Relativity or something [Split from "Pressures"]
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Re: 1067: "Pressures"
Well, a coordinate system is defined as a map from some manifold S to R^{3}. You can see, then, how I might get confused when you want to discuss coordinate systems but refuse to admit the notion of points in the manifold they are functions from. Certainly, you won't get transformations like x' = x  d that presume a fixed point in the manifold to work, but that's hardly news.

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Re: 1067: "Pressures"
steve waterman wrote:I AM NOT TALKING ABOUT THOSE RELATIONSHIPS AT ALL...what is so damn hard about that!...why do i keep hearing about them...they are not part of my proof.
People keep bringing it up because it's what the coordinate transformations are referring to.
Seriously though, please reply to chenille and gmalivuk before you do me. They're generally doing a better job of expressing themselves than I am.
Last edited by JudeMorrigan on Tue Jun 19, 2012 1:29 am UTC, edited 2 times in total.
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Re: 1067: "Pressures"
There is nothing physical in our responses to you, either, except when we use your own illustrations to try to get you to understand something, since you don't seem too good at reasoning about purely abstract mathematical spaces.
But manifolds are purely mathematical. Vector spaces are purely mathematical. Coordinate systems are purely mathematical. A point p in 3D Euclidean manifold M might have coordinates (x,y,z) in a "red" coordinate system with its origin at point r. If we have another "blue" coordinate system with origin at a point b which is different from r, then the point p, which hasn't moved, will have coordinates (x',y',z') in the blue coordinate system.
Again: the point p has two ordered triplets of coordinates, because we can describe the space with two noncoincident coordinate systems. Those two ordered triplets, (x,y,z) and (x',y',z'), are just lists of 3 real numbers. They only happen to refer to the point p in the specified coordinate systems. If we had a third, "green" set of coordinates, the location of p (which still hasn't actually changed in the underlying space M, by the way) could be specified with a third triplet of numbers, (x'',y'',z''), which will not necessarily be at all similar to (x,y,z) and (x',y',z'). We might have (x,y,z) = (1,2,3), and maybe (x',y',z') = (56000,73,0), because the blue origin is rather far away from the red origin. In green, perhaps p (still the same point it always was at the same place it has always occupied) is at (x'',y'',z'') = (pi, e, sin(42)).
If we start out with red and blue coincident, so for every point in M the red coordinates (x,y,z) are the same as the blue coordinates (x',y',z'), and then we shift the blue coordinate system d units to the right, then the point p (which, for those keeping score at home, is still at the same place in M that it has always been, since we're only moving coordinate systems around and leaving p comfortably where it started) is still at (x,y,z) in the red system, because the red system hasn't moved, but is now at (x',y',z') = (xd,y,z) in the blue system, because the blue system is d units to the right, which means the x'coordinate of every point in M has become d units less than it was before. So if initially p was at (3,3,2) in red and blue, and then we slide blue to the right 5 units, p is still at (3,3,2) in red coordinates (because neither p nor the red coordinates have moved anywhere), but is now at (2,3,2) in blue coordinates, because the blue origin moved and is now on the other side of p than it was when it started.
See? Absolutely nothing physical in this whole account, and yet we still end up with the formula relativity says we should get. No tables, no rulers, no Tokyo. Just pure abstract math.
Do you get it now?
But manifolds are purely mathematical. Vector spaces are purely mathematical. Coordinate systems are purely mathematical. A point p in 3D Euclidean manifold M might have coordinates (x,y,z) in a "red" coordinate system with its origin at point r. If we have another "blue" coordinate system with origin at a point b which is different from r, then the point p, which hasn't moved, will have coordinates (x',y',z') in the blue coordinate system.
Again: the point p has two ordered triplets of coordinates, because we can describe the space with two noncoincident coordinate systems. Those two ordered triplets, (x,y,z) and (x',y',z'), are just lists of 3 real numbers. They only happen to refer to the point p in the specified coordinate systems. If we had a third, "green" set of coordinates, the location of p (which still hasn't actually changed in the underlying space M, by the way) could be specified with a third triplet of numbers, (x'',y'',z''), which will not necessarily be at all similar to (x,y,z) and (x',y',z'). We might have (x,y,z) = (1,2,3), and maybe (x',y',z') = (56000,73,0), because the blue origin is rather far away from the red origin. In green, perhaps p (still the same point it always was at the same place it has always occupied) is at (x'',y'',z'') = (pi, e, sin(42)).
