Iso (math fool)
@isomorphicphi.bsky.social
Background in theoretical physics/mathematics. Interested in mathematics, philosophy and physics. Now I teach. Some kind of anarchist communist, I guess. Swe/Eng.He/they.
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)
March 25, 2025 at 3:51 PM
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
March 20, 2025 at 5:23 PM
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
March 20, 2025 at 3:49 PM
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
"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
March 18, 2025 at 8:02 AM
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
"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
Dear boooks, please provide insight
March 11, 2025 at 6:25 PM
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
I literally just reprinted the notes from my course in the way back
March 11, 2025 at 6:16 PM
There is some metric isotropy group of the bundle too, right?
I literally just reprinted the notes from my course in the way back
I literally just reprinted the notes from my course in the way back
Right, so that's very infinite dimensional
March 11, 2025 at 5:55 PM
Right, so that's very infinite dimensional
Quasi-finitist going, in desperation, "something is finite, right?"
March 11, 2025 at 5:17 PM
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?
March 11, 2025 at 5:13 PM
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?
March 11, 2025 at 4:01 PM
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
March 11, 2025 at 3:26 PM
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?
March 11, 2025 at 1:44 PM
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
March 11, 2025 at 11:35 AM
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"
"Newton's law of gravitation is rotation invariant, but the elliptical orbit has a prefered plane"
March 11, 2025 at 6:46 AM
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"
"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"
"We cannot know; we must not know"
March 11, 2025 at 6:41 AM
Ignorance is bliss; as David Bizarro-Hilbert once said:
"We cannot know; we must not know"
"We cannot know; we must not know"
Frege is OK. Decent philosopher
March 10, 2025 at 8:16 PM
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
For any x fitting a definite description, any y distinct from x fails to meet that description
March 10, 2025 at 6:41 PM
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
For any x fitting a definite description, any y distinct from x fails to meet that description
Right, that too
March 10, 2025 at 5:42 PM
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
March 10, 2025 at 5:39 PM
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
March 10, 2025 at 4:53 PM
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