Lincos consists of a variety of mathematical terms and phrases, to be encoded into specific combinations of radio pulses and signal shapes and then beamed out into space. It is devised purely in terms of semantics and human logic, and accomplishes understanding by building from simple beginnings. Statements are arranged in words, sentences, and paragraphs.
Freudenthal’s program begins by establishing the meaning of the terms "plus" and "equals." He would, for instance, send signals something like "beep bloop beep tweet beep beep" (1 + 1 = 2), perhaps followed by "beep bloop beep beep tweet beep beep beep" (1 + 2 = 3) and so on. Eventually it should become clear that "bloop" represents addition and "tweet" signifies equality. In the first chapter of his book on Lincos, Freudenthal goes on similarly to introduce the concepts of subtraction, multiplication, division, basic symbolic logic ("and," "or," and "follows"), negatives, integers, decimals, fractions, and zero. In the second chapter the concept of time makes its appearance, including "seconds," duration, wavelength, frequency, "before," "after," and "occurs."
In chapter 3, Freudenthal develops concepts of correct and incorrect, right and wrong, good and had; to count, to search, to find, to describe, to prove, to change, to add or omit; to know, guess, understand, and mention; nearly and approximately, much and little, soon and long ago, age and now; necessary and possible, enable, be forced, allowed, forbidden; politely; conflict between necessity, duty, and desire; and so forth. For example, Freudenthal’s language lesson to teach the concepts "correct" and "incorrect" to ETs runs as follows:
As vocabulary slowly builds, ever more sophisticated statements become possible. In chapter 4 of Freudenthal’s book, mechanics and spatial extent are dealt with, including concepts of distance, position, length, growth, volume, motion, waves and oscillations, speed of light, mass, and astronomical concepts. Later chapters delve into geography, anatomy and physiology including the human reproductive process. By staging "plays" between symbolic human "actors," Lincos ultimately should be capable of portraying diverse facets of human behavior, emotions, social conventions, philosophies and religious rituals.
*Ba Inq Hb•?x.100x=1010: Human-a asks Human-b: If 4x = 10, how much is x? Hb Inq Ha.1/10: Human-b tells Human-a: x is 1/2. Ha Inq Hb Mal: Human-a tells Human-b: That is incorrect. Hb Inq Ha.101/10: Human-b tells Human-a: x is 5/2. Ha Inq Rh Ben* Human-a tells Human-b: That is correct. End of lesson.