A Decoded NSA Extraterrestrial Radio Signal from Outer Space

INTRODUCTION

In the previous blog post NSA Discloses We have made Extraterrestrial Contact, I showed a document that NSA published in 2011 after they lost a court lawsuit, showing that they we have received an extraterrestrial radio signal from outer space.  For the most part they were successful decoding it, but in the last message there were many symbols that were left unresolved and undeciphered. There are three opinions on this document:

1. This is simply a "cryptographic exercise" for students at the NSA. This is a popular answer I have seen to explain why there is no attention in mainstream media to this. I discuss this in more detail at the end, it is an easy mistake to make.
2. This was a series of radio messages from a Russian Sputnik satellite. This one is strange, there is no source given for this information.
3. It is what it says it is: an extraterrestrial communication to earth, but "cleaned" for limited release within the NSA in 1969.

For theory #1, the web site NSA practices deciphering ET signals says this:

Some have assumed that these documents were pertaining to messages received from extraterrestrials, an easy mistake to make with article titles such as “Key to the Extraterrestrial Messages.” These documents are actually related to exercises for practicing deciphering coded messages that extraterrestrials may send us in the future.

What I am going to do here now, is completely decode the message.  In my book, The Decoded Prophecies of Nostradamus, I had used some of these decoding techniques to decipher the prophecies of Nostradamus. Nostradamus used anagrams, obscure languages, numbers, astrology - taking years to decipher. Compared to the quatrains of Nostradamus, this one was a piece of cake. Plus Campaigne had done some major legwork. But in the NSA document we have, Campaigne still could not completely decipher it. Why would he present an exercise for which he had no answer? I am going to prove the following:

1. The theory that this was simply a "cryptographic exercise" is false.
2. The story that this came from a Russian Sputnik satellite is also false, and looks like a piece of disinformation spread on UFO sites on the internet.

The post Official ET Disclosure? NSA Document Admits ET Contact brings up some arguments against theory #1, which is easy to miss from people who do not actually read the document:

I contacted someone who is formerly associated with the NSA and still has TS clearance, and asked him to view the document. I asked him to give me his take on it. There was no question about its authenticity since it was published in the NSA Journal, and was released by the NSA on their web site. What I wanted to know was whether this document had any particular impact or importance (other than its startling revelations) for someone familiar with the inner workings of the NSA. It did.
My contact told me that he was blown away by the wording of the document. He said that NSA communications are filled with words like “possibly” , “allegedly”, and “thought to be”.
He said, “This document has none of the normal NSA disclaimer words in it. They just come out and say ‘we received messages from outer space’ and this is the way to decode those messages.”
I asked, “What does that mean to you?”
His reply was instant.
“Disclosure, pure and simple. They aren’t making any fanfare about it, but there it is. They have just made open disclosure.”

I am going to now completely decode it, so I am going to embed the actual document again for those who wish to follow along:

  NSA Alien Message

The document which shows the first 29 messages is here: http://www.nsa.gov/public_info/_files/cryptologic_spectrum/extraterrestrial_intelligence.pdf.
The follow up, showing 31 messages, is here: http://www.nsa.gov/public_info/_files/ufo/key_to_et_messages.pdf

THE INTERPRETATION

Now let us go through the series of the 31 messages:

1. The list of all 22 symbols: ABCDEFGHIJKLMNOPQRSTUV

Comment: it is not said what the radio signal looks like, nor when and where it originated (probably classified). Alphabetic letters are used in place of specific radio signals. Although the document states that the alphabetic letters are used as a matter of convenience for writing down the signals, it will be shown below that the alphabetic letters do in fact provide clues to the actual meaning of each radio signal. Also the NSA document says there are 21 symbols, which is incorrect, there are 22.

2. A is 1, B is 2, C is 3, D is 4, E is 5, F is 6, G is 7 (A is 1 is implied)
3. 1=1, 2=2, 3=3, 4=4, 5=5, 6=6, 7=7 (L means "equal", and the syntax is operator followed by operands.
4. 1+1=2. 1+2=3. 2+1=3. 1+3=4. 2+2=4. 3+1=4. 1+4=5. 2+3=5. 3+2=5. 4+1=5. 1+5=6. 2+4=6. 3+3=6. 4+2=6. 5+1=6. (The letter "K" defines a group to add)
5. (3+2)+1=6. (1+2)+3=6. (4+2)+1=7. (3+1)+3=7. (3+2+1)=(3+2)+1. (Last statement has 2 extra K symbols. "LK" means "equal" where "KK" appear together.)
6. 2-1=1. 3-1=2. 3-2=1. 4-1=3. 4-2=2. 4-3=1. 5-1=4. 5-2=3. 5-3=2. 5-4=1. (M defines a group to subtract. For subtraction, order is important, unless M means "difference" between the following numbers. So at this point not sure if the order of the operands is important.)

Comment: all the numbers go up only to seven. It is possibly that this is an octal numbering system. The symbol for "M" can stand for "minus" in the English language. If that is the case, "K" can stand for "combine" or "accumulate". Also, the letter "L" means "equal" as the letter "L" is the last letter in the word "equal". Could this mean familiarity with the English language? It would also indicate that this signal, wherever it came from, was intended for an English speaking nation (i.e., the United States of America).

7. 1-1=0. 2-2=0. 3-3=0. 4-4=0. 5-5=0. 6-6=0. 7-7=0. (N means 0)
8. 1x1=1. 1x0=0. 1x2=2. 2x1=2. 2x0=0. 0x2=0. 2x2=4. 1x4=4. 1x6=6. 2x3=6. (The letter "O" means multiply).
9. (2x3)x1=6. (1x2)x3=6. (1x3)x2=6. (4x5x6)=(5x6)x4. (Last statement has 2 extra O symbols. "LO" means "equal" where "OO" appear together.)

Comment: For message #7, notice how the letter "N" is again the initial for the meaning of the letter. The letter "N" means "nothing" for the number 0. Message 7, a number substracted from itself is 0, corresponds to message 3, which is the identity of the first seven numbers. Messages 8 and 9 for multiplication correspond to messages 4 and 5 for addition.

