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.
11. Translates into $ 2^{4}-4+4; 2^{4}=1+7; 2^{4}=2 \times 4; 2^{2}-4. $ verifying our previous conclusions.
12. Translates into $ 3^{2}-4+5; 3^{2}=3 \times 3. $ Further verification.
Note: In our culture we use parentheses to group closely associated terms, and as a first step it helps, even though it is not necessary, to put in parentheses. To do so unambiguously, start at the right and read left to the first operator symbol; put parentheses about the operator and the two quantities to its right. Repeat until no pair of parentheses contains more than an operator and two quantities.
13. Translates into $ J=2^{4}; $ $ J=1\mid 7; $ $ J\mid 1=3\times 3; $ $ J\mid 1=3^{2}, $ therefore $ J=8. $
14. We can only introduce parentheses by assuming P is an operator, so we get 2 P84; 4-P82; 1-P33; and 3 P62. Thus $ \mathrm{P}\times\mathrm{Y}=\mathrm{X}\div\mathrm{Y} $ division.
15. Assume U is an operator, getting U12; U23; U34; U58; U68; U78; $ U 2^{3} 3^{2}=U 8 9 $ . The smaller is first in each case; so perhaps UXY means X precedes Y or $ X < Y $ .
16. The new character Q must be an operator. Transcribed it gives us Q: O=1; Q: 1=3; Q: 1=1+1; Q: O=1×1; Q: $ 2^{2}=2 $; Q: 2<2; Q: H(1=1) (1=2); Q|Q: 3=3|; Q: 8<7.
Clearly Q means "the following statement is false." Then the next to the last is read "it is false that $ 3 \neq 3 $." QL will be translated $ \neq $ . The second new symbol is not clear, except that it is an operator whose operands are statements, not quantities, a Boolean operator.
Note: Q is an operator with only one operand, unary.
17. Putting in parentheses shows that S is also a unary operator operating on statements. Transcribed they are: S: 1-1; S: 1-2; S: 2=111; S: 1=1 $ \times $ 1; S: O=1-1; S: H $ \mid $ (6-1 $ \times $ 6) (1-6:6) $ \mid $ S: H $ \mid $ (1 1) (2-2) $ \mid $ It is apparent that S means "the following statement is true" or "it is asserted that." The next to the last message shows that HXY means "X implies Y" or "X is a consequence of Y" or maybe "X is logically equivalent to Y."
18. Our rule for parentheses breaks down unless T is a different kind of symbol. The first message shows that T may be a unary operator on quantities, so that AT or TA is a quantity. The third message shows that it must be the first, since T is last. Putting in parentheses this way gives $ 1 \mathrm{T}=1; 2 \mathrm{T}=1 \mathrm{T}+1; 5 \mathrm{T}=2 \mathrm{T}+3 \mathrm{T}; 6 \mathrm{T}=3 \mathrm{T} \times 2 \mathrm{T}; 7 \mathrm{T}=7; 1 0 \mathrm{T} $ 8. T must be an ending. On one digit it makes no difference. It combines the two digits 10 to make 8. Octal arithmetic?
19. Transcribes to $ 1 2 3 T=1 \times 8^{2}+(2 \times 8^{1}+3); $
$ 3 2 1 \mathrm {T} = 3 \times 8^{2} + \left(2 \times 8^{1} + 1 \times 8^{n}\right); $
4567¹¹ = (4 × 8¹ | 5 × 8²) + (6 × 8¹ | 7 × 8²).
Clearly T indicates that "the preceding digits form an octal number." Possibly it is an octal point; if so, digits may occur after it. 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.