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Originally posted by KellyJay…Here is the bottom line, once you put a bend in the line it isn't
Here is the bottom line, once you put a bend in the line it isn't
a completely straight line, once you put a curve in it, it is curved
where the curve is, and that is true no matter how you look at it
in reality.
Kelly
a completely straight line,…
I repeat my question; -in 1-dimentions or 2-dimentions or 3-dimentions?
You are just choosing to completely ignore the context of the particular coordinate system that is being used to define all the points along the line thus I assume you insist that the answer to my above question is always “3-dimentions” because you refuse to think outside the box for fear that this might conflict with your beliefs about physics (which you continually display ignorance of).
-ok, despite this goes against modern understanding in geometry of what a straight line is defined as ( http://en.wikipedia.org/wiki/Line_(mathematics) ), lets for the sake of argument define a “straight line” as always meaning a straight line in 3-dimentions and never just in 1-dimentions or 2-dimentions and never in 4-dimentions; that would mean that, by your definition, a line that is straight in 3-dimentions is still “straight” even if it has 4-dimensional curvature because it doesn’t make sense to talk about such a line “not being “straight” in 4-dimensions” because, by definition, the line is still “straight” because it is “straight” in 3-dimensions;
-but the 4-dimensional curvature of that line would still exist regardless of what you call that line (straight or bent) -so what is your argument against the scientific fact of the existence of 4-dimensional curvature of space now? -I mean, using your wordplay and insisting that the line is simply “straight” in any coordinate system by completely ignoring the fact of the existence of 4-dimensional curvature is just that, wordplay;
-how does simply defining a line that is straight in 3-dimentions but not in 4-dimentions as simply “straight” demonstrate that it is not curved in 4-dimentions?
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Originally posted by Andrew HamiltonIf you bend a line, it has a bent in it, you think how many dimentions
[b]…Here is the bottom line, once you put a bend in the line it isn't
a completely straight line,…
I repeat my question; -in 1-dimentions or 2-dimentions or 3-dimentions?
You are just choosing to completely ignore the context of the particular coordinate system that is being used to define all the points along the line thus I assume you ...[text shortened]... but not in 4-dimentions as simply “straight” demonstrate that it is not curved in 4-dimentions?[/b]
are going to matter, does it change the fact there is a bend in it or not?
Kelly
Originally posted by KellyJayIn which dimension? According to me, it all depends on the context of the dimensions you are referring to. But, apparently, according to you, what the context of the dimensions that are being referred to makes no difference to whether or not it is “straight” dispute the fact this goes totally against the way a line is defined in basic geometry ( http://en.wikipedia.org/wiki/Line_(mathematics) ),
If you bend a line, it has a bent in it, you think how many dimentions
are going to matter, does it change the fact there is a bend in it or not?
Kelly
-but what has this got to do with my question? -you still haven’t answered it.
Originally posted by Andrew HamiltonSorry for the misspelling; it should have been:
In which dimension? According to me, it all depends on the context of the dimensions you are referring to. But, apparently, according to you, what the context of the dimensions that are being referred to makes no difference to whether or not it is “straight” dispute the fact this goes totally against the way a line is defined in basic geometry ( http ...[text shortened]... hematics) ),
-but what has this got to do with my question? -you still haven’t answered it.
“…whether or not it is “straight” despite the fact this goes…”
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Originally posted by twhiteheadI've defined straight for you, it changes from that description it isn't
I am still hoping that you can come up with a method to determine whether or not a line in real 3d space is straight.
straight any more, it is no different than giving a circles four equal
corners, we then could call that a square depending on some other
variables.
Kelly
Originally posted by KellyJaybut we already told you that a line that is apparently straight can be curbed in a higher dimension.
I've defined straight for you, it changes from that description it isn't
straight any more, it is no different than giving a circles four equal
corners, we then could call that a square depending on some other
variables.
Kelly
if you draw a line from let's say new york to chicago, then walk on that line, do you realize it is curbed? assuming you know nothing about the third dimension(ie earth is round). if you walk on that line you will get from new york to chicago in a completely straight fashion => it is a straight line. it is only when you realize the existance of the third dimension that you learn that a line from new york to chicago cannot be straight. in 3d. it is straight in 2d.
think of it this way. a line is the shortest distance between two points. but what if the nature of geometry tells you to go on a curbed path to reach the second point?
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Originally posted by KellyJay…I've defined straight for you…
I've defined straight for you, it changes from that description it isn't
straight any more, it is no different than giving a circles four equal
corners, we then could call that a square depending on some other
variables.
Kelly
Using how many dimensions and what coordinate system?
What is your rational for insisting that what is meant by a “straight line” is different from that of the accepted basic geometry: ( http://en.wikipedia.org/wiki/Line_(mathematics) )?