The question arises, why would the letter "O" be used for the multiply operator? In Math, there is a concept known as "big O notation" which is used to measure the growth of functions. The concept is similar to multiplication, but broader: big O measures functions as a product, a sum, or multiplication by a number.

10. 2^2=4. 2^1=2. 2^0=1. 3^1=3. 3^0=1. (The letter "R" means exponentiation).
11. 4+4=2^3. 1+7=2^3. 2x4=2^3. 4=2^2.
12. 4+5=3^2. 3x3=3^2.

Comment: Here we discover the letter "R" is an operator meaning "exponentiation". The meaning can also be worded as "raise to the power." The letter "R" is the first letter in the word "raise" and the last letter in the word "power". There is another meaning to "R" which is discussed later.

13. J=2^3. J=1+7. J+1=3x3. J+1=3^2.

Comment: This messages means "the letter J is the number 8". This is odd. One would expect the letter H to be the number 8, as the letter G is the number 7. This message is letting us know that it is skipping the letters H and I to continue the numbering at letter J. Could this be on purpose? If these radio signals were intended to be translated into the English alphabet, then the letters H and I might be skipped to send a message to earth: "HI." "Hi there!" "Hello!" What a clever way to send a message of greetings, if true. Another reason why J=8: in our mathematics, we use base 10 numbers. In their mathematics, they use base 8 numbers. Thus they are changing the value of J from the expected 10 to 8. They are saying: "we use octal numbers, not decimal numbers." Which means: they know we use decimal numbers in our mathematics.

14. 8/4=2. 8/2=4. 3/3=1. 6/2=3. (The letter "P" means division)

Comment: the letter "P" may have been chosen for division. The letter P is the first letter in the word "part" and "partial".

15. 1 is less than 2. 2 is less than 3. 3 is less than 4. 5 is less than 8. 6 is less than 8. 7 is less than 8. 2^3 is less than 3^2. (The letter "U" means "less than")

Comment: the letter "U" is the first letter of the English word "under" - another way of saying "less than". Also, the symbol for "less than" (<) is a sideways U! Another indication that the translation of the radio signals to the English alphabet was intentional, and not just a matter of convenience for writing it down. Did the folks at NSA completely miss this?

16. It is false that 0=1. It is false that 1=3. It is false that 1+1=1. It is false that 1x1=0. It is false that 2^2=2. It is false that 2<2. (undeciphered). It is false that 3 is not equal to 3. It is false that 8<7. (The letter Q means "not" or "the following statement is false. "QL" means "not equal".)

Comment: The letter Q means "not" or the following is false. Q happens to be the first letter of the word "Questionable". Which may indicate, in the culture that generated this message, it may be customary not to declare someone outright wrong or a statement as false, but to bring up a question, is that true or false?

Now in this message there is an undeciphered statement: QHLAALAB, which is transliterated in the NSA document as Q: H(1=1)(1=2). The NSA document says: "The second new symbol is not clear, except that it is an operator whose operands are statements, not quanties, a Boolean operator." We see that 1=1 is true, and 1=2 is false. The letter "H" may mean "implies" or "is the same", and QH means "does not imply" or "is not the same". Thus the undeciphered statement means, "1=1 does not imply 1=2", or vice versa.

We should note, that the letter J was originally not a part of the alphabet, and originally was an alternate way of spelling the letter I. In the alphabet sequence, we have HIJ. This would mean "the letter I implies J", or "the letter J implies I" - which it did, in the earlier English alphabet!

If I were to guess what English word is implied by the letter H, all I can come up with now is the word "hither", meaning "from here to there", an alternative way of saying "implies". The word "hither" is also close to the phrase, "Hi there!", again indicating that the letters HI means "hi". Thus we have "Hi there from here to there". The letter H comes after the first seven letters - could this mean the seven known planets of our solar system from antiquity? Thus we have, "Hi there, from beyond your solar system to earth". The word "EARTH" is a valid anagram of "THERE". This is a message derived from implication, which is what H means. Special attention should be given to this statement, as unlike all the others which preceded it, it pops up once in the message making it harder to decipher.

Another reason why I think the first seven letters may indicate the seven known planets of our solar system is that in antiquity, there were seven vowels of the alphabet, and each of these were considered to be symbols of the seven planets of the known solar system. The NSA folks may have missed this as they are probably unfamiliar with ancient mythology. NSA also probably presumed that the senders of the radio signal know nothing about us. That is becoming apparently not true. Or as they would say, "questionable".

17. It is true that 1=1. It is true that 1<2. It is true that 1+1=2. It is true that 1x1=1. It is true that 1-1=0. It is true that 6/6=1 implies 1x6=6. It is true that 1=1 implies that 2=2. (the letter "S" means "the following statement is true")

Comment: the letter "S" is opposite in meaning to the letter "Q". As "Q" is the first letter of the word "questionable" (meaning false), the letter "S" is the first letter of the word "statement" (meaning true).

18. 1T=1. 1T+1=2T. 2T+3T=5T. 3Tx2T=6T. 7T=7. 10T=8.

Comment: the letter "T" indicates a decimal point (more accurately, an octal point), and means "the preceding numbers form an octal number". The last statement is revealing: 1 and 0 are put next to each other to indicate 10, which in an octal numbering system would be equivalent to 8. The other thing to note, which NSA again missed, is that the letter "T" may stand for the English word "terminator". In our language, the period is used to terminate a statement, and is also used for a decimal point. Note that in the alphabet, "T" comes after the letter "S". As the letter "S" stands for "statement", it is followed by a "T" which "terminates" the statement. Very clever intelligence here: they are trying to communicate with symbols that we know.

19. 123T = 1 x 8^2 + (2 x 8^1 + 3). 321T = 3 x 8^2 + (2 x 8^1 + 1 x 8^0). 4567T = (4 x 8^3) + (5 x 8^2) + (6 x 8^1) + (7 x 8^0).

