Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Tue Jul 30, 2013 5:24 pm UTC

steve waterman wrote:PLEASE!
We begin with x and y coincident

NOOOOOOOOOOOOOOOOOO! We begin with the given. That is NOT x = y.

I refer you to Schrollini's post about not getting caught up in the symbols.

I simply substituted numbers for coordinate systems to illustrate the fault in your logic.
Using the symbols S and S' and x and x' does not magically change the basic logic.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Tue Jul 30, 2013 5:34 pm UTC

SecondTalon wrote:
steve waterman wrote:Cartesian system with no point(s)?
Isn't that kinda like a hamburger with no meat, no bread, no additives, no sauces, no plate and no table?

And I mean that seriously - I was under the impression the points were the entire point, and the whole X/Y/Z nonsense was so we could talk about them by specifically pointing out particular points, so.. by not having points, the thing doesn't exist.

A Cartesian system would be more like the menu.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Tue Jul 30, 2013 5:34 pm UTC

steve waterman wrote: NOOOOOOOOOOOOOOOOOO! We begin with the given. That is NOT x = y.


Re-read. beojan's making a point.

beojan wrote:1. We begin with x and y coincident (i.e. x = y). For a concrete example, lets say x = y = 5


So.. yeah, the given we're working with here is x=y. You throw your shit of "x='x and y='y" to the trash for a minute and follow along. It's math. You start with some rules and such, and when the first line of the problem says that x=y, then you have an x that's exactly the same as a y.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 5:42 pm UTC

steve waterman wrote:
SexyTalon wrote:
steve waterman wrote:Cartesian system with no point(s)?
Isn't that kinda like a hamburger with no meat, no bread, no additives, no sauces, no plate and no table?

And I mean that seriously - I was under the impression the points were the entire point, and the whole X/Y/Z nonsense was so we could talk about them by specifically pointing out particular points, so.. by not having points, the thing doesn't exist.

A Cartesian system would be more like the menu.

Then it's a menu with no items. Which would make it structurally no different than a painting with no paint, or a newspaper with no print. That is to say, it is nothing. A menu with nothing on it is not a menu at all. A Cartesian coordinate system with no points is not a coordinate system, because the entire function, the raison d'être of a coordinate system is to give labels to points. Nothing else. Not mathematically, not physically, not anything.

By the way, if you could have a Cartesian coordinate system with no points, what is the intersection of your axes? Where would you put it?

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Tue Jul 30, 2013 6:05 pm UTC

WibblyWobbly wrote:
steve waterman wrote:
SexyTalon wrote:
steve waterman wrote:Cartesian system with no point(s)?
Isn't that kinda like a hamburger with no meat, no bread, no additives, no sauces, no plate and no table?

And I mean that seriously - I was under the impression the points were the entire point, and the whole X/Y/Z nonsense was so we could talk about them by specifically pointing out particular points, so.. by not having points, the thing doesn't exist.

A Cartesian system would be more like the menu.

Then it's a menu with no items. Which would make it structurally no different than a painting with no paint, or a newspaper with no print. That is to say, it is nothing. A menu with nothing on it is not a menu at all. A Cartesian coordinate system with no points is not a coordinate system, because the entire function, the raison d'être of a coordinate system is to give labels to points. Nothing else. Not mathematically, not physically, not anything.

By the way, if you could have a Cartesian coordinate system with no points, what is the intersection of your axes? Where would you put it?


Sorry, I was off topic...this is not about a menu. Given S(x,y,z)...my intersection of your axes is at S(0,0,0).
The S notation means wrt S(0,0,0).

the existence of the empty/null Cartesian set...and the Cartesian product...

http://math.stackexchange.com/questions/305766/why-is-the-cartesian-product-of-a-set-a-and-empty-set-an-empty-set
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Cartesian_product.html
http://www.mathcaptain.com/algebra/cartesian-product.html
http://c2.com/cgi/wiki?NullSet
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 6:17 pm UTC

steve waterman wrote:
WibblyWobbly wrote:
steve waterman wrote:
SexyTalon wrote:
steve waterman wrote:Cartesian system with no point(s)?
Isn't that kinda like a hamburger with no meat, no bread, no additives, no sauces, no plate and no table?

And I mean that seriously - I was under the impression the points were the entire point, and the whole X/Y/Z nonsense was so we could talk about them by specifically pointing out particular points, so.. by not having points, the thing doesn't exist.

