The Arecibo Message

The message sent in 1974 from the Arecibo radio telescope
toward the globular cluster M13 consisted of 1679 “bits” of
information. A “0” is represented by an “off” radio pulse,
while a “1” is represented by an “on” radio pulse.
 

0000001010101000000000000101000001010000000100100010001000100

1011001010101010101010100100100000000000000000000000000000000

0000011000000000000000000011010000000000000000000110100000000

0000000000101010000000000000000001111100000000000000000000000

0000000001100001110001100001100010000000000000110010000110100

0110001100001101011111011111011111011111000000000000000000000

0000010000000000000000010000000000000000000000000000100000000

0000000001111110000000000000111110000000000000000000000011000

0110000111000110001000000010000000001000011010000110001110011

0101111101111101111101111100000000000000000000000000100000011

0000000001000000000001100000000000000010000011000000000011111

1000001100000011111000000000011000000000000010000000010000000

0100000100000011000000010000000110000110000001000000000011000

1000011000000000000000110011000000000000011000100001100000000

0110000110000001000000010000001000000001000001000000011000000

0010001000000001100000000100010000000001000000010000010000000

1000000010000000100000000000011000000000110000000011000000000

1000111010110000000000010000000100000000000000100000111110000

0000000010000101110100101101100000010011100100111111101110000

1110000011011100000000010100000111011001000000101000001111110

0100000010100000110000001000001101100000000000000000000000000

0000000001110000010000000000000011101010001010101010100111000

0000001010101000000000000000010100000000000000111110000000000

0000001111111110000000000001110000000111000000000110000000000

0110000000110100000000010110000011001100000001100110000100010

1000001010001000010001001000100100010000000010001010001000000

0000001000010000100000000000010000000001000000000000001001010

00000000001111001111101001111000

This picture was generated by arranging the 1679 bits above into 23 columns of 73 rows, 23 and 73 being the two prime numbers, which when multiplied together equal 1679. A box representing a “one” has been colored black, while a box representing “zero” has been colored white. Unfortunately, the image is “parity reversed, ” i.e., it was generated by scanning right to left, i.e., the first bit in the message occupies the upper row, rightmost cell. The next bit is the in the top row, next cell proceeding to the left. Many books have printed the picture this way. Maybe they think aliens are likely to be left-handed or maybe it is meant to tell them that all the amino acids that make up proteins in life on Earth are “left-handed” except for those that have no handedness. You should be able to see, though, that the "handedness" of the image is completely irrelevant

 How to Count in Binary…
 

10	1	16	8	4	2	1	Number
10^1	10^0	2^4	2^3	2^2	2^1	2^0
0	0	0	0	0	0	0	0
0	1	0	0	0	0	1	1
0	2	0	0	0	1	0	2
0	3	0	0	0	1	1	3
0	4	0	0	1	0	0	4
0	5	0	0	1	0	1	5
0	6	0	0	1	1	0	6
0	7	0	0	1	1	1	7
0	8	0	1	0	0	0	8
0	9	0	1	0	0	1	8
1	0	0	1	0	1	0	10
1	1	0	1	0	1	1	11
1	2	0	1	1	0	0	12
1	3	0	1	1	0	1	13
1	4	0	1	1	1	0	14
1	5	0	1	1	1	1	15
1	6	1	0	0	0	0	16
1	7	1	0	0	0	1	17
1	8	1	0	0	1	0	18
1	9	1	0	0	1	1	19
2	0	1	0	1	0	0	20

 
Our numbering system is “place based.” Each digit in a number represents that number
times a base number raised to a power. For example, in the base 10 system, which we
normally use to count, etc., the first place represents 10 raised to the power 0, which is 1.
The second place (normally one place to the left of the first) represents 10 raised to the
power 1, which is 10. The third place (the next place to the left) represents 10 raised to
the power 2, which is 100, and so on. Each succeeding place is a power of ten higher
than the preceding one. Thus, the base 10 number 378 means 3x100 + 7x10 + 8x1.
Note 10 different digits, 0 - 9, are needed to represent all possible numbers in the base 10
system.
 
The binary system works the same way … only the base number is 2 --- not 10! Thus,
only two binary digits, called bits, are needed to represent all possible numbers. The
possible bits are 0 and 1 (yes, any number can be represented by a “string” of 0’s and
1’s). Note that each succeeding place in the binary system is a power of 2 higher than the
preceding one. You can see this pattern in the columns above where I have counted from
0 to 20 in both the base ten and binary systems.

The Arecibo Message Explained

Here, I’ve redrawn the first figure according to normal convention by filling the cells left to right. In other words, the first bit occupies the left-most, upper row cell, and so on. Also, I’ve colored the 1’s and left the 0’s black.

 Numbers 1-10

Atomic numbers for H, C, N, O, P

 Formulas for sugars, bases and phosphate in DNA nucleotides

Double helix structure of DNA surrounding binary number that represents the number of nucleotides in the human genome

Height of human being marked on the left and human population marked on right

Schematic of solar system (human stands on 3^rd planet)

Arecibo transmitting telescope

Diameter of telescope

The Numbers

The first bit pattern tells the aliens how humans count in binary from 1-10.

The pixels colored pink represent starting points, or beginning markers, for each binary number. The pixels marked in red are the binary digits (bits) 1. Pixels left black are bits 0. The first number on the left is 1. The next one is 2 (0 1 in binary). Notice, the least significant bit is at the bottom of a column (just above its respective “pink” marker --- each succeeding bit is placed on top of the preceding one). There are 10 such groupings representing the numbers 1 - 10. Examining the encoded numbers 8, 9, and 10 reveals that when more significant bits are required than fit in a given dimension in the image, they continue in another row or column, starting next to the least significant bit of the previous row or column.

The Atoms of Life

Directly below the numbers, which provide the key for interpreting its meaning, is a list of four numbers which give the atomic numbers of the five chemical elements of which DNA is composed, and are the principal elements in all of the molecules of living things. From left to right (the same order as we found in the numbers above) we have:

Atomic Number	Element
1	Hydrogen
6	Carbon
7	Nitrogen
8	Oxygen
15	Phosphorus

I have colored the “1” bits representing these elements differently to provide a key to the section immediately below in the message. Hydrogen is colored grey, Carbon-white, Nitrogen-blue, Oxygen-red, Phosphorus-magenta.

The Chemistry of DNA

Group	Formula	Image
Deoxyribose	C5OH7
Phosphate	PO4
Adenine	C5H4N5
Thymine	C5H5N2O2
Cytosine	C4H4N3O
Guanine	C5H4N5O

This portion of the message assumes that you've figured out the section above giving the elements of which DNA is composed.