Ask HN: Why aren’t leaky abstractions considered bad practice in mathematics?

1•amichail•2h ago

In particular, why don’t mathematicians do a better job of hiding algorithms so that one can apply mathematics without knowing the underlying procedures?

Computers can execute mathematical algorithms, and you shouldn’t need to know how they work.

It seems that software engineering has been more successful at hiding leaky abstractions.

Comments

bigyabai•2h ago

Abstraction is a disadvantage in matters concerning empiricism. This is as true for computers that hide their algorithms as mathematicians who won't show their math.

Jtsummers•1h ago

Can you point out some examples? Or are these hypothetical leaky abstractions?

amichail•1h ago

If math did a good job with encapsulation, you would be able to have an applied math class with no math algorithms.

Jtsummers•1h ago

That's not an example. Can you please provide an actual example of a leaky abstraction instead of merely asserting their existence.

amichail•49m ago

Can you teach applied linear algebra without teaching the algorithms (e.g., Gaussian elimination)?

Jtsummers•45m ago

Does the presence of an algorithm mean that there is a leaky abstraction?

And if that's all it takes (I'm not agreeing with you, I think this is a poorly considered heuristic), then isn't software engineering chock-full of leaky abstractions? So it's at least as bad as mathematics, and likely worse by your own measure of what makes for leaky abstractions.

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