A Cartesian system would be more like the menu.

Then it's a menu with no items. Which would make it structurally no different than a painting with no paint, or a newspaper with no print. That is to say, it is nothing. A menu with nothing on it is not a menu at all. A Cartesian coordinate system with no points is not a coordinate system, because the entire function, the raison d'être of a coordinate system is to give labels to points. Nothing else. Not mathematically, not physically, not anything.

By the way, if you could have a Cartesian coordinate system with no points, what is the intersection of your axes? Where would you put it?


Sorry, I was off topic...this is not about a menu. Given S(x,y,z)...my intersection of your axes is at S(0,0,0).
The S notation means wrt S(0,0,0).

the existence of the empty/null Cartesian set...and the Cartesian product...

http://math.stackexchange.com/questions/305766/why-is-the-cartesian-product-of-a-set-a-and-empty-set-an-empty-set
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Cartesian_product.html
http://www.mathcaptain.com/algebra/cartesian-product.html
http://c2.com/cgi/wiki?NullSet

Why are you calling them "my" axes? The coordinate system without points is yours alone. Does your coordinate system not have axes? Does it not have an origin? Does it even exist? Or are you back to suggesting that coordinate systems have "coordinate points"?

Calling something S(0,0,0) requires there to be a point with coordinates (0,0,0) with respect to some coordinate system. But that in itself should tell you that to even place a coordinate system in the first place, you need a point - the origin. So, a coordinate system, Cartesian or otherwise, that has no points cannot have an origin and thus cannot exist, right?

I'm not sure what you're getting on about with Cartesian products - by itself, I don't think that concept applies to coordinate systems in quite the way you think it does.
Last edited by WibblyWobbly on Tue Jul 30, 2013 6:18 pm UTC, edited 1 time in total.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Tue Jul 30, 2013 6:17 pm UTC

Good god, Steve. By that understanding, French Fries are composed of Au Jus and roast beef.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 6:19 pm UTC

SecondTalon wrote:Good god, Steve. By that understanding, French Fries are composed of Au Jus and roast beef.

Damn you. I could go for a good roast beef sandwich.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby eSOANEM » Tue Jul 30, 2013 6:26 pm UTC

steve waterman wrote:
eSOANEM wrote:And that statement is incorrect.

In order to say S(x,y,z) is coincident with S'(x',y',z') we need to consider all points. Not one, not two and definitely not none. The way we consider every point is by considering a single arbitrary point and then saying "since that point was arbitrary, this proof applies to any other point as well".

This is an important concept in predicate logic and its application to proofs like here is something you should look into because it might help move this along.

So, are you saying that it is mathematically impossible to have a Cartesian system with no point(s)?


Yes.

A co-ordinate system is explicitly defined as a mapping between co-ordinates and points.

Without some set of points to refer to, it cannot exist.

steve waterman wrote:
Spoiler:
beojan wrote:
steve waterman wrote:1. All we have is S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, it is true that x = x'.
3. When S or S' are repositioned to non-coincidence, (noting that there is no point P), x ≠ x', in the manifold.
4. Given x = x', therefore x = x'.

1. We begin with x and y coincident (i.e. x = y). For a concrete example, lets say x = y = 5
2. When x and y are coincident, it is true that x = y
3. When x and y are repositioned to non-coincidence x ≠ y. For the concrete example, lets add 3 to y. Now, x = 5, and y = 5 + 3 = 8
4. But given that we started with x = y, how can this be? 5 ≠ 8 so x ≠ y.

Answer? We changed y. What we said about x and y is no longer true once we change y.

It's the same with coordinate systems.
Once we change (reposition) one or both of S and S', what we said about them before we changed them is no longer (necessarily) true.

Note: For all those confused by the numbered statements, I deliberately used Stevean terminology, which may be a little nonsensical to everyone else.


PLEASE!
We begin with x and y coincident

NOOOOOOOOOOOOOOOOOO! We begin with the given. That is NOT x = y.


Spoilered most of the quote to make this post smaller.

Beojan is illustrating two things. The first is that labels are arbitrary and x can be used for an arbitrary variable (as in this post) or for a co-ordinate. x has no meaning intrinsic to itself. The other thing they're illustrating is that "moving" something with respect to another breaks coincidence. This applies to co-ordinate systems well.

Essentially they're looking at the 1D case where you have S(x) and S'(y).



