Decoding the Arecibo Message

11 min readSep 9, 2024

Somewhere, something incredible is waiting to be known.
- Carl Sagan

Introduction

In 1974, nestled in the lush, green landscapes of Puerto Rico, something extraordinary happened. From the Arecibo Observatory, a giant telescope surrounded by mountains and dense forests, humanity sent a message into space like never before. This message wasn’t just a simple signal; it was a bold statement, a way for us to announce our presence to the universe.

The message, aimed at a distant group of stars called Messier 13, was sent across 25,000 light-years of space. This star cluster, home to hundreds of thousands of ancient stars, became the target of our cosmic greeting.

Crafted by brilliant minds like Frank Drake and Carl Sagan, the Arecibo Message was designed to showcase the wonders of life on Earth. Contained within 1,679 bits of data, this message was much more than a string of numbers — it was a carefully woven digital story. It shared the secrets of our DNA, the map of our Solar System, and a glimpse of who we are, hoping that, one day, it might be received by another intelligent civilization far, far away.

The Semiprime Secret: Unveiling the Mystery of 1,679 Bits

The choice of 1,679 bits was far from arbitrary; it was a deliberate selection grounded in mathematical elegance. The number 1,679 is a semiprime, the product of two prime numbers — 73 and 23. This mathematical property allowed the binary sequence to be arranged into a 2D grid of 73 rows by 23 columns, forming an intelligible image when decoded. This grid was designed to be easily recognizable by any advanced civilization that might intercept the message, as the organization into prime factors is a universal mathematical concept, transcending the boundaries of language and culture.

As the radio waves raced across the void at the speed of light, they carried not just information, but a profound philosophical inquiry: What does it mean to communicate across the vast expanses of space and time? How do we convey the intricacies of our existence to unknown and potentially unknowable minds? The true wonder of the Arecibo Message lies not only in its content but in the audacious questions it poses — questions that challenge the very fabric of reality and our place within it.

The Numeric Prelude: A Cosmic Countdown

The Arecibo Message begins with a basic sequence: counting from 1 to 10. But instead of using the numbers we see every day, it uses binary code, which is like a special language made up of only two symbols: 1s and 0s. Binary is the fundamental language of computers, and it’s also a universal way to represent numbers, making it ideal for communicating across space, where the language or even the way of thinking might be entirely different.

Why Start with Numbers?

In binary, numbers are represented using powers of 2, rather than powers of 10, which is how we normally count. Here’s how the numbers 1 to 10 are represented in binary:

1:  0 0 0 1
2:  0 0 1 0
3:  0 0 1 1
4:  0 1 0 0
5:  0 1 0 1
6:  0 1 1 0
7:  0 1 1 1
8:  1 0 0 0
9:  1 0 0 1
10: 1 0 1 0

Numbers, especially in binary, are universal. They don’t rely on any specific spoken language or cultural understanding — they’re based on pure logic and math, which is the same everywhere in the universe. By presenting the numbers 1 to 10 in binary form, the message lays down a foundation of shared knowledge. If an intelligent civilization intercepts this message, they could recognize the counting sequence and realize that the message was created by beings with a mathematical understanding similar to their own.

The Arecibo Counting Grid

To interpret the binary code for numbers 1 to 7, disregard the bottom row and read the top three rows from top to bottom. For numbers 8, 9, and 10, the binary representation spans an additional column to the right, indicating that numbers too large to fit in a single column can be expressed using multiple contiguous columns. Notably, the additional columns lack the least-significant-digit marker found in the bottom row.

So, this binary sequence is more than just a way to show that we can count; it’s an invitation to connect on a fundamental level. It says, “If you understand this, then you understand us.” It’s the simplest form of communication, breaking down barriers of language and culture by using a mathematical truth that any intelligent life should recognize.

By using binary counting as the first part of the Arecibo Message, we’re opening the door to communication, using the most basic building blocks of knowledge. It’s like putting out a cosmic handshake, hoping someone out there will recognize it and reach back.

