is there such a thing as a straight line?

[CryOfALion]

Perhaps if the straight line was infinitesimally short, but not quite zero. Two quantised volumes of space that are next door neighbors?


eudaimonia,

Mark

Interesting...

There is infinite numbers between infinitesimal point x1 and the next infinitesimal point x2<x1 so that x1-x2 --> infinitesimal. This is because infinitesimal, like infinity is not a number, but a generator of the field of respective null spaces for respective rings.

For example, in 1D if a is the infinity generators of +Z, and b is the infinity generator of +R , and we pick an element in a, a*, as the most infinitesimal point on the number line of a, and b* likewise, we couldn't compute a* - b*, because it could be any form of

c( a * - b *),

with c an integer. And, c has to be nonzero if these elements are abelian, which is what we need. Or, rather, want it. Otherwise, we just get a linearly dependent answer from the operation, which just suggests they are part of the same set/family. And, it implies symmetry. Also, the trivial case c=0 is also linearly dependence, and we choose zero as a limit infinitesimal so that all elements are greater than zero. (I use this because 0 is the limit that 1/x approaches as x gets incredibly large from the left or right.)

The conclusion would be if two elements in respective chosen spaces are linearly independent, and therefore not in the same set/family, then there exists no element k = c( a * - b *) = 0. If the elements are linearly dependent, then there will exist an element k = 0. But, this suggests they are in the same family. So, that is another way of saying in the same "reference frames," or more specifically, same vector space.

So, just like the geometric straight line only existing in the same reference frame on the most infinitesimal level, the algebraic straight line only exists if two points are on the same number line, or ring. For 2D, it must be the same plane, and so on.

And so, one could philosophically akin one's own life journey as "straight," or righteous in one's own reference frame, or world/ego.

 

[PsychoSarah]

You can probably conceptualize a strait line, but if you mean the infinite sort than probably no

 

[sarxweh]

You can probably conceptualize a strait line, but if you mean the infinite sort than probably no

A conceptual straight line is straight until i say its infinite at which point it becomes curved?

 

[sarxweh]

Exactly. That's what I'm saying.

Light acts to take the shortest path.

If the universe were flat, light would travel in straight lines.

But the universe is not flat, so light travels in curves, but these curves are analogous to great circle routes. They are the closest thing to straight lines that exist in a curved space.

"In mathematics, particularly differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". "

So is the lack of a straight line a material problem? That there is simply no material which can be unaffected by the forces surrounding it?

Or is it a law/principal problem, that even given a material that could resist the forces surrounding it, the line would curve on the basis of the fact that the universe is "round"?

 

[essentialsaltes]

So is the lack of a straight line a material problem? That there is simply no material which can be unaffected by the forces surrounding it?

Or is it a law/principal problem, that even given a material that could resist the forces surrounding it, the line would curve on the basis of the fact that the universe is "round"?

IF the question is whether you can make a physical 'ruler' that is 'perfectly straight', that's not so hard, unless you want to be unreasonably accurate. Since matter is made of atoms, any ruler will start to look lumpy if you turn up the magnification until atoms look like beach balls.

 

[PsychoSarah]

A conceptual straight line is straight until i say its infinite at which point it becomes curved?

I am saying you can't actually imagine a line without an end. Even if you symbolically put arrows suggesting it infinitly continues as strait, you are renduring that idea as finite to even think of it

 

[durangodawood]

....But you tell me, is there such a thing as a straight line?

First:

Is there even such a thing as a LINE, of any description ?
.

 

[sarxweh]

Okay. I'm rephrasing. What is "straightness"?

Recap: I (an insignificant work study drone) realize a principal conundrum by inductive reasoning (in a very freaky environment no less) and realize: no line is really straight.

When i realize this I think of all the obvious stuff: things can be "straight enough" (tangents and other small scale examples), the universe in general is "a curved space" (thanks theory of relativity), the general limit in strength inherent in material substances that can stand up to long distances in the universe as we know it (although I'd love to give adamantium its fair chance... Or cyclops' laser beams for that matter), ETC.

BUT THIS IS A PHILOSOPHICAL QUESTION sorry caps were still on

Its a philosophical question to me. The way it struck me at first was the problem of a straight line (given its surroundings) and in that sense the idea of a straight line became a character to me. Traversing the moral plane, so to speak. I don't know how to phrase that exactly now that I'm trying.

 

[PsychoSarah]

Okay. I'm rephrasing. What is "straightness"?

Recap: I (an insignificant work study drone) realize a principal conundrum by inductive reasoning (in a very freaky environment no less) and realize: no line is really straight.

When i realize this I think of all the obvious stuff: things can be "straight enough" (tangents and other small scale examples), the universe in general is "a curved space" (thanks theory of relativity), the general limit in strength inherent in material substances that can stand up to long distances in the universe as we know it (although I'd love to give adamantium its fair chance... Or cyclops' laser beams for that matter), ETC.

BUT THIS IS A PHILOSOPHICAL QUESTION sorry caps were still on

Its a philosophical question to me. The way it struck me at first was the problem of a straight line (given its surroundings) and in that sense the idea of a straight line became a character to me. Traversing the moral plane, so to speak. I don't know how to phrase that exactly now that I'm trying.

Your attempt at making a strait line deep is... interesting

 

[sarxweh]

Did I lose everyone with "straightness"?

