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

Piotr Kalinowski pitkali at gmail.com
Thu Jun 22 18:21:18 EDT 2006

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

> 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.

Piotr Kalinowski

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

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