[ExI] dicovery of irrational numbers

spike spike66 at att.net
Thu Dec 19 00:10:45 UTC 2013


 

 

On Behalf Of Kelly Anderson
Subject: Re: [ExI] dicovery of irrational numbers

 

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. 

 

 

Oy, good point.  My son is reacting much like scientists do when we keep
finding out there isn't really a simple consistent underlying principle, or
if so, we still don't know it.

 

>.Have you introduced him to the concept of significant digits?...

 

Yes.

 

>. That should assuage his little engineer even if his little mathematician
is stomping about inside his head.

 

Ja, that part is OK, but math is clean and precise.  Even I agree that
irrationals are ugly things.  I love them anyway; all numbers are my
friends.  But pi is ugly.  It has inner beauty with that way cool series
expansion.  Actually it has a number of expansions, but my favorite is pi=
4/1-4/3+4/5-4/7.  oh so cool is this.

 

>.If that doesn't help, you can introduce Chaos.

 

I put him off on that one.  He has a physics comic book which mentions
Schroedinger's Cat.  Being an animal lover, he wanted to know what that was
all about.  I deflected into the Uncertainty Principle for now.

 

>. 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...

 

That's been my philosophy: kids can take bad news better than we grownups
can.

 

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

 

I anticipated that one, never introduced the concept.  Living where we do,
there isn't much said about Santa Claus.  Most of my son's friends are
Buddhist from China or Vietnam, a few Hindu, one Muslim, plenty of agnostics
and atheists.  I just dropped him off at the home of the Muslim family for a
play date.  They have a Christmas tree.  Oy.

 

spike  

 

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