IDM : On Qualitative Measurements : Some Properties of Interest

On Qualitative Measurements : Some Properties of Interest.

Abstract

In the process of making qualitative assessments of data, the species uses the method of self-referencing through the concept of recursion of dichotomies to develop lists of categories used in making the assessments. This method comes with some unusual properties reflecting the encoding of the whole in each part and as such the response to a stimulus is encoded in the stimulus and as such is derivable through manipulation of the fundamental elements that make-up the qualitative expression of the stimulus. Since this methodology was used to formally generate the integers (Peano) there are some implications for all quantitative as well as qualitative measurement systems where the seemingly rigid ordering stressing ‘independence’ contains some hidden qualitative associations.

The General

Besides the use of quantitative measurements in the analysis of reality, as a species we are highly dependent on qualitative measurements. In fact, in the realm of the everyday the qualitative outweighs the quantitative where our lives are filled with moments of determining if we like X more than Y.

Analysis of the manner in which our minds seem to function in making qualitative measurements indicates that the root emphasis is expressed in the form of deriving a set of categories based on a dichotomy of A/NOT-A followed by the use of self-reference through recursion where the dichotomy is applied to itself.

The process of recursion allows for the generation of a dimension of qualities covering the poles of A to NOT-A and allowing for the making of finer qualitative distinctions through extending the choices of categories available.

We can use binary notation to demonstrate the categories that emerge:

Level [1] - 1,0 (A/NOT-A)

Level [2] - 11,10,01,00

Level [3] - 111,110,101,100,011,010,001,000

Thus at level 3 we have eight categories usable in describing qualities of <something> where the original A (1) / NOT-A (0) has been refined to allow for four categories covering the A and four the NOT-A.

One method that seems to be used in the brain is that of recruitment and abstraction where the eight categories at level 3 are recruited as sources of analogy in describing qualitative differences within the base set of categories – thus each general category of level 3 is given eight ‘shades’ allowing for a finer set of distinctions to be made WITHIN a distinction. This means that the next level of categories contains 8 octets.

The process of recruitment and abstraction allows for removal of the octet bounding giving us 64 ‘stand-alone’ categories and this process of recruitment and abstraction can go on ad infinitum or until we run out of differences in the sameness through sensory inability to differentiate any further.

For the sake of this paper we will limit the number of categories to 64.

A dimension made-up of 64 categories gives us a good set of categories with which to express qualitative differences between the poles of any A/NOT-A distinction.

What is more often the case is that a number of dichotomies are used and preferences made using just level [1] formats and then the results are summed. This summing process can reflect the hierarchic ordering of the results of the dichotomies and as such we end up using the SAME dimension as we use in level 3 but now applied vertically. (the use of orthgonality gives us the same format as layering dichotomies hierarchically.)

This vertical formatting means that each of the categories developed horizontally in level 3 can become the root quality of further refinements.

In the symbolism used of 0s and 1s, if each 0 or 1 distinction is representative of the results of making a choice between A and NOT-A then at a level of 64 categories each category reflects the specific set of choices from six dichotomies (2^6 = 64) and we can write these as:

000000

000001

000010

000011

000100

000101

000110

000111

…

111000

111001

111010

111011

111100

111101

111110

111111

Thus each of these is representative of a quality falling within the range of 00000 to 111111 as well as a set of qualities reflecting vertical development. This is best expressed listing the above in horizontal format thus:

0 1 0 1 0 1 0 1 … … … 0 1 0 1 0 1 0 1

0 0 1 1 0 0 1 1 … … … 0 0 1 1 0 0 1 1

0 0 0 0 1 1 1 1 … … … 0 0 0 0 1 1 1 1

0 0 0 0 0 0 0 0 … … … 1 1 1 1 1 1 1 1

Qualitatively, we have a ‘smooth’ flow of ‘value’ from left to right as well as ‘value’ within each category vertically where we identify the specific values that go into making the quality.

This set of 64 categories can be used for ANY dichotomy allowing for the sorting of choices etc and as such reflects the species use of self-referencing in analysis of details where the details are reflected not in the things themselves but how we feel about them.

