Re: Euclids postulates and non-Euclidean geometry

"Spaceman" <Realspace@xxxxxxxxxxx> wrote in message
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"T Wake" <taswakeAt@xxxxxxxxxxx> wrote in message
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However, this is because you are too blinkered to look outside your three
dimensional world.

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

Ok. Good for you. I am pleased that your ignorance will remain intact. It
reduces the chance that you will be able to significantly interact with the
human race - other than trolling on USENET. Here, you are just a harmless
crank who can be ridiculed. This keeps us both happy.

Do you hang out with Jeff Relf and share ideas for jokes?

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

Well now you goofed again, but who cares.

Yep. Everyone makes mistakes. When I get something wrong I have no dramas
with correcting myself - or being corrected by others as appropriate.

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.

I never said you stated anything other than what you stated. You try to
argue against things that either havent been said or dont exist.

The conversation is centring on the ability to rationalise movement in a
variety of dimensions simultaneously. This is done by creating an analogy
(i.e. something which is representative of - not a complete description of)
of the real world with less dimensions of movement. Obviously the airplane
analogy requires too much imagination for you to be happy with. We can use
others.

Can you, without resorting to a two dimensional analogy explain how the
cosmological expansion of large scale structures takes place in all
directions and implies no centre? Can you also tell me, without use of less
or more than three dimensions, how you determine the shortest possible
distance between two objects that are recessing in three dimensions
simultaneously?

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.

Can you show me a representation of this line which moves straight between
point A and point B in all three dimensions please.

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.

Only if you are talking about a three dimensional object.

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.

What train is that then? Why do you assume that I have lost "reality" here?
Where have I disagreed with the fact that in our three dimensional existence
the shortest distance is in a straight line?

I am not limiting my understanding, I am using it.

Sadly this is true. You are not limiting your understanding and you are
using it.

However your understanding is limited which is causing you problems.

You are the one limiting something.
you are limiting reality to a surface.

You stated the universe was four dimensional yet you only allow three
dimensions of movement.

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.

Ok. As I said you are correct. All the worlds scientists and mathematicians
are wrong. The Nobel prizes will be returned soon, I am sure.

In fact it was true way before the 17th century also.
And it will be true always unless you can prove it wrong

No one can prove anything to you.

and that will take a lot more than just talking about geodesics.

Yes. Fortunately you will die soon enough.

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.

Really? Prove it. I fall into all three categories and none of the
professional members of the three groups that I know (lots) would agree with
you.

It's too bad you have accepted a geodesic point of view and
lost the facts about measurements not having to follow geodesic
curves.

Again, you demonstrate nothing but a lack of understanding.

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.

I am not sure what you mean here.

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.

Ok. Can you show me how to represent the shortest distance between two
objects recessing from each other in three dimensions please.

A drawing would be nice.

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.

Do you understand what "orders of magnitude" means?


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.

Yes. An in the limited three dimensional world the shortest distance between
the two cities is still curved.

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.

Ok. It is forgotten. Lets talk three dimensional cosmology.

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? Can you cite any evidence to support your claims here?

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.

Glad to hear you like it. The only decent Dr was Tom Baker - the rest are
pale imatations.

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.

How would you go about proving the line was straight in all three
dimensions?

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.

What scale are we allowed to go to, to look at the line and measure how
straight it was?

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.

Yes. So glad you progressed.

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.

You didnt understand my sentence so blathered on some nonsense to try and
discredit it.

Well done.

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 ..

Yes they would. I can think of four who already have. There is another one
in the room with me now who says you are.

Need I go on?

Where is the actual scienctist that is saying I am wrong?

One is standing next to me now.

Please have him speak up now right here.

She said "hello, you are wrong."

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

Nope. You are saying I am wrong and the established ideas are wrong. I say
they are correct.

The burden of proof is upon you.

I am stating as wrong.
The shortest distance between 2 points is a physically straight line

What scale can we use to determine the measurements. What object can we use
to measure the path?

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.

You dont understand the concept you rail against.

Sheesh!
You truly are lost in rubber ***/ruler land.

Yes. Your obsession with rubber appears to be your undoing.


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