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Danu

21:15

@0celo7 The book on the history of Lie groups that Conifold mentions seems fascinating.

0celo7

@Danu maybe

@ACuriousMind Can you please just explain what you meant by the $f=f'$ comment?

skill patrol

@FenderLesPaul do you use twitter?

For your news feeds.

1 hour later…

Joe Stavitsky

22:40

What is meant in the book when it says "if a gaussian cylinder goes through an infinite sheet of charge, E is the same for any distance from the plane?"

In other words, clearly they are not saying that magnitude does not fall off as 1/r^2?

ACuriousMind

@JoeStavitsky Clearly they are saying that.

The electric field of an infinite charged sheet does not fall of with distance.

You can understand that heuristically by trying to draw the field lines. They start normal to the sheet - and they can't do anything but go straight, since there is no reason for them to bend in any one particular direction.

Joe Stavitsky

In other words infinite charge=infinite field at infinite distance?

ACuriousMind

No, the field is finite, it's just constant in space

Joe Stavitsky

o ok for that density expression (density/2eps0) right?

ACuriousMind

Hm? Yeah, $\frac{\sigma}{2\epsilon_0}$ is the field of a sheet with surface charge density $\sigma$.

Joe Stavitsky

22:51

k ty

0celo7

@ACuriousMind Is an isomorphism between vector spaces implicitly a linear map?

ACuriousMind

@0celo7 no, it's explicitly a linear map.

0celo7

hmm...

@ACuriousMind does "isomorphism between vector spaces" imply anything more than a set isomorphism?

Danu

@0celo7 Yes, it's linear.

ACuriousMind

An "isomorphism between vector spaces" is by definition an invertible linear map. What are you on about?

Danu

23:02

Isomorphism in [category X] is map that preserves all structures that belong to objects in [category X]

0celo7

Ok, so it has to preserve the vector space structure

@Danu Well, I'm not sure if the "in [category X]" part applies here!

Now I have to prove linearity of the map, yeesh

ACuriousMind

Vector spaces form a category.

Danu

@0celo7 "in category of vector spaces"

0celo7

All I wanted to know is that if vector spaces $V,W$ are isomorphic as sets, then is the isomorphism linear?

Danu

0celo7

23:04

Ok!

No need to get on my ass

@ACuriousMind Yes, so?

ACuriousMind

@Danu Not necessarily true, e.g. homotopy categories are constructed by "inverting" maps that are not full isomorphisms in the original category.

Danu

Since $\Bbb R^m\cong \Bbb R^n$ for any $m,n$ finite as sets.

0celo7

@Danu Ah, indeed.

Danu

@ACuriousMind Okay I don't know shit about category theory ;)

But the spirit of what I'm saying is right

ACuriousMind

That it is.

Danu

23:05

The minigame where you fight copies of yourself in Transistor is funny

0celo7

@Danu Yes, I know that

Danu

However, using the quick-move + the usual void+strongattack it's too easy.

0celo7

I ask a question and immediately ACM picks the interpretation that makes me sound stupid :(

ACuriousMind

@Danu You talking about it made me actually want to replay it ;)

Danu

@0celo7 There was no intepretation going on anywhere

ACuriousMind

23:07

@Danu All communication is interpretation :)

Danu

@ACuriousMind The second go-round is more fun but way too easy.

I'm running all handicaps except the one that takes away MEM now, and eveyrthing is simple.

ACuriousMind

@Danu Started anew because I didn't remember anything about how to play the game :P

Danu

Void Void Void, Cull/Load-with-speed-upgrade

@ACuriousMind Fair enough :)

Void is really OP

You'll only get it towards the end though :)

I just did the second go-round because I wanted to complete all the backstories of the characters; I only discovered you unlocked them by using all functions in all different ways near the end and thus was unable to do it in time.

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