Cartesian products are not Cartesian co-ordinates. They are completely irrelevant to this discussion.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby firechicago » Tue Jul 30, 2013 6:29 pm UTC

Steve, could you please explain what you think is meant by "Cartesian Product" and how that relates to Cartesian coordinates?

Because I see half a dozen places where the links you've supplied contradict your assertion that you can have a Cartesian coordinate system without points, but I don't think it's worth going through them if, as I suspect, you don't actually have any functional understanding of what you're talking about (whether that understanding is correct or not) and you merely went searching for the words "Cartesian" and "no points" and assumed that whatever you found supported your position without actually taking the time to understand what you were reading.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Tue Jul 30, 2013 6:49 pm UTC

eSOANEM wrote:
steve waterman wrote:
eSOANEM wrote:And that statement is incorrect.

In order to say S(x,y,z) is coincident with S'(x',y',z') we need to consider all points. Not one, not two and definitely not none. The way we consider every point is by considering a single arbitrary point and then saying "since that point was arbitrary, this proof applies to any other point as well".

This is an important concept in predicate logic and its application to proofs like here is something you should look into because it might help move this along.

So, are you saying that it is mathematically impossible to have a Cartesian system with no point(s)?


Yes.

A co-ordinate system is explicitly defined as a mapping between co-ordinates and points.

Without some set of points to refer to, it cannot exist.

Since we know both coordinate systems are cartesian, three points should be enough to show that they are coincident.
This does not mean eSOANEM's statement about proving for an arbitrary point being equivalent to proving for all points is in any way invalid, however.
eSOANEM wrote:
steve waterman wrote:
Spoiler:
beojan wrote:
steve waterman wrote:1. All we have is S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, it is true that x = x'.
3. When S or S' are repositioned to non-coincidence, (noting that there is no point P), x ≠ x', in the manifold.
4. Given x = x', therefore x = x'.

1. We begin with x and y coincident (i.e. x = y). For a concrete example, lets say x = y = 5
2. When x and y are coincident, it is true that x = y
3. When x and y are repositioned to non-coincidence x ≠ y. For the concrete example, lets add 3 to y. Now, x = 5, and y = 5 + 3 = 8
4. But given that we started with x = y, how can this be? 5 ≠ 8 so x ≠ y.

Answer? We changed y. What we said about x and y is no longer true once we change y.

It's the same with coordinate systems.
Once we change (reposition) one or both of S and S', what we said about them before we changed them is no longer (necessarily) true.

Note: For all those confused by the numbered statements, I deliberately used Stevean terminology, which may be a little nonsensical to everyone else.


PLEASE!
We begin with x and y coincident

NOOOOOOOOOOOOOOOOOO! We begin with the given. That is NOT x = y.


Spoilered most of the quote to make this post smaller.

Beojan is illustrating two things. The first is that labels are arbitrary and x can be used for an arbitrary variable (as in this post) or for a co-ordinate. x has no meaning intrinsic to itself. The other thing they're illustrating is that "moving" something with respect to another breaks coincidence. This applies to co-ordinate systems well.

I'm a 'he' by the way.
Also, I wasn't actually trying to illustrate that labels are arbitrary, at least not until Steve got annoyed about the labels being different. I was hoping he had understood that from Pfhorrest's animation.
eSOANEM wrote:Essentially they're looking at the 1D case where you have S(x) and S'(y).

In fact, lets make it clear. Lets use one dimensional coordinate systems, and lets define the manifold on which we are working to be the real number line. Hence, the points are real numbers.

1. We begin with S(x) and S'(x') coincident. To give a concrete example, S(x) = x, and S'(x') = x'
2. When S and S' are coincident, x = x'
3. Now lets reposition S'. For the concrete example, we'll reposition it 3 units left. Hence, S(x) = x, but S'(x') = x' - 3.
4. Now, if S(x) = S'(x'), x ≠ x'. For the concrete example, lets use x = 5.
S(x) = x = 5.
S'(x') = x' - 3 = 5 therefore x' = 5 + 3 = 8
How can this be, when we first said that x = x'? We changed S'. What we said about S and S' (and hence, about x and x') before they were changed is no longer (necessarily) valid after they were changed.

