#cognisance

[neatlymanifolded]

Definition 1.0. Let this be a post.

[megalommi]

Re: he doesn't have a name

I was thinking about that while writing it, and I kept coming back to Cognisance, or Cog for short.

PERFECT

Nightmare!Baggs' name is now Cognisance

[ffauns]

Another sight, another mind See through the vessel See through another sight

http://www.xavibou.com/index.php/project/ornitographies/

[swapndarshak]

NATIONAL EDUCATION DAY 2020

Education is just not about the books and classrooms, it's also mastering over the 'patience and observation' of life around us. It's one of the simplest way to understand the deepest treasures of life by looking for smallest details of our own existence. - Navin Das

[thesingingcanary]

Awareness / Cognisance (2018) 

"her sudden  consciousness  of  the  problem  she  faced"; 

+ & +

[neatlymanifolded]

Danny what are you doing

[neatlymanifolded]

I have been a fool. For 3 months, I have been complaining to my friends and followers that my supervisor has not been reading my paper. Last week, I struck the winning formula, which any boomer could have told me of -- complain to his wife.

This morning, the full paper is annotated.

[neatlymanifolded]

Based on this post, I'm gonna try to explain why I am not really interested in logic. I explicitly want people to argue back! I'd be very happy to be convinced that I'm wrong.

1. First and foremost, its barely Maths. We use logic in maths, sure, but a lot of logic isn't itself maths. That would be like saying that maths is a subfield of physics, just because it's its most well-known application.

Perhaps this is naive, but to me maths could be loosely and circularly defined as "the studied structures* of mathematics, and their applications to science". Here a structure is a Thingy With Axioms, and implicitly includes working in ZFC if there are sets. Maybe you're allowed to care about the continuum hypothesis, but if either assuming it or its contradiction gives better results (meaning that it allows us to prove more things with applications to the real world), then we should just do that. That's maths now. You can study whatever perverse axiom system you like, but that isn't maths. If you care about interpretation, it's Philosophy; if you don't, it's Logic. Maths cares about both intrinsic properties and interpretation of a particular set of "realistic" axioms, and the useful structures we define from them. I also don't think proofs are true if and only if they _are_ fully rigorous, we just the community to agree that they could be. That's good enough.

This is definitely circular, because what about set theory? But yeah, what about set theory? What is up with that?

2. The "interesting/surprising" results aren't that interesting anymore. Gödel is just the previous generation's Milnor/Freedman. I grew up with incompleteness, it doesn't surprise me. It's been a key part of maths since forever, as far as I'm concerned. I've been aware of exotic and non-smoothable manifolds for as long as I've been aware of manifolds, pretty much, so it isn't surprising that they exist. It's just a technical construction exercise. Same as Banach–Tarski isn't a paradox, it's just the statement that some sets aren't measurable, which isn't weird actually! Maybe there are some good results in there, but are they worth it? Not from the logic/model theory courses I watched my friends take.

On this note, I am excited to see what this is for future generations. Maybe they'll get more and more specialised, but I hope something else fun, well-known, and surprising is proven in our lifetimes, that our children will think is natural and boring.

3. Don't you people like fun?? I get that there's some fun in proving a surprising result, but the actual process?? Do you not like intuition? A physical vibe?? Maybe this is the topologist in me, but even the algebraists and analysists are always drawing shapes and diagrams of some kind, and talking about symmetries and actions. Maybe forcing is powerful, but has it any whimsy? I think not.

That's probably it. Maybe someone can explain type theory and HoTT in a way that doesn't make me go "that's maths not logic" and also "ok that's interesting". But Emily Riehl explained it to me and kinda agreed that isn't really logic at all, so I don't have high hopes.