Comment: clearly, they use octal arithmetic, or a base-8 numbering system. In our math we use a decimal or base-10 numbering system. Octal and hexadecimal numbering is often used in computer languages. In ancient times, Native Americans in California used an octal numbering system. Pamean languages in Mexico also have octal systems. The speakers would count using the spaces between the fingers instead of using the fingers themselves. Now, it should be noted that the intelligence community will release information concerning UFOs and extraterrestrials in the form of fiction and fictional movies (e.g., The Day the Earth Stood Still was among the first). That is the only way they can legally release information to the public when something is classified as top secret. Note the following facts:

1. In the 2009 film Avatar, the language of the extraterrestrial Na'vi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand.
2. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, used an octal system of mathematics. 

Coincidence? As for Stargate, there are rumors that the U.S. military has back-engineered extraterrestrial technology to create a teleporter, based on the Philadelphia Experiment in the 1940s and the later experiments at Montauk. Below is a video from Mexico, which shows an alien that teleports out of nowhere and attempts to grab a young man playing soccer. Upon later examination, scientists discovered a high unexplained level of radiation that permeated the area where the alien appeared and disappeared in the cell phone video. How's that for physical proof? Check it out:

In two separate movies we have an extraterrestrial culture that uses octal numbering. In two separate movies it is the U.S. military that makes contact with extraterrestrials. Check out this trailer from the movie Stargate, where someone says "I have identified the seventh symbol", and there happen to be 7 letters for 7 numbers in the very message we are decoding:

Is it a coincidence that researchers have identified links between ancient Egypt and Mars, and Stargate is showing a link to a civilation similar to ancient Egypt? Cairo is Arabic for the planet Mars, and the ancient Egyptian name for the Sphinx - Horus of the horizon - is also the ancient Egyptian name for the planet Mars. And we have the face of Mars that looks like the Sphinx. If the U.S. military has reverse engineered extraterrestrial technology, would they disclose it to the public? I think not. Except they sort of did...I would refer anyone to the book, The Day After Roswell, by Colonel Philip J. Corso.

Back to the radio signals: they now start to get more complicated, so I will also show the original message along with the interpretation. Coincidentally, in the movie Stargate, the seventh symbol has a V in it (see the trailer above). This symbol is also called "the point of origin" - and V is the last letter of this alphabet, returning us back to A, the first letter:

And now we start seeing a ton of the letter V in these messages:

20. (in the following messages the letter "V" indicates a variable)
HLJKAAVLGAV = 1+AV=8 implies AV=7.
HLAATRCAVLBAV = 9=3^AV implies AV=2.
HLCAVLAATRAVB = AV=3 implies 9=AV^2.
HLEAVLFKAAV = AV=5 implies 1+AV=6.
HLCKAGOVLBGOV = 1+GOV=3 implies GOV=2.
HLFOBSOVLCSOV = 2xSOV=6 implies SOV=3.
HLCDOVLAATRDOVB = DOV=3 implies DOV^2=9.
SLKAVPVKPVAV = It is true that AV+PV=PV+AV.
SLOAVPVOPVAV = It is true that AVxPV=PVxAV.
SLKAVKPVTVKKAVPVTV = It is true that AV+(PV+TV)=(AV+PV)+TV.
SLOAVOPVSVOOAVPVSV = It is true that AV*(PV*SV)=(AV*PV)*SV.
HQLAVBVQLMAVBVMBVAV = AV not equal to BV implies AV-BV is not equal to BV-AV.
HQLAVBVQLRAVBVRBVAV = AV not equal to BV implies AV^BV is not equal to BV^AV.

Comment: as explained in the NSA document, the letter "V" stands for variable, and means treat the preceding letters as variables. Again, NSA was blind to the fact - or did not disclose - that these radio signals were intended to be translated into alphabetic letters, for the letter "V" is the first letter of the word "variable". Variables are used in algebra, but are also very common in computer programs. In the above statements we have variables A, GO, SO, DO, P, T, S and B. A few of the above statements are showing the truth of the commutative property for addition and multiplication.

21. (in the following messages "UV" means "or")
HLNKBMRDDDVBODDDVCUVLADDDVLBDDDV = 2+(DDDV^2-(DDDVx3))=0 implies DDDV=1 or DDDV=2.
HUVLADVLMNADVLARDVB = DV=1 or DV=0-1 implies DV^2=1.
HUVLABVLNBVLNMBVRBVB = BV=1 or BV=0 implies BV-BV^2=0.
SUVLAVBVQLAVBV = It is true that AV=BV or AV is not equal BV.
SUVUAVBVUBVAV = It is true that AV

Comment: NSA concluded from the last statement that the letter "U" must mean "less than or equal" instead of just "less than". This is possibly incorrect, if it is assumed that different variable names means they have different values.

22. (in the following messages "TV" means "and")
QTVUAVBVUBVAV = It is false that AVQTVLAVBVQLAVBV = It is false that AV is equal to BV and AV is not equal to BV.HTVLRAVBDUNAVLAVB = AV^2=4 and 0HQUAVBVUVUBVAVLBVAV = AV greater than or equal to BV implies BVSHQTVGVHVUVQGVQHV = It is true that !(GV and HV) implies not GV or not HV.SHQUVGVHVTVQGVQHV = It is true that !(GV or HV) implies not GV and not HV.
LUVAVUVBVCVUVUVAVBVCV = AV or (BV or CV) = (AV or BV) or CV.
LTVAVTVBVCVTVTVAVBVCV = AV and (BV and CV) = (AV and BV) and CV.
LTVAVUVBVCVUVTVAVBVTVAVCV = AV and (BV or CV) = (AV and BV) or (AV and CV)
LUVAVTVBVCVTVUVAVBVUVAVCV = AV or (BV and CV) = (AV or BV) and (AV or CV)

Comment: the fourth statement conclusively shows that the letter "U" means "less than". The fifth statement starts to spell out some axiomatic boolean logic rules used in set theory.

