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42 *IS* The answer to Life, the Universe and Zeta 316

Posted by Hemos from the douglas-adams-was-right dept.
Venusian Treen writes "In their search for patterns, mathematicians have uncovered unlikely connections between prime numbers and quantum physics. The gist is that energy levels in the nucleus of heavy atoms can tell us about the distribution of zeros in Riemann's zeta function - and hence where to find prime numbers. This article discusses this connection, and introduces two physisicts who tell us 'why the answer to life, the universe and the third moment of the Riemann zeta function should be 42.'"
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42 *IS* The answer to Life, the Universe and Zeta More

42 *IS* The answer to Life, the Universe and Zeta

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  • 42 (Score:5, Funny)

    by Anonymous Coward on Monday March 27, 2006 @10:07AM (#15002794)
    I just hope I lose my virginity by the time I'm 42 ...
  • "As soon as you discard scientific rigor, you're no longer a mathematician, you're a numerologist."

  • You mean (Score:5, Funny)

    by stunt_penguin ( 906223 ) on Monday March 27, 2006 @10:08AM (#15002803)
    someone found the question? What was it?

    • Re:You mean (Score:5, Funny)

      by ZombieRoboNinja ( 905329 ) on Monday March 27, 2006 @10:12AM (#15002836)
      The question, apparently, is "What is the third moment of the Riemann zeta function?"

      I'm as surprised as you are.
      • I must have mistranslated your post, I thought it said "go stick your head in a pig."

      • In more detail (Score:5, Informative)

        by l2718 ( 514756 ) on Monday March 27, 2006 @10:41AM (#15003104)

        In fact, the question is:

        What is the arithmetic factor in the asymptotics of the third moment of the Riemann zeta-function?

        In more detail: If you integrate the nth power of the absolute value of the Riemann zeta function on the the critical line between heights -T and T and divide by 2T, you will get a sort of nth moment on average. Random matrix theory predicts the growth of this function to be asymptotic to a "geometric factor" (coming from an integral over the unitary group) times the n^2 power of the logarithm of T. It turned out that the random matrix theory prediction is off by an "arithmetic" factor, so that the correct asymptotics is

        a(n)g(n) (log T)^(n^2)
        where g(n) is the geometric factor from above and a(n) is a rational number. The article is about the prediction a(3)=42.
      • The mice will be disappointed.
      • I read TA and was slightly unsatisfied because no discussion takes place between the relation between 42 and "Life and the Universe", only to Riemann's Zeta function and its history.
    • According to the TV series it was "what do you get when you multiply seven by nine?"... Arthur always thought that there was something fundamentally wrong with the universe.

  • The answer to everything is a Joke (Score:5, Informative)

    by digitaldc ( 879047 ) * on Monday March 27, 2006 @10:10AM (#15002820)
    Douglas Adams [wikipedia.org] was asked many times during his career why he chose the number forty-two. Many theories were proposed, but he rejected them all. On November 2, 1993, he gave an answer on alt.fan.douglas-adams:
    The answer to this is very simple. It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do' I typed it out. End of story.

    Tao Te Ching, Chapter 42:

    The Tao begot one. One begot two. Two begot three. And three begot the ten thousand things. The ten thousand things carry yin and embrace yang. They achieve harmony by combining these forces. Men hate to be "orphaned," "widowed," or "worthless," But this is how kings and lords describe themselves. For one gains by losing and loses by gaining. What others teach, I also teach; that is: "A violent man will die a violent death! " This will be the essence of my teaching.

  • TFA (Score:4, Informative)

    by Anonymous Coward on Monday March 27, 2006 @10:10AM (#15002825)
    In their search for patterns, mathematicians have uncovered unlikely connections between prime numbers and quantum physics. Will the subatomic world help reveal the illusive nature of the primes?

    by Marcus du Sautoy Posted March 27, 2006 12:40 AM

    In 1972, the physicist Freeman Dyson wrote an article called "Missed Opportunities." In it, he describes how relativity could have been discovered many years before Einstein announced his findings if mathematicians in places like Göttingen had spoken to physicists who were poring over Maxwell's equations describing electromagnetism. The ingredients were there in 1865 to make the breakthrough--only announced by Einstein some 40 years later.