The Elements of Life: Decrypting the Elements

Hydrogen [H] has an atomic number of 1
Carbon [C] — has an atomic number of 6
Nitrogen [N] has an atomic number of 7
Oxygen [O] has an atomic number of 8
Phosphorus [P] has an atomic number of 15

Atomic Numbers in Binary

To communicate these elements, the message used their atomic numbers. The atomic number of an element represents the number of protons in the nucleus of an atom of that element, and it’s a fundamental identifier for each element. These atomic numbers were then translated into binary code — the universal language of 1s and 0s — to be transmitted in the message. Here’s how each atomic number was represented in binary:

H    C    N    O    P
----------------------
0    0    0    1    1
0    1    1    0    1
0    1    1    0    1
1    0    1    0    1
----------------------
1    6    7    8    15 <-in decimal

Why This Matters?

By encoding the atomic numbers of these elements, the Arecibo Message was effectively saying, “These are the ingredients of life as we know it.” Any advanced civilization that intercepts this message might recognize these atomic numbers and understand that they represent the building blocks of life, possibly even in their own world.

This part of the message wasn’t just a random selection of elements; it was a deliberate choice to highlight the universality of these essential components. Since chemistry is a universal science, the assumption is that any scientifically advanced civilization would be familiar with these elements and their significance in biochemistry.

From Molecules to Messages: How DNA Was Encoded for the Cosmos

Following the elements, the Arecibo Message included the chemical formulas for the sugars and bases in the nucleotides of DNA.

Nucleotides are the building blocks of DNA, the molecule that carries the genetic information in all living organisms. Each nucleotide consists of three main parts:

Sugar Molecule (Deoxyribose): This forms the backbone of the DNA strand.
Phosphate Group: This links the sugar molecules together, creating the structure of DNA.
Nitrogenous Base: There are four bases in DNA — adenine (A), thymine (T), cytosine ©, and guanine (G). These bases pair together to form the “rungs” of the DNA ladder.

The Molecular Formulas

In the Arecibo Message, the chemical makeup of these nucleotides is described using the molecular formulas of their components. These formulas tell us the number of atoms of each element in the molecule. For example:

Deoxyribose (C5H7O)
Phosphate (PO4)
Adenine (C5H4N5)
Thymine (C5H5N2O2)
Cytosine (C4H4N3O)
Guanine (C5H4N5O)

Here’s how the message does it:

Each element (H, C, N, O, P) is represented in a specific order.
The numbers of each element’s atoms in a molecule are converted into binary and arranged in columns.

For instance, let’s look at deoxyribose: C5H7O

1 1 0 0 0
1 0 0 0 0
1 1 0 1 0
X X X X X
---------
7 5 0 1 0

This sequence is presented in the same order as the DNA elements shown earlier — hydrogen [H], carbon [C], nitrogen [N], oxygen [O], and phosphorus [P] — to maintain consistency and clarity.

Genomic Symphony: Blueprints and Double Helix Dreams

The most complex part of the message was the representation of the DNA double helix. It used a combination of binary numbers and visual graphics to depict the double-helix structure and the nucleotide sequences.

The double helix structure of DNA is represented using binary code — a series of 1s and 0s. Here’s how it works:

Double Helix Shape: The sequence of binary numbers (11, 11, 11, etc.) visually represents the two strands of DNA winding around each other. These numbers are organized in a way that gives the appearance of the double helix when decoded.

Nucleotide Base Pairs: The vertical bar in the middle of the representation symbolizes the central axis around which the two strands of DNA twist. It also encodes the number of nucleotide base pairs in the human genome. The binary sequence provided in the message corresponds to a decimal value. In this case, the sequence:

11111111 11110111 11111011 01011110

When converted to a decimal number, it equals 4,294,441,822. This number was believed to approximate the total number of nucleotide base pairs in the human genome when the message was sent in 1974. At that time, scientists estimated the human genome contained around 4.3 billion base pairs.

Today, we know that the human genome actually contains about 3.2 billion base pairs. While the number encoded in the Arecibo Message was slightly overestimated, it still represented an incredible approximation given the knowledge at the time.

