ChapterZero

I noticed that is approximately the same as . Is there a known proof (or am I just seeing things again)?

We know that and are and , respectively (assuming the function is nice enough to have a unique median). In general, what is ?

In the process of investigating the approximation error, I came across an interesting question. From numerical examples, it seems that , where but this baffles my intuition (which I’ll admit isn’t very sharp), especially for . Here is the Frobenius norm, and is the j-th column of .

Hopefully I’ll have time to look at this later. Besides being counterinuitive, it seems potentially useful: consider a vector of composite length , you could partition this vector into blocks of length then apply this inequality to get a family of bounds on the euclidean length of the vector. Exploit the fact that and you could derive some very weird bounds indeed.

My officemate and I have decided to take 30 minutes or so a week to inform each other about various mathematical topics– on the theory that teaching helps you to cement your own knowledge. I’ll be teaching him something relating to my research, and vice versa: he’ll probably be teaching me about Sobolev spaces, which I’ve wanted to learn about for a while now, so it should be an interesting experience. I’m debating between teaching him what I know of random matrix theory (which I’ve already gotten fuzzy on, despite having learned it last term), working my way through the Cauchy-Schwarz masterclass book (because I’m sure I’ll find those inequalities useful), or basic operator theory (which I know I’ll need down the road as my research becomes more theoretical).

Speaking of my research, I fell in love with the subject all over again. Remember my problem is to find bounds on the error in approximating a given matrix with a sparse matrix ; ideally, these bounds should be a function of only: the whole point of sparsification is to avoid making convoluted computations involving the original matrix ; if we had to make such computations to bound the error, we might as well just calculate it exactly. Anyhow, I saw anew how awesome it is that you *can* get useful bounds that are just a function of . I think it helped a lot that I got nice results

Tonight’s been an insomniac night, just checking out a bunch of blogs. Feeding the addiction

Anyhoo, in the background, I’ve been youtubing various people. For the first time I listened to some of Pharell’s stuff: I’ve been a fan of his forever, because he demonstrably doesn’t think that to be successful in the music business you have to conform to the Jay-Z, Lil’ Wayne, Soulja Boy, etc. stereotypes. He’s being him, doing him, and it’s working for him, same as his bff Kanye.

But I’d never heard his music before; here’s a little sample:

If someone had played these for me, I would have thought the first two were parodies; the third is OK, but can Gwen Stefani have some more lines? On to someone else…

Update: I think in the first two songs he was trying to get the same offbeat feel as when he’s part of NERD; I like what I’ve seen of their stuff. Here’s a good one:

Occasionally I come across so-called feminist blog entries that strike me as particularly vile. Today, one of the articles in the latest Carnival of the Feminists linked directly into the blindered underworld of ‘feminists’ who ascribe everything to twisted male sexuality and the desire for dominance.

In this case, the nominal topic is transgenderism, but it quickly devolves into an attack solely on transwomen:

When transgendered folks get through the final stage of transitioning and reach “the end”, all that gender fluidity goes right out the window and solidifies into the crusty crud on the bottom of my boots.
…
Since you do not need a penis to pick up a hammer, since you do not need a vagina to vaccuum, or validate virility, vanquish vasselage, or *oh my!* vounch for volition, there is also no corresponding need to switch out body parts in order to express what is basically described as internal character, unless the purpose is merely to commodify one’s personality as a dainty girl might wear pink or a goth craves black. The genitalia have been reduced to the status of wardrobe accessory.

And since these folks insist they’re not swapping out genitalia for masturbatory fetish purposes, there too is no need to accessorize oneself with the preferred genitalia of their romantic partner unless they’re also prepared to reverse the surgery again, when they meet someone new who wants yet different genitals to play with.

So many things are wrong with this post, starting with the fact that she confuses transgenderism with transsexualism. One would think you’d take the time to familiarize oneself with the difference before you start spewing vitriol. There’s just too much to shake my head at to even begin deconstructing her ‘arguments’.

Shhh! Don’t tell anyone … I’m a Rihanna fan. I used to think she can’t sing, but I’m steadily losing that conviction– her voice still isn’t the greatest, but maybe she’s been taking lessons, or I’m being brainwashed by the media saturation.

At any rate, my stanness is not predicated on her singing talents: I still can’t listen to most of her songs unless they’re accompanied by the video (or should I say, unless they accompany a video? ). Mostly, it’s that I’m so damn proud of her; what other international stars do we Barbadians have claim to? The other part is that she is the sexiest high profile female musician I can think of, and she manages to stay on the right side of the thin line between sexy and trashy. A lot of her attractiveness is her incredible body, but her accent adds a final je ne sais quoi.

Actually, I guess I do know why her accent is so attractive: she comes across as laidback and approachable, the Barbadian girl-next-door.

It seems that it’s a good idea to have some knowledge of operator space/ -algebra theory in my research area, so I’ve started reading some books on them. Honestly, I find this stuff boring– it’s only the applications that are interesting… that statement probably makes no sense, but lots of things I say don’t– but alternating my time between reading and doing actual research should make it bearable.

I thought the lyrics said “Bill Cosby”, so the song didn’t really make much sense to me, but now I’ve looked up Bukowski, the lyrics still don’t make sense. It seems like he’s saying life sucks so much it’s hard to believe there’s a God, or that if God exists maybe he’s an asshole, but what’s the bit on evil home stereos and weddings about?

Woke this morning and it seemed to me
That every night turns out to be
A little bit more like Bukowski
And yeah, I know he’s a pretty good read
But God, who’d want to be
God, who’d want to be such an asshole?
God, who’d want to be
God, who’d want to be such an asshole?

Well we sat on the edge of the river
The crowd screamed, “Sacrifice the liver!”
If God takes life, he’s an Indian giver
So tell me now why, you’ll tell me never
Who would want to be
Who would want to be such a control freak?
Well who would want to be
Who would want to be such a control freak?

Well, see what you want to see
You should see it all
Well, take what you want from me
You deserve it all
Nine times out of ten
Our hearts just get dissolved
Well, I want a better place
Or just a better way to fall
But one time out of ten
Everything is perfect for us all
Well, I want a better place
Or just a better way to fall

Here we go
If God controls the land and disease
Keeps a watchful eye on me
If he’s really so damn mighty
My problem is that I can’t see
Well who’d want to be
Who’d want to be such a control freak?
Well who’d want to be
Who would want to be such a control freak?

Evil home stereo
What good songs do you know?
Evil me, oh yeah, I know
What good curves can you throw?

Well, all that icing and all that cake
I can’t make it to your wedding but I’m sure I’ll be at your wake
You were talk, talk, talking in circles that day
When you get to the point make sure that I’m still awake, okay?

Went to bed and didn’t see
Why every day turns out to be
A little bit more like Bukowski
And yeah, I know he’s a pretty good read
But God, who’d want to be
God, who’d want to be such an asshole?