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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."

My £100 (equivalent $200) will happily divide by Zero. It displays and "E" on the screen which I take to mean 14 in hex. So anything divided by Zero is 14. Apart from Zero divided by Zero which amusingly it consider to be Zero.

In fact, using proof-by-blatant-assertion,

if 0/0=14 then 0*14 must = 0 which it does therefore 0/0=14 so there !

Seriously though, as I understand it, this is simply another mathematical structure that allows a different scalar much like a real projective line, right? If that is the case, then there is nothing really new here and there can be no application or definition with real numbers or integers. Alternatively by interpreting this as a commutative ring, one might be able to extend this to where division by zero does not always get you in trouble, but the precise interpretation of "division" is fundamentally altered. This too is not a new concept.

However, all of that said, I am a bioscientist and my math skills are not as strong as a formally trained mathematician, so I will defer to those here who are stronger mathematicians than I if this interpretation is incorrect.

Perhaps. OTH, complex numbers are an incredibly useful tool in electrical engineering, yet were deemed so useless when first conceived that they were called imaginary numbers.

At first, numbers were integers - what you could count on your fingers. (N)
Later on, numbers were fractional - in order to express the sharing of things. (Q)
Later on, numbers were negative - in order to express debt. (Z)
Even later on, some numbers were found not to be fractionar (the first proved was square root of 2). Enter R
However, not every polinomial equation has its solutions as real numbers (see x^2+1=0). The solution to this equation was named i, with the property that i squared is -1. It was called imaginary because no real number had such property, and it is as real as a figment of your imagination;)
While other real numbers can be aproximated by integers, negative integers and fractional numbers (with better and better accuracy), i has no aproximation in any of the previous pools of numbers.
In engineering, a useful aproximation for pi is 3. There is no aproximation of i as an integer.

True, but I don't think he has created anything new (unlike complex numbers, which were new and even then had a function). Instead, he is saying that 0/0 is a nullity (the article appears somewhat misstated vs. the video). Well, that's just plain silly. How can you take nothing and divide it by nothing?

If anything 0/0 should be 0. If 1/2 of 0 is 0, and 1/4 of 0 is 0, etc. then 0/0 should also be 0. 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.

Re:Well, thats just nullty. (2, Interesting)

Anonymous Coward | more than 7 years ago | (#17142886)

however, the 'number' nullity has no plausible use - it is just a word for a concept we already understand, that division by zero yields an infinite range so is undefined.

Seriously though...if this interpretation is incorrect.

Your interpretation is correct but for proper mathematical representation it should be reduced to its simplest form.
While simpler reductions may be possible I believe the following best conveys the essence of the equation:
"Dr. Anderson is a pompous idiot."

like databases? (1, Funny)

Anonymous Coward | more than 7 years ago | (#17142588)

ah no, not the same thing. With databases, it means unknown.

Well, maybe it's the same thing. I didn't read the article.

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:

You've got that one upside down. You're dividing zero comments by the number of posters, which is definitely not zero, so the answer is regular old zero.

What he did was assign the previously "undefined" integer with a defined symbol that means the same thing. Infinity in both directions.

While interesting, the concept has little use.

From the article "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.". Now, instead of getting an error message, the computer give a 0 with a line through it, and THEN an error message.

Seriously, it sounds too close to null's, which makes database probramming a royal pain in the arse. Null's are like poison pills that propagate thru an expression and render it useless. This is perhaps useful for some numeric calculations, but a big mistake for strings. Example:

myString = A . B . C . D . E

Assume that "." is string concatenation. Under many RDBMS, if *any* of A, B, C, D, or E is null, the entire expression is null. This is rarely what one wants. One ends up putting a lot of null-fixer functions in expressions to prevent this kind of poison-pill approach. If I die and there is an afterlife, I will hunt down the person that made this a convention and make them eat a Null Pill so that their entire body (spirit?) is nullified. (And you don't want to hear what I'll do to the guy who invented neckties.)

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.

Infinity can also propagate through an expression because you know the sign.

From the example say your auto pilot does divide by 0 when trying to decide to go right or left(As if the ADA code in the air plane wouldn't throw an expression) you could propagate the result through subsequent expressions as + or - inifinity which means maximum possible bank right or left depending on the sign. I'd much rather have the additional sign information than invent a new type without it. (The IEEE floating point spec adds some additional confusion to a novice programmer: 1/x where x=0 equals positive infinity but the floating point hardware does not know how x varies. If x is an iterative variable that approaches from the negative side, it'd be more appropriate to say that 1/x when x gets to 0 = negative infinity)

However inventing higher forms of advanced math to solve safety critical problems is silly. Its up to the programmer to understand the range and possible inputs

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.

Uhm.. What? (0)

Anonymous Coward | more than 7 years ago | (#17142620)

So dividing by zero warps you from the regular number line to an alternate (nullity) number line. Does this make any sense to anyone?

He just created a new model, a new rule set, a new abstraction of math to deal with the case of "x/0". In general, dividing by zero is bad for most algorithms. I mean, from a CPU's perspective, I don't see how adding any additional hardware would help.

Too bad it is not a model of arithmetic. Nonstandard analysis, with its infinite and infinitessimals is, but you still can't divide by zero. IEEE floats, by the way, have both positive and negative infinity as well as NaN.

TFA is all but useless, mercifully so because I don't expect this "invention" breaks any new ground.

The article and Slashdot's synopsis don't make note of it, but Dr. Anderson isn't claiming to have discovered something new in dividing any number other than zero by itself. The video linked in the article shows him saying that 1/0 = infinity, and -1/0 = -infinity, but 0/0 = capital phi (nullity -- we'll ignore the fact that this usually means the golden ratio in mathematics). Math isn't my area of study so I don't know why 0/0 specifically is so important... the article certainly is very much a fluff piece. Anyone feel like explaining the importance of 0/0?

