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.
29. These transcribe to
1 $ 2^{n} $ in JBV; $ 1-3^{n} $ in JBV;
1 $ 4^{n} $ in JBV; $ 1 \overline{{{N V}}}^{n} $ in JBV;
NLV JBV $ - 1 $ assuming NLV is one word. Another possible parsing is LV(JBV, 1) = 0|
1/1 in JCV; 1/2 in JCV; 1/3 in JCV; 1/NV in JCV; NLV JCV O $ \mid $ or LV (JCV, 0) $ - 0 $ . But the two examples suggest that NLV means "a limit of." If NV is an integer this fits perfectly. |
(1 $ 1/2 )^{2} $ in JBV; $ (1-1/3 )^{3} $ in JBV;
(1 $ 1/4 )^{4} $ in JBV; $ \left( 1-\frac{1}{8^{100}} \right)^{n^{100}} $ in JBV;
$ \left( 1-\frac{1}{N V} \right)^{N 1} $ in JBV; NLV JBV in JEV.
If NLV means limit, then JEV contains the number e, a verification of our guess that JEV named the real numbers. The last two lessons - 30 and 31 were not published with the first twenty-nine because it made too long an exercise.
30. The later messages of this group have the mysterious sequences ABCD, ABCDE, DEFG, etc, each ending with STV. If we bunch these each as a unit, the messages parse. They then say JNV 1 natural number; JNV 2 natural number; JNV 3 natural number; JNV 123 STV natural number; conjecture STV means "the preceding is a set (or sequence)," and JNV means "belongs to." There is doubt about the latter, since we thought earlier that it meant "contains"; AV belongs to $ 1 2 3 4 = \cdot $ AV is a natural number; 12345 or 4567 = 45 as sets; 12345 and 4567 = 1234567 as sets.
31. This last group is of impressive magnitude, 41 messages, of which the thirtieth is quite long. Parsing is eased by the parallel construction of the messages. They transcribe to:
JRAV belongs to CHAV; JRBV belongs to CHAV; JRGV belongs to CHAV; the set JRAV, JRBV, JRCV, JRDV, JREV, JRFV, JRGV belongs to CHAV; |Since all the digits appear in these groups, maybe they are used like subscripts and should be read $ \mathrm{J R}_{1}, \mathrm{J R}_{2}, \mathrm{e v c.} $; $ \mathrm{J O}_{1} $ belongs to CHAV; $ \mathrm{J O}_{2} $ belongs to CHAV; $ \mathrm{J O}_{2 2} $ belongs to CHAV; the set $ \mathrm{J O}_{1}, \mathrm{J O}_{2}, \mathrm{J O}_{3}, \mathrm{J O}_{4}, \mathrm{J O}_{5}, \mathrm{J O}_{6}, \mathrm{J O}_{7}, \mathrm{J O}_{1 0}, \mathrm{J O}_{1 1}, \mathrm{J O}_{1 2}, \mathrm{J O}_{1 3}, \mathrm{J O}_{1 4}, \mathrm{J O}_{1 5}, \mathrm{J O}_{1 6}, \mathrm{J O}_{1 7}, \mathrm{J O}_{1 8}, \mathrm{J O}_{1 9}, \mathrm{J O}_{2 2} $ belongs to CHAV; $ \mathrm{U}_{0 1} $ and $ \mathrm{U}_{1} $ 22 $ \mathrm{J O}_{1} $ belongs to CHAV |This one must be parsed wrong or garbled|; $ \mathrm{B L}_{1} $ belongs to $ \mathrm{J R}_{1} $; $ \mathrm{B L}_{2} $ belongs to $ \mathrm{J R}_{1} $; $ \mathrm{B L}_{1} $ belongs to $ \mathrm{J R}_{2} $; $ \mathrm{B L}_{1} $ belongs to $ \mathrm{J R}_{3} $; $ \mathrm{B L}_{1} $ belongs to $ \mathrm{J R}_{2} $;
$ \mathrm{A V} AV · · · BLw belongs to JRs;
$ \mathrm{A V} < 2 3 $ and $ 4 4 < \mathrm{A V} \cdot = \cdot \mathrm{B L} $ belongs to JR: 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.