If we start out with red and blue coincident, so for every point in M the red coordinates (x,y,z) are the same as the blue coordinates (x',y',z'), and then we shift the blue coordinate system d units to the right, then the point p (which, for those keeping score at home, is still at the same place in M that it has always been, since we're only moving coordinate systems around and leaving p comfortably where it started) is still at (x,y,z) in the red system, because the red system hasn't moved, but is now at (x',y',z') = (xd,y,z) in the blue system, because the blue system is d units to the right, which means the x'coordinate of every point in M has become d units less than it was before. So if initially p was at (3,3,2) in red and blue, and then we slide blue to the right 5 units, p is still at (3,3,2) in red coordinates (because neither p nor the red coordinates have moved anywhere), but is now at (2,3,2) in blue coordinates, because the blue origin moved and is now on the other side of p than it was when it started.
See? Absolutely nothing physical in this whole account, and yet we still end up with the formula relativity says we should get. No tables, no rulers, no Tokyo. Just pure abstract math.
Do you get it now?
 steve waterman
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Re: 1067: "Pressures"
gmalivuk wrote:There is nothing physical in our responses to you, either, except when we use your own illustrations to try to get you to understand something, since you don't seem too good at reasoning about purely abstract mathematical spaces.
But manifolds are purely mathematical. Vector spaces are purely mathematical. Coordinate systems are purely mathematical. A point p in 3D Euclidean manifold M might have coordinates (x,y,z) in a "red" coordinate system with its origin at point r. If we have another "blue" coordinate system with origin at a point b which is different from r, then the point p, which hasn't moved, will have coordinates (x',y',z') in the blue coordinate system.
Again: the point p has two ordered triplets of coordinates, because we can describe the space with two noncoincident coordinate systems. Those two ordered triplets, (x,y,z) and (x',y',z'), are just lists of 3 real numbers. They only happen to refer to the point p in the specified coordinate systems. If we had a third, "green" set of coordinates, the location of p (which still hasn't actually changed in the underlying space M, by the way) could be specified with a third triplet of numbers, (x'',y'',z''), which will not necessarily be at all similar to (x,y,z) and (x',y',z'). We might have (x,y,z) = (1,2,3), and maybe (x',y',z') = (56000,73,0), because the blue origin is rather far away from the red origin. In green, perhaps p (still the same point it always was at the same place it has always occupied) is at (x'',y'',z'') = (pi, e, sin(42)).
If we start out with red and blue coincident, so for every point in M the red coordinates (x,y,z) are the same as the blue coordinates (x',y',z'), and then we shift the blue coordinate system d units to the right, then the point p (which, for those keeping score at home, is still at the same place in M that it has always been, since we're only moving coordinate systems around and leaving p comfortably where it started) is still at (x,y,z) in the red system, because the red system hasn't moved, but is now at (x',y',z') = (xd,y,z) in the blue system, because the blue system is d units to the right, which means the x'coordinate of every point in M has become d units less than it was before. So if initially p was at (3,3,2) in red and blue, and then we slide blue to the right 5 units, p is still at (3,3,2) in red coordinates (because neither p nor the red coordinates have moved anywhere), but is now at (2,3,2) in blue coordinates, because the blue origin moved and is now on the other side of p than it was when it started.
See? Absolutely nothing physical in this whole account, and yet we still end up with the formula relativity says we should get. No tables, no rulers, no Tokyo. Just pure abstract math.
Do you get it now?
Again, there is no selected point P...there is no third system..there is no event...in MY PROOF. Dude, there is a point P in {your proof/logic).
You still have no clue what i am talking about ...so very close this time,..but you gotta use my GIVEN for my proof...not your GIVEN point P...I say, no point P, as after all, it is my proof. So...two Cartesian coordinate systems with no selected point in either,,,as depicted visually in observation 1 and 2.
Care to try your logic with no selected points...in accordance with the first two depictions presented ? I would actually like to hear that...
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Re: 1067: "Pressures"
You don't actually have to pick a specific p for it to work. The idea is that it works the same way for any point you might pick in the whole space. That is it works for the whole space. If you slide your blue coordinate system d units to the right, then everywhere in the space will have coordinates (x,y,z) in the red system and (xd,y,z) in the blue system, for some set of real numbers x, y, and z.
What that means is that the *point* (x,y,z)_{RED} = (xd,y,z)_{BLUE}. So the *numbers* x' = xd, y' = y, and z' = z.
What that means is that the *point* (x,y,z)_{RED} = (xd,y,z)_{BLUE}. So the *numbers* x' = xd, y' = y, and z' = z.
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Re: 1067: "Pressures"
gmalivuk wrote:You don't actually have to pick a specific p for it to work. The idea is that it works the same way for any point you might pick in the whole space. That is it works for the whole space. If you slide your blue coordinate system d units to the right, then everywhere in the space will have coordinates (x,y,z) in the red system and (xd,y,z) in the blue system, for some set of real numbers x, y, and z.
However, picking any point oher than P is still selecting a point...NO selected points/named...just coordinate points.
If you slide your blue coordinate system d units to the right, then everywhere in the space will have coordinates (x,y,z) in the red system and (xd,y,z) in the blue system, for some set of real numbers x, y, and z.
