Love and a Triangle

A crisply executed and well imagined novelty story for the time, without much of the “pulpy” overload. I was reminded of the BLIT-like stories as well regarding harmful images from Mars and was left wondering if one of the ancient Greeks like Aristphanes had not written about communicating with Martians…

Julius Corbett, a man of fortune, is in love with an extraordinary woman, Nell Morrison, who is an astronomer. She has a particular penchant for Mars, an in particular, is trying to solve the problem of communicating with the Martians (it is 1900, and people have not yet figured out how to use radio waves for interplanetary communication. Or perhaps they want something simpler in technology). As one of the astronomy books opined,

“It will always be more difficult for us to communicate with the people of Mars than to receive signals from them, because of our position and phases. It is the nocturnal terrestrial hemisphere that is turned toward the planet Mars in the periods when we approach most nearly to it, and it shows us in full its lighted hemisphere. But communication is possible.”

Nell is convinced that the (infamous) “Schiaparelli’s canals” imply there is a thriving civilization on Mars, including Martan astronomers, which would be eager to establish communcation with earth. So great is her obsession with this issue that when Julius proposes marriage to her, she says,

“Talk with the Martians,” said she, “and the next day I will become your wife!”

So a dispirited Julius seeks help from his friend, Marston, an Astronomy Professor at Univ. of Chicago. Marston’s idea is to use electricity and mathematics (“We must use that. And the figures must, of course, be geometrical. Geometry is the same throughout all the worlds that are or have been or ever will be.”). Thus do they end up in the great Pampas of Argentina where “illuminated figures two hundred miles each in their greatest measurement” were made, comprising “only the square, equilateral triangle, circle and right-angled triangle.”

Many months later, the observatories on earth see the startling reply from Mars, in the form of all the figures which the earthlings had made as well as a clear geometric figure of a right-angled triangle with squares drawn on each side, indicating knowledge of the Pythagoras Theorem. As the author exults:

“Ah, it required no profound mathematician, no veteran astronomer, to answer such a question! A schoolboy would be equal to the task. The man of Mars might have no physical resemblance to the man of Earth, the people of Mars might resemble our elephants or have wings, but the eternal laws of mathematics and of logic must be the same throughout all space. Two and two make four, and a straight line is the shortest distance between two points throughout the universe. And by adding this figure to the others represented, the Martians had said to the people of Earth as plainly as could have been done in written words of one of our own languages”:

“Yes, we understand. We know that you are trying to communicate with us, or with those upon some other world. We reply to you, and we show to you that we can reason by indicating that the square of the hypothenuse of a right-angled triangle is equivalent to the sum of the squares of the other two sides. Hope to hear from you further.”

“There was the right-angled triangle, its lines reproduced in unbroken brilliancy, and there were the added lines used in the familiar demonstration, broken at intervals to indicate their use. The famous pons asinorum had become the bridge between two worlds.”

And that is how love and geometry launched an interplanetary discourse.

Commentary: The use of Pythagoras Theorem in visual communication with aliens (in exactly the same manner as described in the Waterloo story) was utilized much earlier, by Jules Verne in 1865 in his novel, “From the Earth to the Moon”. In that story, the President of the Gun Club, Impey Barbicane, tells the members at a meeting on the potential of communicating with the inhabitants of moon:

“ “I have now enumerated,” said Barbicane, ”the experiments which I call purely paper ones, and wholly insufficient to establish serious relations with the Queen of Night. Nevertheless, I am bound to add that some practical geniuses have attempted to establish actual communication with her. Thus, a few days ago, a German geometrician proposed to send a scientific expedition to the steppes of Siberia. There, on those vast plains, they were to describe enormous geometric figures, drawn in characters of reflecting luminosity, among which was the proposition regarding the ‘square of the hypothenuse, commonly called the “Ass’s Bridge” by the French.

“Every intelligent being,” said the geometrician, “must understand the scientific meaning of that figure. The Selenites, do they exist, will respond by a similar figure; and, a communication being thus once established, it will be easy to form an alphabet which sliall enable ns to converse with the inhabitants of the moon.” So spoke the German geometrician; but his project was never put into practice, and up to the present day there is no bond in existence between the earth and her satellite.”

Pythagorean Theorem as a means of alien communication is a device used in another story, “Second Chance” by Walter Kubilius and Fletcher Pratt (Fantastic Story Magazine, Fall 1952), where Venusians who have arrived in earth’s orbit signal the Pythagoras theorem to the military men, as in the following: (the story itself is not really mathfiction but a warning on the dangers of internecine intercontinental wars):

“The screen gave another series of flashes. “We got a picture sequence. Here it comes,” said the speaker. Those in the room saw an outline of an equilateral (note: This should have said right-angled triangle), apparently formed of narrow strips of metal standing on edge. An invisible hand placed a series of little blocks along each edge; then rapidly these detached themselves into two groups, one from the hypotenuse, one from the two sides.
“The Pythagorean theorem,” said Sanchez, smiling.
But Marechal Laporte frowned. “My General,” he said to Weinburger, “we shall never communicate with these beings on this level. I suggest that we have two or three stations flash them simple mathematical problems in systems of dots and dashes.”