Re:Not just "division by zero", but 0/0 specifical (1)

I'm not a math-pro either, but just an idea.... If you divide any number (except 0), by zero you can take the limit of either side and you get -Inf or +Inf. Now, keep in mind that 0 divided by any number (except 0) is always 0: f(x)= x/0 = 0 (x element of R\{0}).

Now combine the two... By using the first statement (using limits), the result of 0/0 should be either -Inf or +Inf. By using the second statement the result should be 0... Somehow, thus, 0/0 should be -Inf, +Inf and 0 at once. Not that I see that as a problem, but hey, as I said: IANAMathematician.

1... 2... 3... Ah, there, is the mathematician with the Clueb *Ouch!*;-)

Re:Not just "division by zero", but 0/0 specifical (2, Funny)

describes how to divide by zero consistently in a non-trivial way. This shows that division by zero is no longer an error. Amongst other things, the paper explains why the standard model of arithmetic is not valid.

explains how to extend calculus so that it works with transreal numbers. This paper disposes of various counter "proofs" that attempt to show that division by zero is impossible. The paper ends with a very simple equation demonstrating the possibility of division by zero and challenges the reader to accept it.

This reminds me of arguing with my Algebra teacher in high school over "Imaginary Numbers". When asked where my homework was, my reply was a terse "It's Imaginary Homework, it's at home playing drinking games with the Imaginary Numbers it was on."

I am the first to admit math has NEVER been my strong suit, but are mathemeticians seriously just making up random rules as they go along so that soemthing which occurs to them suddenly works? Imaginary Numbers, changing the rules so that things work the way you want them to. Why is this (AFAIK) the only field to do this? How often do you hear a Physicist say "So, that whole gravity thing, yea we think it's really the opposite of that. What really happens is that mass PUSHES objects away from it, but they just suck so bad everything sticks anyway. What we've done with this (insert spiffy but questionable invention/theorem/etc here), is design something that would work well in this environment."

Nevermind, I think that does happen actually. But am I just missing the point entirely on this? I mean, even if I am, what does being able to divide by zero really get us? Can dividing by zero usher in some ultra new era for science as a whole? How will this affect computer systems in the next 1,5,10, and 20 years? What are the long term implications of this? If there aren't any, then really this is just a kid standing out in the yard swinging from a branch by their legs saying "Look Ma! No Hands!"

Now I am the last person that should be replying to you, and I'm wasted so it makes it even worse:/, but AFAIK imaginary numbers are considered "satisfactory" because during certain situations they can cancel each other other, therefore the "imaginary" equation becomes a real value. Once again it's been like 5 1/2 years since I've done math so.... (grain of salt)

Imaginary numbers (specifically, complex numbers, which consist of a sum of a real and an imaginary number, and which comprise the "complex plane") are INCREDIBLY important in the "real world."

I'm just a chemist, not a mathematician, but I am well aware that imaginary numbers are critical in the Fourier transforms used every time I take an IR or NMR spectrum.

Ever do electrical engineering? Circuit analysis is made a great deal easier when you can treat circuit elements in terms of complex numbers. All that "impedance" stuff you hear about capacitors and the like that makes it possible to apply Ohm's Law to LRC circuits.

These also are not merely made up properties, they are fundamental to mathematics and thus (if one believes that math is the language of the universe) physics. For example, certain integrals necessarily yield imaginary results. These integrals are not of some ethereal interest, but appear throughout quantum mechanics. This is why the amplitude of a wavefunction (used, for example, in molecular modeling that allows for practical achievements like better medicines) is not the square of the wave function (or, for that matter, its absolute value) but the product of the wavefunction and ITS COMPLEX CONJUGATE.

If you'd like more examples of the utility of complex numbers and other "random rules," check out Boas' "Mathematical Methods In The Physical Sciences."

In my Graphics class I learned about the Quaternion number field, which is essentially like multidimensional complex (real +imaginary) numbers. In addition to the familiar i, you also have j and k. There is a multiplication table showing what you get when you multiply these things with each other. Why are these useful? Because for some reason or other, they can be used to define 3D rotations "better" than just using two or three angles. And you can make quaternion splines to interpolate between various rotations, allowing you to specify key frames and getting an animation out of it. But it's a really weird sort of number to think about.

Re:Imaginary Numbers (2, Interesting)

Anonymous Coward | more than 7 years ago | (#17142744)

yea, actually, you are missing the point.

math is actually the science of making up rules. any real mathematician will tell you that the main idea of math is to start with as few basic axioms as possible, and come up with the rules of the system that follows. see: euclidean geometry, arithmetic. where do the axioms come from? historically, from observing the real world, people saw integers, real numbers, and euclidean geometry. more recently (meaning euclid and a few other clever early dudes, but otherwise in the last 150, maybe 200 years), the axioms are pretty much completely made up. some of them are based on those early systems, integers and real numbers. but there are a multitude of mathematical systems, of all varieties, that have no real world counterpart. and thats what makes it fun.

as for division by zero, it gets us nowhere. the system of arithmetic and real numbers doesn't define division by zero, because that system is used for modeling the real world, where division by zero is meaningless. if you paid attention to the paragraph above, however, you should realize how easy it is to come up with a system where division by zero is clearly defined. my favorite example is the riemann sphere, which can be seen as an extension of the projective real line. of course, in ieee floating point, division by zero is very clearly defined. the result doesn't have a "value" but you can do it, and if you do, your plane doesnt crash.

in short, james anderson is an idiot. yes, i am basing this on my reading of the summary and (pointlessly vacuous) article. if only the video explanation weren't real format...

