# Talk:Dimensions

### From Math Images

## Contents |

## Final review

Htasoff 14:28, 18 July 2011 (UTC)

### Messages to the Future

- Felt no need.

### References and footnotes

- All images are properly attributed.
- No direct quotes.
- No text referenced to, only a link for an image.

### Good writing

The following items are just meant to be reminders. If one of these items needs clarification, or seems like a great idea that you don't know how to implement, see What Makes a Good Math Images Page?.

**Quality of prose and page structuring**

- The entire page is devoted to carefully and intuitively explaining the concept of dimensions. This was the new concept, and I believe, and hope, that I have explained it well.
- The purpose of each section is clearly relevant to the purpose of the page as a whole.

**Integration of Images and Text**

- Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.
- The text explicitly points out what the reader should observe in a picture.

**Connections to other mathematical topics**

- The page is written from a Geometric/ Topological perspective, however does point to connections in Economics and Physics.
- Links to Fractal Dimensions.

**Examples, Calculations, Applications, Proofs**

- Because this is a page geared toward a conceptual understanding of a topic, I've included many examples and analogies, while technical proofs have been left out.

**Mathematical Accuracy and precision of language**

- I feel that this is a good conceptual introduction to the topic of dimensions. Because I am taking an intuitive aproach to the topic, mathmatical nomenclature is minimal. I believe all of my explanations to be accurate. I recieved feedback on this page, but not as much as on other pages.

**Layout**

- No further comments.

# General Comments

# Section-specific Comments

## Basic Description

Kate 15:33, 9 June 2011 (UTC):

- It's mildly (very mildly) confusing to say that "forward
*and*backward" together comprise one direction - I think it might be better to use "forward-backward", "left-right", and "up-down" to emphasize that each really is only one direction.CHECK

- I'm not 100% sure what you mean by a dimension "corresponding" with a certain number of directions. I think it might be clearer to say that a certain dimensional space has that many directions of possible motion.CHECK

- be consistent between things like "one dimensional", "3D", and "zeroth dimension"I'm trying.

- font color=slateblue>Rebecca 02:04, 12 July 2011 (UTC) I'd like to see you add some pictures to this section. Even if they're just there to break up text (like a picture of mario), it think they would improve the section.

### Dimensions of Objects

- Kate 20:06, 11 July 2011 (UTC): I vehemently disagree with the current state of your second paragraph in this section, most specifically with the comment:

*Although one may contend that a string and a flattened quarter are 3 dimensional because they do still have length, width, and height, they are only analogies for an ideal 1 dimensional line and 2 dimensional disk within 3 dimensional space.*

**This is just fundamentally untrue.**A string and a flattened quarter are*not*"only analogies" for mathematical concepts - they are real, physical objects which can be*used*or*interpreted*as analogies. You*cannot say*that a physical object "is" an analogy! That's not what "analogy" means!

- I know you're concerned about not confusing people by going into detail about the difference between something being one dimensional and something
*representing*a one dimensional object, but that is no excuse to totally abandon all accuracy to how things actually are! I contend that a reader will be*more*confused by this assertion that any and all strings and quarters are "only analogies" - readers have handled strings and quarters before, they've held them in their hands, and they understand them to be real, physical objects. When you say that these things are "only analogies", you're saying that*each and every single string and flattened quarter in existence*is not a physical object but rather a linguistic construction used to simplify one thing by comparing it to something familiar - a claim that is false and off-putting to the reader.

- Second, whatever explanation you choose to make about strings and quarters actually being three dimensional, I don't think it should come at the end as an after thought. This is an important issue, and you should mention it
*before*making the comparisons.

CHECK CHECK CHECK CHECK CHECK

*On the disk, (best thought of as a filled in circle) there are two directions akin to up and down, right and left, making the disk two dimensional.*

- I think the comma should come after the parenthetical, not before.CHECK

- I think you should mention that although our representation of a line may have width, we are intending to represent an object with no width. Otherwise, when I think of a string, I can see that it actually does have three dimensions.

- I think that this is confusing. We seem to be contradicting ourselves. I think if we don't complicate it, it won't be as confusing.
- Kate 19:12, 10 June 2011 (UTC): Wait, so you're saying you think it's
*more*confusing to explain that while a*picture of a line*may have height as well as length an actual*line*only has length? I disagree. I know that when I first ran into people talking about dimensions, I thought that it didn't make sense because even though a line that I drew in pencil or on the computer was thin enough that I probably couldn't measure it, it did have more than zero thickness. Zero thickness may be harder to visualize, but I think it's*accurate*and not*contradictory*.

