>
> On Tue, Oct 19, 1999 at 01:55:32AM +0300, Jukka Tapani Santala wrote:
> >you can compare this to something like the value of Pi, relation of the
> >radius to the circumference, which human mind tries to instantly
> >rationalize as a "real" number, demonstrated clearly by the actual attempt
> >to _legalize_ Pi as 3. In fact, ask anyone what Pi is, and majority of
> >them will instantly reply to you "3.14".
>
> I'd say 3.1415926535897932, just to confuse people :-) (Yes, I do remember
> those decimals. Why? For fun.)
>
> A friend of mine, being really tired at a LAN-party, decided we should get
> away with our 10-system, and start using a phi-system instead. Sounds good
> in theory, but then you suddenly can't get to know exactly how many fingers
> you've got either?
>
> >The square of two is another good
> >example of how "irrational" and counter-intuitive mathemathics really is.
>
I would dare say that restricting one's intuition to what some superstition tells you
to accept as intuitive, is much more counter-intuitive thant \sqrt{2}. Let me put it in
an other way. The large Mersenne primes which are tested or proved on GIMPS, with
over 1000000 digits: just how intuitive are they ? Noone could call their full decimal
name in a life time, allthough it is finite in length. You have to allow for formulae
and
symbols, and then you can call their name based upon ``intuitive'' (i.e. integer, and
_reasonably small_ :-) numbers: you name thme 2^p-1. What else is \sqrt{2} than
x^2 - 2 = 0 and x > 0 ? Isn't that intuitive enough ? What else is pi then
1+1/3+1/5+1/7+1/9 and so on ... ? One should not be afraid of not being able to
understand what in fact one can ! I have to wash my glasses every couple
of days.
Friendly,
Preda
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