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42 *IS* The answer to Life, the Universe and Zeta
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.'"
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."
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
someone found the question? What was it?
When the posters fear their moderators, there is tyranny; when the moderators fears the posters, there is liberty.
Douglas Adams 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.
He who knows best knows how little he knows. - Thomas Jefferson
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
Are there any mathematicians who can explain how a non-prime is the third riemann moment in the string of riemann zeros?
Do what you can, with what you have, where you are.
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.
[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?
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.
I mean, "42" really being the answer could be considered infinitely improbable.
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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 together as a child would do, you have two different objects and you combine them...to make a third object. This is logic at it's most basic. Now that we're on level - imagine that you take this a bit further and go beyond what you already know, can you do this?
What this world is coming to - is for you and me to decide.
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.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.
If anyone is interested in a little more detail/background, Ivars Peterson 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 article gives a good overview for the casual reader--if you're interested in the Riemann Zeta Function itself, look here (Zeta Funciton) or here (Zeroes)
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?
>> Standing on head makes smile of frown, but rest of face also upside down.
Indeed. Zeta? Call me when 42 is the answer to Alpha and Omega. Then I'll be impressed.
If a chair is thrown in a forest, and there are no witnesses, did Ballmer still do it?
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.
Pining for the fjords
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.
I dated a girl from Grand Rapids for a while... area code 616.
So yes, 616 *is* the number of the Beast. At least, once you add in 7 other digits.
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Mod me down, you fucking twits. Go ahead. I dare you.
(I read with sigs off.)
"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
The history of Maths is way more interesting that you think . . .
spoonerize "magic trackpad"
I read a science article a while back discussing quantum computing. Apparently, you need to isolate the qubits from the surrounding environment to keep from collapsing the wave function until you are ready to read the result. One of the techniques for creating this isolation is to surround the qubit in a strong brownian motion fluid. Supposedly, since the average effect is zero, it doesn't affect the result, but it maintains a shield from the interference of "observers".
13.37 * Pi = 42 Try to beat that!
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.
Either way leads to mass suicide- so let's go out spectacularly and nuke the mideast!
SJW: a person who perceives an injustice, and while correcting it, commits a greater injustice.
http://www.bbc.co.uk/radio4/history/inourtime/inou rtime_20060112.shtml
Beats me how URLs actually work here; any-one able to tell me?
Hello!
2 000-02.pdf
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 significance of the plain naked number, an integer, 137, has puzzled physicists for decades.
Google's list.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]