I've become increasingly interested in the somewhat metaphysical concept of "structure". What exactly is structure? Many of us might invoke the pornography metric of "I know it when I see it."

According to the dictionary [Merriam-Webster]:

Main Entry: ¹struc·ture
Pronunciation: 'str&k-ch&r
Function: noun
Etymology: Middle English, from Latin structura, from structus, past participle of struere to heap up, build -- more at STREW
Date: 15th century
1 : the action of building : CONSTRUCTION
2 a : something (as a building) that is constructed b : something arranged in a definite pattern of organization <a rigid totalitarian structure -- J. L. Hess> <leaves and other plant structures>
3 : manner of construction : MAKEUP <Gothic in structure>
4 a : the arrangement of particles or parts in a substance or body <soil structure> <molecular structure> b : organization of parts as dominated by the general character of the whole <economic structure> <personality structure>
5 : the aggregate of elements of an entity in their relationships to each other

I guess I am thinking of it in a more general sense; a mathematical sense. What is it that differentiates life from non-life, order from chaos, complexity from simplicity, free will from programmed response? Okay, okay... that's way out there. But there is a kernel of similarity in there somewhere. Something that ties these ideas together and I think of that as "structure".

I am still grappling with this concept, it's meaning and its consequences, however I have a working definition that I think shows promise.

structure: deviation from a uniform background

My thinking of this has been largely motivated by Wolfram's cellular automata [MathWorld]. In these automata, we automatically "recognize" structure. But in many of the more "complicated" automata, we don't recognize any structure at all. What is the difference. The generative process is certainly related for all of these most simple of cellular automata.

Structure can be like positive or negative space in a work of art. Sometimes the "object" of a drawing is represented in the positive space and sometimes in the negative. Escher's tessellations are a good example of this [World of Escher].

In a diamond, an "inclusion" is a break in the uniformity of the carbon matrix that makes up the crystal. We think of the inclusion as being a structure within the diamond; a structure in negative space. Of course, to the eye, the material of the diamond is not visible and has no structure itself. However, it is this uniformity that allows us to resolve the inclusion as being a "structure". If we where to change the scale at which we examine the diamond, we might see the lattice of the diamond against the smooth background of space and say that it is the diamond lattice that has "structure". This scaling can work in both directions; moving down to the subatomic scale or up to the scale of the universe.

The key point being that "structure" is relative to the scale at which we are observing. The Buddhists point out that all things are one. There is no true distinction between the space, the diamond or the inclusion. They are all one. However, defining "structure" allows us to model the world. So, structure is the process by which we abstract the one-ness of things so that we can manipulate them in our minds.

More on this later. For now I just wanted to get these half-baked ideas in print. 5:15:04 PM    comment []  

MIT's Open Courseware initiative marches on with a new release of all the course information for 500 MIT courses [Slashdot]. 4:33:59 PM    comment []  

Disney is launching a service in several test markets has the potential (once it matures) to pull me away from Netflix [ArsTechnica]. Netflix is essentially movies on-demand, but with a slow network. Speed that network up a little bit and you will have an even better service. That's what Disney is trying to do and there are certainly many others waiting in the wings to jump on this opportunity once they finally decide it can be profitable. In them mean time, everyone is cautious to take the plunge. 4:23:25 PM    comment []