This is an introduction to a series of expository blog posts on Araara. Araara is a personal mathematical research programme. Most of the conceptual work was done during a month-long backpacking trip to Aotearoa. It is named after the Māori name for the trevally (Pseudocaranx georgianus). Its aim is
Concatenation already gives us addition. With the Fraktur alphabet, we can also describe how to choose and combine two arguments. Let’s start by choosing just one. Choosing an argument The operator 𝔞 returns the first argument. The operator 𝔟 returns the second. These are the projection functions, usually written π0 and
This is the thirteenth in a series of expository blog posts on Araara. In the preceding post, we introduced Apar: names for variables whose interpretation depends on an ambient type. Let us now introduce another alphabet. We will use this alphabet to define operators, eventually building towards the hyperoperation sequence.
This is the twelfth in a series of expository blog posts on Araara. In Alungo, we extended the numbers we can write. Now let’s give a name to a value we have not yet chosen. We will call this Apar, after the Globasa word parametre. A name that cancels
This is the eleventh in a series of expository blog posts on Araara. The preceding post combined Asoho and Akurto to form Apeundeku. We will now combine two other ingredients: Attic and Akurto. Akurto can already express integers of any size. But its alphabet has a largest positive letter, w,
This is the tenth in a series of expository blog posts on Araara. The preceding post introduced Asoho: reciprocals expressed with uppercase letters. We will now combine Asoho with Akurto. We can already write three as ba, and its reciprocal as BA. But what if we would like to write
This is the ninth in a series of expository blog posts on Araara. The preceding post introduced the Attic alphabet. We will now return to Aglobasa and give its uppercase letters a different arithmetic. It would be nice to have reciprocals (plu soho) as well as integers in Araara. Let
This is the eighth in a series of expository blog posts on Araara. The preceding post explored references to books, atoms, galaxies, and colours. The series begins here. Let us introduce a new alphabet: Attic. We will use the Greek zero sign 𐆊 as its zero element, followed by ten Attic
This is the seventh in a series of expository blog posts on Araara. The preceding post introduced Akurtosks, a shorter way to represent strings. The series begins here. We can now write integers, Unicode code points, strings, and alphabets. But perhaps we would like to refer to a book? Or
This is the sixth in a series of expository blog posts on Araara. The preceding post introduced alphabets as Asks, including gapped alphabets. The series begins here. Normal form gives us an agreed way to represent each integer. But it can be quite long! It would be nice to have
This is the fifth in a series of expository blog posts on Araara. The preceding post introduced Asks: strings formed by concatenating Unicode normal forms in Akurto. The series begins here. We will return to the uses of Akurto terms for Unicode code points later on. But first: what is
This is the fourth in a series of expository blog posts on Araara. The preceding post introduced the Aglobasa alphabet and the Akurto type that uses it. The series begins here. Alphabets are arbitrary Before proceeding, I should make one convention explicit. Choosing Aglobasa as our default alphabet is a