Unfortunately I don't have Real installed to watch this nullity explanation, but I think you're way off base with "imaginary" (now, better known as "complex") numbers. Being able to do math with complex numbers is one of the major reasons all those electrical circuits in your computer and home work. it's a logical construct and has significant practical purpose. As for nullity? Who knows.

Btw, am I the only person who thinks that a pacemaker or any kind of truly mission critical device that "attempts to divide by zero" will not "simply crash?" You'd figure there would be some kind of failsafe in the code that goes at least a step beyond the old B-Movie "THIS DOES NOT COMPUTE...OVERLOAD! OVERLOAD! ARGHHHH...."

I hate to put it this way, but "It'll make sense when you're older". And by older, I mean when you take a higher math course. What is the square root of -1 equal to then? Nothing? Something? Saying it's "imaginary" is merely a construct that allows us to muck with things. We could say they're "happy fun times" numbers, with the symbol "hft", and it'd mean the same thing.

Note: IAAM(athematician). You pose a good question. The game in mathematics, though, is not to "make up random rules so that something that occurs to them suddenly works". It's (broadly speaking) to make up new rules which are completely consistent with all the old rules which allow us to understand a previously mysterious example. This is where "imaginary" numbers succeed tremendously, and "nullity" fails miserably. See my post downthread for why nullity sucks.

"Imaginary" numbers are just the "thingys" which are solutions to polynomials. I.e., mathematicians find it useful to have an answer to the question "for what values of x does x^2 + 1 = 0?" The answers are useful, even though they aren't good at measuring length or breadth or depth or other one-dimensional concepts. They're useful because they allow mathematicians to develop a theory which has answered questions which couldn't be answered before. This is true even though both the question and the answer both lie in the realm of real numbers. Should there be an answer to every question of this type that doesn't use complex numbers? Perhaps, but it certainly doesn't have to be pretty, or easy to discover. Often the shortest path to a "real" truth lies on an "imaginary" line.

Imaginary numbers are a perfectly valid construct, but yes, it's a bad name. Once you start dealing with electrical engineering, imaginary/complex numbers become very useful. The best way to think of them is a number system perpendicular to the one based on 'real' numbers. This allows you to simplify the maths (or even make possible maths that wasn't possible before) when dealing with things like AC waves and phases. Engineers do similar tricks where they substitute a symbol in for a specific function.

It's sort of the mathematical version of using arrays, or variables, it's simply a way of representing 'the real world' in a simpler, more manageable way.

Re:Imaginary Numbers (0)

Anonymous Coward | more than 7 years ago | (#17142928)

Imaginary numbers are useful when dealing with entities that have multiple quantitative attributes eg. electrical components that have both capacitance and inductance.

-1 (natural, linear numbering) is really (-1, 0) or (-1 + 0i).

Re: Limits Anyone? (0)

Anonymous Coward | more than 7 years ago | (#17142668)

Last time I checked, the limit of 1/x for all x positive as x goes to zero is......infinity. The simplest solution to most limits is to substitute the limit, in this case 0, into the problem. As you can see, 1/0 would render, by the professor's solution nullity, which is inconsistent with infinity. Multiplicity of representations should all yield the same results, it is a foundation of mathematics, add 1 to both sides of the equation, and you still have the same answer. Draw your own conclusions.

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"...... (2, Insightful)

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!"

"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."

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.

If it ain't broke, don't fix it (0)

Anonymous Coward | more than 7 years ago | (#17142692)

"... solves the 1200 year old problem that niether Newton nor Pythagoras could solve..."

This is a joke or they don't know what they're talking about--Pythagoras lived roughly 2500 years ago.

It was new problem 1200 years ago that Pythagoras didn't know about 2500 years ago. Time travel has not yet been invented to fix these historical screw ups.

It's sad that he teaches math and thinks this is a worthwhile concept.

For just one example of why it sucks, he BEGINS by defining: (infinity) = 1/0 and
(-infinity) = -1/0.
My conclusion: (0)*(infinity)=1
So 2*0*infinity = 2*1
So 2 = 2*0*infinity = (2*0)*infinity = 0*infinity = 1
And once you know that 2 != 1 and 2 =1, it turns out you can prove quite a bit...

Total nonsense, and the BBC is encouraging it. *shakes head* Although, I've got to say, it's nice, for once in my life, to deservedly be a smug American.

Re:Sad, really... (0)

Anonymous Coward | more than 7 years ago | (#17142806)

Signed and dated. I'm now ashamed to work for the BBC.

Your algebraic conclusions are essentially off-target for the same reason that you have to be careful about how you apply the law of associativity to infinite sums. We all should have seen at one point or another the "proof" that 1=0 that goes:

1=1+(-1+1)+(-1+1)...=(1-1)+(1-1)+...=0

This is not a proof of anything precisely because the associative law doesn't necessarily apply to infinite sums. Infinities of any sort are strange in that manner, and so basically all of your algebra is.

Another good example is limits of sequences, which anyone that has ever taken a basic calculus course is familiar with. Suppose we have a sequence a_n=f(n)/g(n), then while lim as n->infinity might look like 0/0, but we can in fact take the derivative of both f(n) and g(n) and find something that isn't of the indeterminate form, and find the true limit.

Now (0)

Anonymous Coward | more than 7 years ago | (#17142716)

Just tell me what is to happen If I were to divide 5 apples among 0 kids.

This seems to be as useful to a physicist as imaginary number. It may come up in calculations and solutions but any physicist would be laugh out of the conference room if ever equated a measureable quantity to an number with imaginary component. The problem lies in the fact that nullity lacks a physical analog. Call 0/0 anything you want but in the end it useless without knowingwhat a nullity of anything represents. Thank you for participating. NEXT!!!!

That's a good point. Physics make frequent use of the (much) richer structure provided by the mathematics of complex numbers, quaternions, abstract vector states, you-name-it, but at the end of the day, we only measure real things, and the mathematics only helps to predict what we might (really) see.
That having been said, this doesn't really seem like anything new. Perhaps it adds some subtle structure, but I'll wait until I can read a paper...

