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Table 5.5 The QA matrix for
the wave-particle duality of
light. N
Possible answers (N 2 )
Binary questions (N ¼ 2)
1
2
¼
the number of
[1]
0
0
questions
[2]
0
1
[3]
1
0
[4]
1
1
Fig. 5.9 The N -dimensional
hypercube (where N
[ 2 ]
[ 4 ]
2)
representation of the QA
matrix concerning the
wave-particle duality of light
¼
( 0,1)
(1,1)
D 1
* [ E ] (0.2, 0.3)
D 2
(0,0)
(1,0)
[ 1 ]
[ 3 ]
2. Observations : Light has been found to exhibit the dual properties of both
waves and particles, depending on the measuring apparatus employed,
which cannot be readily combined into one picture.
3. Binary questions : The paradoxical observation in (2) can be summarized in
the form of two binary questions.
Is light wave ?
Yes
¼
1, No
¼
0
Is light a particle?
¼
¼
0
4. The QA matrix : The binary questions (Qs) have a finite number of possible
answers (As) suggested by existing knowledge which can be represented as
a QA matrix defined in (2) (Table 5.5 ).
5. N-Dimensional hypercube : The QA matrix can be transformed into an
N-dimensional hypercube (Fig. 5.9 ), where N is the number of the binary
questions related to the wave-particle duality of light. That is, the QA matrix
and its associated N-dimensional hypercube are isomorphic in the sense that
they obey the same set of common logical principles, including the principle
of fuzzy logic (Kosko 1993).
6. Apparatus-elicited answers (AEAs) : To choose among the theoretically
possible answers, experiments are designed and carried out to register
AEAs, that is, the answers provided by nature (including the observer
which, with Bohr,
Yes
1, No
is thought
to comprise a part of the experimental
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