Re: Euclids postulates and non-Euclidean geometry


"T Wake" <taswakeAt@xxxxxxxxxxx> wrote in message
news:Jr2dnSRvP_ksvI_ZnZ2dnUVZ8qGdnZ2d@xxxxxxxxxxxx
"Spaceman" <Realspace@xxxxxxxxxxx> wrote in message
news:R7-dnagLCMU9io_ZnZ2dnUVZ_t-dnZ2d@xxxxxxxxxxxxxx

"T Wake" <taswakeAt@xxxxxxxxxxx> wrote in message
news:WsWdnW7CN4jWl4_ZnZ2dnUVZ8qOdnZ2d@xxxxxxxxxxxx
I was explaining why I said its ability to move up and down was more
limited than its ability to move in the other directions.

You said it can "easily" move in three dimensions as if to discredit my
statement.

As you can see, it is limited in its ability to move in some directions.

Well of course,
It can't fly through the ground, but it still has no bearing
on my statement about the shortest distance is not a geodesic at all.

However, this is because you are too blinkered to look outside your three
dimensional world.

ROFLOL
I look outside it a lot, but mostly it is only because I am watching
SciFi.
LOL


They also can turn left and right so this 2D limit you give them is
complete bull*** to begin with.

How does left and right, combined with forward and backward contradict
the 2D limit?

up down = 1D
left right = 2D
forward backward = 3D

The up / down and left/right are the dimensions in which the plane has
almost unlimited movement. The up / down dimension is limited in both
directions.

You think you want to fix that statement?
The down is limited. and the up is also limited to an airplane.

Yes, you are correct. I meant to say the left /right and forward /
backward are limited.

Well now you goofed again, but who cares.
:)


From the point of view of the plane, you talk about a "mythical" route it
can follow which is the shortest possible route - however it is not a
route the plane can go so effectively (for the purposes of the thought
experiment) doesn't exist.

It can move in 3 directional planes (dimensions).
forward, left and down all at the same time
(that is 3D, not 2D)

However there is a limit on its up and down movement.

So what.
It still moves in 3D. not 2D.

Very true.

You remind me of conversations with my daughter when she was six.

I never said the plane was limited to two dimensions. This is an analogy
trying to use objects that are familiar to you and to help ease
understanding. Obviously it wont work.

That said, the plane can move in three dimensions yet cant follow your
shortest distance. If the plane was a thinking, reasoning creature like
yourself it would doubt the existance of your "shortest distance" and
spend months arguing the toss about this weird thing you had made up.

But T Wake,
Again you are ignoring what I stated,
I never said anything like the plane could follow the shortest distance I am
talking about, I merely stated the shorter distance can always be
measured because measurement is not limited to the geodesic ruling.
Hence the shortest path of the geodesic is not the shortest physical
distance
and never could be since it is curved.


No,
you are babbling on about an airplane when I originally
merely stated the shortest distance between two points
is not a geodesic since a geodesic is curved.
You are shifting away from my statement now completely.

How have I shifted away from your statement? On the other hand you are
diverting from my statements quite significantly. I suspect you assume
that enough nonsensical arguments will give you the "edge" when it comes
to twisting meanings. I have children who do it better than you though.

I agree with you that the shortest distance between two objects in a three
dimensional world, where the asset moving between the two objects is
constrained in its ability to move *may* well not be the same as the
shortest path that asset can move.

Have we determined what is meant by a straight line yet?

Yup, straight in three dimensions.
Such "straightness" is the shortest distance always.


Hold on here again.
Where the hell did I say the shortest path is not a geodesic?
I never said such.
I said the shortest distance is not a geodesic.
Are you going to read that or just make up words I did not say?

Ok, and I will endevour to use the terms you choose.

The shortest distance between two objects is also dependant on the
dimensional constraints that the objects exist in.

No,
that is the shortest "path" it can take.
again you are losing the reality of "measurement".
The shortest "distance" between two points is always
a 3 dimensionally straight line.


They are simplifications that are removing the reality of a shorter
distance being present.
The shortest "distance" is never a geodesic.
Sheesh!

Really? Once more you are limiting your understanding to three dimensions.
You have created an almost arbritrary distinction between path and
distance and you use it to butress your arguments.

Because I am not going to jump aboard the geodesic loss of reality train
like you have.
I am not limiting my understanding, I am using it.
You are the one limiting something.
you are limiting reality to a surface.


However, the problem remains that you refuse to think about any scenario
other than the three spatial dimensions with which you are most
comfortable.

Because as I stated. there is no "other" reality.
If there is.. please prove that the shortest distance between two
points is not a three dimensionally straight line.


As I stated previously this is fine by me. You are more than welcome to
exist in your seventeenth century world. It will keep you happy and allow
you to explain all the things you experience.

I am sorry you think it is 17th century.
It is still true today. nothing has ever proven otherwise.
In fact it was true way before the 17th century also.
And it will be true always unless you can prove it wrong
and that will take a lot more than just talking about geodesics.

