Why are points considered to be zero dimensional? [closed]
Clash Royale CLAN TAG#URR8PPP
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This is a silly observation born out of my own curiosity. I'd love some perspective from more mathematically minded folks.
Please try to evaluate my reasoning, and expand on which assumptions are incorrect or misguided.
General question
Why are points considered to be zero dimensional? Is there a distinction between zero dimensional and dimensionless that I am missing?
Assumptions
- A single point cannot exist in the absence of at least one dimension.
- The point has no meaning beyond its distance from zero along that dimension.
Conclusion
- A single point is not dimensionless.
- Every point is coupled to some dimension(s), and its meaning is generated via its distance to zero along those dimension(s).
- In this sense, every point has content, as it assumes a value on a dimension. A dimensionless point would have no capacity to assume a value.
planar-graph
asked Aug 23 at 6:46
efreezy
41
closed as unclear what you're asking by Lord Shark the Unknown, Hans Lundmark, Yves Daoust, Leucippus, Andreas Blass Aug 23 at 6:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |Â
up vote
-1
down vote
favorite
Aside
This is a silly observation born out of my own curiosity. I'd love some perspective from more mathematically minded folks.
Please try to evaluate my reasoning, and expand on which assumptions are incorrect or misguided.
General question
Why are points considered to be zero dimensional? Is there a distinction between zero dimensional and dimensionless that I am missing?
Assumptions
- A single point cannot exist in the absence of at least one dimension.
- The point has no meaning beyond its distance from zero along that dimension.
Conclusion
- A single point is not dimensionless.
- Every point is coupled to some dimension(s), and its meaning is generated via its distance to zero along those dimension(s).
- In this sense, every point has content, as it assumes a value on a dimension. A dimensionless point would have no capacity to assume a value.
planar-graph
asked Aug 23 at 6:46
efreezy
41
closed as unclear what you're asking by Lord Shark the Unknown, Hans Lundmark, Yves Daoust, Leucippus, Andreas Blass Aug 23 at 6:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
What does "dimension" mean to you, exactly? And "A single point cannot exist in the absence of at least one dimension" is like saying that a line cannot exist in the absence of at least a plane. Of course it can! Finally, "The point has no meaning beyond its distance from zero along that dimension" doesn't describe the point, it describes the ambient space.
– Arthur
Aug 23 at 6:51
You can define the special vector space that only has the point $0$ in it. It has dimension 0.
– ippiki-ookami
Aug 23 at 6:53
1
You are "playing" with concepts that are not clearly defined and your logics lacks rigor. We cannot follow you. For instance, you assume that we understand what you mean by "zero dimensional" vs. "dimensionless". How could we ?
– Yves Daoust
Aug 23 at 6:58
Yves, thanks for the critique. I implore you to encourage those who lack rigor in their formal reasoning, and to strive to understand and improve their mental model. Especially those who indeed have genuine curiosity. A more community-oriented, socially productive rephrasing of your response might read "I am happy to see you playing with these concepts, however I think you would benefit by taking a step back and articulating more clearly what you mean by "zero dimensional" vs "dimensionless"
– efreezy
Aug 25 at 20:02
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Aside
This is a silly observation born out of my own curiosity. I'd love some perspective from more mathematically minded folks.
Please try to evaluate my reasoning, and expand on which assumptions are incorrect or misguided.
General question
Why are points considered to be zero dimensional? Is there a distinction between zero dimensional and dimensionless that I am missing?
Assumptions
- A single point cannot exist in the absence of at least one dimension.
- The point has no meaning beyond its distance from zero along that dimension.
Conclusion
- A single point is not dimensionless.
- Every point is coupled to some dimension(s), and its meaning is generated via its distance to zero along those dimension(s).
- In this sense, every point has content, as it assumes a value on a dimension. A dimensionless point would have no capacity to assume a value.
planar-graph
asked Aug 23 at 6:46
efreezy
41
Aside
This is a silly observation born out of my own curiosity. I'd love some perspective from more mathematically minded folks.
Please try to evaluate my reasoning, and expand on which assumptions are incorrect or misguided.
General question
Why are points considered to be zero dimensional? Is there a distinction between zero dimensional and dimensionless that I am missing?
Assumptions
- A single point cannot exist in the absence of at least one dimension.
- The point has no meaning beyond its distance from zero along that dimension.
Conclusion
- A single point is not dimensionless.
- Every point is coupled to some dimension(s), and its meaning is generated via its distance to zero along those dimension(s).
- In this sense, every point has content, as it assumes a value on a dimension. A dimensionless point would have no capacity to assume a value.
planar-graph
asked Aug 23 at 6:46
efreezy
41
asked Aug 23 at 6:46
efreezy
41
asked Aug 23 at 6:46
efreezy
41
asked Aug 23 at 6:46
efreezy
41
41
closed as unclear what you're asking by Lord Shark the Unknown, Hans Lundmark, Yves Daoust, Leucippus, Andreas Blass Aug 23 at 6:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Lord Shark the Unknown, Hans Lundmark, Yves Daoust, Leucippus, Andreas Blass Aug 23 at 6:56
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
What does "dimension" mean to you, exactly? And "A single point cannot exist in the absence of at least one dimension" is like saying that a line cannot exist in the absence of at least a plane. Of course it can! Finally, "The point has no meaning beyond its distance from zero along that dimension" doesn't describe the point, it describes the ambient space.