Seriously, in elementary school a teacher of mine tried to tell us that 1/0 = infinity

Read up on the definition of division [wikipedia.org] . 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).

New Definition (0)

Anonymous Coward | more than 7 years ago | (#17142800)

nullity: The ratio of women this guy has had in his bedroom to the number who slept with him.

I can prove he's a Quack. (0)

Anonymous Coward | more than 7 years ago | (#17142814)

No math teacher would ever refer to positive and minus infinity.

Last updated 6/12/2006, so not only is this story completly worthless (as anyone who even remotley understood Calc 1 could tell you), but it's 6 months old. Good job slashdot!

Anonymous Coward | more than 7 years ago | (#17142824)

My computer divides with 0 just fine.

> 1/0 inf > atan(1/0)*180/pi 90

I discovered that by accident - wrote a little 3D game, and after getting it to work, it occured to me that walking straight to the east (i.e. 90 degrees) would give me a direction vector of (1,0), which would then make the game calculate 1/0 to find out the angle. Huh? Why doesn't it crash? Let me just try a little test... atan(1/0)*180/pi (the *180/pi part is to get degrees): 90 degrees. So not only does it divide by zero just fine, it even does further calculations on the result, coming up with the correct angle.

Anyway, some people have mentioned that he probably didn't invent inf, but NaN. Nothing new about that either, but NaN does not allow further calculations (the result stays NaN), as the value as NaN is really undefined (where as inf has a defined (albeit abstract) value). Because x/x = 1, and 0/x = 0, the case of x=0 would give 0/0 = 0 and 1 at the same time. Can't do further calculations on that. So, basically he didn't invent any new math, he just came up with a new symbol for NaN. And started teaching it at a lower grade than usual.

Now, where is the "news for nerds" part? I would assume that most "nerds" are a least a little bit of math geeks, and thus, someone "inventing" NaN shouldn't be news at all.

Anonymous Coward | more than 7 years ago | (#17142876)

1. Slashdot should come up with a new section 'jokes'. 2. All editors post there. 3. Let the mod system also turn some readers into editors for a short while.

... where you can actually determine meaningful values for 0/0 in specific cases via calculus?
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_rule [wikipedia.org]

Seriously, it's hard to take someone like this seriously when he uses ignorant scare tactics such as his autopilot example. Either he's performing self aggrandizing hand waving, or he really is completely ignorant about the real world. Trust me - we do account for division by zero in autopilot systems. And - believe it or not - not only does the computer not "stop working" but we actually get a result back. It's called NaN [wikipedia.org] . Furthermore, not only are our systems built with robust libraries that allow us to carry on (no pun intended) we also write downstream code to mitigate propagation of these types of errors. [see Celarier, Sando [acm.org] for a good example of this].

No, he didn't solve it (0)

Anonymous Coward | more than 7 years ago | (#17142904)

He didn't solve the division-by-zero problem at all, he just hid it under a new definition; "nullity".

It's like saying.. what's beyond the end of the universe? Nobody knows.

Oh, wait, I do! It's "schmullity".

Yup, now we know what's beyond the universe's borders. No need to investigate any further.

"Here you see the pattern from which my great work is derived. It expresses the symbolic significance of NULLITY to which TOTALITY must necessarily attach itself, by Kratinjae's Second Law of Cryptorrhoid Affinities, with which you are possibly familiar."

## Argh!!! (5, Funny)

## Travoltus (110240) | more than 7 years ago | (#17142572)

## Re:Argh!!! (5, Funny)

## MountainMan101 (714389) | more than 7 years ago | (#17142632)

In fact, using proof-by-blatant-assertion,

if 0/0=14

then 0*14 must = 0

which it does

therefore 0/0=14

so there !

## Re:Argh!!! (5, Funny)

## buswolley (591500) | more than 7 years ago | (#17142912)

Why is the algorithm producing that? Oh I introduced a nullity.

Furthermore, they shouldn't have called it a nullity. They should have called it a Bush.

## Well, thats just nullty. (5, Interesting)

## BWJones (18351) | more than 7 years ago | (#17142574)

His new number, which he calls "nullity"Well, thats just nullty.

Seriously though, as I understand it, this is simply another mathematical structure that allows a different scalar much like a real projective line, right? If that is the case, then there is nothing really new here and there can be no application or definition with real numbers or integers. Alternatively by interpreting this as a commutative ring, one might be able to extend this to where division by zero does not always get you in trouble, but the precise interpretation of "division" is fundamentally altered. This too is not a new concept.

However, all of that said, I am a bioscientist and my math skills are not as strong as a formally trained mathematician, so I will defer to those here who are stronger mathematicians than I if this interpretation is incorrect.

## Re:Well, thats just nullty. (5, Interesting)

## RodgerDodger (575834) | more than 7 years ago | (#17142660)

## Re:Well, thats just nullty. (4, Informative)

## Calinous (985536) | more than 7 years ago | (#17142860)

## Re:Well, thats just nullty. (1)

## Salvance (1014001) | more than 7 years ago | (#17142868)

If anything 0/0 should be 0. If 1/2 of 0 is 0, and 1/4 of 0 is 0, etc. then 0/0 should also be 0. 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.

## Re:Well, thats just nullty. (2, Interesting)

## Anonymous Coward | more than 7 years ago | (#17142886)

## Re:Well, thats just nullty. (1)

## creimer (824291) | more than 7 years ago | (#17142694)

## Re:Well, thats just nullty. (-1, Flamebait)

## Jason Lind (683680) | more than 7 years ago | (#17142726)

## Re:Well, thats just nullty. (1)

## creimer (824291) | more than 7 years ago | (#17142788)

## Re:Well, thats just nullty. (0)

## Anonymous Coward | more than 7 years ago | (#17142834)

You don't understand it.