    It is striking that Dyson should have written about scientific ships passing in the night. Shortly after he published the piece, he was responsible for an abrupt collision between physics and mathematics that produced one of the most remarkable scientific ideas of the last half century: that quantum physics and prime numbers are inextricably linked.

    This unexpected connection with physics has given us a glimpse of the mathematics that might, ultimately, reveal the secret of these enigmatic numbers. At first the link seemed rather tenuous. But the important role played by the number 42 has recently persuaded even the deepest skeptics that the subatomic world might hold the key to one of the greatest unsolved problems in mathematics.

    Prime numbers, such as 17 and 23, are those that can only be divided by themselves and one. They are the most important objects in mathematics because, as the ancient Greeks discovered, they are the building blocks of all numbers--any of which can be broken down into a product of primes. (For example, 105 = 3 x 5 x 7.) They are the hydrogen and oxygen of the world of mathematics, the atoms of arithmetic. They also represent one of the greatest challenges in mathematics.

    As a mathematician, I've dedicated my life to trying to find patterns, structure and logic in the apparent chaos that surrounds me. Yet this science of patterns seems to be built from a set of numbers which have no logic to them at all. The primes look more like a set of lottery ticket numbers than a sequence generated by some simple formula or law.

    For 2,000 years the problem of the pattern of the primes--or the lack thereof--has been like a magnet, drawing in perplexed mathematicians. Among them was Bernhard Riemann who, in 1859, the same year Darwin published his theory of evolution, put forward an equally-revolutionary thesis for the origin of the primes. Riemann was the mathematician in Göttingen responsible for creating the geometry that would become the foundation for Einstein's great breakthrough. But it wasn't only relativity that his theory would unlock.

    Riemann discovered a geometric landscape, the contours of which held the secret to the way primes are distributed through the universe of numbers. He realized that he could use something called the zeta function to build a landscape where the peaks and troughs in a three-dimensional graph correspond to the outputs of the function. The zeta function provided a bridge between the primes and the world of geometry. As Riemann explored the significance of this new landscape, he realized that the places where the zeta function outputs zero (which correspond to the troughs, or places where the landscape dips to sea-level) hold crucial information about the nature of the primes. Mathematicians call these significant places the zeros.

    Riemann's discovery was as revolutionary as Einstein's realization that E=mc2. Instead of matter turning into energy, Riemann's equation transformed the primes into points at sea-level in the zeta landscape. But then Riemann noticed that it did something even more incredible. As he marked the locations of the first 10 zeros, a rather amazing pattern began to emerge. The zeros weren't scattered all over; they seemed to be running in a straight line through the landscape. Riemann couldn't believe t

  • ? 42 is not prime (Score:4, Interesting)

    by Phoenix666 ( 184391 ) on Monday March 27, 2006 @10:15AM (#15002865)
    Are there any mathematicians who can explain how a non-prime is the third riemann moment in the string of riemann zeros?
    • Maybe that's why it took them so long to find it...

    • Re:? 42 is not prime (Score:3, Informative)

      by teslar ( 706653 )
      I'm not a mathematician, but just from TFA:

      a) "(...) the places where the zeta function outputs zero (which correspond to the troughs, or places where the landscape dips to sea-level) hold crucial information about the nature of the primes."

      b) "There is an important sequence of numbers called "the moments of the Riemann zeta function.""

      So, not only does it not, as far as I understand, claim that the zeroes of the zeta function are actually primes, it also doesn't say that the moments are on the hyp
      • The RH does not say that ALL zeros are primes, just that all primes are zeros.

        this is a conditional, not a bi-directional.

