Properties of Negative Lengths

[Endercreeper01]

If you theoretically had negative lengths, what are some ways they would differ from positive lengths?

[DevilSolution]

Well, if you use a graph you can have a positive correlation starting from say x,10 and going to x,-30, would this be what you mean by minus length?

 

The answer is direction if the above is right.

Edited November 16, 2013 by DevilSolution

[Endercreeper01]

No, I mean if you theoretically had negative measures of lengths, such as -3 meters

[DevilSolution]

You'd be going backwards in time

 

You can have a negative length as a variable in an equation, thats not theoretical. For example if i was 2m away from the post box and walked 3m towards it id be -1 behind it. Im pretty sure it represents direction.

[Unity+]

No, I mean if you theoretically had negative measures of lengths, such as -3 meters

Besides what DevilSolution just stated, you can't have negative distances in a sense of negativity that you speak of...that is not in this Universe.

[Endercreeper01]

No, I mean if you theoretically measured something to be a negative length, such as -3 meters

Edited November 16, 2013 by Endercreeper01

[Unity+]

You'd be going backwards in time

 

You can have a negative length as a variable in an equation, thats not theoretical. For example if i was 2m away from the post box and walked 3m towards it id be -1 behind it. Im pretty sure it represents direction.

But that still wouldn't be the negativity that he speaks of because your merely are changing your direction in time if I am correct.

No, I mean if you theoretically measured something to be a negative length, such as -3 meters

Well, it just seems like your asking "what if unicorns exist" because unless someone develops some system in Mathematics that deals with this kind of situation(if it would even be applicable in real situations) it doesn't exist(unless you begin referring to imaginary systems, but even there it doesn't apply in the way you state it).

[Endercreeper01]

I would basically be asking something like that. I was wondering if there was a mathematical system to describe negative lengths.

And also, if there were negative lengths, would they theoretically be in negative dimensions?

[DevilSolution]

I would basically be asking something like that. I was wondering if there was a mathematical system to describe negative lengths.

And also, if there were negative lengths, would they theoretically be in negative dimensions?

 

Have a look at the cartesian plane, you can have sin, cos, - sin, -cos to represent angles. If you had -sin(20) the angle would be below 0 on the x axis. Its not in a negative dimension though it represents polarity. The same applies with length, a negative length would indicate a direction, as unity said, variable to time.

Edited November 16, 2013 by DevilSolution

[Unity+]

 

Have a look at the cartesian plane, you can have sin, cos, - sin, -cos to represent angles. If you had -sin(20) the angle would be below 0 on the x axis. Its not in a negative dimension though it represents polarity.

I thought he was just referring to distances. On Cartesian planes, yes negative exists.

[DevilSolution]

I thought he was just referring to distances. On Cartesian planes, yes negative exists.

 

I'm just throwing it out there, in 3D graphics distance is represented by the cartesian plane so im probably getting confused.

[Endercreeper01]

I mean negative length as in if you measured something to be negative length, and not as in a number line.

[HalfWit]

I would basically be asking something like that. I was wondering if there was a mathematical system to describe negative lengths.

 

 

The mathematical abstraction that describes distances is called a metric space. In a metric space, distance is required to be a nonnegative real number. There's no mathematical theory of negative lengths. That's not to say that someday someone won't come up with something like that, but it's not currently available. The field's wide open to you.

 

http://en.wikipedia.org/wiki/Metric_space

[decraig]

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If you theoretically had negative lengths, what are some ways they would differ from positive lengths?

 

This is not such a bad idea, and deserves better consideration.

 

The cross product of two vectors yields a signed area of the parallelogram spanned by the vectors. This extends to volumes and so on. Signed values are very important in physics.

 

Does this generalize to one dimensional curves? Anyone?

 

 

 

 

[Endercreeper01]

Oh. I will try to make a theory for negative lengths.

And the theory wouldn't just include lengths, it would also include negative space, which will be defined as space where all the measurements are negative, and also space with positive and negative measurements.

[Unity+]

Oh. I will try to make a theory for negative lengths.

And the theory wouldn't just include lengths, it would also include negative space, which will be defined as space where all the measurements are negative, and also space with positive and negative measurements.

You will need to, however, base it on mathematical concepts that we have today. You can't just go out and declare random jargon such as "-1 m = 1". You would also need someway to translate it into something that is understandable in the ways of the mathematical concepts we have today. For example, Newton didn't just base Calculus on random logic. His basis was around limits, which was based on having multiple steps in an equation.

 

EDIT: For example, I am currently working on something called Collatz Theory, which deals with taking equations as multiple step processes and combining multiple equations together to form matrix solutions. However, I didn't declare jargon, but I use concepts of what is known about mathematics and making it into something useful.

 

Mathematics is an evolution of logic using the basic forms of logic, in a simple case understanding.

Edited November 17, 2013 by Unity+

[DevilSolution]

EDIT: For example, I am currently working on something called Collatz Theory, which deals with taking equations as multiple step processes and combining multiple equations together to form matrix solutions. However, I didn't declare jargon, but I use concepts of what is known about mathematics and making it into something useful.

 

Mathematics is an evolution of logic using the basic forms of logic, in a simple case understanding.

 

 

That sounds interesting, you using formal proof or computational?

[Unity+]

 

That sounds interesting, you using formal proof or computational?

[offtopic]An equal amount of each. I need both in order to go onto the next step of the theory. The problem is it requires much computation to find all matrix solutions of a given equation. If I can find an equation to find how many matrix solutions exist for a given equation, which I am still working on, then it will be easier to start using formal proofs.[/offtopic]

 

But back the point, you will really need to investigate regular mathematical theories in order to establish a grounds for a theory of negative distances(unless someone has already started working on one. First investigate whether it is being looked into or not. There are theories out there that aren't really talked about on the web).

Edited November 17, 2013 by Unity+

[Endercreeper01]

I will base it off of things such as metrics. And also, I have looked into it, and have found no negative length theories.

[studiot]

But we already have a concept and definition of negative length.

 

Work done = force times distance moved in the direction of that force.

 

So distance in the opposite direction (ie against the force) is negative, as is the work.

 

In mechanics, extension is reckoned positive, contraction negative.

[Endercreeper01]

I don't mean negative lengths as in direction, I mean negative lengths as in the measure of a length to be negative

[studiot]

The extension of an unstretched or compressed spring is zero.

 

So if I stretch a spring is the length of the extension positive or negative, given that the spring is now longer?

 

If I compress the spring is the extension now positive or negative, given that the spring is now shorter?

[Endercreeper01]

Would that be an actual measure of negative length? No, that still counts as a change in direction. You are talking about vectors.

[studiot]

 

You are talking about vectors.

 

 

Vectors are most definitely not what I am talking about.

 

Expansion and contraction have 1D, 2D and 3D versions.

Take a cube, heat it up, cool it down.

It expands and contracts

 

Where are the vectors?

 

When it is smaller is the length of side, area or volume that no longer exists negative?

Edited November 18, 2013 by studiot

[Unity+]

When it is smaller is the length of side, area or volume that no longer exists negative?

I think that could be applicable in some ways of being negative.