Systems exhibiting tangled hierarchy are said to have some degree of self-awareness or 'soul', per the writings of Douglas Hofstadter. The following illustrations are provided to demonstrate the tangled hierarchy of the system called Change.
Physicist Amit Goswami argues that systems demonstrating tangled hierarchy (plus non-locality and discontinuity) are related to quantum systems. A sub-theme of these illustrations concerns observers and measurement, salient themes of quantum mechanics
In the Field diagram above, the four concentric regions indicate four "densities" and represent the four Symbols.
The numbers in the diagram indicate the areas of the bounded regions enclosing those numbers.
Each quadrant of the diagram encloses an area of 16 units; thus the two cardinal axes and four densities enfold 6 dimensions and 64 Elements.
We never experience any of the 64 elements directly; we perceive them only indirectly by way of the four Symbols, which we can experience probabilistically, through random selection detailed by the measurement Ritual.
The four Symbols, represented on the Field with colors, give us probability densities represented by their respective bounded areas. The densities reflect the chance of sampling the given Symbol during the measurement Ritual.
The Field comprises six dimensions. An object represented on the Field, or by the Field, or which existence depends on the Field, should reasonably comprise 6 dimensions. Likewise, any such object should be expressible in terms of 6 dimensions.
The figure above right is a stack made of six Fields; thus, these six Places are means of expressing the 6 dimensions.
The Ritual is conducted upon the Field (above left) by randomly sampling a single Symbol from each of its six dimensions, represented by the stack (above center), then interpreting the ordered collection of samples (above right) as one of the 64 Elements.
What is the subject of measurement?
What is the object of measurement?