Why numbering should start at zero

When dealing with a sequence of length N, the elements of which we wish to distinguish by subscript, the next vexing question is what subscript value to assign to its starting element. Adhering to convention a) yields, when starting with subscript 1, the subscript range 1 ≤ i < N 1; starting with 0, however, gives the nicer range 0 ≤ i < N. So let us let our ordinals start at zero: an element's ordinal (subscript) equals the number of elements preceding it in the sequence. And the ...

 The Wonder of a Child Learning Their Native Language

Imagine you are faced with the following challenge: You must discover the underlying structure of an immense system that contains tens of thousands of pieces, all generated by combining a small set of elements in various ways. These pieces, in turn, can be combined in an infinite number of ways, although only a subset of these combinations is actually correct. However, the subset that is correct is itself infinite. Somehow you must rapidly figure out the structure of this system so that you c...

 Teaching with Pokemon Go

Learning objectives that ask students to assemble and integrate data (like a language or math class) are well-suited to the capture and find aspects of Pokémon Go!. Imagine setting up a variety of PokéStops around your campus. Each one can be visited by students as they go about gathering the data they need to accomplish the learning objective you set. Perhaps after traveling about campus, they have to return to your classroom and use the data they’ve gathered like PokéBalls to solve mor...

 Language as Set Theory

The revolution in our understanding of the logic of names began with a basic question: Where do the meanings of words live? There are two likely habitats. One is the world, where we find the things that a word refers to. The other is in the head, where we find people’s understanding of how a word may be used. For anyone interested in language as a window into the mind, the external world might seem to be an unpromising habitat. The word cat, for example, refers to the set of all the cats t...

 RPG as Cooperative Experience

A role-playing game is a cooperative experience between multiple participants. At its simplest, it can be described as an organized form of group make-believe, with a set of rules and procedures to keep things consistent and fair. The goal is not to win - there are no real "winners" in a role-playing game - but simply to have a good time.

 König’s paradox: Ordinals

Let’s start by turning back the clock. It is India in the fifth century BCE, the age of the historical Buddha, and a rather peculiar principle of reasoning appears to be in general use. This principle is called the catuskoti, meaning ‘four corners’. It insists that there are four possibilities regarding any statement: it might be true (and true only), false (and false only), both true and false, or neither true nor false. [...] To get back to something that the Buddha might recognise,...