April 9th, 2018, 02:59 AM  #11  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,125 Thanks: 714 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
This reminds me to the discussion we had a year or two ago when we were discussing spherical polar coordinates and the vectors. I never did get to the bottom of exactly how to find that angle you were trying to find. Quote:
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April 9th, 2018, 03:37 AM  #12  
Senior Member Joined: Jun 2015 From: England Posts: 848 Thanks: 255  Quote:
The point is, of course, that the zero vector [0, 0, 0] has no direction or all directions at once depending how you look at it.  
April 9th, 2018, 06:55 AM  #13  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
One of the distinguishing characteristics of an electrical transformer is the turns ratio. This is the ratio between the respective quantities of two instances of the same thing. I’m referring to the thing that comprises those specific quantities. The difference between a ratio and a quantity is the significant new understanding that is behind this particular theory. Until now, direction has always been a ratio between lengths or distances (diameter and circumference or sides and hypotenuse.) We are no longer using that model of direction. We are tying direction to another completely different object, the turn. The manner in which this is done is not one of those boutique math tricks that are very prevalent these days. It is solidly based in old fashioned (Euclidean) geometry, although spherical trigonometry is useful in solving for some of the unknowns. I suspect quaternions could also be used, but I would predict that someone will show via a mathematical proof that deriving this function using vector manipulation is not possible. The subtlety of what we are showing mathematically is difficult to comprehend. That’s why no one has understood it until now. The idea that there is a turns ratio has a very deep meaning. This is at the very foundation of physics, and it turns out (pun intended) that the answer is buried deep within the very foundations of mathematics, or more specifically, Euclidean geometry. The math that we have presented will some day be understood by someone. When that occurs, that person will also realize that what looks like word salad now is actually the way things are. Like much of physics, the underlying math is what shines the light. In this case, the problem is that no one understands the math that supports the theory, and no one thinks that they must. The skeptics believe that they can poke fun at stuff they don’t understand without suffering any backlash. This isn’t one of those cases. And yes, I am familiar with the crank factor, very familiar, because I am generally considered to be one myself. Don't get me wrong, it's very frustrating, but I also realize the important role that the skeptics play in this scientific endeavor. If anyone can explain how we can have a turns ratio without having a defined thing called a turn, then that explanation will go a long way toward disproving our theory.  
April 9th, 2018, 06:59 AM  #14  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
A. we know what vectors are B. we are not using vectors  
April 9th, 2018, 07:13 AM  #15 
Senior Member Joined: Dec 2015 From: Earth Posts: 238 Thanks: 27 
Example... Consciousnes has no size or direction Post your reply , im curious 
April 9th, 2018, 07:23 AM  #16 
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry  
April 9th, 2018, 09:38 AM  #17  
Senior Member Joined: Jun 2015 From: England Posts: 848 Thanks: 255  Quote:
Firstly turning is defined as a vector perpendicular to the plane of rotation. Setting that aside for the time being consider the attached diagram. To define a turn you need a start point. How do you do this? Assuming you have some way to define OA in the diagram, note that the amount of turn can be represented solely by the distance travelled as from A to B in the diagram. However, as the distance between A and O tend to zero the distance moved by A also tends to zero ie the amount of turn tends to zero and reaches zero as A reaches O. Thus we are back to my 0/0 situation with the vector I originally described in my previous post.  
April 9th, 2018, 11:14 AM  #18  
Senior Member Joined: Jul 2015 From: Florida Posts: 150 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
The only way (that we know of) to reconcile this new tridentity with existing geometry is through the mathematical model that is provided in the proof. There are planes in that proof, sure, but the planes only illustrate the dihedral angles between them. There are absolutely no features that exist in any plane, other than the small circle. It’s only the intersections of planes that we use, so the way you are going about this is not going to work. I understand that this criticism isn’t helping to explain anything. I think that you may better get the idea of what we’re talking about by looking at the BanachTarski paradox. They break the sphere into an infinite number of directions in 3D, then they use a reference that is not part of the surface (sphere center) in order to reposition these directions in space, and then they reassemble the surface using this infinite number of directions, only in another orientation. There is a reason why everything holds together when they do this. Each of the infinite number of directions is a certain magnitude of direction from all of the other directions. This magnitude has nothing at all to do with any length. The magnitude is based on all of the other directions. In other words, we are using the relationship that exists between directions in 3D to specify a quantity of direction. This relationship fits the function $\displaystyle \alpha = f(\lambda)$, or: $\displaystyle \alpha={\cot}^{1 }(\cos\upsilon\tan{\sin}^{1}(\frac{\sin\frac{\lambda}{ 2}}{ \sin\upsilon})) $ on edit >>> Should read: There are absolutely no features that exist in any plane, other than the small circle and the sphere center. Last edited by steveupson; April 9th, 2018 at 11:17 AM.  
April 9th, 2018, 11:59 AM  #19  
Senior Member Joined: Jun 2015 From: England Posts: 848 Thanks: 255  Quote:
One small correction. Most vectors have a length, the zero vector has zero length, but I thought you were not using vectors?  
April 9th, 2018, 12:07 PM  #20  
Senior Member Joined: Aug 2012 Posts: 1,973 Thanks: 551  Quote:
But what you wrote is idiotic. You clearly haven't the slightest notion of why the BanachTarski theorem works. All you've done is embarrass yourself. Last edited by Maschke; April 9th, 2018 at 12:19 PM.  

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