[Jprogramming] Learning Mathematics versus Learning J == learn by theory versus learn by practice?

[Terrence Brannon]

On 7/5/07, Raul Miller <rauldmiller at gmail.com> wrote:
> On 7/5/07, Terrence Brannon <metaperl.j at gmail.com> wrote:


>
> > So, likewise, learning J should be like following a proof in a
> > textbook, right?
>
> What kind of proof?
>
> If I recall correctly, we tend to ask students to study a variety
> of mathematical concepts for years (and try to ensure they
> get a robust practical background in some of those topics)
> before we ask them to understand the simplest of proofs.

yes and because so many people are no good at math, there's clearly
something wrong with this approach.

>
> > But then again, math is limited by Goedel's Incompleteness
> > theorem whereas computers can do more?
>
> That does not match my understanding, of Goedel's
> Incompleteness theorem, nor of the character of computers.
>
> As I understand the incompleteness theorem: a mathematical
> system of sufficient complexity will allow an infinite number
> of statements which are not resolvable simply by recourse to
> previous axioms (definitions).

Actually, your statement refers to half of what I understand about
that theorem. A mathematical system can be either complete, or
correct, but not both. You are talking about a correct system which is
not complete above.

The other possibility is to have a complete system which is not correct.

But my understanding of that theorem is limited to Hofstadter's
(brilliant!) book and nothing more.

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