 

[sarxweh]

Geez

 

[CryOfALion]

I thought people gave some pretty profound philosophical and mathematical answers.

Is there a specific question you may have beyond your op?

 

[sarxweh]

Your attempt at making a strait line deep is... interesting

Accident

 

[Chesterton]

I thought people gave some pretty profound philosophical and mathematical answers.

Is there a specific question you may have beyond your op?

Maybe looking for a philosophical response the next time a cop asks him to do a field sobriety test?

 

[sarxweh]

First:

Is there even such a thing as a LINE, of any description ?
.

Not sure. That's my question

 

[sarxweh]

Maybe looking for a philosophical response the next time a cop asks him to do a field sobriety test?

Cop: do you know why I pulled you over?

Me: not really officer... ?

Cop: .... neither do I .... [Removes glasses, stares off into sunset]

 

[CryOfALion]

A straight line is a curve of constant gradient.

Perfect examples of almost any idealised mathematical concept will be difficult to find in the physical universe.

As usual, it depends what you mean.

In Euclidean geometry, the line has no thickness, and is not made of anything but points, which have no nothing. Needless to say the Euclidean line does not exist as a real object like a banana. It's an idea.

If by straight line, you mean the shortest distance connecting two points, then a laser beam in a vacuum would follow a straight line. (Indeed, any object interacting solely with gravity would follow a straight line.)

On the surface of the earth the shortest distance between two points is a great circle route. It isn't a 'straight line' in the usual sense, because the space (the surface of the earth) is curved. In a curved space, the shortest distance is generally not a line, but a geodesic curve.

General relativity tells us that space is itself curved, and an important consequence is that "the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic."

Interesting...

There is infinite numbers between infinitesimal point x1 and the next infinitesimal point x2<x1 so that x1-x2 --> infinitesimal. This is because infinitesimal, like infinity is not a number, but a generator of the field of respective null spaces for respective rings.

For example, in 1D if a is the infinity generators of +Z, and b is the infinity generator of +R , and we pick an element in a, a*, as the most infinitesimal point on the number line of a, and b* likewise, we couldn't compute a* - b*, because it could be any form of

c( a * - b *),

with c an integer. And, c has to be nonzero if these elements are abelian, which is what we need. Or, rather, want it. Otherwise, we just get a linearly dependent answer from the operation, which just suggests they are part of the same set/family. And, it implies symmetry. Also, the trivial case c=0 is also linearly dependence, and we choose zero as a limit infinitesimal so that all elements are greater than zero. (I use this because 0 is the limit that 1/x approaches as x gets incredibly large from the left or right.)

The conclusion would be if two elements in respective chosen spaces are linearly independent, and therefore not in the same set/family, then there exists no element k = c( a * - b *) = 0. If the elements are linearly dependent, then there will exist an element k = 0. But, this suggests they are in the same family. So, that is another way of saying in the same "reference frames," or more specifically, same vector space.

So, just like the geometric straight line only existing in the same reference frame on the most infinitesimal level, the algebraic straight line only exists if two points are on the same number line, or ring. For 2D, it must be the same plane, and so on.

And so, one could philosophically akin one's own life journey as "straight," or righteous in one's own reference frame, or world/ego.

Exactly. That's what I'm saying.

Light acts to take the shortest path.

If the universe were flat, light would travel in straight lines.

But the universe is not flat, so light travels in curves, but these curves are analogous to great circle routes. They are the closest thing to straight lines that exist in a curved space.

"In mathematics, particularly differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". "

Maybe looking for a philosophical response the next time a cop asks him to do a field sobriety test?

I would love to see a YouTube video of a person arguing sobriety saying one of these theories above.

It would be interesting to see how a mathematician defends himself in court for failing a straight line DUI test.

 

[quatona]

Did I lose everyone with "straightness"?

You surely lost me when you seemed to define "philosophy" in a way that requires it to be absolutely useless for any given purpose.

A "straight line" in the sense you define it is an abstraction and therefore doesn´t, can´t and isn´t expected to exist in the real world. Just like "39" doesn´t exist in the real world.

 

[sarxweh]

You surely lost me when you seemed to define "philosophy" in a way that requires it to be absolutely useless for any given purpose.

A "straight line" in the sense you define it is an abstraction and therefore doesn´t, can´t and isn´t expected to exist in the real world. Just like "39" doesn´t exist in the real world.

What? I'm not sure what you mean. In what way have i defined philosophy?

Agreed. I thought a line not being possible was what I realized with the buckets... That it can only be theoretical. That's correct right? Seems to be the consensus here at least (which is encouraging).

Anyway, my op was an effort to think through the implications. I'm education is incomplete

 

[quatona]

What? I'm not sure what you mean. In what way have i defined philosophy?

You tell me. When saying it was a "philosophical question" (in all caps) what did you mean to contrast it to?

Agreed. I thought a line not being possible was what I realized with the buckets...

Well, a line - as determined by the given purpose and intent is possible.
It´s just not the same as the abstract "philosophical" line you seem to be demanding.

That it can only be theoretical. That's correct right? Seems to be the consensus here at least (which is encouraging).

Yes, an entirely theoretical abstract line can only be theoretical, abstract.
Concrete lines (as defined by the purposes the are drawn to suit) are possible.

Anyway, my op was an effort to think through the implications.

So what are these implications you would like me to think through?

I'm education is incomplete

I beg your pardon?