Universal UP or DOWN (split from Fields and ether)

[J.C.MacSwell]

Doesn't the ability to define a coordinate system help make it clear that there is no universal up or down?

Do any of us agree which way is up using the system described?

[Strange]

11 minutes ago, steveupson said:

The three planes intersect at the earth center. 

OK. That's an important detail that was missing!

10 minutes ago, steveupson said:

I don't know of anything that I can say that will make understanding these things any simpler to understand.  It can only be explained using math, as far as I know.  I can tell you that these things are true, but the only way to explain why they are true is by using the math.

Go on then.

50 minutes ago, steveupson said:

Orthogonal directions have another very special relationship with each other which can be expressed as an additional tridentity.

But your three planes are not (in general) orthogonal. In the case that they are orthogonal, then the system appears identical to traditional Euclidean coordinates.

[studiot]

Rethink

Edited January 3, 2019 by studiot

[swansont]

1 hour ago, steveupson said:

 The directions cannot be the same as one another.  You must specify three directions that are unique to one another.

 Latitude is not a direction. You told me I had to draw a circle that went through the north pole. A great circle has its center at 0º latitude

If I am at the north pole, the latitude at my feet is 90º

You claimed you could tell me what direction I was facing. But you can't. Your system doesn't work.

 

But OK, I will draw a different circle. Its center is at a latitude of 45º (I can pick any value an have this work) I am still at 90º latitude. You still can't tell me what direction I am facing, since my choice of circle doesn't depend on the direction I'm facing.

 

 

 

 

[studiot]

16 hours ago, steveupson said:

Draw a circle of any size on the surface of the earth, such that the circle passed through the north pole.   Start walking around the circle.  Then tell me the latitude of the center of the circle, and the latitude where your feet are, and I will tell you what direction you are facing.

What do you mean by the latitude of the centre of the circle?

[Strange]

4 hours ago, swansont said:

But OK, I will draw a different circle. Its center is at a latitude of 45º (I can pick any value an have this work) I am still at 90º latitude. You still can't tell me what direction I am facing, since my choice of circle doesn't depend on the direction I'm facing.

Plugging those into the equation gives a result of 0°. But I don't know what that means; 0° from what? That is the trouble with specifying directions: it always has to be relative to something. 

But maybe 0° means "up"?  

1 hour ago, studiot said:

What do you mean by the latitude of the centre of the circle?

Isn't that obvious? (It is about the only thing that is!)

1 hour ago, Strange said:

Plugging those into the equation gives a result of 0°.

If anyone else wants to test other values: https://www.wolframalpha.com/input/?i=cot^-1(cos(v)+tan(sin^-1(sin(L%2F2)%2Fsin(v)))),+v%3Dpi%2F4,+L%3Dpi%2F2 (replaced lambda with L for simplicity)

Assuming I have got that right, this gives imaginary results for some inputs. I'm not sure what that is supposed to mean, in terms of direction.

 

[studiot]

1 hour ago, Strange said:

1 hour ago, studiot said:

What do you mean by the latitude of the centre of the circle?

Isn't that obvious? (It is about the only thing that is!)

 

Not at all.

I know what he means, but it isn't what he said.

If he wants to claim the mathematical high ground he must be precise and accurate.

The actual centre of the circle has no latitude.

This, when described properly, leads to the undefined unresolved situation Swansont highlighted.

Edited January 3, 2019 by studiot

[Strange]

8 minutes ago, studiot said:

The actual centre of the circle has no latitude.

I just noticed that you described the circle, earlier, as being "inside" the sphere(*), whereas I was thinking of it being drawn on the surface of the sphere. (sorry for the rather vague description; I'm not sure how to formalise it to make it precise!)

Perhaps epicentre would be a better term?

(*) Or at least, I thought you did...

Edited January 3, 2019 by Strange
Footnote

[steveupson]

5 hours ago, J.C.MacSwell said:

Doesn't the ability to define a coordinate system help make it clear that there is no universal up or down?

Do any of us agree which way is up using the system described?

