Robert pointed out, that the metaphor with the holes in the bucket isn't applicable in our situation. Maybe it has some merit for patterns you have never seen before, but that represents only about 2-5% of the patterns, maybe. For the remaining 95% he is absolutely right.
Look at a problem I solved.
- In 2012 I solved it in 12 seconds
- In 2013 I needed 3 min 46 seconds
- In 2014 I failed it after 2 minutes 23 seconds
- In 2015 I failed after 34 seconds
- In 2016 I needed 28 seconds
- In 2017 I needed 12 minutes 16 seconds to get the right solution
- In 2020 I got it right after 51 seconds
Somehow there is no system in this. As if I have a bucket with totally different holes each time. Why does the past doesn't give clues for prediction of the future?
The pattern in the problem is very familiar. So where do the fluctuations in solving time and correctness stem from?
Presumably, the fluctuations are caused by the course that system 2 (thinking) is following during the solving time. And apparently, that course is not equal, every time. The course of system 2 seems to be governed by chance.
That must mean something for the method to acquire skills. But what?
In the past, I have tried to discipline system 2 by adopting a thought process. But there are two draw backs with that:
- A thought process is executed by system 2, which is slow by default
- A thought process needs a lot of redundant rules in order to be applicable for a wide range of problems. Which slows it down too much.
|Diagram 1. White to move|