23. (in the following messages, "JNV" means "contains", as in set theory. "UV" ("or") now means the union of the two sets, and "TV" ("and") means the intersection)
JNVUVBAVCAVBAV = (BAV or CAV) contains BAV.
JNVBAVTVBAVCAV = BAV contains (BAV and CAV).
JNVUVBAVCAVTVBAVCAV = (BAV or CAV) contains (BAV and CAV).
HJNVBAVCAVLBAVUVBAVCAV = BAV contains CAV implies (BAV or CAV) = BAV.
HJNVBAVCAVLCAVTVBAVCAV = BAV contains CAV implies (BAV and CAV) = CAV.
HTVJNVBAVCAVJNVCAVBAVLBAVCAV = (BAV contains CAV) and (CAV contains BAV) implies BAV = CAV.
HJNVBAVCAVJNVQCAVQBAV = BAV contains CAV implies (not CAV) contains (not BAV).
SHTVJNVBAVCAVJNVCAVJNVCAVDAVJNVBAVDAV = CAV contains DAV BAV contains DAV

Comment: the letters "JNV" were probably used to mean "contains" as "JNV" could mean "everything from 8 to 0", which would be significant in a culture that uses octal numbering. Just as we traditionally countdown from 10 to 0 in rocket launch sequences. The messages began with the simple variable "AV", which for us would mean "variable A". In the set theory statements, it is always "CAV" or "BAV", to indicate "the set of variables". Also, A is the beginning of the alphabet, and V is the ending of the alphabet, and put together they form the beginning and end, containing the whole set of letters. Thus in the above statements, BAV, CAV, and DAV translate into "the sets of B, C, and D".

24. 1 is a member of JAV. 2 is a member of JAV. 3 is a member of JAV. 4 is a member of JAV. 5 is a member of JAV. 6 is a member of JAV. 7 is a member of JAV. 8 is a member of JAV. 9 is a member of JAV. 10 is a member of JAV. H NKV AV JAV NKV K AV A JAV = AV is a member of JAV which implies AV+1 is a member of JAV.

Comment: in the above, "NKV" is a verb meaning "is a member of" in set theory. The reason for that is presumably it is composed of "N" meaning nothing and "K" meaning add or combine. Here we see a pattern: the letter "V" may not only just stand for the word "variable", but now "verb". Thus we also have "UV" = or, "TV" = and, "JNV" = contains. "Or" and "and" can be taken to be verbs in set theory, for they can indicate an action done on sets. The above statement is trying to convey the message, "the set of positive integers". But notice it goes from 1-10, showing an awareness of the decimal system. The reason why "JAV" is chosen as the set name is that it can indicate the set of numbers from 1 (A) to 8 (J) in their octal numbering system.

25. 1 and 2 are members of JAV. 1 and 2 and 3 are members of JAV. 14 and 17 are members of JAV. 77 and 100 and 101 are members of JAV. HTVJNVAVNMVJNVBVNMVJNVTVAVBVNMV = AV contains NMV and BV contains NMV implies (AV and BV) contains NMV. 0 is a member of JAV. 8 is a member of JAV. 8^2 is a member of JAV. 8^3 is a member of JAV. 8^4 is a member of JAV. 8^8 is a member of JAV. 8^10 is a member of JAV. 8^100 is a member of JAV. 8^1000 is a member of JAV. BV is a member of JAV which implies 8^BV is a member of JAV.
H NKV TV BV CV JAV NKV K BV CV JAV = (BV and CV) as a member of JAV implies (BV + CV) is a member of JAV.
H NKV TV BV CV JAV NKV O BV CV JAV = (BV and CV) as a member of JAV implies (BV x CV) is a member of JAV.
H NKV TV BV CV JAV NKV R BV CV JAV = (BV and CV) as a member of JAV implies (BV^CV) is a member of JAV.
It is false that 1/2 is a member of JAV. It is false that 1-2 is a member of JAV. It is false that 0-3 is a member of JAV. It is false that 7/6 is a member of JAV.

Comment: this message confirms the previous message, that the set JAV was the set of positive whole numbers. The only difference here is that 0 is included in the set JAV, which would mean the set of non-negative whole numbers. Two letter symbols such as "AV" and "BV" indicate variables, three letter symbols such as "BAV" and "JAV" indicate sets of variables.

26. JAV is a member of JOV. 0-1 is a member of JOV. 0-BV as a member of JAV implies that BV is a member of JOV. 1/2 is a member of JOV. (AV and BV) as a member of JOV implies that AV-BV is a member of JOV. It is false that 1/0 is a member of JAV. It is false that 1/0 is a member of JOV.
It is true that (AV/BV)x(CV/DV)=(AVxCV)/(BVxDV).
It is true that (AVxBV)<(BVxCV)=(AV/BV)<(CV/DV). BV x DV is not equal to 0.
H NKV AV JAV U M N A AV = AV as a member of JAV implies 0-1 < AV.

Comment: the set JOV is the set of rational numbers, which does not include numbers divided by 0. The set of rational numbers includes the set of non-negative whole numbers, which is indicated by the set JAV.

27. (AV implies BV) and (BV implies AV) implies that AV and BV are logically equivalent. The logical equivalence of AV and BV implies (AV implies BV) and (BV implies AV).  The logical equivalence of AV and BV is logically equivalent to (AV implies BV) and (BV implies AV).

Comment: in this message we have a new verb, "HV" meaning "logically equivalent". This word is built up from "H" meaning "implies". Conceivably the letter "L" for "equal" could have been used, but this indicates equality of numbers is viewed as a separate concept from logical equivalence. However, in a previous message the letter "L" for equality was used for a set theory statement. What is curious, is that math and set theory is being used to build up to higher logical concepts. The mathematician Bertrand Russel went in the opposite direction: he wrote over 300 pages of logical statements in his work Principia Mathematica to prove that 1+1=2. This would indicate that in this culture, math is considered the foundation of logic, not the other way around. Or it is understood that it is easier to begin teaching with math before moving to higher logical statements. From logic, the next step would be to start creating words. And these words can be used as a form of communication. The letter "V" was first a variable, then a verb, now it is more generalized as a "word" (the Letter "W" is a double V). This is a much better way for establishing contact than the Arecibo message that Carl Sagan conceived of years ago.

28. 3=GV^2 implies GV is not a member of JOV. 2=GV^2 implies GV is a not member of JOV. 5=GV^2 implies GV is a not member of JOV. 5=GV^2 implies GV is a member of JEV. JOV is a member of JEV. JAV is a member of JEV. 0-1=GV^2 implies GV is not a member of JEV.

Comment: in message 26 it was stated that the set of JOV is the set of rational numbers. In this message, the set of JEV is the set of real numbers. The last statement states that this set does not include imaginary numbers. Imagine that. They know of imaginary numbers.

