Quantifying the Physical Property of Direction.

[Strange]

In the same way that having a length does not necessitate a coordinate system is my guess. Representing a line without a coordinate system would seem awkward. We aren't really trying to represent an angle (analogous to a line), we're trying to represent the magnitude of the angle (analogous to a length).

 

 

I kind-of see what you are getting at. But the reason a length doesn't require a coordinate system is because it is a scalar value. But, I'm not sure that is even true: in order to define a length, you need to specify the two end points, which requires a coordinate system. The very fact that you have units (metres, parsecs, inches) implies a coordinate system.

 

Similarly, there seem to be contexts where you can treat an angle as a purely scalar thing, for example the phase of a signal. But then it isn't defining a direction. (Actually, that isn't true either. The angle defines a direction in a 2D phase space and sometimes it is easier to convert your signals to that coordinate system.) As soon as you want to talk about direction, then you are no longer referring to just the magnitude of the angle, but its relationship to the basis of the coordinate system.

[ajb]

... you need to specify the two end points, which requires a coordinate system.

To specify we do use a coordinate system, but the points exists independent of any coordinate system.

 

Also, one has to be careful here in general. The length of a vector is defined using the Riemannian metric, it gives us an inner product on the tangent space at each point of the manifold. You can then use this to define the length of a vector at that point and the angle between two vectors at that point.

 

The distance between two points is not really so well defined, but what is well defined, and again uses the metric is the length of a curve joining two points. This is also independent of the coordinates used, but one usually specifies coordinates in order to calculate the length. The minimal length curves are of course the geodesics.

[steveupson]

 

 

I kind-of see what you are getting at. But the reason a length doesn't require a coordinate system is because it is a scalar value. But, I'm not sure that is even true: in order to define a length, you need to specify the two end points, which requires a coordinate system. The very fact that you have units (metres, parsecs, inches) implies a coordinate system.

 

 

I'm not sure how this same argument would be made for the [math]/ cos[/math] function. I really believe that if someone here would help derive the function, or at least compose it, then everyone could at least be talking about the same thing.

To specify we do use a coordinate system, but the points exists independent of any coordinate system.

 

Also, one has to be careful here in general. The length of a vector is defined using the Riemannian metric, it gives us an inner product on the tangent space at each point of the manifold. You can then use this to define the length of a vector at that point and the angle between two vectors at that point.

 

The distance between two points is not really so well defined, but what is well defined, and again uses the metric is the length of a curve joining two points. This is also independent of the coordinates used, but one usually specifies coordinates in order to calculate the length. The minimal length curves are of course the geodesics.

 

There might be some misunderstanding of what we're talking about. The statements that I made about not needing a coordinate system were in regards to composing and deriving the function.

 

I'm not sure how it's done, I've never had to figure it out for myself, but I would be a little bit surprise to find that a coordinate system needs to be decided on before it can be done.

 

If we just had something that we could all look at together, so that we knew we were all talking about the same thing, maybe in some form of symbolic language....

Edited May 18, 2016 by steveupson

[Strange]

I'm not sure how this same argument would be made for the [math]\cos[/math] function.

 

As I say, I think you can treat the input an output of the cos function as just "values". But as soon as you try and treat the angle as being related to direction, then it is the angle (or direction) relative to some coordinate system.

 

I really believe that if someone here would help derive the function, or at least compose it, then everyone could at least be talking about the same thing.

I think the problem is that no one understands what you are trying to do well enough to write it down in mathematical terms.

[ajb]

There might be some misunderstanding of what we're talking about. The statements that I made about not needing a coordinate system were in regards to composing and deriving the function.

 

I'm not sure how it's done, I've never had to figure it out for myself, but I would be a little bit surprise to find that a coordinate system needs to be decided on before it can be done.

All meaningful concept in geometry should be independent of any chosen coordinate system. This is also true of any deep meaningful concept in physics.

 

It may be the case that there are some natural classes of coordinates for the problem at hand. It may be the case that finding the function (not that I an quite sure what you are trying to do) will be easier in some coordinate systems than others.

 

Anyway, I am not sure that from a physics perspective there is anything like 'properties of direction'.

