[wellpast]

The CPU does not care about your abstractions. Abstractions are entirely wrt the human dealing with them. A good abstraction is only “good” with respect to some context/purpose—there is no such thing as a universally/generally good abstraction. And often a “great” abstraction will hurt your performance — so then is it so great?

But setting aside performance concerns, when we speak of a “good” abstraction we are usually (or should be) saying this is good for some purpose—good for readability, for example.

But even better—or of utmost importance in the real world-is this: is the abstraction under question “good for business”? And that is entirely asking this: does the abstraction allow for rapidly acting on business ideas, creativity, needs, etc.

However, I believe that once the context is fixed/agreed upon, that there is an objective answer to which of this or that abstraction is better. However experience in the practical world of today’s software development painfully has shown me that the “better” abstractions are harder to come by...and when “found”, don’t tend to stick. This is because most practitioners don’t have the ability to produce powerful algebraic systems (which is what “good” abstractions are—“alegebras” over a business domain) because practitioners are generally not mathematicians, even have a philistine dislike/disdain for powerful systems if they have a whiff of mathematical-like power to them at all.

In this sense one could argue for an abstraction being “good” with respect to the social context in which they are operated in (i.e., if your team members don’t understand how to correctly wield an abstraction, is that abstraction good?) However I don’t like these kinds of arguments bc a lesser system is still capped in its power even if all its users understand it.

There are limits in what you can do with, say, Euclidean Geometry, even if it is much simpler to understand than other Gemotries. An often retort to this is No it isn’t. But that usually comes form perspectives with limited imagination. That said, many businesses are fine and thrive with limited imaginations.

[chrisweekly]

>"The CPU does not care about your abstractions. Abstractions are entirely wrt the human dealing with them."

Yes!

>"Programs must be written for people to read, and only incidentally for machines to execute." - Abelson, preface to [SICP](http://mitpress.mit.edu/sicp/full-text/sicp/book/node3.html)

[qznc]

Imho an abstraction by itself can be incomplete or unsuitable [0]. If it is neither, it is a good abstraction. I concede that suitability is often hard to quantify.

What you describe with algebras, I would label the "precision" [1] of an abstraction. Precise abstractions/algebras require a good specification though and that is often missing in the business domain.

[0] http://beza1e1.tuxen.de/leaky_abstractions.html [1] http://beza1e1.tuxen.de/precise_abstractions.html

[seanmcdirmid]

Great abstractions are not always algebraic. Words and vocabulary are incredibly successful as abstractions, as are ontologies. In fact, an entire programming paradigm has been constructed around such abstractions and has been reasonably successful.

[wellpast]

Words and vocabulary aren’t enough. Not the colloquial/dictionary sense, at least.

So if we’re talking about “facts” in an “ontology” — these are still (they must be if they are going to be processed by a machine) concrete formalisms - that’s what I mean by algebras.

If we are not machine-processing these ontologies but just printing them out for users, then I don’t count that. Because we’re not really programming over those abstractions. We’re just giving them back to the humans.

[seanmcdirmid]

Instructing someone how to do something and the computer how to do it is basically the same thing. Yes, humans have more latitude in how they follow instructions, but the same skills ofnabsteaction are applied. The whole point about OOP is that you could still weild abstractions without being a mathematician.

Now, how often do people learn chess algebraically?