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The ability to abstract surely is important. However, I find the "four levels" a little strange. The first three aren't even abstractions! Abstract is the oppos

by tasuki 9y ago

The ability to abstract surely is important. However, I find the "four levels" a little strange. The first three aren't even abstractions! Abstract is the opposite of concrete. Abstraction is by definition not a concrete object.

paultopia 9y ago
I was thinking something similar. The first few levels of "abstraction" seem to me to be more about visualization skills and spatial reasoning. For example, we'd expect a painter to be particularly good at those, but not necessarily good at math or monads. The 4th level seems like a totally different kind of category from the first three. Which, come to think of it, matches my personal experience. I have zero spatial ability---back in the 80's in California they actually gave us standardized tests in elementary school including a spatial ability section, and my scores were always like 90+%-ile math, verbal, and like 20%-ile spatial. Never been able to draw for shit. But was always advanced in math, 99th percentile lsat (logic-heavy) scores, top grades in stats, etc. So am I at the 4th level but not at all at the first three?
ilaksh 9y ago
The author of the article has enlarged the meaning of the word abstraction. It's just the wrong definition. It would make more sense if he described it as 'important cognitive skills'. My definition of abstraction is moving from specific examples to more general systems. I definitely remember the process as I was teaching myself programming through my childhood of learning and improving my software abstraction skills in particular ways. One type of abstraction that took a bit of practice to get good at when I was starting out like eight years old was recursion. I got better at using this type of abstraction by specifically practicing with the goal of converting loops to recursion. Another type of abstraction is creating classes in order to reuse your code. This was something I learned about and gradually got better at over the years through practice and initially from a few books like Turbo Pascal Disk Tutor when I was in middle school. Sure there are some innate abilities but I think it's not quite so cut and dry as the author makes it out to be with innate versus learned ability.
SAI_Peregrinus 9y ago
And there's at least one extra level: the ability to think about things that can't be imagined. It's not that difficult to visualize a hyperbolic plane and learn to visualize hyperbolic space. It's much, much harder to visualize the real projective plane, and essentially impossible to visualize a quaternionic projective space. Yet these can still be worked with using geometric and topological intuition in a way that feels (to me) fundamentally different from manipulating abstract formulae or matrices.
- tasuki 9y ago
  This is a great point. I wanted to add something along those lines but wasn't able to formulate it this well.

by tasuki 9y ago

paultopia 9y ago

I was thinking something similar. The first few levels of "abstraction" seem to me to be more about visualization skills and spatial reasoning. For example, we'd expect a painter to be particularly good at those, but not necessarily good at math or monads. The 4th level seems like a totally different kind of category from the first three. Which, come to think of it, matches my personal experience. I have zero spatial ability---back in the 80's in California they actually gave us standardized tests in elementary school including a spatial ability section, and my scores were always like 90+%-ile math, verbal, and like 20%-ile spatial. Never been able to draw for shit. But was always advanced in math, 99th percentile lsat (logic-heavy) scores, top grades in stats, etc. So am I at the 4th level but not at all at the first three?

ilaksh 9y ago

The author of the article has enlarged the meaning of the word abstraction. It's just the wrong definition. It would make more sense if he described it as 'important cognitive skills'. My definition of abstraction is moving from specific examples to more general systems. I definitely remember the process as I was teaching myself programming through my childhood of learning and improving my software abstraction skills in particular ways. One type of abstraction that took a bit of practice to get good at when I was starting out like eight years old was recursion. I got better at using this type of abstraction by specifically practicing with the goal of converting loops to recursion. Another type of abstraction is creating classes in order to reuse your code. This was something I learned about and gradually got better at over the years through practice and initially from a few books like Turbo Pascal Disk Tutor when I was in middle school. Sure there are some innate abilities but I think it's not quite so cut and dry as the author makes it out to be with innate versus learned ability.

SAI_Peregrinus 9y ago

And there's at least one extra level: the ability to think about things that can't be imagined. It's not that difficult to visualize a hyperbolic plane and learn to visualize hyperbolic space. It's much, much harder to visualize the real projective plane, and essentially impossible to visualize a quaternionic projective space. Yet these can still be worked with using geometric and topological intuition in a way that feels (to me) fundamentally different from manipulating abstract formulae or matrices.

tasuki 9y ago
This is a great point. I wanted to add something along those lines but wasn't able to formulate it this well.