Relativity or something [Split from "Pressures"]
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 Monika
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Re: 1067: "Pressures"
steve,
Imagine you stand in a room. Look at it from the top. In the bottom left corner you have a yellow coordinate system, with the x, y and z axis along the edges of the room (x to the right, y to what is the top from where you are looking, z going to the real top of the room i.e. towards you). Your feet are located at (2/5/0) in the yellow coordinate system.
In the bottom right corner there is a green coordinate system, its x, y, z being other edges of the room (x to the top from your perspective, y to the left (i.e. it coincides/overlaps with the yellow x axis, but with opposite direction and other origin) and z also going to the real top towards you). Your feet are located at (5/1/0) in the green coordinate system. (I.e. the room has a width of 3 from left to right, and some length over 5 in the "topbottom" direction from your perspective.)
If you didn't have a room handy to say "there's the yellow origin and axes" and "over there's the green origin and axes" you would have to describe one in terms of the other, e.g. green in terms of yellow. You could say: Turn the yellow coordinate system around the z axis by 90° (mathematically positive = counterclockwise) and move the origin by 3 along the yaxis (the yaxis after the 90° turn) (or +3 of the xaxis before the 90° turn).
Does this mean you have been rotated by 90° and moved by 3 units to the right? Hell no. You are still standing there where you were standing at the beginning. We just defined a second coordinate system and described its origin and axes in terms of the first one, nothing more.
Does it mean you now exist twice? Once at (2/5/0) in the yellow coordinate system and once at (2/5/0) in the green one? Hell no. Of course you exist just once. There may be nothing at all at (2/5/0) of the green system (besides air molecules). Or maybe (if there is another room behind the left wall) there is a chair. Are you a chair, just because your coordinates in one system happen to be the same as those of a chair in another system? Hardly. You would only be a chair if both you and the chair are located at (2/5/0) in the SAME coordinate system.
Now imagine the right wall (i.e. the wall where the green system has the axis that does not coincide with one of the yellow axes) moves. It slowly moves away, at 1 unit per hour. (Much preferable to moving closer at 1 unit per hour, as this would mean you would be squished within 3 hours.) The origin of the green system shall be taped to that wall (not e.g. to the floor or to the nonmoving wall) and the axis that is "dragged" along can be dragged along freely.
Now your coordinates in the green system change. You stand still. After one hour you are still at (2/5/0) in the yellow system. But you are not anymore at (5/1/0) in the green system. You are at (5/2/0) in the green system!
One more hour passes. You get tired from standing still at (2/5/0) in the yellow coordinate system, but you keep standing still, because it's for math! In the green system you are now at (5/3/0). While you grow more and more tired the wall continues moving and your green coordinates are now (5/4/0), then (5/5/0) and so on.
At 0 hours your green coordinates were (5/1/0). After t hours, they are (5/1+t/0).
Imagine the speed of the wall had been 2 units per hour or just half a unit per hour, i.e. v = 2u/h or v = 0.5u/h. Then after t hours your green coordinates would be (5/1+t*v/0).
Now let's say not only could the right wall move, but the coordinate system could be moved in two or all three directions. At time 0 your coordinates in the green system are some (xyz). Within each hour it moves by some vector, let's say every hour it moves 3 in x direction, 4 in y and 5 in z direction (instead of only 1 in y direction as before). Instead of adding 1 to the y coordinate every hour, you add 3 to the x coordinate every hour, 4 to y, 5 to z. You are still not moving (in terms of the yellow coordinate system). So if you are at some location (xyz) at time 0, you are at (x+3ty+4tz+5t) in terms of the green system after t hours. I.e. at your starting point (xyz) + t*(345). And if we use some random speed and direction v=(xmymzm) instead of speed and direction (345)/hour you are at (xyz)  t*(xmymzm) = original coordinate  t*v after time t, in terms of the green coordinate system. You haven't moved. You are still standing at the yellow coordinates (2/5/0). You are a bit knackered now from standing still so long.
You still don't exist twice nor have you turned into a chair.
Imagine you stand in a room. Look at it from the top. In the bottom left corner you have a yellow coordinate system, with the x, y and z axis along the edges of the room (x to the right, y to what is the top from where you are looking, z going to the real top of the room i.e. towards you). Your feet are located at (2/5/0) in the yellow coordinate system.
In the bottom right corner there is a green coordinate system, its x, y, z being other edges of the room (x to the top from your perspective, y to the left (i.e. it coincides/overlaps with the yellow x axis, but with opposite direction and other origin) and z also going to the real top towards you). Your feet are located at (5/1/0) in the green coordinate system. (I.e. the room has a width of 3 from left to right, and some length over 5 in the "topbottom" direction from your perspective.)
If you didn't have a room handy to say "there's the yellow origin and axes" and "over there's the green origin and axes" you would have to describe one in terms of the other, e.g. green in terms of yellow. You could say: Turn the yellow coordinate system around the z axis by 90° (mathematically positive = counterclockwise) and move the origin by 3 along the yaxis (the yaxis after the 90° turn) (or +3 of the xaxis before the 90° turn).
Does this mean you have been rotated by 90° and moved by 3 units to the right? Hell no. You are still standing there where you were standing at the beginning. We just defined a second coordinate system and described its origin and axes in terms of the first one, nothing more.
Does it mean you now exist twice? Once at (2/5/0) in the yellow coordinate system and once at (2/5/0) in the green one? Hell no. Of course you exist just once. There may be nothing at all at (2/5/0) of the green system (besides air molecules). Or maybe (if there is another room behind the left wall) there is a chair. Are you a chair, just because your coordinates in one system happen to be the same as those of a chair in another system? Hardly. You would only be a chair if both you and the chair are located at (2/5/0) in the SAME coordinate system.
Now imagine the right wall (i.e. the wall where the green system has the axis that does not coincide with one of the yellow axes) moves. It slowly moves away, at 1 unit per hour. (Much preferable to moving closer at 1 unit per hour, as this would mean you would be squished within 3 hours.) The origin of the green system shall be taped to that wall (not e.g. to the floor or to the nonmoving wall) and the axis that is "dragged" along can be dragged along freely.
Now your coordinates in the green system change. You stand still. After one hour you are still at (2/5/0) in the yellow system. But you are not anymore at (5/1/0) in the green system. You are at (5/2/0) in the green system!
One more hour passes. You get tired from standing still at (2/5/0) in the yellow coordinate system, but you keep standing still, because it's for math! In the green system you are now at (5/3/0). While you grow more and more tired the wall continues moving and your green coordinates are now (5/4/0), then (5/5/0) and so on.
At 0 hours your green coordinates were (5/1/0). After t hours, they are (5/1+t/0).
Imagine the speed of the wall had been 2 units per hour or just half a unit per hour, i.e. v = 2u/h or v = 0.5u/h. Then after t hours your green coordinates would be (5/1+t*v/0).
