#tangent bundle

Pueblo

In doing research for this article, I discovered that the “Pueblo” in Pueblo Corporate Council was not named for Pueblo, Colorado, which does indeed lie within PCC boundaries. Plus, since I never took Spanish, I learned that “pueblo” means “town”, and so would have been slapped across a wide range of places by the Spanish colonizers of the region. This term was later used as an exonym for the entire collection of tribes of that region: the Puebloans.

In 2050, the PCC is dominated and roughly equally split by two tribes: the Zuni and the Hopi.

Tangent!

The concept of a tangent line to a curve can be generalized to an arbitrary number of dimensions. Given a manifold M that is differentiable at a point x ϵ M, you can define a tangent space TxM and a tangent vector v ϵ TxM, along a curve traveling through x ϵ M. I mean, if you wanted to. What you do with your manifolds is up to you.

NAN, V. 1 uses “Zuñi” instead of “Zuni” for the tribe – the “ñ” being indicative of its Spanish origin. The accepted spelling now (2020) is Zuni, which I will use here. Of course, this is not the name the Zuni use for themselves, which is A:shiwi. Same with the Hopi, which is a shortened version of Hopituh Shi-nu-mu.

While we might point to the disrespect that the Spanish (and later, American) had for the integrity of the tribal peoples when it came to their name, it’s common across all languages to not use the same name that people from another country use for themselves. In English, we refer to the French and the German, while in their respective languages they would be Français (or Française, depending upon gender) and Deutsche, respectively.

And everybody does it: The Deutsche word for Français(e) is Französisch, which is at least a little similar, while the Français(e) word for Deutsche is Allemand(e). 

What the drek, France?

Pulling back out of the tangent…

The tangent bundle – the union of all possible tangent spaces, defined in the previous image’s caption, on a manifold – is an example of a vector field. The tangent bundle is also an example of a differential form on a manifold. The pullback of a vector field is a smooth map between the tangent bundle and its original manifold.

That explains the “Pueblo” in the country’s name. The “Corporate” derives from the fact that all PCC citizens are shareholders in a corporation and receive voting privileges and dividends as such. Like the situation now in Alaska, where the Alaska Permanent Fund pays out a chunk of $$ to its residents every year. How does this work out for the PCC?

“The Pueblo nation is the most prosperous country in North America. They boast the highest standard of living, and the government offers the widest range of social services of any nation.”

So, pretty good, in fact. The PCC’s strength is in its tech sector – specifically information processing and computer programming, making this a good way to work it into, say, a Seattle-based campaign – time for a Matrix run!

“Chummers, you may think you’ve seen sophisticated computer systems… but you ain’t seen nothing till you’ve tried to deck the Pueblo corporate system… It’s part of the Matrix, but the level of sophistication is literally years ahead of any other part of the net. And, chummer, you might think you can cut any ice, but I’d be willing to bet anything you can’t cut theirs… [their] deckers can trace and dump you and the cops will be there to pick you up before your head stops spinning.”

Ok, so maybe not. 

Maybe a quick Astral jaunt? Better think about…

Kachina

Here is another example where the Shadowrun magic system, specifically shamanic magic, doesn’t mesh well with the actual tribal spiritual beliefs.

”The Kachina Society is a group of masked dancers, all male, who perform rain ceremonies to ensure good crops.”

Boo.

This is an appropriation of the Kachina Dancer tradition, whose dress evokes and pays respect to the kachina spirits of the Pueblo peoples, and such dances are not done purely for meteorological purposes. Similarly for the Great Ghost Dance, which is stated in the text to be a Hopi tradition, but the (real) Ghost Dance was most recently founded by the Paiute Wovoka (and in Shadowrun, by the Ute Howling Coyote). And while the country by be new-wave corporate in structure, the justice system is run by shamanic tribunals, who are most assuredly not having any of your Awakened runner’s drek when they are caught snooping around astrally.

Absolutely none.

20121113, Prof. Leeb.

I.4.4. The differentiable structure on the tangent bundle.

natural topology and diff. structure of tangent bundle

topology on T M has countable basis, Hausdorff property

I.4.5. Tangent vectros as derivations

regard tangent vectors as differentiable operators.  to tangent vector, assign directional derivative

Properties

(i)R-linear

(ii) product rule

Definition of derivation

germs of functions

denote I_p \subset \mathcal{C}^k(M)_p the maximal ideal of the germs

subjectivity of T_pM \to \mathcal{D}_p(M), v \mapsto \partial_v (*)