Euclid takes the 5th (was crank magnets)

From: The Sceptical Chymist (polyzonis.kostas_at_elzymi.invalid)
Date: 12/24/04 

Date: Fri, 24 Dec 2004 09:24:23 +0200

Ο "David McAnally" <D.McAnally@i'm_a_gnu.uq.net.au> έγραψε στο μήνυμα
news:cqfn7i$g81$1@bunyip.cc.uq.edu.au...
> Uncle Al <UncleAl0@hate.spam.net> writes:
>
> >No self-consistent mathematical construct can be internally falsified,
> >Euclid or Einstein. Euclid fell when his Fifth (Parallel) Postulate
> >fell - Riemann, and Bolyai and Lobechevsky; then Thurston to do them
> >all,
>
> I saw one person describe the work of Bolyai and Lobachevsky as a
> vindication of Euclid, on the basis that Euclid was aware enough to make
> his Fifth Postulate a Postulate, and not attempt to make it a Proposition.
> In other words, it vindicated Euclid because he never attempted to prove
> it, but chose, instead, to assume it.
>
> David

Isaac Asimov has written a great little essay called "Euclid's Fifth", in
which he says that choosing the 5th postulate as a postulate rather than
trying to prove it, cumbersome and long-winded though it was compared to the
other four, was a great insight and possibly the biggest achievement of his
geometry. Lesser mathematicians tried unsuccessfully for centuries to prove
it from the rest until some realised in the 19th century that they could
build self-consistent geometries without it (it could have happened earlier
if a certain Italian had the nerve to accept the implications of his line of
thoughts).

Kostas Polyzonis

Anyone who believes that the laws of physics are mere social conventions is
invited to try transgressing those conventions from the windows of my
apartment.
Alan Sokal

To reply my prtivate email, replace invalid with gr

Relevant Pages

  • Euclid takes the 5th (was crank magnets)
    ... > vindication of Euclid, on the basis that Euclid was aware enough to make ... > his Fifth Postulate a Postulate, and not attempt to make it a Proposition. ... Anyone who believes that the laws of physics are mere social conventions is ...
    (sci.physics)
  • Re: Euclid takes the 5th (was crank magnets)
    ... >> vindication of Euclid, on the basis that Euclid was aware enough to make ... >> his Fifth Postulate a Postulate, and not attempt to make it a Proposition. ... Lesser mathematicians tried unsuccessfully for centuries to prove ...
    (sci.physics)
  • Euclid takes the 5th (was crank magnets)
    ... > vindication of Euclid, on the basis that Euclid was aware enough to make ... > his Fifth Postulate a Postulate, and not attempt to make it a Proposition. ... Anyone who believes that the laws of physics are mere social conventions is ...
    (sci.physics.relativity)
  • Re: Euclid takes the 5th (was crank magnets)
    ... >> vindication of Euclid, on the basis that Euclid was aware enough to make ... >> his Fifth Postulate a Postulate, and not attempt to make it a Proposition. ... Lesser mathematicians tried unsuccessfully for centuries to prove ...
    (sci.physics.relativity)
  • Re: Euclid takes the 5th (was crank magnets)
    ... >> vindication of Euclid, on the basis that Euclid was aware enough to make ... >> his Fifth Postulate a Postulate, and not attempt to make it a Proposition. ... Lesser mathematicians tried unsuccessfully for centuries to prove ...
    (sci.chem)