Quantifying the Physical Property of Direction.

[ajb]

It IS on paper.

 

It's a protractor.

So what is the problem?

 

You know how to map the coordinates of the point shown as a little ball to an angle? Or you don't?

 

As Mordred has suggested, it is probability not much more than some trig functions.

[Strange]

If someone would actually take the effort and do the math, then you'd see.

 

 

Why would anyone try and solve this problem for you?

 

I have done the math.

 

Then show us.

 

Now, strange has graphed the function

 

I just took the numbers from your animation and put them into a spreadsheet.

 

and the argument becomes, yeah, but it ain't nothin special.

 

That has always been my argument. Which is why no one is going to do this for you.

 

Someone please take the effort to graph the function at 30 and 60 degrees.

 

The graph I posted goes over the full range of your animation. So you can work out the values at 30 and 60 from that. But 30 degrees is one of the numbers in the animation.

30 -> 35.3

60 -> 15.5

[Mordred]

Steve all you need to do is look for two simultaneous trig operations. Look at how point e moves. If calling two simultaneously operated trig functions count as a new function ( which it doesn't) then sure it's a new function.

 

Every change relates to a change in degrees in two simultaneously operated trig operations.

 

For e one is y to x, the other is z to x.

 

The other clue is the angle between longitude and tangent planes is identical at times.

 

In essence he is applying the same change on the logitude plane and the tangent plane and calling this a new trig function.

One example plot f(x,y)=sine(x)+y

Edited May 24, 2016 by Mordred

[steveupson]

 

 

 

It just shows some planes being rotated around the surface of a cone. One thing that isn't clear is what it means by the angle between two planes. I decided that the easiest way to define that is in terms of the surface normals, which are vectors.

 

 

 

 

That's the description of the

 

So what is the problem?

 

You know how to map the coordinates of the point shown as a little ball to an angle? Or you don't?

 

As Mordred has suggested, it is probability not much more than some trig functions.

 

Yes, some trig functions. But if you won't actually do the math then it's simply a lot of handwaving, imho.

 

I have done the math so I do know that all the opinions about how simple (and foolish) it is are incorrect.

 

Everyone is missing the sophistication of the model by many, many orders of magnitude.

 

What is the blue line in the graph.

 

If it is the simple function you claim it is, then you've seen it before.

 

What is it?

[Mordred]

Then post the math. Quite frankly programming this animation is straight forward.

Edited May 24, 2016 by Mordred

[steveupson]

 

 

 

The graph I posted goes over the full range of your animation. So you can work out the values at 30 and 60 from that. But 30 degrees is one of the numbers in the animation.

30 -> 35.3

60 -> 15.5

 

The animation shown is for a small circle have a specific dimension and orientation.

The animation has a small circle dimension of 45 degrees latitude and is tilted 45 degrees from the horizontal such that it intersects the pole.

This produces the function that you graphed.

 

We need another animation with a small circle with a dimension of 30 degrees latitude tilted 30 degrees from horizontal such that it intersects the pole.

 

Then we need a third animation with at small circle with a dimension of 60 degrees lattitude tilted 60 degrees from the horizontal such that it intersects the pole.

 

Each of these will produce a different function.

Then post the math. Quite frankly programming this animation is straight forward.

 

I would think that a passing familiarity with geometry would be beneficial, but sure, it is straightforward for someone with the skills.

 

The math is posted. Why can't you see that. All we have is this model.

 

The function is waaaaaaaaaaaaaaaaaaaaaaaaaaaay too complicated to describe any other way, at this point in time.

[Mordred]

No you don't you just need a 3d trig function which combines two 2d trig functions.

[steveupson]

 

It is implicit in Mathematica. So now you want people to reverse engineer the code (*) for Mtahematica to solve your non-existent problem.

 

(*) Illegal in some jurisdictions.

 

 

Think about what you're saying.

 

There is a function that was produced by some factors that are implicit in Mathematica and at the same time it is a simple, straightforward, function that no one should waste their time on and because it's so simple and straightforward, no one has ever seen it graphed before and somehow you think that I should know more about it than simply how to create the model.

 

Then, when I say that I do know more about it but I need actual help from actual mathematicians in order to explain it I'm told that I'm simply too lazy to do it myself.

 

Sorry for the rant, but it is very frustrating. I've asked for very specific help with a very specific request and everyone tells me why I should't be doing what I'm doing. I will find a way to do this, eventually. And I do appreciate all the help that has been provided.