29. 1 - 2^(0-1) is a member of JBV. 1 - 3^(0-1) is a member of JBV. 1 - 4^(0-1) is a member of JBV. 1 - NV^(0-1) is a member of JBV. 1 is the limit of JBV. 1/1 is a member of JCV. 1/2 is a member of JCV. 1/3 is a member of JCV. 1/NV is a member of JCV. 0 is the limit of JCV. (1-(1/2))^2 is a member of JBV. (1-(1/3))^3 is a member of JBV. (1-(1/4))^4 is a member of JBV. (1-(1/8^100))^(8^100) is a member of JBV. (1-(1/NV))^NV is a member of JBV. The limit of JBV is a member of JEV.

Comment: in this message we have a new word: "NLV" which means "limit".  In the first 3 statements, as the subtracting number gets higher, the answer approaches the limit of the number 1. This increasing number is generalized as "NV". "NLV" is chosen as "limit" as "N" means nothing or 0, and "L" means equal: as one number gets smaller and approaches zero, the answer will tend to equal the limit.

30. JAV contains 1. JAV contains 2. JAV contains 3. JAV contains the sequence 1,2,3. The sequence 1,2,3,4 contains AV implies JAV contains AV. The sequence 4,5 = the intersection of the sequence 1,2,3,4,5 and the sequence 4,5,6,7. The sequence 1,2,3,4,5,6,7 = the union of the sequence 1,2,3,4,5 and the sequence 4,5,6,7.

Comment: There is a new verb here, "STV", which means "the sequence", and when found the preceding numbers are to be treated as a sequence. This is similar to "T" where the preceding numbers are to be treated as a single octal number. The reason why "STV" is chosen for the word "sequence" is that "STV" uses "S" for statement and "T" for terminator. In the NSA document, there is doubt here about the meaning of the verb "JNV": instead of "contains" it is now thought it means "belongs to". However I still interpret it as "contains", but with the operands reversed. The verb "contains" means the variable that is the group should contain the singular variable. Or there is just an error in the original message where they accidentally switched the order of the operands.

THE DECODED PERIODIC TABLE OF THE ELEMENTS

This message is big. And it contains some big surprises, which was not understood in the original NSA document. And now, it is completely decoded for the first time:

31. CHAV contains JR1V. CHAV contains JR2V. CHAV contains JR7V. CHAV contains the sequence JR1V, JR2V, JR3V, JR4V, JR5V, JR6V, JR7V.
CHAV contains JO1V. CHAV contains JO2V. CHAV contains JO18V. CHAV contains the sequence JO1V, JO2V, JO3V, JO4V, JO5V, JO6V, JO7V, JO8V, JO9V, JO10V, JO11V, JO12V, JO13V, JO14V, JO15V, JO16V, JO17V, JO18V.
(0 < AV) and (AV < 18) implies CHAV contains JOAVV.

Comment: we have a few variable names, and it looks like A,B,C etc. in the variable names indicate numbers. So instead of listing "JRAV" I have listed "JR1V" and so on, using the decimal representation. The NSA document did not bother to convert to decimal, making it rather confusing.

I want to discuss the statement "(0 < AV) and (AV < 18) implies CHAV contains JOAVV." NSA thought this message was garbled. At first I thought there was an extra V in JOAVV, but what that seems to mean is that "AV" should be taken as a variable for subscripts. It seems to reference the previous statement, where 18 "things" are declared as part of CHAV. This group of "things" is then referenced as JOAVV. However there is a slight error here, AV < 18 should be AV < 19.

As stated in the NSA document, this message begins to describe the periodic table of the elements, but does not explain everything accurately and I am not sure if NSA understood all the terminology here. Again, NSA failed to note the alphabetic connection. "CHAV" simply means "chart".  It could also possibly be "the set of chemicals", or "chemical chart". This chart has 18 "things" - and this can only mean the 18 groups of the periodic table. These groups are the columns of the periodic table, and columns are indicated by the letter "O" in variables such as "JO1V", which refers to the first group or column. Then the first statement is easy: the variables "JR1V" through "JR7V" are the 7 periods or rows of the periodic table. The "R" in each of these variables stands for row. Simple! However, the NSA document misinterprets the information. It states, "JRx means column x, an JOy means row y." This is completely wrong: JR refers to the row, and JO refers to the column. All one has to do is take a look at the periodic table, which I will include so that the interpretation is easy to see:

So, this is obvious: the 18 "things" are the 18 groups of the periodic table. So how come Howard Campaigne missed this?  I did a little research on the periodic table, and found this from Wikipedia:

...groups 8, 9 and 10 used to be treated as one triple-sized group, known collectively in both notations as group VIII. In 1988, the new IUPAC naming system was put into use, and the old group names were deprecated.

To see the proposal in 1988 to change the periodic table to have 18 groups, see the actual IUPAC proposal here: http://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf.  Discussion to change the groups of the periodic table began in the 1980s. SO IF THIS WAS AN NSA CRYPTOGRAPHIC EXERCISE FOR STUDENTS IN 1969, EXPLAIN TO ME, HOW IS IT A SIMPLE STUDENT EXERCISE WOULD HAVE A PROPOSAL FOR THE PERIODIC TABLE OF THE ELEMENTS THAT WAS 20 YEARS AHEAD OF ITS TIME? As we shall see, this periodic table described in this coding is still different from our periodic table.

For a nice dynamic periodic table of the elements in your browser, check out: http://www.ptable.com/.  Now we continue with message 31, which I will break up in sections as it is long:

JR1V contains BL1V. JR1V contains BL2V.
JR2V contains BL3V. JR2V contains BL4V. JR2V contains BL10V.
(AV >= 3) and (10 >= AV) is logically equivalent to JR2V contains BLAVV.
(AV >= 11) and (18 >= AV) is logically equivalent to JR3V contains BLAVV.
(AV >= 19) and (36 >= AV) is logically equivalent to JR4V contains BLAVV.
(AV ?>=? 37) and (54 >= AV) is logically equivalent to JR5V contains BLAVV. (message is missing a "U" marked by ?)
(AV >= 55) and (86 >= AV) is logically equivalent to JR6V contains BLAVV.
(AV >= 87) and (98 >= AV) is logically equivalent to JR7V contains BLAVV.