 

 

I think the problem is that no one understands what you are trying to do well enough to write it down in mathematical terms.

I agree with this statement.

[steveupson]

 

As I say, I think you can treat the input an output of the cos function as just "values". But as soon as you try and treat the angle as being related to direction, then it is the angle (or direction) relative to some coordinate system.

 

I think the problem is that no one understands what you are trying to do well enough to write it down in mathematical terms.

 

Let's try it on as a semantic argument. We are used to saying that a vector has magnitude and direction, and it works fine, because everyone does it that way, because we have quantified length as a property which allows us to assign it to the scalar value in the vector.

 

The only real difference here is, now we are saying something we are not used to saying, which is that a vector has direction and magnitude, which should also work just fine, because we have quantified direction as a property which allows us to assign it the scalar value in a vector.

 

But honestly, that isn't what I'm trying to do right now. I'm not trying to apply the function to anything at all. I'm just trying to derive the function.

 

Again, for the gazillionth time (I should go back and count just for fun) what I am trying to do, what I would like someone to help me with, is first, composing the function in generic algebraic lingo. I was hoping that we wouldn't be necessary to actually express the function as a formula, just express the nature of how it's to be structured, using algebra.

 

The model was built in Mathematica. The function should give the same inputs and outputs as the model.

 

I wish everyone would at least admit that they understand what I'm trying to do, and I would be very grateful for anyone's help.

Anyway, I am not sure that from a physics perspective there is anything like 'properties of direction'.

 

 

I don't think anyone is.

I agree with this statement.

 

I am simply trying to derive a function.

 

I am simply trying to explain to everyone that I am trying to derive a function.

[ajb]

We are used to saying that a vector has magnitude and direction, and it works fine, because everyone does it that way, because we have quantified length as a property which allows us to assign it to the scalar value in the vector.

This is true for vectors in a Euclidean space (or more generally a normed space), that is we have a metric and so we can define the notion of a length. Direction I think is less meaningful unless one choses some basis (ie coordinates).

 

 

... which is that a vector has direction and magnitude, which should also work just fine, because we have quantified direction as a property which allows us to assign it the scalar value in a vector.

You want some well defined map from the 'direction' of a vector to the real numbers?

 

You will need to define 'direction' in a meaningful way. I am not sure that this can be done: that is in a coordinate or basis free way.

[studiot]

 

ajb

You will need to define 'direction' in a meaningful way. I am not sure that this can be done: that is in a coordinate or basis free way.

 

 

Steve,

I think this call is time to refer to previous discussions on direction.

You will also note that this starts off by suggesting what many have already said, notably you need two points to establish (a reference) direction.

 

 

Here are some first principles you keep shying away from.

Unfortunately this forum is not the best to introduce diagrams but here are some I hope you can read.

 

Starting from(1) and working through and considering 'direction' from first principles.

 

That is

 

What do we mean by direction

Is is a property of a point or is it a property of a coordinate system or is it a property of a collection of points or what?

Can it be represented by a mathematical function?

Does a (magnetic) compass always point in the same direction or towards the same point; is there a difference?

 

So starting with (1) that merely contains the point A.

Direction appears to have no meaning at all, and certainly there is no preferred direction.

 

So in (2) is direction a property from A towards P, as shown by the arrow?

Does it therfeore require two points (minimum)?

What happens if we introduce more points, P1, P2, P3 etc.

 

Well in (3) we see that we can generate a star from A and 'get to' any other point in a plane, starting from A.

 

Is this the only way?

Well in (4) if we reverse all the arrows does the idea direction is towards a point mean anything?

 

Mathematically this is interesting because it is an inverse or reciprocal diagram.

 

But wait, is either unique?

 

Well in (5) if we extend the arrow AP1 to P2 we can reach P2 which is therefore in the same direction as P1 from A.

This is a serious mathematical impediment if we wish to consider direction as a function.

 

So what about other approaches?

 

Well in (6) suppose we have a curve as shown and define direction as being perpendicular to the curve at any point or, if you like perpendicular to its tangent.