The definitions (axioms) used for different coordinate systems are at the heart of the matter.  In our normal understanding of Euclidean 3-space, the xyz directions are defined as being perpendicular to each other.  This seems to work well for the space or volume that exists inside abstract solids, but it doesn't work for relativistic space (like the stuff that the universe is made up of.)   In most cases, directions (up or down) are defined by the axioms used to establish the coordinate system, and the sign + or - is used to distinguish between these "opposites."   This method of defining space is different because there are no "opposites" that can be determined mathematically.  In other words, in this coordinate system the use of + or - is associated with one of the other properties (or physical base properties) of space, of which there are two: time or distance. 

I know, it sounds like gibberish, but these words are not really the symbols that express this relationship.  The relationship is expressed by the symbols of mathematics.  If we try to define these ideas without using math, it just sounds ridiculous.  The math is the only way to show how these things are related to one another.

I think the math won't determine what direction is the universal or absolute up, it only proves that there must be one.  If we look deeply into the structure of the universe we can see that it contains bound and unbound energy, and that they require time and space in order to exist.  We can model the space individually (discrete from time), but it cannot exist in nature without the persistence of time.  Some might think that this is a philosophical argument, but I think that a case can be made that because of our observations that show relativity is a thing that exists, it sort of rules out any possibility that there can be space or volume in nature that does not possess these relativistic qualities.

The math shows that directions are connected to one another everywhere, and that one of the factors that determines direction in nature is time.  This is spelled out very distinctly by the first few responses to the OP in this thread.  Members assert that "up" is dependent upon the motion of the earth, for example.  In any event, once we have a coordinate system that ties every direction for all the particles in the universe together, and since they all share a common future with regards to time, then we get a mathematical construction where "up" anywhere is the same as "up" everywhere.  Of course in order for everything to have the same direction for the future, with regards to time, then time must be viewed as having different effects on the math whenever it is considered to be an instant as opposed to an interval.  Since distance can be (and is) expressed as light travel time, we can completely eliminate distance from the calculus such that, in this particular coordinate system, events at opposite ends of the universe are adjacent to one another.   In this system, distance can be ignored in favor of direction as a "metric."   We've chosen to call this synchronous geometry.

 

[Strange]

1 minute ago, steveupson said:

I think the math won't determine what direction is the universal or absolute up, it only proves that there must be one.

How does it do that?

3 minutes ago, steveupson said:

The math shows that directions are connected to one another everywhere, and that one of the factors that determines direction in nature is time.  This is spelled out very distinctly by the first few responses to the OP in this thread.  Members assert that "up" is dependent upon the motion of the earth, for example. 

The direction of up, for a particular location, does depend on the movement of the Earth.

But eve if you ignore movement and time, there is still no consistent definition of "up". For fairly obvious reasons.

5 minutes ago, steveupson said:

We've chosen to call this synchronous geometry.

You can call it what you like but you need to use it to support your claims.

[steveupson]

2 hours ago, Strange said:

Plugging those into the equation gives a result of 0°. But I don't know what that means; 0° from what? That is the trouble with specifying directions: it always has to be relative to something. 

But maybe 0° means "up"?  

Isn't that obvious? (It is about the only thing that is!)

If anyone else wants to test other values: https://www.wolframalpha.com/input/?i=cot^-1(cos(v)+tan(sin^-1(sin(L%2F2)%2Fsin(v)))),+v%3Dpi%2F4,+L%3Dpi%2F2 (replaced lambda with L for simplicity)

Assuming I have got that right, this gives imaginary results for some inputs. I'm not sure what that is supposed to mean, in terms of direction.

 

There's a very good Youtube series on octonians that was put together by Cohl Furey.  Video #8 is the part where it starts to become relevant to your question.  Keep in mind that there is also the property of chirality, which is also associated with the imaginaries, or so it would seem, although I'm not really any good at using algebra.  I can read it pretty well, and I understand the derivations, I'm just not skilled enough in its use to show whether this kind of thing is true or not, based on the mathematics.  I do have a gut feeling or comfortable conjecture that chirality is related in this way, mathematically.

