Francis Galton was interested in communicating with Mars as early as 1892, when he wrote a letter to the Times suggesting that we try flashing sun signals at the red planet. At a lecture the following year he described more specifically a method by which pictures might be encoded using 26 alphabetical characters, which could then be transmitted over a distance in 5-character “words,” in effect creating a low-resolution visual telegraph. As a study he reduced this profile of a Greek girl to 271 coded dots, which he found yielded “a very creditable production.”

This had huge implications, he felt. In 1896 he imagined a whole correspondence with a civilization of intelligent ants on Mars; in three and a half hours they catch our attention; teach us their base-8 mathematical notation; demonstrate their shared understanding of certain celestial bodies and mathematical constants; and finally propose a specified 24-gon in which points can be situated by code, like stitches in a piece of embroidery.

That opens a limitless avenue for colloquy — the Martians send images of Saturn, Earth, the solar system, and domestic and sociological drawings, a new one every evening. Galton concludes that two astronomical bodies that are close enough to signal one another with flashes of light already have everything they need to establish “an efficient inter-stellar language.”

From Lee Sallows:

As the reader can check, the English number names less than “twenty” are composed using 16 different letters of the alphabet. We assign a distinct integral value to each of these as follows:

E   F   G   H   I   L   N   O   R   S   T   U   V   W   X   Z  
3   9   6   1  -4   0   5  -7  -6  -1   2   8  -3   7  11  10

The result is the following run of so called “perfect” numbers:

Z+E+R+O       =   10 + 3 – 6 – 7          =    0
O+N+E         =   –7 + 5 + 3              =    1
T+W+O         =    2 + 7 – 7              =    2
T+H+R+E+E     =    2 + 1 – 6 + 3 + 3      =    3
F+O+U+R       =    9 – 7 + 8 – 6          =    4
F+I+V+E       =    9 – 4 – 3 + 3          =    5
S+I+X         =   –1 – 4 + 11             =    6
S+E+V+E+N     =   –1 + 3 – 3 + 3 + 5      =    7
E+I+G+H+T     =    3 – 4 + 6 + 1 + 2      =    8
N+I+N+E       =    5 – 4 + 5 + 3          =    9
T+E+N         =    2 + 3 + 5              =   10
E+L+E+V+E+N   =    3 + 0 + 3 – 3 + 3 + 5  =   11
T+W+E+L+V+E   =    2 + 7 + 3 + 0 – 3 + 3  =   12

The above is due to a computer program in which nested Do-loops try out all possible values in systematically incremented steps. The above solution is one of two sets coming in second place to the minimal (lowest set of values) solution seen here:

 E   F   G   H   I   L   N   O   R   S   T   U   V   W   X   Z 
–2  –6   0  –7   7   9   2   1   4   3  10   5   6  –9  –4  –3

But why does the list above stop at twelve? Given that 3 + 10 = 13, and assuming that THREE, TEN and THIRTEEN are all perfect, we have T+H+I+R+T+E+E+N = T+H+R+E+E + T+E+N. But cancelling common letters on both sides of this equation yields E = I, which is to say E and I must share the same value, contrary to our requirement above that the letters be assigned distinct values. Thus, irrespective of letter values selected, if it includes THREE and TEN, no unbroken run of perfect numbers can exceed TWELVE. This might be decribed as a formal proof that THIRTEEN is unlucky.

But not all situations call for an unbroken series of perfect numbers. Sixteen distinct numbers occur in the following, eight positive, eight negative. This lends itself to display on a checkerboard:

Choose any number on the board. Call out the letters that spell its name, adding up their associated numbers when on white squares, subtracting when on black. Their sum is the number you selected.

(Thanks, Lee.)