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> That's because the article doesn't think that can happen. I don't see what else he could mean by "lattice" or "partial ordering", except an admission that th

by ken 8y ago

> That's because the article doesn't think that can happen. I don't see what else he could mean by "lattice" or "partial ordering", except an admission that this can and does happen. Help me understand. > I fail to see how being a lattice allows there to be two elements where each is greater than the other. My criticism doesn't depend on partial vs. strict ordering Isn't that exactly what a lattice allows? The absolute ordering of Lisp and Haskell is undefined, while both are greater than some (like Cobol), and probably less than others. Users of either might think theirs is greater, but each has features the other doesn't, which is what makes the ordering merely partial.

AnimalMuppet 8y ago
If I understand correctly, a lattice or partial ordering means that A = B is possible for different A and B, but if A < B, then "B < A" is false. But even if I'm wrong about a lattice, my claim is still true for programming languages. Perl > Haskell... for certain situations. Even assembly > Lisp... for certain situations. And yet assembly and Lisp are so far apart on the "power curve" that, if Lisp is not > assembly always, then... do we have any kind of ordering at all? I view programming languages as being a tree, with branches spreading in all different directions. Some languages reach further in certain directions than other languages do. Your program is a vector. (Really, it's a bunch of different vectors, of different lengths, pointing in different directions, but one direction is the problem that makes it the hardest to write the program that you're trying to write.) Pick the language that reaches the farthest in the direction of whatever makes it hard to write the program that you're trying to write. This means that your problem imposes an order on languages... for that problem. It's not a universal order, though. Others, with a different kind of problem, may view your order as completely wrong. And they are right - for their problem, your order is in fact wrong.
- thisiszilff 8y ago
  You are thinking of a total order (in fact total orderings or often defined with the '>=' relation). A partial order is like a total order except there may be some elements that are not comparable, so given elements {A, B, C} we can have C < A and C < B but whether A < B or B < A can remain undefined. A lattice is a kind of partially ordered set.

by ken 8y ago

AnimalMuppet 8y ago

If I understand correctly, a lattice or partial ordering means that A = B is possible for different A and B, but if A < B, then "B < A" is false. But even if I'm wrong about a lattice, my claim is still true for programming languages. Perl > Haskell... for certain situations. Even assembly > Lisp... for certain situations. And yet assembly and Lisp are so far apart on the "power curve" that, if Lisp is not > assembly always, then... do we have any kind of ordering at all? I view programming languages as being a tree, with branches spreading in all different directions. Some languages reach further in certain directions than other languages do. Your program is a vector. (Really, it's a bunch of different vectors, of different lengths, pointing in different directions, but one direction is the problem that makes it the hardest to write the program that you're trying to write.) Pick the language that reaches the farthest in the direction of whatever makes it hard to write the program that you're trying to write. This means that your problem imposes an order on languages... for that problem. It's not a universal order, though. Others, with a different kind of problem, may view your order as completely wrong. And they are right - for their problem, your order is in fact wrong.

thisiszilff 8y ago
You are thinking of a total order (in fact total orderings or often defined with the '>=' relation). A partial order is like a total order except there may be some elements that are not comparable, so given elements {A, B, C} we can have C < A and C < B but whether A < B or B < A can remain undefined. A lattice is a kind of partially ordered set.