[Paleopsych] Fwd: Universal Footprint: Power Laws

[Hannes Eisler]

Dear Howard,

After Val Geist's fascinating account I cannot refrain from a  
contribution of my own, having worked in psychology with power  
functions since the fifties. I usually describe myself as a  
mathematical psychologist, or as a psychophysicist, depending on  
circumstances.

Most sensations (in the technical sense) or experiences do not agree  
with the corresponding physical measures. For instance, after  
lightning a second candle in a dark room it does not feel twice e as  
bright. The function describing the growth of the experienced  
magnitude with the physical is called the psychophysical function. Up  
to the fifties one considered the psychophysical function to be  
logarithmic; S. S. Stevens proposed a power function instead.  It was  
part of my doctoral thesis to describe the experimental conditions  
for either. Note that the physical continuum need not be some kind of  
energy; it is for, e.g., sound or light; but length of line or  
duration (time) are examples of non-energy continua.
The exponent varies greatly, between approximately .3 (sound and  
light) and 3 (electric shock). As one can expect is the exponent for  
length of lines close to unity and somewhat below (.9) for durations  
up to minutes.

No agreed on theory exists. One hypothesis is that in order to be  
able to handle or cope with one's sensations a range between zero and  
about 200 would be suitable. That means expansion of the physical  
range for continua with high exponents and compression for those with  
low. So the huge natural range of sound—0 to 110 db, that is, 0 to  
several millions in energy units—is compressed into a manageable  
subjective range.

Again, power functions!

Bests
Hannes