Graham’s Message for E.T.

Decoding the Pictogram

The following datastream was presented at the end of my previous article on SETI — the Search for Extraterrestrial Intelligence — with the comment that it represents a message which is more truthful about the human race than the pictures of a smiling entity expressing warmth and friendliness, as was inscribed on the Pioneer spacecraft.

111111111111111111111111110000011111111111100000000011111111100111011100111111110

011101110011111111001100011001111111100000100000111111111000101000111111111100000

000011111111111010101011111111111101010101111111100110000000110011100011100000111

000110000011111110000011111000011100001111111111000000011111111111111000111111111

111110000000111111111100001110000111110000011111110000011000111111111110001110011

11111111100111111111111111111111

So how do we decode this stream of binary digits and recover the information?

The first thing we should do is to see how long it is.  To save you the job of counting, I can tell you that it’s 437 characters.  Now, if our extraterrestrial species is mathematically proficient (and it probably is, given the fact that they’ve managed to receive our message), they’ll realize without too much trouble that 437 is the product of two prime numbers.  What this means is that 437 can only be made up of two numbers multiplied together in one way — 19 times 23.  This is significant because the data is asking to be displayed as a grid with these dimensions.  In fact, the pictogram broadcast from Arecibo in 1974 consisted of something very similar — a message of 1679 bits in length, which can only be displayed as a grid of 73 by 23.

So what do we get if we take the message above and lay it out on a grid?  We need to make an educated guess about whether the characters go across first then down, or down first then across — or indeed from left to right, right to left, bottom to top, or top to bottom — there’s no “obvious” way of doing it.  And even if we get this right, the message may still not appear if the information is arranged as 19 by 23 instead of 23 by 19.  However, we’re dealing with an intelligent extraterrestrial species here, so let’s assume that through some experimentation, they hit on the fact that that the information can wrap horizontally in either direction, then top to bottom, that the width is 19 characters, and the height is 23.  The following message will greet them — let’s hope they understand it.

Tags: E.T., SETI

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