Edited to fix the direction the coordinate system moved.
Last edited by beojan on Tue Jul 30, 2013 7:02 pm UTC, edited 1 time in total.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby addams » Tue Jul 30, 2013 6:53 pm UTC

http://www.google.com/imgres?imgurl=&im ... iJSQwpM%3A

Hi; Where on That drawing is X=2 Y=0.5.

Well? The artist did not know, either.
The math you are doing must be very hard.

You all are using the same glossary. Correct?
Is this an educational program?

Back to the Tutorial.
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I don't have to understand multi=dimensional manifolds.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby addams » Tue Jul 30, 2013 7:04 pm UTC

Pfhorrest wrote:It was my birthday vacation this weekend, so I made a present for Steve that I hope the rest of you can enjoy too.

Steve, please watch it all the way through (until it loops) and tell me what you think about it, I put a lot of work into this gift for you.

Image

I know. Double post!
But; I think I get it!

That was so great!
Taking d to zero made it so clear.
Then extrapolating to the very few cases where Xprime and d=0 happen.

That was fun. Even if I did not understand it.
What a great explanation!

Sorry, Steve. Do you have a tutorial?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Tue Jul 30, 2013 7:06 pm UTC

addams wrote:http://www.google.com/imgres?imgurl=&imgrefurl=http%3A%2F%2Fwww.zenerpower.com%2FMC%2520Escher%2Fimage26.html&h=0&w=0&sz=1&tbnid=FXHIksliJSQwpM&tbnh=329&tbnw=153&zoom=1&docid=Sk0X_e3JfVLMKM&hl=en&ei=vwn4UZT5FIOsjALZ8oCwDQ&ved=0CAYQsCU#imgdii=FXHIksliJSQwpM%3A%3BFHhChNexJ3-nMM%3BFXHIksliJSQwpM%3A

Hi; Where on That drawing is X=2 Y=0.5.
Point 0,0 is not defined, so we cannot say.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Tue Jul 30, 2013 7:34 pm UTC

steve waterman wrote:So, are you saying that it is mathematically impossible to have a Cartesian system with no point(s)?
Yes. That is exactly what we are saying.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Pfhorrest » Tue Jul 30, 2013 8:11 pm UTC

I think the important point to drive home here is:

Steve, whether or not you are trying to talk about points, the Galilean transformation (and every other coordinate transformation) is talking about points, so if you read statements like "x' = x - d" to mean something that has nothing to do with points, you're reading something different from what anyone else is saying, so if you somehow proved what you read to be wrong, it still wouldn't prove what anyone else said to be wrong.

If a woman tells you she is a lesbian, and you somehow pull her birth certificate and prove that she was not in fact born in Lebanon... so what? She never said she was. You misunderstood her and thought she was saying something else (that she was Lebanese), and then disproved that thing she never said. And now she's corrected you over and over again and you keep trying to talk about her country of origin while she's trying to tell you something about her sexual orientation. Isn't that ridiculous?

You don't want to talk about points or manifolds or functions, but you do want to talk about the Galilean transformation, and the Galilean transformation is all about points and manifolds and functions, so what you want is contradictory and to resolve that you have to choose: do you want to talk about the Galilean transformation (or other related transformation), and subsequently about points and manifolds and functions and so on; or do you want to talk about something else that has nothing to do with the Galilean or any other coordinate transformation?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Tue Jul 30, 2013 8:47 pm UTC

I posted this just moments ago and somehow it ended up up page 13, and then page 14 has an old post, that it certainly out of order, so I will post this again...and stop for today.

Mathematically,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x.
3. When S or S' are not coincident, x' = x.

Galilean transformation,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x because vt = 0.
3. When S and S' are not coincident, x' = x -vt.

Given S(x,y,z)...does S have inherent coordinates (x,y,z) wrt S(0,0,0)?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 8:53 pm UTC

steve waterman wrote:I posted this just moments ago and somehow it ended up up page 13, and then page 14 has an old post, that it certainly out of order, so I will post this again...and stop for today.

Mathematically,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x.
3. When S or S' are not coincident, x' = x.

Galilean transformation,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x because vt = 0.
3. When S and S' are not coincident, x' = x -vt.

Given S(x,y,z)...does S have inherent coordinates (x,y,z) wrt S(0,0,0)?


Go back and watch Pfhorrest's animated tutorial a few dozen more times. For the love of Ahura Mazda, he made it clear enough that a chimpanzee could understand it.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Tue Jul 30, 2013 10:02 pm UTC

WibblyWobbly wrote:
steve waterman wrote:I posted this just moments ago and somehow it ended up up page 13, and then page 14 has an old post, that it certainly out of order, so I will post this again...and stop for today.

