fine article, perhaps the professor meant something else.
Anyone want to attempt a practical application of this so called *invention*?
I still fail to see how this helps people with pacemakers and computer related problems. Firstly any decent computer programmer making high integrity systems must care for situations where the divisor could be zero. Secondly there is no magical solution just by inventing a new concept. If your computer program should - even after your persistent effort - in an unforseen circumstance throw an divide-by-zero exception then just handle the exception and carry on.
How much nothing can you fit in nothing?
none. one nothing. Ten nothings. Twenty nothings. A billion nothings. Nothing * Anything = nothing.
Its not a number. Its a nonsense.
Excuse the Unicode crap in my posts. That's an apostrophe, and slashdot is busted.
If this is real, who will solve the problem of divide by nullity? Sounds like he's just adding another problem to solve the first one.
That's why he's defined a new arithmetic - he calls it transreal - where division by zero is defined. The PDFs on his website clearly explain what he's done.
It isn't rubbish. In second year high school mathematics they had us "invent" our own arithmetic. We could define whatever operations we like (eg, a funny symbol that would multiple the left hand value by 2 and add it to the inverse of the right hand value) and then we had to prove whether the operation was commutative, distributive, etc. This guy has done the same thing but with a new "number" he calls nullity. He has defined what happens when you add a real to nullity, when you multiply a real by nullity, when you divide nullity by nullity, etc. It's an internally consistent number system.
It's interesting for grade schoolers because it gets them thinking about number theory. Instead of thinking "you can't divide by zero" they instead think "oh, well that's just a law for the real numbers, but I'm not constrained by real numbers, I can invent a number system where division by zero is allowed". That is far more insightful and creative than "you can't divide by zero". A child who grasps that concept has the potential to become a great mathematician. A child who merely parrots "you can't divide by zero" will become a bus driver or a computer programmer :-P
It's hard to explain abstract concepts such as number theory. Congratulations to him for making it look like fun.
No, the process of "splitting something among 0 people", makes no sense. Which is the very reason that division by zero is undefined. "Sharing something among people", or "dividing" implies that there is non-zero denominator. And yes, I do think that analogy extends to negative numbers and fractions, but NOT to zero.
What's your GCNSEQNO?
Sounds a lot like the Time Cube to me ...
Honestly, it's like Cantor never existed.
What a long, strange trip it's been.
This is actually what the whole "angels dancing on the head of a pin" thing was about.
What a long, strange trip it's been.
Descartes or some long dead mathematician did just that for sqrt(-1). He said, we know sqrt(-1) doesn't exist, so let's make it equal to some number i. By using numbers that included a component of i, he was able to get real results.
So why can't we do this for other items that are not a number, i.e. x/0?
Yes, actually it is, and there are different sets of rules (aka axioms) that are used. For example, Euclid chose to include the Parallel Postulate among the axioms that define his geometry, but there are various well-developed -- and useful! -- non-Euclidean geometries that assume the parallel postulate is not true. There are many branches of mathematics that modify what most would consider the "normal" rules in various ways. Many of them prove to be useful in the real world, too.
Mathematicians realized a century ago that their work is a discipline of arbitrary rules, and that none of their theorems have any inherent real-world truth or falsehood. Math is simply an abstract model. By choosing the right set of axioms one can create a model that maps well onto various aspects of reality, making it useful for physics, engineering and much, much more. Sometimes the common rule set doesn't map well, and even physicists and engineers use the alternative rule sets mathematicians have devised.
This concept of "nullity" isn't something that mathematicians would call wrong. For it to be wrong, it would have to be inconsistent with the results of whatever other axioms Anderson has chosen to use. What mathematicians would call it, however, is an old, uninteresting idea. There have been many others that postulated a placeholder "value" for infinity and explored the results of that assumption. Some of the results are even occasionally useful in simplifying useful calculations. And sometimes the alternative system produces results that don't map well onto reality, and the distinction between the cases is well-explored and well-understood.
I may be stating that too strongly, though. It's possible that Anderson has adjusted his definition in a way that makes it useful for a broader set of problems. Honestly, though, I doubt it. This is thoroughly plowed-over terrain.
I think it's most likely that Anderson has discovered some specific, important problems in optics(which involves some very high-powered mathematics, BTW, much more so than most engineering disciplines) that can be simplified by postulating a nullity, and that he published the work in an appropriate journal to an appreciative audience.
