## Dream works

In a recent posting, I wrote about a vivid long-running dream I’d had,

a murder mystery (never solved) involving art shows in the San Francisco Bay Area, my neighbors in Cambridge MA 50 years ago, the Cape Cod National Seashore, and … Batavia NY. I’ve been having a lot of these dreams in recent weeks, mostly involving blog postings I “work on” in my sleep — on topics that turn out to be entirely illusory, though I can’t help checking the details out when I wake up.

Most of these dream postings are about the analysis of linguistic data, but they are mostly so complex that I can’t retrieve the point when I wake up. But there are some I made notes on, or rehearsed upon awakening.

Here’s one with a clearly linguistic point: a dream about inveterate numbers, a number-theoretic concept I wasn’t aware of before. I dream-busied myself with proving theorems about inveterate numbers until I woke up and discovered there was no such technical term.

I’m guessing that the trigger for this was imperfect numbers, numbers that are not perfect:

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself [for instance: 6 (= 1 + 2 + 3), 28 (= 1 + 2 + 4 + 7 + 14), 496, 8126] (link)

From the same article, more surprising technical terms:

The sum of proper divisors gives various other kinds of numbers. Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant. These terms, together with perfect itself, come from Greek numerology. A pair of numbers which are the sum of each other’s proper divisors are called amicable, and larger cycles of numbers are called sociable. A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number.

Numbers that aren’t practical are impractical. On the basis of imperfect and impractical numbers, I wondered whether there were impenetrable, impermeable, incompetent, or impervious numbers. But apparently not.

In another dream, I was clambering over rocks with friends in a place that looked a lot like Ithaca, New York. At one point, one of these friends remarked that our friend Melinda regularly gathered with people in a tech group that met in places with outdoor challenges; the most recent gathering was “on the bluffs overlooking Lincoln, Nebraska”. When I woke up I went to verify my recollection that Lincoln was a pretty flat place, with no bluffs. The dreams can be persuasive.