Human Equation: Blue, Red, and 4 Billion Lives

The next segment of the message illustrated a simple human figure, alongside a graphical representation of the average height of humans and the population of Earth at the time of transmission (approximately 4 billion).

A Cosmic Measure: How Tall Are We?

To the left of the human figure, the message encodes the average height of an adult male at the time, which is 1.764 meters (or about 5 feet 9.4 inches). This value is expressed using binary code:

1110 (binary) = 14 (decimal)

The number 14 in decimal is significant because it is meant to be multiplied by the wavelength of the transmitted message, which is 126 millimeters.

14 * 126 mm = 1,764 millimeters

To the right of the human figure, another piece of information is encoded — the size of the global human population in 1974. The binary code for this is:

000011 111111 110111 
111011 111111 110110 (binary)
= 4,292,853,750 (decimal)

Celestial Harmonies: Yellow Notes from the Cosmos

The Arecibo Message also included a representation of our Solar System. This section illustrated the Sun and the nine planets of the Solar System at the time, with Earth highlighted to indicate the origin of the message. Just above the representation of Earth, the message also included a human figure. This was to reinforce that the message was coming from intelligent beings on the third planet from the Sun. By placing the human figure near Earth, it signaled the connection between our planet and humanity.

The yellow section of the message conveyed the relative positions of the planets, and the emphasis on Earth highlighted our place within the Solar System. This cosmic note was meant to orient potential recipients about our planetary neighbourhood.

Arecibo’s Odyssey: Purple Dishes and Celestial Blueprints

This final section of the Arecibo Message provides information about the Arecibo Radio Telescope itself, the very instrument used to send the message into space.

Binary Representation of the Diameter

The diameter of the Arecibo Radio Telescope, which is a key feature of its construction, was encoded in binary as 2,430. This number was chosen because it represents the telescope’s size in relation to the wavelength of the signal.

The binary number 2,430 was multiplied by the wavelength of the radio waves used in the transmission (which was 126 millimeters). This calculation results in a diameter of 306.18 meters (or 1,004 feet 6 inches), giving precise information about the telescope’s size.

The graphic includes a part that looks like the letter “M”. This shape isn’t random — it represents the curved, concave mirror of the Arecibo Radio Telescope. The concave shape is a key design feature of the telescope, as it helps focus the incoming radio waves onto a receiver located at the center of the dish.

A Galactic Whisper: Reflections on Arecibo’s Message

The Arecibo Message stands as a remarkable milestone in humanity’s quest to understand its place in the universe. What began in 1974 as a brief, three-minute transmission aimed at the stars is now a testament to our desire for connection — one that transcends our planet, our species, and even our time.

Encoded within 1,679 carefully chosen bits of binary data is more than just scientific knowledge — it’s a message of curiosity, discovery, and hope. It tells the story of life on Earth, from the most fundamental building blocks of DNA to the vast cosmic neighbourhood of our Solar System. Every aspect of the message, from the prime numbers that structure it to the intricate depictions of our biological and planetary makeup, serves as a universal invitation to any intelligent life that might be out there, waiting to listen.

But perhaps the greatest gift of the Arecibo Message is the way it challenges us to think beyond our own existence. It asks profound questions: How do we communicate across the unimaginable vastness of space? How do we share the complexities of life, science, and existence with minds we cannot fathom? In the act of sending this message, we acknowledge the possibility of others — and, in doing so, reaffirm our own place in the cosmos.

Though it may take millennia for the message to reach its intended destination, or for a reply to return, the Arecibo Message continues to inspire wonder. It reminds us that we are not just inhabitants of Earth, but explorers of the universe — always reaching, always searching, always hopeful that we are not alone.

As we continue to push the boundaries of space exploration, the legacy of the Arecibo Message endures. It is a symbol of human ingenuity and imagination, and, most of all, a reminder that somewhere, something incredible may indeed be waiting to be known.

Thanks for reading! If you enjoyed this dive into the Arecibo Message and want to explore more, you can check out the full version of this article on my blog. I go deeper into the science and significance of our attempt to communicate with the cosmos.

View my original post here!