When you use geodesics at all, you are removing a dimension.
(the dimension that could show a shorter distance.)
measurement is not limited to surfaces.

No but it is limited to the dimensions available to the person doing the
measuring. The observed curvature of space due to large mass objects
defines the shortest distance between objects either side of that large
mass as not being the "straight line" you imply unless you bring in extra
dimensions.

Feel free to think otherwise.

I do, and so do engineers and scientists and even astronomers.
It's too bad you have accepted a geodesic point of view and
lost the facts about measurements not having to follow geodesic
curves.


You are actually using the "rubber ***" without realizing it
when you talk about geodesics having the shortest paths at all.

The rubber *** you enjoy is a two dimensional analogy to help people
understand the concept. If you think it is the concept in itself then that
is also fine by me.

It is what you are using when you speak about geodesics.
If you can't see so, it is your problem,, not mine.
I am merely trying to show you that you have lost the
good old fact about the shortest distance being a straight line.
If you can't leave your surface to find a shorter distance,
you truly are stuck on the rubber *** analogy still even if you
don't think so.


You are hung up on the sentence - "For the
purpose of the plane (and within orders of magnitude) it can only go in
two
dimensions."

No,
The plane can move in 3 dimensions
simple as that.
If it could not,
it could either not land, (up or down) plane)
not take a turn, (left or right plane)
or not move forward. (forward or backard plane)
It is not limited to 2 dimensions at all.


Yet you have agreed with me on this, the plane has unlimited flight
forwards, backwards, left or right - for the sake of argument lets say
150,000,000 km with several inflight refuling hooks. Yet it is limited to
a climb / descent of around 15 km in each direction.

So there are 10 orders of magnitude difference between its range of
movement in two dimensions to the third. This is what I meant that for the
purposes of the thought experiment it was restricted.

It still is not 2D only.
it is limited 3D and nothing less than such.


Let our experimental object be a line on a peice of paper. It cant move
off the paper but can extend lenght or width at will. The paper is curved
around a three dimensional ball.

Again,
not leaving a surface is a rubber *** analogy.
You need to get away from that terrible abtract world.
Measurement is not limited to such a surface and never will be.
I just crumpled your paper and threw it in the 3D trash barrel
so forget it.

You, yourself, have already introduced an extra dimenson when you
discussed time.

That is not a physical dimension.
and time has nothing to do with shortest distance.
It is an abstract and is only needed to "time" motion
and have a human know how long it took to do so..
It is not actually needed to make the motion itself.



Really. How can he move through space - time? I have never understood it
myself, but then again science fiction is simply that. Fiction. Some
people may have trouble understanding that word, but then again they
probably think Tom Clancy writes political textbooks.

You see,
Dr Who's TARDIS.
(Time and relative dimensions in space) machine
can change the entire universe to fit where he wants to be.
but
who cares..
It is only great SciFi and the new series will be hitting the SciFi
channel soon.
:)


There are three directions for the line to go in. You are still assuming
that the line is straight like _________________________________ where as
that is far from three dimensional.

It is only physically straight when you can prove such from three planes.
You can easily make a curved line that "looks" stright to one plane.
Of course that is not physically straight.


If you are asserting that the shortest distance between (say) London and
New York is the straight line through the centre of the Earth, then yes
that single dimensional line is straight.

Actually it is a single dimensional line that is straight to all dimensions.


If you really don't think so.
This is a total waste of time because you have lost reality and could
never
use a 3D animation program without screwing up massively.

Actually, I do use them. But that is irrelevant. You dont understand the
concept you are arguing against.

I understand it well, and dropped it almost 20 yrs ago when
I could see it was full of bull***.
It is pretty sad you are still living in that rubber *** world.

Distances are limited to a surface all the time. You mean the three
dimensional structure you feel most comfortable with.

This sentence is so full of bull***, I can not believe you could actually
type
it in a science group.
Distances are never limited to a surface.
If that was true, tunnels would not be possible.
and spheres would never be able to be measured by
a micrometer.

Go ahead.
You give an example that shows the shortest "distance" between
two points is not a 3D straight line. (straight line to all 3 dimensions)

No, its your experiment. You are making the claim that scientists the
world over are wrong. You back up your statement. Please dont spoil your
good work by trying to twist things at this late stage.

Scientists would not say i am wrong ..
Where is the actual scienctist that is saying I am wrong?
Please have him speak up now right here.


Remember, its your experiment. You have to prove it (or disprove it if you
wish to follow the "proper" scientific method).

Several times in the last few weeks I have gone to great lenghts to pander
to your rantings because it amused me, but now you need to demonstrate
that in all possible circumstances the shortest distance between two
objects is a three dimensional straight line.

Before you do though, what scale are we doing the measuring at?

Again,
You are saying i am wrong, you need to prove the postulate
I am stating as wrong.
The shortest distance between 2 points is a physically straight line
I know you can't do such so you will always say it is my job to
prove it is.. yet..
It has been proven, everytime a physically straight tunnel is built.
Sheesh!
You truly are lost in rubber ***/ruler land.
LOL


.

Loading