 

[Strange]

2 minutes ago, steveupson said:

There's a very good Youtube series on octonians that was put together by Cohl Furey. 

Why do you think this is relevant?

 

[steveupson]

1 hour ago, studiot said:

 

Not at all.

I know what he means, but it isn't what he said.

If he wants to claim the mathematical high ground he must be precise and accurate.

The actual centre of the circle has no latitude.

This, when described properly, leads to the undefined unresolved situation Swansont highlighted.

There are several of these imprecise descriptions in my discussion on this thread.

To quote myself an earlier post, I said:

" Note that this is the same angle as what occurs when we slice horizontally through the earth to create a line of latitude at the circle center, and then form a similar cone having the segment from the earth center to the north pole as the axis, and the segment from the earth center to the circle center as a generatrix."

This should more properly be stated as "a similar cone having the axis lying in the segment between the earth center and the north pole, and having a generatrix that contains the segment from the earth center to the circle center."  

The .pdf has a more formal presentation of the material.  Any comments about any vagaries or imprecision in that document will be greatly appreciated.  It would be very helpful to have some feedback.

30 minutes ago, Strange said:

How does it do that?

The direction of up, for a particular location, does depend on the movement of the Earth.

But eve if you ignore movement and time, there is still no consistent definition of "up". For fairly obvious reasons.

You can call it what you like but you need to use it to support your claims.

We prove it using math comprising a lot of numbers and symbols.  And I completely agree with your other comments.  The math only shows that there must be a consistency.

 

20 minutes ago, Strange said:

Why do you think this is relevant?

 

I don't know, because I'm good at solving problems?

We are once again treading dangerously close to the usual ad hominem arguments that seem to the last refuge for some people.  Please don't go there.

Edited January 3, 2019 by steveupson

[studiot]

15 minutes ago, steveupson said:

There are several of these imprecise descriptions in my discussion on this thread.

To quote myself an earlier post, I said:

" Note that this is the same angle as what occurs when we slice horizontally through the earth to create a line of latitude at the circle center, and then form a similar cone having the segment from the earth center to the north pole as the axis, and the segment from the earth center to the circle center as a generatrix."

This should more properly be stated as "a similar cone having the axis lying in the segment between the earth center and the north pole, and having a generatrix that contains the segment from the earth center to the circle center."  

The .pdf has a more formal presentation of the material.  Any comments about any vagaries or imprecision in that document will be greatly appreciated.  It would be very helpful to have some feedback.

A sphere is a 2 dimensional surface, such as the idealisation of the surface of the Earth.

A line of latitude has a particular definition in relation to a particular surface. To whit the surface of the Earth.
Such a line is wholly contained within that 2 D surface.

A circle is a plane figure which is generated by the intersection of a plane and (in this case) a sphere.
The centre of this circle (and any circle) lies in the plane of the rest of the circle.

The only parts of the circle that intersect the sphere of the Earth's surface are the cicle itself.
The centre is indeed within the body of the solid figure of the Earth.
Therefore it cannot be on the surface of the Earth.
But only points on the surface of the Earth possess lie on a line of latitude.
Therefore the centre of that circle does not possess a latitude.

 

So it is up to you (not me) to properly describe what you mean by the "The latitude of the centre of the circle".

I will however supply a hint, since you seem to like projections, the proper description involves a projection.

Edited January 3, 2019 by studiot

[Strange]

12 minutes ago, steveupson said:

We prove it using math comprising a lot of numbers and symbols. 

Has this actually been proved? Or is it just a guess?

13 minutes ago, steveupson said:

I don't know, because I'm good at solving problems?

We are once again treading dangerously close to the usual ad hominem arguments that seem to the last refuge for some people.  Please don't go there.

I don't see why you think there is any ad hominem involved. I am just curious why you brought this up. Presumably you think there is some connection between your idea and octonions? Can you expand on that?

(I am actually going to make an exception to my usual practice and take a look at these videos; I have read about Furey's work and it is pretty interesting.)

[steveupson]

37 minutes ago, studiot said:

A sphere is a 2 dimensional surface, such as the idealisation of the surface of the Earth.

