Vanity press: Exploring physics with geometric algebra

August 27, 2023 math and physics play

I just printed a copy of my ancient notes compilations for geometric algebra and physics, a compilation of old blog posts, using kindle direct publishing.

Amazon author copies don’t seem to be available in Canada anymore, so I had to buy a regular copy (printed in Bolton, Ontario, Canada!), but did so my setting the price as low as possible on amazon.ca (about $20 CAD each).  That means that I got bound and printed books, with 469+503 pages, in 8.5×11″ format for about $40 (buying an author copy from the US amazon.com would have cost more after shipping and currency conversion.)  I don’t think that I could have gotten bound print copies that cheap at one of the St George copy houses that service the university.

Now that I have my copies, I’ll un-publish these from amazon, so that nobody buys them by mistake.  I just wanted a copy of each as a reference for myself (as I do refer to parts of them sometimes — like the Pauli matrix/GA-equivalents writeup.)

This leaves me with 9 active titles on amazon (one is my book, and the rest are all course notes.)

Video: Spherical basis vectors in geometric algebra

August 8, 2023 Geometric Algebra for Electrical Engineers , ,

I’ve made a new manim-based video with a geometric algebra application.

In the video, the geometric algebra form for the spherical unit vectors are derived, then unpacked to find the conventional vector algebra form. We will then use our new tools to find the expression for the kinetic energy of a particle in spherical coordinates.

Prerequisites: calculus (derivatives and chain rule), complex numbers (exponential polar form), and geometric algebra basics (single sided rotations, vector multiplication, vector commutation sign changes, …)

You can find the video on Google’s censorship-tube, or on odysee.

Geometric algebra: a very short video introduction.

August 1, 2023 math and physics play , ,


Here’s another geometric algebra video, weighing in at a massive 2:29 (minutes.)

This video is a very short introduction to geometric algebra, showing the most basic concepts and how to apply them to the 2D geometric algebra of the Euclidean plane. Those concepts aren’t developed further in this video, but the idea is just to show the most basic consequences of the definitions.

Prerequisites: basic vector algebra (basis, vector space, dot product space, arrow representation of vectors, graphical vector addition, …)

If you watched yesterday’s video, don’t both watching this one, since it is extracted from that with no additions.

You can find the video on Google’s censorship-tube, and on odysee.

Video: Circular velocity and acceleration with geometric algebra

July 31, 2023 math and physics play , , , ,

Months ago, I used Manim to create a outline a geometric algebra treatment of the derivation of the circular velocity and acceleration formulas that you would find in a first year undergrad physics course.  I never published it, since overlaying audio and getting the timing of the audio and video right is hard (at least for me.)  I’m also faced with the difficulty of not being able to speak properly when attempting to record myself.
Anyways, I finally finished the audio overlays (it was sitting waiting for me to record the final 10s of audio!), and have posted this little 11 minute video, which includes:
  • A reminder of what circular coordinates are.
  • A brief outline of what is meant by each of the circular basis vectors.
  • A derivation of those basis vectors (just basic geometry, and no GA.)
  • A brief introduction to geometric algebra, and geometric algebra for a plane, including the “imaginary” \( i = \Be_1 \Be_2 \), and it’s use for rotation and polar form.
  • How to express the circular basis vectors in polar form.
  • Application of all the ideas above to compute velocity and acceleration.
  • Circular coordinate examples of velocity and acceleration.
It probably doesn’t actually make sense to try to pack all these ideas into one video, but oh well — that’s what I did.
You can find the video on google’s censorship-tube, and on odysee.

Cleaning the exhaust vents on my NUCs

July 3, 2023 electronics , , , , ,

My NUC needed an SSD brain transplant, which presented a good opportunity to clean the dust out of the fan exhaust vents.  It was almost completely clogged:

I vacuumed it out, which didn’t work too well, since the dust was a little greasy, so I hauled out the carpentry tools (my compressor and blower attachment),

and gave it a good blast.  Check out the after picture for the vents:

Here it is, reassembled

Ready to be my little workhorse once again.  I also blew the dust out of my older non-skull canyon NUC, which I had abandoned (switching to a backup) when it started emitting a strong burnt electronics smell.  That unit is now fully functional again too, and doesn’t smell like burnt electronics anymore!

These NUCs are nice little machines, but are really susceptible to dust clogs, as the vent spacing is really tight.  Once those gets clogged, there’s basically no airflow possible.