Now let's say not only could the right wall move, but the coordinate system could be moved in two or all three directions. At time 0 your coordinates in the green system are some (xyz). Within each hour it moves by some vector, let's say every hour it moves 3 in x direction, 4 in y and 5 in z direction (instead of only 1 in y direction as before). Instead of adding 1 to the y coordinate every hour, you add 3 to the x coordinate every hour, 4 to y, 5 to z. You are still not moving (in terms of the yellow coordinate system). So if you are at some location (xyz) at time 0, you are at (x+3ty+4tz+5t) in terms of the green system after t hours. I.e. at your starting point (xyz) + t*(345). And if we use some random speed and direction v=(xmymzm) instead of speed and direction (345)/hour you are at (xyz)  t*(xmymzm) = original coordinate  t*v after time t, in terms of the green coordinate system. You haven't moved. You are still standing at the yellow coordinates (2/5/0). You are a bit knackered now from standing still so long.
You still don't exist twice nor have you turned into a chair.
Last edited by Monika on Fri Jun 15, 2012 4:08 pm UTC, edited 2 times in total.
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Re: 1067: "Pressures"
Steve,
Imagine you're in a desert, walking along in the sand, when all of a sudden you look down...
Imagine you're in a desert, walking along in the sand, when all of a sudden you look down...
 steve waterman
 Posts: 1610
 Joined: Mon Nov 14, 2011 4:39 pm UTC
Re: 1067: "Pressures"
eran_rathan wrote:If P and Q are coincident, then you can simply use P as the point, with the subscript blue or red for the system you are writing the coordinate in.
Moving Blue +3 wrt Red:
P_{Red} is (2,0,0)
P_{Blue} = P_{Red} + (3,0,0) = (5,0,0) in Blue
Moving Red 3 wrt to Blue:
P_{Blue} is (2,0,0)
P_{Red} = P_{Blue}  (3,0,0) = (1,0,0) in Red
good start eran...using your notationing, I see these transformation equations as this...
Moving Blue +3 wrt Red:
P_{Red} is (2,0,0)
P_{Red} (2,0,0) (3,0,0) transforms to P_{Blue} (1,0,0)
Moving Red 3 wrt to Blue:
Q_{Blue} is (2,0,0)
Q_{Blue} (2,0,0) + (3,0,0) transforms to Q_{Red} (5,0,0)
We end up with four selected points...
our two given selected points
P_{Red} is (2,0,0)
Q_{Blue} is (2,0,0)
and the two that are their respective transformations
P_{Blue} (1,0,0)
Q_{Red} (5,0,0)
Are you okay with these transformation equations and attached system names ( Red or Blue ) to each selected/'lettered"/quantized point ?
"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 waterman wrote:eran_rathan wrote:If P and Q are coincident, then you can simply use P as the point, with the subscript blue or red for the system you are writing the coordinate in.
Moving Blue +3 wrt Red:
P_{Red} is (2,0,0)
P_{Blue} = P_{Red} + (3,0,0) = (5,0,0) in Blue
Moving Red 3 wrt to Blue:
P_{Blue} is (2,0,0)
P_{Red} = P_{Blue}  (3,0,0) = (1,0,0) in Red
good start eran...using your notationing, I see these transformation equations as this...
Moving Blue +3 wrt Red:
P_{Red} is (2,0,0)
P_{Red} (2,0,0) (3,0,0) transforms to P_{Blue} (1,0,0)
Moving Red 3 wrt to Blue:
Q_{Blue} is (2,0,0)
Q_{Blue} (2,0,0) + (3,0,0) transforms to Q_{Red} (5,0,0)
We end up with four selected points...
our two given selected points
P_{Red} is (2,0,0)
Q_{Blue} is (2,0,0)
and the two that are their respective transformations
P_{Blue} (1,0,0)
Q_{Red} (5,0,0)
Are you okay with these transformation equations and attached system names ( Red or Blue ) to each selected/'lettered"/quantized point ?
sure.
And P != Q.
"Trying to build a proper foundation for knowledge is blippery."
"Squirrels are crazy enough to be test pilots."
"Google tells me you are not unique. You are, however, wrong."
straight outta here.
"Squirrels are crazy enough to be test pilots."
"Google tells me you are not unique. You are, however, wrong."
straight outta here.
 steve waterman
 Posts: 1610
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Re: 1067: "Pressures"
Monika wrote:steve,
Imagine you stand in a room. Look at it from the top. In the bottom left corner you have a yellow coordinate system, with the x, y and z axis along the edges of the room (x to the right, y to what is the top from where you are looking, z going to the real top of the room i.e. towards you). Your feet are located at (2/5/0) in the yellow coordinate system.
In the bottom right corner there is a green coordinate system, its x, y, z being other edges of the room (x to the top from your perspective, y to the left (i.e. it coincides/overlaps with the yellow x axis, but with opposite direction and other origin) and z also going to the real top towards you). Your feet are located at (5/1/0) in the green coordinate system. (I.e. the room has a width of 3 from left to right, and some length over 5 in the "topbottom" direction from your perspective.)
If you didn't have a room handy to say "there's the yellow origin and axes" and "over there's the green origin and axes" you would have to describe one in terms of the other, e.g. green in terms of yellow. You could say: Turn the yellow coordinate system around the z axis by 90° (mathematically positive = counterclockwise) and move the origin by 3 along the yaxis (the yaxis after the 90° turn) (or +3 of the xaxis before the 90° turn).
Does this mean you have been rotated by 90° and moved by 3 units to the right? Hell no. You are still standing there where you were standing at the beginning. We just defined a second coordinate system and described its origin and axes in terms of the first one, nothing more.
Does it mean you now exist twice? Once at (2/5/0) in the yellow coordinate system and once at (2/5/0) in the green one? Hell no. Of course you exist just once. There may be nothing at all at (2/5/0) of the green system (besides air molecules). Or maybe (if there is another room behind the left wall) there is a chair. Are you a chair, just because your coordinates in one system happen to be the same as those of a chair in another system? Hardly. You would only be a chair if both you and the chair are located at (2/5/0) in the SAME coordinate system.
Now imagine the right wall (i.e. the wall where the green system has the axis that does not coincide with one of the yellow axes) moves. It slowly moves away, at 1 unit per hour. (Much preferable to moving closer at 1 unit per hour, as this would mean you would be squished within 3 hours.) The origin of the green system shall be taped to that wall (not e.g. to the floor or to the nonmoving wall) and the axis that is "dragged" along can be dragged along freely.
Now your coordinates in the green system change. You stand still. After one hour you are still at (2/5/0) in the yellow system. But you are not anymore at (5/1/0) in the green system. You are at (5/2/0) in the green system!