A line of latitude has a particular definition in relation to a particular surface. To whit the surface of the Earth.
Such a line is wholly contained within that 2 D surface.

A circle is a plane figure which is generated by the intersection of a plane and (in this case) a sphere.
The centre of this circle (and any circle) lies in the plane of the rest of the circle.

The only parts of the circle that intersect the sphere of the Earth's surface are the cicle itself.
The centre is indeed within the body of the solid figure of the Earth.
Therefore it cannot be on the surface of the Earth.
But only points on the surface of the Earth possess lie on a line of latitude.
Therefore the centre of that circle does not possess a latitude.

 

So it is up to you (not me) to properly describe what you mean by the "The latitude of the centre of the circle".

Please.  Spare me.  Angels dancing on the heads of pins.  From Todhunter's textbook.  If you have any comments on the more formal proof provided in the .pdf, then please share.  Especially if you find errors, technical, grammatical, or anything else. 

 

 

35 minutes ago, Strange said:

Has this actually been proved? Or is it just a guess?

I don't see why you think there is any ad hominem involved. I am just curious why you brought this up. Presumably you think there is some connection between your idea and octonions? Can you expand on that?

(I am actually going to make an exception to my usual practice and take a look at these videos; I have read about Furey's work and it is pretty interesting.)

I have a theory that the sign isn't really associated with any single parameter (time, distance, direction) and that it should be accounted for separately using quaternions.  This is fundamentally the answer to the question in the OP.

on edit>>>>> 

I'm really talking about the Fano plane.   And also, there are some interesting probabilities that are being sorted out by real mathematicians:

https://johncarlosbaez.wordpress.com/2018/07/10/random-points-on-a-sphere-part-1/

https://johncarlosbaez.wordpress.com/2018/07/12/random-points-on-a-sphere-part-2/

 

Edited January 3, 2019 by steveupson

[studiot]

And how many centuries ago was Todhunter?

You have to convince modern mathematicians.

Nor does that detract from the geometry of what I was saying.

A point on the surface of the Earth cannot possibly be the centre of a circle drawn on the surface unless that circle has zero radius.

Edited January 3, 2019 by studiot

[steveupson]

4 minutes ago, studiot said:

And how many centuries ago was Todhunter?

You have to convince modern mathematicians.

Nor does that detract from the geometry of what I was saying.

A point on the surface of the Earth cannot possibly be the centre of a circle drawn on the surface unless that circle has zero radius.

I don't have to do anything.

[Strange]

38 minutes ago, steveupson said:

I have a theory that the sign isn't really associated with any single parameter (time, distance, direction) and that it should be accounted for separately using quaternions. his is fundamentally the answer to the question in the OP.

The sign of what?

And if you think your question in the OP can be answered by quaternions (not octonions?) then what is the relationship of that to your equation? Why aren't you pursuing the answer using quaternions?

56 minutes ago, steveupson said:

And also, there are some interesting probabilities that are being sorted out by real mathematicians:

https://johncarlosbaez.wordpress.com/2018/07/10/random-points-on-a-sphere-part-1/

https://johncarlosbaez.wordpress.com/2018/07/12/random-points-on-a-sphere-part-2/

That is interesting (for people who find that sort of thing interesting!) as is almost anything by Baez, but it just seems like another tangent from your equation.

Can you explain how your equation realties to octonions and/or quaternions?

[studiot]

28 minutes ago, steveupson said:

I don't have to do anything.

That's quite true.

You don't have to be believed or taken seriously either.

 

Especially if you try to convince someone that the centre of a circle lies out of plane.

[Strange]

On 1/2/2019 at 6:01 PM, steveupson said:

I can explain how they are the same.  Using my math.

It looks like that wasn't true.

[steveupson]

1 hour ago, studiot said:

That's quite true.

You don't have to be believed or taken seriously either.

 

Especially if you try to convince someone that the centre of a circle lies out of plane.

