Bayoubill’s Ongoing Ponderance of the “Four-Corners” Question

[Amelia]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Imagine drawing the corner of one state with a pen of zero width. No matter which state boundary you try to trace around that corner, you have to pass directly over the corner spot (in order to start moving your pencil perpendicular to the line you just traced to get to the corner) THEREFORE: The corner point is shared by all four states.

It is understood and accepted that all four states share the common point...

consider this though... if Colorado and Arizona are in contact with each other,

it therefore creates a barrier that prevents Utah and New Mexico from making contact...

If you say that they share the common point, then they touch. You are using part of Utah and New Mexico to form that supposed barrier. Your barrier can't be shutting Utah and New Mexico out if it actually includes part of Utah and New Mexico.

 

[007]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Imagine drawing the corner of one state with a pen of zero width. No matter which state boundary you try to trace around that corner, you have to pass directly over the corner spot (in order to start moving your pencil perpendicular to the line you just traced to get to the corner) THEREFORE: The corner point is shared by all four states.

It is understood and accepted that all four states share the common point...

consider this though... if Colorado and Arizona are in contact with each other,

it therefore creates a barrier that prevents Utah and New Mexico from making contact...

If you say that they share the common point, then they touch. You are using part of Utah and New Mexico to form that supposed barrier. Your barrier can't be shutting Utah and New Mexico out if it actually includes part of Utah and New Mexico.

Exactly. The OP is assuming that the imaginary boundary lines have mass. They're just lines on a map, not something that exists in the real world separating the states.

Of course all the states are touching.

 

[bayoubill]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Imagine drawing the corner of one state with a pen of zero width. No matter which state boundary you try to trace around that corner, you have to pass directly over the corner spot (in order to start moving your pencil perpendicular to the line you just traced to get to the corner) THEREFORE: The corner point is shared by all four states.

It is understood and accepted that all four states share the common point...

consider this though... if Colorado and Arizona are in contact with each other,

it therefore creates a barrier that prevents Utah and New Mexico from making contact...

If you say that they share the common point, then they touch. You are using part of Utah and New Mexico to form that supposed barrier. Your barrier can't be shutting Utah and New Mexico out if it actually includes part of Utah and New Mexico.

arrgggh... you make me wanna kill baby kittehs with that argument, Steph...

on a four-region Cartesian plane, with Colorado, Utah, Arizona, and New Mexico representing the four regions...

if it was somehow established that Colorado and Arizona touch each other,

then Utah and New Mexico could not be in contact with each other because of the barrier created by the contact between Colorado and Arizona...

 

[deaddogseye]

how many states can dance on the head of a pin?

 

[bayoubill]

It is understood and accepted that all four states share the common point...

consider this though... if Colorado and Arizona are in contact with each other,

it therefore creates a barrier that prevents Utah and New Mexico from making contact...

If you say that they share the common point, then they touch. You are using part of Utah and New Mexico to form that supposed barrier. Your barrier can't be shutting Utah and New Mexico out if it actually includes part of Utah and New Mexico.

Exactly. The OP is assuming that the imaginary boundary lines have mass. They're just lines on a map, not something that exists in the real world separating the states.

Of course all the states are touching.

please explain to me how Utah and New Mexico can touch each other at the same time that Colorado and Arizona touch each other...

 

[007]

If you say that they share the common point, then they touch. You are using part of Utah and New Mexico to form that supposed barrier. Your barrier can't be shutting Utah and New Mexico out if it actually includes part of Utah and New Mexico.

Exactly. The OP is assuming that the imaginary boundary lines have mass. They're just lines on a map, not something that exists in the real world separating the states.

Of course all the states are touching.

please explain to me how Utah and New Mexico can touch each other at the same time that Colorado and Arizona touch each other...

Please explain to me why they can't.

If all four corners aren't all touching in the same manner, then none of them are.

But you're still assuming that there's some sort of physical separation between them. What is that and where did it come from?

AND HAVEN'T YOU GOTTEN THAT BOOGER OUT OF YOUR NOSE YET? Must be one MUTHA FUCK OF A BOOGER!

 

[Amelia]

It is understood and accepted that all four states share the common point...

consider this though... if Colorado and Arizona are in contact with each other,

it therefore creates a barrier that prevents Utah and New Mexico from making contact...

If you say that they share the common point, then they touch. You are using part of Utah and New Mexico to form that supposed barrier. Your barrier can't be shutting Utah and New Mexico out if it actually includes part of Utah and New Mexico.

arrgggh... you make me wanna kill baby kittehs with that argument, Steph...

on a four-region Cartesian plane, with Colorado, Utah, Arizona, and New Mexico representing the four regions...

if it was somehow established that Colorado and Arizona touch each other,

then Utah and New Mexico could not be in contact with each other because of the barrier created by the contact between Colorado and Arizona...

The argument which would be used to establish that Colorado and Arizona touch each other would apply equally to Utah and New Mexico.

The only way for them to be deemed to touch each other would be for them to have a non-zero intersection. All FOUR states would have to intersect at that point where CO and AZ intersect unless you wished to give to Colorado and Arizona rights not granted to Utah and New Mexico, and I don't think that would stand up in the Supreme Court.

 

[Ernie S.]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Well said. Except I went the other direction in my answer. I went with it belonging to none of them.

Has anyone looked at the issue legally? Does the border between two states belong to each state? Or to neither?

Does it matter? The border is a zero width line and the corner is an infinitesimally small point. The more I think about it, I have to consider that in all practicality, the border and intersection don't exist, so, no. New Mexico and Utah do not touch.

 

[Amelia]

Bill, if you want to think about it in terms of the Cartesian plane, then you are defining Colorado as the closure of the first quadrant -- that is to say as the union of Q I, the origin, the positive x-axis and the positive y-axis.

Utah would be defined as the closure of Q II -- i.e., the union of Q II, the origin, the positive y-axis and the negative x-axis.

Arizona would be defined as the closure of Q III.

And New Mexico as the closure of Q IV.



The intersection of those four closures would be the origin.






Edit: Well, you seem to want to define only Colorado and Arizona in those terms. But if you define Colorado and Arizona that way, then you'd pretty much have to define Utah and New Mexico that way. Or we're back in the Supreme Court. ( :

 

[bayoubill]

ah fuck it... at least for the time being...

meantime...

[ame="http://www.youtube.com/watch?v=jVdlxwX6A7g"]http://www.youtube.com/watch?v=jVdlxwX6A7g[/ame]