True...yes, agreed, correct. nice of you to mention this again. this is the relationship of the coordinates in one system to the other.
Now, that aside...if we got us NO SELECTED POINTS, and just the two Cartesian coordinate systems...
is the equation in observation 1 correct ?
is the equation in observation 2 correct ?
Last edited by steve waterman on Tue Jun 19, 2012 2:12 am UTC, edited 1 time in total.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
"Be careful of what you believe, you are likely to make it the truth."
steve
Re: 1067: "Pressures"
You can't just have two coordinate systems, steve, you need a set M (I was calling it S) where they are defined. It's not a third system, it's the domain of the functions. That's inherent in what a function is. In particular, you will note RED and BLUE are not functions on coordinates. You can get a function from R^{3} to itself by composing RED and BLUE^{1}. If that's what you want, note (0,0,0) does not map to (0,0,0).
If you think we are missing something, it might help if you offered an actual proof. All you are giving is some diagrams, which look like there is an underlying manifold represented by the table so are misleading if there is not, but nothing in terms of math. After the transformation where we define the function BLUE = RED + (3,0,0), why do you insist x' = x? That's the equation that looks wrong.
Edited for clarity, I hope.
If you think we are missing something, it might help if you offered an actual proof. All you are giving is some diagrams, which look like there is an underlying manifold represented by the table so are misleading if there is not, but nothing in terms of math. After the transformation where we define the function BLUE = RED + (3,0,0), why do you insist x' = x? That's the equation that looks wrong.
Edited for clarity, I hope.
Last edited by chenille on Tue Jun 19, 2012 2:22 am UTC, edited 3 times in total.
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Re: 1067: "Pressures"
If there are no points, then there is no underlying space. If there is no underlying space, your coordinate systems don't actually mean anything. As in, they are literally meaningless. Nonsense. Not even wrong.steve waterman wrote:However, picking any point oher than P is still selecting a point...NO points are selected.
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Re: 1067: "Pressures"
chenille wrote:You can't just have two coordinate systems, steve, you need a set M (I was calling it S) where they are defined. It's not a third system, it's the domain of the functions. That's inherent in what a function is. In particular, you will note RED and BLUE are not functions on coordinates; you can get a function on them by composing RED and BLUE^{1}, but that's very different than a transformation of coordinates.
If you think we are missing something, it might help if you offered an actual proof. All you are giving is some diagrams, which look like there is an underlying manifold represented by the table so are misleading if there is not, but nothing in terms of math. After the transformation where we define the function BLUE = RED + (3,0,0), why do you insist x' = x?
can you tell me if observation 1 is correct, in your opinion...observation 2 ?
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
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Re: 1067: "Pressures"
No, your observations are not correct. They are not even wrong, because you're talking about coordinate systems without an underlying space, which doesn't make sense. (And note that I'm not simply claiming it doesn't make sense to me. I'm claiming that it literally has no meaning.)
Last edited by gmalivuk on Tue Jun 19, 2012 2:32 am UTC, edited 1 time in total.
Re: 1067: "Pressures"
steve waterman wrote:can you tell me if observation 1 is correct, in your opinion...observation 2 ?
No, I can't. Your pictures look like coordinate systems on a manifold, and if that is what we were talking about, observation 1 would be true and observation 2 would not, since the functions x' and x are different at nearly every point in said manifold. That's the setup people use when they define coordinate transforms, where there is no problem defining x' = x + d.
However, you have repeatedly refused to admit a manifold or points, so I have no idea what you think your pictures show. I'd need you to actually define your terms. If x' and x aren't functions on a common domain, what are they, and what does it mean to move one?
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Re: 1067: "Pressures"
chenille wrote:steve waterman wrote:can you tell me if observation 1 is correct, in your opinion...observation 2 ?
No, I can't. Your pictures look like coordinate systems on a manifold, and if that is what we were talking about, observation 1 would be true and observation 2 would not, since the functions x' and x are different at nearly every point in said manifold. That's the setup people use when they define coordinate transforms, where there is no problem defining x' = x + d.
However, you have repeatedly refused to admit a manifold or points, so I have no idea what you think your pictures show. I'd need you to actually define your terms. If x' and x aren't functions on a common domain, what are they, and what does it mean to move one?
x is not a function...it is the variable distance along x from the red origin...x is a variable coordinate
coordinates NEVER move wrt their own system...
coordinates points of course do move, wrt the other system, which you are focused upon..and continue to ignore this fact.
coordinates locations/values NEVER change wrt their OWN system... can you agree with that or not?
Last edited by steve waterman on Tue Jun 19, 2012 3:00 am UTC, edited 2 times in total.
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Re: 1067: "Pressures"
whateveries wrote:time for a youtube video.
Yes, perhaps it is time for that...
