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Ideas

Formal Order Analsis is based on five main ideas:

  • Sequence as a Whole Object - Treat a symbolic sequence as a unique whole, focusing on its internal structure and emergent properties.

  • Order as a Property - By replacing each symbol in a sequence with its index in a dynamic alphabet, we define an "Order" — a new property that separates the content of the sequence from its composition.

  • Congeneric Decomposition - This method breaks a symbolic sequence into layered sub-sequences where each layer isolates a single symbol’s positions, preserving the sequence’s internal order and making its structure more analyzable.

  • Interval as a Basic Information Unit - Intervals measure the distance between repeated elements, revealing hidden patterns in repetition and spacing.

  • Geometric Mean as Alternative to Probability - Using measurements based on the geometric mean of intervals instead of the probability of symbols (the arithmetic mean of occurrence) allows us to move from recording simple frequency to recording the underlying structure and regularity in the arrangement of symbols.