This approach is taken in differential geometry and leads to the Frenet Formulae.

 

The directions in (6) don't point anywhere in particular, but suppose we make a curve a circle?

 

Then all the directions point to one particular point, the centre of the circle.

Note also that this is basically the same diagram as (4). (General direction towards).

 

So is direction towards a better definition?

 

Well, 8 is part of a Mercator Map and as you can see there are lots of different lines pointing North. Further on the map they do not point to the same place or point.

 

However if we look at (9) all the north lines point to one point, the North Pole.

This conforms to what we expect a compass to do, ie always point to the same point.

 

This brings us several new ideas and questions.

 

First the Mercator Map and the 3D globe exhibit a coordinate system, that we have not used up to now.

 

Secondly the mathematical idea of a manifold.

 

Does direction depend upon the coordinate system and/or the manifold?

 

Note that a sphere is not (mathematically) a 3D object.

It is a 2D object that is the surface of a 3D object, often called a ball.

It is a manifold.

 

On to sheet 2 to consider coordinate systems, again starting simple.

 

So in (10) we have an x-y (plane) coordinate system and placed our faithful point A on it.

 

In (11) we have the direction from A to B as before and extending on towards C. This is shown with no particular significance or preference in relation to the coordinate system.

 

Now we have a question.

Consider the point D, somewhere else on the plane.

What is the same direction from D as AB?

 

Is it

 

1) The line DB, as shown by the arrows in (12)?

After all, AB point from A to B so should DB also point from A to B?

 

2) Or should the direction at D be the same as at A in relation to the coordinate system? that is the line DE.

The drawback to this definition is that by going in the 'direction' DE you can never reach any point on the line AB, although you can get to other points.

 

Think back to the idea of direction being how to get there from here.

 

Finally, for now in (13) a couple of new definitions.

 

The angle a that AB makes with the x axis (actually the Z-x plane) is called the direction angle and its cosine is called the direction cosine or direction coefficient.

Only one is required in plane geometry, 3 direction cosines define (straight) line in 3D geometry.

 

Note that this picks out the parallel line definition in (12) and that the angle b is not a direction cosine.

 

 

 

 

Please note also that you originally presented the following as your proposed 'function'

but could not tell me if the angle units were radians or degrees, although you only talk of degrees.

Are you now ready to answer that question?

 

 

The relationship of the angle α, formed between the tangent of a point along a 45° small circle laid on the surface of a sphere and tilted to 45° (such that the small circle intersects both the pole and the equator) and a line of longitude passing through that same point, and the elevation angle E of this point (defined as the angle between the equator and tangent point as measured from the center of the sphere) is:

 

α = cot ((1 – sin E) / sin E) = cot (1/sin E – 1)

 

 

Edited May 18, 2016 by studiot

[Strange]

Let's try it on as a semantic argument. We are used to saying that a vector has magnitude and direction, and it works fine, because everyone does it that way, because we have quantified length as a property which allows us to assign it to the scalar value in the vector.

 

That is one way of describing what a vector means. Another is to define it in terms of three (or whatever) lengths in the coordinate system, for example [x, y, z]. You can equally well define it in terms of three angles, [a, b, c]. There are functions to convert between these (and presumably other) representations.

 

It still isn't clear to me what other representation you are trying to define. If you could define it, then it would be straightforward to define the function mapping from it to one of the others (which is, presumably, the function you are grasping for).

 

 

The only real difference here is, now we are saying something we are not used to saying, which is that a vector has direction and magnitude, which should also work just fine, because we have quantified direction as a property which allows us to assign it the scalar value in a vector.

 

In the first description (magnitude and direction) the direction is described [somehow] in terms of the three (or whatever) axes of the coordinate system. While the magnitude is a scalar. (I think that is what you are saying.)

 

If you turn this around and make the "direction" a scalar, then you will need three values for the "magnitude". So you end up with something like [x,y,z,theta]. But this seems redundant to me.

 

On the other hand, it does remind me of the homogeneous coordinate systems we use in 3D graphics where a vector in 3D space is represented by [x,y,z,w], where w is a sort of scaling factor (if you normalise the vector, it becomes the magnitude). This is used because it simplifies the maths by allowing you to use the same format for all matrix transformations.