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
"Be careful of what you believe, you are likely to make it the truth."
steve
Re: 1067: "Pressures"
Steve,
I have a footlong ruler here marked in inches. I bought it at the grocery store, from their stationary section. Do you have something like that? I suspect you do. Doesn't even need to be an inchruler, yours can be marked in cm if you like. Please pull it out, and hold on to it for a sec. Don't put it down on any table or any other surface. I'm doing the same with mine. Just rulers considered in the abstract apart from anything they're measuring.
Look at the third mark on your ruler. I'm looking at the third mark on mine. Does your third mark equal my third mark?
Does that question even make sense, unless we're putting our rulers down against something we're both measuring?
I have a footlong ruler here marked in inches. I bought it at the grocery store, from their stationary section. Do you have something like that? I suspect you do. Doesn't even need to be an inchruler, yours can be marked in cm if you like. Please pull it out, and hold on to it for a sec. Don't put it down on any table or any other surface. I'm doing the same with mine. Just rulers considered in the abstract apart from anything they're measuring.
Look at the third mark on your ruler. I'm looking at the third mark on mine. Does your third mark equal my third mark?
Does that question even make sense, unless we're putting our rulers down against something we're both measuring?
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Re: 1067: "Pressures"
steve waterman wrote:coordinates locations/values NEVER change wrt their OWN system... can you agree with that or not?
I can maybe agree, though it's not normal terminology. The distance between points is a function, coordinates are defined to be functions, and yet you say x is a distance, coordinate, and still an independent variable. Ok, let's say that it is really the last; we only look at variables (x,y,z) with values in R^{3}, which I take it you do not believe to be changed by when we move the system. Sure, triples are triples.
But then what does a coordinate transformation mean, if it's not about different coordinates being assigned to points, the way it is normally defined? And what can any of it prove about the transformation x' = x  d, which as explained is really a statement about functions taken over points on a manifold, and so does not actually apply to your variables in R^{3} at all?
Because, you know, that formula works when coordinates are defined as functions on a manifold, it is useful, and that framework is what the Galilean transformations are based on. It seems you require x' = x when you're talking about something else entirely; well, great, but that has nothing to do with what mathematicians or physicists are doing, so there's no real contradiction.
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Re: 1067: "Pressures"
1 coordinates remain affixed to to their own systems
being once coincident...regardless of which triplet is chosen as numeric values...
(x',y',z' ) in its own system of BLUE maps exactly to (x,y,z) in the RED system.
2 letting (x',y',z' ) in Blue = ( xd,y,z) in Red reassigns the fixed coordination in the moved Blue system
being once coincident...regardless of which triplet is chosen as numeric values...
(x',y',z' ) in its own system of BLUE no longer maps exactly to (x,y,z) in the RED system.
Presently, i am alone in seeing the above logical scenario as generating a mathematical inequality.
and apparently also alone in this complete understanding as well...
I accept that ...(x',y',z') in Blue transforms to (x,y,z) in Blue d [ comparing blue to transformed blue ]
I accept that... (x,y,z) in Red transforms to (x',y',z') in Red +d [ comparing red to transformed red ]
i deny that ...(x',y',z' ) in Blue = (xd,y,z) in Red [ comparing transformed blue to red ]
because...(x',y',z' ) in Blue = (x,y,z) in Red [ comparing blue to red ]
Someone put on your thinking cap, and work out what I am saying above. Remember PLEASE PLEASE...nothing Physics or physical, AND
as well, no selected triplets..just coordinate points.
Does (x',y',z' ) in Blue = (xd,y,z) in Red in this depiction???? Surely Not.
being once coincident...regardless of which triplet is chosen as numeric values...
(x',y',z' ) in its own system of BLUE maps exactly to (x,y,z) in the RED system.
2 letting (x',y',z' ) in Blue = ( xd,y,z) in Red reassigns the fixed coordination in the moved Blue system
being once coincident...regardless of which triplet is chosen as numeric values...
(x',y',z' ) in its own system of BLUE no longer maps exactly to (x,y,z) in the RED system.
Presently, i am alone in seeing the above logical scenario as generating a mathematical inequality.
and apparently also alone in this complete understanding as well...
I accept that ...(x',y',z') in Blue transforms to (x,y,z) in Blue d [ comparing blue to transformed blue ]
I accept that... (x,y,z) in Red transforms to (x',y',z') in Red +d [ comparing red to transformed red ]
i deny that ...(x',y',z' ) in Blue = (xd,y,z) in Red [ comparing transformed blue to red ]
because...(x',y',z' ) in Blue = (x,y,z) in Red [ comparing blue to red ]
Someone put on your thinking cap, and work out what I am saying above. Remember PLEASE PLEASE...nothing Physics or physical, AND
as well, no selected triplets..just coordinate points.
Does (x',y',z' ) in Blue = (xd,y,z) in Red in this depiction???? Surely Not.