## Re:Well, thats just nullty. (5, Funny)

## itwerx (165526) | more than 7 years ago | (#17142900)

Seriously though...if this interpretation is incorrect.Your interpretation is correct but for proper mathematical representation it should be reduced to its simplest form.

While simpler reductions may be possible I believe the following best conveys the essence of the equation:

"Dr. Anderson is a pompous idiot."

## like databases? (1, Funny)

## Anonymous Coward | more than 7 years ago | (#17142588)

Well, maybe it's the same thing. I didn't read the article.

## Not everyone's happy (5, Funny)

## BadAnalogyGuy (945258) | more than 7 years ago | (#17142590)

## Umm... NaN? (5, Funny)

## The boojum (70419) | more than 7 years ago | (#17142596)

## Re:Umm... NaN? (0)

## Anonymous Coward | more than 7 years ago | (#17142648)

(funny, captcha is "megabits")

## YaNaN? (3, Funny)

## Marbleless (640965) | more than 7 years ago | (#17142696)

## Re:Umm... NaN? (3, Funny)

## Tablizer (95088) | more than 7 years ago | (#17142712)

Is it just me or does it sound like he thinks he's invented the NaN?But he gets the credit because "Nullity" sounds smarter, so Nanny Nan Na to you!

## Re:Umm... NaN? (5, Insightful)

## El_Muerte_TDS (592157) | more than 7 years ago | (#17142766)

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

## Re:Umm... NaN? (4, Funny)

## creimer (824291) | more than 7 years ago | (#17142802)

## Hmm (5, Funny)

## mdemonic (988470) | more than 7 years ago | (#17142600)

## Re:Hmm (1)

## ceoyoyo (59147) | more than 7 years ago | (#17142630)

## Re:Hmm (1)

## mdemonic (988470) | more than 7 years ago | (#17142670)

## Re:Hmm (2, Informative)

## whmac33 (524094) | more than 7 years ago | (#17142700)

## Re:Hmm (1)

## NETHED (258016) | more than 7 years ago | (#17142634)

But seriously, great comment

## But wait (1, Redundant)

## iriefrank (41550) | more than 7 years ago | (#17142604)

## Audio/Video is Real-encoded (2)

## BadAnalogyGuy (945258) | more than 7 years ago | (#17142606)

## And this is important, why? (5, Funny)

## NETHED (258016) | more than 7 years ago | (#17142618)

What he did was assign the previously "undefined" integer with a defined symbol that means the same thing. Infinity in both directions.

While interesting, the concept has little use.

From the article

"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.".Now, instead of getting an error message, the computer give a 0 with a line through it, and THEN an error message.

## Re:And this is important, why? (2, Interesting)

## Tablizer (95088) | more than 7 years ago | (#17142690)

I can make up numbers too...Let's call it "snerg".

Seriously, it sounds too close to null's, which makes database probramming a royal pain in the arse. Null's are like poison pills that propagate thru an expression and render it useless. This is perhaps useful for some numeric calculations, but a big mistake for strings. Example:

myString = A . B . C . D . E

Assume that "." is string concatenation. Under many RDBMS, if *any* of A, B, C, D, or E is null, the entire expression is null. This is rarely what one wants. One ends up putting a lot of null-fixer functions in expressions to prevent this kind of poison-pill approach. If I die and there is an afterlife, I will hunt down the person that made this a convention and make them eat a Null Pill so that their entire body (spirit?) is nullified. (And you don't want to hear what I'll do to the guy who invented neckties.)

## Re:And this is important, why? (4, Insightful)

## jrockway (229604) | more than 7 years ago | (#17142838)

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.

## Re:And this is important, why? (1)

## Nyall (646782) | more than 7 years ago | (#17142890)

From the example say your auto pilot does divide by 0 when trying to decide to go right or left(As if the ADA code in the air plane wouldn't throw an expression) you could propagate the result through subsequent expressions as + or - inifinity which means maximum possible bank right or left depending on the sign. I'd much rather have the additional sign information than invent a new type without it. (The IEEE floating point spec adds some additional confusion to a novice programmer: 1/x where x=0 equals positive infinity but the floating point hardware does not know how x varies. If x is an iterative variable that approaches from the negative side, it'd be more appropriate to say that 1/x when x gets to 0 = negative infinity)

However inventing higher forms of advanced math to solve safety critical problems is silly. Its up to the programmer to understand the range and possible inputs

## Re:And this is important, why? (2, Insightful)

## dbIII (701233) | more than 7 years ago | (#17142764)

## Uhm.. What? (0)

## Anonymous Coward | more than 7 years ago | (#17142620)

## Re:Uhm.. What? (1)

## advocate_one (662832) | more than 7 years ago | (#17142780)

about as much sense as the square root of -1 does... that concept has proved highly useful...

## Warp Zone! (2, Funny)

## Fallingcow (213461) | more than 7 years ago | (#17142894)

## mod post up by ... (5, Funny)

## b1ufox (987621) | more than 7 years ago | (#17142638)

## Re:mod post up by ... (2, Funny)

## Tablizer (95088) | more than 7 years ago | (#17142762)

mod original post up by 0/0 points :) Well, that explains all the goddam dupes

## That's quite exceptional (0)

## Anonymous Coward | more than 7 years ago | (#17142642)

-NaN

## didn't "solve" anything (2, Interesting)

## Doppler00 (534739) | more than 7 years ago | (#17142644)

## Re:didn't "solve" anything (1)

## thestuckmud (955767) | more than 7 years ago | (#17142738)

TFA is all but useless, mercifully so because I don't expect this "invention" breaks any new ground.