One more hour passes. You get tired from standing still at (2/5/0) in the yellow coordinate system, but you keep standing still, because it's for math! In the green system you are now at (5/3/0). While you grow more and more tired the wall continues moving and your green coordinates are now (5/4/0), then (5/5/0) and so on.
At 0 hours your green coordinates were (5/1/0). After t hours, they are (5/1+t/0).
Imagine the speed of the wall had been 2 units per hour or just half a unit per hour, i.e. v = 2u/h or v = 0.5u/h. Then after t hours your green coordinates would be (5/1+t*v/0).
Now let's say not only could the right wall move, but the coordinate system could be moved in two or all three directions. At time 0 your coordinates in the green system are some (xyz). Within each hour it moves by some vector, let's say every hour it moves 3 in x direction, 4 in y and 5 in z direction (instead of only 1 in y direction as before). Instead of adding 1 to the y coordinate every hour, you add 3 to the x coordinate every hour, 4 to y, 5 to z. You are still not moving (in terms of the yellow coordinate system). So if you are at some location (xyz) at time 0, you are at (x+3ty+4tz+5t) in terms of the green system after t hours. I.e. at your starting point (xyz) + t*(345). And if we use some random speed and direction v=(xmymzm) instead of speed and direction (345)/hour you are at (xyz)  t*(xmymzm) = original coordinate  t*v after time t, in terms of the green coordinate system. You haven't moved. You are still standing at the yellow coordinates (2/5/0). You are a bit knackered now from standing still so long.
You still don't exist twice nor have you turned into a chair.
My challenge is only regarding the math, so no time element or physical anything is involved at all...
Since coordinate move with their system, then it is quite apparently true that Red coordination in Red will always be equal to the Blue coordination in Blue.
What y'all seem to to be missing is that the Galilean, is saying by virtue of x = x vt..is precisely the opposite...and this concept is wickedly hard to grasp since there are no selectedpoint_{systems} notation present. factually, they always have x in red and x' in blue...hence, logically, they are saying that the Red assigned/eternal coordinate values and not the same as the Blue assigned/eternal coordinate values...cause this equation somehow magically ignores that the simple fact that the "Red coordination in Red will always be equal to the Blue coordination in Blue"....x' = xvt, denies 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
 steve waterman
 Posts: 1610
 Joined: Mon Nov 14, 2011 4:39 pm UTC
Re: 1067: "Pressures"
eran_rathan wrote:steve waterman wrote:eran_rathan wrote:If P and Q are coincident, then you can simply use P as the point, with the subscript blue or red for the system you are writing the coordinate in.
Moving Blue +3 wrt Red:
P_{Red} is (2,0,0)
P_{Blue} = P_{Red} + (3,0,0) = (5,0,0) in Blue
Moving Red 3 wrt to Blue:
P_{Blue} is (2,0,0)
P_{Red} = P_{Blue}  (3,0,0) = (1,0,0) in Red
good start eran...using your notationing, I see these transformation equations as this...
Moving Blue +3 wrt Red:
P_{Red} is (2,0,0)
P_{Red} (2,0,0) (3,0,0) transforms to P_{Blue} (1,0,0)
Moving Red 3 wrt to Blue:
Q_{Blue} is (2,0,0)
Q_{Blue} (2,0,0) + (3,0,0) transforms to Q_{Red} (5,0,0)
We end up with four selected points...
our two given selected points
P_{Red} is (2,0,0)
Q_{Blue} is (2,0,0)
and the two that are their respective transformations
P_{Blue} (1,0,0)
Q_{Red} (5,0,0)
Are you okay with these transformation equations and attached system names ( Red or Blue ) to each selected/'lettered"/quantized point ?
sure.
And P != Q.
Did you mean instead to say that.... ( since there are two point P; P in Red and the transformed to P in Blue)
...saying point P without saying the P and in which system, is hugely adding unwanted/counterproductive confusion here.
P_{Red} is (2,0,0) = Q_{Blue} is (2,0,0)...agreed ?... (as you just did above to these two of the four equations...now isolated/compared.)
"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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 Joined: Tue Jan 26, 2010 1:26 pm UTC
Re: 1067: "Pressures"
That's the thing. There are NOT two Ps. P has different coordinates in the two systems, but is only a single point.
Also, let me revisit the PRed is (2,0,0) = QBlue is (2,0,0) thing. I can't shake the feeling that I've come across as agreeing to more about that than I actually do. Based on the pictures you've posted, it's seemed like all you're saying with that is that P is two units to the right of the orgin of the red axis and Q is two units to the right of the origin of the blue axis. And as far as that goes, it's fine. But expressing it as an equality like that seems to imply that they're the same point. And that I emphatically do NOT agree with. The are clearly not the same point.
Also, let me revisit the PRed is (2,0,0) = QBlue is (2,0,0) thing. I can't shake the feeling that I've come across as agreeing to more about that than I actually do. Based on the pictures you've posted, it's seemed like all you're saying with that is that P is two units to the right of the orgin of the red axis and Q is two units to the right of the origin of the blue axis. And as far as that goes, it's fine. But expressing it as an equality like that seems to imply that they're the same point. And that I emphatically do NOT agree with. The are clearly not the same point.
 gmalivuk
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Re: 1067: "Pressures"
Moving red and blue coordinates doesn't move any points. P remains in the same place in space regardless of what numbers you attach to that location. My location might be (3,2,0) measuring from the corner of the room and (0,2,1) measuring from the center, but I haven't moved.

Relativity, though, often moves the different sets of coordinates together with different objects, which are in motion relative to each other. In that case, both objects would most sensibly be at (0,0,0) in their own coordinates, and moving in the other object's coordinates.
So suppose that instead of P and Q referring to abstract points in space (which we are free to define and move however we feel like), they refer to two physical objects which are in the same place at t = 0 seconds, and move away from each other at v meters / second. Suppose that P and Q orient their coordinate systems the same way (so all the axes are parallel), and are each treated as being at the origin in their own system.
Then from P's perspective, P remains at (0,0,0) and Q is at (0,0,0) + v t (for vector v describing Q's motion from P's perspective)
while from Q's perspective, P is at (0,0,0)  v t (for the same v as before).
For convenience, we can color P's coordinate system red, and we can color Q's coordinate system blue, and we can furthermore say that they are not at the origins of their system, but at coordinate locations x and x', respectively. If the coordinate systems are still oriented the same way, we now have
In RED coordinates: P is at x and Q is at x + v t
In BLUE coordinates: P is at x'  v t and Q is at x'

Relativity, though, often moves the different sets of coordinates together with different objects, which are in motion relative to each other. In that case, both objects would most sensibly be at (0,0,0) in their own coordinates, and moving in the other object's coordinates.
So suppose that instead of P and Q referring to abstract points in space (which we are free to define and move however we feel like), they refer to two physical objects which are in the same place at t = 0 seconds, and move away from each other at v meters / second. Suppose that P and Q orient their coordinate systems the same way (so all the axes are parallel), and are each treated as being at the origin in their own system.