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Re: 1067: "Pressures"
steve waterman wrote:Does (x',y',z' ) in Blue = (xd,y,z) in Red in this depiction???? Surely Not.
No, no no, of course it doesn't. That's just silly.
You've rotated one of the frames.
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Re: 1067: "Pressures"
Steve 
you are misunderstanding, once again.
Your reasoning is specious, mostly because you are misunderstanding what the Galilean function does.
At d=0, (x',y',z') = (x,y,z)
at 0<d<0, (x',y',z') = (x+d,y,z)
The Galilean function deals explicitly with moving coordinate systems (what physicists generally call 'reference frames' or 'inertial reference frames'). I'm not sure how to make this any clearer.
you are misunderstanding, once again.
I accept that ...(x',y',z') in Blue transforms to (x,y,z) in Blue d [ comparing blue to transformed blue ]
I accept that... (x,y,z) in Red transforms to (x',y',z') in Red +d [ comparing red to transformed red ]
i deny that ...(x',y',z' ) in Blue = (xd,y,z) in Red [ comparing transformed blue to red ]
because...(x',y',z' ) in Blue = (x,y,z) in Red [ comparing blue to red ]
Your reasoning is specious, mostly because you are misunderstanding what the Galilean function does.
At d=0, (x',y',z') = (x,y,z)
at 0<d<0, (x',y',z') = (x+d,y,z)
The Galilean function deals explicitly with moving coordinate systems (what physicists generally call 'reference frames' or 'inertial reference frames'). I'm not sure how to make this any clearer.
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Re: 1067: "Pressures"
eran_rathan wrote:Steve 
you are misunderstanding, once again.I accept that ...(x',y',z') in Blue transforms to (x,y,z) in Blue d [ comparing blue to transformed blue ]
I accept that... (x,y,z) in Red transforms to (x',y',z') in Red +d [ comparing red to transformed red ]
i deny that ...(x',y',z' ) in Blue = (xd,y,z) in Red [ comparing transformed blue to red ]
because...(x',y',z' ) in Blue = (x,y,z) in Red [ comparing blue to red ]
Your reasoning is specious, mostly because you are misunderstanding what the Galilean function does.
At d=0, (x',y',z') = (x,y,z)
at 0<d<0, (x',y',z') = (x+d,y,z)
The Galilean function deals explicitly with moving coordinate systems (what physicists generally call 'reference frames' or 'inertial reference frames'). I'm not sure how to make this any clearer.
Of course it does, I agree. however, my proof is not about the Galilean yet..it is about x' = xd.
coordinates stay affixed to their own system even if d is (2,3,5.678)...mathematical fact
The Galilean alters the moved set of coordinate values, fixed and equal in both systems at coincidence....mathematical fact
I fear that conversation between you and I will only continue to be circular. You and I can only agree that we disagree.
At this point, no one has gotten it...perhaps i will try and make a tiny video...and so, I will want time to switch gears and not continue flogging this here.
i gave it a shot or two. Got some good feedback, got some poor feedback too. So, since i have close to zero agreement here, it makes sense to depart xkcd forums for a while. Y'all have my coordinates and know how to reach me if you have something mathematical to say. if you have any comments with even a pinch of Physics or anything physical, please do not share them with me.
http://watermanpolyhedron.com/3picgalilean.html
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
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Re: 1067: "Pressures"
steve waterman wrote:coordinates stay affixed to their own system even if d is (2,3,5.678)...mathematical fact
It's a mathematical fact which is completely irrelevant to the subject of coordinate transformations.
The Galilean alters the moved set of coordinate values, fixed and equal in both systems at coincidence....mathematical fact
No, it doesn't. Not in the sense that you mean it.
I fear that conversation between you and I will only continue to be circular.
Well, yeah. That much has become pretty obvious.
Y'all have my coordinates and know how to reach me if you have something mathematical to say. if you have any comments with even a pinch of Physics or anything physical, please do not share them with me.
And as a final comment, your definitions of what does or does not qualify as mathematical remain peculiar at best.
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Re: 1067: "Pressures"
I apologize for breaking my own damn rules, to you all. No wonder why i am having so much difficulty.
The word Galilean should never have been said by me...what a terrible goof.
Since this IS a math challenge only, that should have been obvious to me prior to this...so be it.
So, ..the page is now called...my coordinate geometry challenge
all three depictions have been redone to reflect this math only restriction...
so as impossible as it might be to ignore every damn thing said here at xkcd...by me, i was misdirecting this voyage,
and I do so wish,t hat the page could be scrutinized as standalone...and all comments directed at it...not to any xkcd posted so far,
well anything said about the G word, or the ruler word, etc
Perhaps I will actually get my desire "math only" point across this time, perhaps not...
http://watermanpolyhedron.com/3picgalilean.html
The word Galilean should never have been said by me...what a terrible goof.
