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Lambda calculus is the computational equivalent of compass and straightedge geometrical construction[1]. It's about starting with fundamental and simple compone

by sgk284 12y ago

Lambda calculus is the computational equivalent of compass and straightedge geometrical construction[1]. It's about starting with fundamental and simple components and building higher-level abstractions upon these firm foundations. Euclid's Elements, which heavily relied on this approach and made it famous, was arguably the most influential mathematical text ever written. By combining simple constructs according to simple rules, you can be certain that more complex constructs are themselves correct. This also often highlights simplicity and elegance in the underlying structure of otherwise complex constructs. [1] http://en.wikipedia.org/wiki/Compass-and-straightedge_construction http://en.wikipedia.org/wiki/Compass-and-straightedge_constr...

sklivvz1971 12y ago
... and just as Euclidean geometry, nobody actually uses it, and it is a controversial matter whether it is a good teaching tool [1]. It's elegant, but elitist, because it's unnecessarily difficult and hostile. [1]: http://mathoverflow.net/questions/152352/is-euclid-dead http://mathoverflow.net/questions/152352/is-euclid-dead
- Crito 12y ago
  Oh give me a break. Lambda calculus was created to study computation. To study computation in a rigorous manner, a mathematical model of computation was necessary. The more complex the model of computation, the more axioms you need. Complex models with many axioms are more difficult to reason about but are not actually more powerful (since they are all equivalent...) With a simple model of computation you can quickly build yourself more user-friendly systems (such as demonstrating how Church Encoding works, then proceeding to use it instead of writing it all out every time). It wasn't created out of some sense of elitism, it was created out of pragmatism. Do you really think that Alonzo Church made his own work more difficult just to make others feel excluded? That's ludicrous.
  - sklivvz1971 12y ago
    ... just like Euclidean geometry, it was created by a geometer for "internal usage". I am not contesting the usefulness of lambda calculus in academic contexts! I am just saying that lambda calculus is not the best approach in an engineering context, because it's too abstract, just like in practical terms, I see little use of Euclidean geometry in proving new theorems.

by sgk284 12y ago

sklivvz1971 12y ago

... and just as Euclidean geometry, nobody actually uses it, and it is a controversial matter whether it is a good teaching tool [1]. It's elegant, but elitist, because it's unnecessarily difficult and hostile. [1]: http://mathoverflow.net/questions/152352/is-euclid-dead http://mathoverflow.net/questions/152352/is-euclid-dead

Crito 12y ago
Oh give me a break. Lambda calculus was created to study computation. To study computation in a rigorous manner, a mathematical model of computation was necessary. The more complex the model of computation, the more axioms you need. Complex models with many axioms are more difficult to reason about but are not actually more powerful (since they are all equivalent...) With a simple model of computation you can quickly build yourself more user-friendly systems (such as demonstrating how Church Encoding works, then proceeding to use it instead of writing it all out every time). It wasn't created out of some sense of elitism, it was created out of pragmatism. Do you really think that Alonzo Church made his own work more difficult just to make others feel excluded? That's ludicrous.
- sklivvz1971 12y ago
  ... just like Euclidean geometry, it was created by a geometer for "internal usage". I am not contesting the usefulness of lambda calculus in academic contexts! I am just saying that lambda calculus is not the best approach in an engineering context, because it's too abstract, just like in practical terms, I see little use of Euclidean geometry in proving new theorems.