Great article about using prime number sequences to communicate with alien civilisations!

http://student.uml.edu/primes/

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Climate Change Australia

So confuse...

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We come without a thing and gone without a thing. We need simple life. A cup of teas and a couple of meals per day, that is good enough. And this is my standard of living.

Alternatively, just rent / buy the movie "Contact" or read the book

It would be nice to think an alien civilisation would choose to communicate in this way... but to be honest, I can't see it happening...

I like what this guy's done though... it's exactly the sort of thing I probably would have done at college, if I'd had the braincells to think of it. I have a kind of anal fascination for stats and numbers LOL

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"The stars are my home"
"I've seen things you people wouldn't believe... Attack ships on fire off the shoulder of Orion... I've watched c-beams glitter in the dark, near the Tanhauser Gate... all those moments will be lost, in time... like tears in the rain..."

The movie "contact" dramatically simplified the idea. There is so much complicated mathematics that can be derived from the distribution of prime numbers. The Riemann Hypothesis still remains unsolved after 150 years!

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Climate Change Australia

okay, i know i will be in trouble for asking this what is the Riemann Hypothesis?

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Damien,
International Baccalaureate Physics teacher
Optics, Photogrammetry and Remote Sensing Instrumentation Major
Admin: Pacific Science and Art

The Riemann Hypothesis is the assertion that the nontrivial zeros of the Riemann zeta-function lie on the critical line 0=1/2 h34r:

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We come without a thing and gone without a thing. We need simple life. A cup of teas and a couple of meals per day, that is good enough. And this is my standard of living.

Tiny, that doesn't really help... please don't just post one word replies like that because it doesn't explain or answer anything.

RE "Contact" - true, the film simplified things (it had to) but I seem to remember the book being more detailed.

Somehow though, I can't see an intelligent species using radio to comunicate. After all, within a few decades, the Earth will cease to be sending out it's television and radio signals because the medium will be completely digital. I don't know *how* an alien civilisation would communicate with another system, but I'm sure they'd find radio to be rather antiquated.

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"The stars are my home"
"I've seen things you people wouldn't believe... Attack ships on fire off the shoulder of Orion... I've watched c-beams glitter in the dark, near the Tanhauser Gate... all those moments will be lost, in time... like tears in the rain..."

Basically, Riemann extended Euler's zeta function to the entire complex plane.




There are no zeroes where the real part of s is greater than or equal to one. When the real part of s is less than or equal to zero, there are zeroes at negative even integers (-2, -4, -6 etc.). All the other zeroes (non trivial zeroes) lie between Re(s)=0 and Re(s)=1. The Riemann Hypothesis asserts that all these non-trivial zeroes will lie on the line Re(s) = 1/2. If you can proove this (which nobody has been able to do for nearly 150 years), then the Clay Mathematics Institute will give you 1 million US dollars.

The Riemann Hypothesis relates directly to the distribution of prime numbers. The distribution of prime numbers seems apparently random, however the function pi(x) has shown to be true to remarkable degree of accuracy:



I don't have the mathematical knowledge to show or explain how this is related to the Riemann Hypothesis directly, but if you do some googling I'm sure you'll find many websites devoted to the topic.

An equivalent hypothesis is Merten's Conjecture. It is asserted that there are three types of numbers:
1.) a number with an even no. of prime factors (eg. 6 = 2 x 3)
2.) a number with an odd no. of prime factors (eg. 30 = 2 x 3 x 5)
3.) a number with at least one set of repeated prime factors (eg. 12 = 3 x 2 x 2)

Using a standard graph, start at (1,0), and work your way across one integer at a time. For type 1 numbers go up one unit, for type 2 numbers go straight across, and for type 3 numbers go down one. You will get a random walk type of graph built of discreet steps. Merten's Conjecture asserts that this graph will not cross the line c * x^(1/2)...i.e. a sideways parabola with coefficient c. You must find c and proove that the mertens function never intersects this line. Apparently this correspons exactly to proving the Riemann Hypothesis, although I'm not sure how exactly.

This stuff is absolutely fascinating. I'd love for someone to find that it relates exactly to some astract form of cosmology in a way that gives the Universe a whole new meaning. Even better, that it relates to the construction of DNA! Hmmm....

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Climate Change Australia

Holy crap, you lost me after "Basically..."!!!

Tell me, are there an infinity of prime numbers? What's the highest prime number they've discovered? How can an infinity of prime numbers be a subset of an infinite set of natural numbers? Can there be "smaller" and "larger" infinities?

Also, is pi definitely an infinite fraction? How would they know? Perhaps the fraction stops after a googol-plex of decimal points??? Once again, to what decimal place have they worked out pi??

It staggers me how there are so many infinities in this "finite" Universe!!!?

Could an alien intellect know about "pi"? Even if they have a different numerical system, surely "pi" is "pi" regardless? Might be a good way to signal to other intelligences - just broadcast pi!!

(Don't forget the sauce!)

Quote Faukner:
"Holy crap, you lost me after "Basically..."!!!"

:huh: For once I totally agree with you Faulkner.

Still - if you have an IQ of 177 and did a Phd in maths you should be able to understand this stuff.

Hmmm ... let's see - "(eg. 6 = 2 x 3)" - THAT I can understand!

Hey chook, I have an IQ of 177, but a PhD in progress in environmenta education...

I am beginning to understand whaat kashi has posted. What is described, i think has been linked to DNA but I am floundering a bit to remember where.