-I mean, the way you define it is clearly totally contradicted by mathematics because you just idiotically ignore the context of the dimensions used.
But, much more importantly for this discussion:
-What is your argument that a line cannot be both straight in 3-dimentions and bent in 4-dimentions?
-so far you haven’t given any argument what so ever. -simply saying that such a line is simply not defined as “straight” has no relevance to this regardless of how you define “straight”.
-I can draw a shortest line between two points on a surface of a sphere and, regardless of whether or not you define such a line as “straight”, that line still can exist! Would you deny this? -it would be idiotic to imply that such a line couldn’t exist. -and if you admit that such a line, without logical contradiction, can exist on the surface of a sphere regardless of whether or not you call it “straight” then it is idiotic of you not to admit that such a line, without logical contradiction, can exist in 3-dimentions but be curved in 4-dimentions regardless of whether or not you call it “straight”.
Also, how this for a definition of a straight line:
“a straight line is a shortest route entirely contained WITHIN the specified dimensions between two points that are also entirely contained WITHIN the SAME specified dimensions”
This would be an entirely consistant definition with the conventional definition (and is implied from the conventional definition) of the straight line in basic geometry: ( http://en.wikipedia.org/wiki/Line_(mathematics) ),
And, using this definition, it is clear that you can have a line that is BOTH straight in the 2-dimentions WITHIN the surface of a sphere but which is curved WITHIN the 3-dimensional coordinate system that defines the same sphere -do you deny this?
-to deny this would be to deny commonly excepted basic geometry and virtually the whole of modern physics.
Originally posted by KellyJayFrom what I recall, you said that a line is straight if it has no curves in any dimension.
I've defined straight for you, it changes from that description it isn't
straight any more, it is no different than giving a circles four equal
corners, we then could call that a square depending on some other
variables.
Kelly
My question is, how can we know if a line is straight? If I gave you a yard stick could you identify whether it was straight?
You have placed a yardstick next to a spherical globe and declared the yardstick straight and the globe curved. How do you tell? If you could only see a section of the surface of the sphere, could you tell using some sort of instrument whether or not it was straight or curved?
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Originally posted by ZahlanziI also told you that once you force a straight line to curve, it isn't a
but we already told you that a line that is apparently straight can be curbed in a higher dimension.
if you draw a line from let's say new york to chicago, then walk on that line, do you realize it is curbed? assuming you know nothing about the third dimension(ie earth is round). if you walk on that line you will get from new york to chicago in a comple ...[text shortened]... but what if the nature of geometry tells you to go on a curbed path to reach the second point?
straight line any more. If you draw a line from New York to Chicago
it isn't straight it is curved (forced) by the curve of the earth.
Think about building a house if you eye ball the lines you use to
construct the house and use the land scape to help guide you in
building the house straight up and down, you run the risk of aligning
it to a slanted landscape. You require tools like plum lines and levels,
point being straight up and down can be achived.
Kelly
Originally posted by twhiteheadI said straight has no curves, if a dimension forces it to bend, it isn't
From what I recall, you said that a line is straight if it has no curves in any dimension.
My question is, how can we know if a line is straight? If I gave you a yard stick could you identify whether it was straight?
You have placed a yardstick next to a spherical globe and declared the yardstick straight and the globe curved. How do you tell? If you co ...[text shortened]... e sphere, could you tell using some sort of instrument whether or not it was straight or curved?
straight any more where it is bending.
Kelly
Originally posted by Andrew Hamilton“a straight line is a shortest route entirely contained WITHIN the specified dimensions between two points that are also entirely contained WITHIN the SAME specified dimensions”
[b]…I've defined straight for you…
Using how many dimensions and what coordinate system?
What is your rational for insisting that what is meant by a “straight line” is different from that of the accepted basic geometry: ( http://en.wikipedia.org/wiki/Line_(mathematics) )?
-I mean, the way you define it is clearly totally contradicted by ...[text shortened]... is would be to deny commonly excepted basic geometry and virtually the whole of modern physics.[/b]
You are a chess player correct, you know this isn't true.
Kelly
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Originally posted by KellyJayCan you give me an example of when and where the shortest route between two points on the surface of a chess board is not a straight line?
“a straight line is a shortest route entirely contained WITHIN the specified dimensions between two points that are also entirely contained WITHIN the SAME specified dimensions”
You are a chess player correct, you know this isn't true.
Kelly
-and if you are talking about the shortest route a chess piece can take around obstacles (i.e other chess pieces) then that doesn’t count because the shortest route in the context of my definition means the shortest route if nothing is in the way because we are just talking about dimensions here and lines and points defined within those dimensions and not objects that exist within those dimensions.