42 *IS* The answer to Life, the Universe and Zeta 316
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.'"
42 (Score:5, Funny)
Re:42 (Score:2)
(Checks watch) With eight hours to spare.
242723920317613145364418177377134 (Score:4, Insightful)
Re:242723920317613145364418177377134 (Score:5, Funny)
Re:242723920317613145364418177377134 (Score:2)
You mean (Score:5, Funny)
Re:You mean (Score:5, Funny)
I'm as surprised as you are.
Re:You mean (Score:2)
In more detail (Score:5, Informative)
In fact, the question is:
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
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.Re:In more detail (Score:5, Funny)
Re:You mean (Score:2)
Re:You mean / wrong article title? (Score:2)
Re:You mean (Score:2)
Re:You mean (Score:2)
this cant be The Question, since the universe did not reboot...
There is another theory which states that this has already happened.Re:You mean (Score:2)
Re:You mean (Score:2)
Re:You mean (Score:5, Interesting)
6x9 = 54 (base 10) = 42 (base 13).
Re:You mean (Score:2)
First, you can never watch too much Star Trek, secondly, touche. You are indeed correct.
Re:You mean (Score:2, Funny)
That statement isn't entirely true. It's possible to watch too much Voyager.
The answer to everything is a Joke (Score:5, Informative)
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.
Re:The answer to everything is a Joke (Score:3, Funny)
Well it was one of the input parameters, wasn't it? Only thing missing was if he'd drawn it from a sack of scrabble letters. Oh wait, you don't know... *nabs another bit of cheese* This Internet thing is great you know, never see who's at the other end. Well, that ape decendant that lives here should be home soon, guess I better go.
Re:The answer to everything is a Joke (Score:4, Funny)
Brother Maynard: [imdb.com] Skip a bit, Brother.
And three begot the ten thousand things.
Re:The answer to everything is a Joke (Score:3, Funny)
And thus scientology was born... oh wait that is a different thread.
Re:The answer to everything is a Joke (Score:2)
Re:"42" is used in a POSIX standard (Score:2)
TFA (Score:4, Informative)
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)
Re:? 42 is not prime (Score:2)
Re:? 42 is not prime (Score:3, Informative)
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
Re:? 42 is not prime (Score:2)
this is a conditional, not a bi-directional.
Re:? 42 is not prime (Score:2)
Rather prime numbers are integers that are not negative or fractional or imaginary. 1 is skipped because every Integer is divisible by 1, and instead we start at 2.
Re:? 42 is not prime (Score:4, Informative)
Re:? 42 is not prime (Score:2)
Re:? 42 is not prime (Score:5, Informative)
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.
Re:? 42 is not prime (Score:2)
d00d, like, I don't see that anywhere in the D&D 3.5 rules. What kind of deities will I find there?
For those who didn't read the article (Score:2, Informative)
Re:For those who didn't read the article (Score:2)
Actually the real reason (I think) to get excited about it is the fact that there is a link between primes and quantum mechanics
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)
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?
Re:How clever! (Score:2)
Re:How clever! (Score:2)
Re:How clever! (Score:5, Funny)
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.
Re:How clever! (Score:2)
For example, "index gymnastics" is actually a mathematical term you can look up on mathworld, hehe.
Re:How clever! (Score:2)
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)
Re:Ooh really funny. (Score:4, Interesting)
On the other side, every slashdotter thinks they have something funny to say.
Re:Ooh really funny. (Score:3, Informative)
the link i think is this one: http://slashdot.org/my/comments/#karma_bonus [slashdot.org]
Re:Ooh really funny. (Score:2)
It makes sense (Score:3, Funny)
Re:It makes sense (Score:2)
Oops. So much for encryption (Score:5, Interesting)
--
Keep my family fed. Visit http://www.RLT.com [rlt.com] Today!