Then from P's perspective, P remains at (0,0,0) and Q is at (0,0,0) + v t (for vector v describing Q's motion from P's perspective)
while from Q's perspective, P is at (0,0,0)  v t (for the same v as before).
For convenience, we can color P's coordinate system red, and we can color Q's coordinate system blue, and we can furthermore say that they are not at the origins of their system, but at coordinate locations x and x', respectively. If the coordinate systems are still oriented the same way, we now have
In RED coordinates: P is at x and Q is at x + v t
In BLUE coordinates: P is at x'  v t and Q is at x'
Last edited by gmalivuk on Fri Jun 15, 2012 5:33 pm UTC, edited 1 time in total.
 Monika
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Re: 1067: "Pressures"
steve waterman wrote:We end up with four selected points...
our two given selected points
P_{Red} is (2,0,0)
Q_{Blue} is (2,0,0)
and the two that are their respective transformations
P_{Blue} (1,0,0)
Q_{Red} (5,0,0)
Wrong, there are not four points, there are two points.
Why do you insist on making any kind of relationship between a point (2,0,0) in one system and another point (2,0,0) in another system? They have nothing to do with each other. They are certainly not equal in any sense.
steve waterman wrote:My challenge is only regarding the math, so no time element or physical anything is involved at all...
How can you say "no time element"? The t in the vt in the function you object to is time!
Since coordinate move with their system, then it is quite apparently true that Red coordination in Red will always be equal to the Blue coordination in Blue.
No, (2,0,0) in red is most certainly not equal to (2,0,0) in blue.
What y'all seem to to be missing is that the Galilean, is saying by virtue of x = x vt..is precisely the opposite...and this concept is wickedly hard to grasp since there are no selectedpoint_{systems} notation present. factually, they always have x in red and x' in blue...hence, logically, they are saying that the Red assigned/eternal coordinate values and not the same as the Blue assigned/eternal coordinate values...cause this equation somehow magically ignores that the simple fact that the "Red coordination in Red will always be equal to the Blue coordination in Blue"....x' = xvt, denies that!
Identical coordinates in red and blue are not equal (a couple of them may coincide depending on the exact relationship between the two system, but if it's a translation, none inside). That's like saying 1.3 kilometers = 1.3 miles, because it's both 1.3.
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 eran_rathan
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Re: 1067: "Pressures"
steve waterman wrote:Did you mean instead to say that.... ( since there are two point P; P in Red and the transformed to P in Blue)
...saying point P without saying the P and in which system, is hugely adding unwanted/counterproductive confusion here.
P_{Red} is (2,0,0) = Q_{Blue} is (2,0,0)...agreed ?... (as you just did above to these two of the four equations...now isolated/compared.)
No, and I think you are being intentionally abstruse.
There is only P and Q. Relative to each other, they are 3 units apart. The systems they are in is immaterial.
once again, YOU CANNOT COMPARE THE COORDINATES IN ONE SYSTEM TO ANOTHER WITHOUT APPLYING THE TRANSFORMATION.
let me reiterate that last part: YOU CANNOT COMPARE RED TO BLUE COORDINATES WITHOUT APPLYING THE TRANSFORMATION. PERIOD.
"Trying to build a proper foundation for knowledge is blippery."
"Squirrels are crazy enough to be test pilots."
"Google tells me you are not unique. You are, however, wrong."
straight outta here.
"Squirrels are crazy enough to be test pilots."
"Google tells me you are not unique. You are, however, wrong."
straight outta here.
 steve waterman
 Posts: 1610
 Joined: Mon Nov 14, 2011 4:39 pm UTC
Re: 1067: "Pressures"
Monika wrote:steve waterman wrote:We end up with four selected points...
our two given selected points
P_{Red} is (2,0,0)
Q_{Blue} is (2,0,0)
and the two that are their respective transformations
P_{Blue} (1,0,0)
Q_{Red} (5,0,0)
Wrong, there are not four points, there are two points.
Why do you insist on making any kind of relationship between a point (2,0,0) in one system and another point (2,0,0) in another system? They have nothing to do with each other. They are certainly not equal in any sense.steve waterman wrote:My challenge is only regarding the math, so no time element or physical anything is involved at all...
How can you say "no time element"? The t in the vt in the function you object to is time!Since coordinate move with their system, then it is quite apparently true that Red coordination in Red will always be equal to the Blue coordination in Blue.
No, (2,0,0) in red is most certainly not equal to (2,0,0) in blue.What y'all seem to to be missing is that the Galilean, is saying by virtue of x = x vt..is precisely the opposite...and this concept is wickedly hard to grasp since there are no selectedpoint_{systems} notation present. factually, they always have x in red and x' in blue...hence, logically, they are saying that the Red assigned/eternal coordinate values and not the same as the Blue assigned/eternal coordinate values...cause this equation somehow magically ignores that the simple fact that the "Red coordination in Red will always be equal to the Blue coordination in Blue"....x' = xvt, denies that!
Identical coordinates in red and blue are not equal (a couple of them may coincide depending on the exact relationship between the two system, but if it's a translation, none inside). That's like saying 1.3 kilometers = 1.3 miles, because it's both 1.3.
Why do you insist on making any kind of relationship between a point (2,0,0) in one system and another point (2,0,0) in another system? They have nothing to do with each other. They are certainly not equal in any sense.
Think please....by a coordinate, we mean the distance from its origin along either the x or y or z axis. ALL Red (x,y,x) coordinate distances, regardless of what values you elect, with locate an imaginary point ( nothing physical in my math challenge ) the same RELATIVE distances away from THEIR OWN ORIGIN.
P in Red is 2 units from its own origin along the x direction...the EXACT same ( no need to measure it...its math) distance that Q in Blue is from its origin.
agreed?
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Re: 1067: "Pressures"
Yes, as long as the units in both coordinate systems are the same. But that's not really relevant to any physics, because the origins can be put wherever we want.
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Re: 1067: "Pressures"
RECAP: Why the Galilean aka Voigt transformation process is mathematically invalid....the equation in question, x' = xvt.
To examine this as a math discipline, we substitute d (distance) for vt (velocity times time)... x' = xd
1 According to the Galilean transformation, x is always in the Red system and x' is always in the Blue system.
2 So, the Galilean transformation is really x' in Blue = x in Red  d
3 Given Red and Blue coincident system and NO selected points at all, and we relocate either one of them, or both, as is shown below after being moved
then x' in Blue = x in Red...because coordinates mimic their origin's move....(remain affixed to their own system)
CONCLUSION: since x' in Blue = x in Red is true, then x' in Blue = x in Red  d is false.
Q.E.D.
IMPACT: Relativity without x' = xvt has no time dilation nor length contraction viability. I realize that this flies in the face of numerous experimental results with physical measurement s, however, the issue is all about the math, FIRST..and IF and ONLY IF x' in Blue = x in Red  d was true, can x' = xvt be allowed to derive squat.
