Editing Lincos language (section)

==Concepts and range==
The Lincos "[[dictionary]]" is intended to be transmitted first before any additional messages. It teaches natural numbers by a series of repeated pulses, separated by pauses. It then teaches >, <, =, +, -, by examples such as '''. . . . . > . . .''' (an extended pause is shown around > in this example so as to suggest to an alien that > is a new separate symbol; otherwise, an alien might think that the whole pattern is a new symbol of unknown meaning). In introducing =, unary notation is shown for numbers: '''.''' = 1, '''. .''' = 2, and so on. This progresses to multiplication, division, variables, and constants, then [[propositional logic]], [[set theory]], and [[first-order logic]]. The dictionary tries to introduce questions by leaving mathematical expressions unsolved (e.g., ? x x + 101 = 11).{{citation needed|date=March 2022}}

The next section of the Lincos dictionary introduces a word for [[second]], "Sec", by playing pulses of various lengths, followed by Sec, and the number of seconds, "until the receiver may be expected to remark that the numbers... are proportional to the durations",<ref name="lincos">{{cite book | title=Lincos, Design of a Language for Cosmic Intercourse | publisher=[[North-Holland Publishing Company|North-Holland]] | author=Freudenthal, Hans | date=1960 | location=Amsterdam}}</ref> thus teaching both that Sec is a unit of time, and exactly how long it is. It then introduces means for measuring durations, referring to moments in time, and talking about past and future events.{{citation needed|date=March 2022}}

Freudenthal's third section is perhaps the most complex, and attempts to convey the concepts and language necessary to describe behavior and conversation between individuals. It uses examples to introduce actors speaking to each other, asking questions, disapproving, quoting other people, knowing and wanting things, promising, and playing. The first steps (having already introduced sets of numbers and questions) are to introduce some new symbols (distinctive patterns of pulses), say that they are NOT numbers, and transmit sequences showing two of these new symbols separated by the word "Inq" (inquiry), followed by a question about an equation, then the symbols reversed, followed by the answer (example below). It is thus expected that, after many repetitions, the recipient will determine that these new symbols are entities asking and answering the questions, rather than some other context for the questions.{{citation needed|date=March 2022}}

Finally, the fourth section describes the concepts and language relating to [[mass]], [[space]], and [[motion (physics)|motion]]. This last section goes so far as to describe physical features of human beings and of the [[Solar System]].<ref name=":0" />

A second book by Freudenthal, planned but never written, would have added four more sections to the dictionary: "Matter", "Earth", "Life", and "Behavior 2". Other researchers have since extended the language somewhat on their own. One example is [[CosmicOS]]. Another is a second-generation ''Lingua Cosmica''<ref>{{cite web|url=http://www.alexanderollongren.nl|title=This is the index page of Dr. Alexander Ollongren's home page|work=alexanderollongren.nl}}</ref> developed by the Dutch-Swedish astronomer and mathematician [[Alexander Ollongren]]<ref>{{cite web|url=http://ieti.org/who/ollongre.htm|title=Invitation to ETI: Alexander Ollongren|author=Prof. Allen Tough|work=ieti.org}}</ref> of [[Leiden University]], using [[constructive logic]].<ref name=":0" />

Freudenthal's book on Lincos discusses it with many technical words from linguistic and logical theory, usually without defining them, which may have reduced its general interest, though the main chapters can be understood without these technical terms: appellatives, binding, formalization, function, lexicology, logistical, ostensive, quasi-general, semantics, syntax, variables, etc.{{citation needed|date=March 2022}}