## Rubbish (4, Funny)

## Mkoms (910273) | more than 7 years ago | (#17142650)

## Re:Rubbish (1, Funny)

## neuro.slug (628600) | more than 7 years ago | (#17142760)

## Not just "division by zero", but 0/0 specifically (2, Informative)

## RobHornick (170481) | more than 7 years ago | (#17142654)

## Re:Not just "division by zero", but 0/0 specifical (1)

## RobHornick (170481) | more than 7 years ago | (#17142664)

## Re:Not just "division by zero", but 0/0 specifical (1)

## jawtheshark (198669) | more than 7 years ago | (#17142734)

I'm not a math-pro either, but just an idea.... If you divide any number (except 0), by zero you can take the limit of either side and you get -Inf or +Inf. Now, keep in mind that 0 divided by any number (except 0) is always 0: f(x)= x/0 = 0 (x element of R\{0}).

Now combine the two... By using the first statement (using limits), the result of 0/0 should be either -Inf or +Inf. By using the second statement the result should be 0... Somehow, thus, 0/0 should be -Inf, +Inf and 0 at once. Not that I see that as a problem, but hey, as I said: IANAMathematician.

1... 2... 3... Ah, there, is the mathematician with the Clueb *Ouch!* ;-)

## Re:Not just "division by zero", but 0/0 specifical (2, Funny)

## creimer (824291) | more than 7 years ago | (#17142828)

Anyone feel like explaining the importance of 0/0?It's what math professors think about when they're too old to bonk a student during those intense one-on-one tutoring sessions.

## Dr. James Anderson's actual papers (5, Informative)

## Bananatree3 (872975) | more than 7 years ago | (#17142902)

The first paper [bookofparagon.com] he describes as:

The second paper [bookofparagon.com] he says:

## Imaginary Numbers (-1, Flamebait)

## PixieDust (971386) | more than 7 years ago | (#17142658)

I am the first to admit math has NEVER been my strong suit, but are mathemeticians seriously just making up random rules as they go along so that soemthing which occurs to them suddenly works? Imaginary Numbers, changing the rules so that things work the way you want them to. Why is this (AFAIK) the only field to do this? How often do you hear a Physicist say "So, that whole gravity thing, yea we think it's really the opposite of that. What really happens is that mass PUSHES objects away from it, but they just suck so bad everything sticks anyway. What we've done with this (insert spiffy but questionable invention/theorem/etc here), is design something that would work well in this environment."

Nevermind, I think that does happen actually. But am I just missing the point entirely on this? I mean, even if I am, what does being able to divide by zero really get us? Can dividing by zero usher in some ultra new era for science as a whole? How will this affect computer systems in the next 1,5,10, and 20 years? What are the long term implications of this? If there aren't any, then really this is just a kid standing out in the yard swinging from a branch by their legs saying "Look Ma! No Hands!"

## Re:Imaginary Numbers (1)

## ET_Fleshy (829048) | more than 7 years ago | (#17142720)

lastperson that should be replying to you, and I'm wasted so it makes it even worse## Re:Imaginary Numbers (5, Informative)

## Alchemist253 (992849) | more than 7 years ago | (#17142722)

Imaginary numbers (specifically, complex numbers, which consist of a sum of a real and an imaginary number, and which comprise the "complex plane") are INCREDIBLY important in the "real world."

I'm just a chemist, not a mathematician, but I am well aware that imaginary numbers are critical in the Fourier transforms used every time I take an IR or NMR spectrum.

Ever do electrical engineering? Circuit analysis is made a great deal easier when you can treat circuit elements in terms of complex numbers. All that "impedance" stuff you hear about capacitors and the like that makes it possible to apply Ohm's Law to LRC circuits.

These also are not merely made up properties, they are fundamental to mathematics and thus (if one believes that math is the language of the universe) physics. For example, certain integrals necessarily yield imaginary results. These integrals are not of some ethereal interest, but appear throughout quantum mechanics. This is why the amplitude of a wavefunction (used, for example, in molecular modeling that allows for practical achievements like better medicines) is not the square of the wave function (or, for that matter, its absolute value) but the product of the wavefunction and ITS COMPLEX CONJUGATE.

If you'd like more examples of the utility of complex numbers and other "random rules," check out Boas' "Mathematical Methods In The Physical Sciences."

## Re:Imaginary Numbers (2, Interesting)

## lexarius (560925) | more than 7 years ago | (#17142742)

## Re:Imaginary Numbers (2, Interesting)

## Anonymous Coward | more than 7 years ago | (#17142744)

math is actually the science of making up rules. any real mathematician will tell you that the main idea of math is to start with as few basic axioms as possible, and come up with the rules of the system that follows. see: euclidean geometry, arithmetic. where do the axioms come from? historically, from observing the real world, people saw integers, real numbers, and euclidean geometry. more recently (meaning euclid and a few other clever early dudes, but otherwise in the last 150, maybe 200 years), the axioms are pretty much completely made up. some of them are based on those early systems, integers and real numbers. but there are a multitude of mathematical systems, of all varieties, that have no real world counterpart. and thats what makes it fun.

as for division by zero, it gets us nowhere. the system of arithmetic and real numbers doesn't define division by zero, because that system is used for modeling the real world, where division by zero is meaningless. if you paid attention to the paragraph above, however, you should realize how easy it is to come up with a system where division by zero is clearly defined. my favorite example is the riemann sphere, which can be seen as an extension of the projective real line. of course, in ieee floating point, division by zero is very clearly defined. the result doesn't have a "value" but you can do it, and if you do, your plane doesnt crash.

in short, james anderson is an idiot. yes, i am basing this on my reading of the summary and (pointlessly vacuous) article. if only the video explanation weren't real format...

