Self-describing language

Question

Lately I saw a video about the messages that have been written into satellites that go into deep space. Most of them are based in mathematical constructs, assuming that math is a universal language, and because math can be incrementally self explained by constructing on previous concepts.

EX:by defining units * we can explain equality * = * and with int we can explain addition * + * = **

but math is very limited when it comes to explain the complexity of human thought, for that, the natural language is better suited, currently the only way we humans can learn a foreign natural language (think hieroglyphs) is if there are some translations of parts of the language. that allows us to understand some symbols and derive others.

But my assumption is that those text where not written with the intent of being interpreter by a foreign speaker. if they were, they might have been written differently..

so the final question is.. Is it possible (any proof or theory) to create a language, or a text from a existing language, that is self-describing? so that a foreign 'entity' could learn it without external resources.

A small example that probably would not work for aliens is a text like this : "this text is written in words, words are a collection of one or more letters, a letter is a symbol from the predefined set abdcefghijklmnopqrstuvwxyz"

Answer 1

This has been done, in the form of Lincos.

The problem with any attempt at a language from first principles is that it has to presuppose common ground. How much common ground can we assume?

On one hand, intelligent alien life could be so alien as to render communication impossible.

On the other hand, we can look at it from an evolutionary perspective. Life on other planets would have been subject to selection pressures, as we were. While the specific pressures could've differed, it stands to reason that basic tendencies like avoiding death, reproduction, etc... apply to them. Can we build on those?

Answer 2

How distant a culture from ours would you intend to target?

What is possible - for about any human culture - is to create a pictorial dictionary where nouns, verbs and adjectives are defined through images or set of images depicting them. After establishing the vocabulary, pictorial stories could define grammar giving example sentences. Once initial set of language is established, it could be used for self-expansion.

This still depends on the targets being able to recognize the actions and objects depicted, and even on them possessing a sense of sight similar to ours.

Yes, pure mathematics is very difficult to describe complex but down-to-Earth concepts - show a picture of a person with one leg extended, the other trailing, off balance and you have the definition of "walk". But scientists spent decades trying to program functional walking robots - in other words, define "walking" in terms of mathematics. And what if your target audience is only ever rolling or floating in water? How would you depict "walking" for them in a way they'd understand?

So, while creating a language deriving its complete meaning from mathematics would be extremely, impossibly difficult, it's still quite possible to create a self-describing language based on mathematics, that contains such trivial concepts as "nitrogen", "wavelength spectrum", "light year", "electromagnetism", "fission", "atmosphere", "Oberth maneuver", "Planck time", while being utterly helpless with complex ideas like "sneeze" or "cookie".

Edit: since it's far too long for a comment...

First, you establish the language of mathematics: notation of numbers, operators, the whole "grammar" of mathematic expressions. We've established this is perfectly doable.

Then draw a hydrogen atom, dimensions described in multiples of Planck Length. Any civilization understanding proportions, knowing composition of hydrogen and knowing Planck Length will easily recognize the familiar dependency, both recognizing the unit of distance and the type of atom, together with symbols for proton and electron.

Add deuterium, with its mass, next to hydrogen's mass; we have a unit of mass and a symbol for neutron.

Depict emission of a photon to obtain its symbol, a unit of energy, a unit of frequency and a unit of time.

Armed with geometry, electron, proton and neutron you can define chemistry, all of the universe's composition. Using chemistry and geometry you can begin depicting physical macroscopic objects.

Armed with time and distance you can describe motion and change. Together with motion comes temperature. Wavelengths define colors. Photon layout of reflected light creates image/sight.

With motion, mass and location you can define gravity.

Define air (mix of oxygen and nitrogen, temperature, inter-particle distances) and derive pressure. Add waves to define sound.

With composition, temperature and mass you can describe stars. Frequency of pulsars will give a firm macroscopic coordinate system.

After describing our Sun, you can get to describing Earth. Sphere, air, water, soil, hot core, surface temperature and pressure.

Afterwards, proteins and DNA for describing life. Plants (chlorophyll, unmovable), animals (hemoglobin, moving). Human.

Afterwards, depicting how human's body works (eyes as light sensors, ears as sound sensors, hands and legs as actuators) you can proceed to technology. Physics and chemistry will be essential.

And so on, and so on - explaining how each element fits with the ones explained so far, you can build the whole dictionary. And yes, while possessing descriptions of motion and gravity, concepts of "Oberth Maneuver" are easy to explain. But to understand "cookie" you must know plants, grasses, grains, seeds, grinding, flour, sugar, baking, human digestion, sense of taste, and concept of pleasure. And while some are simple enough (taste = chemical analysis), others like pleasure will be incredibly hard and lengthy to describe, delving into evolution of instinct, separation of conscious mind from primal desires, and a whole course in human psychology.

Answer 3

A formal language that describes the syntax of other languages (including its own syntax) is called a metalanguage. For example, a formal grammar for Backus-Naur form can be written in Backus-Naur form.

Similarly, a word that describes itself is called an autological word.

Answer 4

Yes and no. Yes because computer programs are written in machine language and all of maths can be described with a "base dictionary" (concepts like value/amount, recursion, lists, etc.). Machine language can write any program (at least that the computer is capable of processing) by "stringing together" chains of the "base tokens" to make new definitions/meaning/instructions (classes, structs, functions, etc. (basically literally all programs) would be examples of this). No because there will automatically have to be "base tokens" that must be figured out by the intended target using its own intelligence in order to build anything more complex (you can't build something out of nothing). On another note, most human languages are already largely self-contained with the main exception being the environment that we live in being difficult to explain accurately. Definitions of words are pretty much the same as with mathematics and machine language; you "string together" words that already exist/have been defined to create meaning. You are implying that you can't build a natural language with mathematics at its base but I disagree; concepts like value/amount, recursion, lists, etc. are all both mathematical and real life concepts that you need in order to build things up. The only "base tokens" that might not fit into mathematics strictly are things that pretty much all intelligent entities could understand like good/bad (you don't need empathy for morality because you will still have joy/pain to judge what is good/bad). You could describe the shape of a surface or the way things sounds/look with randomality/probability and mathematics involving things like perlin noise.