# Periodocoty and Modularity

Many things distinguish homosapiens from other animates, but the organising of adjectival plethorate information into a modular structure is the most unique.

Periodicity is a natural consequence of a motion field which is fundamentally a rotational motion field. The fundamental spaciometric rotation is an apprehension of a boundary surface. These boundary surfaces exist because of and are effects of underlying, relativistic rotational motions. As a consquence self assembly, self order arises over vast regions of space at various scales. The distinctive attribute of these material alignments is periodicity of the repeated structures.

Such a structure may be called a module, and indeed many animate organisms are constructed on a modular design. The modules may be rferred to in many ways including cell,podule,array, crystalline ,amorphous, framed tc. etc.

Modularity is therefore a related and consequent attribute of the periodicity found in relativistic rotational motions.

Many animates measure. In particular, i have seen my friends the spiders measure carefully the length of web they require before attaching the spiral web to the anchor lines. They have a kind of rule on their hind legs to give the correct length so the spiral spirals in and out characteristically.

These measurements are straightforward comparisons, but only homo sapiens have adapted this modular structure to define and design their arithmetic aggregate structures, and their operator theory structural syntax.Without modularity the concept of aggregation is entirely dependent on natural forms. Wiyh modularity a type of cypherism is developed , with a syntax reflecting the modular arrangements in forms, but carrying a derived of defined"meaning".

The processes acr on information stored or organised in a modular form, each modular aggregate form recording or representing data or information. For each field of study the requisite modular form has defined rules of transforming the modular forms into actual forms, or data relevant to a form.

With modularity we move, using spaciometric structures, into the realm of algebraic synbolism, logical determinism, and modular transformations on a general level, and man's "sapiens" his wisdom or information processing. recording, representing , and manipulating is engaged in the pragmatics of form construction and transformation.

The modular approach not only allows a spacimetry to be reflected, but also a dynamic spaciometry to be reflected in terms of grammar and syntax.

Thus the very sentences we speak or write ar a modular reflection of a spacimetric form or relationship, nd a dynamic spaciometric relationship. This is why verbs act on an object and the action and object are modified by prepositions, suffixes, prefixes,adverbs and adjectives all arranged geometrically/spaciometrically and governed by syntactical rules reflecting the dynamic spaciometric relations.

Modularity not only contributes to grammar, sysntax and language, but also to memory or information/state storage. As sophisticated as that sounds the RNA and DNA are cases in point indicating the ubiquity of this information system. However this is not to say that sophisticated information processing is going on at every scale, In fact, simple comparison suffices to build the most complex cybernetic systems imaginable, and thus emergent properties, functionalities and behaviours can arise out of simple "matter" transactions, but only because of modularity in information structures.

When Brahmagupta wrote his siddhanta, he was relating an older tradition of modular notation in india. It is interesting that the Sumerians were the first recorded civilsation to have a modular notation. The greeks clearly unserstood and adopted and adapted this system in astronomy, especially Ptolemy, but they used a cultural specific syntax for everyday or commercial useage. The greeks influenced the indians and through thenm the chinese who in turn influenced the indians. The use of Abacus, sticks ,counters, pebbles,clay tablets all combined to determine the names and structures of adjectival numerals and how they were notated.

The indians had a great interest in rhythm and hymnal patterning, and utilised this interest to drive forward methods of noting patterns, and in deriving pattern making formula. One of the most notable of these is the binomial theorem for making special religious verse patterns.This structure derives frm a modular approach to structuring verse rhythms, and is entirel grammatical and syntactical as well as "mathematical".

This theorem is key to modern probabiity theory, and yet it is utilised in a religious rhythmical ritual. To me that says something about the fundmebtal rotational motions that underlie and give rise to everything.

So the subtle system of manipulation using a modular structure based on 9 numerals/ symbols rotating, each module placed geometrically next to the one it is acting on is one syntactical strutcure to represent a form consisting of nested units. This sysntactical structure is the basis of an aggregation structure known as the decimal system, and a specific example of p-adic structures.
It is good to remember that language and mathematics are codependent in this way, and modularity makes a clear link to geometry, and a dynamic spaciometry.