## Re:Imaginary Numbers (1)

## TheGuano (851573) | more than 7 years ago | (#17142758)

Btw, am I the only person who thinks that a pacemaker or any kind of truly mission critical device that "attempts to divide by zero" will not "simply crash?" You'd figure there would be some kind of failsafe in the code that goes at least a step beyond the old B-Movie "THIS DOES NOT COMPUTE...OVERLOAD! OVERLOAD! ARGHHHH...."

## Re:Imaginary Numbers (3, Informative)

## Koiu Lpoi (632570) | more than 7 years ago | (#17142778)

## Re:Imaginary Numbers (4, Insightful)

## RodgerDodger (575834) | more than 7 years ago | (#17142786)

People take mathematical tools and models and apply them to the real world because they are useful. However, that usefulness is a lucky accident.

## Re:Imaginary Numbers (1)

## Tomfrh (719891) | more than 7 years ago | (#17142818)

I am the first to admit math has NEVER been my strong suitYeah?

## Re:Imaginary Numbers (5, Interesting)

## lexDysic (542023) | more than 7 years ago | (#17142842)

completely consistent with all the old ruleswhich allow us to understand a previously mysterious example. This is where "imaginary" numbers succeed tremendously, and "nullity" fails miserably. See my post downthread for why nullity sucks."Imaginary" numbers are just the "thingys" which are solutions to polynomials. I.e., mathematicians find it useful to have an answer to the question "for what values of x does x^2 + 1 = 0?" The answers are useful, even though they aren't good at measuring length or breadth or depth or other one-dimensional concepts. They're useful because they allow mathematicians to develop a theory which has answered questions which couldn't be answered before. This is true even though both the question and the answer both lie in the realm of real numbers.

Shouldthere be an answer to every question of this type that doesn't use complex numbers? Perhaps, but it certainly doesn't have to be pretty, or easy to discover. Often the shortest path to a "real" truth lies on an "imaginary" line.## Re:Imaginary Numbers (1)

## arkhan_jg (618674) | more than 7 years ago | (#17142926)

The best way to think of them is a number system perpendicular to the one based on 'real' numbers. This allows you to simplify the maths (or even make possible maths that wasn't possible before) when dealing with things like AC waves and phases. Engineers do similar tricks where they substitute a symbol in for a specific function.

It's sort of the mathematical version of using arrays, or variables, it's simply a way of representing 'the real world' in a simpler, more manageable way.

## Re:Imaginary Numbers (0)

## Anonymous Coward | more than 7 years ago | (#17142928)

-1 (natural, linear numbering) is really (-1, 0) or (-1 + 0i).

## Re: Limits Anyone? (0)

## Anonymous Coward | more than 7 years ago | (#17142668)

## Re: Limits Anyone? (4, Informative)

## poopdeville (841677) | more than 7 years ago | (#17142870)

You can only perform the substitution lim x->a f(x) = f(a) when f is continuous at a. f(x) = 1/x is (very trivially) not continous at a = 0.

Damnit, why is this sort of thing spilling over from sci.math now?

## The "nullity" Professor... (1)

## agent (7471) | more than 7 years ago | (#17142672)

The Jesus cross in the symbol needs to be bigger!

My bank account is a "nullity".

## NaN (2, Insightful)

## allankim (558661) | more than 7 years ago | (#17142674)

## Dividing by zero is not a "problem"...... (2, Insightful)

## ACAx1985 (989265) | more than 7 years ago | (#17142676)

## Oh, God... (1, Insightful)

## creimer (824291) | more than 7 years ago | (#17142682)

(These old folks know how to scream!)

## Since when is this new? (1)

## Xeriar (456730) | more than 7 years ago | (#17142684)

## testing, exception handling etc. (4, Insightful)

## bananaendian (928499) | more than 7 years ago | (#17142686)

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.

## If it ain't broke, don't fix it (0)

## Anonymous Coward | more than 7 years ago | (#17142692)

This is a joke or they don't know what they're talking about--Pythagoras lived roughly 2500 years ago.

## Re:If it ain't broke, don't fix it (1)

## creimer (824291) | more than 7 years ago | (#17142844)

## Bobby Newmark... (1)

## drapeau06 (1010311) | more than 7 years ago | (#17142702)

## Sad, really... (5, Interesting)

## lexDysic (542023) | more than 7 years ago | (#17142708)

For just one example of why it sucks, he BEGINS by defining: (infinity) = 1/0 and (-infinity) = -1/0.

My conclusion: (0)*(infinity)=1

So 2*0*infinity = 2*1

So 2 = 2*0*infinity = (2*0)*infinity = 0*infinity = 1

And once you know that 2 != 1 and 2 =1, it turns out you can prove quite a bit...

Total nonsense, and the BBC is encouraging it. *shakes head* Although, I've got to say, it's nice, for once in my life, to

deservedlybe a smug American.## Re:Sad, really... (0)

## Anonymous Coward | more than 7 years ago | (#17142806)

I'm now ashamed to work for the BBC.

## Re:Sad, really... (2, Insightful)

## Rhinobird (151521) | more than 7 years ago | (#17142884)

0*infinity=nullity

0 * infinitity becomes:

(0)*(1/0) becomes:

(0*1)/0 becomes:

0/0 = nullity

## Re:Sad, really... (1)

## sohare (1032056) | more than 7 years ago | (#17142914)

1=1+(-1+1)+(-1+1)...=(1-1)+(1-1)+...=0

This is not a proof of anything precisely because the associative law doesn't necessarily apply to infinite sums. Infinities of any sort are strange in that manner, and so basically all of your algebra is.

Another good example is limits of sequences, which anyone that has ever taken a basic calculus course is familiar with. Suppose we have a sequence a_n=f(n)/g(n), then while lim as n->infinity might look like 0/0, but we can in fact take the derivative of both f(n) and g(n) and find something that isn't of the indeterminate form, and find the true limit.