    • Re:? 42 is not prime (Score:4, Informative)

      by slo_learner ( 729232 ) on Monday March 27, 2006 @10:43AM (#15003128)
      It's quite elementary actually. This should get you started. http://arxiv.org/PS_cache/math/pdf/0508/0508378.pd f [arxiv.org] No but really, http://en.wikipedia.org/wiki/Zeta_distribution [wikipedia.org] Good luck see you in a week
    • It's a moment, not a zero. 0 is the first Riemann moment and isn't a prime either.

    • Re:? 42 is not prime (Score:5, Informative)

      by Coryoth ( 254751 ) on Monday March 27, 2006 @10:46AM (#15003159) Homepage Journal
      Are there any mathematicians who can explain how a non-prime is the third riemann moment in the string of riemann zeros?

      Well the Riemann zeta function [wikipedia.org] is an otherwise innocuous looking function where zeta(z) = 1 + 1/(2^z) + 1/(3^z) + 1/(4^z) + ...

      It has some surprising and intriguing properties however. One of the more interesting is that it ends up appearing inside a formula to approximate the prime number counting function (which counts the number of primes less than n). Because of the way it appears in the integral that provides the formula (as log(1/zeta(z))) and "poles" (essentially points where the function shoots of to infinity like asymptotes, except on the complex plane) of the function being integrated are vitally important for determining these particular kinds of integral (complex path integrals) it turns out that determining when the Riemann zeta funtion is zero has a lot to say about the distribution of prime numbers.

      This means we've converted the problem from studying the distribution of prime numbers (very hard) to studying the distribution of the zeros of a particular function (hard, but a definite improvement). So what can we say about the distribution of zeros of the Riemann zeta funtion? Well without actually knowing where all the zeros are we can at least potentially talk about the moments of the distribution [wikipedia.org] which is basically just a series of statistical measures. The first moment of a distribution is the mean, the second moment is the variance. What they have found is the third moment, the next step up from the variance, of the distribution of zeros of the Riemann zeta function - whih, as we've seen, in deeply connected to the distribution of prime numbers.

      The third moment of ther distribution of zeros of the Riemann zeta function can thus be any number: it isn't required to be prime; it is simply a measure describing properties of the distribution. Exactly what that number is though, can actually say a lot about how prime numbers are distributed.

      Jedidiah.
  • The reason we are excited because the third number in the sequence of the moments of the Riemann zeta function is 42. It was calculated only few years ago.

    • Actually the real reason (I think) to get excited about it is the fact that there is a link between primes and quantum mechanics

      They discovered that if you compare a strip of zeros from Riemann's critical line to the experimentally recorded energy levels in the nucleus of a large atom like erbium, the 68th atom in the periodic table of elements, the two are uncannily similar.

      Of course, this has apparently been known since 1972, so I guess just noting that 42 is the third moment is really the only news i

  • How clever! (Score:5, Funny)

    by Pedrito ( 94783 ) on Monday March 27, 2006 @10:20AM (#15002919)
    [Reimann] realized that the places where the zeta function outputs zero ... hold crucial information about the nature of the primes. Mathematicians call these significant places the zeros.

    Man, those mathematicians are really clever at naming stuff. Next thing you know, they're going to call the places where the function outputs ones, "ones". Will it never end?
    • It's really clever, because the values, for which the Zeta functions puts out zero, are not zero by themselves. So calling a value 'a zero', because used as value in a certain function it returns zero is already somewhat nontrivial.
    • Some people also call the zeros of a function its roots. A lot of important information can be determined about a function by studying its roots, which is why we bother to give them a name (whether roots or zeros). However, the places where a function takes the value one are less obviously important. In particular, they change if you multiply your function by a constant or by another continuous function. The roots do not. The 'ones' of a function are only important when the function f(x)-1 is important

    • Re:How clever! (Score:5, Funny)

      by Sax Maniac ( 88550 ) on Monday March 27, 2006 @12:11PM (#15003838) Homepage Journal
      Indeed. I once took a language theory class from a math bigot. He clearly hated computer science and (shudder) actual physical objects like computers.