Mathematically,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x.
3. When S or S' are not coincident, x' = x.

Galilean transformation,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x because vt = 0.
3. When S and S' are not coincident, x' = x -vt.

Given S(x,y,z)...does S have inherent coordinates (x,y,z) wrt S(0,0,0)?


Go back and watch Pfhorrest's animated tutorial a few dozen more times. For the love of Ahura Mazda, he made it clear enough that a chimpanzee could understand it.


added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 10:11 pm UTC

steve waterman wrote:
WibblyWobbly wrote:
steve waterman wrote:I posted this just moments ago and somehow it ended up up page 13, and then page 14 has an old post, that it certainly out of order, so I will post this again...and stop for today.

Mathematically,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x.
3. When S or S' are not coincident, x' = x.

Galilean transformation,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x because vt = 0.
3. When S and S' are not coincident, x' = x -vt.

Given S(x,y,z)...does S have inherent coordinates (x,y,z) wrt S(0,0,0)?


Go back and watch Pfhorrest's animated tutorial a few dozen more times. For the love of Ahura Mazda, he made it clear enough that a chimpanzee could understand it.


added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Go back and watch Pfhorrest's animated tutorial a few dozen more times. It's covered in there.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Tue Jul 30, 2013 10:18 pm UTC

steve waterman wrote:added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Could you point me to where in the 5000+ post ex-"pressures" thread you posted your mathematical background?
Alternatively, could you re-post that information?

I ask because the answer to "In S(x,y,z) = ... what is x" should be obvious to anyone who knows how function notation works. x is the first argument of the function S.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby eSOANEM » Tue Jul 30, 2013 10:21 pm UTC

steve waterman wrote:I posted this just moments ago and somehow it ended up up page 13, and then page 14 has an old post, that it certainly out of order, so I will post this again...and stop for today.

Mathematically,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x.
3. When S or S' are not coincident, x' = x.

Galilean transformation,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x because vt = 0.
3. When S and S' are not coincident, x' = x -vt.

Given S(x,y,z)...does S have inherent coordinates (x,y,z) wrt S(0,0,0)?



No, your mathematical 3 is false. That contradicts the definition of "not coincident".
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 10:25 pm UTC

beojan wrote:
steve waterman wrote:added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Could you point me to where in the 5000+ post ex-"pressures" thread you posted your mathematical background?
Alternatively, could you re-post that information?

I ask because the answer to "In S(x,y,z) = ... what is x" should be obvious to anyone who knows how function notation works. x is the first argument of the function S.

I think he was pointing to this earlier.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Tue Jul 30, 2013 10:31 pm UTC

beojan wrote:
steve waterman wrote:added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Could you point me to where in the 5000+ post ex-"pressures" thread you posted your mathematical background?
Alternatively, could you re-post that information?

I ask because the answer to "In S(x,y,z) = ... what is x" should be obvious to anyone who knows how function notation works. x is the first argument of the function S.

S was defined as a Cartesian coordinate system.

Mathematically,
Given Cartesian coordinate system S(first coordinate,second coordinate),
the first coordinate wrt S(0,0) = the distance from S(0,0) to S(the first coordinate,0)

Given Cartesian coordinate system S'(first coordinate,second coordinate),
the first coordinate wrt S'(0,0) = the distance from S'(0,0) to S'(the first coordinate,0)
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Tue Jul 30, 2013 10:34 pm UTC

steve waterman wrote:
beojan wrote:
steve waterman wrote:added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Could you point me to where in the 5000+ post ex-"pressures" thread you posted your mathematical background?
Alternatively, could you re-post that information?

I ask because the answer to "In S(x,y,z) = ... what is x" should be obvious to anyone who knows how function notation works. x is the first argument of the function S.

S was defined as a Cartesian coordinate system.

Mathematically,
Given Cartesian coordinate system S(first coordinate,second coordinate),
the first coordinate wrt S(0,0) = the distance from S(0,0) to S(the first coordinate,0)

Given Cartesian coordinate system S'(first coordinate,second coordinate),
the first coordinate wrt S'(0,0) = the distance from S'(0,0) to S'(the first coordinate,0)

The first coordinate of what with respect to S(0,0)? If you're trying to do coordinate systems without points, what are the coordinates pointing to?

