Prime Numbers and the Search for Extraterrestrial Intelligence

Prime Numbers and the Search for Extraterrestrial Intelligence

Carl Pomerance, Bell Labs—Lucent Technologies

Apart from tabloid devotees, no one knows for sure if we human beings are alone in the universe as an intelligent species or if there are others, perhaps many others. Given the vast distances involved, it is reasonable to guess that if there is ever contact between humans and intelligent aliens, it will be through the radio spectrum. Fair enough, but how possibly might we actually transmit useful information to each other? English is becoming the “universal” language on our planet at this point, but it is ridiculous to assume that at first contact our alien correspondents would communicate with us in English, or any other Earth language.
The problem of accurate communication even between humans is quite daunting. Our history is marked with episodes of misunderstanding often caused by words or nuances that are misinterpreted. Despite the tragic loss of languages spoken by small and isolated groups of people, one might argue that it is a good thing that we are moving towards just a few principal languages.
We also have some experiences communicating with other species, such as our pets. A dog owner can sometimes tell from the tenor of a bark or a whimper what’s up with Fido. And sometimes Fido hears and obeys his owner’s command. We have also tried to teach apes to speak in sign language, with limited success, and we have tried to interpret the whistles and clicks of dolphins and other whales. While this research is exciting, we still have not found a Rosetta stone that allows for free communication across species. It may be that as technological beings, we just don’t have enough in common with other Earth species.

Which brings us again to possible extraterrestrial civilizations. Could there possibly be a message they could send us that we would be able to understand? Could we likewise send a message that an alien recipient could decipher? In 1960, a German/Dutch mathematician and philosopher, Hans Freudenthal, suggested a language heApart from tabloid devotees, no one knows for sure if we human beings are alone in the universe asan intelligent species or if there are others, perhaps many others.

Given the vast distances involved, it is reasonable to guess that if there is ever contact between humans and intelligent aliens, it will be through the radio spectrum. Fair enough, but how possibly might we actually transmit useful information to each other?
English is becoming the “universal” language on our planet at this point, but it is ridiculous to assume that at first contact our alien correspondents would communicate with us in English, or any other Earth language.

The problem of accurate communication even between humans is quite daunting. Our history is marked with episodes of misunderstanding often caused by words or nuances that are misinterpreted. Despite the tragic loss of languages spoken by small and isolated groups of people, one might argue that it is a good thing that we are moving towards just a few principal languages.



We also have some experiences communicating with other species, such as our pets. A dog owner can sometimes tell from the tenor of a bark or a whimper what’s up with Fido. And sometimes Fido hears and obeys his owner’s command. We have also tried to teach apes to speak in sign language, with limited success, and we have tried to interpret the whistles and clicks of dolphins and other whales. While this research is exciting, we still have not found a Rosetta stone that allows for free communication across species. It may be that as technological beings, we just don’t have enough in common with other Earth species.

Which brings us again to possible extraterrestrial civilizations. Could there possibly be a message they could send us that we would be able to understand? Could we likewise send a message that an alien recipient could decipher?
In 1960, a German/Dutch mathematician and philosopher, Hans Freudenthal, suggested a language he called Lincos to use for possible extraterrestrial communication. It was sort of a pidgin of Latin and logic with short words using the roman alphabet together with logical symbols.2 One could well argue that such a language is not transparent enough.

* 1 Some have argued for an adaptation of Esperanto as a more logical language that is easily learned, but it has yet to catch on in a meaningful way.
* 2 See http://www.geocities.com/monicavdv/informatie-hans/Lincos.html.


