[ExI] dicovery of irrational numbers

[Kelly Anderson]

On Wed, Dec 18, 2013 at 11:34 AM, John Clark <johnkclark at gmail.com> wrote:

> On Wed, Dec 18, 2013 at 12:58 PM, spike <spike66 at att.net> wrote:
>
> > I am open to suggestion for how to present irrationals in a more
>> friendly way, especially since I have more bad news for that lad: most
>> numbers are irrational.
>>
>
> It's even worst than that, at least with PI (and e) there is a infinite
> series that produces it so you can find a decimal that is as close to PI as
> you like, but most irrationals, nearly all in fact, are not like that, no
> infinite series or anything else can produce them, they're not computable,
> so you can't even get good approximations.  We can't even point at most
> numbers.
>

Have you introduced him to the concept of significant digits? That should
assuage his little engineer even if his little mathematician is stomping
about inside his head. If that doesn't help, you can introduce Chaos, the
fact that the minimalist difference in numbers can, and does in practice,
often get magnified to the point that you can not predict stuff far out.
Then he can throw out the notion of Newton's "Clockwork Universe"
altogether and have only one upset instead of two. He won't like it when he
finds out about chaos later, so you might as well tell him about this now
as well...

I'll leave it up to you as to when to introduce the truth of Santa Claus.
:-)

-Kelly
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