Comment: this now describes in detail each row or period of the periodic table of the elements. The first line above says that the first period (JR1V) contains the elements of Hydrogen (BL1V) and Helium (BL2V). The second row contains the elements from Lithium (BL3V) to Neon (BL10V). And so on. Again there is an alphabetic connection: "BL" in these variables simply stand for "block". Each of the elements is a block in the periodic table. The number that follows BL is the atomic number - something the NSA document missed.

One important to make here: period or row 7 is declared to have up to 98 elements, which at present time goes up to 118. Element 118 is Ununoctium which was was shown to exist in 1999. Element 98 is Californium which was discovered in 1950. Element 99 is Einsteinium which was discovered in 1952. Fermium, element 100, was also discovered in 1952. Mendelevium, element 101, was discovered in 1955. This particular article was published at NSA 1969, according to http://www.nsa.gov/public_info/declass/tech_journals.shtml.

So what is going on here? Here is what I think: this message was received between the years of 1950 and 1952. This means those stories going on around the internet that this was received by Sputnik are false. I was suspicious of it as I can not find the original source for that information. Sputnik was launched in 1957. It would seem that is a planted story to spread disinformation - and the disinformant is present in UFOlogical circles. The NSA article mentions element 103 in its interpretation, which was discovered in 1961 - indicating the article was written after that time. The disinformants thought they could get away with passing this message off as having been received by Sputnik. But this message was received some time back in 1950 to 1952, which is closer in time to the Roswell crash in New Mexico in 1947.

So why is the message trying to describe the periodic table? Because we now have words for every single element. If we now want to say the word "water", we can simply write a phrase saying "water is the set that includes two hydrogens and one oxygen". Bingo. We now have a method of communication via radio signals.

JO1V contains the sequence BL1V BL3V BL11V BL19V BL37V BL55V BL87V.

Translation: group 1 contains Hydrogen, Lithium, Sodium, Rubidium, Caesium, Francium.

JO2V contains the sequence BL2V, BL4V, BL12V, BL20V, BL38V, BL56V, BL88V.

Translation: group 2 contains Helium, Beryllium, Magnesium, Calcium, Strontium, Barium, Radium.

This is odd. Helium, in the period tables, is in group 18. But this message is putting it in group 2. Why is that? For this, I found the wiki question, Why can Helium be placed in group 2?.  Here is the answer:

The reason it can be placed in group II is because it has 2 electrons in its outside shell (also its only shell) and the groups represent how many electrons in the elements outside shell. The reason it is normally placed in group 8 or 0 is because the first shell has a maximum of 2 electrons and all elements that have a full outside shell are placed in group 8/0 and can't normally react.

This is interesting. All periodic tables I have seen have put Helium in group 8.

JO3V contains the sequence BL5V, BL13V, BL31V, BL49V, BL81V.

Translation: group 3 contains Boron, Aluminum, Gallium, Indium, Thallium.

WHAT IS GOING ON HERE? All of those elements are in group 13 in our periodic table. This is another indication this was not a cryptographic exercise at NSA. Has anyone bothered to decipher this message? Apparently not. This is describing a different periodic table of the elements. At this point, it is skipping the transition metals, which are supposed to be groups 3 through 12. This was unexpected. Upon further examination, all of these elements have 3 electrons in their outer shell. So...perhaps it makes sense to skip the transition metals, and put these under group number 3 instead of 13. Digging a little deeper, I decided to research the history of the periodic table of the elements. A the Chemogenesis web site, I found The Modern Periodic Table from 1950. Check it out, it will completely explain the message:

We see Helium above Beryllium, and the p-Block follows the s-Block. This is still not historically accurate as it is including elements that were not known in 1950. As will be seen below, the message is basing itself on this 1950 periodic table. The Chemogenesis web site states, "The problem with this mapping is that the generated sequence is not continuous with respect to atomic number."  Also, it does not show the f-Block elements in their proper location as the modern periodic table does. Also note: THE 1950 PERIODIC TABLE OF THE ELEMENTS MAY NOT EVEN HAVE HAD THE CONCEPT OF "GROUPS". This again explains why Campaigne missed it: the message contains information that was ahead of its time.

JO4V contains the sequence BL6V and BL14V and BL32V and BL50V and BL82V.

 Translation: group 4 contains Carbon and Silicon and Germanium and Tin and Lead.

This is actually describing group 14, not group 4 in our most recent periodic table. It begins to follow the pattern of the 1950 periodic table. The other strange thing about this message is that they decided to add the word "and" between each element, in case we didn't get it yet. If we examine all the elements, guess what? They all have four electrons in their outer shell. Group 4 makes sense.

JO5V contains the sequence BL7V, BL15V, BL33V, BL51V, BL83V.

Translation: group 5 contains Nitrogen, Phosphorus, Arsenic, Antimony, Bismuth.

This is actually group 15, skipping the transition metals. All of these elements have 5 electrons in their outer shell.

JO6V contains the sequence BL8N, BL16V, BL34V, BL52V, BL84V. (there looks like a transcription error here, where a V was mistaken for an N: BL8N should be BL8V.)

Translation: group 6 contains Oxygen, Sulfur, Selenium, Tellurium, Polonium.

This is actually group 16, skipping the transition metals. All of these elements have 6 electrons in their outer shell. One remark: is it possible that the original message contained BL8N instead of BL8V for the element oxygen? They might be calling attention to this element, as our planet has an oxygen atmosphere. The letter "N" means nothing. This possibly means: their atmosphere is nothing, that is, outer space. Whoever sent it comes from outer space where there is no oxygen.

JO7V contains the sequence BL9V, BL17V, BL35V, BL53V, BL85V.

Translation: group 7 contains Fluorine, Chlorine, Bromine, Iodine, Astatine.

This is actually group 17, skipping the transition metals. I believe all of these elements have 7 electrons in their outer shell.

JO8V contains the sequence BL10V, BL18V, BL36V, BL54V, BL86V.

Translation: group 8 contains Neon, Argon, Krypton, Xenon, Radon.

