A short note about vectors

Posted by on Jan 18, 2013 in Science | 0 comments

I have read a lot of trash about vectors on the Tubes of the Internet. I have read that vectors are different than line segments because vectors don’t have a start and end, they only have a start and continue to infinity (whatever that might mean). I’ve read that vectors have no position, and et cetera. I believe that it’s worth establishing some very basic things about vectors. The most basic vector is a simple position vector. It is a directed line segment from the origin of some set of coordinates. To keep things extremely basic, let’s assume we have Cartesian...

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Parallel transport and curvature

Posted by on Jan 13, 2013 in Science | 0 comments

Parallel transport and curvature

In the most basic physics, we learn that the most basic equations are generally vector equations. This is true of Newton’s equations involving force, , and acceleration, , and equally true of the Maxwell equations that involve vectors for the electric and magnetic fields, , and . Moreover, we learn things like acceleration is proportional to force, force is proportional to charge, rotational acceleration is proportional to torque, and in consideration of the fact that all of these quantities are vectors, that the resultant vector is in the same direction as the vector it is...

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