Fig. 3 Learning and building statistics with an exponential (genetic) model.
An exponential learning curve has (maximum) two intersections with a linear
learning curve. If we choose a great enough learning time, the exponential
function will win (overtake the linear curve). But our gut feeling will tell: exponential
learning consumes much more time. When we implement learning
the Mach-Kaila way (which gives room for Gestalt processes, Psychophysics and
Erkenntnistheory and seems to “crawl” along extremely slowly), the gut feeling
tends to be dominant in time perception. In an experimental arrangement we
give exactly the same time Δt as in the linear model. The impact of the Mach-Kaila
model and the exponential slope will correct gut feeling. At the arrêt, we can
even measure transfer to other contents. The slope of the tangents to the exponential
function of learning was found experimentally by Alfred Binet (the inventor
of the intelligence scale) during experiments in the school of Vaney between
1907 and 1910 (see Fig. 4).