“Demystifying” Bivectors: A video for (and in support of) high-school teachers of Geometric Algebra

[@garthgoldwater5256]

thank you!!! i was inspired to start checking out geometric algebra again by freya holmer’s recent talk and this has ABSOLUTELY clarified a lot of concrete questions i had about what a bivector actually “is”

[@JimSmithInChiapas]

Thank you for your kind words. I hope that you will check out the channel "Pre-University Geometric Algebra Videos", and consider joining the associated LinkedIn group, which is linked in the Description.

[@thomasolson7447]

The area (with the scalar product) seems like it would fit nicely on the complex plane.

[@scotth.hawley1560]

Thanks for posting this, Jim. That was good.

[@JimSmithInChiapas]

Thanks, Scott. I don't have a good voice for doing videos, but it's the voice I have, so ... (shrug) One of the things that I try to communicate to prospective teachers and students of GA is how certain specific, geometric aspects of real-world problems motivated the invention of abstract, widely applicable ideas like vectors and bivectors. As we know, David Hestenes' recognition that the 19th-Century inventors of GA had intended to capture geometric aspects of reality via vectors and bivectors (etc.), in what subsequently became the rather abstract "Clifford Algebra", was key to Hestenes' revival/re-invention/expansion of GA starting in the 1960s. Therefore, I follow the advice of a computer programmer who once wrote (regarding a certain Python feature) that the best way to understand that feature was by finding out what problem(s) it was intended to solve.

[@dadir_alvarez9748]

¡Interesante contenido!, hasta hace poco me enteré de la existencia del álgebra geométrica. Saludos desde la Ciudad de México

[@JimSmithInChiapas]

¡Saludos desde Chiapas! Y muchas gracias por tus amables comentarios. La verdad es que la Republica Mexicana cuenta con muchos expertos en la GA. (¡No soy yo uno de dichos expertos!)

[@tomasgarza6090]

@@JimSmithInChiapas pues para no ser experto lo manejas muy bien. Excelente presentación!

[@crazyingenieur3277]

The video is about 23 mins... and I still don't have a clear idea of what a bivector is. Why could we not use cross product for Torque instead? He said bivector solves problems like Torque.. what does bivector solve that cross product can not?

[@JimSmithInChiapas]

In the video description, I've now added a "stack exchange" link (just after the first paragraph) that may be useful.

[@imaginarypoint]

more symbols, cartoons and talk.. nothing actual.

[@JimSmithInChiapas]

Concepts like forces, torques, distances, and areas have no basis in reality?! Well, you're a Flat Earther who also believes that volcanoes are fake, so ...

[@imaginarypoint]

@@JimSmithInChiapas - Nope.. it is YOU that believes that. All i've pointed at is that YOU have never actually seen this so called hot red lava coming out of the ground with your own eyes face to face and poked a stick at it to say it is real. Same with your 'earth' object pizza or ball. YOU have never actually seen it. Only on TV... or books etc. Symbols. Cartoons.

[@imaginarypoint]

@@JimSmithInChiapas BTW:.. see who you can't help but call everyone a Flat Earther that don't believes in your beliefs??

[@JimSmithInChiapas]

@@imaginarypoint You claim you're no FE, but you're a defender of FEs "Peter and Pete". How revealing, that you continue to spend your time in this comment section, posturing as being superior, and continuing to evade the following simple opportunity to demonstrate the supposed superiority of your approach to understanding our physical world: kzbin.info/www/bejne/qGi4Zmupj7ppeM0 . Elsewhere, I've already shown you the description of that video: _"Big-name Flat Earthers have appointed themselves to tell the rest of us what science is, and how to do it, even though FEs as a group have made no Flat-Earth-based contributions to science in the last 100+ years. Here's a chance for those FEs to redeem themselves by demonstrating the supposed superiority of their approach to understanding our world."_

[@imaginarypoint]

@@JimSmithInChiapas - Nope... Wrong. you have never actually seen the so called 'earth' object that you believe.