 

I guess you could come up with an equivalent representation using angles (homogeneous polar coordinates?). That might be close to what you are looking for?

[steveupson]

 

It still isn't clear to me what other representation you are trying to define. If you could define it, then it would be straightforward to define the function mapping from it to one of the others (which is, presumably, the function you are grasping for).

 

 

One of what others of what?

 

 

I guess you could come up with an equivalent representation using angles (homogeneous polar coordinates?). That might be close to what you are looking for?

 

 

I explained exactly, precisely, what I am looking for in my very first post:

 

http://community.wolfram.com//c/portal/getImageAttachment?filename=NSTF.gif&userId=93385

 

There is a function that expresses the relationship between the small numbers that are changing in the top of the image and the numbers that are changing in the rectangular box. I want to express this function in algebraic fashion.

 

Also, an additional request has been made for help in deriving the function of the group of functions that will reveal their relationship to one another.

To specify we do use a coordinate system, but the points exists independent of any coordinate system.

 

Yes, that's one of the things that I noticed when I started playing around with the function and doing some thought experiments with it.

 

I found the function in some of my notes from ten years ago, so I don't recall exactly how it came about, but I do know that I was working with small circles on a sphere, trying to develop some geometry to map their slope as a function.

 

Some months ago I found it in my notes and couldn't stop thinking about it, and thinking about how it might be useful for something. There are a lot of peculiarities about it, that much I know.

 

So far, no one I've discussed it with has ever seen a function that is even close to this one, or even in the same genre.

 

I do know for a fact that there is no existing trig that will deal with small circles on as sphere.

 

Steve,

I think this call is time to refer to previous discussions on direction.

 

Why would direction have any importance at all for deriving the function? If you tell me why it's necessary then I'll figure out how the express it. It seems to me as though we have all the necessary information to proceed.

[Strange]

 

One of what others of what?

 

Representations of vectors.

 

I explained exactly, precisely, what I am looking for in my very first post:

 

http://community.wolfram.com//c/portal/getImageAttachment?filename=NSTF.gif&userId=93385

 

There is a function that expresses the relationship between the small numbers that are changing in the top of the image and the numbers that are changing in the rectangular box. I want to express this function in algebraic fashion.

 

I was not aware that was what you were attempting to define (your first post doesn't say that). That looks like a fairly straightforward problem in trigonometry. The upper number is how far round the circle you are. I'm not sure what the lower number is. What is the "angle between the longitude and tangent planes"? I assume the "longitude plane" is the green one? And the "tangent plane" is the yellow one? (Even though it isn't at a tangent.)

 

Also, an additional request has been made for help in deriving the function of the group of functions that will reveal their relationship to one another.

 

What group of functions?

 

I do know for a fact that there is no existing trig that will deal with small circles on as sphere.

 

I find that hard to believe.

Why would direction have any importance at all for deriving the function?

 

In your initial post this was all about direction.

Edited May 18, 2016 by Strange

[steveupson]

 

I was not aware that was what you were attempting to define (your first post doesn't say that).

 

 

You have to click on the link: "This function is the one that I have a lot of trouble with, for some reason or other. How is this function expressed?"

 

Representations of vectors.

 

 

The function doesn't use vectors.

 

That looks like a fairly straightforward problem in trigonometry. The upper number is how far round the circle you are. I'm not sure what the lower number is. What is the "angle between the longitude and tangent planes"? I assume the "longitude plane" is the green one? And the "tangent plane" is the yellow one? (Even though it isn't at a tangent.)

....

 

I find that hard to believe.

 

 

So did I.

 

The green is the longitude plane, correct, and the tangent plane is the one that's moving in a conical orbit around the small circle, dark blue.

 

I gave it a lot of effort and was not successful. It should be straightforward (for any math genius).

[Strange]

That is a completely different thread which I had not seen. It doesn't, at first glance, appear to have any connection to the subject of this thread. (Other than referencing the same animation.)