This is a math challenge still, questioning that x in Blue = x in Red  d. Being a math issue, it is either 100 percent right or 100 percent wrong. This is not subjective, nor does it have shades in between. Nor does it matter who I am or what else i may or may not know, indeed nothing about me is at all relevant to the math challenge itself being presented. Comments to this math challenge presented, about physical things of any kind, are not applicable.
To examine this as a math discipline, we substitute d (distance) for vt (velocity times time)... x' = xd
1 According to the Galilean transformation, x is always in the Red system and x' is always in the Blue system.
2 So, the Galilean transformation is really x' in Blue = x in Red  d
3 Given Red and Blue coincident system and NO selected points at all, and we relocate either one of them, or both, as is shown below after being moved
then x' in Blue = x in Red...because coordinates mimic their origin's move....(remain affixed to their own system)
CONCLUSION: since x' in Blue = x in Red is true, then x' in Blue = x in Red  d is false.
Q.E.D.
IMPACT: Relativity without x' = xvt has no time dilation nor length contraction viability. I realize that this flies in the face of numerous experimental results with physical measurement s, however, the issue is all about the math, FIRST..and IF and ONLY IF x' in Blue = x in Red  d was true, can x' = xvt be allowed to derive squat.
This is a math challenge still, questioning that x in Blue = x in Red  d. Being a math issue, it is either 100 percent right or 100 percent wrong. This is not subjective, nor does it have shades in between. Nor does it matter who I am or what else i may or may not know, indeed nothing about me is at all relevant to the math challenge itself being presented. Comments to this math challenge presented, about physical things of any kind, are not applicable.
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Re: 1067: "Pressures"
We're objecting to your math not *just* because the theory that results is contrary to observation. We're also objecting because you still don't seem to get how coordinate transforms work.
Re: 1067: "Pressures"
If origin_{blue} = (origin  d)_{red}, then x_{blue} = (x  d)_{red}.
That is, if you have to subtracy d from origin_{red} to get origin_{blue}, then if you take the coordinates in red of any point (and call them x), that point's coordinates in blue (call them x') are equal in value to the that point's coordinates in red minus d.
All that says, is that that point's position relative to the red origin is d less than its position relative to the blue origin.
Lets punch some actual numbers in here.
If (0,0)_{blue} = ((0,0)  (3,0))_{red}, then (1,0)_{blue} = ((1,0)  (3,0))_{red}.
All that says is that the point which has coordinates (1,0) in blue, has coordinates (2,0) in red, because blue origin is red origin minus (3,0).
In other words, x' (the coordinates of any point in blue) = x (the coordinates of that point in red)  d.
That is, if you have to subtracy d from origin_{red} to get origin_{blue}, then if you take the coordinates in red of any point (and call them x), that point's coordinates in blue (call them x') are equal in value to the that point's coordinates in red minus d.
All that says, is that that point's position relative to the red origin is d less than its position relative to the blue origin.
Lets punch some actual numbers in here.
If (0,0)_{blue} = ((0,0)  (3,0))_{red}, then (1,0)_{blue} = ((1,0)  (3,0))_{red}.
All that says is that the point which has coordinates (1,0) in blue, has coordinates (2,0) in red, because blue origin is red origin minus (3,0).
In other words, x' (the coordinates of any point in blue) = x (the coordinates of that point in red)  d.
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Re: 1067: "Pressures"
Pfhorrest wrote:If origin_{blue} = (origin  d)_{red}, then x_{blue} = (x  d)_{red}.
That is, if you have to subtracy d from origin_{red} to get origin_{blue}, then if you take the coordinates in red of any point (and call them x), that point's coordinates in blue (call them x') are equal in value to the that point's coordinates in red minus d.
All that says, is that that point's position relative to the red origin is d less than its position relative to the blue origin.
Lets punch some actual numbers in here.
If (0,0)_{blue} = ((0,0)  (3,0))_{red}, then (1,0)_{blue} = ((1,0)  (3,0))_{red}.
All that says is that the point which has coordinates (1,0) in blue, has coordinates (2,0) in red, because blue origin is red origin minus (3,0).
In other words, x' (the coordinates of any point in blue) = x (the coordinates of that point in red)  d.
SW  In MY depiction directly above ( showing Red and Blue no longer coincident.) .. in your opinion, does (x ,y',z') in Blue = (x,y,z) in Red ?
If not, why not please.
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Re: 1067: "Pressures"
gmalivuk wrote:We're objecting to your math not *just* because the theory that results is contrary to observation. We're also objecting because you still don't seem to get how coordinate transforms work.
SW  I understand that that is your stance. so, you should have no trouble responding regarding the above diagram...
[ depiction of two systems, (Red and Blue), formerly coincident...which are no longer coincident. ]
Does (x,y,z,) in Red = (x',y',z') in Blue...???
if not true, please explain why ( please, not with your own new equation or new scenario or other depiction etc} ...
just this one depiction...just this one question...please
perhaps you have a mathematical objection to answering...then state that please.
Again, I have grasped that you believe I am wrong and confused, and reiteration of your estimation, would be redundant, at best.
"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"
steve waterman wrote:Does (x,y,z,) in Red = (x',y',z') in Blue...???
(x,y,z) and (x',y',z') for what? Remember coordinates are by definition functions of points, and in your latest picture you haven't shown what point you are applying them on. Since the two systems are rotated there will be an axis F where RED(F) = (x(F), y(F), z(F)) and BLUE(F) = (x'(F), y'(F), z'(F)) are the same, somewhere well below the picture, but they're obviously different in general.
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Re: 1067: "Pressures"
Yeah, when one is rotated, the conversion between them is no longer a simple matter of adding or subtracting some single vector d or vt or whatever.
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Re: 1067: "Pressures"
chenille wrote:steve waterman wrote:Does (x,y,z,) in Red = (x',y',z') in Blue...???
(x,y,z) and (x',y',z') for what? Remember coordinates are by definition functions of points, and in your latest picture you haven't shown what point you are applying them on. Since the two systems are rotated there will be an axis F where RED(F) = (x(F), y(F), z(F)) and BLUE(F) = (x'(F), y'(F), z'(F)) are the same, somewhere well below the picture, but they're obviously different in general.
I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Let me try this conceptually,
Do you understand that when Red and Nlue are coincident, that regardless of whatever particular numeric values chosen for a relocation of one of them, that (x,y,z) in Red = (x',y','z') in Blue
worth repeating....
I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Y'all are still missing the relationship of coordinates to their own system, and continue to insist in ignoring the relationship that I am referring to.
So...not the relationship of one moved system to the other....I am saying, Red coordination in RED, equates to Blue coordinate lengths/distances/values in BLUE. Anyone?
