Talking to Aliens With Wheat

In 1784, a seven-year-old German child began elementary school. During a mathematics lesson, the child’s teacher asked the class to sum all the integers from 1 to 100. As the other students slogged through the calculations, the young Johann announced the answer to his instructor: 5,050.

The teacher was astonished. How had young Johann computed the solution so quickly?

He responded that the task was simple. The integers between 1 and 100 consist of 50 pairs of numbers that sum to 101. So, it was easy to multiply 101 by 50 and hit 5,050.

The instructors realized they had a mathematical prodigy on their hands. Even if this story is apocryphal, this young talent, known to the world as Carl Friedrich Gauss, went on to put the “poly” and the “math” into the term “polymath.”

Gauss is a towering figure in mathematics. He proved the fundamental theorem of algebra. He set the foundations for 19th-century number theory with his classic work Disquisitiones Arithmeticae, which pioneered modular arithmetic, quadratic polynomials, and factorization. He discovered and named non-Euclidean geometry. He revolutionized statistics, developing the method of least squares, and his name now adorns the Gaussian distribution.

This snapshot inadequately summarizes his mathematical achievements, but Gauss excelled in other fields, too.

As an astronomer, he helped identify the dwarf planet Ceres. His work on how planetary gravity disrupted the motion of smaller bodies yielded the Gaussian gravitational constant.

Magnets, how do they work? Gauss led us to the answer. He invented the magnetometer to probe Earth’s magnetic field; he pointed us toward electromagnetism via potential theory. Along with Wilhelm Eduard Weber, Gauss crafted the first electromagnetic telegraph. Today, a unit of magnetic flux density bears his name.

Thanks to an interest in cartography and geodesy, Gauss became one of the founders of geophysics. He advanced map theory and accurately surveyed Hanover. During his work on geodesy, he devised the heliotrope, an instrument that uses mirrors to reflect sunlight over many miles, allowing surveyors to increase their accuracy and speed.

This guy’s scientific curiosities seem to have had no limits.

Even Outer Limits.

Perhaps inspired by the communicative properties of his electromagnetic telegraph and heliotrope, Gauss deeply desired to send messages to extraterrestrials.

Seriously.

Of course, the connotation of such a statement differed between the 19th and 21st centuries. Gauss had no UFOs, Roswells, abductions, or Area 51s informing his viewpoint of aliens. The notion of life beyond Earth was not new in the era, but it took a different timbre. Democritus proposed the idea of a “plurality of worlds” that was later adopted by early Christian writers. Augustine described many possible globes “throughout the boundless immensity of space” in The City of God. During the Middle Ages and into the 19th century, philosophers such as Nicholas of Cusa and Descartes believed the worlds beyond Earth could be inhabited by living beings or “intelligent creatures.”

And if they were populated by smart ETs, we wanted to show them we were smart, too.

How could we show these magnificent, albeit speculative, beings that we knew fancy things like mathematics?

In 1820, the story goes, Carl Friedrich Gauss developed a (very literally) big idea.

If someone lived on the Moon or Mars, Gauss assessed that we could theoretically construct something large enough with the Earth as a canvas for the extraterrestrial to see. And, though the beings would have no idea about the human being named Pythagoras, being studious, they would likely know “his” theorem.

Most students learn the famous equation that relates the sides of a right triangle: a^2 + b^2 = c^2 (a-squared plus b-squared equals c-squared).

More formally, the Pythagorean theorem deals with triangles and squares. A square whose side is the hypotenuse of a right triangle (with a side “c” in the equation) has an area equal to the sum of the areas of the squares whose sides are the lengths of the other edges of the triangle. As displayed in the image above, the light purple square has an area equal to that of the red square plus the blue square. The right triangle sits in the middle.

We could build a version of this diagram so large that eyes could see it on another world. When they spied such a construct, they would be imbued with the knowledge that the inhabitants of Earth were worthy of intelligent communication.

Where could we make something so gigantic?

Siberia!

In the vast, unpopulated Russian tundras, we could seed long strips of pine forests to make the outlines of the right triangle and squares, while planting enormous wheat fields inside the shapes to provide maximum contrast.

Such was the Gaussian plan.

How large would such a structure need to be?

The resolution of the human eye is approximately 1 arcminute (1/60th of a degree). This statistic means the smallest angle we can perceive between two points is 1/60th of a degree. Based on the average distance to the Moon, one arcminute covers about 112 kilometers (70 miles). So, something 70 miles wide would appear like a dot to a human eye on the Moon. (For reference, the popular notion that the Great Wall of China is visible from the Moon is false; even though the wall is much longer than 112 km, it is only about 10 meters wide, making it indistinguishable from everything else)

To make the Pythagorean squares and triangles distinguishable on the Moon, we’d need to go much bigger.

Distinct sides might not emerge until lengths of about 400 kilometers (248 miles), with a hypotenuse on the scale of 566 kilometers (351 miles). From side to side, a structure of this size would stretch for about 1,000 kilometers (621 miles). With an area of over 160,000 square kilometers, the shapes would be about the size of Tunisia!

Unfortunately for Gauss and the rest of us, the math isn’t so kind to extraterrestrials living on Mars. The complex would need to be about 16,000 kilometers wide, which is more than 3,000 kilometers longer than Earth’s diameter.

The wheat-and-tree plan never materialized. The project would have been massive, and it might have been difficult to grow wheat in the Siberian tundra.

Today, we might view such an idea as a joke, but it was a widespread notion among scientists at the time. It was so prevalent that some historians do not believe Gauss initiated the thought.

Various sources cite different scientists as the source. Gauss was seriously interested in signaling aliens, though, so connecting him to the Pythagorean shapes is a possibility. He considered refining the heliotrope for long-distance communication. In this era, he could shoot cohesive light up to eight miles away with only a one-square-inch mirror.

Writing to astronomer Heinrich Olbers, Gauss said, “With 100 separate mirrors, each of 16 square feet, used conjointly, one would be able to send good heliotrope-light to the moon … This would be a discovery even greater than that of America, if we could get in touch with our neighbors on the moon.”

Today, we send signals into the ether via radio waves, hoping to contact intelligent life. As someone into electromagnetism, Gauss would likely approve.