[Haskell-cafe] Functional progr., images, laziness and alltherest

[Piotr Kalinowski]

On 23/06/06, Brian Hulley <brianh at metamilk.com> wrote:
> > This equation is just a shortcut, so I can't see how can it be
> > ill-typed. It means something like: if you add one element to an
> > infinite list, will it be longer?
>
> What does your intuition say about this?

It won't be longer. How can it be? It's already infinite ;) It's like
throwing things into bottomless hole and expecting it to get more
"full."

> But this explanation might just be vapid sophistry. Do you *really* want to
> trust it?

I perceive it as a way to explain to beginner students where bijection
idea comes from. It's all it means to me. I suppose the whole idea is
to start at something intuitive and then extend it to completely
counter-intuitive notion of being infinite.

> Just that there is a conflict with intuition no matter which option you
> choose: if I think that the list would be longer, I have to reject any proof
> to the contrary, but then my intuitions about valid proof are confounded,
> whereas if I accept the proof, my intuition about physical objects is
> confounded: if the list doesn't get longer, then where *is* the thing I
> added to it? Did it just disappear?
> So for these reasons I find that infinity is a troublesome concept.

I suppose infinity can't be totally intuitive in the end. We are not
used to handle infinite objects and intuition as such was not
developed to handle them.

Regards,
Piotr Kalinowski

-- 
Intelligence is like a river: the deeper it is, the less noise it makes