- Kate 19:12, 10 June 2011 (UTC): Wait, so you're saying you think it's

- I recognize the importance of explaining the imperfections in one's analogies. Nevertheless, it is trick to be able to do so without sounding hypocritical or confusing. I put this at the end of the paragraph in question, hopefully it is explanatory without being contradicting: Although one may contend that a string and a flattened quarter are 3 dimensional because they do still have length, width, and height, they are only analogies for an ideal 1 dimensional line and 2 dimensional disk within 3 dimensional space.
- Disagree so much. See above.

- I recognize the importance of explaining the imperfections in one's analogies. Nevertheless, it is trick to be able to do so without sounding hypocritical or confusing. I put this at the end of the paragraph in question, hopefully it is explanatory without being contradicting: Although one may contend that a string and a flattened quarter are 3 dimensional because they do still have length, width, and height, they are only analogies for an ideal 1 dimensional line and 2 dimensional disk within 3 dimensional space.

- xd 21:08, 13 June 2011 (UTC) I don't think the sentence "the circle is a LINE joint front to back" is accurate. LINE extends infinitely to both direction. LINE segment has a starting and ending point. So in this case, if you insist on this analogy, you should say LINE SEGMENT instead of line.CHECK

### Dimensions of Spaces

- Is the Snake in the game really 1D? It clearly has height in the image. I understand the point you're trying to make, but I think there's got to be a better example. What about a movie projected on a screen?

- It's the only half-way decent image of the game I could find.
- I think you misunderstood me - it's not an issue with the quality of the picture. In that game, I maintain that the snake itself is 2D, as the blocks it's made out of have both height and width.

- rectified

- Rebecca 02:04, 12 July 2011 (UTC) Infinitely many dimensions exist, and when talking about and arbitrary dimension, the term "n-dimensional" is used. The use of multiple dimensions has many concrete applications as well.

- What about... "There are in fact an infinite number of dimensions, so when we talk about an arbitrary number of dimensions, we use the term "n-dimensional." Feel free to use your own wording, I just thought your original sentence was a bit clunky.

## Four Dimensions

Kate 15:33, 9 June 2011 (UTC):

- It'd be nice to have sort of a mission statement for this section - let the reader know that you're going to be building up to an understanding of four-dimensionality.

- Also, why are you enclosing your tuples in curly brackets? Isn't it typical to write points like (x), (x,y), (x,y,z), etc.?

- I don't know, maybe because that is how you do it in mathematica. Thanks for letting me know.

### 1D

*Dimensions are represented mathematically by a coordinate variable.***An**point specified by one variable, such as x=8, can be plotted on the 1D number-line, also known as the x-axis, at the point {8}, as shown below.

- This makes almost no sense to me. I don't think that your first sentence is accurate - the whole concept of a dimension isn't represented by a single coordinate. Although, do you mean that something like "X" in "x-axis" stands in for one direction? I thought you were saying something like (8) represented the concept of one-dimensionality. Also, typo at the beginning of the second sentence.CHECK

### 2D

- This section is clearer than the 1D section, but check it for typos.

### 3D

- Again, check for typos.

- The image is a little confusing. I'd like it if the negative z axis continued beyond the horizontal dotted line. Also, your z-coordinate is given as positive 6, but the line appears to be going backwards.After much editing, I fixed both the braces and the z-axis problems.

### 4D

- Since what you've (presumably) been trying to do all along is present an analog in lower dimensions, I think you should bring up the point about how 2D points can look the same when viewed in 1D earlier, and instead just refer back to it here.

I changed the example.

- As part of that example, I don't think you mean "when looked at from above", but rather something like "when looked at from the x-axis" or something. To me, above is out of the graph looking down (like looking out of an airplane).

I changed the example.

- I'm not sure this section would really explain 4D to me if I didn't already feel comfortable with it, but I can't really put my finger on what should be added. It just seems too short to adequately address the issue.

- xd 21:12, 13 June 2011 (UTC) Why don't you mention the 4th physical dimension being time. For example, the first three coordinates describes where the object is in space, and the forth variable describes where it is in time.CHECK

SteveC -- The figures in the 3D and 4D sections all refer to (8,7.*) where * is a scalar or a pair. Since (8,7) comes from the 2D figure, is was probably assumed that these coordinates would naturally carry over to the 3D and 4D cases. However, the 2D grid does not carry over and the x- and y-axes do not have the values 8 and 7 indicated, and that might make it awkward for a novice reader to understand the figure in the 3D discussion. This is probably even harder to see for the 4D figures. I'm unclear on what you are trying to convey. When I first read the left-hand figure in the 4D section, I had a hard time seeing the point that (8,7,0) and (8,7,6) project to the same 2D point. I looked at the figure in 3D and was not sure for a bit about the difference between this and the first 4D figure. I believe that if you put a 7 on the Y-axis and 8 on the X-axis, this would be clearer. This point may seem minor but if it makes the figures clearer for even a few people, I believe it's worth doing.

In the first line under *nDimensions* there's a typo in "and arbitrary dimension"</font>