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the Fundamental Object

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(written: august 3 1998 | up to david's home)

the Fundamental Object

This is not intended to be a semiotic or epistemological treatise. It is simply meant to provide a working definition of the term "fundamental object," as used in fractal-based design theory.

The fundamental object of fractal-based design theory is inherently informational in nature. It is not inherently instructional in nature, on the contrary, a fundamental object is never inherently, or independently, instructional. A fundamen tal object is any representation uncombined with any other representation, including another of its own type. It stimulates a single sense, i.e., the visual (a graphic representation) or the auditory (a sound). As technology progresses, a representation i n any new medium that stimulates one sense (be it visual, auditory, olfactory, gustatory, or tactile) could be considered a fundamental object iff (if and only if) it is presented uncombined with any other representation.

However, we live in the world of practical realities – not of idealized theories. Because of the practical considerations of working with current systems, the initial instantiation of a learning environment whose organization relies upon fractal-ba sed design theory will of necessity be forced to include objects which are not truly fundamental. Such graphic representations might include words, phrases, sentences, paragraphs, chapters, or even entire articles or volumes (which are all combinations of individual letters, spaces, and special characters, which are themselves true fundamental objects). They might also include animations and video (the temporal combination of several graphic representations in sequence, each of which may be a funda mental object) and three-dimensionally layered or "stacked" graphic representations (a graphic representation combined with another graphic representation in a physically proximal manner, as opposed to the temporal proximity of still images comb ined to form video). Non-fundamental auditory representations would include narration, speeches, music, and other combinations of individual sounds, the true fundamental objects. Table 1 displays some sample graphic representations.


Fundamental ?





a Shakespearean sonnet


a map


a map with cities indicated graphically


a map with cities labeled with text


Table 1. Some graphic representations classified as fundamental or non-fundamental.

A second practical difficulty emerges with the recognition and acceptance of this practical difficulty in implementing fractal-based design theory in its purity. According to fractal based design theory, the degree to which objects are truly fundam ental predicts the degree to which they can be repurposed. Thus, creating an environment which is not based exclusively on fundamental objects will limit the ability of participants in the environment to create meaningful combinations of the objects. That is, basing an environment on objects which are not truly fundamental limits the potential experiences of participants in the environment in proportion to the degree to which the constituent objects do not meet the criteria for being "fundamental.&qu ot; So where do we draw the line? How close to fundamental is close enough for our current purposes in learning environment organization?

We would be fortunate if this were the only nuisance with which we were compelled to grapple. Matters of intellectual property and copyright will prevent us from deconstructing some combined objects (the opposite of fundamental objects) into their elementary representations. This forces the participator in the environment to "take it or leave" the object the way it is, with no possibility for individualization or repurposing. The result: a single-use object, i.e., the object with the lowe st number of possible uses.

Are we benefited by totally excluding combined objects from the learning environment? Not at all. It is possible that at some future point a participant will have need for the single use of which a specific combined item is capable. However, it sho uld be clear that the practical impossibility of predicting every student’s need and creating individual single-use objects to match each need is significantly greater than the difficulty of creating and archiving a finite number of fundamental objects wh ich students would be able to custom combine in order to meet their needs.

So what is the answer to the question, "how close to truly fundamental objects do we desire for our learning environment?" Given the current states of technology and intellectual property law, the answer will vary from representation to r epresentation.

Requiring all text documents to be "versions," i.e., combinations of truly fundamental letters, special characters, and spaces, is not technologically practical. Therefore an amount of text which is as repurposable as possible should be s ought for. The degree of repurposability is not inversely proportional to the length of the text, but it is inversely proportional to the number of ideas, concepts, facts, or meanings represented in the text. For example, an article in an encyclopedia whi ch is a representation of only a few closely related ideas, concepts, facts, or meanings will be more repurposable than the entire encyclopedia.

Requiring images to be fundamental is not currently impractical. Fundamental images would be images which have not been combined with other media (including other images) in anyway. Again, the degree of repurposability is not inversely proportional to the size of the image, but it is inversely proportional to the number of ideas, concepts, facts, or meanings represented in the image. For example, a picture or drawing with a caption or explanation inset is less repurposable than the picture alone.

Requiring audio representations to be truly fundamental is currently the least practical of all forms of representation. However, the rule described twice above still holds true: the degree of repurposability of the representation is not inversely proportional to the length of the audio, but it is inversely proportional to the number of ideas, concepts, facts, or meanings represented in the audio. And therefore, audio segments should be divided into pieces which provide the best possible maximizati on of repurposability and practicality. For example, an audio representation of an entire sonata will be less repurposable than separate representations of the sonata’s parts.

I hope this rambling has cleared up the definition of the term "fundamental object" as it is used in fractal-based design theory. I would be pleased if you would point out non-examples and contradictions implied by or inherent in this att empt to establish a working definition.

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Last modified 2004-06-14 10:08 PM