Again, we might be trying to contact beings so entirely different from us that we would have no common ground upon which to build understanding. They might not even respond as we do to the same stimuli. Their appearance, evolution, structure, environment and thinking processes could even be beyond the limits of our imaginations. But a signal could come--an impulse from out of the boundless abyss telling us we are not alone. What would be the nature of this message? And how could we reply? Assuming that our senders are using radio wavelengths and have enough similarity to us for mutual understanding, we would first have to isolate the signals from the hash of natural static. Next, we would have to “crack the code.” The usual cryptographic techniques, which depend on some basic knowledge of the language and letter frequencies, would not be adequate. We can only hope that the callers give us some clues. Scientists expect any messages received will be mathematical in nature, since mathematical principles may be regarded as universal constants. The message might be a simple numeral progression or the numbers of a constant, such as the wave length of the hydrogen atom or the speed of light. They might send _pi_, for example, the ratio of the circumference of a circle to its diameter. It’s a non-stop number, but we would understand if it was worked out to six or eight decimal places. “_Pi_ from the sky” would be the story of the ages. Once we had received this signal for recognition and replied in equally simple terms would come the real problem of interpreting or devising a means for transmitting speed. * * * * * Hans Fruedenthal, professor of mathematics at the University of Utrecht (Netherlands), has devised a system he calls Lincos (meaning “Lingua Cosmica” or “Cosmic Language”). It consists of teaching the meaning of certain sounds by using numbers. The numbers would be signified by “dots” or “beeps”; the sounds by radio signals of various frequencies and lengths. To illustrate the method, let us assume that the sound “bloop” stands for “equal.” Three dots would be sent, then bloop, then three dots. This would be repeated with other numbers until the listeners associated the sound with equal numbers. The concept of “less than” would similarly be sent by several dots, another sound (like “tweet”), followed by a greater number of dots. The reverse--like a greater number of dots, another sound, and a lesser number of dots--would signify “greater than.” Once these concepts were understood, the operative signs like add, subtract, etc. could be taught. Thus a mathematical vocabulary would be established.