Hey /sci/, I started a blog where I have been roughing out t

Thanks OHP, will check it out.

>>8609038
Apologies for any typos, I am pretty wired right now and a lot of the stuff is stream-of-consciousness. The whole project is really so that I can maintain a more robust dialogue with myself to better hone my ideas, but I figured you chaps would find it at least a schizophrenic curiosity. Hahaha

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>Mathematics is the language of the realm of mind; it is the very fabric of mental activity.
doubt it.

>The image I have in my head is one of those Japanese paper fans, where the basepoint is the hinge, the algebra is the handle, and the paper folds are copies of the algebra held together by algebraic rules.
Interesting.
>copies of the algebra
It's representations?

>held together
do you speak of maps among those copies, or the rules of the algebra that the copies obey?

>duality
>R^n and Z^{\oplus n}
If we were to start from Z^{\oplus n} (which appears inherently countable), and work through to R^n from there, where do we introduce a seed of accountability here?

I read the other posts when I come back from the dentist. Add dates to the posts.

>>8609054
Lel. Looking forward to reading your deranged musings.

>>8609030
>went there to shitpost on a retarded popsci fag talking about quantum physics and hard consciousness
>actually about hard math

I was pleasantly surprised

>>8609030
OR YOU COULD GO HERE YA FUCKING DANIEL!

PRETTY SURE THE GUY THAT RUNS IT (HINT: IT'S FUCKING /SCI/MON) WILL LET EVERYONE CONTRIBUTE AND ENGAGE DISCUSSION

https://github.com/Y-O-S-H

Or you can go edit wikipedia pages. That'd be awesome.

Don't forget to didjabringyabeeralong

>>8609055
Regarding the duality, it's just Pontryagin duality. Coproducts are dual to products, yada yada. It would have been more clear if I mentioned "Pontryagin," but again, these are really my private musings.

Regarding representations: sort of. I am referring to module theory here, but representations are very closely connected. I mean, hell, Tannaka reconstruction tells the whole story if you are familiar with that. Grothendieck was a beast.

>>8609060
Thanks Simon, I'm checking it out now!

>>8609062
Okay, so then the uncountability is there from the start, in form of the cardinality of the circle group.

Okay, I read all posts now. Although the F1 post is at the very bottom, so I read that one last - but it seems you refer to it in other posts.

>the field on one element showing up
Do you write "on" on purpose here?

>>8609030
Looks fun and interesting. I don't understand anything of it though. I haven't found math very useful in my line of work (I do cosmology), so I've never studied it intensively.

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>>8609258
Thinking about the field with one element and infinity-categories is hands down the field of math which is most remote from any applications.

nice blog

>>8609224
Yes, in the nature of talking about structure /on/ a set. The reason is actually important: the homotopy type of the point is intrinsically identical (contrary to type-theoretic foundations) to the field on one element. The only difference is in the ambient category. I choose to take this view because it motivates a more coherent mathematics, where we ought to be able to seamlessly flow between different structures.

>>8609188
Oh, yes, thanks! I was getting a bit presumptuous with my philosophical liberties, so it's quite nice to get external feedback.

>>8609309
I think the network of applicability is not in fact one-dimensional or even metric at all, but I agree that it is alarmingly abstract for the (large part of the) modern academic climate. Nonetheless, I hope to see my perspectives open new avenues of understanding in the future! They certainly have already, as I am applying higher categories to dynamical systems in a more formal environment.

>>8609188
Oh, what is quite fun is that loops (a la U(1), the circle group) behave much like vectors do in linear algebra, inasmuch as they constitute points in a very appropriate tangent space. I think the free loop space bundle is remarkably underappreciated. I have done some discrete modeling of how these behave like tangent spaces using directed graphs, but I haven't polished it enough to want to integrate it yet. That said, I am seeing how this all ties back to some thoughts I had over the summer about the relationship between Ricci flow and transport in homotopy type theory.

>>8609309
Hands down? What? Legs up?

>>8609383
Face down, ass up, that's the way we like to fuck.

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Sphere spectrum post is now live; get it while it's hot. I'm also trying to bump this, since I saw that it was shared on Facebook and I would like to proliferate links as much as possible to increase visibility and perhaps even the brightness of mathematic's future.

(Oh, it has original pictures! Oooooh!)

polite bump