>One question I would ask you is: what is _similar_ about them? Could you express all of these with one abstraction? Is there a difference between choosing `class` as the base abstraction, vs a closure?

The answer is yes you can. But you're thinking in the wrong direction.

First let's make things clear. A function is just a one line expression where all values are immutable. There is no concept of time or procedures in a function.

function

  def f(x):
     return ((x + 1) * 2)/3

procedure:

  def f(x):
     x = x + 1
     x = x * 2
     x = x / 3
     return x

You are saying that a procedure is isomorphic to an object which is to say you can define an object in terms of a procedure and a procedure in terms of an object. People often mix up the two terms, procedure and function but it's no big deal. The issue is, you used the term "Higher Order" function and the second issue I had was that it's actually quite an obvious thing presented as if it was novel.

Well first off all computers are procedural machines. The underlying machine is just executing machine code which is a series of procedures. So all programming languages on top of this are implemented with procedures.

That means OOP languages are implemented with procedures.

That means FP languages are implemented with procedures.

That means procedural languages are implemented with procedures.

Basically your post is just reiterating how an object is implemented by a compiler.

However the title of your post used "Higher Order Function." This implies you don't know the distinction between procedures and functions as "Higher order" functions are usually reserved for true functions, not procedures.

That was the point of my post, to help you see the distinction because although you can create objects from procedures, you cannot create objects from functions because objects require mutation which is a primitive that a function cannot actually provide. The relationship is surjective or unidirectional.

>harder to learn new things this way, and unless you are almost finished with your career, it can be detrimental

This is the internet. I can communicate without a filter on the internet with little consequence. Filters slow things down as do a lack of filter. Either way I can get to the point quickly without worrying about offending someone.