– Arthur
Aug 23 at 6:51
You can define the special vector space that only has the point $0$ in it. It has dimension 0.
– ippiki-ookami
Aug 23 at 6:53
1
You are "playing" with concepts that are not clearly defined and your logics lacks rigor. We cannot follow you. For instance, you assume that we understand what you mean by "zero dimensional" vs. "dimensionless". How could we ?
– Yves Daoust
Aug 23 at 6:58
Yves, thanks for the critique. I implore you to encourage those who lack rigor in their formal reasoning, and to strive to understand and improve their mental model. Especially those who indeed have genuine curiosity. A more community-oriented, socially productive rephrasing of your response might read "I am happy to see you playing with these concepts, however I think you would benefit by taking a step back and articulating more clearly what you mean by "zero dimensional" vs "dimensionless"
– efreezy
Aug 25 at 20:02
add a comment |Â
1
What does "dimension" mean to you, exactly? And "A single point cannot exist in the absence of at least one dimension" is like saying that a line cannot exist in the absence of at least a plane. Of course it can! Finally, "The point has no meaning beyond its distance from zero along that dimension" doesn't describe the point, it describes the ambient space.
– Arthur
Aug 23 at 6:51
You can define the special vector space that only has the point $0$ in it. It has dimension 0.
– ippiki-ookami
Aug 23 at 6:53
1
You are "playing" with concepts that are not clearly defined and your logics lacks rigor. We cannot follow you. For instance, you assume that we understand what you mean by "zero dimensional" vs. "dimensionless". How could we ?
– Yves Daoust
Aug 23 at 6:58
Yves, thanks for the critique. I implore you to encourage those who lack rigor in their formal reasoning, and to strive to understand and improve their mental model. Especially those who indeed have genuine curiosity. A more community-oriented, socially productive rephrasing of your response might read "I am happy to see you playing with these concepts, however I think you would benefit by taking a step back and articulating more clearly what you mean by "zero dimensional" vs "dimensionless"
– efreezy
Aug 25 at 20:02
1
1
What does "dimension" mean to you, exactly? And "A single point cannot exist in the absence of at least one dimension" is like saying that a line cannot exist in the absence of at least a plane. Of course it can! Finally, "The point has no meaning beyond its distance from zero along that dimension" doesn't describe the point, it describes the ambient space.
– Arthur
Aug 23 at 6:51
What does "dimension" mean to you, exactly? And "A single point cannot exist in the absence of at least one dimension" is like saying that a line cannot exist in the absence of at least a plane. Of course it can! Finally, "The point has no meaning beyond its distance from zero along that dimension" doesn't describe the point, it describes the ambient space.
– Arthur
Aug 23 at 6:51
You can define the special vector space that only has the point $0$ in it. It has dimension 0.
– ippiki-ookami
Aug 23 at 6:53
You can define the special vector space that only has the point $0$ in it. It has dimension 0.
– ippiki-ookami
Aug 23 at 6:53
1
1
You are "playing" with concepts that are not clearly defined and your logics lacks rigor. We cannot follow you. For instance, you assume that we understand what you mean by "zero dimensional" vs. "dimensionless". How could we ?
– Yves Daoust
Aug 23 at 6:58
You are "playing" with concepts that are not clearly defined and your logics lacks rigor. We cannot follow you. For instance, you assume that we understand what you mean by "zero dimensional" vs. "dimensionless". How could we ?
– Yves Daoust
Aug 23 at 6:58
Yves, thanks for the critique. I implore you to encourage those who lack rigor in their formal reasoning, and to strive to understand and improve their mental model. Especially those who indeed have genuine curiosity. A more community-oriented, socially productive rephrasing of your response might read "I am happy to see you playing with these concepts, however I think you would benefit by taking a step back and articulating more clearly what you mean by "zero dimensional" vs "dimensionless"
– efreezy
Aug 25 at 20:02
Yves, thanks for the critique. I implore you to encourage those who lack rigor in their formal reasoning, and to strive to understand and improve their mental model. Especially those who indeed have genuine curiosity. A more community-oriented, socially productive rephrasing of your response might read "I am happy to see you playing with these concepts, however I think you would benefit by taking a step back and articulating more clearly what you mean by "zero dimensional" vs "dimensionless"
– efreezy
Aug 25 at 20:02
add a comment |Â
1 Answer
1
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Here's just one viewpoint.
You may be interested in the difference between affine dimension and linear dimension. For flat things:
- The affine dimension is the least number of points needed to specify the thing.
