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“pushing nature past its limits”
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New resorts continue to open in the Maldives, as the press continues to
announce its demise due to the burning of fossil fuels. The Maldives New
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3 comments :
Apologies for off topic.
I've looked at your site for a long time and never got what Clifford Algebra was really about. Until I saw this comment on a random site a while ago about Geometric Algebra,
"...Geometric Algebra. It’s fantastic, it’s true, it’s representative of how the universe works, it’s relatively (hah!) simple, it’s predictive, and it’s almost completely ignored in scientific education. The behavior of both complex numbers and quaternions emerges GA. Quantum spinors emerge from GA. Maxwell’s 4 equations become a single GA equation describing the relationship between electric charge and magnetism. And all this derives from a single, simple, unifying principle..."
So then I find this is...Clifford Algebra!
What this appears to my limited understanding is a "fairly, easy way to do complex calculations with vectors and many other problems including those of many dimensions. It's been so long since I studied math but I remember taking class on complex numbers and how you could change them to vectors and in consequence multiplying, manipulating them, solving electrical problems became very easy. I think this is much the same. You place what you are computing into this vector format, and then it becomes fast, low computing power needed to manipulate them. The power of this impressed me, as you can take Maxwell's electromagnetic Quanterion math and reduce it to an easier manipulated vector for calculations. So I get it now. You should add some sort of explanation at the top, like the comment I copied. This seems to be a very powerful technique to use one set of math skills to tie together a vast amount of physics.
I can see how this would fascinate you. Very big picture stuff.
Hi Sam,
I am glad you looked into it, it's well worth it. You are absolutely right that my presentations lack readability but I am not really good at writing books-sized essays unless there is some element of interraction. I didn't feel motivated enough to spent time polishing the presentations/articles to make them more readable, but I am going to add that aspect over time, as long as time allows me (I also have a 9 to 5 job) Right now I have been preparing some draft versions of the Clifford Tutorial part 2 article describing a very important discussion of the 3 different forms of the transformation rules on the three classes of physical entitites: 1/ spinors, 2/ 4-vectors, and 3/ electromagnetic field operators ,
In tensor calculus formulation of QM those transformation rules are given as assumptions, in Clifford they follow from basic rules of the algebra just like everything else. Transformation rules are in fact defining the physical properties of physical entities.
There is also a part I am working on to describe how to formulate 4-vectors (including time-space) out of spinors, and how to formulate electromagnetic field operator out of 4-vectors.
I think I am going to publish that Clifford Tutorial part 1 and the new part 2 on Substack.
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