Biomedical Engineering Reference
In-Depth Information
almost generally follow power functions of adequate stimulus variables, except at very
low values of these variables. When the threshold approaches within which the variables
can be detected, their subjective magnitudes converge on either direct proportionality to
the stimulus intensity or some other related variable. Line length squared would be an
example of such a variable. For sufficient lengths, the subjective line length tends to be
directly proportional to the physical line length. As surprising as it may appear, this is
no longer true for very short thin lines that become somewhat difficult to see. Accord-
ing to measurements by Sanpetrino (unpublished result), the subjective line length then
becomes proportional to the square of the physical line length. This phenomenon can be
explained by the physiological noise that is added to the visual line image. In agreement
with the theory of signal detectability, such a process can be expected to take place near
the threshold in which all sensory stimuli can be detected and would be consistent with
a linear relationship of subjective magnitudes to stimulus intensity.
As previously mentioned, according to this law, all subjective magnitudes grow linearly
with the intensities of the stimuli that evoke them near their detectable thresholds. The rela-
tionship was first discovered during auditory measurements of Stevens' Power Law and
is described here initially for loudness, then generalized. When sufficiently small stimulus
magnitudes were included, the resulting loudness curves deviated from the Power Law
and, on double-logarithmic coordinates when bent downward, became gradually steeper.
A typical example is shown in Figure 10.6, where loudness magnitudes of a 1000 Hz tone
are plotted over sound-intensity abscissas expressed in decibels [37]. The solid curve has
been determined by the method of ME based on two reference standards, as described in
Chapter 9 [36]. The slanted crosses show averages of 12 studies computed by Robinson
[38], in which various methods were used. Filled circles indicate the data of Stevens [39]
obtained by ME with the reference standards chosen by the observers themselves; open
symbols and filled triangles, the data of Scharf and Stevens [40] obtained by ME with a
designated reference standard and by halving and doubling; the vertical crosses, the data
determined by Feldtkeller
et al
. [41] with the help of the same method. The excellent
agreement between the various sets of data and the curve suggests that the curve accu-
rately represents the loudness of a 1000 Hz tone as a function of its intensity. Of particular
interest is the asymptotic convergence of the curve on a linear relationship between loud-
ness and sound intensity near the threshold of audibility, as indicated by the straight line
having the coordinates of 0.01 at 0 SL (threshold of audibility) and 1 at 20 dB [32].
10.4.3 Law of Additivity
This law states that in ME and MP, subjects that are tested experimentally tend to pair
numbers with sensation magnitudes on absolute rather than ratio scales. This implies that
not only sensations, but also numbers acquire absolute psychological magnitudes. The
specific experiments are performed on loudness and line lengths. The latter reveals that
the subjective magnitudes of numbers are formed before the age of six and do not change
after that age. It is suggested that the absolute coupling of numbers with sensation mag-
nitudes originates from the concept of numerics where numbers have absolute meanings.
Additivity of subjective magnitudes is introduced as the third law by Zwislocki [32].
Nevertheless, the existence of additivity has been demonstrated with scientific certainty
in hearing, touch, and vision, although the situation in chemical senses had to be left
unresolved [32].