And as pi is just the ratio between the circumference and the diameter of any circle then yes, it would seem to be an appropriate message to send, especially as it pertains to a physical object.

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Damien,
International Baccalaureate Physics teacher
Optics, Photogrammetry and Remote Sensing Instrumentation Major
Admin: Pacific Science and Art

One Million kashi? I'll get to work on that one right away

Yes there are an infinite number of primes, and the proof is simple. Suppose there were a largest prime. Multiply it and all the lesser primes together, and add 1. The resulting number is not evenly divisible by any of them, so either it is prime itself, or it is divisible by a prime that's larger than the largest prime. A contradiction, so the assumption must be incorrect.

I don't know what the current largest prime is, but it is changing all the time.

Infinity is a strange thing. One infinity can be smaller than another, but ones that seem to be different sizes are sometimes the same size. For instance, it is obvious that there are an infinite number of even numbers. What isn't obvious is that there are the same number of even numbers as there are natural numbers (even though the even numbers is a subset of the natural numbers). Both are "countable" infinities - you can set up a one to one relationship with the natural numbers (the first even is 2, the second even is 4, the third even is 6, ... the nth even is 2n...), so you can "count" them. Mathematicians call that infinity Aleph0. There are larger infinities.

Aleph0 and Aleph1 will give you a hint about what's going on here.

Yes we know pi has an infinite number of decimal places. It's not hard to prove that it is a special type of irrational number called a transcendental number (don't go meditating on that now ).

Aliens who have developed far enough for us to communicate with them will certainly be aware of pi, although they may use a different number system to represent it (I doubt they'll be into greek letters). Pi in binary, or maybe the first couple of hundred bits of it, might be a good signal, because it would almost certainly be understood for what it is, and couldn't be a natural phenomenon. Good idea.

Cheers, Mr Thorn!

I confess advanced mathematics is not my strong point ast all! But this stuff interests me. I picked up a book once about Cantor & his investigation of "transfinite numbers"...it lost me in many places, but some of the ideas I gleaned were quite incredible!

But...I have to ask myself this. Maths seems to represent reality extremely well - nature's own language, so to speak. But when it starts delving into infinities etc, I wonder if perhaps its not a 100% true description of reality?

I'm curious, too, just how we've worked out that pi is, in fact, an infinite fraction? I guess I can look that up myself. Interesting, tho'...!

Another thing: is there a pattern to the distribution of prime numbers? Or does it seem completely random?

My training (a long time ago in a place far, far away) was in Math. One thing that came through loud and clear was that IF (big if) Math in some way can be used to represent reality, well, that's nice, but purely accidental and of no importance to a pure Mathematician. There are lots of pieces of Math that no one has found a use for (yet), they just don't get much press until someone does find a use for them (if ever). That doesn't bother Mathematicians, they just keep right on developing the stuff because of it's own beauty. In fact, to pure Mathematician extremist, there's something kind of dirty about useful Math. Damn physicists are always griming up perfectly beautiful pieces of Math by finding uses for them .

Pi is "worse" than just an infinite fraction (ie. an irrational number). It is transcendental. Transcendental numbers are a type of irrational numbers, but they are even harder to define because they cannot even be represented as the root of an algebraic equation, the way the square root of two (also irrational) can. They can only be represented as the limit (or sum) of an infinite series.

Check out Transcendental Numbers for more.

As far as a pattern in prime numbers goes, my understanding is that they appear perfectly random, but there are some patterns there. For instance, there are a class of primes called the Mersenne primes (2^n - 1). Turns out that for n=1 to 10, that number is prime. And for a lot of higher n's, but not for all n.

You seem to think that there are no patterns in random numbers. That's not actually true. That's what statistics is all about. The Normal distribution is a pattern that is different than, for instance, the Exponential distribution, even though both are completely random. You can predict the pattern (eg. the bell curve), just not an individual occurence.

The symbol "pi" in my last post has nothing to do with the "pi" that is that ratio of the radius of a circle to its circumference. They just used that symbol to represent the distribution of prime numbers over x.

If aliens are able to communicate with us, then they would have to know about pi (the geometric one), which was discovered on Earth several thousand years ago (it is mentioned in part of the old testament I believe).

Now I have a plane to catch in a couple of hours. If you'll excuse me

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Climate Change Australia

Have a good flight Kashi, send me back Tokyo as a souvenir...

That is exactly what i am talking about, about pi being a universal constant taht one could be sure that is known by any intelligent life out there...or is that way too anthropogenic

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Damien,
International Baccalaureate Physics teacher
Optics, Photogrammetry and Remote Sensing Instrumentation Major
Admin: Pacific Science and Art

hmm is this the same theory that also uses square numbers because of the odd number of factors? If so I think I have heard of it before.

But since our number system is based on ten, does that mean we have to assume an alien race has to have ten fingers as well for this to work?

Yes that is an assumption, but we can represent a geometric symbol of pi diagrammatically somehow....but yes, we already have a myriad of counting systems in use on Earth.

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Damien,
International Baccalaureate Physics teacher
Optics, Photogrammetry and Remote Sensing Instrumentation Major
Admin: Pacific Science and Art

Again, #'s if used in proper text do make sense. I would assume order is pertainable in all scenarios.

Order is relatively easy to achieve, however, I believe it would be highly unwise to take the view to assume that aliens will understand a human numbering system. Thats where geometric diagrams such as that for pi would come in handy.

__________________
Damien,
International Baccalaureate Physics teacher
Optics, Photogrammetry and Remote Sensing Instrumentation Major
Admin: Pacific Science and Art