Another factor that affects learning is the degree to which a particular pattern is already familiar. We would not expect much change in a subject’s ability to identify letters of the alphabet in a short experiment, because most people have already been exposed to millions of alphabetic characters. Rapid learning can only be expected for patterns that are unfamiliar. The change in rate of learning over time is captured by the “power law of practice” , which has the following form:
\(log(T_n) = C-\alpha log(n)\)
This law states that the \(log\) of the time to respond on the nth-trial (\(T_n)\) is inversely proportional to the \(log\) of the number of trials. The constant \(C\) is the time taken on the first trial (or block of trials).
The power law of practice is usually applied to manual skill learning, but it has also shown to apply to the perception of complex patterns. Kolers (1975) found that the power law applied to the task of learning to read inverted text. (…) Initially, it took subjects about 15 minutes to read a single inverted page, but when over 100 pages had been read, the time was reduced to 2 minutes. (…) Consider a hypothetical task where peopole improve by 30% from the first day’s practice to the second day. Doubling the amount of practice has resulted in a 30% gain. According to the power law, someone with 10 years of experience at the same task will require a further 10 years to improve by 30%. In other words, practice yields decreasing gains over time.
Taken from Information Visualization - Perception for Design by Colin Ware.