Why go off-topic with this drivel?  Why don't you start a thread in "Speculation" about whether or not steveupson is worthy of having a discussion at this forum.  This topic isn't about ME!  I knew the ad hominem argument (your entire post is about ME!) was on its way as soon as the conversation started getting dragged down into irrelevant minutiae.  It seems to be a last resort that is used by some members to try to win or something.  I don't have a lot of choice here, but I do have choice to not be bullied by anyone.  I choose not to be.  There's enough win for me in the fact that the OP even exists as a thread.  The self-unawareness is staggering.  The thread was split from a thread on Fields because the OP supposedly has no meaning or bearing at all on fields, and then the same members only want to discuss fields in their first few posts.  It would be funny if weren't so tragic.

For those members that are interested in the conversation, a good point was raised, although in a very left-handed way.  The history of this development is probably very important to understanding the math.   If you bothered to read the introduction to the .pdf you will have seen:

Quote

"The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook Spherical trigonometry for the use of colleges and Schools... "

https://en.wikipedia.org/wiki/Spherical_trigonometry

At about the same time, Grassmann was developing a new process that would allow the construction of mathematical models of physical relationships.  He's an interesting figure in all of this because his work went virtually unnoticed until math historians started looking into how we ended up here, mathematically, sometime around the 1970's.   In the original thread, the one that is off-topic here, studiot posted some pages from math history books from that time period.  I'd be very interested to know if Grassmann's work had been rediscovered by then.  His contemporaries paid very little attention to his work, although all of them of note seemed to have borrowed very heavily from him.   The original ideas were his, not Gibbs or Heaviside.  It literally took the likes of Leibniz decades to catch up with him.   Things for a while devolved into science taking sides between quaternions vs not-quaternions.  That argument seems to have only recently been resolved by the application of quaternions to computer graphics.  Still, some folks don't quite see the relationship that this use of different forms has on our grasp of physics.

Continuing the wiki quote above:

Quote

... "The only significant developments since then have been the application of vector methods for the derivation of the theorems and the use of computers to carry through lengthy calculations."

The development of non-Euclidean geometries and affine spaces were used to solve these types of problems, and of course to explore the discovery of relativity.  This type of geometry, the type that we've resurrected in the .pdf has been lying dormant since Todhunter's and Grassmann's times.  So it seems somehow appropriate to go back to try and gain a little understanding of how things were back in their days.  But sure, today a sphere is a surface.  It's a set of points.  Oddly, this set of points does not include the point at the sphere center.  We're changing that back so that the sphere includes the surface and the center.  I don't care what you like to call it, a ball or a sphere with a point at the center, it seems to be necessary in order to construct the new geometry.

2 hours ago, Strange said:

The sign of what?

And if you think your question in the OP can be answered by quaternions (not octonions?) then what is the relationship of that to your equation? Why aren't you pursuing the answer using quaternions?

That is interesting (for people who find that sort of thing interesting!) as is almost anything by Baez, but it just seems like another tangent from your equation.

Can you explain how your equation realties to octonions and/or quaternions?

I think that we might need to use octonians in order to keep track of the sign, later, when we start introducing distance into the geometry.  At this time, they are not needed.  It will probably take the expertise of a trained mathematician to understand how to perform that particular step.

The sign keeps track of the relationships between a lot of things.  In planar geometry it "quantifies" direction in a haphazard sort of way.  It's a mathematical choice of how, or for what, we can use the sign.

1 hour ago, Strange said:

It looks like that wasn't true.

Not without doing a lot of math.  I'll walk you through it if you're really interested.  The process includes using the new geometry in order to construct a model that illustrates Mach's principle.  No one has done that yet.  

Edited January 3, 2019 by steveupson

[studiot]

2 hours ago, studiot said:

Especially if you try to convince someone that the centre of a circle lies out of plane.

Are you still claiming that the cente of your circle, drawn according to your instructions, lies on the surface of the Earth?

You are the one that requires the 'latitude'.

I am simply asking for instruction to calculate this quantity.

You have now had many opportunities to say how, but seem to always avoid the question.

Is that because you actually don't know where the centre is?

[Strange]

1 hour ago, steveupson said:

I think that we might need to use octonians in order to keep track of the sign, later, when we start introducing distance into the geometry.

