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Thread: The size of an axis

  1. #1 The size of an axis 
    Forum Freshman Ozolnyex's Avatar
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    What is a size of axis of the rotating object? Probably 0, but from point of math 0 can not have any size.


    Ozolnyex
     

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  3. #2 Re: The size of an axis 
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    Quote Originally Posted by Ozolnyex
    What is a size of axis of the rotating object? Probably 0, but from point of math 0 can not have any size.

    What do you mean by size ?

    An axis is a line. It is infinite in length, and has zero radius.


     

  4. #3  
    Forum Freshman Ozolnyex's Avatar
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    I mean axis of a material object for example cylinder, if it has 0 radius, the mathematical conclusion would be - it does not exist.
    Ozolnyex
     

  5. #4  
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    Quote Originally Posted by Ozolnyex
    I mean axis of a material object for example cylinder, if it has 0 radius, the mathematical conclusion would be - it does not exist.
    No, it wouldn't. It would be a line. Lines exist in the mathematical sense.
     

  6. #5  
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    Quote Originally Posted by Ozolnyex
    I mean axis of a material object for example cylinder, if it has 0 radius, the mathematical conclusion would be - it does not exist.
    The "mechanical" conclusion is that it does not exist, which is true: there isn't actually something tangible there.
     

  7. #6  
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    Quote Originally Posted by Bender
    Quote Originally Posted by Ozolnyex
    I mean axis of a material object for example cylinder, if it has 0 radius, the mathematical conclusion would be - it does not exist.
    The "mechanical" conclusion is that it does not exist, which is true: there isn't actually something tangible there.
    You can calculate the moment of inertia about that axis that "doesn't exist" and get a quantity that is perfectly meaningful.

    An axis is not an axle.

    The axis exists, even for a material objecct. It is not supposed to be a part that you can buy at the local NAPA store.

    I fear you may be feeding Ozolnyex's delusion, and he has plenty of misconceptions already.
     

  8. #7  
    Forum Freshman Ozolnyex's Avatar
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    So general conclusion would be that mathematics or geometry is not "always" applyable to matter?
    Ozolnyex
     

  9. #8  
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    Miscoceptions Sorry I try to learn that way.
    Ozolnyex
     

  10. #9  
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    Quote Originally Posted by DrRocket
    You can calculate the moment of inertia about that axis that "doesn't exist" and get a quantity that is perfectly meaningful.

    An axis is not an axle.

    The axis exists, even for a material objecct. It is not supposed to be a part that you can buy at the local NAPA store.

    I fear you may be feeding Ozolnyex's delusion, and he has plenty of misconceptions already.
    I admit that my post wasn't the best from an educational point of view. I contemplated not posting halfway through but in the end submitted it anyway.
    There isn't a "the" axis of an object though, an object can rotate around any axis. There is a "the" axis of a rotation, which is probably what you meant.
     

  11. #10  
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    Quote Originally Posted by Ozolnyex
    So general conclusion would be that mathematics or geometry is not "always" applyable to matter?
    Applicability of mathematics is dependent on knowing what the mathematics means. To the extent that one understands it, the applicability is there.
     

  12. #11  
    Forum Freshman Ozolnyex's Avatar
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    Ok guys, I wanted to hear Your Thoughts, I personally believe that a rotational axis in a material object has radius >0, because othervise it wouldn't exist at all. Mathematically 0 means a state of non existance as I understand it.
    Ozolnyex
     

  13. #12  
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    an axis is a theoretical concept, like numbers and mathematics as a whole
    no it does not exist. Nor does a surface or an individual.
    Dick, be Frank.

    Ambiguity Kills.
     

  14. #13  
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    The axis of rotation is defined as all the points that don't move while the object is rotating. Depending on your definition of "points" and "move" you could say it has a radius of 1 atom, 1 neucleon or 0. It's really pretty inconsequential though, since the physical existence of the axis has nothing to do with anything really.
     

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    Quote Originally Posted by Ozolnyex
    Ok guys, I wanted to hear Your Thoughts, I personally believe that a rotational axis in a material object has radius >0, because othervise it wouldn't exist at all. Mathematically 0 means a state of non existance as I understand it.
    Okay, what's the radius then?
     