 

The graph of the 45 degree function was not at all what I was expecting, not that I was expecting anything in particular. I just wasn't prepared for it to be symmetrical although it does make a lot of sense in retrospect.

No you don't you just need a 3d trig function which combines two 2d trig functions.

 

No, that's a complete misunderstanding of the model.

 

Turn off everything except the longitude, tangent, elevation and equator.

 

There is some spline routine in Mathematica that is returning the function without ever knowing what it is.

Edited May 24, 2016 by steveupson

[Strange]

 

I have done the math

 

Good. Then you can answer the following questions:

 

What is the blue line in the graph.

 

What is it?

 

Come on then, if you have done the math, let us know.

 

Stop all the vague handwaving about how complex it is and just tell us.

[Mordred]

So let's ask the question "why would you think this animation suggests that direction has a property?"

 

Many of your posts along those lines simply distract from solving the math behind the animation.

 

As far as that goes we've supplied the needed clues as to how to program that animation.

In all honesty it merely appears complex.

Edited May 24, 2016 by Mordred

[steveupson]

 

Good. Then you can answer the following questions:

 

 

Come on then, if you have done the math, let us know.

 

Stop all the vague handwaving about how complex it is and just tell us.

 

 

I have told you, and you won't believe me because you haven't done the math.

 

The graph shows the invariant quantity of 45 degrees.

 

You want to know how I know that this it true, but you won't look at the math.

 

 

 

What we need, what will help it make much more sense, is a similar graph that shows the invariant quantity of 30 degrees, and 60 degrees.

 

How do I know it is invariant? Because it has to be. It has no choice in the matter. It's math. Simply math.

[Strange]

Think about what you're saying.

 

Why don't you read what I said, instead of making stuff up.

 

There is a function that was produced by some factors that are implicit in Mathematica and at the same time it is a simple, straightforward, function that no one should waste their time on and because it's so simple and straightforward

 

1. You said that it is implicit in Mathematica. Therefore it is not explicitly described by the code you have posted (which, BTW, I haven't looked at because I am not familiar with Mathematica).

 

2. The fact is is implicit in Mathematica does not necessarily mean it is complex. The implementation of the sine function is built into Mathematica. That is not particularly complicated.

 

3. I never said it was simple. But I can't imagine it is particularly complicated.

 

4. I never said no one should waste time on it because it is so simple. I said that you are the only one interested in the function so either you need to learn enough basic trigonometry to work out the equation for yourself or you need to give others a reason to look into it (cash has been suggested).

 

So if you have quite finished with the lies and straw man arguments, we can move on.

 

you think that I should know more about it than simply how to create the model.

 

If you know how to create the model then you can work out the equation.

 

Or does "knowing how to create the model" have the same level of truthiness as "I have done the math"?

 

Then, when I say that I do know more about it but I need actual help from actual mathematicians in order to explain it I'm told that I'm simply too lazy to do it myself.

 

That sounds about right.

 

I ask for very specific help with a very specific request and everyone tells me why I should't be doing what I'm doing.

 

You have made a series of incoherent and largely meaningless posts about direction, vectors and scalars . It wasn't until 110 (one hundred and ten!) posts that you said you were looking for the equation that related the angle between two planes.

 

There is some spline routine in Mathematica that is returning the function without ever knowing what it is.

 

Splines are usually used to fit a curve to a series of points. I don't see how that is relevant here.

[Mordred]

 

 

I have told you, and you won't believe me because you haven't done the math.

 

The graph shows the invariant quantity of 45 degrees.

 

You want to know how I know that this it true, but you won't look at the math.

 

 

 

What we need, what will help it make much more sense, is a similar graph that shows the invariant quantity of 30 degrees, and 60 degrees.

 

How do I know it is invariant? Because it has to be. It has no choice in the matter. It's math. Simply math.

Fine if the math is so simple to describe as being invariant and you claim to have done that math then post it.

 

It is your claim no one else's. It's time for you to mathematically defend that claim

Edited May 24, 2016 by Mordred

[Strange]

I have told you, and you won't believe me because you haven't done the math.

 

You haven't done the math, which is why I see no reason to believe you.

 

The graph shows the invariant quantity of 45 degrees.

 

What does that even mean? What is invariant? You have two changing (and apparently related) values. In what sense are they "invariant"?

