the traditional story is that Liu Bang* accidentally allowed some prisoners to escape and, having already earned a death sentence for that, jumped straight into banditry and rebellion

*perhaps better known as the founder of the Han Dynasty?

tbh I think that if the US _actually_ invaded Canada or Greenland there would be a moral duty to do a lot of stuff

most of that stuff I would find extraordinarily inconvenient but it would be necessary

we can take the mild inconvenience instead

if the national environment is ~D+10

which is a reasonable estimate

and Alaska was R+13 in an R+1.5 year

then Peltola needs to pull +1.5 points over General Erick Dem to take the seat, a margin which is only comparable to the required margin in eg Kentucky in the sense that both are numbers

And now they all see you
Hiding the hem of your skirt, because it is bloody
With the blood of your
Best children.

(orig:
Und dabei sehen dich alle
Den Zipfe deines Rockes verbergen, der blutig ist
Vom Blut deines
Besten Sohnes.)

algebraic geometers in shambles

The spirit of '89 is as applicable today as it was the day Lafayette wrote the Declaration of the Rights of Man and the Citizen: Women (and men) are born and remain free and equal in rights.

if the test was well-designed/properly graded, I would actually expect it to have a pretty strong cutoff where a bunch of people fall into the "95-100/100; can unquestionably read at a third-grade level" bucket w/very little internal differentiation

note the load-bearing "if" clause, though

Spirit Island (complicated but VERY good)
Root
Mystic Vale
Oath
Wingspan
Smallworld
Sentinels of the Multiverse
Azul
Tsuro
really want to get into Scythe

Thank you; that's a very practical piece of advice!

(an (n x m) matrix represents a map from R^m-->R^n so if you are really insistent on making the notation line up with the underlying facts you either have to go very crazy or just say that your matrix is a map, uh

R^n<--R^m

or something)

(There's a similar convention adopted in the dimensions of matrices---(n x m) matrices are named so that if you have an (n x m) matrix and an (m x k) matrix, you can multiply them in that order to get an (n x k) matrix

but actually there's a reversal here as well)

because if you have xAB, the matrix A is applied first, and then followed by the matrix B

real purists of this school of thought apply their _functions_ on the right so you'll get something like ((x)f)g or so forth

tragically I think this is a slightly misaligned case of trying to make it easier---it's so that the T's line up in the middle of the matrix multiplication on the left up there

there are some people who like to do their matrix multiplication _on the right_ for this reason

ABx means "the vector we get when we apply A to the vector Bx; A(Bx)"

so if we have change of basis matrices P_{S<-T} and P_{T<-R} then the change of basis matrix from R to S is the product

P_{S<-T} * P_{T<-R} = P_{S<-R}

your professor is presumably trying to make it easy to _compose_ change of basis matrices when written in the standard order of matrix multiplication

Chris Murphy makes a detailed case that Trump is on the brink of meaningfully restricting the space in which the opposition can do politics, in the competitive authoritarian model of autocracies abroad.

"If we are not already there, we are really, really close." 4/

newrepublic.com/article/2013...