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Math Science

Professor Comes Up With a Way to Divide by Zero 1090

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."
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Professor Comes Up With a Way to Divide by Zero

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  • Argh!!! (Score:5, Funny)

    by Travoltus ( 110240 ) on Thursday December 07, 2006 @03:02AM (#17142572) Journal
    So much for my $200 calculator.
    • Re:Argh!!! (Score:5, Funny)

      by MountainMan101 ( 714389 ) on Thursday December 07, 2006 @03:09AM (#17142632)
      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 !
      • Re:Argh!!! (Score:5, Funny)

        by buswolley ( 591500 ) on Thursday December 07, 2006 @03:53AM (#17142912) Journal
        Great, a whole new class of errors just got introduced into my code.

        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.

    • Re:Argh!!! (Score:5, Funny)

      by fintler ( 140604 ) on Thursday December 07, 2006 @08:31AM (#17144226)
      So much for my $200 calculator.

      wait, you paid $200 for a calculator?

      b = $100
      a = b
      a^2 = ab
      a^2-b^2 = ab-b^2
      (a+b)(a-b) = b(a-b)
      a+b = b
      since a = b
      b+b = b
      2b = b
      $200 = $100

      They ripped you off. $200 is really only worth $100
  • by BWJones ( 18351 ) * on Thursday December 07, 2006 @03:02AM (#17142574) Homepage Journal
    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.

    • by RodgerDodger ( 575834 ) on Thursday December 07, 2006 @03:14AM (#17142660)
      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.
      • by Calinous ( 985536 ) on Thursday December 07, 2006 @03:44AM (#17142860)
        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.
      • by Dachannien ( 617929 ) on Thursday December 07, 2006 @11:57AM (#17146718)
        were deemed so useless when first conceived that they were called imaginary numbers

        Those of us with an electrical engineering background prefer to call them jmaginary.

    • by itwerx ( 165526 ) <itwerx@gmail.com> on Thursday December 07, 2006 @03:49AM (#17142900) Homepage
      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."
    • by mwvdlee ( 775178 ) on Thursday December 07, 2006 @05:01AM (#17143244) Homepage
      As I understand it; you take a famous problem (e.g. division-by-zero), give it a new name (e.g. nullity) and claim you've solved the problem.

      So, I hereby claim to have solved the well-known Poincaré Conjecture by naming it "frooblewompy". There, problem solved.
      • by kongit ( 758125 ) on Thursday December 07, 2006 @05:47AM (#17143488)
        If you wouldn't mind emailing me your name, address, and credit card number (used only for verification and other stuff) I will send you 1 (one) Nobel prize in the field of mathematics for a limited time offer not exceed 5 days. By accepting this offer you are agreeing that I, the arbitrary nullity, will thus forth be bequeathed of all known possessions you, the numbskull who happens to be still reading this. Furthermore, without further ado, we bring you something completely differential.
    • by Ayanami Rei ( 621112 ) * <rayanami&gmail,com> on Thursday December 07, 2006 @01:09PM (#17147868) Journal
      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.
  • by BadAnalogyGuy ( 945258 ) <BadAnalogyGuy@gmail.com> on Thursday December 07, 2006 @03:04AM (#17142590)
    The professors at 'Rithmetic State were non-plussed upon hearing the news.
  • Umm... NaN? (Score:5, Funny)

    by The boojum ( 70419 ) on Thursday December 07, 2006 @03:04AM (#17142596)
    Is it just me or does it sound like he thinks he's invented the NaN?
  • Hmm (Score:5, Funny)

    by mdemonic ( 988470 ) on Thursday December 07, 2006 @03:05AM (#17142600)
    There's zero comments yet. Wonder how many comments that is per poster
  • by NETHED ( 258016 ) on Thursday December 07, 2006 @03:07AM (#17142618) Homepage
    I can make up numbers too...

    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.
  • by b1ufox ( 987621 ) on Thursday December 07, 2006 @03:09AM (#17142638) Homepage Journal
    mod original post up by 0/0 points :)
  • by Doppler00 ( 534739 ) on Thursday December 07, 2006 @03:10AM (#17142644) Homepage Journal
    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.
  • Rubbish (Score:4, Funny)

    by Mkoms ( 910273 ) on Thursday December 07, 2006 @03:12AM (#17142650)
    Only Chuck Norris can divide by zero.
  • by bananaendian ( 928499 ) on Thursday December 07, 2006 @03:18AM (#17142686) Homepage Journal
    "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.

  • Sad, really... (Score:5, Interesting)

    by lexDysic ( 542023 ) on Thursday December 07, 2006 @03:22AM (#17142708)
    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.
  • by Lord Aurora ( 969557 ) on Thursday December 07, 2006 @03:26AM (#17142740)
    ...move along.

    Helpful little hint from the end of the video:

    You've just solved a problem we haven't been able to solve for twelve hundred years. And it's that simple.

    Yeah. It was that simple.

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

    a = b

    a^2 = ab

    a^2 + a^2 - 2ab = ab + a^2 - 2ab

    2(a^2 - ab) = 1(a^2 - ab)

    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..."

