The Longest Now

While still recovering from a Rein’s Deli hangover, I found myself the subject of the Ragesoss lens last weekend.   Good energy, well captured.

@Ragesoss: It is a mathematical notion applied to ideas. A conceptual space around a theme is full of different concepts, each related to the theme in some way. Such a space can be described in terms of facets that can be used to describe a concept: for instance, you might describe ideas for laying out a garden in terms of their complexity, suitable climate, or total size… or many others. Complexity and size are sometimes linked. You can imagine the conceptual span of a set of facets, or their dependency on one another, as corrolaries of the span and independence of vectors being used as the basis for an abstract space.

A mesh is a limited set of elements that can be used to effectively describe an infinite space of ideas.  Human languages are full of concept meshes.  The easiest to discuss are one-dimensional meshes (ideas that span the spectrum of a single facet):

• color words – the spectrum of visible colors is split into a set of common colors.  this set of names is a casual mesh for the visible color spectrum. (casual in that there is no explicit metric used to determine whether all parts of the visible spectrum are ‘equally’ represented by words)
• shape words – shapes may be described as circular or oval, square or rectangular.  There is a humorous ‘proof’ that the only skew triangle has angles (45, 60, 75) – that all others are roughly equilateral, isoceles, or right.

Higher-dimensional meshes include texture words (smooth, rough, bumpy, prickly, soft, firm, sticky… – covering facets of friction, give, tangible local structure, and more).  Most higher-dimensional meshes in language are incomplete (we rarely form words for concepts whose realizations are not in common use).

If you define a metric for the distance between two points on a spectrum, you can construct an “equally-spaced” subdivision of the space, or a balanced mesh.  This splits a space into a set of characteristic elements (here, concepts) or nodes which can be used to describe anything elsewhere in the space.

Choosing a metric is important and difficult.   For instance, once we found a way to measure color by the wavelength of its light, we could ask for enough common color words such that every frequency of visible light is no more than 50nm from the wavelength of one of the characteristic colors.  In practice, humans see different parts of the color spectrum with differing degrees of sensitivity, and we become familiar with certain constant colors in our environment .  So while the rendered spectrum does not devote much space to Yellow or Orange (in contrast with green and red), we have many more characteristic words for yellows and blues than a straight “wavelength subdivision” would suggest.

It is also difficult to define facets that are independent of one another; but this is not necessary.  It is mainly important for each facet to be easy to observe and agree on.

For a given metric, you can describe the fineness of a mesh in terms of the maximum distance from any concept to the closest characteristic element.  (or sometimes twice that distance – as a description of the “largest” concept that could “slip through” the mesh without including any of the characteristic elements.)  If you have different metrics for each facet, a synthetic combined metric must be created that is consistent with each.

A balanced mesh is then one in which the fineness of the mesh is essentially the same for all subsets of the conceptual space — so, a set of color words that provides equal facility in describing perceived colors at all points on the color spectrum.   (Again, a suitable metric here might be one that stretches out the spectrum in regions perceived very well by the human eye, or colors that come up frequently in human life — the latter a metric that changes with social context.)

One can often have a clear definition of a mesh without having words for some of its characteristic elements.   This happens often with a multifaceted space, where the intersection of well-known values of each facet is an unknown combination that has no word to describe it.   One common way of constructing a balanced mesh involves creating a balanced mesh for each facet, and then defining a concept for every combination of those single-facet ideas.  Building a “complete” set of characteristic concepts can be thought of as mesh completion.  It is a way of thoroughly grokking a space of related concepts.  And the fineness of the resulting mesh is a measure of how effectively one has used language, imagery, or other methods to illustrate the limitless variety possible within the constraints of that conceptual space.

(More after the jump…)

One way to complete a mesh is to identify characteristic concepts that are familiar, then to look for the nearest familiar concepts for each remaining node and to try to imagine something combining their qualities / falling in-between them.   Sometimes new words and imagery need to be defined for concepts that can be conceived but do not have their own common phrase.  Other times, there may be theoretical concepts that ‘exist’ in the synthetic context of a given mesh, but do not match anything that seems real or that one can conceive [at the moment].   Identifying and clarifying these concepts can expand ones capacity to differentiate and perceive the surrounding cluster of ideas; can point to a poor choice of facets; and can point to gaps in the language used itself.   To the extent that developing words and phrases for important topics is the fundamental unit of language-building,  creating and completing meshes to describe sets of concepts offers a step towards describing anything truly new.

The practice of picking out facets that seem meaningful in a situation and viewing the situation in terms of them, can be seen as considering a variety of perspectives.   Generalizing from a particular situation and perspective to a related mesh offers a way to characterize different perspectives — even a way to measure their applicability or flexibility in the context of that situation.

Exploring how granular one can make a mesh before running out of obvious candidate concepts for each node offers an estimate of how effective one’s current language/dialect is for describing related concepts, and how nuanced one’s analysis using that language is liable to be.  One can also pick facets based on some context-free reason — for instance how accurately, quickly, or precisely they can be measured, or how extensive and well-defined they are — to produce meshes with very precise matches in one’s personal experience, and with many gaps.

The practice of naming and illustrating new concepts to fill gaps in a well-defined mesh is a creative part of mesh completion.  Supporting this process — building complete, balanced meshes rather than using the best available unbalanced mesh to describe a situation or idea — is what I mean when I say I am a mesh completionist.

This involves identifying current perspectives and measures, assessing the effectiveness of current language in new contexts, connecting a patchwork of partial local meshes into a whole reflecting the entire space of concepts under consideration, considering the fineness of the familiar parts of the mesh and the gaps in its new parts, filling in the mesh with existing concepts where possible, and creating new language where needed.  Often the unknown parts of a mesh cannot be made as fine as its well-worn parts, at which point it is important to decide whether to give extra weight to the familiar parts simply because they have more named nodes.