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby bluebambue » Tue Jul 30, 2013 10:41 pm UTC

steve waterman wrote:Mathematically,
Given Cartesian coordinate system S(first coordinate,second coordinate),
the first coordinate wrt S(0,0) = the distance from S(0,0) to S(the first coordinate,0)

Given Cartesian coordinate system S'(first coordinate,second coordinate),
the first coordinate wrt S'(0,0) = the distance from S'(0,0) to S'(the first coordinate,0)

To avoid confusion, I think this should be changed to:

Given Cartesian coordinate system S(first coordinate in S,second coordinate in S)*,
the first coordinate wrt S(0,0) = the distance from S(0,0) to S(the first coordinate,0)

Given Cartesian coordinate system S'(first coordinate in S',second coordinate in S')**,
the first coordinate wrt S'(0,0) = the distance from S'(0,0) to S'(the first coordinate of S',0)

As first coordinate in S doesn't necessarily equal first coordinate in S'
*Which would denote a point
**Also denotes a point

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Tue Jul 30, 2013 10:52 pm UTC

steve waterman wrote:
beojan wrote:
steve waterman wrote:added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Could you point me to where in the 5000+ post ex-"pressures" thread you posted your mathematical background?
Alternatively, could you re-post that information?

I ask because the answer to "In S(x,y,z) = ... what is x" should be obvious to anyone who knows how function notation works. x is the first argument of the function S.

S was defined as a Cartesian coordinate system.

Mathematically,
Given Cartesian coordinate system S(first coordinate,second coordinate),
the first coordinate wrt S(0,0) = the distance from S(0,0) to S(the first coordinate,0)

Given Cartesian coordinate system S'(first coordinate,second coordinate),
the first coordinate wrt S'(0,0) = the distance from S'(0,0) to S'(the first coordinate,0)

Heavily simplified (i.e. for cartesian coordinate systems, oriented such that the x or x' axis is →, and the y or y' axis is ↑, etc.), to move from the origin of a coordinate system to a point, you must go along some distance, then up some distance.

The first coordinate in any coordinate system is the distance moved along, and the second is the distance moved up.

As should hopefully be obvious, if the origins of two coordinate systems are not in the same place, the distance moved along the x axis from the origin of the first coordinate system to the point is not (necessarily) the same as the distance moved along the x axis from the origin of the second coordinate system to the point, and the distance moved up the y axis from the origin of the first coordinate system to the point is not (necessarily) the same as the distance moved up the y axis from the origin of the second coordinate system to the point.

WibblyWobbly wrote:
beojan wrote:
steve waterman wrote:added - instead of the above question, I would rather hear the answer to this one. please.
Given S(x,y,z) ...does x = the distance from S(0,0,0) to (x,0,0)?

Could you point me to where in the 5000+ post ex-"pressures" thread you posted your mathematical background?
Alternatively, could you re-post that information?

I ask because the answer to "In S(x,y,z) = ... what is x" should be obvious to anyone who knows how function notation works. x is the first argument of the function S.

I think he was pointing to this earlier.

Thank you WibblyWobbly.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Pfhorrest » Tue Jul 30, 2013 11:08 pm UTC

steve waterman wrote:Given Cartesian coordinate system S(first coordinate,second coordinate),
the first coordinate wrt S(0,0) = the distance from S(0,0) to S(the first coordinate,0)

The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.

steve waterman wrote:Given Cartesian coordinate system S'(first coordinate,second coordinate),
the first coordinate wrt S'(0,0) = the distance from S'(0,0) to S'(the first coordinate,0)

The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point.

Coordinates tell you how far away a given point is from the origin of a given coordinate system. That's all they do. That's what they're for.

If we're talking about the same point, which we are when translating coordinates, then those distances will only be the same if the origins are in the same place.

If the origins are in different places, then the distances from them to any given point will be different, so the first coordinate of that point will differ between those two systems.

The distances between the two origins and two points each the same distance away from their respective origins will still be the same, because duh, we just picked those two points to be the same distance away from the two origins. But that has nothing to do with coordinate transformations (which are about the differences in coordinates of one point in two coordinate systems), so what does that matter?