 

But I see it does answer the questions about which plane is which (my guess was wrong). I don't have the time (or interest) for trying to work out the relationship between those angles. But I am surprised that it is so much of a challenge. It looks like it should be fairly easy.

Edited May 18, 2016 by Strange

[steveupson]

 

In your initial post this was all about direction.

 

 

This whole thread is about direction, yep, sorry, you're right.

It doesn't, at first glance, appear to have any connection to the subject of this thread.

 

 

The only reason for that is because no one is willing to do the math. No one is willing to even help me to do it myself.

I don't have the time (or interest) for trying to work out the relationship between those angles. But I am surprised that it is so much of a challenge. It looks like it should be fairly easy.

 

Thanks for interest and your input. Isn't there some sort of program that can do it if you feed it inputs and outputs? I've never talked to anyone who's used something like that, but it does seem like I've heard of such a thing. Or maybe I'm thinking of de-compilers for computer code.

 

Looks sure fooled me.

Doh!

 

Mathematica must have the formula in order to put the numbers into the model.

 

Does anyone know how to get it out of there?

 

How can I post the .cdf file?

 

This might be simple, if anyone knows how to do it.

[studiot]

 

How can I post the .cdf file?

 

This might be simple, if anyone knows how to do it.

 

 

Change the extension to .txt or something that will lodge here or put it into a zip file.

 

Provide instructions to others to change it back before use.

 

Edited May 18, 2016 by studiot

[steveupson]

 

Change the extension to .txt or something that will lodge here or put it into a zip file.

 

Provide instructions to others to change it back before use.

 

 

There ya go, a plan.

 

The attachment is the .cdf for the model, and credit and gratitude go to Hans Milton, the author.

 

Just change the extension back to .cdf after download.

 

NewSphericalTrigFunction, Nr 2, v9.txt

[studiot]

Since you like Wolfram alpha, perhaps you might like to look through this about principle axes and see if it lights up any lightbulbs.

 

http://reference.wolfram.com/applications/structural/AnalysisofStress.html

Edited May 18, 2016 by studiot

[Mordred]

That's a nice article, thanks Studiot.

[steveupson]

... and see if it lights up any lightbulbs.

 

 

Actually, a lightbulb did light up over my head. In reviewing the thread (in order to see what it was I said that made you think that I would benefit somehow from reading what appears to me to be a very standard application of math and physics), it became clear that the miscommunication that has been going on is all on me.

 

I realize now that I'm holding all the cards here, and no one knows what I have. Every time someone asks "show me your cards" I throw them face-down on the table shouting "I've already shown you my cards."

 

Two things, maybe three, can clear a lot of this up.

 

The most productive thing would be to start turning each card over by doing the math. That really is the only way that I can show you my cards.

 

The second thing I can do is ask your indulgence in reading yet another wall of text from me. Having reviewed the thread, I now realize that most (but not all) of the confusion is caused by a phenomenon where I have accepted certain symmetries that have changed the way that I communicate. This is aggravated by the fact that our language is not symmetrical. By this I mean, we only have certain words that mean certain things, and there is no language that can precisely state the symmetries using our current set of structures (which are not symmetrical).

 

Although I have been very precise with my language, it has little or no effect because of the gross lack of symmetry to it. Some people reading this thread have paid very close attention to this (probably intuiting that this is where some of the problem lies) but is hasn't been all that effective because I haven't taken the trouble to ensure that it is understood, even though I have tried to explain it many times.

 

Because of the symmetries, I no longer consider "direction" and "unit vector" to be one and the same. Starting now, I will use the expression |direction| to show that what I am saying is something other than a unit vector. If this shuts down the conversation because of the pseudo-science woo-factor then it really doesn't matter. We'd all be wasting more of our time anyhow.

 

Another forum member here keeps mentioning that a point and a position are not the same thing. I've stated that length and line are different, and now I understand (having considered it in a new light) that line and curve are different if they are considered in different coordinate systems (good catch!).

 

These subtleties are super-important here. Again, this is because the meanings and usage of many of our terms are not symmetrical.