      Upon trying to describe a stack, he stumbled, paused and said: "Why do you computer people use such strange words like "push" and "pop"? Why not call it 'stick it on the end' and 'take it off the end?' It's so needlessly complicated".

      Without a beat, he then writes a bunch of greek symbols on the board, epsilon prime-prime-underbar-hat, muttering on about nondeterministic finite automata and pumping lemmas.

      Years ago, I learned never to take any computer science classes from anyone who held only degrees in math, but sadly I had no choice that semester.
      • It's actually sort of funny, because the mathematicians I've met take sort of a delight in inventing odd terminology for things.

        For example, "index gymnastics" is actually a mathematical term you can look up on mathworld, hehe.
      • Why do you computer people use such strange words like "push" and "pop"? Why not call it 'stick it on the end' and 'take it off the end?' It's so needlessly complicated".

        SequentialCollectionOfObjects *my_sequential_collection_of_objects = new SequentialCollectionOfObjects();

        my_sequential_collection_of_objects->StickItOnTheE nd(my_first_object_being_stuck_on_the_end);

        standard_output_object_for_the_language_coming_aft er_c << my_sequential_collection_of_objects->TakeItOffTheE nd();

        Ah yes, so much

  • Ooh really funny. (Score:5, Funny)

    by Anonymous Coward on Monday March 27, 2006 @10:31AM (#15003004)
    The ratio of funny to informative posts is ridiculous. Why aren't discussions on Slashdot informative; seems like half the replies are jokes that don't really further the conversation.

  • It makes sense (Score:3, Funny)

    by jayhawk88 ( 160512 ) <jayhawk88@gmail.com> on Monday March 27, 2006 @10:31AM (#15003008)
    I mean, "42" really being the answer could be considered infinitely improbable.

  • Oops. So much for encryption (Score:5, Interesting)

    by RonTheHurler ( 933160 ) on Monday March 27, 2006 @10:36AM (#15003050)
    If the article is true, and prime numbers can be gleaned from quantum stuff, and quantum computers are just around the corner... will that obsolete all our public key encryption tools? How does this affect quantum encryption? Will we have to wait for our household Mr. Fusion reactors to power these systems to maintain encryption? Will all this happen within the next 5 years?

    --

    Keep my family fed. Visit http://www.RLT.com [rlt.com] Today!

    • If the article is true, and prime numbers can be gleaned from quantum stuff, and quantum computers are just around the corner... will that obsolete all our public key encryption tools?

      IIRC, Elliptic Curve crypto is based on Discreet Logs and not large primes. Thus, figuring out a rapid way to factor primes will not totally obsolete PKI -- just the PKI that relies on prime keys.

      Quantum encryption is a different animal, more related to quantum teleportation of keys than anything else. It is the idea of gett
    • If the article is true, and prime numbers can be gleaned from quantum stuff, and quantum computers are just around the corner

      Well all of that is only tenuously related, but okay...

      will that obsolete all our public key encryption tools?

      Quantum computers will, yes. Not because information about the distribution of prime numbers is intertwined within quantum energy levels, but because there exist polynomial time algorithms for factoring and discrete logarithms given a quantum computer. Since all our current pu

  • The Zeta function (Score:5, Funny)

    by Anonymous Coward on Monday March 27, 2006 @10:38AM (#15003083)
    4, 8, 15, 16, and 23 are also significant. Hey, wait a minute......
  • It's possible to conclude virtually *anything* with numbers such as we know them. It's a matter of finding a formula / sequence - call it what you want.

    But here's the kicker:

    Thinking beyond know numbers takes a mind that are capable of thinking beyond our existing collective knowledge. We tend to agree and pat each other on the back on every single connected discovery we make.