Seriously, watch the damn animation again. It explains exactly what we all mean by x and x' and so on, and how it's different from what you take those to mean. It's all about the different distances from one point to two different origins, and it has nothing to do with equal lengths being equal, which is totally trivial and completely accepted by everyone.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Wed Jul 31, 2013 12:01 pm UTC

Wow, what wonderful feedback and animation. These comments and definitions should definitely help.

overview-
I quite understand how this appears to be conclusive for your side....
the line segment x' = the line segment x - line segment d. This is of course true.
However, you are using line segments not restricted to distances from an origin.
I will come back to explain this in greater detail after I check to see if what written below is okay, with all.

Let point P be at S(2,0) when S and S' are coincident.
x' = The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point.
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
Therefore, x = x', when S and S' are coincident.
OKAY?

added -
let S and S', now become separated from their temporary coincidence,
The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point =
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
TRUE?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Wed Jul 31, 2013 12:33 pm UTC

Steve, you begin with two (3d, cartesian) coordinate systems (say, S and S') which are coincident.
You then reposition one, so that they are no longer coincident.

Can you rigorously define (and explain) what you mean by:
1) coincident
2) reposition / move

Edit: Steve, when answering this post (and only for the purpose of answering this post), please ignore the posts below.
I really don't think Steve defines either of those words in a way close to how the rest of use define them, so it's probably best to wait for him to define them.
Last edited by beojan on Wed Jul 31, 2013 12:56 pm UTC, edited 1 time in total.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby eSOANEM » Wed Jul 31, 2013 12:48 pm UTC

steve waterman wrote:Wow, what wonderful feedback and animation. These comments and definitions should definitely help.

overview-
I quite understand how this appears to be conclusive for your side....
the line segment x' = the line segment x - line segment d. This is of course true.
However, you are using line segments not restricted to distances from an origin.
I will come back to explain this in greater detail after I check to see if what written below is okay, with all.

Let point P be at S(2,0) when S and S' are coincident.
x' = The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point.
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
Therefore, x = x', when S and S' are coincident.
OKAY?

added -
let S and S', now become separated from their temporary coincidence,
The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point =
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
TRUE?


To the overview: it is important to note that S and S' do not necessarily have the same origin.

To the second section: yes

To the third: very nearly. A corrected version is given below:

let S and S', now become separated from their temporary coincidence,
The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point
x = The first coordinate (in S) of the same point as in the previous line is the distance along the first axis (of S) from the origin (of S) to that point.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Wed Jul 31, 2013 12:50 pm UTC

steve waterman wrote:Let point P be at S(2,0) when S and S' are coincident.
x' = The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point.
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
Therefore, x = x', when S and S' are coincident.
OKAY?
To be more precise, and given the common definition of distance in the cartesian plane, the numeric value of x is what is equal to the distance. But this isn't the issue, really, so I'll gloss over it, and accept what you've written above. Notice I've colored your conclusion in green.

steve waterman wrote:let S and S', now become separated from their temporary coincidence,
At this point the green statement, above, becomes irrelevant. It is now a different situation because S and S' are no longer coincident. x no longer equals x'. Nothing which relies on that equality is true any more.

steve waterman wrote:The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point =
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
TRUE?
No. Not true.

The blue part is true enough by itself. (but not the orange equal sign at the end)
The green part is true enough by itself.
The equality in orange is the part that is false. It depends on x=x' from the first part, (highlighted there in green) which is no longer true because you moved the system out of coincidence.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Wed Jul 31, 2013 1:29 pm UTC

steve waterman wrote:Let point P be at S(2,0) when S and S' are coincident.
x' = The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point.
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
Therefore, x = x', when S and S' are coincident.
OKAY?

added -
let S and S', now become separated from their temporary coincidence,
The first coordinate (in S') of a point is the distance along the first axis (of S') from the origin (of S') to that point =
x = The first coordinate (in S) of a point is the distance along the first axis (of S) from the origin (of S) to that point.
TRUE?


Your first block S = S'

Your second block S =/= S'

SO WHY IS IT A FUCKING SURPRISE WHEN x =/= x' !?!?!?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Chaoszerom » Wed Jul 31, 2013 1:52 pm UTC

If that's not enough, let's try some numbers. S and S' are two 2D coincident systems. I'm going to pick a point P, and it can be found at S(2,0) or S'(2,0). The x coord of S equals the x coord of S' when the systems are coincident (2=2)

Now let's "move" S' four units in the negative x direction. Now, the point can be found at S'(6,0), but still at S(2,0). If we tried to equate the x coords now, we'd get 2=6. The thing is, these systems are now not coincident, and so we can't just equate the x coords like that. We now need a mapping, such that we can convert from one coordinate system to the other (in this case, we add 4 to the x coord in S to get the x coord in S' (we get 6=2+4, which looks oddly like x'=x-d, dontcha think?)).