 

You want to know how I know that this it true, but you won't look at the math.

 

If you want people to (a) understand what you are talking about and (b) believe it then you need to post the mathematics of this relationship. (Or pay someone else to do it for you.)

 

What we need, what will help it make much more sense, is a similar graph that shows the invariant quantity of 30 degrees, and 60 degrees.

You "know how to produce the model" and you "have done the math" so why don't you create these graphs?

 

How do I know it is invariant? Because it has to be. It has no choice in the matter. It's math. Simply math.

Until you show us that math, I see no reason to believe that.

And stop blaming other people for your laziness and inability to do the necessary maths.

[steveupson]

 

Why don't you read what I said, instead of making stuff up.

 

 

 

Splines are usually used to fit a curve to a series of points. I don't see how that is relevant here.

 

 

I apologize, I meant you all, not you specifically.

 

That's what the model does, in reverse. It fits a series of points to a curve, and then calculates what plane those points lie in.

 

Or I assume that's how it does it. That would be the simplest method, I would think.

Fine if the math is so simple to describe as being invariant and you claim to have done that math then post it.

 

It is your claim no one else's. It's time for you to mathematically defend that claim

 

 

I have posted the math. The math is the function that strange plotted. What other math do you expect there to be?

[Mordred]

Funny I don't see a single math equation in any of your posts. I see a lot of claims but no equations

Edited May 24, 2016 by Mordred

[steveupson]

 

And stop blaming other people for your laziness and inability to do the necessary maths.

 

 

What do you think the function that you plotted is?

 

Explain to me what you think it is, and then maybe I will know what to say in order to get things on track.

Funny I don't see a single math equation in any of your posts. I see a lot of claims but no equations

 

 

I don't want to be a smart ass, but a function has been plotted and graphed. Are you arguing that this was accomplished without math?

[Mordred]

No I want you to show why that plot means 45 degrees is invariant.

[steveupson]

No I want you to show why that plot means 45 degrees is invariant.

 

Yes, and I want to show you that.

 

We agree.

What is special about this function is that the angle between the two directions (45 degrees) is specified in the space surrounding the plane that the two directions (45 degrees) lie in.

 

In other words, we don't have to know how they relate to one another in the plane that they are both in.

 

If we know that they have this relationship to one anther in space then we know they are 45 to one another in the plane they both occupy.

 

The angle between the two is specified in the space surrounding them.

 

There is nothing, no metric, used in the plane that they are in.

 

Tell me what you think that means.

[Mordred]

Are you aware that angles are considered invariant quantities?

 

"Angles and ratios of distances are invariant under scalings, rotations, translations and reflections. These transformations produce similar shapes, which is the basis of trigonometry"

 

https://en.m.wikipedia.org/wiki/Invariant_(mathematics)

[steveupson]

Yes, but the new quantity is invariant under Lorentz transformation.

 

Relativistic invariance.

Edited May 24, 2016 by steveupson

[Mordred]

Ah now that's a relationship of a completely different stripe as to what's been presented thus far this thread. However the 45 degree line used in Lorentz is a convenient choice. None of the models presented so far this thread has a ct axis.

Edited May 25, 2016 by Mordred

[steveupson]

Ah now that's a relationship of a completely different stripe as to what's been presented thus far this thread.

 

That's the only significance of the model.

[Mordred]

Ok show how ct is represented.

 

Also specify what specifically the 45 degree axis represents on a ct vs x graph.

 

I'd like to see if you truly understand why the 45 degrees is chosen in spacetime graphs.

Edited May 25, 2016 by Mordred

[steveupson]

Ok show how ct is represented.

 

Also specify what specifically the 45 degree axis represents on a ct vs x graph.

 

I'd like to see if you truly understand why the 45 degrees is chosen in spacetime graphs.

 

My understanding is that it is done that way by convention.

 

If there is a mathematical significance, I'm not aware of it. The same things could be shown if the diagram were composed of a 180 degree angle and one 90 degree angle rather than a 90 degree angle and a 45.

 

 

 

on edit> there's no particular significance for why the model uses 45 degrees, other than it was easier to describe it having that form. The thing to remember is that the model produces a function, and that function will change depending on what the angle is between the ordinal and cardinal directions.

 

second edit> after further thought my first response isn't correct. I spoke too soon. The 45 is used because it places time and space on symmetrical axes.

Edited May 25, 2016 by steveupson