- The linear dimension is the number of orthogonal directions available to someone living on the thing.
For example, since there's a unique line through any two points, ergo a line has affine dimension $2$. But if you're living on a line, there's only one direction along which you can move back and forth, so it has linear dimension $1$.
In general, the linear dimension is always $1$ less than the affine dimension.
Since a point takes $1$ point to specify, its affine dimension is $1$. Thus its linear dimension is $0$. Since "dimension" usually means "linear dimension", hence a point can be considered $0$-dimensional.
answered Aug 23 at 6:53
goblin
35.6k1154182
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Here's just one viewpoint.
You may be interested in the difference between affine dimension and linear dimension. For flat things:
- The affine dimension is the least number of points needed to specify the thing.
- The linear dimension is the number of orthogonal directions available to someone living on the thing.
For example, since there's a unique line through any two points, ergo a line has affine dimension $2$. But if you're living on a line, there's only one direction along which you can move back and forth, so it has linear dimension $1$.
In general, the linear dimension is always $1$ less than the affine dimension.
Since a point takes $1$ point to specify, its affine dimension is $1$. Thus its linear dimension is $0$. Since "dimension" usually means "linear dimension", hence a point can be considered $0$-dimensional.
answered Aug 23 at 6:53
goblin
35.6k1154182
add a comment |Â
up vote
1
down vote
Here's just one viewpoint.
You may be interested in the difference between affine dimension and linear dimension. For flat things:
- The affine dimension is the least number of points needed to specify the thing.
- The linear dimension is the number of orthogonal directions available to someone living on the thing.
For example, since there's a unique line through any two points, ergo a line has affine dimension $2$. But if you're living on a line, there's only one direction along which you can move back and forth, so it has linear dimension $1$.
In general, the linear dimension is always $1$ less than the affine dimension.
Since a point takes $1$ point to specify, its affine dimension is $1$. Thus its linear dimension is $0$. Since "dimension" usually means "linear dimension", hence a point can be considered $0$-dimensional.
answered Aug 23 at 6:53
goblin
35.6k1154182
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Here's just one viewpoint.
You may be interested in the difference between affine dimension and linear dimension. For flat things:
- The affine dimension is the least number of points needed to specify the thing.
- The linear dimension is the number of orthogonal directions available to someone living on the thing.
For example, since there's a unique line through any two points, ergo a line has affine dimension $2$. But if you're living on a line, there's only one direction along which you can move back and forth, so it has linear dimension $1$.
In general, the linear dimension is always $1$ less than the affine dimension.
Since a point takes $1$ point to specify, its affine dimension is $1$. Thus its linear dimension is $0$. Since "dimension" usually means "linear dimension", hence a point can be considered $0$-dimensional.
answered Aug 23 at 6:53
goblin
35.6k1154182
Here's just one viewpoint.
You may be interested in the difference between affine dimension and linear dimension. For flat things:
- The affine dimension is the least number of points needed to specify the thing.
- The linear dimension is the number of orthogonal directions available to someone living on the thing.
For example, since there's a unique line through any two points, ergo a line has affine dimension $2$. But if you're living on a line, there's only one direction along which you can move back and forth, so it has linear dimension $1$.
In general, the linear dimension is always $1$ less than the affine dimension.
Since a point takes $1$ point to specify, its affine dimension is $1$. Thus its linear dimension is $0$. Since "dimension" usually means "linear dimension", hence a point can be considered $0$-dimensional.
answered Aug 23 at 6:53
goblin
35.6k1154182
edited Aug 23 at 7:03
answered Aug 23 at 6:53
goblin
35.6k1154182
answered Aug 23 at 6:53
goblin
35.6k1154182
answered Aug 23 at 6:53
goblin
35.6k1154182
35.6k1154182
add a comment |Â
add a comment |Â
1
What does "dimension" mean to you, exactly? And "A single point cannot exist in the absence of at least one dimension" is like saying that a line cannot exist in the absence of at least a plane. Of course it can! Finally, "The point has no meaning beyond its distance from zero along that dimension" doesn't describe the point, it describes the ambient space.
– Arthur
Aug 23 at 6:51
You can define the special vector space that only has the point $0$ in it. It has dimension 0.
– ippiki-ookami
Aug 23 at 6:53
1
You are "playing" with concepts that are not clearly defined and your logics lacks rigor. We cannot follow you. For instance, you assume that we understand what you mean by "zero dimensional" vs. "dimensionless". How could we ?
– Yves Daoust
Aug 23 at 6:58
Yves, thanks for the critique. I implore you to encourage those who lack rigor in their formal reasoning, and to strive to understand and improve their mental model. Especially those who indeed have genuine curiosity. A more community-oriented, socially productive rephrasing of your response might read "I am happy to see you playing with these concepts, however I think you would benefit by taking a step back and articulating more clearly what you mean by "zero dimensional" vs "dimensionless"
– efreezy
Aug 25 at 20:02