My belief is that humans are pattern matchers, even in the context of abstraction or logical thinking. The pattern of skill transfer is the experience of transferring skills. That opens the mind to the pattern of colliding different learned patterns into situations that seem not relevant just as patterning the logic leads to being able to develop logical proofs because the pattern of doing logic is being recognized.
For example, proving an identity looks like solving an equation. So that is why many students naturally put down a proof that looks like solving an equation. And it can be a proof if the observation is that for each x, the statement holds as all steps are observable. Students rarely make that last step, however, because the pattern they are following breaks down: 1=1 has no expression of x. They kind of just move on at that point.
By contrast, someone trained in mathematics would most likely prove an identity by taking one side and transforming it into the other side as they have the experience of that flow of proofs and the goal there is clear: one stops with the right-hand side.
It is not logical thinking, but logical pattern application. Transfer skills are similarly learned. We all have them, after all. I have never met anyone bothered by counting markers being a different skill than counting pebbles. But that is a skill transfer too. It just happens at such a young age and is so ubiquitous that we don't even notice it.
I would be surprised if meditation helps with any of this. It helps with many other things, such as being more aware of events, particularly emotional states, as that is the pattern being developed, but it is hard to imagine it will help bridge the gap of checkbook balancing to general numbers. What one needs is the experience of numbers in multiple contexts.
The pattern in the patterns is the path to abstraction and it no doubt takes a number of patterns to get there. And learning the different kinds of abstractions requires different kinds of patterns.
For example, proving an identity looks like solving an equation. So that is why many students naturally put down a proof that looks like solving an equation. And it can be a proof if the observation is that for each x, the statement holds as all steps are observable. Students rarely make that last step, however, because the pattern they are following breaks down: 1=1 has no expression of x. They kind of just move on at that point.
By contrast, someone trained in mathematics would most likely prove an identity by taking one side and transforming it into the other side as they have the experience of that flow of proofs and the goal there is clear: one stops with the right-hand side.
It is not logical thinking, but logical pattern application. Transfer skills are similarly learned. We all have them, after all. I have never met anyone bothered by counting markers being a different skill than counting pebbles. But that is a skill transfer too. It just happens at such a young age and is so ubiquitous that we don't even notice it.
I would be surprised if meditation helps with any of this. It helps with many other things, such as being more aware of events, particularly emotional states, as that is the pattern being developed, but it is hard to imagine it will help bridge the gap of checkbook balancing to general numbers. What one needs is the experience of numbers in multiple contexts.
The pattern in the patterns is the path to abstraction and it no doubt takes a number of patterns to get there. And learning the different kinds of abstractions requires different kinds of patterns.