  16. #15  
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    Quote Originally Posted by MagiMaster
    The axis of rotation is defined as all the points that don't move while the object is rotating. Depending on your definition of "points" and "move" you could say it has a radius of 1 atom, 1 neucleon or 0. It's really pretty inconsequential though, since the physical existence of the axis has nothing to do with anything really.
    Any of those are too large.

    The axis of rotation need not be found within the body -- you can rotate a whole object around and object just like a horse on a merry-go-round. In that case there are no stationary points for the body itself.

    An axis of rotation is a line in the mathematical sense and its "existence" is also in the mathematical sense.

    If you want to look at the situation from a purely mathematical perspective, then the axis of rotation corresponds to an eigenvector for a unitary matrix which represents a rigid body motion which fixes the origin. The associated eigenvalue will be 1.
     

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    i think its like a double cone conected by the tip
     

  18. #17  
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    Quote Originally Posted by luxtpm
    i think
    That is not obvious.
     

  19. #18  
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by MagiMaster
    The axis of rotation is defined as all the points that don't move while the object is rotating. Depending on your definition of "points" and "move" you could say it has a radius of 1 atom, 1 neucleon or 0. It's really pretty inconsequential though, since the physical existence of the axis has nothing to do with anything really.
    Any of those are too large.

    The axis of rotation need not be found within the body -- you can rotate a whole object around and object just like a horse on a merry-go-round. In that case there are no stationary points for the body itself.

    An axis of rotation is a line in the mathematical sense and its "existence" is also in the mathematical sense.

    If you want to look at the situation from a purely mathematical perspective, then the axis of rotation corresponds to an eigenvector for a unitary matrix which represents a rigid body motion which fixes the origin. The associated eigenvalue will be 1.
    I did include 0 for the purely mathematical axis. As for the rest, it's just for argument's sake. But yeah, I forgot about the case where the axis is outside the body rotating.
     

  20. #19  
    Forum Freshman Ozolnyex's Avatar
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    There is non rotatating line (axis) while object rotates. Geometry does not say that radius of a point or a line is 0.

    Harold, I don't know what is the radius, should be smaller than any material particle.[/quote]
    Ozolnyex
     

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    Quote Originally Posted by Ozolnyex
    There is non rotatating line (axis) while object rotates. Geometry does not say that radius of a point or a line is 0.
    Geometry says a line has only one dimension, so it has no radius. To have a radius it needs to have three dimensions.

    For most purposes, I guess not having a radius is equivalent to a radius of 0.
     

  22. #21  
    Forum Freshman Ozolnyex's Avatar
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    Maybe a line as a dimension, has to have it's own subdimension to exist
    Ozolnyex
     

  23. #22  
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    Quote Originally Posted by Ozolnyex
    Maybe a line as a dimension, has to have it's own subdimension to exist
    That doesn't make any sense. A line is defined as having only one dimension.
     

  24. #23  
    Forum Freshman Ozolnyex's Avatar
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    Ok guys, thanks for the attention, I will have to think about it for another couple of years.
    Ozolnyex
     

  25. #24  
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    If you cut or fold a piece of paper isn,t there a - real - cutting line ?

    If you draw a line with a pencil on paper dont you see a real line running around the drawn line (that is actually a stripe) ?

    That line marks on the paper where there is ink and where there is no ink. Such lines are just as real as the ink and the paper.

    it,s "funny" (and confusing) to try and draw a conventional mathemathic three dimensional axes-frame with real lines that have no thickness instead of stripes. You have to mark the areas with different colours or tones ....
     

  26. #25  
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    Draw a line on a piece of paper and pull out a magnifying glass. The edge of that is going to be pretty fuzzy. If you were to pull out an electron microscope, what you'd see would look nothing at all like a mathematical line. The same would be true with a cut, no matter how perfect it was.
     

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    That may be but still the line of a cut with a cissor is real and not "something palpable" also without a width even when it is a fuzzy cut.

    Thus apparently not being something palpable is not a valuable argument for not being real.

    For instance a carpenter has to be aware of the difference between the cut of a saw (with a width) and the lines, and measurements he needs for what he wants to make.
     

  28. #27  
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    I couldn't understand your first two sentences at all, and I don't see how the second adds anything to either argument.
     

  29. #28  
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    Quote Originally Posted by MagiMaster
    I couldn't understand your first two sentences at all,,,.
    That speaks well for your rationality.
     

  30. #29  
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    You yourself say that witha magnifying glass you see a fuzzy line. Could you indicate the width of that line please ? Maybeyou meassure a width of 1 mm. But how, between which lines or points did you measure and what is the width of those lines then ?
     

  31. #30  
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    How do you measure the width of something fuzzy? I mean, you could measure the distance from 100% dark to 0% dark, or from 25% dark to 75% dark. They'd be equally valid measurements depending on what you're using it for. I still can't understand about half of what you're saying though.
     

  32. #31  
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    If I would ask what's the thickness of the cut of a cissor or a knive would you start measuring that way and then tell me what the thickness is ?

    The cutting line may be less or more sharp or straigth, but it still has no thickness or width.
     

  33. #32  
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    Ghrasp, after You have cut something, there is a gap between peaces anyway
    Ozolnyex
     

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    Not necessarily, if you cut something elastic like rubber not completely through just a cut, you won,t even see that there is a cut. But it is there. You can,t see it or weigh it but that doesnt keep it from being real. If you cut it once more, perpendicular to the first cut, where these cuts cross there is a line. Anyway to me it seems a closer representation to the mathematic definition of a line then the stripe of a pen on paper.

    If you cut through there also is not a defined gap, the distance can vary. But the cut stays as a membrance which is also real and shows on both surfaces.
     

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    Quote Originally Posted by Ghrasp
    Not necessarily, if you cut something elastic like rubber not completely through just a cut, you won,t even see that there is a cut. But it is there. You can,t see it or weigh it but that doesnt keep it from being real. If you cut it once more, perpendicular to the first cut, where these cuts cross there is a line. Anyway to me it seems a closer representation to the mathematic definition of a line then the stripe of a pen on paper.
    Regardless of whether it is a close representation or not, it's quite a bit less practical.
     

  36. #35  
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    But it shows that not being tangible or having a width or weigth does not mean a line, a point or a surface in the mathematical sense (or a string ?) does not exist.
     

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    There's still no rubber cut or anything else at a rotational axis, though.

    Nobody claimed that axis doesn't exist in way.
     

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    Maybe a line as a dimension, has to have it's own subdimension to exist.

    This remark of ozolnyex led me to react with the example/idea of a cut - line that is not three dimensional but does exist.

    I have Ozolnyex problem with a point though. A point is supposed to be zero dimensions. That seems strange to me. If something exists in reality it should have at least one dimension shouldn't it. I would say position (related to other points, lines, surfaces, things, time etc) is the dimension of a point. Not point as a merely abstract notion but a real point. Or math would be only an abstract game and not connected to the real world.

    Then a line would be two-dimensional, a surface three and things four ?

    Offcourse in a (x,y, z) dimensional system a point takes no space as such a sytem of space lacks time and motion. But how is that for four dimensional space-time. I can imagine you could see a moving point also as sort of a cut in "the fabric of spacetime" in stead of in a potato or rubber. Then a point has a dimension.
     

  39. #38  
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    It'd help if you had a clue what dimension meant. A point is 0 dimensions because it doesn't need any degrees of freedom to specify it. A position is (typically) 3 dimensional since it needs 3 degrees of freedom to specify it. A line is 1 dimensional, a surface 2, a volume 3, a position 3, a time 1, a meeting 4 (time and location), a position and orientation is 6.

    A true, mathematical line (or point, or surface) does not exist in real life since reallity has 3 spatial dimensions. And, yes, math is an abstract game, but one that has important connections to the real world.
     

  40. #39  
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    A point is 0 dimensions because it doesn't need any degrees of freedom to specify it.
    That may be in three dimensions but we don,t live in a three dimensional universe. In four dimensions there is a freedom to move that a three dimensional math system doesn,t offer. So that argument only counts within three dimensional math. For instance when someone studies math in a book in a train and looking at / thinking of point (x, y ,z ) within a axes sytem on a certain page of the book I could see that point (with the axes system) move. It has a degree of freedom to me as the axes system itself has. Or the point in a three dimensional math-sytem doesn,t exist but for the peron holding the book. Then math woudln,t exist in the real world.
     

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    Ghrasp, MagiMaster has a point that you should first gain some understanding in what a dimension is.

    What you describe as a point which can move in time, is actually a line (or a curve) in a four-dimesional space, thus it is indeed a onedimensional object and certainly not a point.
    A point in our four-dimensional space with 3 spatial and one time dimension would be a point that only exists at one specific time, and has, as defined, 0 dimensions.

    An axis which exists through time is a plane in four-dimensional space (or some kind of other two-dimensional surface).
     

  42. #41  
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    Where does that line come from then ? if it is not from a moving point ? Why should a point become a line if one moves related to that point (or the point moves related to... ). Why would the movement of something (as you say in a dimension) suddenly add a dimension to it.

    Or is it that there is no point at all and never has been, just a line that just emerged out of the blue.
     

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    The point is also a line in four-dimensional space time if it does not move, but continues to exist over time.

    If you add time to the model, you add a dimension to everything that continues to exist, so 0 dimensions becomes 1 dimension i.e. a line (or other curve)
     

  44. #43  
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    I just can't see why a point would become a line if you add time. For instance a train seen as a collection of points and every point would become a line the train would never leave the station and get longer and longer ?


    Why not give it chronologic (linear) time as a dimension instead off length. chronologic-time as dimension of the moving train and circular time of the clock used as a tool to meassure/express the dimension time for spacetime. (circular because clock's "go round" , work on repetition).

    I know some filosophers used this idea of circular time and chronologic time to understand time as a whole, how we experience it.

    in that line of thinking chronologic and cyclic could exist as dimensions in time.

    the chronologic dimension off the train connects it to all train stations it passed and ever will pass (it,s past, present and future) and to the first train ever, the inventors etc.

    Dont ask me which measuring unit to use. But as it is also a dimension of time, another aspect of how we experience it , it is also logical that it can be compared with cyclic time(years, seconds etc) and doing this fysics expresses time in seconds.
     

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    If you add time as a dimension, you have to treat it exactly the same as the three spatial dimensions.

    In four four dimensions, the train is indeed always connected to the station, which does not mean it becomes longer. At different points in time, it is at different points in space.
    In fact, it doesn't become anything and is in a way completely static, because there is no other dimension to move in left. You can't use concepts of past, present or future if you look down upon four-dimensional spacetime.

    If you don't get it after this, I am going to give up on trying to explain you the basic concept of dimension, because I really don't know what else to write to clarify it.
     

  46. #45  
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    I'll just add that if you're moving relative to the point, then what you care about is the point's position, which is a three-dimensional quantity. The point itself is still 0-dimensional.

    Also, when you start considering time as a dimension, you need to look into the concept of world lines. So a point is 0-dimensional, but the world line of that point (that point throughout time) is 1-dimensional.
     

  47. #46  
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    At different points in time, it is at different points in space.
    But at one time (and thus all the time, every moment) it can't be at different places, not the train nor a point or a line of that train. So a point or a line on the train, to me, stays what it is, a point or a line. Even if (and allthough) for the line you have to deal with length contraction. For a point itself length contraction doesnt exist only it's distance to other points changes. Lengthcontration doesn't add a dimension.
     

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    No it doesn't, nor does it have anything to do with the current discussion.
     

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    I think this is not off topic as the discussion was if a axis of rotation which is supposed to be a mathematical line has a width.

    A train has a lot of such rotational axes and if the train is viewed in motion, and a time dimension added to tree-dimensional space, a length-dimension would be added for (mathematical) objekts like a line thus the rotational axis would have a width (become a plane) in four dimensional spacetime ? I just don,t see it.
     

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    Perhaps it is too early for you to make such abstractions. It is better to keep to three spatial dimensions for now, in which case a axis of rotation is always a one-dimensional line without a width.
     

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    So as I understand it to you, in the case of four dimensions, an axis has a width ? Then what keeps it from becoming a surface ? And the surface becoming a fysical objekt ?

    As a biside could you stop lecturing and making arrogant degrading remarks as in the above post, some people can really get agressiv because of such. Easy say behind a screen butthat,s theprolem with such remark also ; easy.
     

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    An axis/line in a three dimensional space that exists in a certain continuous domain in a fourth dimension is indeed a surface in the four dimensional space. Add another dimension, and it would become a volume. Neither the surface nor the volume have much to do with with physical objects. Those are all abstract mathematical representations of things that don't physically exist. If you wish, they do exist in a way that also has little to do with physical objects.

    About the "degrading" remark: several posters have tried in a number of ways to explain it to you, but your responses make me assume that you have insufficient understanding of the basic principles underlying this discussion. Your time might be better spent learning these basics. The remark was never meant to be degrading.

    You also give the impression of being stuck with certain ideas, and that you won't accept what contradicts those ideas. Then there is the fact that you keep drawing in concepts that add nothing to the discussion and then you draw strange conclusions from them, which make it more difficult and confusing for yourself. This makes it a bit frustrating from the point of view of an instructor.
     

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    I just can't see (as easy as you apparently can), why a wheel of a riding train would suddenly rotate around a surface if the train starts to ride.

    Off course in seeing something there is time, no vision without frecquency,s and no frecquency without time. That can cause that if I would stare at the railroad at one point and the train suddenly passes by I don't see it at one place, motionless. The wheel moves and thus the axis even during a theoretical single quantum of the light, the minimum time I would need for any sight. That makes I dont see it as a line. The same as when you see the spikes of a bicycle as a surface if it rotates quickly. So I agree.

    But in case of the train and the axes of the wheel, I am perfectly capable of following the wheel with my eyes or by rotating my head with the motion of the train.
    Then I still see the axes as one dimensonal.

    There is no natural law that subscribes the way I look at it or says I should stand still and stare in front of me motionless to get a real sense of reality.
    Between these two ways of viewing ; completely motionless and perfectly focussed moving with the motion there is an endless realm.

    So that makes the axes a surface and a line at the same time depending on how we look at it ?
    So we,re both rigth...
     

  54. #53  
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    Quote Originally Posted by Bender
    Perhaps it is too early for you to make such abstractions. It is better to keep to three spatial dimensions for now, in which case a axis of rotation is always a one-dimensional line without a width.
    An axis is always a line. It is one dimensional. It does not matter how many dimensions one is working in .

    A line in higher dimensions is just like a line in 3 dimensions. And a line in 3 dimensiions is just like a line in 2 dimensions or even in 1 dimension.
     

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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Bender
    Perhaps it is too early for you to make such abstractions. It is better to keep to three spatial dimensions for now, in which case a axis of rotation is always a one-dimensional line without a width.
    An axis is always a line. It is one dimensional. It does not matter how many dimensions one is working in .

    A line in higher dimensions is just like a line in 3 dimensions. And a line in 3 dimensiions is just like a line in 2 dimensions or even in 1 dimension.
    Are you following the discussion? You are pulling my statement completely out of context. An axis in three dimensions that exists in more than one point in a fourth dimension is no longer a line. It also isn't an axis in four dimensions, because there is no rotation in these four dimensions.


    Ghrasp: the wheel would not rotate around a surface. Either you look at it in three dimensions, and the wheel rotates around a moving axis, or you look at it in four dimensions, nothing moves and what corresponds to the moving axis in three dimensions is now a plane, consisting of of all the rotational axes of the wheel for every point in time. Our eyes don't see four dimensions, but three.
     

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    It also isn't an axis in four dimensions, because there is no rotation in these four dimensions.
    I dont understand this, according to fysics reality is supposed to be (at least) four dimensional. Are you saying that in reality rotation doesn't exist for fysics and math ? You can't be serious about that.

    Dr Rocket your idea would mean that not only one line is at one specific place at one specific moment for one specific observer but also every line, point, surface and objekt would be theoretically determinable for a given moment. That is a deterministic point of view.
    Offcourse you,re not referring to a -vague - line in general but to a specific line an observer watches and focusses on so an observer moves with the line as the line moves. Then I might agree.

    But I also tend to agree with the idea of two dimensions for instance a camera focussed on a point where a wheel passes. Suppose for the observation there is just one quantum involved. That quantum has a wavelength and frecquency so you dont see it at a moment of time, it take time to observe. At first there is a beginning of information andthe line is at point x but it is not a completed observation. The camera doesn,t know yet what it will see, it can be blue or yellow round or square.

    So the camera or an oberver focussed to a specific point in space (througha peepinghole) sees the line (determined by therotating wheel in this case) not at a given position in space, the position will be smeared out according to principles of uncertainty and also photography, when you make picture of something moving the position can be visably smeared out on the foto just the same.

    But I dont think you therefor can conclude that ita line thus stops being a line in itself and becomes a surface. [/u][/quote] But maybe, Bender, you mean something completely different. In that case I,m curious.
     

  57. #56  
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    Quote Originally Posted by Bender
    Quote Originally Posted by DrRocket
    Quote Originally Posted by Bender
    Perhaps it is too early for you to make such abstractions. It is better to keep to three spatial dimensions for now, in which case a axis of rotation is always a one-dimensional line without a width.
    An axis is always a line. It is one dimensional. It does not matter how many dimensions one is working in .

    A line in higher dimensions is just like a line in 3 dimensions. And a line in 3 dimensiions is just like a line in 2 dimensions or even in 1 dimension.
    Are you following the discussion? You are pulling my statement completely out of context. An axis in three dimensions that exists in more than one point in a fourth dimension is no longer a line. It also isn't an axis in four dimensions, because there is no rotation in these four dimensions.

    No one can really follow the discussion. The mangling of definitions and terminology has resulted in a bunch of word salad.

    In particular this sentence is utter nonsense, word salad without meaning: " An axis in three dimensions that exists in more than one point in a fourth dimension is no longer a line. It also isn't an axis in four dimensions, because there is no rotation in these four dimensions."

    What is of some concern is that you think that these words might mean something.
     

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    Quote Originally Posted by DrRocket
    No one can really follow the discussion. The mangling of definitions and terminology has resulted in a bunch of word salad.

    In particular this sentence is utter nonsense, word salad without meaning: " An axis in three dimensions that exists in more than one point in a fourth dimension is no longer a line. It also isn't an axis in four dimensions, because there is no rotation in these four dimensions."

    What is of some concern is that you think that these words might mean something.
    Maybe my English is failing me, and I certainly mixed up some terms in a failed attempt to clarify. I don't even know how this simple discussion became so needlessly complicated.
    Always using the exact mathematical terms is not always the best method to clarify an idea, and I personally don't always know the commonly used English terms for them.

    You might ignore everything I said, because it doesn't really affect the original question, but since you are curious about what I meant :wink::

    My point remains valid, even though it is not properly formulated.
    Let's try a more visual approach: suppose you have an apple slice inside a cake. If you cut the cake, you see the apple slice as (approximately) a line.
    One step further, you can take a three dimensional space with a surface. Take a single position in one of those three dimension (=cutting the cake), and look at the plane of that cut: of the surface, you only see a line in the plane cut.
    Now instead of a three dimensional space with a surface, you can take a four dimensional space with a surface. Take a single position in one of those four dimensions (=cutting a four-dimensional cake), and you see a line.

    In the example of the rotational axis: the single position you take to cut the four-dimensional cake is a certain moment in time. In that moment, you see an axis, but in the four-dimensional cake, there is a whole apple slice of the axis over time. If the axis stays in the same three dimensional location, the apple slice is flat and parallel to the edges of the cake. If the axis moves, the apple slice has a different shape and/or orientation.
     

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    No one can really follow the discussion.
    Did you ask all forum members and readers ? If not you shouldn,t speak for them.

    Can you explain why for a particle the principles of uncertainty of position would count but not for points and lines ?
    If a point's position is not determined exactly but vague (or by chance) you loose the idea of exact position which is typical for a point.

    But unlike a particle you can follow a line or point with you're eyes or even a camera because it is determined by for instance a rotating wheel. As you can see the wheel you see the line/axis. Thereby (the focus idea of observing) the line is constantly determined (for someone focussing on it) by a position and direktion and thus stays a line.

    For instance a tennis-match, the axis of a spinning ball is more determined for the tennis player who focusses on the ball then for a referree who watches the net on serve.
    The latter gets a vague image of the ball and thus the line. But allthough his image is vague he knows that for the players it is different, by focussing they contact with what they see and it kinda stands still (relativity) for them because of that.
     

  60. #59  
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    Quote Originally Posted by Ghrasp
    No one can really follow the discussion.
    Did you ask all forum members and readers ? If not you shouldn,t speak for them.
    Correct I should have said that no knowledgeable and intelligent participant could follow the gibberish. I clearly should have excluded the delusional.

    [quote="Ghrasp"}Can you explain why for a particle the principles of uncertainty of position would count but not for points and lines ?[/quote]

    Certainly. The principle of uncertainty is a quantum mechanicsl principle. It applies to particles that are modeled as points. It has nothing to do with lines.

    A line does not not have a single location. That is because it consists of a lot of points.

    You might approximate a line as a finite set of points, but that is not quite what you asked.
     

  61. #60  
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    Quote Originally Posted by Bender
    Quote Originally Posted by DrRocket
    No one can really follow the discussion. The mangling of definitions and terminology has resulted in a bunch of word salad.

    In particular this sentence is utter nonsense, word salad without meaning: " An axis in three dimensions that exists in more than one point in a fourth dimension is no longer a line. It also isn't an axis in four dimensions, because there is no rotation in these four dimensions."

    What is of some concern is that you think that these words might mean something.
    Maybe my English is failing me, and I certainly mixed up some terms in a failed attempt to clarify. I don't even know how this simple discussion became so needlessly complicated.
    Always using the exact mathematical terms is not always the best method to clarify an idea, and I personally don't always know the commonly used English terms for them.

    You might ignore everything I said, because it doesn't really affect the original question, but since you are curious about what I meant :wink::

    My point remains valid, even though it is not properly formulated.
    Let's try a more visual approach: suppose you have an apple slice inside a cake. If you cut the cake, you see the apple slice as (approximately) a line.
    One step further, you can take a three dimensional space with a surface. Take a single position in one of those three dimension (=cutting the cake), and look at the plane of that cut: of the surface, you only see a line in the plane cut.
    Now instead of a three dimensional space with a surface, you can take a four dimensional space with a surface. Take a single position in one of those four dimensions (=cutting a four-dimensional cake), and you see a line.
    I think what you are talking about is the intersection of a plane (ordinary 2-dimensional) with another plane, surface, or hypersurface. That could give you a point, a curve, a straight line, or a plane.



    Quote Originally Posted by Bender
    In the example of the rotational axis: the single position you take to cut the four-dimensional cake is a certain moment in time. In that moment, you see an axis, but in the four-dimensional cake, there is a whole apple slice of the axis over time. If the axis stays in the same three dimensional location, the apple slice is flat and parallel to the edges of the cake. If the axis moves, the apple slice has a different shape and/or orientation.
    Are you looking at the locus in space-time swept out by an axis ? That will be some sort of surface.
     

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    Yep, that's what I was trying to clarify.

    Don't ask me why.

    I purposefully left out the special cases of a plane and a point because they don't apply to this situation.
     

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    I think what you are talking about is the intersection of a plane (ordinary 2-dimensional) with another plane
    That,s another way to define a line. You could say two different types (real and or mathematical) of a line. One connected to a rotating objekt one to the intersection of two planes. Why not refer to lines as strings (and to planes as membranes), could be interesting, but all kowledgable and intelligent readers might get confused.
     

  64. #63  
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    Ghrasp,

    An axis is an abstract line with no movement in it, everybody will agree to it, whether it has a width or not. Of course in a 3 dimensional understanding it has not width, but the dimension itself has to have some state of existance, the smallest unmesurable state. I would say it is something rather than nothing. It should have a width if we agree that it exists. Of course it is not radius, I am sorry I used this word.
    Ozolnyex
     

  65. #64  
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    Merry Christmas guys :wink:
    Ozolnyex
     

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    The abstractness does not mean that you can't see it because you see what rotates and with that automatically the axisis determined and visible also. It,s just not tangible. Therefor it doesn't need a seperate (from what rotates) state of existence to be real.
     

  67. #66  
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    Let's turn on logic. In geometry axis exist theoreticallly? No doubt - Yes. Rotation exist physically - Yes, There is a rotational axis of real "existing" physical rotation. Does axisexist physically? - Should exist.
    Ozolnyex
     

  68. #67  
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    So after couple of years I have more clear thougts about this subject . An axis has size, but we can not measure it, because it is a smallest spacial unit. It is a dimension itself.
    Ozolnyex
     

  69. #68  
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    An axis has no size. It represents a dimension.
     

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    Along the one dimension we allow for an axis, it it goes on to infinity and in both directions to boot. What is so small about that?
    "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense." --Buddha (563BC-483BC)
     

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    ..........?
     

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    Correct me if I am wrong, but the term "dimension" is from the Latin "dimensio", "a measuring".

    A dimension is a measuring.

    It is, according to physics, a measuring of reality "as" space and time.

    Space has three dimensions of measurement, time only one dimension. The measuring of reality as space-time, as a measurement of space-time, does not "change" reality.

    Reality is independent of the measuring, and is thus independent of space and time. Space and time are terms we use to define how we measure reality.

    Correct me once again if I am wrong, but an "axis" is a term used in alliance with how we "measure" space or time. It alone does not quantify reality unless given the specxific task to thumbprint a dimension, in which case it as an axis abides by the format of measurement as per the axiomatic dimensions chosen for reality, namely the 3 dimensions for space and one dimension for time.
     

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    ^^ What he said ^^
     

  74. #73  
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    It really amazes me how such a simple question as the one originally posed leads to a thread 73 posts long :-D
    After everything is said and done, it is really quite simple :
    1. An "axis" is a theoretical concept related to the rotational symmetry of the system. It is the set of all points that remain invariant under rotational transformations. An axis in this context is not a physical, tangible object and as such has no width.
    2. The concept of "dimension" is well defined both mathematically and physically. Please refer to
    ::::::
    Dimension - Wikipedia, the free encyclopedia

    Enough said
     

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    ......."physically"?

    Dimensio.....a measuring.

    Don't go down the path of thinking what you measure will change anything like you matter........
     

  76. #75  
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    Quote Originally Posted by theQuestIsNotOver View Post
    ......."physically"?

    Dimensio.....a measuring.

    Don't go down the path of thinking what you measure will change anything like you matter........
    I have no idea what you are saying
     

  77. #76  
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    The definitions in this article

    Rotation around a fixed axis - Wikipedia, the free encyclopedia

    as well as the article referenced in post #73 provide all required answers to the original post. No further discussion or argument is needed.

    Best of luck,
    Markus
     

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    We "measure" when we decide to use "measurements".

    Some people have rulers, you know, like "30cm" long.

    Others have watches. Like wrist watches. Like the things they wear on their wrist.

    It's a Daa of trying to "adapt".

    ....to reality.....


    I mean, you can measure, or you can "work with"........you know?

    You wearing a suit right now? You were measured? Forget it? What's "the point"?
     

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    You don't wear a suit, right?

    I don't....you know, just to make you feel special.
     

  80. #79  
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    Yes, I am wearing a suit right now, because I am at work.
    My suits, however, don't usually rotate around their axis.
     

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    When you asses a covet beyond your own space, you tend to use "dimensions", after knowing your own...........you ask "what is greater than this that I can not just adapt to but maybe understand"........it's a game, right?

    "compassion" is easy.........."stating" something you feel you should share.......something else.

    (btw, this is not "physics"....but why knit-pick)

    (I'm just answering a question)

    An axis is as you imply something one rotates around. It implies something we have yet entertained........."time".

    "time"is a dimesnion. "Space" also is a dimension.

    "sizing" an "äxis" is purely "ficticious" without proper "äpplication" to what we "äpplicate".

    They're ways we "measure", what's "äbout".........what pervades.
    Last edited by theQuestIsNotOver; December 4th, 2011 at 12:14 PM.
     

  82. #81  
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    This question has been fully answered and the thread is now drifting into la-la land. Time to let it rest in peace.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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