Key to the Extraterrestrial Messages by H. Campaigne

Read from the scan by GLM-OCR; expect the odd misread word.

22. We notice that TV is used in every message, and parallels the usage of UV. Assuming TV is a binary Boolean operator, the messages parse.

$$
\text {I t is false that} \mathrm {T V} \mid \mathrm {A V} \leq \mathrm {B V} \mid \left\{\mathrm {B V} \leq \mathrm {A V} \right\};
$$

$$
\text {I t is false that} \mathrm {T V} | \mathrm {A V} = \mathrm {B V} | | \mathrm {A V} \neq \mathrm {B V} |;
$$

$$
\mathrm {T V} \left| \bar {A V} ^ {2} = 4 \right| \left| 0 \leq A V \right| = \cdot A V = 2;
$$

$$
\mathrm {A V} > \mathrm {B V} = \cdot | \mathrm {B V} \leq \mathrm {A V} | \text {o r} | \mathrm {B V} = \mathrm {A V} |;
$$

$$
\text {I t is true that not} \mathrm {T V G V H V} = \cdot \mathrm {G V o r H V};
$$

$$
\text {I t is true that G V and H V} = \cdot \mathrm {T V G V H V};
$$

$$
\mathrm {A V} \text {o r} (\mathrm {B V} \text {o r} \mathrm {C V}) = (\mathrm {A V} \text {o r} \mathrm {B V}) \text {o r} \mathrm {C V};
$$

$$
\mathrm {T V} | \mathrm {A V} ^ {\prime} \mathrm {T V} | \mathrm {B V C V} | | = \mathrm {T V} | | \mathrm {T V} \mathrm {A V B V} | \mathrm {C V} |;
$$

$$
\mathrm {T V} | \mathrm {A V} | \mathrm {B V} \text {o r} \mathrm {C V} | | = \mathrm {T V} | \mathrm {A V B V} | \text {o r} \mathrm {T V} | \mathrm {A V C V} |;
$$

$$
\mathrm {A V} \text {o r} \mathrm {T V} | \mathrm {B V C V} | = \mathrm {T V} | \mathrm {A V} \text {o r} \mathrm {B V} | | \mathrm {A V} \text {o r} \mathrm {C V} |.
$$

It is apparent that TV means "and." Notice that L is used here to mean "logically equivalent to," although I have written "=".

Note: U is used here for $<$, not $ \leq $

Either there is a mistake, or the usage varies.

23. The parsing falters until we realize that JNV occurs in each message, and is probably a word. BAV and CAV also occur in each message. They transcribe into:

$$
J N V \mid B A V o r C A V \mid B A V;
$$

$$
J N V B A V \mid B A V a n d C A V \mid ;
$$

$$
\mathrm {I N V} | \mathrm {B A V} \text {o r C A V} | | \mathrm {B A V} \text {a u d C A V} |;
$$

$$
\mathrm {I N V B A V C A V} = \cdot \mathrm {B A V} = (\mathrm {B A V o r C A V});
$$

$$
\mathrm {J N V B A V C A V} = \cdot \mathrm {C A V} = (\mathrm {B A V} \text {a n d C A V}).
$$

The last two conclusions look like set theory statements. JNV parses like a binary operator. JNV XY could mean "X contains Y" in the set theory sense. Then if UV is "or" in the set theory sense, the union, and TV is "and" in the set theory sense, the intersection, the statements above can be rewritten:

$$
\mathrm {B A V} \cup \mathrm {C A V} \supset \mathrm {B A V}
$$

$$
\mathrm {B A V} \supset \mathrm {B A V} \cap \mathrm {C A V}
$$

$$
\mathrm {B A V} \cup \mathrm {C A V} \supset \mathrm {B A V} \cap \mathrm {C A V}
$$

$$
\mathrm {B A V} \supset \mathrm {C A V} = \cdot \mathrm {B A V} = (\mathrm {B A V} \cup \mathrm {C A V})
$$

$$
\mathrm {B A V} \supset \mathrm {C A V} = \cdot \mathrm {C A V} = (\mathrm {B A V} \cap \mathrm {C A V}).
$$

24. NKV looks like a binary operator of which at least the first operand is a quantity. JAV is uniformly the second operand. From 23 above we are alert to set theory statements. Could it be that NKV says something is a member of some set? Try it. They become

$$
1 \mathrm {c J A V}; 2 \mathrm {c J A V}; 3 \mathrm {c J A V}; 4 \mathrm {c J A V}; 5 \mathrm {c J A V}; 6 \mathrm {c J A V}; 7 \mathrm {c J A V}; 1 1 \mathrm {c J A V};
$$

$$
1 2 \epsilon \mathrm {J A V}; \mathrm {A V} \epsilon \mathrm {J A V} = - \mathrm {A V} + 1 \epsilon \mathrm {J A V}.
$$

$$
J A V \mathrm {i s} \mathrm {e t e s t o f p o s i t i v e i n t e g e r s !} \mathrm {I t f i t s !}
$$