Lemuria

At their next meeting, Marius spoke first “This is what I have so far. I’m afraid it isn’t much.” Following Kat’s lead, he was wearing the tasteful gray lipstick of a gentleman. It had the waxy look of a homemade cosmetic, but it suited him. To a point, the crew could create personal items from the processing units on the ship. The coffee was getting better. A monitor lit up with an array of curved two-dimensional surfaces. “First of all, the information on each modality was redundant, as if they are encouraging us to pick a method and stick with it this time”.

Helga raised an eyebrow as Marius continued. “The first few microseconds of information relate back to us exactly what we sent them, but in a format that suggests that their grasp of mathematics is very different from our own.” The first surface was a flat field, with time and frequency as the x and y-axis, and amplitude as the z-axis. It showed fifteen distinct, conical peaks. The meaning was immediately obvious. Spaced at the appropriate intervals along the time axis were each of the first ten prime numbers. Also indicated were slightly taller peaks indicating; pi, e, and three transcendental numbers unknown to terrestrial mathematicians. The second surface clearly revealed a Fibonacci series of ten numbers. The sequences were not in a line, suggesting some counterintuitive relationship between frequency and time.

“Notice their apparent emphasis on transcendental numbers.” remarked Vigo as he craned his neck for a better view.

“The next series follows our lead, it is a matrix. The dimensions are a prime number by a prime number, etc. Ours was two-dimensional. It appears that theirs is 23 dimensional.” The computer flashed through a series of three-dimensional solids in an attempt to illustrate a figure too complex for the human mind to visualize. “Each entry in the matrix is a curved surface. Most of them have obvious solutions and can be simplified using calculus. I have no idea what they mean.”

“I notice there don’t seem to be any pictures.” commented Tatiana.

“You’re right.” interjected Helga, “They sent literally millions of surfaces, and other than mathematical solids, not a single one is a recognizable illustration.”

This last point was an important one because Terrestrial linguists had often tacitly assumed humans would be able to exchange abstract ideas in the form of figures and diagrams. At the height of humankind’s second great age of science, the first radio message intentionally sent into space had included abstract figures representing humans, the solar system, and a radio telescope. The first spacecraft sent on an interstellar voyage included abstracted line drawings of humans holding hands, as well as highly anthropocentric messages in the form of music, and recordings of human voices. Even at the time these attempts at communication were sent, it was not clear that an alien civilization at the technological level necessary to receive them could ever decode them. Science is as anthropocentric as any other human endeavor, however, and the reliance on pictograms representing visible objects had persisted over the intervening centuries.

“So, we came all this way and all we can talk about is math?” interjected Kat.

“We’re lucky we made it at all, and that we can at least talk about math.” replied Vigo laconically.

Helga sensed the tension building. Before the exchange continued, she broke in authoritatively, “Both points are correct. For any single mission, the probability of encountering an intelligent civilization of this caliber must be vanishingly small. Given that we have come so close to contact with an incredibly advanced civilization, it is a bit frustrating to lack a common ground for communication, other than a few basic mathematical relationships. Marius and I are open to suggestions on that matter.”

“You can try using set theory and logic.” volunteered Tat. “That should cover a lot of the basics. Once those are established, all we need is to identify a few key objects, and the interconnections become obvious.”

“That sounds a little optimistic. Why don’t we try pointing?” quipped Vigo.

Noticing the possible sardonicism of his own comments, he continued diplomatically “Seriously, we could use an optical laser-we could even reflect it off of a small orbiting mirror if we wanted to point to ourselves”

“Both are excellent suggestions, thank you.” concluded Helga. The meeting broke up in silence.