    Imagine that we go beyond what we know - and if you have NO clue what I'm rambling about - picture this: You put two and two to

  • Watch New Age people pick up on this... (Score:3, Insightful)

    by dildo ( 250211 ) on Monday March 27, 2006 @10:47AM (#15003163)
    One thing I dislike about modern physics is how they phrase things in an inappropriately magical way. And then what happens is that New Age people start hideosly misinterpreting the results, fuse one piece of magic to another, and before you know it, people saying things like "physics is just confirming what the Taoists knew thousands of years ago..." -- in short, garbage.

    It is very likely that it is just a coincidence that the Riemann Zeta function describes some properties of quantum physics. If you study mathematics you will find all sorts of coincidences like these. It doesn't mean anything; more often than not it is just a consequence of the rules of arithmetic.

    But I imagine that New Age people are going to interpret this as that civilizations inside of each atom are trying to signal us "Contact" style by sending out zeros of the Riemann Zeta Function.... sigh.

    • I have to agree with this. My grandpa found a new age religion he really enjoys, and hell, I'm happy with him. As far as I'm concerned it's more innocuous than the other religions I've seen and teaches better values.

      But the way the man is led to read and misinterpret physics and math are astounding. People keep seeing meaning that's not there, parroting it from books written by authors who have the same fundamental misunderstandings.

      As far as I'm concerned, mathematics and physics parallel so closely beca
    • One thing I dislike about modern physics is how they phrase things in an inappropriately magical way.

      It's not really the physicists themselves that do it: it's the organization that they work for. A few months ago, I began working for a research group at my university. Soon after, I learned that my college actually has staffers to write press releases, who have B.A.s in English, but no experience in the field which they are writing about. It's actually quite ridiculous, because the professors and grad s

  • For a little more detail (Score:3, Informative)

    by MarkusQ ( 450076 ) on Monday March 27, 2006 @10:48AM (#15003170) Journal

    If anyone is interested in a little more detail/background, Ivars Peterson [sciencenews.org] wrote about this (minus the latest development of course) back in 1999.

    -- MarkusQ

    P.S. Am I the only one who thinks it sad when a link to an article by Ivars Peterson adds details to a discussion? The posted article said...basically nothing about the topic. Not surprising when you've got the equivalent of one typewritten page to work with and you feel the need to start by explaining what primes are. But still sad.

  • The Ugly Math (Score:2, Informative)

    by IorDMUX ( 870522 )
    The article gives a good overview for the casual reader--if you're interested in the Riemann Zeta Function itself, look here (Zeta Funciton) [wolfram.com] or here (Zeroes) [wolfram.com]

    I love reading about this stuff, but the actual relation between the zeroes and the prime number theorem must have passed right over my head. Anyone else get it?
    • My basic understanding of it is this: The Riemann Zeta function can be re-written using the product function as a product of primes. Now, if the zeta function is zero, then you can't rewrite that number as a product of other primes can you? That means it's a prime number itself. See wikipedia for more information on the euler product formula connection. http://en.wikipedia.org/wiki/Riemann_zeta_functio n [wikipedia.org]

  • Obligatory Alan Turing reference (Score:5, Interesting)

    by Flying pig ( 925874 ) on Monday March 27, 2006 @11:06AM (#15003339)
    The connection with the computer industry is that Alan Turing had a grant from the Royal Society to build an analog system (using gears no less) to investigate the zeroes of the Riemann Zeta Function.

  • The Slashdot Conjecture (Score:5, Funny)

    by sidles ( 735901 ) <(moc.liamg) (ta) (seldisaj)> on Monday March 27, 2006 @11:12AM (#15003385)
    The Slashdot Conjecture: All mathematical and physics problems that arise naturally in everyday life are in complexity class NP-hard. The Slashdot Corollary: All meaningful discussion of these problems will require either oversimplification or humor.
    • That conjecture does not apply to articles which, when cast onto the numeric system of base pi, multiplied by the current diameter of the nooverse taken to the log of base e, and divided by the user ID of the first poster, has a value of 42.

