Dimensions

leveni · 09-28-2010, 08:46 AM

Dimensions.
I was browsing Wikipedia the other day and had a look at Dimensions.
I now have questions about dimensions that Wikipedia didn't cover.
I just want to go through step by step in a slow tedious logical manner and obtain a reasonable answer to my questions.
Hope someone can help.

Q1. Is the 1st dimension just a perfectly straight line on a plane of infinite length that never bends.
Or can it also be a bendy line that curves all over the place in 3 dimensions?

Personally I think it can only be a perfectly straight line. But need conformation.

Q2. This line, could also never have any width or height it could only have length. Is this true?
If it did have width it would then be 2 dimensional.
If it had height again it would be 2 dimensional.
If it had both width and height it would be 3 dimensional.
Are these three statements also true?

Jahrta · 09-28-2010, 11:20 AM

I believe your initial understanding and assertions are all correct - if something is one dimensional it cannot have thickness, only length. Think of an infinitely thin pencil line, like Prince's mustache. More helpfully, think of the "x" axis on a line graph. If we were to consider a two-dimensional plane, that would give us the "y" axis, but this two-dimensional figure would still lack depth, or what is sometimes labeled as a "z" axis on 3-d graphing.

dogpet · 09-28-2010, 11:37 AM

Quote:

leveni wrote

Dimensions.
I was browsing Wikipedia the other day and had a look at Dimensions.
I now have questions about dimensions that Wikipedia didn't cover.
I just want to go through step by step in a slow tedious logical manner and obtain a reasonable answer to my questions.
Hope someone can help.

Q1. Is the 1st dimension just a perfectly straight line on a plane of infinite length that never bends.
Or can it also be a bendy line that curves all over the place in 3 dimensions?

Personally I think it can only be a perfectly straight line. But need conformation.

Q2. This line, could also never have any width or height it could only have length. Is this true?
If it did have width it would then be 2 dimensional.
If it had height again it would be 2 dimensional.
If it had both width and height it would be 3 dimensional.
Are these three statements also true?

No that's wrong. If you think of the first dimension as width, it's any point, or distance to your left or right. The second is height, anything up or down from a point on the first. The third is depth, which is if you imagine another 2 dimensional view at right angles to the first.

Jahrta · 09-28-2010, 12:16 PM

yeah, sure..what he said

dogpet · 09-28-2010, 12:39 PM

Quote:

Jahrta wrote

yeah, sure..what he said

was on the phone & came back to it.

leveni · 09-28-2010, 07:43 PM

Quote:

dogpet wrote

No that's wrong. If you think of the first dimension as width, it's any point, or distance to your left or right. The second is height, anything up or down from a point on the first. The third is depth, which is if you imagine another 2 dimensional view at right angles to the first.

Ok thanks for the quick response, just need to get the terminology/semantics correct.
In that case:
Q2. This line, could also never have any depth or height it could only have width. Is this true?
If it did have depth it would then be 2 dimensional.
If it had height again it would be 2 dimensional.
If it had both width and depth it would be 3 dimensional.

is this now correct.

dogpet · 09-29-2010, 05:20 AM

Quote:

leveni wrote

Ok thanks for the quick response, just need to get the terminology/semantics correct.
In that case:
Q2. This line, could also never have any depth or height it could only have width. Is this true?
If it did have depth it would then be 2 dimensional.
If it had height again it would be 2 dimensional.
If it had both width and depth it would be 3 dimensional.

is this now correct.

Being a simple line jockey & not a proper mathematician, I'm unable to complicate it too much. Yes, Q1 & Q2 are interchangeable. Depth is the projection from behind & in front of you, & is always false unless viewed on a right plane, ie at 90 degrees to the projection, making it 2D. Think of a ladder against a wall.
So the universe is 2D with the third element down to perception.

leveni · 09-29-2010, 08:00 PM

I going to change it back to my original definition, which happened to be the same as Wikipedia's.
wikipedia
"Lines are an idealization of such objects and have no width or height at all and are usually considered to be infinitely long."

Before I go to the next step, I need consensus in regards to definitions. That's all I'm doing right now.

Any problems with Wikipedia's definition.

dogpet · 09-30-2010, 01:21 PM

Quote:

leveni wrote

I going to change it back to my original definition, which happened to be the same as Wikipedia's.
wikipedia
"Lines are an idealization of such objects and have no width or height at all and are usually considered to be infinitely long."

Before I go to the next step, I need consensus in regards to definitions. That's all I'm doing right now.

Any problems with Wikipedia's definition.

I wouldn't use width to mean depth.