steve waterman wrote:beojan wrote:(I am assuming the notation S(2,0,0) means "the point at coordinates (2,0,0) as measured in system S [

Yes, exactly.

S'(2,0,0) means the point at coordinates (2,0,0) as measured in system S'

Given S(2,0,0) and given S'(2,0,0) are coincident,

if we then elect to move either system, does S(2,0,0) = S'(2,0,0)?

It's important to start with two systems that are stationary relative to each other, but not coincident.

Take two coordinate systems, S and S', such that S'(0,0,0) = S(1,0,0)*. Does S(2,0,0) = S'(2,0,0)? Obviously not, S(2,0,0) = S'(1,0,0).

Please read my post about the trees in the field and reply to it, this is essentially what I am trying to explain in that post.

*also assuming the x, y and z axes of the two coordinate systems are each parallel, i.e. there is no rotation.

And... he's decided to add something to his previous post instead of creating a new reply.steve waterman wrote:SOOO...I are talking about lineal distances being equal, NOT points being nor even coordinates being equal nor locations being equal!

The lineal abscissa distance is the DISTANCE +/- FROM the system origin to (abscissa,0,0).

Seems I am comparing absolute lengths from the origin and you are comparing points, not lengths!!!

Very very interesting. I am going to take a break and try to reflect upon this new "revelation" that perhaps I am a distance comparing dude and the Galilean is a point comparing dude.

1. I think you mean linear, not lineal.

2.

The lineal abscissa distance is the DISTANCE +/- FROM the system origin to (abscissa,0,0).

So you've now defined "lineal abscissa distance" to be the absolute value of the x coordinate. If we are talking about an individual, fixed point, and multiple coordinate systems, this is

not the same in all coordinate systems, for the simple reason that the origins of the multiple coordinate systems are not all (necessarily) in the same place.

3.

Very very interesting. I am going to take a break and try to reflect upon this new "revelation" that perhaps I am a distance comparing dude and the Galilean is a point comparing dude.

I have no idea what you are talking about here.

And he's edited his post againsteve waterman wrote:Very very interesting. I am going to take a break and try to reflect upon this new "revelation" that perhaps I am a vector from (0,0,0) 2d comparing dude and the Galilean is a location/point 1d comparing dude.

That might do well explain a portion of our verbal mental conceptual stances.

The second part ("the Galilean is a location/point 1d comparing dude") is wrong. The Galilean transform can be used with any number of dimensions, although, due to living in 3 spatial dimensions, its 1, 2, and 3d versions are the ones used more often.

However, on the first part ("I am a vector from (0,0,0) 2d comparing dude"), ignoring the fact that (0,0,0) is 3 dimensional, such vectors, from a defined origin to a point, are called

position vectors. It is these position vectors that the Galilean transform works with, converting a position vector with regard to one origin to a position vector with regard to a different origin, which may be displaced from the first, and may be moving relative to the first. Referring back to the field with trees, if a person, who we shall define as the origin, moves, the position vector of some particular tree changes as the origin (person) moves, even though the location of the tree relative to the center of the earth, and the other trees, does not change. (In fact, it is impossible to give an absolute location for an object or point. All that can be given is a position vector relative to some origin).