Let's Read: Jorge Luis Borges's Dreamtigers

In this post, we summarize every single entry in  Dreamtigers (Borges, 1964). We also add commentaries on particularly obscure references.

Dreamtigers, first published in 1960 as El Hacedor ("The Maker"), is a collection of poems, short essays, and literary sketches by the Argentine author Jorge Luis Borges. Divided fairly evenly between prose and verse, the collection examines the limitations of creativity. 

Let's Read: A Problem

In this post, we read through Borges's story A Problem, which is about Don Quixote, a story written by Cervantes:

The story follows the adventures of a nobleman named Alonso Quixano who reads so many knightly stories that he goes insane and decides to become a knight-errant, reviving chivalry and serving his country, under the name Don Quixote de la Mancha. He recruits a simple farmer, Sancho Panza, as his squire. 

His name means "Don Quixote, of la Mancha". La Mancha is a region in central Spain, where Don Quixote lived in.

A Problem

Jorge Luis Borges

Let's read: Dead Men's Dialogue

In this post we read through Borges's story Dead Men's Dialogue, which, other than the usual kind of maddening riddles that writers play, where they only say half of what is said, and I have to fill in the other half, is extra hard to read for me because it is full of references to South American history that I don't know.

So I'll fill in all the blanks here.

Dead Men’s Dialogue

Jorge Luis Borges

A story of an eusocial human species: Antman

This is a sketch of a eusocial human species modelled on ants. Let's call this species Antman.

The Antman has 3 castes: Workers, Soldiers, Researchers. Most of them are specialized, but a few are generalists who act as synthesizers and communicators between specialized areas.

Some of the generalists also act as temporary leaders, but there are no formally elected leaders.

An Antman society unit is a nest. The size of a nest depends on the local geography, but usually would grow up to that of a big modern city. The size is a balance between economy of scale, which favors bigness, and speed of moving things around inside, which favors smallness. Nearby nests usually cooperate very closely, more than a modern state.

The binomial numbers, the Rule 60 celluar automata, and the Sierpinski triangle

Consider the pattern of the parity of the binomial numbers. Color the even numbers white and odd numbers black. You get a Sierpinski Triangle.

We will prove this using spacetime-geometric reasoning. It would help a lot if you have done some geometry of special relativity.

Define the parity function $f(t, n) = C(t, n) \mod 2$, defined on $\mathbb{N}\times\mathbb{Z}$.

We can consider $f(t, n)$ as encoding a 1-d celluar automata, with $t \ge 0, n \in \mathbb{Z}$. Then we have the evolution rule:

$$ f(t+1, n) = f(t, n) + f(t, n-1) \mod 2$$

This is just the Rule 60 celluar automata. 

Then it's easy to prove the following: