CAG@LOCS#22
There's something ugly about 18-wheelers unloading products in small-town alleyways, slowing traffic (pedestrian, cyclic, and automotive) and generating noise. But there's an element of absurdity in the same situation when the tractor trailer reads "Quality Organically Grown Fresh Food". Especially living in Virginia, but pretty much anywhere, i can think of some obvious ways to get fresh food that don't involve nearly as much transportation. And OK, that's not to say that locally-grown foods can necessarily feed the local population or slake their lust for variety. And it's not to say that organic, fresh products aren't a much better option than factory-farm or heavily processed ones. But only upon this truck's arrival on Draper did the chasm of difference between buying organic and buying local occur so starkly to me.* I resolve to make a stronger effort to base my diet upon as large a local component as practical, and i encourage everyone to do the same, or at least to keep an eye out for the local stuff when shopping casually.
Speaking of local business, i had a few minutes ago my first danish from Bollo's. Apparently you have to show up shortly after a batch is made to be able to get one, and i understand why. They don't look as stylish as the hurricane-shaped ones you'd see at Au Bon Pain, but they're delicious, with crisper bread components than most and big ol' chunks of fruit. They're good to me even without coffee.
My task for the next hour and a quarter is to do as many by-hand comparisons as possible between the intersections of Borel orbits in the matrix Schubert variety Y|w| with (a) the ideal generated by my equations, which i hope turns out to be the whole ideal, and (b) the Euclidean topological closure of the preimage of the affine Schubert variety. The Euclidean closure is clearly contained in the Zariski closure (i.e. the set of all stuff that satisfies every equation satisfied by the original things) because "= 0" (satisfying an equation) is an E-closed condition. And there's a nice decomposition of the MSV as a disjoint union of these Borel orbits, and in each it suffices to look at an arbitrary echelon form. If every echelon-form matrix from a Borel orbit in the Z-closure can be expressed as an E-limit of matrices in the preimage of the variety (where everything comes from in the first place), then i'm done. But the E-closure need not be the Z-closure, so my hope is that i can at least narrow the concern to a smaller collection of orbits.
Of course, all this has to be gerealized to arbitrary cases for it to help me with the set-theoretic argument, and to do this i need a lot of examples in which (to hope) to find a pattern. Hence the current task.
I also got new underwear from Home Body today. ^_^ It's form-fitting but not constrictive, and so far doesn't bunch up at the cusp (isn't that a pretty word?) because it clings to . . . well, you know.
* It's not just the truck, of course, that inspired this realization; the truck brought to life a variety of documented arguments for local consumerism i've read over years. If you're interested, good ones are not hard to find.
Speaking of local business, i had a few minutes ago my first danish from Bollo's. Apparently you have to show up shortly after a batch is made to be able to get one, and i understand why. They don't look as stylish as the hurricane-shaped ones you'd see at Au Bon Pain, but they're delicious, with crisper bread components than most and big ol' chunks of fruit. They're good to me even without coffee.
My task for the next hour and a quarter is to do as many by-hand comparisons as possible between the intersections of Borel orbits in the matrix Schubert variety Y|w| with (a) the ideal generated by my equations, which i hope turns out to be the whole ideal, and (b) the Euclidean topological closure of the preimage of the affine Schubert variety. The Euclidean closure is clearly contained in the Zariski closure (i.e. the set of all stuff that satisfies every equation satisfied by the original things) because "= 0" (satisfying an equation) is an E-closed condition. And there's a nice decomposition of the MSV as a disjoint union of these Borel orbits, and in each it suffices to look at an arbitrary echelon form. If every echelon-form matrix from a Borel orbit in the Z-closure can be expressed as an E-limit of matrices in the preimage of the variety (where everything comes from in the first place), then i'm done. But the E-closure need not be the Z-closure, so my hope is that i can at least narrow the concern to a smaller collection of orbits.
Of course, all this has to be gerealized to arbitrary cases for it to help me with the set-theoretic argument, and to do this i need a lot of examples in which (to hope) to find a pattern. Hence the current task.
I also got new underwear from Home Body today. ^_^ It's form-fitting but not constrictive, and so far doesn't bunch up at the cusp (isn't that a pretty word?) because it clings to . . . well, you know.
* It's not just the truck, of course, that inspired this realization; the truck brought to life a variety of documented arguments for local consumerism i've read over years. If you're interested, good ones are not hard to find.