A decade later, the American astronomer Frank Drake came up with a brilliant scheme for extraterrestrial
communication involving prime numbers. To get an idea of this, say you were to receive a message of dotsand dashes:

−−•−−−•−•−•−−−•−•−•−−−•−−−−−−−−−−−−−−−−−−−−••−••−−•−•−•

and to distinguish it from noise, after a short pause, it repeats, and then again, and again, and so on. The
repetitive nature would certainly be an eye opener. But what possibly could it mean?
You begin analyzing. The “message” has 55 symbols. Hmmm. The number 55 can be factored into primes
as 5 × 11 or 11 × 5. This suggests putting the symbols into a rectangular array. Lets try 11 × 5:

− − • − − − • − • − •
− − − • − • − • − − −
• − − − − − − − − − −
− − − − − − − − − − •
• − • • − − • − • − •

No, this does not seem to help, it still looks like random noise. Let’s try the other way, 5 × 11:

− − • − −
− • − • −
• − − − •
− • − • −
− − • − −
− − − − −
− − − − −
− − − − −
− − − • •
− • • − −
• − • − •

Wait, this no longer looks so random. Clearly there is some sort of diamond shape at the top. Could the aliens be baseball fans? Probably not, it is likely just a pleasing symbol to get our attention, But what is this strange staircase design at the bottom?
With just 55 pixels it is hard to communicate very much, but an inspired guess might be that the staircase design is counting in binary from 1 to 5. Think of a dot as a 1 and a dash as a 0, and read the bottoms of the 5 columns from left to right: 001, 010, 011, 100, 101. Yes, these are the base-two representations of the numbers 1, 2, 3, 4, 5.

It is easy to imagine that using a longer repetitive message, one might easily send more detailed images.
Even images of photographic quality. And by then sending different pictures, it is conceivable that one could transmit a movie in this way. Which one would you send? My favorite: Attack of the Killer Tomatoes. Well, maybe not, we don’t want to give the aliens any ideas.
The key thing is that each repetitive string should have length pq where p, q are primes, so there are at most two essentially different ways of putting the string into a rectangular array.
In the novel Contact by Carl Sagan, this is exactly the method that the aliens chose to communicate with us earthlings. Currently, SETI (Search for ExtraTerrestrial Intelligence) is systematically searching for messages from outer space, enlisting the aid of people all over the world who have spare computer time.
They haven’t found anything too remarkable as yet, but in some sense we have only just begun our search. In the meantime, have we sent any such messages specifically for alien consumption? Yes, we have.

When the Arecibo radio telescope was inaugurated in Puerto Rico, one of its first jobs was to send a repetitive message into space.5 This message had length 1679, which factors as 23×73. Arranged the long way from top to bottom, the picture contains an amazing wealth of information: the numbers from 1 to 10, the atomic numbers of hydrogen, carbon, nitrogen, oxygen, and phosphorous (the principal elements on which most life on Earth is based), the formulas for sugars and bases in nucleotides of DNA, the number of nucleotides in DNA, a picture of a double helix of DNA, a picture of a person, the human population on Earth, the height of a human, a schematic showing our solar system with Earth in a distinguished position, a schematic of the radiotelescope at Arecibo, and the diameter of the telescope. Measures such as the telescope diameter and the height of a person were calibrated using the wavelength of the transmission of the message, namely 12.6 centimeters. Perhaps a bit crowded to my taste, but it was merely a demonstration of an idea.
The Arecibo message was beamed to the globular cluster M13 which is about 25,000 light years away. Maybe in 50,000 years we will get a reply!

