#transposition

Imagine a space where you can see the form of time from some standpoint, and imagine if you can only see if it you can tell it apart from a similar form that does not result in a second mirror world eating you up when you weren't noticing the details. This is how my continued foray into the following paper feels.

We begin with a quick clip by one of favorite mathematicians, Cohl Furey. At the time when I found out about her, 2018, I didn't have the spoons, the space, the time or the safety to further pursue my interest in what she taught. It is true that apolitical positions are privileged positions, and that some people are successfully perched on a safety that allows them to pretend like evading the boiling lava of politicization is a choice. That, or they are just completely blind to their own political positions and consequences, or simply in denial. Only now I have I finally ended the relationship that took me from several opportunities in analyticity. I revisit her work.

Her teaching is void of unnecessary distraction, organized, preplanned, clear, and distinctly moving forward with an insight for the student in mind. She shows high comprehensive skill therefore.

Still curious about division algebras, I found out that they are fields that are associative, aka, more or less coupled with their cancelling function with the exception of the Cayley numbers. Oddly, these are another name for the octonions, though apparently they were discovered independently.

In addition, Cayley numbers are non-associative. That means that changes in groupings have real effects, even if the contents are the same. It sounds like what I am learning about in complexity science and emergence. In addition to being non-associative, we also have to remember that as a division algebra the multiplication operation doesn't necessarily commute, meaning that direction of multiplication may have an effect as well. So, so far we know there are real effects on direction and group. When I hear that, I immediately think time--direction going to physics, group going to finance, and the link between the two going to complexity theory.

Moving on, we touch on involution--where I take to mean the shape of something coupled with its functional instantiation results in the identity. My hypotheses are that this identity can be either considered the (a) category or (b) some kind of pivotal location necessitated by the system constraints for this form to both exist and operate. It is dark, but I think of a gothic cathedral, and a gothic cathedral when it is on fire, operating, made of stuff. Genes, and genes when they are in the burning, mortal version of a human life.

Learning about involution and inversion, I couldn't help but to think how a shift in direction of an operation related to the inverting function. It seems to me inversion is just multiplicative commutation but on a different dimension. I often love to teach inversion to my kids using the fraction's bar as the mirror, and the fractions jump across the mirror world to find themselves in the identity function 1. Interestingly, the identity function is, as we see in the following video, also the first generator of a potential Cayley graph...this is me looping back to how Cayley category theory ties into graph theory.

This piece by Visualmath is amazing not only because it is visual, and most mathematics is best taught with the end in mind (the final picture; I always view the computational approach as an artist who sketches a lot of lines while drawing each individual piece of a picture, which is more than a little energetically expensive, and I view a mathematician as one who draws in a preplanned, certain way) but because I love that he laughs and says intimidating elements of math are actually really simple and easy to understand. I wish more math was taught this way. In fact, I wonder why it isn't?

Some things to note: I will be noting one after another the additions I have to make to my original reading to show why autodidactic, thorough mathematical endeavor has a serious complexity issue that I don't think the university system solves.

Initial inquiry http://www.csun.edu/~asethura/papers/DegreeDetVars.pdf

Resulting supporting inquiries while trying to solve the initial inquiry to be read as supplement while reading 1, added August 26, 2022 (https://inspirehep.net/files/1e02ad81af7a278f19b217e99715a973)

https://www.researchgate.net/publication/308943414_Commutativity_Theorems_in_Rings_with_Involution

Supplementary reading: Applications of category theory, to be looped into each entry as an extra challenge.

Other items to note; subvariety is a smaller item in a larger field. The question of codimension is how many dimensions are not shared...I find this an interesting use of the word co. So essentially, "what is the distance between that I am, and that which contains me, dimensionally speaking?" What's even more interesting is that, if I understand correctly, which I probably don't, the smallest possible difference between a subvariety and a field is the field's dimension, and the larger the subvariety becomes, the "greater" the codimension terminologically speaking, while it is actually numerically smaller. All I can think to explain this is that the term is referencing how much space they mutually compare. To me this seems like an inverse function. Anyone else irked by this?

Finally, I was also interested in the transposition here and how it relates to commutativity, associativity, and the real effect of direction and group--perhaps the group formed by the traces themselves.

Well, we're one small paragraph into a six page paper, and already in this deep. I've always been one for a steep learning curve though...I've been celebrating completing my financial analysis specialization! My favorite quote or something like it being finance is, in the end, the study of time. Forever the metaphysician.

“Nourishment Pavilion”, Regent’s Park, London, UK _ Student: Nuralein Ali / BA3 _ 18.01.2022

The students were asked to design a “Nourishment Pavilion”, which should include a basic food preparation and serving area, a café and an art space. You need to critically re-interpret the idea and significance of “mind & body” nourishment, as well as address the issue of autonomous architecture and propose a variety of spatial solutions that could benefit and enhance the functions and atmospheres of the adjacent urban fabric of Regent’s Park and its environs, i.e. the areas around London Zoo, Regent’s University, the Open Air Theatre, the Outer Circle, etc.). The pavilion should include a basic food preparation and serving area, a café and an art space.

Each student defined his/her main theme: this was inspired from a variety of sources, e.g. site & context related, and was linked to the site and precedent analysis phase, Landscape Formation One [LF1], by Zaha Hadid.

The disassembling and reassembling operations can be both physical and conceptual. The precedent is analysed thoroughly. The operations and results are geared to help the students develop a basic working method around the ideas of transformation, transposition and displacement of specific elements or/and methodologies into new contexts, providing novel meanings and solutions to London’s dense city fabric.

Using a Kamea or Magic Square — I learned a few things from @arnemancy and his class on magic & cryptography in the Renaissance...

For the last few weeks I was taking Arnemancy’s class, The Other Trithemian Art, on codes and ciphers in magic. It’s quite an interesting class, and I’ve been enjoying the brain stretch to think about using codes and ciphers in magical and occult practice. It’s not an easy thing to think about — as John Michael Greer has opined, occultism can be defined as ‘discarded knowledge’ of one kind or…