Glossary: dense and meaningless / dense and homogenous
These try to capture notions of overexplaining theories and overconnected
concepts. It's terminology that has become part of my jargon because the
pattern seems to crop up all the time when you talk about meaning and theories.
Theories, here, are indexes to knowledge, much like there are indexes to books.
They make it accessible/comprehensible without requiring to hold the full data
in your head. To use a space metaphor, they're meaning graphs suspended in
factspace.
Meaning is a nebulous term, I will not try to define it here.
Now consider this thought experiment: The Library of Babel has a librarian and
she needs to consult an index - how large would that index be? It turns out
that to uniquely identify a book in the library, an address exactly the length
of one of its books is needed. Since there are as many addresses as there are
books, the index is exactly the size of the library. Not being smaller than the
library, it is not a very useful index. Better bring your own meaning.
(In fact, the library best serves as its own index, but that is irrelevant here)
In effect, the library is:
Dense: All possible books are realized, bookspace is filled densely.
Homogenous/Smooth: Little distinguishes each book from its brethren.
Meaningless: It resists indexing. There are no distinctions meaning can attach to.
An intuition follows: At a certain ratio of known information to knowable
information (the part of factspace filled by theories), new information doesn't
help, new connections in fact reduce overall meaning.
There seems to be a certain sweet spot of connectedness that maximizes meaning,
the usefulness of a theory or its explanatory/distinctory power, and it is not
located at "full knowledge".
PS: It seems to me like judicious application of Ramsey theory could help put
these notions on well-defined feet, but that is out of scope for now.
PPS: There are implications for art: Adding "more of the same" to the corpus
becomes progressively more meaningless. A connection to an information
theoretic approach to art, where adding more of the same results in only
minimal complexity gain as measured by the length of the compressed corpus.
published: Jul 12 2016.
epistemic status: explorative.
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