Tables Turned

The experimenter across from you, wearing a lab coat and an identification tag, places his clipboard on the table. He explains the day’s experiment. “I’m thinking of a rule which generates triples of integers,” he begins. “I’ll first give you one example of a triple conforming to the rule. Then, you must propose additional triples, and I’ll give immediate feedback: yes or no. You must try to guess the rule after submitting as few questions as possible. Ready?”

The experiment begins. “2, 4, 6.”

  1. You: “4, 6, 8?” Experimenter: “Yes”.
  2. You: “6, 8, 10?” Experimenter: “Yes”.
  3. You: “10, 12, 14?” Experimenter: “Yes”.

“Ascending triples of consecutive even integers?” you blurt out. “No. Ascending sequences in general,” the experimenter responds, as he leans back and disdainfully scribbles something on his board. You’ve been defeated. Continue reading


Wild Grammar

This article is part of a series entitled Language Games. See also:
1. Wild Grammar; 2. Combinatorial Grammar; 3. Pragmatic Grammar

“Isn’t it true that example-sentences that people that you know produce are more likely to be accepted?” – De Roeck et al., 1982 [1]

“The man the dog the cat scratched bit died.” – Dan Scherlis, a former linguistics classmate of my mother

An Investigation

Chomsky first articulated the distinction between grammaticality and what he called performance. Making a grammatical sentence is one thing. Transmitting it successfully is another, and many potential obstacles – from distracting noise to the capacity of the human mind – can get in our way.

In particular, certain sentences are grammatical, but effectively incomprehensible. These sentences are typically complex, and they might contain intricately nested clauses and phrases. The capacity of our minds is limited. Language’s capacity for recursion is not. Who could be surprised that space eventually runs out? (The two sentences above contain double center embeddings, which are notoriously difficult to parse.)

Some sentences, though, feature an inscrutability difficult to explain on account of their complexity alone. Continue reading

A Reasoned Happiness

This article is part of a series called The Scientist Theist. See also:
1. The View From High; 2. The Science of Religions; 3. A Reasoned Happiness

In the first post of the series, we stressed the fact that religious thought is engendered by feeling alone, and thus isn’t vulnerable to logical detractors. In the second, we concluded that religion, though produced by feeling, can be interpreted and communicated by reason. Here, we make the claim that religious thought can actually be produced by reason alone.


Follow me into a strange, disorienting world, where many a scientist might feel uncomfortable.

Continue reading