Documents / FOIA release
This unclassified article by H. Campaigne, published in the NSA Technical Journal, Vol. XIV, No. 1, gives a key to a series of 31 hypothetical radio messages from outer space that Campaigne had presented earlier. Step by step it decodes symbols for numbers, arithmetic, logic, set theory, octal notation, the rational and real numbers, limits, and finally the periodic table of the elements. The article concludes that any civilization able to send messages across space would share basic concepts of number, sets and physical constants.
Read from the scan by GLM-OCR; expect the odd misread word.
# NSA Technical Journal Vol. XIV, No. 1
# Key To The Extraterrestrial Messages
BY H. CAMPAIGNE
Unclassified
Dr. Campaigne presented a series of 29 messages from outer space in "Extraterrestrial Intelligence." NSA Technical Journal, Vol. XI, No. 2, pp. 101 ff. and in the Special Mathematics and Engineering Issue of the Journal, pp. 117 ff. The following article develops a key to these messages. Paragraph numbers parallel the serial numbers of the messages reprinted in the appendix below. This includes two new series--30 and 31-not included in the previous article.
At every step in the solution we make a guess at the meaning. Evidence will quickly accumulate to verify or refute this guess. The possibility of ambiguity of two consistent solutions is very remote. Only in the last steps, where verification is thin, could this happen.
1. There are 21 symbols, in the order given by this message.
2. B is equivalent to AA, C to AAA, etc. That is. A = 1; B = 2; C = 3; D = 4; E = 5; F = 6; G = 7.
3. The symbol L means the two things that follow are the same. LXY means $ x=y $ .
4. Each statement has 5 symbols, and begins with L. The 4 symbols after L must be considered as two things. Each statement has a K as the third letter, which must be the start of the second thing. Is $ \mathbf{B}=\mathbf{KAA} $; $ \mathbf{C}=\mathbf{KBA} $; $ \mathbf{C}=\mathbf{KAB} $; $ \mathbf{D}=\mathbf{KCA} $? If KBA means $ \mathbf{B}+\mathbf{A} $, it tits.
5. These verify our conclusions on 4. The first means $ 6=1+(2+3) $ the last means $ 1+(2+3)=(1+2)+3. $
6. Each has five symbols as in 4. They mean 1 = M21; 2 = M31; 1 = M32. Obviously MXY means x - y.
7. These translate $ N=1-1 $; $ N=2-2 $; $ N=3-3 $. N stands for zero. 0.
8. These translate 1=011; 0=001; 2=012; 2=021; 0=002; 0=020; 4=022, etc. OXY means the product $ \mathrm{X}\times\mathrm{Y}. $
9. These verify the conclusions of 8. The first says that $ 6=1\times 2\times 3. $ the last $ 4\times(5\times 6)=(4\times 5)\times 6. $
Note: So far we have seen two kinds of symbols: digits A through G and N, and operators L, K, M, and O. The two digits following the operator are the operands.
10. Translates into $ 4=R22; 2=R21; 1=R20; 3=R31; 1=R30. $ RXY must mean $ X^{\prime} $ , exponentiation. R is another binary operator. Not linked to a story yet.
FOIA release, from the nsa collection. The PDF is mirrored here; the original link is above. The text was read from the page images by GLM-OCR; expect the odd misread word. 11 pages are in the text index: search them above, or from the library's search.