I'm a mathematician who taught linear algebra for decades. I love Einstein notation. I don't find Cracovians interesting at all.
Old texts got really worked up whether a vector was a row or column. The programming language APL resolved this quite nicely: A scalar has no dimensions, a vector has its length as its one dimension, ... Arbitrary rank objects all played nicely with each other, in this system.
A Cracovian is a character or two's difference in APL code. There's a benign form of mental illness learning anything, where one clutches onto something novel and obsesses over it, rather than asking "That was exciting! What novel idea will I learn in the next five minutes?" I have friends from my working class high school who still say "ASSUME makes an ask of you and me" as if they just heard it for the first time, while the most successful mathematicians that I know keep moving like sharks.
I wouldn't stall too long thinking about Cracovians, as amusing a skim as the post provided.
I mean theres nothing special about naming binary operations on tensors of fixed rank. Matrices have some nice mathematical properties which is why they are studied so much in mathematics. But for number crunching there is no reason to prefer then to cracovians, or vice versa, without knowing what the underlying memory layout is in hardware.
Old texts got really worked up whether a vector was a row or column. The programming language APL resolved this quite nicely: A scalar has no dimensions, a vector has its length as its one dimension, ... Arbitrary rank objects all played nicely with each other, in this system.
A Cracovian is a character or two's difference in APL code. There's a benign form of mental illness learning anything, where one clutches onto something novel and obsesses over it, rather than asking "That was exciting! What novel idea will I learn in the next five minutes?" I have friends from my working class high school who still say "ASSUME makes an ask of you and me" as if they just heard it for the first time, while the most successful mathematicians that I know keep moving like sharks.
I wouldn't stall too long thinking about Cracovians, as amusing a skim as the post provided.