 

 

 

 

 

 

Let me take a break here for some navel gazing. If we look at the c/2 situation where a light is bounced off a mirror and its round-trip time is noted, several things can be observed. First, if it is a perfect reflection then the particle will occupy the same space (position) at two different times. One time is on the way there and the other time is on the way back. Since were not seeing a lot of stuff that returns to the same position all the time, we can conclude that there is no perfect reflection in nature.

 

Except - if direction is the property that actually commutes, instead of length as we are taught, then the outcome of a perfect reflection is slightly different in that now the particle is occupying two places at the same time, as is what actually happens in quantum entanglement.

 

Again, if this type of thought experiment is what gets the thread shut down because it's too speculative, oh well. Maybe someone who wants to continue the conversation can join some other group where I'm already a member and start a new thread.

 

 

 

 

 

 

Now, back to business. The first piece that is necessary in order to show you my cards is that I need to have an algebraic expression of the function.

 

Without that, we cannot go on. It will be more of:

 

"Show us what the function does."

 

"It does this."

 

"Oh really, how does it do that?"

 

"I'd love to explain how the function works, I've been dying to show you how it works, but in order for you to know what it's actually doing you'll have to actually evaluate it."

 

I really don't see any other way forward without doing some real math.

 

Enough for now, but more to follow. I hope someone, anyone, has questions, and I hope that someone, anyone, will volunteer to help write a "simple looking" formula.

 

 

Oh, by the way, the function returns |direction|.

Edited May 18, 2016 by steveupson

[studiot]

 

Actually, a lightbulb did light up over my head.

 

Well perhaps progress is being made, sounds good.

 

 

Because of the symmetries, I no longer consider "direction" and "unit vector" to be one and the same. Starting now, I will use the expression |direction|

 

I never have considered direction to be synonymous with unit vector.

They may not even exist in the same space. (I will expand on that in a moment).

 

But two things from the above quote.

 

1) I think a good part of everyone's difficulty is that you are continually suddenly pulling apparantly unconnected mathematical ideas out of a hat or somewhere without any explanation of why you are now incorporating them. It is very confusing. This time I am referring to 'symmetry'

2) Please explain why you are now enclosing the direction in modulus lines

 

Now for the bit about vectors they don't tell you in school when you are studying vector triangles or parallelograms.

 

Vectors often do not exist in the same space we are working in, they exist in their own space.

The part of the vector common to both spaces is their direction.

This was one of the things about direction I was going onto after the infamous post 64 from the other site and that I have reproduced here (in post 108).

It is a very important property of tangent vectors for instance.

 

 

Finally

 

 

in order to see what it was I said that made you think that I would benefit somehow from reading what appears to me to be a very standard application of math and physics

 

Yes indeed it is an important standard application of something very similar to what many suspect you are talking about.

 

Since I realise that you are not talking about simple standard applications, but something more advanced, I have been trying to offer standard applications you may not have heard of, in case one resonates with you.

 

So we all await seeing the cards turned face up.

 

And if you wish to discuss the comment about direction and spaces then I can explain further with a diagram.

 

[steveupson]

 

Well perhaps progress is being made, sounds good.

 

...

 

1) I think a good part of everyone's difficulty is that you are continually suddenly pulling apparantly unconnected mathematical ideas out of a hat or somewhere without any explanation of why you are now incorporating them. It is very confusing. This time I am referring to 'symmetry'

2) Please explain why you are now enclosing the direction in modulus lines

 

 

 

The specific symmetry that I am talking about involves vectors.

 

The structure of:

 

vector = length x direction

 

where length is the scalar quantity and direction is the vector quantity

 

has symmetry with:

 

vector = length x direction

 

where direction is the scalar quantity and length is the vector quantity.

The modulus lines indicate that it is the scalar quantity representing the magnitude:

|direction| = magnitude of "direction"

 

 

 

So we all await seeing the cards turned face up.

 

 

 

 

 

First card,

tell me what the relationship is between the small numbers that are changing at the top of the animation and the small numbers that are changing in the rectangular box.

 

This might actually be fun.

on edit> see attachment

length as a vector quantity.doc

Edited May 18, 2016 by steveupson

[studiot]

 

The specific symmetry that I am talking about involves vectors.