This is actually group 18, skipping the transition metals. Perhaps they like to do this as one would end up with 8 groups in the periodic table, as it would be more "elegant" for those who used an octal numbering system. However it makes sense: all of these elements have 8 electrons in their outer shell.

JO9V contains the sequence BL21V, BL39V, BL57V, BL58V, BL59V, BL60V, BL61V, BL62V, BL63V, BL64V, BL65V, BL66V, BL67V, BL68V, BL69V, BL70V, BL71V, BL89V, BL90V, BL91V, BL92V, BL93V, BL94V, BL95V, BL96V, BL97V, BL98V.

Translation: group 9 contains Scandium, Yttrium, elements 57 through 71, elements 89 through 98.

This is actually group 3, the start of the transition metals. In this big long list, it properly includes the Lanthanoids and Actinoids. All of these elements have 9 electrons in their secondmost outer shell - the outer shell actually contains 2 electrons. This is the one line that the NSA document interprets correctly, stating: "On consulting a table we find, sure enough, that elements 57 through 71 are rare earths, and are lumped into one cell. Some, but not all, authorities also list 89 through 103 as rare earths. Elements 21 and 39 are Scandium and Yttrium." For Campaigne, this may not have made sense, but in our modern periodic table it does: Scandium and Yttrium are in the same group as elements 57 through 71 and elements 89 through 118.

JO10V contains the sequence BL22V, BL40V, BL72V.

Translation: group 10 contains Titanium and Zirconium and Hafnium.

This is actually group 4 in our periodic table. This statement also adds unnecessary "ands". All of these elements have 10 electrons in their secondmost outer shell.

JO11V contains the sequence BL23V, BL41V, BL73V.

Translation: group 11 contains Vanadium, Niobium, Tantalum.

This is actually group 5 in our periodic table. All of these elements except Niobium have 11 electrons in their secondmost outer shell. Niobium has 12.

JO12V contains the sequence BL24V, BL42V, BL74V.

Translation: group 12 contains Chromium, Molybdenum, Tungsten.

This is actually group 6 in our periodic table. Only Tungsten as 12 electrons in its secondmost outer shell, the others have 13.

JO13V contains the sequence BL25V, BL43V, BL75V.

Translation: group 13 contains Manganese, Technetium, Rhenium.

This is actually group 7 in our periodic table. All of these elements have 13 electrons in their secondmost outer shell.

JO14V contains the sequence BL26V, BL44V, BL76V.

Translation: group 14 contains Iron, Ruthenium, Osmium.

This is actually group 8 in our periodic table. All of these elements except Ruthenium have 14 electrons in their secondmost outer shell.

JO15V contains the sequence BL27V, BL45V, BL77V.

Translation: group 15 contains Cobalt, Rhodium, Iridium.

This is actually group 9 in our periodic table. All of these elements except Rhodium have 15 electrons in their secondmost outer shell.

JO16V contains the sequence BL28V, BL46V, BL78V.

Translation: group 16 contains Nickel, Palladium, Platinum.

This is actually group 10 in our periodic table. Here things break down a bit: Nickel and Platinum have 17 electrons in their secondmost outer shell; Palladium has 18. However Darmstadtium, not listed here, does have 16.

JO17V contains the sequence BL29V, BL47V, BL79V.

Translation: group 17 contains Copper, Silver, Gold.

This is actually group 11 in our periodic table. All of these elements have 18 electrons in their secondmost outer shell, so the group number does not quite fit here.

JO18V contains the sequence BL30V, BL48V, BL80V.

Translation: group 18 contains Zinc, Cadmium, Mercury.

This is actually group 12 in our periodic table. All of these elements have 18 electrons in their secondmost outer shell.

CHAV contains K SPV.

Comment: this probably means "the periodic table contains all of the above" as "K" was an operator for "add" or "combine". The word "STV" means the previous sequence, thus "SPV" means the previous lines. The NSA document could not understand this, and said, "The meaning of KSPV is not known, except that it is a generalization for periodic table." The original NSA document had stated "The transcription leaves a lot to be resolved. There are several words the meanings of which are yet to be determined....given more data, with a little labor we could establish its translation."  Back in 1969, this message was still undecoded.

THE NEXT STEP

The first NSA article published 29 messages. The second article published 31 messages.  If I were to guess, more radio messages followed.  Are we to believe that they made contact just for this? ATTENTION PLANET EARTH. WE ARE HERE TO ENLIGHTEN YOU, AND TELL YOU SECRETS NEVER BEFORE REVEALED: 1+1=2. 2+2=4. 3+3=6.....I do not think so. Yes, we did take our math classes, thank you ETs.

Each message builds up from the previous message. I think there were more messages after message 31. In communicating the periodic table of the elements, we now know variables JRy signify row, and variables JOx signify column. "R" means row, and "R" means raise to the power. Exponentiation is often shown by X^y - the power we raise things to is almost always indicated by y. The Y-axis indicates row. Another reason why JO indicated column is that the letter "O" stands for "orthogonal". Columns are orthogonal to rows. The periodic table is perfect for communicating this, as it is all based on number.

We now have a method of communicating a grid.  We can now send drawings to each other.  And, it is now a simple matter of sending latitude and longitude. Latitude and longitude for what? For arranging a location for landing of course. And it is a simple matter to also send messages to arrange a date and time. Except Campaigne messed it up, and got JR and JO reversed. Latitude would have been switched with longitude and vice versa. What a screw up if they were sent to the wrong place.  These kinds of messages - showing place and date - would of course be classified.

For the first time in over 60 years, this extraterrestrial signal has been completely decoded. At least, publicly decoded - surely NSA knew the decoding? Take a look at the following scene from Stargate, where the portal is opened for the first time: seven symbols are needed to open the portal, and must be terminated with the "V" symbol, indicating point of origin:

 Note the robot that is first sent through. It is similar to the Curiosity rover on Mars.

SUMMARY THOUGHTS

In conclusion, the NSA decoding missed quite a few things. Foremost, it missed the fact that the alphabet letters themselves were significant, and allowed us to guess the meaning of many of the words. Why did they miss this? Because since the radio signal came from outer space, it may have been assumed they have no knowledge of us. But whoever sent this has quite a bit of knowledge about us - they know our alphabet, they know about our math, our logic, our periodic table, our English language...in short: this signal did not come from far away. Whoever they were, they were already here.