## Now (0)

## Anonymous Coward | more than 7 years ago | (#17142716)

## Re:Now (1)

## Eco-Mono (978899) | more than 7 years ago | (#17142756)

## Finally! (0)

## Tablizer (95088) | more than 7 years ago | (#17142732)

## Nothing to see here, people... (5, Funny)

## Lord Aurora (969557) | more than 7 years ago | (#17142740)

Helpful little hint from the end of the video:

Yeah. It was that simple.

I'm just reminded of that proof from way-back-when that 2 = 1:

All this guy has done is provide another little fun "proof" that you can use to win bar bets. "Betcha I can divide by zero..."

## Re:Nothing to see here, people... (1)

## vinnythenose (214595) | more than 7 years ago | (#17142922)

All you've done is said 2 * 0 = 1 * 0 then divided both sides by 0.

So this one "proof" can prove 2 = 1, 0 = 0, infinity = infinity and indeterminate = indeterminate.

AHH MY HEAD HURTS!!

Now to go on and prove that black is white and get killed in the next zebra crossing.

## I don't think he help the physicists (1)

## Enrique1218 (603187) | more than 7 years ago | (#17142746)

## Re:I don't think he help the physicists (1)

## Gil-galad55 (707960) | more than 7 years ago | (#17142782)

## I suspect (3, Interesting)

## the_tsi (19767) | more than 7 years ago | (#17142750)

## Even I knew this was wrong as a 10 year old (4, Insightful)

## joe_cot (1011355) | more than 7 years ago | (#17142784)

Read up on the definition of division [wikipedia.org] . 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

realidea is that, for an equation 1/x = y, yapproachesinfinity as xapproaches0. 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).

## New Definition (0)

## Anonymous Coward | more than 7 years ago | (#17142800)

## I can prove he's a Quack. (0)

## Anonymous Coward | more than 7 years ago | (#17142814)

minusinfinity.## Not just old, but wrong too (1)

## Jason Lind (683680) | more than 7 years ago | (#17142816)

## Re:Not just old, but wrong too (1)

## MeanMF (631837) | more than 7 years ago | (#17142850)

## Re:Not just old, but wrong too (1)

## 01arena (890407) | more than 7 years ago | (#17142880)

## Re:Not just old, but wrong too (1)

## Xayma (892821) | more than 7 years ago | (#17142888)

## Re:Not just old, but wrong too (1)

## Jason Lind (683680) | more than 7 years ago | (#17142908)

## My computer can divide with 0. (0)

## Anonymous Coward | more than 7 years ago | (#17142824)

> 1/0

inf

> atan(1/0)*180/pi

90

I discovered that by accident - wrote a little 3D game, and after getting it to work, it occured to me that walking straight to the east (i.e. 90 degrees) would give me a direction vector of (1,0), which would then make the game calculate 1/0 to find out the angle. Huh? Why doesn't it crash? Let me just try a little test... atan(1/0)*180/pi (the *180/pi part is to get degrees): 90 degrees. So not only does it divide by zero just fine, it even does further calculations on the result, coming up with the correct angle.

Anyway, some people have mentioned that he probably didn't invent inf, but NaN. Nothing new about that either, but NaN does not allow further calculations (the result stays NaN), as the value as NaN is really undefined (where as inf has a defined (albeit abstract) value). Because x/x = 1, and 0/x = 0, the case of x=0 would give 0/0 = 0 and 1 at the same time. Can't do further calculations on that. So, basically he didn't invent any new math, he just came up with a new symbol for NaN. And started teaching it at a lower grade than usual.

Now, where is the "news for nerds" part? I would assume that most "nerds" are a least a little bit of math geeks, and thus, someone "inventing" NaN shouldn't be news at all.

## So... (1)

## frank_adrian314159 (469671) | more than 7 years ago | (#17142852)

## Suggestion. Mod me offtopic but heck (0)

## Anonymous Coward | more than 7 years ago | (#17142876)

2. All editors post there.

3. Let the mod system also turn some readers into editors for a short while.

## What about l'Hopital? (2, Insightful)

## rrohbeck (944847) | more than 7 years ago | (#17142892)

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

## Awesome! (2, Informative)

## derubergeek (594673) | more than 7 years ago | (#17142898)

This fantastic new math is also helpful in solving this intractable problem: http://mcraefamily.com/MathHelp/JokeProofFactoring .htm [mcraefamily.com]

How cool is that?

Seriously, it's hard to take someone like this seriously when he uses ignorant scare tactics such as his autopilot example. Either he's performing self aggrandizing hand waving, or he really is completely ignorant about the real world. Trust me - we do account for division by zero in autopilot systems. And - believe it or not - not only does the computer not "stop working" but we actually get a result back. It's called NaN [wikipedia.org] . Furthermore, not only are our systems built with robust libraries that allow us to carry on (no pun intended) we also write downstream code to mitigate propagation of these types of errors. [see Celarier, Sando [acm.org] for a good example of this].

## No, he didn't solve it (0)

## Anonymous Coward | more than 7 years ago | (#17142904)

It's like saying.. what's beyond the end of the universe? Nobody knows.

Oh, wait, I do! It's "schmullity".

Yup, now we know what's beyond the universe's borders. No need to investigate any further.

## Nothing new here (1)

## Neeth (887729) | more than 7 years ago | (#17142906)

"Here you see the pattern from which my great work is derived. It expresses the symbolic significance of NULLITY to which TOTALITY must necessarily attach itself, by Kratinjae's Second Law of Cryptorrhoid Affinities, with which you are possibly familiar."

## Oooo... Actual papers! (1)

## realbadjuju (870896) | more than 7 years ago | (#17142910)

## it's another imaginary number (1)

## gogodidi (885953) | more than 7 years ago | (#17142920)