Since this IS a math challenge only, that should have been obvious to me prior to this...so be it.
So, ..the page is now called...my coordinate geometry challenge
all three depictions have been redone to reflect this math only restriction...
so as impossible as it might be to ignore every damn thing said here at xkcd...by me, i was misdirecting this voyage,
and I do so wish,t hat the page could be scrutinized as standalone...and all comments directed at it...not to any xkcd posted so far,
well anything said about the G word, or the ruler word, etc
Perhaps I will actually get my desire "math only" point across this time, perhaps not...
http://watermanpolyhedron.com/3picgalilean.html
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
"Be careful of what you believe, you are likely to make it the truth."
steve
 eran_rathan
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Re: 1067: "Pressures"
Steve 
I think that these two articles might shed some light on this subject for you:
http://en.wikipedia.org/wiki/Coordinate ... te_systems
http://en.wikipedia.org/wiki/Translation_(geometry)
I think that these two articles might shed some light on this subject for you:
http://en.wikipedia.org/wiki/Coordinate ... te_systems
http://en.wikipedia.org/wiki/Translation_(geometry)
"We have met the enemy, and we are they. Them? We is it. Whatever."
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ
Re: 1067: "Pressures"
Steve, you got it across. You are talking about something different than functions of points in a manifold. Therefore formulae like x' = x  d, which are explicitly concerned with values of functions on points in a manifold, don't work in your scenario. That is straightforward enough, I understand it.
It is not a problem, though, for the formula x' = x  d, because that does work for functions of points in a manifold. And as the sheer confusion over the lack of a manifold here should show you, when mathematicians and physicists talk about coordinate transforms, this is always what they mean. It has nothing to do with physical quantities vs. math; they simply don't have your problem with the formula because they're not doing anywhere close to the same thing as you. Does that make sense to you?
It is not a problem, though, for the formula x' = x  d, because that does work for functions of points in a manifold. And as the sheer confusion over the lack of a manifold here should show you, when mathematicians and physicists talk about coordinate transforms, this is always what they mean. It has nothing to do with physical quantities vs. math; they simply don't have your problem with the formula because they're not doing anywhere close to the same thing as you. Does that make sense to you?
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Re: 1067: "Pressures"
eran_rathan wrote:Steve 
I think that these two articles might shed some light on this subject for you:
http://en.wikipedia.org/wiki/Coordinate ... te_systems
http://en.wikipedia.org/wiki/Translation_(geometry)
Eran 
There is NO transformation in either observation 1 or 2.
Translation, I have found, means different things to different people.
I use the word relocation...
meaning...the mathematical static condition...
in which case, the relocation IS mathematically considered to BE at its final location.
There is definitely NO TRANSFORMATION of any points BETWEEN the two Red and Blue systems...agreed?
The relocated system keeps its own coordinates does it not ?
So this is also NOT about transformations, the G equation, Relativity, selected triplets, translation, displacement, rotation, or motion.
We simply relocated one system away from coincidence...neither having any selected triplets.
btw, i shifted this "G challenge" from my Physics section into my Math section on my home page.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
"Be careful of what you believe, you are likely to make it the truth."
steve
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Re: 1067: "Pressures"
steve waterman wrote:There is definitely NO TRANSFORMATION of any points BETWEEN the two Red and Blue systems...agreed?
"Transformation of a point" or "Transformation of points" doesn't make any sense. Only coordinates can be transformed. Which the formula / function you object to is about.
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Re: 1067: "Pressures"
steve waterman wrote:Eran 
There is NO transformation in either observation 1 or 2.
Translation, I have found, means different things to different people.
I use the word relocation...
meaning...the mathematical static condition...
in which case , the relocation IS at its final location.
There is definitely NO TRANSFORMATION of any points BETWEEN the system...agreed?
So this is also NOT about transformations.
We simply relocated one system away from coincidence...neither having any selected triplets.
relocation == translation. You are MOVING (e.g., translating) one coordinate system IN RELATION to another (in your 2rd image, you state "No longer formerly coincident coordinate systems", i.e., "I had two coordinate systems, but I moved one of them.")
Mirriam Webster says:
relocation: v: to locate again : establish or lay out in a new place
translate: v: to bear, remove, or change from one place, state, form, or appearance to another : transfer, transform <translate ideas into action>
In your initial observation, you postulate coincident coordinate systems. Assuming that said systems are at the same scale, (x',y',z') = (x,y,z).
In your second postulate, you have applied a translation on one of the coordinate systems.
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Re: 1067: "Pressures"
Monika wrote:steve waterman wrote:There is definitely NO TRANSFORMATION of any points BETWEEN the two Red and Blue systems...agreed?
"Transformation of a point" or "Transformation of points" doesn't make any sense. Only coordinates can be transformed. Which the formula / function you object to is about.
