From: Derik van Zuetphen (derik@pool.informatik.rwth-aachen.de)
Date: 7-Feb-95 (8:52:25 GMT)
Subj: Interpretation of 1st message

Taucetians read lines in a very differnt way than we do. Each line is read
simultanously from the left and right margin to the middle. They must have
two independant cognitive regions in their brain, so the can read one symbol
at the right margin and one at the left. If these two symbols are equal,
the only see one, if they are not equal, they register two, but are not
aware in which sequence these symbols belong. For sequent-dependant
arithmetic function, like substraction, they need two operations,
subtracting the larger from the smaller number and vice versa.

A taucetian word like 1+3+2 can translate to a human word, when I fold
the word in the middle, giving [1+3], and read the two lines
[2+ ]
simutanously from left to right, e.g. "one and two, added, gives 3".

Here follows my interpretation of the first message. I have split the message in
lines (like "G" <line> "G") and replaced the characters with Mnemonics.

First they present their numbersystem in an unary code.

"B" = "1" is the number "one", first used as unary, later as digit

1
11
111
1111
11111
111111

They only introduce six number. This is possibly the base of their
arithmetics.

"H" = "+" adds two numbers

1 + 11 + 1                      i.e. 1+1 = 2
11 + 111 + 1                    i.e. 1+2 = 3
1 + 111 + 11                    i.e. 1+2 = 3
1 + 1 +                         i.e. 0+1 = 1
+ 1 + 1                        i.e. 0+1 = 1
11 + 1111 + 11                  i.e. 2+2 = 4

"I" = "-" means subtracting the larger number from the smaller

11 - 1 - 1                      i.e. 2-1 = 1
1 - 1 - 11                      i.e. 2-1 = 1

"J" = "_" means subtracting the smaller number from the larger
"K" = "(0-)" is the negation function (unary minus)

11 _ (0-) 1 (0-) _ 1            i.e. 1-2 = -1
1 _ (0-) 1 (0-) _ 11            i.e. 1-2 = -1
1111 _ (0-) 111 (0-) _ 1        i.e. 1-4 = -3
1111 - 111 - 1                  i.e. 4-1 = 3

"L" = "*" is multiplication

1 * 1 * 1                       i.e. 1*1 = 1
11 * 111111 * 111               i.e. 2*3 = 6
1 * 11 * 11                     i.e. 1*2 = 2

"M" = "/" means dividing the larger number thru the smaller

111111 / 11 / 111               i.e. 6/3 = 2
11 / 111 / 111111               i.e. 6/2 = 3
1111 / 11 / 11                  i.e. 4/2 = 2
11 / 11 / 1111                  i.e. 4/2 = 2

"N" = "\" means dividing the smaller number thru the larger
"O" = "(1/)" is the reciprocal function

111111 \ (1/) 11 (1/) \ 111     i.e. 3 / 6 = 1/2

(1/) 11 (1/) * (1/) 1111 (1/) * (1/) 11 (1/)
i.e. 1/2 (1/*) 1/2 = 1/4
where "(1/*)" or "(1/) *" or  "OL" represents multiplication of reciprocals

"P" = "=" is the equals sign

1 = 1 = 1                       i.e. 1=1
11 = 11 = 11                    i.e. 2=2
111 = 111 = 111                 i.e. 3=3

Now the digital numbers to base 6 are presented. I add the suffix u for
unary numbers and d for digital to clearify the destinction.

"A" = "0"
"B" = "1"  (we know it already)
"C" = "2"
"D" = "3"
"E" = "4"
"F" = "5"

"Q" = "#" is used to introduce digital numbers.
=  # 0 #  =                            i.e. 0u = 0d
1 =  # 1 #  = 1                         i.u. 1u = 1d
11 =  # 2 #  = 11
111 =  # 3 #  = 111
1111 =  # 4 #  = 1111
11111 =  # 5 #  = 11111                 i.e. 5u = 5d
111111 =  # 101 #  = 111111             i.e. 6u = 10d
1111111 =  # 111 #  = 1111111           i.e. 7u = 11d
11111111 =  # 121 #  = 11111111         i.e. 8u = 12d
111111111 =  # 131 #  = 111111111       i.e. 9u = 13d
111111111111 =  # 202 #  = 111111111111 i.e. 12u = 20d

Let's now calculate with digitals. "# +" means adding, "# -" subtracting,
and so on

# 1 #  +  # 3 #  +  # 2 #               i.e. 1d + 2d = 3d

"R" = ".t." means: it is true that ... holds
"S" = ".f." means: it is wrong that ... holds

.t. # 1 #  +  # 2 #  +  # 1 # .t.       i.e. 1+1 = 2 is true
.f. # 1 #  +  # 3 #  +  # 1 # .f.       i.e. 1+1 = 3 is false
.t. # 2 #  -  # 1 #  -  # 1 # .t.       i.e. 2-1 = 1 is true
.f. # 2 #  -  # 2 #  -  # 1 # .f.       i.e. 2-1 = 2 is false

-Derik.

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