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Grammar is Outdated. Let’s Mathematize It

The function of a language is to reconcile the goal of the speaker with the perceived meaning of his utterance. Modern human languages — Mandarin, Hindi, Russian, etc. — are unable to securely bridge the gap between intention and result. Language reforms and attempts to create hybrid languages are needed now in any case — to learn to communicate with an AI. Let’s reflect on reforms to come.

Despite centuries of active theology, no common philosophical definitions have emerged in languages. Each thinker is forced to invent and verbosely explain his monads. There is no metaphysics in natural languages. Categories in language rely on direct experience, on physics.

In every language, even the most primitive, there is a concept and word for “I,” there is a “you” and there is a “he.” For a speaker, “he” and “you” are not “I,” even though I don’t fully know what I am.

In many languages, there is the absolute today, yesterday, and tomorrow. There are verb tenses, although time flows differently for each object (in terms of physics) and each subject (in terms of physiology).

As a result of the evolution of language, the grammatically geometric concepts of bring-up, get-off, and double-down have derivational meanings. In general, spatial concepts are quite complex. When we choose a verb, we focus on WHICH objects or subjects that verb refers to.

For example, in Russian a sparrow always “sits” on the branch, a chocolate bar always “lies” on the table, and a house — “stands.” And some things can only hang. In other languages, a house or a mountain may sit; and there are reasons for that.

There is a simple principle based on orientation, position in space. If the body is oriented more vertically and rests on the legs (feet), the object is standing. If it is predominantly horizontal, then it is lying. But there is also a more complex principle — the functional one.

For example, if we are not resting on our feet, but on our butt, we are “sitting.” And if the case is not about a human being, we anthropomorphize the described object in our minds. A sparrow is not “standing” on a branch, although it is leaning on its feet and not “lying down.” It SITS.

And what about a heron? It STANDS. It doesn’t matter if it does it on one leg or two. Why? Because the sparrow is small and the heron is large. Our anthropocentric mind makes the decision accordingly. A fly and any other insect would always “sit” for the same reason. But a dead insect, regardless of the position of the corpse, can only lie down.

Another example from the Russian language. A table always “stands.” A tray and a plate “stand” on the table even though they are stretched out horizontally in the plane, that is, they should be “lying” on the table, not standing. However, if we move that same tray to the floor and turn that same plate upside down on the table, no Russian person will say that they are “standing.” They both would be “lying down.”

When the plate is upside down (no matter where) and the tray is on the floor, it means these objects are not ready to be used as a container. When the tray or plate is positioned correctly, when they are fit for their direct duties — they “stand.” The same can be said of the male erection. A penis that is fit for its job is “standing.”

These things are useful but poorly formalized. Prefixes, suffixes, endings and verb types/tenses only partially create structure. You have to guess about a lot of things. And many important categories simply do not exist at the grammatical level. The possibilities for developing languages by mathematizing them are enormous.

Updated Gramma

It makes sense to introduce new grammatical constructions. A couple of examples follows.

Core Semantics Needs To Bе Indexed

You probably know about the 23 years old Semantic Web initiative to make Internet data machine-readable, originally expressed by Berners-Lee. For human-to-human languages, at least a thousand of the most used nouns should be indexed too. When you have coordinates in the n-dimensional matrix of human activities — field of activity, industry, etc. — right in the gramma, you can get rid of a lot of chaos and add tons of nuances.

Categorization of Time Intervals

The way we describe limited time intervals is already embedded in the applications. And it really is, as it always is in life. All movements, whether physical or mental, do not occur linearly, but with a certain span. The fact that we assume by default that all processes in between are linear degrades both description and understanding.

Here are a few more examples for you to think about on your own:

  1. Time: an event occurs in between two points in time, as a “ray” (from this moment and forever into the past or the future), forever (without definite boundaries)
  2. Time-density: interval could be continuous or scattered
  3. Time-boundaries: the blurring degree of the interval’s edges
  4. Time: the point “when” is fixed at a certain place in the interval (“center of gravity”)
  5. Time: number of dimensions of time (one-dimensional as usual or two-dimensional where various probability tracks exist)
  6. Enumerations and lists: choice of a predefined priority system (neutral alphabetical order or a deliberately selected type of bias)
  7. Enumerations and lists: matrix dimension (linear sequence or table)
  8. Events: the flow itself, the derivative of the flow, the integral of the flow.
  9. Events: the nature of action development (typical functions)
  10. Relevance to the addressee: the dependence of the verb on the actor (not only gender, as we have now in many languages but also who it is concerning the action — novice, average, experienced)
  11. Sets (inclusion, intersection, non-intersection)
  12. The concept of field and force
  13. The notion of dimensionality of decision space



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