Theory of Everything  

  
Go Back   Theory of Everything > Tools > Mathematics
Reload this Page orthogonality
Register Website Toe Club Your Blog Arcade

Reply
 
LinkBack Thread Tools Display Modes
orthogonality
Old
  (#1 (permalink))
Raider of the lost time
AntonioLao is just really niceAntonioLao is just really nice
 
AntonioLao's Avatar
 
Status: Offline
Posts: 5,274
Thanks Given: 714
Thanked 121x in 119 Posts
Join Date: Nov 2003
Rep Power: 73
   
orthogonality - 07-03-2006, 01:29 PM

In a universe with positive or negative curvature, parallel lines do not exist, therefore in such a universe, orthogonality is one-sided from a vantage point of view (POV). As shown by the image below, lines AB and CD are not parallel. Therefore, distances lq, mr, and ns are meaningful only from POV of line AB and distances qm, rn, and sk are meaningful only from POV of line CD.
Attachment 256


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

Last edited by AntonioLao : 01-14-2008 at 03:27 PM.
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#2 (permalink))
Moderator
mkirkpatrick is a splendid one to beholdmkirkpatrick is a splendid one to beholdmkirkpatrick is a splendid one to beholdmkirkpatrick is a splendid one to behold
 
mkirkpatrick's Avatar
 
Status: Offline
Posts: 7,316
Thanks Given: 347
Thanked 687x in 645 Posts
Join Date: Aug 2005
Rep Power: 94
   
Smile Re: orthogonality - 07-03-2006, 02:07 PM

Quote:
Originally Posted by AntonioLao
In a universe with positive or negative curvature, parallel lines do not exist, therefore in such a universe, orthogonality is one-sided from a vantage point of view (POV). As shown by the image below, lines AB and CD are not parallel. Therefore, distances lq, mr, and ns are meaningful only from POV of line AB and distances qm, rn, and sk are meaningful only from POV of line CD.
Attachment 256
Great diagram Antonio,but is not the drawing one of straight lines?

kind regards michael.


Humilty,coupled with boldness,surprises truth to
reveal herself?
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#3 (permalink))
The Thinker
Guille is a jewel in the rough
 
Guille's Avatar
 
Status: Offline
Posts: 3,278
Thanks Given: 14
Thanked 9x in 9 Posts
Join Date: Mar 2005
Rep Power: 47
   
Re: orthogonality - 07-04-2006, 04:17 AM

Antonio,

I've noticed that if you extend the lines AB and CD from the points A and C until the lines join at the end, and then you draw a third line from point B to point D, you create a non right angle triangle. But if you continue the sequence of lines within the trinagle, lqmrnsk... Until you cover the whole riangle from side to side, you can use the triangles formed by those lines to calculate the area of the whole triangle. What is the meaning of the area? Could it be the field in which the force acts now that it's not orthogonal?
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#4 (permalink))
6th degree Black Belt
harmonygirl will become famous soon enough
 
Status: Offline
Posts: 844
Thanks Given: 43
Thanked 15x in 15 Posts
Join Date: Jan 2006
Rep Power: 18
   
Cool Re: orthogonality - 07-04-2006, 11:39 AM

Antonio, is this in 3 dimensional space?


The first is only interesting if it is the beginning of something. The first is not interesting if it is the only - Djanet Sears
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#5 (permalink))
Raider of the lost time
AntonioLao is just really niceAntonioLao is just really nice
 
AntonioLao's Avatar
 
Status: Offline
Posts: 5,274
Thanks Given: 714
Thanked 121x in 119 Posts
Join Date: Nov 2003
Rep Power: 73
   
Re: orthogonality - 07-09-2006, 03:21 PM

Quote:
Originally Posted by harmonygirl
is this in 3 dimensional space?
No. It is in a 4 dimensional curvilinear space and time.
Quote:
Originally Posted by Guille
What is the meaning of the area? Could it be the field in which the force acts now that it's not orthogonal?
No triangles no areas and no areas no volumes. But if triangles exist then inequalities exist. However, equalities exist only if there is no areas and only primary forces exist. Secondary forces can exist only in inequalities.
Quote:
Originally Posted by mkirkpatrick
but is not the drawing one of straight lines?
Yes. They are straight lines in the strictest sense. However, 90 degrees lines exist only with respect to one straight line not two or more straight lines.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#6 (permalink))
6th degree Black Belt
harmonygirl will become famous soon enough
 
Status: Offline
Posts: 844
Thanks Given: 43
Thanked 15x in 15 Posts
Join Date: Jan 2006
Rep Power: 18
   
Cool Re: orthogonality - 07-09-2006, 04:45 PM

but Antonio, if one accepts the hypothesis that space is curved (I am not sure how to incorporate time), couldn't AB and CD be parallel (or have they been defined as not parallel?)


The first is only interesting if it is the beginning of something. The first is not interesting if it is the only - Djanet Sears
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#7 (permalink))
Raider of the lost time
AntonioLao is just really niceAntonioLao is just really nice
 
AntonioLao's Avatar
 
Status: Offline
Posts: 5,274
Thanks Given: 714
Thanked 121x in 119 Posts
Join Date: Nov 2003
Rep Power: 73
   
Re: orthogonality - 07-15-2006, 03:12 PM

Quote:
Originally Posted by harmonygirl
if one accepts the hypothesis that space is curved (I am not sure how to incorporate time), couldn't AB and CD be parallel (or have they been defined as not parallel?)
For one, I don't think space is curved locally but it is very difficult to refute Einstein's special and general relativity even though these theories are global theories. For me, AB and CD are always parallel to each other at the local infinitesimal region of space and time.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#8 (permalink))
6th degree Black Belt
harmonygirl will become famous soon enough
 
Status: Offline
Posts: 844
Thanks Given: 43
Thanked 15x in 15 Posts
Join Date: Jan 2006
Rep Power: 18
   
Cool Re: orthogonality - 07-16-2006, 02:28 PM

are you saying that the curvature of space may be the way to incorporate time? so AB and CD are parallel now, but over time are not?


The first is only interesting if it is the beginning of something. The first is not interesting if it is the only - Djanet Sears
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
Re: orthogonality
Old
  (#9 (permalink))
Raider of the lost time
AntonioLao is just really niceAntonioLao is just really nice
 
AntonioLao's Avatar
 
Status: Offline
Posts: 5,274
Thanks Given: 714
Thanked 121x in 119 Posts
Join Date: Nov 2003
Rep Power: 73
   
Re: orthogonality - 07-22-2006, 03:33 PM

Quote:
Originally Posted by harmonygirl
are you saying that the curvature of space may be the way to incorporate time? so AB and CD are parallel now, but over time are not?
Maybe what you have in mind is positive curvature as that found on the surface of a sphere where no parallel lines can be drawn. What I have in mind is negative curvature as that found on hyperboloid surfaces where an infinite number of parallel lines can be drawn.


Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²
  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Spurl this Post!Reddit!
Reply With Quote
The Following User Says Thank You to AntonioLao For This Useful Post:
harmonygirl (07-22-2006)
Reply


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
inward vs. outward orthogonality AntonioLao Mathematics 15 04-24-2006 02:25 PM



Powered by vBulletin® Version 3.6.8
Copyright ©2000 - 2008, Jelsoft Enterprises Ltd.
Content Relevant URLs by vBSEO 3.2.0
vBulletin Skin developed by: vBStyles.com