so many mathematical things to do,

and i did none of them, today.

..

then again, that's not quite true .. not in spirit, anyway. i did teach today, though i think it went poorly. last night i got excited about this one "application" of stoke's the0rem [1] that i realised that i could explain.

put in layman's terms,

`"the surface integral of the curl of "any" 3-dimensional vector field, over a 2-sphere, is zero."`[2]

after i finished those few minutes of explanation, i noted that my students' eyes were more glazed than usual.

*oh well*.

at any rate, i did do some sort of labor today. as for research, i did read a 3-page research note from 2003. from it, i learned something:

the more i think about it,

the less i really know about d0ub1ing measures.

[1]

*isn't it strange how badly math jargon translates, to non-mathematicians? for example, when someone in pure maths refers to an application, (s)he's probably not talking about physics or chemistry or anything related to the world.*

similarly, when i say that i will estimate a certain quantity, i don't mean that i will give you a decimal number of a quantity that can actually be measured physically.

similarly, when i say that i will estimate a certain quantity, i don't mean that i will give you a decimal number of a quantity that can actually be measured physically.

[2]

*i.e. sufficiently smooth vector fields in R*

^{3}. sadly, to most calculus students, every function has a derivative.
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