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Lindsey Kuper

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"So, you want more pain?" [Feb. 19th, 2004|12:32 am]
Lindsey Kuper
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Whew. Today was the first day that I didn't get the Automata homework done. It wasn't for lack of trying. We had to do a couple of proofs, and I got one done, but the other's really a beast. I feel bad about breaking my streak of turning stuff in, but this is, what, the fifth week of classes already? or something like that, and I've gotta cut myself some slack. I still went to class and went to talk to the prof, so I'm okay for now.

Then there's piano. I'm taking lessons from the same person who taught my jazz arranging course last semester, which was the first time I had done jazz piano. When I went in for my first lesson, he said, "So, you want more pain?" I responded with a rather too enthusiastic "YES!" It's true -- trying to commit all these difficult progressions to brain memory and finger memory is painful -- but I know where I'm going. Eventually, I'll be able to look at a chart and play complicated chords in any number of different voicings, combining them in a way that's smooth and musical. It hurts so nice.

I've started the fourth week of running. When I run more than three miles, I take a short walking break at the three-mile point(s), but I had a kind of exciting moment during my five-miler on Sunday when I started to slow down to a walk at the three-mile point, but my legs just sort of refused to slow down, and they just kept going as if I wasn't in control of them anymore. In fact, I sped up! I took a walking break later, at about the four-mile point, but still, it was cool.

Running has been good for my self-esteem. In fact, I think that it's had a bigger effect on me mentally and emotionally than physically. I'd be more likely to recommend it to someone for their mental and emotional health than for their physical health, since, in some ways, running this much is actually bad for your physical health. I mean, my feet are kinda blistered and my legs are kinda sore, and besides, if someone wants to get in shape, there seem to be more effective ways of doing it than this (see earlier posts re: not looking or weighing any different). But I feel good.


[User Picture]From: underwhelm
2004-02-18 11:18 pm (UTC)
I'm interested to hear some of the products of all this learning.
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[User Picture]From: lindseykuper
2004-02-19 07:09 am (UTC)


Sure! Suppose to the contrary that the palindrome language on {a, b}* is regular, and let p be the pumping length given by by the pumping lemma. Let the string s = a^pba^p. Because s is a member of L and has length more than p, the pumping lemma guarantees that s can be split into three pieces, s = xyz, satisfying the conditions of the lemma. The second and third conditions state, respectively, that |y| > 0 and |xy| <= p. Thus, y must consist of one or more as from the initial substring a^p of s, and z must end with the substring ba^p of s. Under these conditions, no string xyyz in L can exist, since...

Oh. Right. Yeah, soon, when I start sucking less.
(Reply) (Parent) (Thread)
From: (Anonymous)
2004-02-19 06:54 pm (UTC)


Whoa, that takes me back. Go go Pumping Lemma!

-- Will
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[User Picture]From: lindseykuper
2004-02-20 08:03 am (UTC)



And now we're on the pumping lemma for context-free languages! s = uvxyz, baby!
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