Iso (math fool)

Whaddup groupoids?

My phaneron has itchiness predicated of it

Abstract nonsense is way easier to understand the sixth time you go through it

She's called an inner product space because she's got a product in 'er

I don't know off the top of my head if anyone writes about this, but it seems to me correct that conspiracy theories are pseudo-paradigms (ie what Kuhn confusingly calls pre-paradigmatic paradigms)

I am back to looking at "geometry stuff", so maybe I should have a look soon

I only have Gauge Theory & Variational Principles by Bleecker. I haven't read it so I don't know if it's good

It's a 'long book is long' problem. It's like the old joke

"I thought the book was longer than it is."

"Well, that's silly. No book is longer than it is!"

Capital is longer than it is.
length(Capital)<length(Capital).
Contradictory? It's dialectics, or something

[In optimistic naïvité:] I should start reading the Marx man again

Dear boooks, please provide insight

There is some metric isotropy group of the bundle too, right?

I literally just reprinted the notes from my course in the way back

Right, so that's very infinite dimensional

Quasi-finitist going, in desperation, "something is finite, right?"

Yeah, I think so too. Really need to brush up on DG. But something is finite dimensional, though. Is it the Lie group of some bundle? Because local Poincaré is the maximal dimension of... something, right?

Now I'm confused, Roch. Isn't the diffeomorphism group the diffeomorphism group of a manifold M (ie a 'solution' to the field eq) while the equations of motion have general covariance? Like that the dimension of Diff(M) is smaller than the 10 dimensions of local Poincaré?

Yeah, I'm always highly suspicious of probability arguments where you measure over potential cosmologies like that (because of the measure problem). I was thinking just mathematically that there is no reason every symmetry of the dynamics should manifest itself in the solutions

Could you elaborate what you mean?

Isn't it exactly the same? A solution to the equations of motion has "fewer" symmetries than the equations of motion

In a sense, I find this no more strange than this claim
"Newton's law of gravitation is rotation invariant, but the elliptical orbit has a prefered plane"

Ignorance is bliss; as David Bizarro-Hilbert once said:
"We cannot know; we must not know"

Frege is OK. Decent philosopher

I'm gonna go for the troll answer, since I in reality basically agree with you:

For any x fitting a definite description, any y distinct from x fails to meet that description

Right, that too

I don't have the dates, but Peirce may have beaten Frege to it. Certainly, it was not an idea unique to Frege at the time

I agree with much of this. "Something" "happened" to mathematics in the middle of the 19th century. One of my favorite throwaway lines from Kuhn is that this something happened at very different rates in different places

I have very large sympathies with this view (probably with some very post-Kantian philosophy of mind/intension tacked on)

But, like, in Kant's defence, viewing mathematics as analytic splits what Kant thought to be mathematics into eg the analytic theory of the Dedekind-Peano-(Peirce) axioms and the empirical theory of its utility in counting

Missing as in failing to realize, rather than failing to consider. But Peirce has the great benefit of being later than Gauss-Bolyai, Boole-DeMorgan as well as Hamilton and his dad

Peirce, who in many ways is a Kantian, critized him for "missing" that mathematics is analytic rather that synthetic

My favorite kind of sheaf is the mist-sheaf