Topology for artists, walkers and other non-mathematicians
One of my little dreams is to make and give a workshop about topology for artists, walkers and outher outsiders. It might be called:
The topological toolkit. What you didn't know about spaces. These are preliminary notes:
YouTube topology,
Styles of topology, Spaces and maps. and
Translation. I try to post small updates often, to keep myself working on this.
I love the remarks of John Ciardi about his Dante translation. They are a perfect example of spatial and structural thinking. Here, once again, he describes the structure of languages and the difficulty of mapping from one space to the other. He describes the complex structure of words and uses a spatial metaphor:
We tend to use only the top slice of a word in speech usage. But once the other levels of a word are allowed into consideration, no word is a simple thing. It becomes a complex. But if a single word is a complex, then a phrase is a complex of complexes, and a line is a complex of complexes of complexes, and a stanza, and a poem are ... and so forth and so on.
And the picture is even more complicated. It reminds me of these complex fractal spaces:
The word has different positions in this space, in different planes of meaning and feeling. You can build many spatial models for this situation and below I use the simplest one:
The American word “daisy,” for example, labels the same flower the French intend by "la marguerite" and the Italians by "la margherita" ... those are the words one would naturally use in these three tongues for labeling any particular daisy. Semantically, that is to say, the denotations are reasonably firm.
But words consist of much more than denotation. Every word has a certain muscularity. That is to say, it involves certain speech muscles. Certainly any man who is a word-sensitive is likely to linger over the difference between the long-drawn Italian "carina" and the common, though imprecise, American usage “cute” when applied to an attractive child. …
Every word has an image locked into its roots. The English word “daisy” is a contraction of the earlier “day’s eye,” which is to say, “the eye of day”— a lovely root image. Marguerite and margherita also have a root connotation of all girls named Margaret/Marguerite /Margherita—and bless them all as lovely images. …
And the place of the word inside its spaces of meaning and feeling changes over time. Complicating the picture further:
Every word, moreover, has a history. Sometimes the history changes out from under the word very rapidly. English “broadcast” once meant specifically “a way of sowing” and was borrowed by radio as an analogy. Meanwhile new machines all but eliminated the old methods of broadcast-sowing, and the word has just about lost all farm-connotation. …
This complexity of the language spaces precludes simple translation even at the world level:
Translation is, in fact, the wrong word for the process of rendering from one language to another. The idea of “translation” seems to suggest that there exists in Language A some word that will equal any given word in Language B, and that the translator need only find that equivalent word and put it in place … But such an assumption ignores the nature of words.
One could say that the space of language is complicated, deep and wild. I will talk about "wildness" in one of the next posts.
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