Super Artificial Intelligence, a naive approach

[W.D.Clinger]

Perhaps I did.

But we know you didn't, because you are still making mistakes such as:

As you've just pointed out, both the manifold, and fiber sequence of said Rⁿ are euclidean in nature.

That is not at all what I said.

Neither of the two examples I gave involves Rⁿ.

For the two examples I gave, I said the fibers were Euclidean even though the manifold is not Euclidean.

The two examples I gave do of course involve locally Euclidean manifolds, because all Riemannian manifolds are locally Euclidean. You are having a great deal of trouble understanding that locally Euclidean and Euclidean are not the same thing.

Albeit, we see that based on your last quote, your prior quote (below), is not entirely true:

I said "The fibers can be Euclidean even if the manifold is not."

That is entirely true.

I gave examples, which you failed to understand even though you are pretending to understand words you learned at the University of Google.

 

[ProgrammingGodJordan]

But we know you didn't, because you are still making mistakes such as:

That is not at all what I said.

Neither of the two examples I gave involves Rⁿ.

For the two examples I gave, I said the fibers were Euclidean even though the manifold is not Euclidean.

The two examples I gave do of course involve locally Euclidean manifolds, because all Riemannian manifolds are locally Euclidean. You are having a great deal of trouble understanding that locally Euclidean and Euclidean are not the same thing.


I said "The fibers can be Euclidean even if the manifold is not."

That is entirely true.

I gave examples, which you failed to understand even though you are pretending to understand words you learned at the University of Google.

(A)
Cylinders appear to have something to do with Rⁿ, contrary to your expressions of the contrast.
https://en.wikipedia.org/wiki/Projective_plane


(B)
Locally euclidean or euclidean, both are degrees of the euclidean paradigm.
In simpler, toddler like words, at some point, both are euclidean.
So, the mistake is not mine.

 

[W.D.Clinger]

Cylinders appear to have something to do with Rⁿ, contrary to your expressions of the contrast.
https://en.wikipedia.org/wiki/Projective_plane

Although cylinders are locally Euclidean, which does have something to do with R², the word "cylinder" does not appear within that Wikipedia article.

Citing Wikipedia articles that don't support your claim would be a fine April Fool's joke, but doing so all year round might be noticed.

Locally euclidean or euclidean, both are degrees of the euclidean paradigm.
In simpler, toddler like words, at some point, both are euclidean.
So, the mistake is not mine.

Toddlers might not see anything wrong with your argument.

 

[ProgrammingGodJordan]

Although cylinders are locally Euclidean, which does have something to do with R², the word "cylinder" does not appear within that Wikipedia article.

Citing Wikipedia articles that don't support your claim would be a fine April Fool's joke, but doing so all year round might be noticed.

(1)
It is optimal to see that you have corrected your prior blunder, where you nonsensically expressed: "cylinders don't involve Rⁿ".


(2)
Oh, but the projected plane did have something to do with why I referenced it:

Manifold -> A finite cylinder may be constructed as a manifold by starting with a strip [0, 1] × [0, 1] and gluing a pair of opposite edges on the boundary by a suitable diffeomorphism. A projective plane may be obtained by gluing a sphere with a hole in it to a Möbius strip along their respective circular boundaries.

Toddlers might not see anything wrong with your argument.

(3)
Perhaps one should be more like toddlers, such that one avoids seeing non-errors where possible, and avoid presenting nonsense such as cylinders don't involve Rⁿ. etc.
That toddler would probably recognize that the above was not 'my argument'.