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Re: 1067: "Pressures"
steve waterman wrote:chenille wrote:steve waterman wrote:Does (x,y,z,) in Red = (x',y',z') in Blue...???
(x,y,z) and (x',y',z') for what? Remember coordinates are by definition functions of points, and in your latest picture you haven't shown what point you are applying them on. Since the two systems are rotated there will be an axis F where RED(F) = (x(F), y(F), z(F)) and BLUE(F) = (x'(F), y'(F), z'(F)) are the same, somewhere well below the picture, but they're obviously different in general.
I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Let me try this conceptually,
Do you understand that when Red and Nlue are coincident, that regardless of whatever particular numeric values chosen for a relocation of one of them, that (x,y,z) in Red = (x',y','z') in Blue
worth repeating....
I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Y'all are still missing the relationship of coordinates to their own system, and continue to insist in ignoring the relationship that I am referring to.
So...not the relationship of one moved system to the other....I am saying, Red coordination in RED, equates to Blue coordinate lengths/distances/values in BLUE. Anyone?
I'll take a shot at this in order to go through this argument very slowly and deliberately. Assuming we are working with Cartesian coordinates (although it generalizes to other systems, I believe; it's just natural to work in Cartesian), then yes, the coordinate (2,0,0) in any coordinate system is 2 units (for some definition of the units) in the direction of the xaxis; it is a coordinate 2 units from the origin of its system. What is the next claim?
Last edited by Radical_Initiator on Sun Jun 17, 2012 1:08 am UTC, edited 1 time in total.
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Re: 1067: "Pressures"
gmalivuk wrote:Yeah, when one is rotated, the conversion between them is no longer a simple matter of adding or subtracting some single vector d or vt or whatever.
SW  "Rotation is irrelevant, indeed all movement is inconsequential, regardless,
ALL Red coordinates in Red share equal distancing to ALL Blue coordinates in Blue."
Mathematically, this can be represented by this equation...(x,y,z) in Red = (x',y',z') in Blue.
Hopefully, you better/properly understand THE particular comparison to which I wish to highlight/question...
as per a posting a few minutes ago...some more details/blurb/flogging there...
Agree or still disagree,? (x,y,z) in Red = (x',y',z') in Blue..in the depiction of the separated Red and Blue systems above...
"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"
steve waterman wrote:I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Y'all are still missing the relationship of coordinates to their own system, and continue to insist in ignoring the relationship that I am referring to.
So...not the relationship of one moved system to the other....I am saying, Red coordination in RED, equates to Blue coordinate lengths/distances/values in BLUE. Anyone?
Um, whatever it is that you are trying to say ...
When you say one thing equates to another ... it is a relationship.
Analogies, transforms, etc.
If you yell at the wind, you're engaged in a relationship with the wind.
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Re: 1067: "Pressures"
Radical_Initiator wrote:steve waterman wrote:chenille wrote:steve waterman wrote:Does (x,y,z,) in Red = (x',y',z') in Blue...???
(x,y,z) and (x',y',z') for what? Remember coordinates are by definition functions of points, and in your latest picture you haven't shown what point you are applying them on. Since the two systems are rotated there will be an axis F where RED(F) = (x(F), y(F), z(F)) and BLUE(F) = (x'(F), y'(F), z'(F)) are the same, somewhere well below the picture, but they're obviously different in general.
I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Let me try this conceptually,
Do you understand that when Red and Nlue are coincident, that regardless of whatever particular numeric values chosen for a relocation of one of them, that (x,y,z) in Red = (x',y','z') in Blue
worth repeating....
I am not talking about the relationship of one system to other
Everyone's attention is focused there.
Y'all are still missing the relationship of coordinates to their own system, and continue to insist in ignoring the relationship that I am referring to.
So...not the relationship of one moved system to the other....I am saying, Red coordination in RED, equates to Blue coordinate lengths/distances/values in BLUE. Anyone?
I'll take a shot at this in order to go through this argument very slowly and deliberately. Assuming we are working with Cartesian coordinates (although it generalizes to other systems, I believe; it's just natural to work in Cartesian), then yes, the coordinate (2,0,0) in any coordinate system is 2 units (for some definition of the units) in the direction of the xaxis; it is a coordinate 2 units from the origin of its system. What is the next claim?
SW  Thanks...good feedback.
1 I want a Red Cartesian coordinate system with (x,y,z) to be coincident with a Blue Cartesian coordinate system with (x',y',z').
2 I want to relocate one of them so that Red and Blue are no longer coincident.
Okay so far ?
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Re: 1067: "Pressures"
steve waterman wrote:SW  Thanks...good feedback.
1 I want a Red Cartesian coordinate system with (x,y,z) to be coincident with a Blue Cartesian coordinate system with (x',y',z').
2 I want to relocate one of them so that Red and Blue are no longer coincident.
Okay so far ?
Perfectly. Next point, please.
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Re: 1067: "Pressures"
Radical_Initiator wrote:steve waterman wrote:SW  Thanks...good feedback.
1 I want a Red Cartesian coordinate system with (x,y,z) to be coincident with a Blue Cartesian coordinate system with (x',y',z').
2 I want to relocate one of them so that Red and Blue are no longer coincident.
Okay so far ?
Perfectly. Next point, please.
Rather than pontificating at you, I also need to understand what your understanding is...so I like to ask a good questions to do that.
That way, it helps to not walk down unwanted directions.
3 At coincidence, do Red coordinations in Red equate to Blue coordinations in Blue ?
4 Likewise, at coincidence, does (x,y,z) in Red = (x',y',z') in Blue?
Rules ?... feel comfortable to ask, if the question is not totally clear to you, please....still okay, with me asking a few key questions ?
Also, if you agree with anything, you may go back and debate that later/change your stance.
I do need to get your responses though.,to 3 and 4, before forging ahead...is there a problem with either question 3 or 4?; logic, wording, etc
still waiting...now it is Sunday the 17th...
Should i anticipate an answer eventually to either question 3 or 4...or have these questions left you speechless ?
Last edited by steve waterman on Sun Jun 17, 2012 1:41 pm UTC, edited 1 time in total.
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Re: 1067: "Pressures"
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I had no idea what this was about, until today I came across this tweet https://twitter.com/gedankenstuecke/sta ... 1520688128 and from there to this UD entry http://www.urbandictionary.com/define.p ... %20machine
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Re: 1067: "Pressures"
Given coincident Cartesian coordinate systems Red and Blue, Red coordination in Red = Blue coordination in Blue.
Therefore, at coincidence, Red (x,y,z) = Blue (x',y',z') Anyone have a counterexample ?
Therefore, at coincidence, Red (x,y,z) = Blue (x',y',z') Anyone have a counterexample ?
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
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Re: 1067: "Pressures"
If they start out coincident why are you even bringing in x', y', and z'? That's what's confusing things, because you haven't told us what those numbers are.