The other big surprise here is the information contained in the periodic table: this is not our periodic table. It is somewhat based on the 1950 Modern Periodic Table, and yet it shows a knowledge of chemical groups ahead of its time. Whereas our periodic table is primarily ordered by atomic number, this one is ordered primarily by group. In this periodic table, the group numbers are determined by the number of electrons in the outer shell, or the secondmost outer shell. In chemistry this is important, for it is the outer shell which primarily determine how elements interact, thus their ordering makes a bit more sense than ours. Moreover, this periodic table ends at element 98, which shows that this message was received probably between 1950 and 1952. This has nothing to do with Sputnik which first launched several years later. From the wording of the document, and the periodic table, this is not looking like a cryptographic exercise for internal use at NSA. That does not fit the facts. The significant piece of information from the periodic table is they sent the message "NO OXYGEN." That is, we are from outer space.

As for the primary message here, it is contained in messages 13 and 16:

Hi

Hi there!

Hi from here to there.

Hi from beyond your solar system to earth.

It should be noted that of the 22 letters, the letter I is not once used in any single message. Why is it there? It is there to simply tell us hello.

Another point to make, which should not go unnoticed: there are 22 letters in the Hebrew alphabet. Hebrew is read from right to left. And the best way to read many of these messages is from right to left. The 10th letter of the Hebrew alphabet is yod, which is used to spell Yahweh or Jehovah. Abbreviated in Hebrew, it is JHVH. J for them is the number 8. In many of the messages, "JNV" comes up which means "contains", used in set theory. If we use set theory in a philosophical manner, we can imagine that which contains all things. He who contains all things is God, who calls Himself the alpha and omega. In other words, whoever they are, they are probably monotheistic. Or they already know about our monotheistic religion.

Many of the words begin with J. In the information about the Roswell crash of 1947, there are witnesses who have said that perhaps one of the aliens survived, and remained with the military in area 51. And his name? J-ROD. What an unusual name. And yet that name is very similar to the words that begin with J in this extraterrestrial signal.

UPDATE: FURTHER RESEARCH

This particular NSA document has been an interesting and fun challenge.  I wanted to add here some further research concerning this area. The reason why many consider the documents to be purely "hypothetical exercises" is from another declassified NSA article called Communication with Extraterrestrial Intelligence by Lambros D. Callimos, who was a U.S. Army cryptologist and was among the first to join the NSA when it was first formed. He started to serve the U.S. Army in 1941 as a cryptologist - an interesting date, as this is before the Roswell crash of 1947.  He also started the NSA Technical Journal - see the NSA biography at http://www.nsa.gov/about/cryptologic_heritage/hall_of_honor/2003/callimahos.shtml. It should be kept in mind, that when information is classified, those "in the know" can only talk about it publicly by releasing the information as fiction, or talk about it "hypothetically". I am aware of another story, leaked out through unofficial channels, where remote communication was established...and if this is true, then Callimos may have been involved.  In that leaked story, an amazing read in itself, a landing site was arranged, but a mistake was made in the coordinates given for latitude and longitude.  So, when I decoded the extraterrestrial signal in the document Key to Extraterrestrial Messages by Howard Campaigne, it became obvious that Campaigne had inverted the X and Y coordinates as Y and X.

In the article Communication with Extraterrestrial Intelligence Callimos describes how to devise a signal to communicate with extraterrestrials:

"In 1952 the British mathematician, Lancelot Hogben delivered an address before the British Interplanetary Society entitled "Astraglossa, or First Steps in Celestial Syntax." Hogben pointed out that number is the most universal concept for establishing communication between intelligent beings; therefore, mathematics forms the basis for the first steps in extraterrestrial communication. He then illustrated how he could transmit pulses representing integers, and distinctive signals or "radioglyphs" representing "+", "-", "=", and so on. Morrison later carried out the basic idea a little further, using different pulse shapes to represent elementary mathematical symbols."

He next shows an example of a radio transmission which could be used to initiate communication: the first transmission is an enumeration of 32 different symbols to be used in communication. The second transmission then states:

"A represents the integer 1, B the integer 2, ..., J the integer 10. In the first twenty transmissions there are introduced symbols for the introductory expository treatment in teaching us their mathematics. Among the items treated are: addition, subtraction, multiplication, and division; decimal notation and the concept of zero; inequalities and approximation; powers and roots; and definitions of pi and e."

So now, we have a little bit of context here.  The message format Callimos is proposing is similar to the one that Howard Campaigne is trying to decipher.  But there are some issues...some of the messages are "garbled", sometimes there are mistakes, and sometimes a "mistake" is introduced which is not a mistake but to introduce a new concept. So this is the background theory. Here is what I think may have happened: we send a message that says this:

A is 1, B is 2, C is 3 ....and J is 10.

We then get a response that says this:

A is 1, B is 2, C is 3 ....and J is 8.

Which shows the mistake we made: we assumed every culture uses base 10 mathematics. But they communicate back to us that they use base 8 mathematics. Which explains the following statement:

13. J=2^3. J=1+7. J+1=3x3. J+1=3^2.

Where they are saying "J is not 10, it is the number 8." They skip the letters H and I, and by doing that, they say, "HI" back to us. The other surprise is that they sent back the periodic table, and that was not part of our theory for establishing communication with extraterrestrials.

The other point, which I think is significant, is that by 1952 - and probably earlier - we had already had a proposed method for communicating with extraterrestrials using mathematics.  NSA was also formed in 1952. And the extraterrestrial message that Campaigne was trying to interpret contains a description of the periodic table -- similar to the one that was in existence between 1950 and 1952, and yet contains the concept of the 18 groups of the periodic table that did not become standard until 1988. This is why Campaigne did not see what to us is now very obvious with our modern periodic table. And it shows that these extraterrestrials are far more scientifically advanced than we are. Was the NSA formed in reaction to an actual extraterrestrial contact?  NSA intelligence gathering is supposedly limited to "foreign communications" - and any extraterrestrial contact would fall under the domain of the NSA.