It is interesting that prime numbers would have an application that makes communication transparently simple. Especially so, since many cryptographic systems, designed to hide messages from unauthorized recipients, are also based on prime numbers. And it was not so long ago that prime numbers were merely the province of the curious, with no discernible applications at all. What are the chances that there is an alien species in existence close enough for us to contact? Of course this question is very difficult to answer. Those who think there are other civilizations out there point to the enormous number of stars in the universe. Even if only 1/10 of them have planetary systems, and even if only 1/10 of these have a planet such as Earth that can support life as we know it, and even if only 1/10 of these actually have spawned life, and even if only 1/10 of these have life that has evolved into intelligent creatures, that still leaves a tremendous number of intelligent aliens out there. On the minus side, we might
argue that human civilization has only existed for a very brief time on a cosmic scale, and the technological aspect of our civilization only for a few hundred years at most. Moreover, there are indications that we will not be around very long! We use our technology to foul our own planet and make it less habitable, maybe even uninhabitable. Even though we have clear archaeological and historical records of earlier human civilizations that vanished because of climate changes, we continue to burn fossil fuels as if there were no tomorrow, literally. And when the most advanced and richest country, which produces the most pollutants, is called on the question, its leaders claim that it would hurt our economy to significantly cut back on emissions, and this greenhouse thing really hasn’t been proved anyway. So, if one were to extrapolate to
alien civilizations in outer space, one might conceivably guess that if they are at all like us, they won’t be around very long either. So, while there may have been many intelligent civilizations, the chance that one exists at the same brief time as ours, and also within shouting distance, may be very slim indeed. Nevertheless it is fun to contemplate such contact. And the exercise may help us to be a bit more introspective and responsible as stewards of our own lovely planet.

For further reading on prime numbers:
R. Crandall and C. Pomerance, Prime numbers: a computational perspective, Springer-Verlag, New York, 2001.
For further reading on the liklihood of extraterrestrial civilizations, and how we might detect and communicate with them:
A. G. W. Cameron, Editor, Interstellar communication, Benjamin, New York, 1963.
S. A. Kaplan, Editor, Extraterrestrial civilizations; problems of interstellar communication, (translated from the Russian edition of 1969), Israel Program for Scientific Translations, Jerusalem, 1971.
C. Sagan and F. Drake, The search for extraterrestrial intelligence, Scientific American, May, 1975, pp. 80–89.
I. S. Shklovskii and C. Sagan, Intelligent life in the universe, Emerson-Adams Press, 1998.
W. Sullivan, We are not alone: the continuing search for extraterrestrial intelligence, Plume, 1994.
S. Webb, If the universe is teeming with aliens . . . where is everybody? Fifty solutions to the Fermi Paradox and the problem of extraterrestrial life, Copernicus, New York, 2002.
Finally, a link to the Seti Institute: http://www.seti-inst.edu/.

called Lincos to use for possible extraterrestrial communication. It was sort of a pidgin of Latin and logic with short words using the roman alphabet together with logical symbols.2 One could well argue that such a language is not transparent enough.

Hoofed winged Aliens in Florida

Hoofed winged Aliens witnessed in North Port Florida
These beings sound similar to the famous Witch of Monterrey, which i myself witnessed in Barcelona flying above the San Andreu cemetery about 50 meters above me in broad daylight. The being had black tattered wings and was gliding through the air. This wotness laid a plaster of paris footprint trap to collect evidence, which resulted in what apparently indicates the Aliens to have cloven feet/hooves.

Disclose.tv Original Report Aliens North Port Florida Video

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Google's UFO crop circle doodle logo

Why did google use a ufo making crop circles as it's "doodle" logo in the beginning of September?
Why did clicking on it lead to the search results page for Crop Circles? was this an omen of coming events? a Joke? or some part of a Government Secret disinformation plan? Whas it mere conincidence, or google's choice of the month?
Who knows, but it sure is strange that google chose such a topic for their doodle design and search term.
Is it part of the plan to prepare us for coming events?

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Vimanas - Ancient UFOs?

According to Ancient Indian Beliefs, Aircraft Technology was recieved by Maharshi Bharadwaj from Prajapati.

Maharishi Bharadwaj wrote a book "Vyamanik Siddhanta" was a part of "Yantra Sarvasva" containing description of 25 ancient Indian aircrafts like - Rukma, Shakun, Sundar, Pushpak etc...

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Ufo Evidence

Sit back and watch hours and hours of UFO and alien presence evidence documentaries in one mega playlist. The list starts with "Out of the Blue" the whole series, then a few short fascinating clips, followed by ECETI orbs, more clips of various ufo and ET related evidence, followed with "the Disclosure Project"s, press conference from 2008, and concluded with a host more miscellaneous clips of various et and ufo related material. Hours and hours of fascinating and convincing video evidence.