When they are coincident, it means the coordinates (x,y,z) in the red system refer to the same point in space as the coordinates (x,y,z) in the blue system.
When they are coincident, it means the coordinates (x,y,z) in the red system refer to the same point in space as the coordinates (x,y,z) in the blue system.
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Re: 1067: "Pressures"
gmalivuk wrote:If they start out coincident why are you even bringing in x', y', and z'? That's what's confusing things, because you haven't told us what those numbers are.
When they are coincident, it means the coordinates (x,y,z) in the red system refer to the same point in space as the coordinates (x,y,z) in the blue system.
This is taken from Wikipedia...
The notation below describes the relationship under the Galilean transformation between the coordinates (x,y,z,t) and (x′,y′,z′,t′) of a single arbitrary event, as measured in two coordinate systems S and S', in uniform relative motion (velocity v) in their common x and x’ directions, with their spatial origins coinciding at time t=t'=0:
x'=xvt\,
y'=y \,
z'=z \,
t'=t \,
SW  I am substituting distance for vt and Red for S and Blue for S'...my focus is the initial x' = xvt equation.
What are the numbers ?...it works for EVERY number....pick any,, say, (3, 3.1, 0.116)
then, in Red and Blue...those two coordinate locations...IN RELATION TO THEIR OWN ORIGIN, are equal/identical...
for any values of x,y,z one might select.
"It describes of a single arbitrary event"...actual, that is false...it does not. It describes the coordinate relationship between the two systems.
Coordinates are NOT EVENTS. Selected points would be events...but I have no events...no selected points ...just coordinates. Again, no time component, indeed, this has no physical anything of any sort; x' = xd...
Unwittingly, x' = x d means, coordination in one system differs from another system, that once were both coincident with one another! This is mathematically impossible. The issue..is Red in Red ALWAYS equal to Blue in Blue. Whereas, Not the issue/focus/proof/concern...what red in blue is, nor what blue in red is...neither has squat to do with this short proof.
Last edited by steve waterman on Sun Jun 17, 2012 3:26 pm UTC, edited 1 time in total.
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Re: 1067: "Pressures"
Yes, that is true, and is what I already said, and everyone else in this thread also understands it to be true: When the two systems are coincident (i.e. neither is displaced or rotated relative to the other and neither is moving relative to the other), then any given point in space will have identical coordinates in both systems.steve waterman wrote:What are the numbers ?...it works for EVERY number....pick any,, say, (3, 3.1, 0.116)
then, in Red and Blue...those two coordinate locations...IN RELATION TO THEIR OWN ORIGIN, are equal/identical...
for any values of x,y,z one might select.

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Re: 1067: "Pressures"
steve waterman wrote:Radical_Initiator wrote:steve waterman wrote:SW  Thanks...good feedback.
1 I want a Red Cartesian coordinate system with (x,y,z) to be coincident with a Blue Cartesian coordinate system with (x',y',z').
2 I want to relocate one of them so that Red and Blue are no longer coincident.
Okay so far ?
Perfectly. Next point, please.
Rather than pontificating at you, I also need to understand what your understanding is...so I like to ask a good questions to do that.
That way, it helps to not walk down unwanted directions.
3 At coincidence, do Red coordinations in Red equate to Blue coordinations in Blue ?
4 Likewise, at coincidence, does (x,y,z) in Red = (x',y',z') in Blue?
Rules ?... feel comfortable to ask, if the question is not totally clear to you, please....still okay, with me asking a few key questions ?
Also, if you agree with anything, you may go back and debate that later/change your stance.
I do need to get your responses though.,to 3 and 4, before forging ahead...is there a problem with either question 3 or 4?; logic, wording, etc
still waiting...now it is Sunday the 17th...
Should i anticipate an answer eventually to either question 3 or 4...or have these questions left you speechless ?
Sorry; I tend to like to sleep in on Sunday.
3.) Not necessarily. "Coincident" coordinate systems, as far as I know, means the coordinate origins are located at the same position, and the coordinate axes are aligned. It does not necessarily say the scale of the two systems is the same. That may be a point where I am wrong, but it illustrates a need to define "coincident" to those of us who may have the wrong idea, to make sure you're not misunderstood. But either way, I think you can wave this away by either saying that the scale of the systems is identical or that yes, it is true that each coordinate in red can be mapped to a coordinate in blue with identical components.
4.) This, as far as I can see, is trickier, and brings in the problem of scale. If you claim x, y and z are constants and that (x,y,z) is a coordinate referring to the position of a point with respect to the Red origin, then when the two systems are coincident (actually, when they're not coincident, but that's looking ahead), there exist x', y' and z' for which the coordinate (x',y',z') refers to the position of the same point in Blue, or that there exists a point whose position in Blue is represented by the coordinate (x',y',z') with respect to the Blue origin and x=x', y=y' and z=z'.
I would ask that you be a bit clearer with nonstandard terminology. I don't normally hear "coordination" used in the form you're using to refer to the concepts you seem to be illustrating, and you may be carrying with it some concept that I would not normally attribute. Also, be even more pedantic; what are x, y, z, x', y' and z'?
EDIT: Tried to clear up some weird English.
Last edited by Radical_Initiator on Sun Jun 17, 2012 3:39 pm UTC, edited 1 time in total.
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Re: 1067: "Pressures"
This is the important bit.Radical_Initiator wrote:If you claim x, y and z are constants and that (x,y,z) is a coordinate referring to the position of a point with respect to the Red origin, then when the two systems are coincident (actually, when they're not coincident, but that's looking ahead), there exist x', y' and z' for which the coordinate (x',y',z') refers to the position of the same point in Blue, or that there exists a point whose position in Blue is whose coordinate representation is (x',y',z') with respect to the Blue origin and x=x', y=y' and z=z'.
Steve, you can't ask us if we agree that (x,y,z) in Red = (x',y',z') in Blue, unless you *also* tell us what relationship there is between x and x', y and y', and z and z'. Yes, we all agree that for coincident systems (which I would guess does mean scale is the same, but in any case let's assume it does for this discussion)
(x,y,z) in Red = (x',y',z') in Blue if and only if x=x', y=y' and z=z'
Without the last part, no one will say whether they agree, because you never made clear what they're agreeing *to*.
 steve waterman
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Re: 1067: "Pressures"
Radical_Initiator wrote:steve waterman wrote:Radical_Initiator wrote:steve waterman wrote:SW  Thanks...good feedback.
1 I want a Red Cartesian coordinate system with (x,y,z) to be coincident with a Blue Cartesian coordinate system with (x',y',z').
2 I want to relocate one of them so that Red and Blue are no longer coincident.
Okay so far ?
Perfectly. Next point, please.
Rather than pontificating at you, I also need to understand what your understanding is...so I like to ask a good questions to do that.
That way, it helps to not walk down unwanted directions.