Note to ACs: I usually delete AC replies without reading them. If you want to talk to me, log in.
You persist in thinking that there is "right" math and "wrong" math. That is not true. Math is just a big pile of abstract formalisms. As long as they're self-consistent they're correct, by definition. What most people learn as math is just a small subset of mathematics which is relatively simple and maps well onto common, everyday reality.
If your goal is to teach kids how to count widgets and manipulate dollars, then there's no sense in exploring broader mathematical ideas. If your goal is to create budding young mathematicians, then it's a really good idea to expose them to the idea that math is both bigger and more malleable than the set of ideas their teachers are going to present.
The best, of course, is to do both. Give all of the kids a good grounding in ordinary arithmetic, geometry, algebra and (ideally) calculus since everyone needs arithmetic skills and many, many people need algebra and calc (including many who get by without it). While you're at it, though, throw in an occasional bit about the broader sweep of what mathematics is and what mathematicians do. Try to avoid confusing those that don't have the ability to think about such abstractions, but by all means exercise the potential of those that do, because there are more of them than you might think.
Finally, your crack about mathematicians being isolated from reality just shows that you don't know any mathematicians.
Note to ACs: I usually delete AC replies without reading them. If you want to talk to me, log in.
This is a LIGHT BULB JOKE. It may be only slightly funny, and it certainly isn't "insightful", but it's not a troll. It's a JOKE.
Shouldn't be a problem if you put a space before the exclamation point. :-)
Anyway, ambiguity can be fun. Perl modules need to evaluate to true, so people usually end them with "1". I usually wrote "3!=6", which is doubly true
Fuck the system? Nah, you might catch something.
The geometry of a Euclidean plane is, possibly, something that (pre-)human minds has indirectly handled for far longer than any counting beyond fingers and toes whatsoever... Real numbers aren't very fundamental, if they were, the mental resistance against irrational numbers would have been much lower.
I read most of the comments above me, but I didn't see any mention of this. Nullity is a term used in linear algebra to describe the dimension of the null space of a vector space. It isn't as widely used as rank is; however, it still exists.
It's not even a new symbol - it looks to me like capital phi.
The article seems lacking in detail. By contrast, proper mathmagicians can't even get to 2 without using a long and difficult proof.
My 2 cents: wouldn't 0/0 be the set of all complex numbers? If x = 0/0 then 0 = 0x would work for any x.
He introduced a multiplicative inverse for the additive identity (0), and added it to the real number field.
Unfortunately, he just complicates things, because he doesn't define how the + and * operators map up with it (nullity + a = ?)... if he doesn't then he breaks assoc/commu/trans properties (no longer a field then). And of course that number we need additive/mult inverses which may require nullity-prime, and so on, and he's just going in circles.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
So then this "nullity" just serves to make any value x for f(x)=(x)*(nullity) equal to any other number in R, all at once. That's either profound and interesting, or silly and impossible. Reminds me of quantum mechanics...
occultae nullus est respectus musicae - originally a Greek proverb
Congratulations on completely missing the mark and adding yourself to the group of clueless on slashdot. Do not pass go, do not score any marks for reading comprehension.
A theorem that guarantees the existence of a nice continuous version of a function does not help in any way when you're trying to do arithmetic with a non-continuous function. Do you know what arithmetic is? Do you know what a computer is? Do you realize that you're reading the work of a computer scientist discussing arithmetic for the specific purpose of proposing that computers use a different abstract machine model?
Your "argument from intuition" is not a good one. Mathematics often comes up with nonintuitive results. In fact, that's the point, in a way. Mathematics is a set of rules and a language meant for re-expressing known truths in forms that lead us to realize new truths, all by rearranging things by the rules of logic. Here's an example: exponents were created to describe the number of times you multiply a number together with itself to get an example. 2^6 is 2 multiplied by itself 6 times. So what sense does it make to raise a number to a negative power? Well, ok, it's dividing one by that number a certain number of times. Or how about a fractional power, even more bizarrely? It turns out that devising rules that "make sense" often only make sense in the context of exactly the kind of discussion this guy has, purely within the realm of mathematics. I'm not saying his idea is good, rather that your argument is bad. :-)
Currently hooked on AMP