31:45 absolutely love your description of cross products. Like programming in a language without types - "it's so easy to learn!" but the truth is you are not escaping types, you are just exclusively using the "Any" or "Object" type and not doing your future self many favors
enjoyed so much watching your stream! where can I watch your lectures? I want to learn more about this Geometric Algebra, it sounds awesome! And is there any resource that I can read or listen to ?
I suck at even remembering most of the math in high school. What are the minimum concepts i need to relearn to be able to properly learn geometric algebra? Thank you.
1. When you add any two objects together, you get an object "between" them 2. Your basic objects are three orthogonal planes through the origin called e1, e2, and e3. There is a "plane at infinity" called e0. 3. The "geometric product" is transform composition. 4. Planes, lines, and points exist and are simultaneously both objects and transformations. e1 is a plane, but is also a planar reflection. 5. If you have a thing B and want to transform it using A, you use the formula ABA⁻¹ That's the minimum amount to remember! Here are some examples -Adding two points gets the point between them -Adding two rotations gets the rotation between them -e1*e2 = e12. e1 and e2 do planar reflections, so e12 is a 180 degree rotation, and it looks like a line, the axis - it happens to be the line where the e1 and e2 planes meet. Its inverse is -e12. -e013 is a "point at infinity". If you want to rotate it using e12, you take e12 * e013 * -e12 = -e013, which is the point at infinity in the opposite direction
Wish you had live streams on CZcams. Love the "why you should do so and so" talks.
31:45 absolutely love your description of cross products. Like programming in a language without types - "it's so easy to learn!" but the truth is you are not escaping types, you are just exclusively using the "Any" or "Object" type and not doing your future self many favors
Fantastic talk with lots of lore. Great history for people born into GA like me instead of a conventional LA/matrix background
enjoyed so much watching your stream! where can I watch your lectures? I want to learn more about this Geometric Algebra, it sounds awesome! And is there any resource that I can read or listen to ?
I suck at even remembering most of the math in high school. What are the minimum concepts i need to relearn to be able to properly learn geometric algebra? Thank you.
1. When you add any two objects together, you get an object "between" them
2. Your basic objects are three orthogonal planes through the origin called e1, e2, and e3. There is a "plane at infinity" called e0.
3. The "geometric product" is transform composition.
4. Planes, lines, and points exist and are simultaneously both objects and transformations. e1 is a plane, but is also a planar reflection.
5. If you have a thing B and want to transform it using A, you use the formula ABA⁻¹
That's the minimum amount to remember! Here are some examples
-Adding two points gets the point between them
-Adding two rotations gets the rotation between them
-e1*e2 = e12. e1 and e2 do planar reflections, so e12 is a 180 degree rotation, and it looks like a line, the axis - it happens to be the line where the e1 and e2 planes meet. Its inverse is -e12.
-e013 is a "point at infinity". If you want to rotate it using e12, you take e12 * e013 * -e12 = -e013, which is the point at infinity in the opposite direction