What is wrong in Euclidean geometry?
V.Gopal
combine the two is impossible; but to lack both is unworthy of the
place that Euclid occupied in education" Bertrand Russell. It seems
that even the proof that one and only one STRAIGHT line can pass
through two points in space, is wrong and even the definition of
straight line is wrong. I wish to know whether this incorrectness is a
mathematical/logical error or it has to do something with physics.
josX
Non euclidian geometry is just lines on a sphere in euclidian geometry.
They call it "non euclidian" when they change defitinions of words
like line and parallel and straight etc. Obviously there can't be a
straight line on a sphere, so they redefined the word "straight" to
mean "cross section through the sphere", it is only a confusion serving
no real purpose (besides creating a 'cool' jargon for mathematicians).
--
jos
Uncle Al
>
> "A book should contain either intelligibility or correctness;
You don't see it at all. Tommy Aquinas was a tumor.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
James Hunter
"V.Gopal" <vgop...@rediffmail.com> wrote in message
news:38af3945.02110...@posting.google.com...
It has something to do with physics.
Bertrand Russell was an inept, semi-educated dork,
educated in the straight-jacket school of logic.
Every two points have an infinite number of straight lines
passing through them. Gravity is the universe's filter
which separates the normal intelligent lines from
the moronic, plasticene renormalized lines.
Darren G. Lorent
> vgop...@rediffmail.com (V.Gopal) wrote:
> > "A book should contain either intelligibility or correctness; to
> > combine the two is impossible; but to lack both is unworthy of the
> > place that Euclid occupied in education" Bertrand Russell. It seems
> > that even the proof that one and only one STRAIGHT line can pass
> > through two points in space, is wrong and even the definition of
> > straight line is wrong. I wish to know whether this incorrectness is
> > a mathematical/logical error or it has to do something with physics.
>
> Non euclidian geometry is just lines on a sphere in euclidian geometry.
It is MUCH more than that!
> They call it "non euclidian" when they change defitinions of words
> like line and parallel and straight etc. Obviously there can't be a
> straight line on a sphere, so they redefined the word "straight" to
> mean "cross section through the sphere", it is only a confusion serving
> no real purpose (besides creating a 'cool' jargon for mathematicians).
What is the shortest course from New York to London? I bet the
airlines think that this question has a "purpose" when they are buying
jet fuel!
Darren
Gregory L. Hansen
It's those dang Christoffel symbols, I tell you! Too many indices to keep
track of.
--
"A nice adaptation of conditions will make almost any hypothesis agree
with the phenomena. This will please the imagination but does not advance
our knowledge." -- J. Black, 1803.
Jim
V.Gopal
from our dictionary. But he did not say what what should we to with
the word 'effect'. One reason that he gives in support of his
contention is that the word cause never appears in gravitational
astronomy and in most parts of physics. Does it mean that the word
'cause' does not fit anywhere in physics?
Same way Einasten said, "When the propositions of mathematics refer to
reality, they are not certain, and when they are certain, they donot
refer to reality." Are not these comments confusing?
Gregory L. Hansen
josX <jo...@mraha.kitenet.net> wrote:
>vgop...@rediffmail.com (V.Gopal) wrote:
>> "A book should contain either intelligibility or correctness; to
>> combine the two is impossible; but to lack both is unworthy of the
>> place that Euclid occupied in education" Bertrand Russell. It seems
>> that even the proof that one and only one STRAIGHT line can pass
>> through two points in space, is wrong and even the definition of
>> straight line is wrong. I wish to know whether this incorrectness is
>> a mathematical/logical error or it has to do something with physics.
>
>Non euclidian geometry is just lines on a sphere in euclidian geometry.
>They call it "non euclidian" when they change defitinions of words
That's an example of a non-Euclidean geometry, the simplest. And rotating
reference frames are another exmaple, useful for working out things like
Coriolis forces. But there's also goemetries with intrinsic curvature
that really can't be attributed to a manifold curved in flat space.
Nat Silver
> "A book should contain either intelligibility or correctness; to
> combine the two is impossible; but to lack both is unworthy of the
> place that Euclid occupied in education" Bertrand Russell.
Here, Russell is talking about the difference in presentations
between an intuitive vs. a formal exposition of a subject.
According to Russell, one of these has to be done well
if the presentation is to have any value (worth).
> It seems that even the proof that one and only one
> STRAIGHT line can pass through two points in space,
> is wrong...
It's a statement of a theorem you are talking about, not a proof
of the statement. The theorem is not wrong but requires
a "euclidean context" to be true and so is not universally correct.
> and even the definition of straight line is wrong.
A "straight line" cannot be defined, using today's
standares of rigor, only described, and there
are competing points of view, which lay claim
to be as legitimate as euclidean straight lines.
> I wish to know whether this incorrectness is a
> mathematical/logical error or it has to do
> something with physics.
It has to do with the fact that there are several
models of (neutral) geometry which fit the axioms
of Euclid up to the Parallel Postulate.
V.Gopal
> It's those dang Christoffel symbols, I tell you! Too many indices to keep
> track of.
the phenomena". This is perfectly true BUT-
If we try that, we will definitely know whether we we should believe
in the existence of God, whether God is Omnipotent, whether we should
fear God or should not fear because he does interfere with the affairs
of this world,
or whether God is cunning deceiver or everythig good that we atrribute
to him. We may even find solutions to eradicate evils from the society
and moralize people without preaching. These are equally important
aspect of human existence as progress is.
keith stein
news:6481fc56.02110...@posting.google.com...
>(josX) wrote
> > Non euclidian geometry is just lines on a sphere in euclidian geometry.
> It is MUCH more than that!
> > They call it "non euclidian" when they change defitinions of words
> > like line and parallel and straight etc. Obviously there can't be a
> > straight line on a sphere, so they redefined the word "straight" to
> > mean "cross section through the sphere", it is only a confusion serving
> > no real purpose (besides creating a 'cool' jargon for mathematicians).
>
> What is the shortest course from New York to London?
Along the "Great Circle" running through New York and London, of course.
> I bet the
> airlines think that this question has a "purpose" when they are buying
> jet fuel!
> Darren
You seem to be confirming JosX point Darren, unless you really believe
that it is impossible to determine the shortest course from New York to
London using Euclidean Geometry.
keith stein
Darren G. Lorent
the Great Circles!
Darren
> keith stein
Dik T. Winter
> vgop...@rediffmail.com (V.Gopal) wrote:
> > It seems
> > that even the proof that one and only one STRAIGHT line can pass
> > through two points in space, is wrong and even the definition of
> > straight line is wrong.
> Non euclidian geometry is just lines on a sphere in euclidian geometry.
> They call it "non euclidian" when they change defitinions of words
> like line and parallel and straight etc.
An interesting reply when the subject is Euclidean geometry...
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/