William Huff is an honorary member of the Symmetry Society with a fascinating background in architecture and design. He always gives an interesting talk at the Congresses with a different topic each time. At the Hiroshima Congress, his talk was on symmetries in word pairs. You can have two words that are spelled the same but have different meanings, for example.

The three primitives are: spelling (the nature of the written word), sound (the nature of the spoken word) and the meaning of the word. Each primitive quality has an affirmative and negative instance; for example two words are spelled the same or they are not. Combining the symmetries, you could have as many instances as there are hexagrams in the I Ching which uses the same permutation math. (There is absolutely no correlation between the assignments of the hexagrams in Huff’s paper to the Chinese oracular meanings.)

This was a project with a student and many examples were created.

— Same sound, same spelling, same meaning: This isn’t strictly possible if we are talking about pairs of different words..

— Same sound; same spelling; different meaning. To qualify, the two words need to come from different roots. Rose (flower) and Rose (having risen) Fine (penalty) and Fine (good)

— Same sound; different spelling; same meaning. Gray and Grey Draft and Draught

— Same sound; different spelling, different meaning. Rose (flower) and Rows (lines) Colonel (military rank) and Kernel (central part)

— Different sound; same spelling; same meaning. The (THē) and The (THə) Either (ēTHər) and Either (īTHər)

— Different sound; same spelling; different meaning. Rows (lines) and Rows (fights) Entrance (entryway) and Entrance (charm)

— Different sound; different spelling; same meaning. Synonym. Rows and Tiers Big and Huge

— Different sound; different spelling; different meaning. Basically all other word pairs not in one of the other categories.

This work has interested me since I first heard of it. The reason is that we handle our left hand side via relations and operations that can be characterized and possibly viewed through symmetries. Kutachi-inspired proposals are likely to leverage this.

What about the right hand side? As it happens now, right hand sides are governed by ontologies that can be described as a formal set of relations between tokens (words). Ontological networks are (when at their best) strictly structured so far as the description logic used to make the connections, but the resulting graphs are pretty random.

What if ontologies were structured so that every written word was paired with every other, and overlain with pairings of every spoken word and pairings of every word-grained concept? This would be massive but extremely well structured. Wonderful efficiencies could come from the operations involved in natural language recognition; this is clear.

Better: a whole visualization vocabulary can be enabled that used relevant parts of the lattices to show context and narrative. We are still talking about the easy stuff, the right hand side, but now we have a way of combining situated order on the right with the more elusive order on the left hand side.

What is missing from the Huff work that would enable this? Maybe too much to add. We’d need to add the dimension of the components of a predicate, keeping track of whether the words were nouns or verbs. And we’d likely need concepts from all over the globe mapped to some critical mass of languages. This would be so that deep concept structures (what we call narratives) could be separated from artifacts of grammar.

And we’d need the cinematic equivalent.

The Relationship to Kutachi

Our ontology graphs will be constructed to have internal symmetries and possibly use cactus trees.

Links

Homonym, Homonym, Homonym, and Other Word-Pairs. William S. Huff. 1992. [Culture & Science v3]

The Kutachi essay on Semantic Distance. (not online yet)