Fats, Vitamins and Minerals

Introduction to Crochet and Computability
by Edward Nutmeg (February 27, 2007)

“Crochet and computability” present relationships that go beyond the “craft geometry” used to describe the modeling of planar surfaces in 3-D space. In this sense, I am interested in “crochet” as a distinct formal language and grammar system rather than crochet as an instrument for creating plane models for hyperbolic geometry, or manifolds of strange attractors or other such silly things.

So, what is “crochet”?

Crochet is the process of pulling loops through other loops with a single hook and a strand of thread. Crochet, like weaving, has an underlying mathematical structure (pattern) and can therefore be understood from the computational perspective. In the process of pattern development (for crochet or other), data classification is based on either statistical information extracted from the patterns or on the (syntactic) inter-relationships of pattern features. This process involves:

A Sensor: observer
A Computer: which translates observation into numeric or symbolic data (data defining points in a multidimensional space)
A Taxonomy: a scheme of classifying and describing data (which may be a priori or priori (self-referential/statistical)

Being the simple dog that I am, I am glad to leave the crocheting to my alpha caregiver (as opposed to ‘caretaker’) Fatima Lasay, and the philosophical chitchat to her partner (and honorary beta dog) Trevor Batten, although occasionally, I may be modeling my caregiver’s crocheted articles, and engaging her partner in some mental gymnastics. These will all be presented here in my “Crochet and Computability” (CnC) website.

And so, what about “computability”?

To answer this question, we have to first ask what a “computer” is. There are three known examples:

1. Deterministic Finite State Machine - a finite state machine with a finite set of state and state transitions capable of accepting regular languages
2. Non-deterministic Pushdown automaton - a finite state machine with an infinite stack medium to accept context-free languages
3. Turing Machine - finite state machine with a storage or memory medium that allows it to accept a language of an infinite number of states (recursively enumerable languages)

In defining a computer, formal languages and thus formal grammars and their hierarchies are important; language serves as a kind of test for models of computation. In computability, we can therefore refer to “language” as a proto-medium for problem-solving (the internalization and externalization of concepts). Computability, therefore, is the process of describing the complexity of the problem-question “will Maria serve chicken with rice tonight?”

In the enormous spare time, I have embarked on a regular lesson of programming in Prolog (logged in “Our Daily Prolog”) for dogs. I have chosen Prolog because – being a rather lazy dog that I am – Prolog seems to provide very good armchair exercises of describing, rather than actually solving, problems. Maria can do all the cooking, and I can enjoy ruminating on the wide variety of taste possibilities in her procedural cuisine. Whether or not we actually get to eat anything is of no larger significance than starving to death if we don’t. Surely, my own declarative cooking is often without any eatable results.

And with this brief introduction to CnC, Edward wishes all an enjoyable time. Woof-woof!

EMail This Post This entry was posted by Edward on Tuesday, February 27th, 2007 at 9:40 pm and is filed under Intro/Concepts. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.