The best counter-argument was given by Alfred North Whitehead back in 1912:
"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments."
OP was me annoyingly quoting myself, and here's my refutation annoyingly quoting OP:
"Software libraries suck. Here's why, in a sentence: they promise to be abstractions, but they end up becoming services. An abstraction frees you from thinking about its internals every time you use it. A service allows you to never learn its internals."
"Confusingly, I've been calling Iverson's notion of subordination of detail 'abstraction', and Iverson's notion of abstraction 'service' or 'division of labor'. Though lately I try to avoid the term "abstraction" entirely. That seems on the right track. Regardless of terminology, this is a critical distinction."
As I hope these clarify, I have nothing against true abstractions as you describe them.
>Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
I love this analogy. People who aren't accustomed to doing long form, extended, in-depth thought about a single problem don't seem to understand this. That your attention and mental effort is a finite resource, that can be frivolously wasted or put to good use. It requires real concerted effort, and it isn't easy. Thus, why most people never really think about anything.
You can’t do much carpentry with your bare hands and you can’t do much thinking with your bare brain. (i.e. using appropriate Thinking Tools and Intuition Pumps) As Daniel Dennett says, "we are productive now because we have downloaded more apps to our necktops (i.e. brains)"
Basically, the human brain works in chunks for short and medium term memory, this is well known by psychological studies. Likely the same applies to long term recall and processing, since it's a neural network and the "chunks" are physically encoded neurons and synapse connects that symbolically represent "chunks"
If you had to deconstruct those chunks to first mathematical and physical principles, we'd never get anywhere. It would be like Zeno's paradoxes: each step forward is a seemingly infinite descent into detail.
"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments."
https://en.wikiquote.org/wiki/Alfred_North_Whitehead