Alien Cylinder sprays in flight

Is this man made or Alien?

Aldebaran Mystery

The Aldebaran Mystery:
The Nazi/ET UFO Connection by Jim Nichols Feb 10, 2008


Dr. Hermann Oberth who pioneered rocket design for the German Reich during World War II and later advanced rocket technology for the American manned space launches, cryptically stated: "We cannot take the credit for our record advancement in certain scientific fields alone; we have been helped." When asked by whom, he replied: "The people of other worlds."Initiates of both the Thule and Vril societies were determined to develop an 'alternative science' and 'alternative technologies' based on principles possessed by the great 'lost' civilization of Atlantis; a "spiritual "dynamo−technology" superior to the mechanistic notions of modern science". Thus to rediscover this source of universal free energy and make it readily available as a benefit to themodern world became their goal.According to the legend of the German Vril society, a fateful meeting was held in 1919 at an old hunting lodge near Berchtesgaden, where Maria Orsic presented to a small group assembled from the Thule, Vril and Black Sun Societies, telepathic messages she claimed to have received from an extraterrestrial civilization existing in the distant Aldebaran solar system, sixty eight light years away, in the Constellation of Taurus.
One set of Maria's channeled transmissions was found to be in a secret German Templar script unknown to her.
A second series of transmissions appeared to be written in an ancient eastern language, which Babylonian scholars associated with the Thule group, recognized as ancient Sumerian.
Maria Orsic along with Sigrun, another of the Vril Society's female mediums, began the task of translating these transmissions and discovered they contained instructions for building a
circular flight machine. It should be important to consider the possible motivation behind the Aldebaran civilization's offer to assist the Vril Group and Germany. Researcher Wendelle Stevens tells us that, rather than a militant gesture of aid to aggressive Nazis, the Aldebarans perceived an economic disparity in Earth cultures that fueled perpetual wars and conflict.
To alleviate this disparity the Aldebarans reasoned that by offering 'free−energy' technologies, used to create affordable mass transportation devices, a new innovative generation of industries, promoting prosperity and greater peaceful interaction between nations migh result;thus diminishing violent wars.Dr W. O. Schumman and his associates from the University of Munich realized the channeling actually contained viable physics, and over the ensuing years construction was initiated to make this flying machine a reality. By 1922 development of a working prototype was underway. By 1934, the first manned test flight of the RFZ1 took place.
Before the end of that year a much improved version, the five meter RFZ2, was test flown successfully and eventually flying disc development was taken over by Division SS EIV of the
Nazi military. The fundamental physics were as simple as a child's spinning gyroscope circular discs spun in counter-rotation create an anti-gravity effect...