Good, now we are may be getting someplace...
No...coordinates NEVER transform...
There is no transformation of any kind required to perform a simple relocation of a once coincident system...because,
they coordinates do stay with their own system.
Only selected and named triplets can be transformed between systems,. as would be point P in Red transforms to the SAME POINT NAME, point P in Blue.
Like me ask you this...red and blue coincident...is that a transformation BETWEEN systems?...or are the coordinates inherent to their own systems and hence it requires NO TRANSFORMATION when the systems are coincident..??? Is observation a transformation ? because no selected points were renamed/mapped to the other system.
Again, it is given that we got no selected points.
if we got no selected points and red and blue coincident...and we relocate blue +3 along x...
The coordinate point at (6,8,1)in Red...has the same relative coordinate lengths ( from their own origin )
as the coordinate location (6,8,1) in Blue... because, as some have already agreed...
if we relocate a system...we also relocate their coordinates, correspondingly.
like to hear a few voices here...and get a consensus of any sort...now that I have actually made this math only....please.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
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Re: 1067: "Pressures"
eran_rathan wrote:steve waterman wrote:Eran 
There is NO transformation in either observation 1 or 2.
Translation, I have found, means different things to different people.
I use the word relocation...
meaning...the mathematical static condition...
in which case , the relocation IS at its final location.
There is definitely NO TRANSFORMATION of any points BETWEEN the system...agreed?
So this is also NOT about transformations.
We simply relocated one system away from coincidence...neither having any selected triplets.
relocation == translation. You are MOVING (e.g., translating) one coordinate system IN RELATION to another (in your 2rd image, you state "No longer formerly coincident coordinate systems", i.e., "I had two coordinate systems, but I moved one of them.")
Mirriam Webster says:
relocation: v: to locate again : establish or lay out in a new place
translate: v: to bear, remove, or change from one place, state, form, or appearance to another : transfer, transform <translate ideas into action>
In your initial observation, you postulate coincident coordinate systems. Assuming that said systems are at the same scale, (x',y',z') = (x,y,z).
In your second postulate, you have applied a translation on one of the coordinate systems.
so...it is NOT a translation...as that implies MOVING...relocation is MOVED/STATIC/establish or lay out in a new place/mathematical
it is not the moving part of that change...just the changed location part. So, relocation is the concept I am going for...translation is totally not.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
"Be careful of what you believe, you are likely to make it the truth."
steve
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Re: 1067: "Pressures"
These two sentences prove beyond any doubt that you are using at least one of the following words in a completely nonstandard way: coordinates, transform, relocation.steve waterman wrote:No...coordinates NEVER transform...
There is no transformation of any kind required to perform a simple relocation of a once coincident system...because,
they coordinates do stay with their own system.
If you want to discuss something using the language of mathematics, you have to make some effort to use the vocabulary correctly, or there is literally no point.
Re: 1067: "Pressures"
steve waterman wrote:No...coordinates NEVER transform...
See this postulate? This is why you don't get coordinate transformations like x' = x  d to work, you're assuming they won't right in your definitions. They're not the definions everyone else uses, which is why x' = x  d works fine for us. Will you acknowledge that difference?
Last edited by chenille on Tue Jun 19, 2012 5:00 pm UTC, edited 1 time in total.
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Re: 1067: "Pressures"
steve waterman wrote:so...it is NOT a translation...as that implies MOVING...relocation is MOVED/STATIC/establish or lay out in a new place/mathematical
it is not the moving part of that change...just the changed location part. So, relocation is the concept I am going for...translation is totally not.
(emphasis mine)
...
you really don't see the contradiction there, Steve, do you.
"I don't want to change the location, I just want to change the location."
My gast is completely flabbered.
"We have met the enemy, and we are they. Them? We is it. Whatever."
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ
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Re: 1067: "Pressures"
gmalivuk wrote:These two sentences prove beyond any doubt that you are using at least one of the following words in a completely nonstandard way: coordinates, transform, relocation.steve waterman wrote:No...coordinates NEVER transform...
There is no transformation of any kind required to perform a simple relocation of a once coincident system...because,
they coordinates do stay with their own system.
If you want to discuss something using the language of mathematics, you have to make some effort to use the vocabulary correctly, or there is literally no point.
okay...that i why I ask questions...to agree on terms...is part of it...
Is observation 1 ...coincident systems...a transformation, according to your understanding/definition?
Given just the Red system...are its coordinates fixed?
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
"Be careful of what you believe, you are likely to make it the truth."
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Re: 1067: "Pressures"
steve waterman wrote:okay...that i why I ask questions...to agree on terms...is part of it...
Is observation 1 ...coincident systems...a transformation, according to your understanding/definition?
Given just the Red system...are its coordinates fixed?
Define what you mean by 'fixed'.
