Brouwer and spiders.
- From: Bill Taylor <w.taylor@xxxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 25 Sep 2008 23:08:56 -0700 (PDT)
Just catching up on some backed-up downloads here.
A little while ago, Achava (the loving snake) posted
a little snippet which caught my eye. It was part of
a longer article, but this bit was cool.
I was told that the introduction to some book on foundations
had an intro or preface which told the tale of a great castle
which had stood for centuries. In the basement of the castle
were a large number of spiders very actively weaving webs all
through the basement. One day a property manager was hired
& he had the entire basement cleaned up. The spiders survived,
but their webs did not. The became frantic, spinning webs
as quickly as they could, because they were convinced that
if they did not, the entire structure would collapse.
<<<
NICE ONE!
And, it reminded me of an excerpt from Bishop & Bridges'
book on Constructive Analysis, where Bishop noted that
"Brouwer feared that the real line would turn out to be
discrete unless he personally intervened to prevent it!"
Also wonderful, and very, very similar.
Platonists, no doubt, see Brouwer et al as the spiders.
Constructivists so probably see Weirstrass, Cantor & Hilbert.
Engineers and physicists probably see them all as spiders.
Bishop probably thought of himself as one of those clearing
away the webs so that the castle walls can properly be seen.
What fun to extend a parable beyond its useful life! :)
-- Bible-bashing Bill
** Intuitionism - mathematical solipsism
.
- Follow-Ups:
- Re: Brouwer and spiders.
- From: herbzet
- Re: Brouwer and spiders.
- Prev by Date: Denominator Postulate.By Aiya-Oba
- Next by Date: Re: An argument for the redundancy of truth
- Previous by thread: Denominator Postulate.By Aiya-Oba
- Next by thread: Re: Brouwer and spiders.
- Index(es):
Relevant Pages
|