By 1941, the successful Vril−2 levitation craft was employed for transatlantic reconnaissance flights. Th e RFZ-2 craft employed the "Schumman-Levitator" drive for vertical lift and when activated, the craft displayed effects commonly described in many UFO accounts; blurring of visible contours, and luminous ionization colors relative to the craft's engine acceleration; varying from orange to green, blue to white. As well, the craft made radical90 degree turns characteristic of UFO flight.Following the success of the RFZ-2, a single pilot combat mod el was designed. The advanced Vril-1 Fighter was capable of 12000 km/h with full speed right angle turns with no adverse G-effects on the pilot. Since the craft flew in a self-contained envelope of its own gravitational field , the pilot experienced no sense of motion or inertia.Subsequent levitation -craft advances between 1941 and 1944 spawned the "Haunebu" series, the 'heavy hitters' of Reich's saucer fleet Development of powerful tachyon magneto gravitic drives "Thule-Tachyonators" (speculated to be large spheres of vertically rotating mercury) allowed design of foot diameter armored saucer ships equipped with armaments such as Panzer tank cannon turrets mounted to the underside.
Other craft were equipped with klystron laser cannons.By Christmas of 1943, medium Maria Orsic of the Vril Gesellschaft, claimed that subsequent transmissions from Aldebaran revealed there were two habitable planets orbiting that star and that the ancient Mesopotamian civilization of Sumeria was linked to earlier colonies of Aldearan explorers.
The seers discovered that the Aldebaran written language was identical to that of the Sumerians and was phonetically similar to that of spoken German.It was also revealed that a 'dimension channel' or 'worm-hole' existed connecting our two solar systems. Thus in January of 1944, possibly aware that Germany's war efforts were faltering Hitler and Himmler authorized an audacious plan to send a Vril-7 saucer ship into the dimensional channel, perhaps to s ecure assistance from the Aldebaran civilization.
The venture resulted in near disaster, the Vril returned with its hull reportedly aged as if it had been flying for a hundred years and its surface damaged in several places.
In 1944, a massive bombing raid was launched against the critical ball bea ring plant at Schweinfurt. Within a matter of hours a squadron of ten to fifteen Nazi discs managed to shoot down as many as one hundred and fifty British and American bombers
one quarter of the entire bomber contingent. Still, facing overwhelming odds the crumbling Reich lacked sufficient saucer squadrons to turn the tide.
Hans Kammler, a protoge' of Heinrich Himmler, had earned a reputation with his skills for rapid development and implementation of underground manufacturing facilities, and vast mobilization of slave labor consignments from concentration camps. By Kammler had secure d control over all top secret SS projects that were missile or 'aircraft' related. Certainly, Vril projects would have been one of his foremost priori ties. Kammler easily bore the qualifications to mastermind construction of 'special projects' facilities at the South Pole. And as of April 17, 1945, Kammler disappeared from Germany, presumably escaping capture aboard a lumbering, six engine Junkers 390 cargo plane bound for an unknown destination.
A massive 250−foot diameter Haunebu III dreadnaught armed with four, tripl e−gun, heavy caliber naval turrets and capable of space flight was allegedl y completed by April of 1945.Just one month prior to the Haunebu III's comp letion a cryptic message was sent by Maria Orsic to all members of the Vril Society, simply stating:"None are staying here." The psychic medium Maria was never heard from again, perhaps having escaped like Kammler, to South America, the Antarctic, or possibly even Aldebaran! Admiral Richard E. Byrd & Sec Of Defense James Forrestal Coordinated "Operation High Jump" (1947)By inevitably seizing the rocket facilities and personnel at Peenemunde, the advancing Allied Army leadership was only too well aware of how dangerously advanced German technology had become. Despite the Third Reich's unconditional surrender in a potential Nazi threat still haunted Allied i ntelligence. Had the German High Command sacrificed its European operation to buy time for installation of a 'fall-back' position in the Antarctic capable of launching future retaliations from its South Polar redoubt? Posts cript to this legend is the account of "Operation High-Jump".In January of 1947, an American military task force, "Operation High-Jump," complete with thirteen ships including, an aircraft carrier, seaplanes, helicopters and 4000 combat troops was dispatched to the Antarctic under the command of Admiral Richard E. Byrd for the stated purpose of 'mapping' the coastline. This task force was provisioned for an eight month polar stay, but after eight weeks and an undisclosed loss of planes and personnel, Byrd withdrew his forces.Rumor was Byrd encountered overwhelming hostile action, he described as "fighters that are able to fly from one pole to another with incredible speed " He also intimated that he had in fact engaged a German contingent being assisted as well by an 'advanced civilization' with formidable technologies Whatever occurred with Byrd's expedition at the South Pole remains shrouded in mystery since all reports, including Byrd's personal log entries, remain classified.
In then Secretary of Defense Forrestal was sequestered and sent to convalesce for a nervous breakdown at Bethesda Naval Hospital. However after allegedly ranting to hospital staff about the Antarctic, UFOs and an underground Nazi city, Forrestal was denied all visit ors and shortly thereafter, died in a fall from his hospital room window. His death was labeled a 'suicide'.