  • I suspect (Score:4, Interesting)

    by the_tsi ( 19767 ) on Thursday December 07, 2006 @03:27AM (#17142750)
    Mr. L'Hopital would have something to say against this.
  • by joe_cot ( 1011355 ) on Thursday December 07, 2006 @03:33AM (#17142784) Homepage
    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).
    • by Christianson ( 1036710 ) on Thursday December 07, 2006 @05:06AM (#17143272)
      A fundamental part of his explanation pivots on the following being true: 1/0 = infinity -1/0 = -infinity

      And for him it is true; he's defined infinity to have these values. He very specifically wants a fixed value for 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.

      Nor does this work. Division, in his system, is not the multiplicative inverse, but the reciprocal. So, for him: 1/0 = infinity implies 0/1 = 1/infinity, which does in fact meet our expectations.

      Basically, what he's done with his system is come up with a (completely consistent, as far as I can tell from scanning from his website) framework where singularities now have a defined value, which means that all functions are defined everywhere on the real line (or the transreal line, which is what he calls his infinity-and-nullity supplemented system). Which is great, as far as it goes. But there's a big trade-off for this: there is now no longer a guarantee that if both f(x) and the limit at x of f both exist, that they will have the same value. The example he himself gives is the hypebolic tangent at infinity; the limit is 1, but by direct evaluation, it ends up being nullity. To get around this, he proposes a hierarchy of value determinations; a function is defined at a point by its transreal arithmetic value only if a different value isn't suggested by analysis. So tanh(infinity) would be treated as 1, even though working through the definition of tanh requires the value to be nullity in his system.

      So in summary, he's defined terms so that division by zero is consistent and workable, but the price is that even relatively simple calculus becomes a lot more complicated. Nor is it all clear that transreal arithmetic will hold up with higher mathematics at all (when infinity is valued rather than defined by limits, how does cardinality work?). So I think he's got to a better job selling it than "it's better than NaN or having values undefined," because I can't see how it is.

  • The real link (Score:4, Informative)

    by albalbo ( 33890 ) on Thursday December 07, 2006 @04:01AM (#17142970) Homepage

    Submitter couldn't be bothered to do the research, but there is a paper written by this guy [bookofparagon.com] about the concept.

  • Don't sneeze at it (Score:5, Interesting)

    by mattr ( 78516 ) <mattr.telebody@com> on Thursday December 07, 2006 @04:02AM (#17142984) Homepage Journal
    How does James Anderson's "nullity" differ from Douglas Adams' "a suffusion of yellow"?

    Seriously though this is the sort of thing that you don't want to sneeze at, it can sound both inane and brilliant. Anderson is not such a crackpot, I found a presentation [bookofparagon.com] of his on optical computing and an introduction to its underlying theory called perspex algebra ( "Representing geometrical knowledge." [nih.gov]). He seems to be a geometer stating his perspective in the first line of that presentation: "Aims: To unify projective geometry and the Turing machine".

    He's a geek hero! Who knows if his nullity will end up just NaN with a British twang or the next best thing to sliced bread and i?

    I was unable to hear the realaudio casts but from Book of Paragon, The Perspex Machine [bookofparagon.com] (Anderson mentions transreal arithmetic) and Exact Numerical Computation of the Rational General Linear Transformations [bookofparagon.com] (a mathematical treatise with applications to computer vision and robotics) just glancing I'd have to say the guy seems to be a real mathematician, geek and philosopher-king. I don't know if he's up there with Newton but he at least deserves an honorable mention for his wonderfully witty (and to me as yet inscrutable) naming of the Walnut Cake Theorem (see page 10 of Perspex.pdf). It seems that he was motivated to create nullity in order to make reliable advanced computers that would not barf when asked questions about the universe, and to him "Not-a-Number" is vomit. I'd say read some of his stuff before assigning him to the 9th Hell. Would like to hear what any mathematicians or other people with brain cells over the age of 12 have to think about it. It's okay if he reinvented something but it appears he is trying to make a machine that can handle infinities and other tough numerical concepts with ease, and that's worth something. Oh, that and his quantum computer looks neat.

  • by saforrest ( 184929 ) on Thursday December 07, 2006 @04:36AM (#17143140) Journal
    Wow. Looking over the guy's axioms [bookofparagon.com], 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.
  • by feepness ( 543479 ) on Thursday December 07, 2006 @05:27AM (#17143378) Homepage
    I will never forget when I was about 8 years old going up to the adding machine in my grandfather's home office. It was about twice the size of a toaster and made of that old typewriter metal. It looked like it weighed as much as a car and had probably cost as much new. Just to see what would happen I entered '0', '/' and '0'. Without hesitation it began producing line after line of '0', '0', '0' on the paper tape accompanied by a cacaphony of mechanical gears. It became apparent to me in a split second that it had no intention of stopping. Ever. It had come alive and was angry.

    I yanked the plug from the wall socket and ran from the room in terror.
  • new things (Score:5, Funny)

    by yakumo.unr ( 833476 ) on Thursday December 07, 2006 @06:11AM (#17143612) Homepage
    If he can make up numbers, then I cam make up words,

    this whole thing is utterly stuipfluous.
  • the problem (Score:4, Informative)

    by idlake ( 850372 ) on Thursday December 07, 2006 @09:01AM (#17144444)
    The problem isn't that people haven't figured out ways of dividing by zero, the problem is that there are many different ways in which you could reasonably define division by zero, and they are not mutually consistent. Wikipedia lists some of them. [wikipedia.org]

Doubt is not a pleasant condition, but certainty is absurd. - Voltaire