The sign of what?

And why does introducing distance make a difference? Direction has a sign (is that what you are referring to?) but distance doesn't.

And this seems unbelievably complicated. You are starting with a very complex equation, then you think you need to add octonions (another very complex mathematical structure) to address its shortcomings. But you can't provide any rational reason for that, it is just a belief.

And for what? You have not yet shown that this equation has any advantages. You claim it will solve all sorts of problems, but have presented no reason for anyone to believe that.

You can't even use this equation to solve problems that are trivial using existing geometry. 

While we are are on that, can you go from this equation:

to an equation for v or lambda?

1 hour ago, steveupson said:

Not without doing a lot of math.  I'll walk you through it if you're really interested.

Go on then.

A couple of questions (which have been asked before).

1. You asked people to provide an example circle and position and the equation would calculate alpha, the direction they were facing. When I do that for the most recent example, I get the value of alpha = 0°. Can you explain what that means? 0° with respect to what?

2. For some value of v and lambda, the resulting value of alpha is imaginary; what does that mean?

 

[steveupson]

1 hour ago, studiot said:

Are you still claiming that the cente of your circle, drawn according to your instructions, lies on the surface of the Earth?

You are the one that requires the 'latitude'.

I am simply asking for instruction to calculate this quantity.

You have now had many opportunities to say how, but seem to always avoid the question.

Is that because you actually don't know where the centre is?

I'm sorry, I'm trying to learn to be more patient with people.   Some folks cannot grasp some of these complicated concepts as easily as others do.

By center of the circle on the earth, I mean the point on the surface at the intersection of equal length arcs drawn from the circle.

56 minutes ago, Strange said:

The sign of what?

And why does introducing distance make a difference? Direction has a sign (is that what you are referring to?) but distance doesn't.

And this seems unbelievably complicated. You are starting with a very complex equation, then you think you need to add octonions (another very complex mathematical structure) to address its shortcomings. But you can't provide any rational reason for that, it is just a belief.

And for what? You have not yet shown that this equation has any advantages. You claim it will solve all sorts of problems, but have presented no reason for anyone to believe that.

You can't even use this equation to solve problems that are trivial using existing geometry. 

While we are are on that, can you go from this equation:

to an equation for v or lambda?

Go on then.

A couple of questions (which have been asked before).

1. You asked people to provide an example circle and position and the equation would calculate alpha, the direction they were facing. When I do that for the most recent example, I get the value of alpha = 0°. Can you explain what that means? 0° with respect to what?

2. For some value of v and lambda, the resulting value of alpha is imaginary; what does that mean?

 

I think that the sign will represent chirality in the completed geometry (when distance is derived.)  And as far as it being very complicated, I can't really offer any apologies for that.  The fact that vector manipulation won't readily solve the problem should provide ample illustration of its worth.  

I'm not really that good with algebra, but the equation is the resulting function from combining two simultaneous equations that relate alpha and lambda to another variable phi.  It's in the proof.  Do the math.  How many times do I have to tell you that as far as I can tell it is completely impossible to understand any of this without doing the math.

1.  The alpha = 0° result means that you are facing normal to the meridian plane.  Or, the tangent to the circle where you are standing is parallel to the surface normal to the meridian plane.  There is no angle between them.  The two planes that set up this relationship are the one that is tangent to the cone having the small circle as its base, and the meridian plane, where both are intersecting at your feet.  

2.  I'm not sure what that means, or what you are referring to.  If we use negative values for some of the inputs then the outputs are also negative.  That could be what you're talking about.  Maybe?

There is a complicated issue of how to keep track of the sign for alpha.  I may have gotten that particular calculation crossed up so that I am actually calculating the complementary angle for alpha instead of alpha, but it really is the best that I can do considering my very limited abilities with algebra.  I wasn't able to come up with the actual formula that is being used.  It was someone (Did) from mathstackexchange who helped with that.   The simultaneous equations that give the parameterization of alpha are:

 

Also, in addition to alpha=f(lambda), these same equations can be combined in order to produce the tridentity: