Conceptual Space Density

Ideas (concepts) have more or less typical interpretations. Some ideas are easily denoted by signs and illustrated by choosing their realizations in typical individuals.

For example, the idea of a "table" can be illustrated by several typical variants of a table. But most likely, you will simply imagine your table, the one you most often sit at.

Searching for typical interpretations also applies to longer linguistic expressions.

When you hear "a computer fell off the table", you imagine your laptop falling off your table. These are references typical to you because you see this laptop and this table every day. If someone else sees different laptops and tables, they will also imagine different representative examples of these ideas, taking into account the context and experience. We will all imagine different laptops and different tables, but none of us will think of a glass of Coca-Cola flying into space!

People understand signs for some ideas more similarly than for others.

When we say "table" or "a phone is lying on the table", people imagine more similar things than when we say "justice" or "fair trade".

There are ideas for which the number of sign references (interpretations, realization searches) is very large, and some of them differ significantly from each other.

Take the concept of "love", it is quite complex and abstract. There is "love for a woman", "brotherly love", "parental love", "love for one's country", "love for humanity", "love for one's profession", and much more. If you are asked to imagine a situation in life that illustrates "love", the range will be even wider. Most likely, you will imagine something completely different from what your neighbor or colleague would imagine.

But most likely, everything you imagine will be situations that fall under the same spectrum of circumstances and feelings, not in any other. In this spectrum, there will be few manifestations of violence (although...), or, for example, indifference.

To characterize these differences, there is the theory of conceptual space density.

Try to imagine a "space of linguistic signs" and overlaid on it a "space of objects" that embody the ideas expressed by these signs. Somewhere in this space, signs and corresponding homogeneous objects will be evenly densely located. Such concepts are called specific, with a dense conceptual space.

For example, all tables will be "tables", all laptops will be "laptops", and for each specific subcategory of tables (for example, "office table" or "dining table"), there will be easily imaginable objects that belong exactly to this subcategory.

In other areas of this space, near one sign, there will be many very dissimilar objects, situations. One sign ("love" or "justice", for example) is as if spread over many situations embodying many ideas, not just one idea of "love". We will say that these are concepts with a sparse conceptual space.

The simplest reason for the sparsity of the conceptual space is homonymy (when the same word has different meanings). If we have simply a polysemantic word - to clarify its meaning, it is sufficient to refer to the dictionary entry, as with the word "project".

However, this is not the only possible reason. For many concepts with a sparse conceptual space, a simple dictionary explanation of the term does not help imagine a single typical representative embodying all the features of the corresponding concept exhaustively.

The conceptual space of the concept of "project", whether in an engineering or managerial sense, is not very dense: projects in different fields, in different industries, in different companies can be very different. When talking about a "project", two managers from different industries or countries may still imagine completely different things.

It can be noticed that in the engineering context, the conceptual space of a "project" is relatively denser than in the managerial context. Although not all engineers and not all managers would agree with this!

Computational linguistics has been able to formalize the concept of conceptual space density using mathematical statistics. To do this, texts (documents, books) from one or more semantic communities (that is texts from one or more subject areas) are taken, and each occurrence of a word, term is encoded by coordinates in a multi-dimensional space so that nearby words (or words in the same document) correspond to close points. In the resulting space filled with these points, some points corresponding to one word are very close together, which means that everyone talks about this object in approximately the same way, in the same context. And if it is sparse - it means that the concept is not very defined.

For example, if you take all Russian texts without distinction (literary, managerial, engineering, medical, ...), the points for the word "project" will fall into one of two relatively dense areas (corresponding to managerial and engineering uses), as well as be relatively dispersed throughout all other space, reflecting the "ordinary", non-specialized use of this word in various other senses.

It is necessary to have a good understanding of the density of the conceptual space in different subject areas and for different roles we encounter (both by performing these roles ourselves and working with other agents in these roles).

Even when dealing with concepts in a conceptual space with high density, it is still necessary to carefully select precise terms (signs), but there is more to choose from.

When we encounter a sparse conceptual space, we need to dedicate much more time to accurately delineating objects, understanding the ideas behind them, selecting signs (names) with precise reference. Our explanations become more verbose, and there is a need for more precise languages.

Without understanding this, communication in a sparse conceptual space will always be at risk of failure.