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

@Danu maybe

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

@FenderLesPaul do you use twitter?

For your news feeds.

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?

@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.

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

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

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

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

k ty

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

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

hmm...

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

@0celo7 Yes, it's linear.

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

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

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

Vector spaces form a category.

@0celo7 "in category of vector spaces"

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

No

Ok!

No need to get on my ass

@ACuriousMind Yes, so?

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

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

@Danu Ah, indeed.

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

But the spirit of what I'm saying is right

That it is.

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

@Danu Yes, I know that

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

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

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

@0celo7 There was no intepretation going on anywhere

@Danu All communication is interpretation :)

@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.

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

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.