Quantifying the Physical Property of Direction.

[Strange]

The model was produce from these three animations posted to youtube.

 

And how were those animations produced?

 

And why; i.e. what is the purpose of those animations?

 

And why are you releasing this information so slowly? Why don't you just tell us the whole story?

[studiot]

 

strange

Why don't you just tell us the whole story?

 

 

 

+1

Edited May 25, 2016 by studiot

[Strange]

 

The input and output of a function have been provided.

 

Why is that not math?

 

If you think that is satisfactory, why do you need anything else?

 

In summary:

 

1. You think that the animation is math, but you still want someone to do the math for you.

 

2. You "have done the math" but you still want someone to do the math for you.

 

3. You "know how to create the model" but you want someone else to do it for you.

 

4. You believe the model represents something of significance but you want someone else to do the math to prove it.

 

5. "Its is just simple math" but it is more complex than it looks and no one has seen it before. (But but you want someone else to do the math to prove that.)

 

6. I think you have also said it can't be done, but you want someone to do it.

 

I still don't really know if this is dishonesty or laziness. But it doesn't encourage anyone to help.

[Mordred]

 

The input and output of a function have been provided.

 

Why is that not math?

Well I'm glad your satisfied with what's hidden in mathematica.

 

Personally if I wanted to fully understand an animation. I'd like to be able to apply it to any programming language. Even basic.

 

( with the exception of PLC based lanquages I'd hate to try this in ladder logic or booleon lol)

Edited May 25, 2016 by Mordred

[Klaynos]

 

 

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Moderator Note

That's not doing any maths that's just writing out seemingly random things. If you've done the maths you shouldn't need mathematica, it's just a tool to make some things easier not to replace a piece paper or LaTeX to explain what you've done to others.

 

Last chance or the thread is closed for not meeting our minimum requirements in speculations.

[studiot]

So let us study the subject of invariance further, particularly in relation to magnitude, direction and since you have introduced it, orientation.

 

When Studio T was first formed we did a lot of animations., but I no longer have the resources to do these.

Happily there is not need, as Klaynos observes.

Pencil and paper will suffice.

 

So start with a well fixed signpost as in Fig1.

 

Add a Euclidian coordinate system as in Fig2.

Since we are looking for quantities that are the same in all coordinate systems any system will do so I have picked a convenient one with the signpost aligned along the positive x axis.

 

Now consider a 90^o rotation of the axes as shown in Fig3, around the z axis.

 

Note the signpost does not move and continues to point in its original direction.

 

The transformation is shown in Fig4, including the mathematical formulae.

 

It is immediately seen that the signpost is now pointing in the negative y direction so neither direction nor orientation are preserved.

 

So they are not invariants in Euclidian systems.

 

But what about magnitude?

 

Well suppose we use the standard measure

[math]L = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} [/math]

 

and allow the sign to be 10 units long so in Fig2 it stretches from

 

x₁ = 0 to x₂ = 10

y₁ = 0 to y₂ = 0

z1= 0 to z₂ = 0

 

[math]L = \sqrt {{{\left( {10 - 0} \right)}^2} + {{\left( {0 - 0} \right)}^2} + {{\left( {0 - 0} \right)}^2}} = 10[/math]

 

and in fig4

 

x'₁ = 0 to x'₂ = 0

y'₁ = 0 to y'₂ = -10

z'1= 0 to z'₂ = 0

 

and the measure is

[math]L = \sqrt {{{\left( {\left( { - 0} \right) - \left( 0 \right)} \right)}^2} + {{\left( {0 - 10} \right)}^2} + {{\left( {0 - 0} \right)}^2}} = 10[/math]

showing that, at least for this transformation, length is invariant.

 

Edited May 25, 2016 by studiot

[steveupson]

Now we're getting somewhere. The example uses a rotating body in a fixed reference frame. The same exercise can be done with a fixed post and a rotating reference frame. The rules are different because there we are dealing with a non-Euclidean frame.

 

What I'm talking about is a geometric truth that can be applied to either case. We only believe that length is constant and direction is changing because that's how we've always done the math. The reason we've always done the math that way is because the way we express direction doesn't commute, while length does.

 

What I'm talking about is a technique for expressing direction in a manner that commutes mathematically in the same way that length does in our conventional methods.

[Strange]

Now we're getting somewhere. The example uses a rotating body in a fixed reference frame. The same exercise can be done with a fixed post and a rotating reference frame. The rules are different because there we are dealing with a non-Euclidean frame.

 

What I'm talking about is a geometric truth that can be applied to either case. We only believe that length is constant and direction is changing because that's how we've always done the math. The reason we've always done the math that way is because the way we express direction doesn't commute, while length does.

 

What I'm talking about is a technique for expressing direction in a manner that commutes mathematically in the same way that length does in our conventional methods.

 

Please show us the maths that you have done that supports these wild claims.

 

After all, you have said repeatedly that you have "done the math". You have vanishingly little credibility left. Time to put up or shut up.

Now we're getting somewhere.

 

This is schoolboy mathematics. If you think this is some sort of revelation or insight, then you are not getting anywhere.

[studiot]

 

steveupson

The example uses a rotating body in a fixed reference frame. The same exercise can be done with a fixed post and a rotating reference frame. The rules are different because there we are dealing with a non-Euclidean frame.

 

 

 

I am not sure which or whose example you are referring to but you have been told many times by several mathematicians of world renown that the standard geometry of the sphere is Euclidian. Euclid himself did some of it. You were also told that the Cartesian geometry I offered in my example in post231 is also Euclidian, although Euclid never did any of this.

I am not going to go there again.

 

I recently asked you not to introduce spurious terms you do not understand. So please ask if you need to know if something is Euclidian or non Euclidian.

 

Nor , I think, do you understand the word 'commute'.

It does not mean 'shuttle back and fore between frames or coordinate systems'

I means that you get the same result for two operations A and B whichever order you perform them in.

 

I don't see two operations here.

 

Now I clearly specified a fixed object

 

 

studiot

well fixed signpost

 

However, as you say, this seems to have brought out into the open your 'hopeful insight' that not only does is length invariant but also something you call direction.

 

You could have started this thread with that proposal.

[steveupson]

It probably is time to close the thread. Everyone stopped listening long ago. We're rehashing stuff that is already redundant in this discussion.

 

Thanks everyone.

 

I'll probably resume these discussion at in few days. Anyone interested stop by and join in. If anyone out there gets the gist of what I've been saying, please join in. Or if you just have questions, join in.

 

If anyone figures out the formula for the function, please post it.

 

Thanks again for hosting this discussion.

[Klaynos]

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Moderator Note

Thread closed, op hadn't done the maths.

Do not reintroduce this topic.

Also, advertising link removed.

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