If someone has two transparency sheets and a video camera, I can think of a demonstration of system ideas that would work.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Wed Jul 31, 2013 2:40 pm UTC

Image


Image
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Vetala » Wed Jul 31, 2013 2:56 pm UTC

steve waterman wrote:Two pointless images

Nope, nope, nope, nope, nope. And once more for good measure.... nope.

You're still (quite deliberately) using the terms differently from the rest of reality. Go back and watch Pfhorrest's animation again. I'd suggest at least 5 more times. It's not even worth trying to explain what the errors are in those pictures because it's all in Pfhorrest's animation. Doesn't matter how many times you try to subtly restate your claims, they aren't suddenly going to become right, and I would hope by this point that nobody will accidentally write something that sounds like agreement with you, so you shouldn't be able to trick someone in to "agreeing" either no matter how many ways you rephrase it.

Again, go back and watch Pfhorrest's animation (and this time as something more than mere entertainment).

Edit to add: Seriously Pfhorrest, that animation needs to be the canonical introduction to coordinate systems for anyone learning geometry. Many kudos. :wink:
Last edited by Vetala on Wed Jul 31, 2013 3:02 pm UTC, edited 1 time in total.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby induction » Wed Jul 31, 2013 2:59 pm UTC

Steve, what is the first coordinate of point P in the blue reference frame of your second picture?

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Wed Jul 31, 2013 3:09 pm UTC

steve waterman wrote:Image
Holy crap, I am horrible at math and I know that's completely and totally irrelevant. You have X = 'X-1

..okay?

In what possible function or usage would it ever matter that 2 away from the origin on the X axis is a different point on two different graphs? How is that relevant to goddamn anything, ever?

Seriously, how is that in any way useful? If your 0,0 points are in two separate places, then your 2,0 points are going to be in two separate places but that's an astounding "No shit, Sherlock" observation.
Last edited by SecondTalon on Wed Jul 31, 2013 3:10 pm UTC, edited 1 time in total.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Wed Jul 31, 2013 3:10 pm UTC

steve waterman wrote:Image


Image

Ok, with those images, can you locate the point (2,3) in the red system (i.e. the point S(2,3)), and post images, with this point marked, with both coincident and non coincident coordinate systems, as before.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby waidh » Wed Jul 31, 2013 3:52 pm UTC

WibblyWobbly wrote:FWIW, I don't think Steve is trolling, personally. He's done too much work, put up websites and YouTube videos and carried on this argument for more than a year.

Much more than one year: his postings on the Wikipedia Talk page for Galilean Transformation date back to September 2009, someone already discussed this with Steve on another forum back in October 2008, and on his own website, one of the diagrams leading Steve to his Theory Of Everything But Relativity bears the note "November 95".

Chaoszerom wrote:If someone has two transparency sheets and a video camera, I can think of a demonstration of system ideas that would work.

Would an image suffice?
Spoiler:
posted by Steve himself, June 2012

Image
You see, even Steve can do the Galilean transformation. But it didn't stop him from questioning the Galilean and after he posted this image (immediatly distracting from his ability to do the transformation by discussing invariance) the discussion went on for another 114 forum pages (à 40 posts) before the thread was permanently locked.


SecondTalon wrote:Your first block S = S'

Your second block S =/= S'

SO WHY IS IT A FUCKING SURPRISE WHEN x =/= x' !?!?!?

I suspect the problem is, that it's just not what Steve wants to hear. He said
[...] I kept getting confronted with
"you cannot say that [the universe is made of packed spheres with fixed size etc.] because of relativity", in numerous meetings at mcGill. Finally I thought, well I have no oyher choice do I, let's check it out.

I had a book with in the transformations with lorentz too, so I started with x' = x-vt, as it does...and worked out ifthe math was okay in each equation...it was. So i concluded that the only chance of it being wrong would have to be that equation. So, my search, quite luckily, started there. [...]

It seems, all he's looking for is a way in which this equation is wrong that makes relativity wrong so people stop discarding Steve's theory because of relativity. He's not looking for the ways in which relativity and the Galilean work to make his theory wrong.


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