 

The structure of:

 

vector = length x direction

 

where length is the scalar quantity and direction is the vector quantity

 

has symmetry with:

 

vector = length x direction

 

where direction is the scalar quantity and length is the vector quantity.

 

 

Oh dear!

Trapped by terminology again.

 

But at least it shows where your misunderstandings lie.

You have mixed up the concepts of scalar, vector and multiplication.

So the above does not make sense.

 

The word scalar comes from scale and actually provides a clue as to the meaning, unlike many 'false friends' in the technical world.

 

The essential property of a scalar is that you can use it to scale a vector.

That is you multiply the vector by a scalar to get a bigger or smaller vector.

But you must end up with another vector of the same type as you started with.

 

Direction and angles are not scalars since you cannot do this with either of them.

In fact you can only 'multiply by an angle' in limited circumstances and you do not get a vector as the result.

 

For our purposes of geometric vectors scalars are numbers, but not all numbers are scalars.

 

 

|direction| = magnitude of "direction"

 

We can assign a number to direction but it is not a 'magnitude'.

This number represensts a deviation from a reference direction.

In 2D it is unique, in 3D a second number is required for uniqueness.

 

This may underlie what you are thinking of, but I'm not sure.

 

 

First card,

tell me what the relationship is between the small numbers that are changing at the top of the animation and the small numbers that are changing in the rectangular box.

 

I'm sorry I thought turning your cards over meant showing your cards and explaining what was on them.

 

 

Attached

 

There is nothing in this file that can't be posted in the thread.

This is preferred at ScienceForums.

 

I have no idea what most of this means as it carries on the misconception about vectors, scalars and multiplication, but the last sentence echoes what I said about vectors not existing in the same space and offered to expand on.

 

 

Note that the magnitude of direction does no appear in the plane in which the vector lies, but in all other space, excluding that plane.

Edited May 19, 2016 by studiot

[Strange]

tell me what the relationship is between the small numbers that are changing at the top of the animation and the small numbers that are changing in the rectangular box.

 

Why not go back to the author of the simulation and ask him? He clearly knows. I'm not sure why you think anyone else is going to take the time to reverse engineer it for you.

[steveupson]

 

Why not go back to the author of the simulation and ask him? He clearly knows. I'm not sure why you think anyone else is going to take the time to reverse engineer it for you.

Because I have no way of contacting him.

 

The thread that we used for our collaboration has been purged from not only the site, but also from the internet archive.

 

Also, as of the last time we communicated, he had not been able to do it.

 

 

 

 

I'm sorry I thought turning your cards over meant showing your cards and explaining what was on them.

 

 

 

 

 

You are not thinking correctly.

 

Seriously.

 

Explain to me how to turn over my cards without math?

 

 

You don't understand that I do understand the part where you think I don't understand.

 

 

Vectors often do not exist in the same space we are working in, they exist in their own space.

 

The part of the vector common to both spaces is their direction.

 

This was one of the things about direction I was going onto after the infamous post 64 from the other site and that I have reproduced here (in post 108).

 

 

Since I realise that you are not talking about simple standard applications, but something more advanced, I have been trying to offer standard applications you may not have heard of, in case one resonates with you.

 

So we all await seeing the cards turned face up.

 

And if you wish to discuss the comment about direction and spaces then I can explain further with a diagram.

 

 

The reasons you give for our mathematical booking regarding scalars and vectors is correct.

 

You are correct in everything you say except for your continued assumption that I don't know what you are saying. I do!

 

 

 

 

You seem to be stuck on some notion that nature somehow cares how we assign these values.

 

Nature doesn't care, at all.

 

We make the choice of using the assignments that you are familiar with.

 

I have shown a method for making a different choice, one that facilitates modeling the isotropic curvature of space-time.

 

But you simply refuse to do the math.

 

You are not alone.

[ajb]

Hans Milton seems to have been posting questions on http://community.wolfram.com/ 9 days ago. Maybe you can contact him through that forum.

 

As he had made some computer graphics, I imagine that he has used some parameterisations to construct the circle on the sphere and then derive the tangent space.