"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.
vgopa...@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 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
> "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.
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.
jo...@mraha.kitenet.net (josX) wrote in message <news:3dc298ca$0$46602$e4fe514c@news.xs4all.nl>... > vgopa...@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
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.
jo...@mraha.kitenet.net (josX) wrote: >vgopa...@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 >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).
"James Hunter" <jim.hun...@jhuapl.edu> wrote in message <news:apu5lt$ba9$1@houston.jhuapl.edu>... > "V.Gopal" <vgopa...@rediffmail.com> wrote in message > news:38af3945.0211010656.20badfde@posting.google.com... > > "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.
> 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.
Bertrand russell also suggested that the word 'cause' must be removed 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?
In article <3dc298ca$0$46602$e4fe5...@news.xs4all.nl>,
josX <jo...@mraha.kitenet.net> wrote: >vgopa...@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. -- "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.
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.
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.
> It's those dang Christoffel symbols, I tell you! Too many indices to keep > track of.
"A nice adoptation of conditions will make any hypothesis agree with 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.
>(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.
> >(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.
You have to use spherical geometry, which is NOT Euclidean, to fing the Great Circles! Darren
In article <3dc298ca$0$46602$e4fe5...@news.xs4all.nl> jo...@mraha.kitenet.net (josX) writes:
> vgopa...@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/
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