The Particular

My own area of interest is in identifying the source of meaning from the level of the species and in this context I have analysed the properties and methods associated with dichotomisations. In particular I have focused on two disciplines that are strongly reliant on layering dichotomies, on the use of self-referencing to derive detailed meanings, and are also popular where they elicit a sense of ‘meaning’ (regardless of any ‘facts’ contradicting the value of the disciplines themselves)

The two disciplines concerned are the commonly used typology system called the Myers-Briggs Type Indicator ® and commonly used divining/philosophy system called the I Ching, or Book of Changes. The latter comes from ancient China and is the source of the notions of Yin and Yang etc.

In the I Ching, the 0/1 representations we have used above directly correspond to the uses of yin (0) and yang (1) symbolisms where yang is fixed line and yin a broken line. E.g.

The ordering of the I Ching into the binary sequence gives us a general order of quality measurement from ‘pure yin’ (000000) to ‘pure yang’ (111111) expressed as hexagrams e.g.:

Without getting into the details of the properties and methods of the I Ching as a discipline (covered with the MBTI elsewhere, for example see http://pages.prodigy.net/lofting/MBTIX.htm ) I wish to identify an interesting phenomena that emerged within the I Ching but in doing so reflects some underlying patterns rooted in the method of recursion in that the binary sequence of the I Ching emerges from the use of recursion on the root ‘Yang/Yin’ dichotomy.

Each category in the dimension of qualities is, in the I Ching, identified by what is called a hexagram – a six-line symbol (see sample above)

Each hexagram has a specific meaning stemming from its position within the binary sequence, for example there is a hexagram called ‘excess’ and it covers the ‘raw’ sense of too much of something as well as the ‘refined’ sense of going beyond what is required – to exceed.

A detailed analysis of each hexagram can give us a ‘parts list’ of qualities representative of all expressions of quality WITHIN the general quality of the hexagram. This parts list as such identifies an ontology – a set of states of ‘IS-ness’ within the context of the hexagram.

As such, this list of expressions of qualitative differences within the sameness of the hexagram, develops vertically, orthogonal to the horizontal development of the 64 categories from extreme yin to extreme yang.

A property that has emerged from the study of the binary sequence of the I Ching stems from a simple act, the changing of the top and bottom lines of the hexagram - akin to changing the 0/1 values of the top/end and bottom/begin sequences of 0s and 1s given above.

It turns out that this change identifies qualitatively the GOAL of a hexagram and so a consequence of action. For example, in hexagram of pure yin (111111), a hexagram that includes as a meaning the concept of ‘singlemindedness’, changing the first and last ‘bits’ gives us 011110. This is a pattern associated with the hexagram covering the concept of transcendence, of going BEYOND or exceeding something.

What this ‘says’ is to achieve the goal of transcendence requires the method of being singleminded. Read in an alternative manner we have “with singlemindedness comes transcendence”.

Analysis of all of the hexagrams in the sequence of 64 reflects this pattern where changing the first and last bits identifies the goal/outcome of the hexagram.

The point is that the bit changes have nothing to do with the hexagram per se, but more with the ordering of the set of qualities used to reflect differences in the I Ching. In other words the pattern is present in ANY attachment of the dimension to a dichotomy. Thus in the MBTI ® we can identify the preferred general goal of persona types as well as just their type.

What is being represented in this pattern? The answer is the consequence of self-referencing where ANY A/NOT-A applied recursively will elicit the same patterns.

As such we can introduce the dichotomy of stimulus/response that is synonymous with the dichotomy of context/habit in that as a species a context ‘drives’ us and can/does elicit ‘habits’. Thus the bit changes reflect the encoding of a stimulus/response relationship for each quality in the set of qualities encoded in the yin-yang dimension; each quality not only represents a response to something but also is a stimulus in its own right and the encoding of one ensures the encoding of the other – context then ‘decides’ the distinction of the categorisation of stimulus/response.

This is extremely efficient for memory storage and habit formation and seems to be a property encoded in the species as part of our tools to analyse reality.

As mentioned in the abstract, Peano used recursion to develop the concepts of integers where he applied the empty set recursively and from that created the sense of 1,2,3,4 etc.

Without adding qualitative differences using concepts as positive/negative etc the above derivation process would, based on what I have identified earlier re the encoding of a goal in a stimulus, encode the notion of ‘transcendence’ as a quality of ‘one’ !

As such, the patterns identified as properties of the method of self-referencing suggest we need to research further this method we use to measure qualitatively since it is ‘entangled’ with the qualities of the quantitative as well as the qualitative and as such can tell us a lot about our maps and ourselves.

Chris Lofting