Measuring paradoxical reality
Presenting polymetric analysis

Josep Burcet © 1995
        revised © 2002

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Introduction

Classical techniques for sample analysis in social sciences are built on the assumption according to which subjects under observation have attributes instead of paradoxes. So, measurement is addressed to assess if such attributes are present. Conventional analysis does not observe to what extent paradoxes are present and how they act.

Nevertheless, paradoxes occur very often in complex reality, like human individuals, groups and other sort of cultural artifacts. For instance, attitudes towards computers, new communications and, in general, fast emerging technology are paradoxical in the sense that the same person may feel attraction and repulsion, hope and fear, anger and appeasement. People may feel that way sequentially and, even, simultaneously.

This means that each subject in a sample may be characterized by the presence of antagonistic attributes and, what is more important, he/she will behave under the influence of such paradoxes.

Terminology conventions

In the framework of this paper, I will call monometric perception, all the forms of insight which take into account the presence of an attribute and ignores the presence of their antagonistic one (i.e. she is very introverted, he is not happy, they are very hostile).  

Conversely, I will call polymetric perception, all forms of awareness which recognize cohabitation of antagonistic attributes. (i.e. he-she is lovely and repulsive).

Polymetric perception in social research

Independent observation of antagonistic attributes allows us to asses the degree to which each of them is present. Suppose we want to measure feelings aroused by the Internet. We may ask to what extent a subject feels afraid of Internet. And afterwards, we may ask him/her to what extent he/she feels courageous in front of it. Independent assessment of these elements will allow us to discriminate differences which could not be assessed if common measurement scales were used. If we use independent scales ranging from 1 to 9 for each antagonistic attribute, observations may take the following form:   

John is not specially afraid of Internet. He does not expect unwanted consequences from it. And he feels neither courageous in front of it

John is 1 afraid

><
1 courageous
Mary is specially afraid of Internet. It appears to her as a menacing source of troubles. She does not feel courageous. She thinks that she will never be able to understand and handle it.
Mary is 7 afraid
><
1 courageous
Peter is afraid of Internet. For him it is something that will produce a lot of changes and he feels insecure about the future of his job. But, at the same time, he thinks that he could be able to acquire all the required skills and expects that perhaps he could take advantage of it.
Peter is 8 afraid
><
8 courageous

 

Criticism to conventional measurement scales

Suppose that John, whose reaction to Internet is 1 afraid > < 1 courageous, is asked to place himself in an ordinal scale ranging from afraid to courageous. His answer will be somewhere in between the two extremes. Peter (8 afraid> < 8 courageous) should be forced to give a similar answer. So, under monometric scrutiny, John and Peter cases look the same when, in fact, their emotional responses are very different.

Between John and Peter there are

differences on the precursors of their respective reactions
differences on the reactions in themselves, and,
differences on the behavior which will follow from those reactions

As far as social research is aimed at i) detecting precursors of observed behavior ii) understanding characteristics of observed behavior, and iii) forecasting future behavior following from current behavior and its precursors, it is obvious that conventional scales do not always provide serious ground for consistent analysis.

General considerations about data recollection

Let us consider the case of Mary, who was 7 afraid > < 2 courageous. Her condition fits conventional analysis. If all the members of a sample have the same absence of paradoxical condition, then data may be treated in conventional way. We could then say that we are dealing with monometric reality. That is, an aspect of reality which is characterized by the fact that when one attribute is present, its antagonistic is absent.

So, at the stage of questionnaire design we should first realize whether our questions address to monometric or to polymetric issues. If we are going to deal with a non-paradoxical issue, we may use conventional scales. But if we expect paradoxical conditions, we should prepare our questions in order to collect data of both antagonistic attributes.

On the nature of polymetric reality

Attitudes, values, beliefs and emotions in general are precursors of behavior. Generally speaking, there is a relationship between the intensity to which such precursors are present and the energy involved in the behavior that follows. This principle applies both to monometric and polymetric conditions.

But when two or more antagonistic attributes cohabit, then the level of paradox supplies an additional load of energy. So, energy that results from polymetric condition depends on:

  • the intensity of each antagonistic attributes, and
  • the existing level of paradox between them

According to this, a 5a > <3w condition will arise more energy than a 7a > <1w condition, even if the overall intensity of attributes involved are the same.

 Strategies for the analysis of paradoxical condition

Such considerations apply to the analysis strategy. If we collect polymetric data, we may:

1/    look for the precursors of each antagonistic factors, which are not contaminated by their respective antagonistic

In the John’s case, for instance, we could undertake a multivariate analysis for explaining his score in the afraid dimension, which was 1 in a 9 point scale. And we could do the same for Peter, whose score was 8. Note that in conventional scales we have been forced to look for independent variables for a say 5 score in the dimension afraid/courageous in both cases.

2/   describe the intensity of energy arousal produced by paradoxical condition, if found

The function e=a *w +a +w gives an evaluation of the amount of energy arousal, where e is an index of energy summoned; a and w represent the intensity of each antagonistic attributes

3/ look for concomitant variables of energy arousal

Using a 1 to 9 scale, the e=a *w +a +w function produces an index ranging from 1 to 99. Such an index is susceptible of multivariate analysis  (see annex 1)

Designing questions aimed at collecting paradoxical data

Questions aimed at collecting paradoxical data may arise defensive reactions against insinuated paradox. For instance:

Usually people are culturally induced to avoid incoherence and think monometrically. As a consequence, paradoxical related questions may be difficult both to be formulated and to be understood.

Under the pressure of the value that postulates coherence, people may be prone to hide inner paradoxes and give congruous answers ( if one admits that he-she dislikes computers, he-she may be prone to hide that he-she likes them as well to some extent).

As far as awareness of one’s own paradoxes may induce anxiety, some people may try to cancel distress by refusing to understand a question on paradox issue or by giving fake answers.

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If you read Spanish, you may click here to see the polymetric paradigm applied to the novelty intake process. 

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Annex

Values resulting from the e=α*ω+α+ω function

Energy summoned index

  1 2 3 4 5 6 7 8 9
1 3 5 7 9 11 13 15 17 19
2 5 8 11 14 17 20 23 28 29
3 7 11 15 19 23 27 31 35 39
4 9 14 19 24 29 34 39 44 49
5 11 17 23 29 35 41 47 53 59
6 13 20 27 34 41 48 55 62 69
7 15 23 31 39 47 55 63 71 79
8 17 28 35 44 53 62 71 80 89
9 19 29 39 49 59 69 79 89 99

 

The energy summoned depends on:

a) the level to which every attribute is present, and
b) the amount of existing paradox

So, the α6><ω6 condition (6+6=12) summons more energy than α9><ω3, where the overall presence of attributes is 12 as well.

α6><ω6 gives 48
α9><ω3 gives 39

Other examples:

α dimension ω dimension sum of
 attributes
level of paradox energy summoned
case 1 9 1 10 very low 11
case 2 8 2 10 low 28
case 3 5 5 10 medium 35
case 4 9 9 18 very high 99

 

 

 

 

 

 

 

 

 

 

 

 

 



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