  • The Music of the Primes (Score:3, Interesting)

    by ElephanTS ( 624421 ) on Monday March 27, 2006 @11:30AM (#15003533)
    "Music of the primes" is a great book for the non- or semi-mathematician that deals extensively with the Riemann function. In this book the author touched on the weird significance of "42" to the function but I'm afraid I can't explain it but sort of understood while I read it. Great book though - check it out . . . http://www.amazon.com/gp/product/0066210704/102-69 90660-1984935?v=glance&n=283155 [amazon.com] The history of Maths is way more interesting that you think . . .
  • Ahh, if only the title of this article had been:
    42 *IS* The answer to Life, the Universe, and That Zeta Thing
  • Will there be a useful algorithmic relationship between 1st, 2nd, and 3rd Reimann moments? What will its geometry look like? Will it correlate further with physical matter relationships? Can it be fractalized into producing other moments?

    Adam's 42 was what happens when you roll die (dice) together-- the meaning of life is that it's a craps shoot. But what of the symmetry of primes? These are juicy bits for numbers heads, algo-freaks, and the rest of us autistically-deranged-from-birth geeks.

    And I eagerly aw
  • 13.37 * Pi = 42 Try to beat that!

    • Re:That's nothing! (Score:3, Interesting)

      by Da Schmiz ( 300867 )
      Well... I hate to burst your bubble, but 13.37 times pi is actually 42.0030937784954923... ad infinitum.

      The number you want is probably closer to 13.369015219719221985830700904996......

  • How unexpected is it really? (Score:3, Insightful)

    by LesPaul75 ( 571752 ) on Monday March 27, 2006 @12:20PM (#15003895) Journal
    They make it sound like it's a huge surprise that the most basic levels of physics are strongly connected to the most basic mysteries of mathematics (primes, for example). I would expect that just about every mathematician and physicist, even down to the hobbiest level, has suspected this in some form or another. Some modern scientists like Wolfram and Fredkin have based their careers on this idea, and have built loyal followings. It makes sense that there's a strong connection between the two. And it's what we secretly want to believe, as logical beings -- that there's a simple pattern to be found at the most basic level of existence.
    • It's a very big surprise. Prime numbers pop up in number theory all the time but we don't expect to see them appear in physics. For the longest time it was unusual to see integers at all in physics - classical mechanics deals with real valued (or vector valued) properties like mass, velocity and force. Classical phenomena that pick out integers are contrived or rare.

      With quantum mechanics we start seeing integers. For example the energy levels of a hydrogen atom are proportional to 1/m^2-1/n^2 where m an

      • "I saw seminars on Gutzwiller's work connecting the quantum mechanics of chaotic systems with the Riemann zeta function years ago."

        Actually I thought that was THE link between quantum mechanics and Rimann's zeta function.
        The folklore I've heard is that Dyson was introduced to Montgomery and asked him what he was doing.
        Montgomery then starting explaining his work on the zeta function mentioning some particular equation he had come across at which point Dyson recognized it as an entity appearing in the t
        • But there is another big connection which for some reason is frequently overlooked even though it's known by just about every single theoretical physicist. Briefly it's this: frequently when doing quantum mechanics you find yourself with an infinite series to sum. Unfortunately they often turn out to be divergent series so there is no sum. So physicists cheat and use a technique called zeta regularisation [wikipedia.org] to extract a finite answer. Bizarre as it seems, it sometimes gives physically sensible results. It's j
  • Hello!

    Here is an article by Jon P. Keating and Nina C. Snaith

    Random Matrix Theory and zeta(1/2+it)
    http://www.hpl.hp.com/techreports/2000/HPL-BRIMS-2 000-02.pdf [hp.com]

    Roman
  • I'm guessing that the mathematicians and the physicists will issue a joint statement announcing that they have, in fact, established this connection, and that the number which lies at the heart of both the physical world and the abstract world of mathematics is, in fact, 42.

    The announcement will be made at a press conference this Saturday, April 1.

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