Biology Reference
In-Depth Information
arrangement and the registering device). Three AEAs are indicated in
Fig.
5.9
, two of which are well established and the third is hypothetical:
Photoelectric experiment
¼
[2]
Two-slit experiment
¼
[3]
¼
A novel experiment
[E] (0.2, 0.3).
7. Kosko entropy, S
K
: The Kosko entropy, defined in (8) above, of the
fuzzy answer [E] can be calculated from the coordinates given in the two-
dimensional hypercube, Fig.
5.9
:
S
K
(E)
¼
D
1
=
D
2
n
o
1
=
2
n
o
1
=
2
2
2
2
2
¼ð
0
0
:
2
Þ
þð
1
0
:
3
Þ
= ð
1
0
:
2
Þ
þð
00
:
3
Þ
1
=
2
1
=
2
10
2
10
2
10
2
10
2
¼
4
þ
49
=
64
þ
9
53
1
=
2
73
1
=
2
¼ð
0
:
Þ=ð
0
:
Þ
726
1
=
2
¼
0
:
¼
0
:
852
(5.39)
8.
Uncertainties of crisp (or nonfuzzy) statements
: Applying Eq.
5.29
to crisp
answers [2] and [3], the associated uncertainties, defined in (10), can be
calculated as:
S
K
½
ðÞ
2
100
¼
0
:
85
100
¼
85
%
(5.40)
S
K
½
ðÞ
3
100
¼ð
1
0
:
85
Þ
100
¼
15
%
(5.41)
Equations
5.40
and
5.41
indicate that crisp answers [2] and [3] are 85% and
15% uncertain, respectively, relative to the apparatus-elicited answer [E].
Applying Eq.
5.29
to the Airy experiment (AE) (Herbert 1987, pp. 62-63),
two calculations are possible:
The Airy pattern is an experimental evidence that light is both waves and
particles, that is, crisp answer [4] (1, 1), supporting the de Broglie equation,
l ¼
h/p:
S
K
½
ðÞ¼
4
0
(5.42)
Uncertainty
ðÞ¼
½
4
0
%
(5.43)
The Airy pattern demonstrates that light is particles when observed over a
short time period and waves when observed over a long period of time:
S
K
(AE)
¼
1
;
since D
1
¼
D
2
;
and Uncertainty
¼
S
K
(AE)
100
¼
1
100
¼
100
%
(5.44)
