Tuesday, January 1, 2013

Quantum Measurement

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?


  1. The goal of this entry is to demonstrate a model of quantum measurement based on Change, the subject of I Ching.

    The canonical roles of the observer are to
    1) choose the aspect of the object to be measured,
    2) provide the device to perform the measurement, and
    3) record the result, provided by Nature, of the measurement.

    Our model did not explicitly treat point (1), the observer's choice of that which is to be measured, which Stapp called the Heisenberg choice, i.e. determination of the question to be put to Nature through experimental means. The answer to the question is supplied by the Dirac choice: Nature's selection from the possible outcomes.

    Change-cum-oracle must be asked to speak, but not solely in the sense of requiring the measurement Ritual. The observer must frame a question in order to supply a context for interpreting the answer that Nature provides. Performing a measurement without first having formulated the question which the experiment is designed to address would be of no benefit to the observer. Divination is no different from Science in this regard

  2. In this presentation of Change as quantum measurement, it appears that the observer -- the one posing the question, handling the measuring apparatus, and recording the measurement outcome -- is also the subject of the measurement, the thing being measured. In the words of J. Krishnamurti, "observer is the observed."

    The presentation of the model largely omitted mention of the human participant and its roles in order to demonstrate that Change gives the appearance of tangled hierarchy, independent of any human involvement. The Field, Symbols, Images, and Ritual are not easily separable into independent entities. Rather, they all appear as aspects of a single whole. Adding the observer to the model does not seem to have diluted the force of our arguments. By doing so, we see how the observer is drawn into the strange loop, becoming both subject and object, observer and observed.

    Accepting this conclusion supports a premise presented at the introduction of this entry: that Change-cum-divination involves tangled hierarchy, which Dr. Goswami has posited as characteristic of a quantum system. By posing Change as quantum measurement, the boundary between subject and object seems to collapse or converge into the human participant.

  3. http://en.wikipedia.org/wiki/Measurement#Definitions_and_theories
    Measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle.