What does a line in space look like?

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Discussion Overview

The discussion revolves around the nature of a line in space, particularly focusing on its dimensionality, visibility, and representation in both mathematical and physical contexts. Participants explore the implications of viewing a line from different angles and the utility of geometric lines in describing physical objects.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants question how a line in space, having no thickness, can be distinguished from its surroundings when viewed from different angles.
  • Others assert that a geometric line is a one-dimensional mathematical object and an abstract idea, not a physical object that can be seen or touched.
  • One participant raises the question of why physical objects are described using coordinates if lines are abstract, suggesting that this method allows for useful and accurate predictions.
  • Another participant points out that the inability to distinguish a line from certain angles does not diminish its usefulness in describing physical objects.
  • A humorous remark is made about the implications of this discussion for string theorists, suggesting a playful acknowledgment of the complexities involved.

Areas of Agreement / Disagreement

Participants express differing views on the visibility and physicality of lines, with some emphasizing their abstract nature while others focus on their practical applications in describing physical objects. The discussion remains unresolved regarding the implications of these perspectives.

Contextual Notes

The discussion highlights the limitations of visualizing geometric concepts in three-dimensional space and the dependence on definitions of mathematical objects versus physical representations.

Kiki
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If a line in space has no thickness, how can I distinguish the line from its surroundings when I look at the line such that I can't see its length? After all, in three dimensional space, you can look at a line from different angles.
 
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jedishrfu said:
A geometric line is a one dimensional mathematical object. It's an abstract idea. It's not a physical object that you might see, touch or run into. The same goes for a point or a plane.

https://en.m.wikipedia.org/wiki/Line_(geometry)
Thanks.

Then why do we describe physical objects with coordinates (i.e. points)?
 
Kiki said:
Thanks.

Then why do we describe physical objects with coordinates (i.e. points)?

Basically because it is an extremely good way of describing objects and the positions of objects that let's us make useful, accurate predictions.
 
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The fact that you can't distinguish the line when looking at some specific angle (this happens in computer graphics, some objects become invisible when the view camera is at some angles/distances) , doesn't tell us much about how useful lines or points are for describing physical objects. In other words, so what if you can't distinguish the line, it is still useful for the reason @Drakkith says.
 
jedishrfu said:
A geometric line is a one dimensional mathematical object. It's an abstract idea. It's not a physical object that you might see, touch or run into.
For heaven's sake, don't tell the string theorists. :wink:
 
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