Re: The Fifth Dimension

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 07/04/04 

Date: Sun, 04 Jul 2004 12:59:55 GMT

"Leonard Pardin" <leoppard@MailAndNews.com> wrote in message
news:d746a243.0407030553.28d231ec@posting.google.com...
> "Cozmo Man" <cozmologist@scientist.com> wrote in message
news:<20040702222600.115$u5@news.newsreader.com>...
> > Leonard Pardin wrote:
> >
> > Leonard (May I call you Leonard? You can call me Cozmo.), I find it
> > fascinating trying to follow how your mind works. Based on what I have
> > seen on this newsgroup so far, I would say that at least 95% of the
> > posters are totally clueless as to modern physics and math. So I am
> > not at all surprised by your many words that include you in that
> > category. But I am surprised that you are just as clueless about the
> > mathematics and the physics of older days. Follow along.
> >
> > > Greek geometry was based
> > > on
> > > imaginary lines: perfect, massless, and absolutely straight.
> >
> > Greek geometry, ala Euclid, Apollonius, Archimedes, etc., WAS based on
> > lines. But to these Greek mathematicians lines meant curves, and
> > STRAIGHT lines were used as a qualification for the more general
> > notion of lines, which were not necessarily straight.
>
>
> Everything in Euclidian geometry is based on the imaginary
> straight line. All the mathematics so loved by the relativist starts
> with the straight line. Pi has no meaning in the absence of the
> straight line.

I really must say something here. There are many ways of looking at pi only
one of which has anything to do with the circumference of a circle. It is
an absolutely fundamental thing popping up in areas as diverse as statistics
and electrical circuit analysis. It is part of one of the most famous
equations in mathematics e^ipi = 1

> Similarly, sine, cosine, tangent, and cotangent are
> meaningless without the imaginary straight line.

Rubbish - they can for example be motivated as solutions to differential
equations.

> Differential calculus
> is based on the slope of the tangent.

Differential calculus is based on the concept of limit - read a book on
analysis.

> If you use calculus, you are
> using the straight line.

Rubbish.

> A curved line is defined by its deviation
> from the imaginary straight line.

Your point being?

> A circle is defined by a point on a
> revolving straight line. Without straight lines there can be no
> coordinate system, no reference frame. Throw away the straight line
> and all mathematics in physics is meaningless.

You are confused between geometrical motivations and abstract mathematics -
read a book on linear algebra. Or even just consider the relation of say
the use of Hilbert space in QM with it complex numbers and countable
infinite dimension then try and relate that to the concept of straight line.

>
>
> >
> > > They went perfectly straight and true, right through anything and
> > everything,
> > > including the earth, the sun and the stars--they even went straight
> > > through "curved space."
> >
> > Euclid provided 5 "postulates" and 5 "common notions". The first
> > postulate stated that it is possible to draw a straight line from any
> > point to any point. But Euclid makes clear that while his "common
> > notions" apply to all the practical sciences, his postulates only
> > apply to geometry, not to any of the practical sciences. Also, you are
> > apparently not aware that Euclid devoted Books XI, XII, and XIII to
> > solid geometry and the method of exhaustions. Euclid defined spheres,
> > cones, cylinders, and generally curvilinear figures for which in Book
> > II he developed theorems for not only volumes but also for areas.
> > Archimedes wrote extensively, in his work On the Sphere and Cylinder,
> > and elsewhere, on determining the surface area of curvilinear figures
> > such as the sphere. Can you not see that curved lines on the surface
> > of a sphere were basic elements to Greek geometry and for the
> > centuries that followed? This is LONG before non-Euclidean geometry.
>
> And all of it--every single bit of it--was based on the imaginary
> straight line. Spheres, cones, cylinders, parabolas, hyperbolas, are
> defined and measured by the straight line.

There is somthing else in goemetry besides lines - they are callled points.

>
>
> >
> > > Einstein thought of Euclidian lines as
> > > "rigid
> > > rods" or "rigid bodies." It was a stupid assertion, one that would
> > > have drawn an "F" on any highschool geometry exam.
> >
> > Leonard, not only do you not understand the geometry that Einstein
> > used in general relativity, you do not even understand the geometry
> > that you think you endorse. Doesn't it embarrass you, even a little,
> > to say such silly and clueless things as you do?
>
> That's the standard reply whenever someone points out some
> Einsteinian stupidity: the claim is that Einstein's genius is just too
> deep for normal people to understand. Well, have you ever read
> anything by Einstein? I mean something he himself wrote, not the reams
> of apologetics flowing out of the netherworld of relativity. Einstein
> wrote that geometric straight lines are really the same as little
> rigid rods.

Enstein wrote that litle ridged rods can be modelled by little straight
lines.

> You may think of that as pure genius, but any high school
> geometry teacher would have made Einstein retake the course.

And was that the reason that at 16 years of age he had a letter from his
math teacher attesting his mathmeatics was already of unversity calber?

Bill

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