3 At coincidence, do Red coordinations in Red equate to Blue coordinations in Blue ?
4 Likewise, at coincidence, does (x,y,z) in Red = (x',y',z') in Blue?
Rules ?... feel comfortable to ask, if the question is not totally clear to you, please....still okay, with me asking a few key questions ?
Also, if you agree with anything, you may go back and debate that later/change your stance.
I do need to get your responses though.,to 3 and 4, before forging ahead...is there a problem with either question 3 or 4?; logic, wording, etc
still waiting...now it is Sunday the 17th...
Should i anticipate an answer eventually to either question 3 or 4...or have these questions left you speechless ?
Sorry; I tend to like to sleep in on Sunday.
3.) Not necessarily. "Coincident" coordinate systems, as far as I know, means the coordinate origins are located at the same position, and the coordinate axes are aligned. It does not necessarily say the scale of the two systems is the same. That may be a point where I am wrong, but it illustrates a need to define "coincident" to those of us who may have the wrong idea, to make sure you're not misunderstood. But either way, I think you can wave this away by either saying that the scale of the systems is identical or that yes, it is true that each coordinate in red can be mapped to a coordinate in blue with identical components.
4.) This, as far as I can see, is trickier, and brings in the problem of scale. If you claim x, y and z are constants and that (x,y,z) is a coordinate referring to the position of a point with respect to the Red origin, then when the two systems are coincident (actually, when they're not coincident, but that's looking ahead), there exist x', y' and z' for which the coordinate (x',y',z') refers to the position of the same point in Blue, or that there exists a point whose position in Blue is whose coordinate representation is (x',y',z') with respect to the Blue origin and x=x', y=y' and z=z'.
I would ask that you be a bit clearer with nonstandard terminology. I don't normally hear "coordination" used in the form you're using to refer to the concepts you seem to be illustrating, and you may be carrying with it some concept that I would not normally attribute. Also, be even more pedantic; what are x, y, z, x', y' and z'?
SW  Just posted why I an using x, y, z, x', y' and z', in an edit to the post above.
3 yes, it is true that each coordinate in red can be mapped to a coordinate in blue with identical components
SW  agreed
4 x=x', y=y' and z=z'.
SW Agreed
If you are not okay with my synopsis of your answers, please mention that, or i will assume this is okay.
SW  So, does x=x', y=y' and z=z', at coincidence and x=x', y=y' and z=z' after the relocated has taken place ?
Remember, we have no selected points at all...just the two mathematical coordinate systems red and blue.
http://en.wikipedia.org/wiki/Cartesian_coordinate_system
Also, be even more pedantic; what are x, y, z, x', y' and z'?
1 I want a Red Cartesian coordinate system with (x,y,z) to be coincident with a Blue Cartesian coordinate system with (x',y',z').
2 I want to relocate one of them so that Red and Blue are no longer coincident.
Okay so far ?[/quote]
Perfectly. Next point, please.[/quote]
man, it is so hard to tell who is the author of these quoted statements...not happy about the poor referencing/tracking/ability to know always who is making which statement...how do a larger discussion group keep track...I am a newbie here and feel there must be some way to do this...
Last edited by steve waterman on Sun Jun 17, 2012 4:24 pm UTC, edited 3 times 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
 steve waterman
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Re: 1067: "Pressures"
gmalivuk wrote:This is the important bit.Radical_Initiator wrote:If you claim x, y and z are constants and that (x,y,z) is a coordinate referring to the position of a point with respect to the Red origin, then when the two systems are coincident (actually, when they're not coincident, but that's looking ahead), there exist x', y' and z' for which the coordinate (x',y',z') refers to the position of the same point in Blue, or that there exists a point whose position in Blue is whose coordinate representation is (x',y',z') with respect to the Blue origin and x=x', y=y' and z=z'.
Steve, you can't ask us if we agree that (x,y,z) in Red = (x',y',z') in Blue, unless you *also* tell us what relationship there is between x and x', y and y', and z and z'. Yes, we all agree that for coincident systems (which I would guess does mean scale is the same, but in any case let's assume it does for this discussion)
(x,y,z) in Red = (x',y',z') in Blue if and only if x=x', y=y' and z=z'
Without the last part, no one will say whether they agree, because you never made clear what they're agreeing *to*.
Bingo, i just have agreement with that last part, in the previous post above, so...that is two for and one against...still in the discussion...
"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
 gmalivuk
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Re: 1067: "Pressures"
The way to do it is to use [quote] tags properly. Check out some other discussions on here: it's not actually hard to know who said what when the name of the person who said it shows up directly above each quote.steve waterman wrote:man, it is so hard to tell who is the author of these quoted statements...not happy about the poor referencing/tracking/ability to know always who is making which statement...how do a larger discussion group keep track...I am a newbie here and feel there must be some way to do this...
 steve waterman
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 Joined: Mon Nov 14, 2011 4:39 pm UTC
Re: 1067: "Pressures"
SW  So, does x=x', y=y' and z=z', at coincidence and x=x', y=y' and z=z' after the relocated has taken place ?
so, Radical_Initiator or Archduke Vendredi of Skellington the Third, Esquire...
You both have been quite silent for some time....should I anticipate an answer/response today ?..or have you decided to ignore this question.
Is your lack of response due to you not understanding the question?
"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
 gmalivuk
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Re: 1067: "Pressures"
If you've moved one of the coordinate planes, then obviously the coordinates of a given point are no longer equal in both systems.
We haven't replied because we're tired of answering your obvious questions when you clearly still don't understand how coordinate transformations work on a deeper level.
Also, it's been less than a day. Some of us have lives or other better things to do with our time than sit in this thread and try to explain basic coordinate geometry to you.
We haven't replied because we're tired of answering your obvious questions when you clearly still don't understand how coordinate transformations work on a deeper level.
Also, it's been less than a day. Some of us have lives or other better things to do with our time than sit in this thread and try to explain basic coordinate geometry to you.
 steve waterman
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Re: 1067: "Pressures"
gmalivuk wrote:If you've moved one of the coordinate planes, then obviously the coordinates of a given point are no longer equal in both systems.
We haven't replied because we're tired of answering your obvious questions when you clearly still don't understand how coordinate transformations work on a deeper level.
Also, it's been less than a day. Some of us have lives or other better things to do with our time than sit in this thread and try to explain basic coordinate geometry to you.
SW  Thanks for responding to the questions that you did. I believe, that you do not speak for Radical_Initiator ( or anyone else ) I would like his response to this one question. I wonder what Randall might say, if he were asked my current question. I do not ever anticipating finding that out...as quite likely, he is not reading/does not care about any/every thread in the Forum. He also seems to wish to not be contacted, which i can appreciate.
"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
 gmalivuk
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Re: 1067: "Pressures"
It has been less than a day. Stop whining about how people have probably just decided to give up on this topic based on their desire to do other things from time to time.
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