Re:Oops. So much for encryption (Score:2)
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
Re:Oops. So much for encryption (Score:3, Insightful)
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
Re:Oops. So much for encryption (Score:2)
While there is certainly going to be processing time devoted to dividing the product by each number on the table, I believe that the bottlenect is finding which numbers are prime in the first place (I could be wrong, that's what I've heard - I can't tell you what pri
The Zeta function (Score:5, Funny)
Re:The Zeta function (Score:3, Informative)
It's all in the interpetation (Score:2, Interesting)
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
Re:It's all in the interpetation (Score:3, Funny)
http://www.timecube.com/ [timecube.com]
Re:It's all in the interpetation (Score:2, Funny)
Re:It's all in the interpetation (Score:2)
I'm still working on that
Watch New Age people pick up on this... (Score:3, Insightful)
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.
Re:Watch New Age people pick up on this... (Score:2)
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
Re:Watch New Age people pick up on this... (Score:3, Informative)
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)
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.
Re:For a little more detail (Score:2)
If you use protons, neutrons and electrons as the analogy it doesn't work quite as well. When you put them together you get atoms, which then have to be in turn combined to get what we see.
The subatomic particles are whatever is going on behind the scenes to make up the primes... wait....
The Ugly Math (Score:2, Informative)
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?
Re:The Ugly Math (Score:2)
Obligatory Alan Turing reference (Score:5, Interesting)
The Slashdot Conjecture (Score:5, Funny)
Important exception (Score:2)
The Music of the Primes (Score:3, Interesting)
Title (Score:2)
A great and meaningful question: what of the 4th? (Score:2)
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
That's nothing! (Score:2, Funny)
Re:That's nothing! (Score:3, Interesting)
The number you want is probably closer to 13.369015219719221985830700904996......
How unexpected is it really? (Score:3, Insightful)
Re:How unexpected is it really? (Score:2)
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
Re:How unexpected is it really? (Score:2, Informative)
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
Re:How unexpected is it really? (Score:2)
Random Matrix Theory and zeta(1/2+it) (Score:2, Informative)
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-
Roman
The proof will be published on Saturday (Score:2)
The announcement will be made at a press conference this Saturday, April 1.
Re:please shut up with this *42* crap (Score:2)
http://www.sportbikes.com/UBBimages3/840937-Beatin gadeadhorse.gif [sportbikes.com]
Re:please shut up with this *42* crap (Score:2, Funny)
Re:please shut up with this *42* crap (Score:2)
Re:please shut up with this *42* crap (Score:2, Funny)
42! hahahaha, you so asked for it
Re:hate to burst your bubble (Score:2)
Re:hate to burst your bubble (Score:2)
The reason for dropping those considerations was that they learned that it only served to complicate otherwise simple mathematicas, because of forcing people to introduce special cases in definitions and proofs to account for those numbers.
You can read more details about this here [wolfram.com].
Re:42... says who?? (Score:2)
Are you in base 13?
Re:article was published five days early (Score:2)
Re:article was published five days early (Score:2)
Re:the answer of life? (Score:2)
Re:Number Stuff (Score:3, Funny)
So yes, 616 *is* the number of the Beast. At least, once you add in 7 other digits.
Re:Improbability Drive (Score:2, Interesting)
Tea Prime (Score:2)
It's obvious that Dyson and Montgomery's "chance meeting over tea" was at one of Princeton/IAS' finite improbability machines.
And the "cup of tea" is really a universe [nasa.gov] of Time.
Once you've read the H2G2, da Nerd Code is revealed.
Re:Are with us or against us? (Score:3, Funny)
Re:ok one question (Score:2)
Re:last idiot (Score:2)
Re-worked link (Score:3, Informative)
http://www.bbc.co.uk/radio4/history/inourtime/inou rtime_20060112.shtml [bbc.co.uk]
Beats me how URLs actually work here; any-one able to tell me?
Re:Re-worked link (Score:2)
Re:Is 42 the answer or the Cause? (Score:2)
It's funny, Schrodinger's Cat has always been brought up to demonstrate the craziness that quantum mechani
Re:I picked 6 x 7 = 42 in third or fourth grade (Score:2)