Two coordinate systems, even if coincident, will have a transformation between them  it may be trivial (scale=1,rotation=0,translation=(0,0,0)), but it is still there.
"We have met the enemy, and we are they. Them? We is it. Whatever."
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ
"Google tells me you are not unique. You are, however, wrong."
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 steve waterman
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Re: 1067: "Pressures"
eran_rathan wrote:steve waterman wrote:okay...that i why I ask questions...to agree on terms...is part of it...
Is observation 1 ...coincident systems...a transformation, according to your understanding/definition?
Given just the Red system...are its coordinates fixed?
Define what you mean by 'fixed'.
Two coordinate systems, even if coincident, will have a transformation between them  it may be trivial (scale=1,rotation=0,translation=(0,0,0)), but it is still there.
That is where we differ.
Please supply your OWN definition for
transformation
a Cartesian coordinate system
fixed  meaning  eternal, forever, unchangeable, constant, not variable, remains the same
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
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Re: 1067: "Pressures"
eran_rathan wrote:steve waterman wrote:so...it is NOT a translation...as that implies MOVING...relocation is MOVED/STATIC/establish or lay out in a new place/mathematical
it is not the moving part of that change...just the changed location part. So, relocation is the concept I am going for...translation is totally not.
(emphasis mine)
...
you really don't see the contradiction there, Steve, do you.
"I don't want to change the location, I just want to change the location."
My gast is completely flabbered.
"I don't want to change the physical location, there are none, I just want to change the imagined mathematical location."
We math dudes can do that without having to go from point A to point B...cause its math...bingo, the system is relocated.
Last edited by steve waterman on Tue Jun 19, 2012 5:36 pm UTC, edited 1 time in total.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
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Re: 1067: "Pressures"
steve waterman wrote:eran_rathan wrote:steve waterman wrote:okay...that i why I ask questions...to agree on terms...is part of it...
Is observation 1 ...coincident systems...a transformation, according to your understanding/definition?
Given just the Red system...are its coordinates fixed?
Define what you mean by 'fixed'.
Two coordinate systems, even if coincident, will have a transformation between them  it may be trivial (scale=1,rotation=0,translation=(0,0,0)), but it is still there.
That is where we differ.
Please supply your OWN definition for
transformation
a Cartesian coordinate system
Cartesian coordinate system: a rectilinear coordinate system in two (or three) perpendicular axes, of equal scale, with any point being defined as (x,y,z), the distances parallel to their respective axes. The intersection of the axes are called the origin, which is (0,0,0).
transformation: the change of one coordinate system to another via translation, rotation, and scale functions; also the change between different coordinate system types (i.e. rectangular to polar coordinates).
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Re: 1067: "Pressures"
steve waterman wrote:"I don't want to change the physical location, there are none, I just want to change the imagined mathematical location."
We math dudes can do that without having to go from point A to point B...cause its math...bingo, the system is relocation.
/facepalm
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"Google tells me you are not unique. You are, however, wrong."
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Re: 1067: "Pressures"
eran_rathan wrote:steve waterman wrote:eran_rathan wrote:steve waterman wrote:okay...that i why I ask questions...to agree on terms...is part of it...
Is observation 1 ...coincident systems...a transformation, according to your understanding/definition?
Given just the Red system...are its coordinates fixed?
Define what you mean by 'fixed'.
Two coordinate systems, even if coincident, will have a transformation between them  it may be trivial (scale=1,rotation=0,translation=(0,0,0)), but it is still there.
That is where we differ.
Please supply your OWN definition for
transformation
a Cartesian coordinate system
Cartesian coordinate system: a rectilinear coordinate system in two (or three) perpendicular axes, of equal scale, with any point being defined as (x,y,z), the distances parallel to their respective axes. The intersection of the axes are called the origin, which is (0,0,0).
transformation: the change of one coordinate system to another via translation, rotation, and scale functions; also the change between different coordinate system types (i.e. rectangular to polar coordinates).
Good..that works. re  Cartesian, So, are the (x,y,z) distances/coordinates fixed in an single red system ?
the change of one coordinate system to another
the change of what...selected points? coordinate points ?
this working definition still needs some work...it needs to include the mapping phrase I believe...
here is a good question...
Are coordinate points mapped, as you suggest, or are coordinate points inherent, as the Cartesian definition implies ?
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve
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Re: 1067: "Pressures"
steve waterman wrote:Good..that works. re  Cartesian, So, are the (x,y,z) distances/coordinates fixed in an single system?
The coordinates are meaningless except in relation to their own system.
the change of one coordinate system to another
the change of what...selected points? coordinate points ?
it says it right there: "the change of one coordinate system to another."
Are coordinate points mapped, as you suggest, or are coordinate points inherent, as the Cartesian definition implies?
The Cartesian definition doesn't imply anything. Points are mapped to coordinates in relation to other points, specifically, the origin and the axes.
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