<?xml version="1.0" encoding="iso-8859-1"?>
<feed version="0.3" xmlns="http://purl.org/atom/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xml:lang="en">
  <title>Frederick Akalin&apos;s Home Page</title>
  <link rel="alternate" type="text/html" href="http://archives.akalin.cx/" />
  <modified>2004-01-14T14:22:24Z</modified>
  <tagline>It looks like you&apos;ve stumbled upon my corner of the Internet.  If you don&apos;t
already know, I&apos;m Frederick Akalin, and I&apos;m currently a coterm student at
Stanford University.
I&apos;m pursuing a B.S. and an M.S. in
computer
science as well as a minor in
music.  Also, my area of concentration for CS is
systems (e.g., operating systems, compilers, databases), for lack of a more interesting sub-area.
If you feel a sudden, pressing need to contact me,
e-mail&apos;s
usually the best way. (I sort of regret making my e-mail address a link, as it
seems the spambots have found my page.  But it&apos;s too late now.) You can also
IM
me as PikaDerf, if you prefer.  And yes, I know it&apos;s strange name.
</tagline>
  <id>tag:,2004:/1</id>
  <generator url="http://www.movabletype.org/" version="2.65">Movable Type</generator>
  <copyright>Copyright (c) 2004, akalin</copyright>
  <entry>
    <title>I finally own my car!</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2004/01/14 - 000040.php" />
    <modified>2004-01-14T14:22:24Z</modified>
    <issued>2004-01-14T06:22:24-08:00</issued>
    <id>tag:,2004:/1.40</id>
    <created>2004-01-14T14:22:24Z</created>
    <summary type="text/plain">I finally got around to getting my car smog checked and going to the DMV to register my car. I&apos;ve already been pulled over once before for having an expired registration, so this will keep the cops off me for...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Personal News</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[I finally got around to getting my car smog checked and going to the DMV to register my car.  I've already been pulled over once before for having an expired registration, so this will keep the cops off me for a while.<BR><BR>
I had to wait two hours at the DMV, though.  I've never quite understood the term "bureaucratic hell" until now; you'd think they'd just give out numbers and call them in increasing order, but nope.  They have this byzantine system of letter/number tickets where seemingly random tickets are assigned to the next window available, with the only discernable pattern being that if ticket x/y is called now, the ticket x/y+1 will be called at some unpredictable point in the future.
<BR><BR>
Ugh.]]>
      
    </content>
  </entry>
  <entry>
    <title>I&apos;m 21!</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2004/01/05 - 000039.php" />
    <modified>2004-01-05T13:47:29Z</modified>
    <issued>2004-01-05T05:47:29-08:00</issued>
    <id>tag:,2004:/1.39</id>
    <created>2004-01-05T13:47:29Z</created>
    <summary type="text/plain">As of almost four hours ago. I am also drunk, from the second celebration of my birthday, the first being two days ago, and the third being this week Friday. Yarrr....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Personal News</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[As of almost four hours ago.  I am also drunk, from the second celebration of my birthday, the first being two days ago, and the third being this week Friday.
<BR><BR>
Yarrr.]]>
      
    </content>
  </entry>
  <entry>
    <title>One thing I&apos;ve learned from watching the movie Contact</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/30 - 000038.php" />
    <modified>2003-12-30T11:55:10Z</modified>
    <issued>2003-12-30T03:55:10-08:00</issued>
    <id>tag:,2003:/1.38</id>
    <created>2003-12-30T11:55:10Z</created>
    <summary type="text/plain">Primer is pronounced prim-er when it refers to a short guide on a topic; however, it&apos;s pronounced prime-er when it refers to a blasting cap. That is all....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Observations</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[Primer is pronounced prim-er when it refers to a short guide on a topic; however, it's pronounced prime-er when it refers to a blasting cap.
<BR><BR>That is all.]]>
      
    </content>
  </entry>
  <entry>
    <title>Public Service Announcement</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/29 - 000037.php" />
    <modified>2003-12-30T05:13:05Z</modified>
    <issued>2003-12-29T21:13:05-08:00</issued>
    <id>tag:,2003:/1.37</id>
    <created>2003-12-30T05:13:05Z</created>
    <summary type="text/plain">Aftershave and pimple cream don&apos;t mix. Ow....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Observations</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      Aftershave and pimple cream don&apos;t mix.  Ow.
      
    </content>
  </entry>
  <entry>
    <title><![CDATA[Evanescence's &quot;My Last Breath&quot;]]></title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/29 - 000036.php" />
    <modified>2003-12-30T03:07:48Z</modified>
    <issued>2003-12-29T19:07:48-08:00</issued>
    <id>tag:,2003:/1.36</id>
    <created>2003-12-30T03:07:48Z</created>
    <summary type="text/plain">Did this song come out as a single yet? If not, it damn well should. It&apos;s easily the best song on the album; I don&apos;t know how I could have missed this the first few times around. Go. Listen to...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Music</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[Did this song come out as a single yet?  If not, it damn well should.  It's easily the best song on the album; I don't know how I could have missed this the first few times around.<BR><BR>
Go.  Listen to it.]]>
      
    </content>
  </entry>
  <entry>
    <title>Icons!</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/29 - 000035.php" />
    <modified>2003-12-29T16:44:30Z</modified>
    <issued>2003-12-29T08:44:30-08:00</issued>
    <id>tag:,2003:/1.35</id>
    <created>2003-12-29T16:44:30Z</created>
    <summary type="text/plain">Shiny pretty icons! My site looks a lot less drab now....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Site News</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      Shiny pretty icons!  My site looks a lot less drab now.
      
    </content>
  </entry>
  <entry>
    <title>Note Hysteria!</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/28 - 000034.php" />
    <modified>2003-12-28T12:16:09Z</modified>
    <issued>2003-12-28T04:16:09-08:00</issued>
    <id>tag:,2003:/1.34</id>
    <created>2003-12-28T12:16:09Z</created>
    <summary type="text/plain">I&apos;ve finally gotten around to putting my CS 248 project up. Enjoy!...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>CS</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[I've finally gotten around to putting my <A HREF="http://cs248.stanford.edu" TITLE="CS 248 - Graphics">CS 248</A> project up.  <A HREF="cs-projects/note-hysteria">Enjoy</A>!]]>
      
    </content>
  </entry>
  <entry>
    <title>Rhapsody progress</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/28 - 000033.php" />
    <modified>2003-12-28T11:45:39Z</modified>
    <issued>2003-12-28T03:45:39-08:00</issued>
    <id>tag:,2003:/1.33</id>
    <created>2003-12-28T11:45:39Z</created>
    <summary type="text/plain">Well, I&apos;ve gotten to the point where I can sight-read my way through the entire set. However, I&apos;m concentrating on the hardest variations, namely the XIth, XVth, and the XXIVth, and so I&apos;ve fleshed out my notes a bit for...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Piano</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[Well, I've gotten to the point where I can sight-read my way through the entire set.  However, I'm concentrating on the hardest variations, namely the XIth, XVth, and the XXIVth, and so I've fleshed out my <A HREF="misc/rach-rhapsody.html" TITLE="Notes on Learning Rachmaninoff's Rhapsody on a Theme of Paganini">notes</A> a bit for those variations.
]]>
      <![CDATA[I'm hoping to get them learned by the end of winter break, but that's a bit optimistic.  However, if I get the XIth, it'll only be a little more effort to get the first movement to playable quality (nothing will be quite performance quality yet).<BR><BR>
Three solid months.  That should be enough time to learn this piece.  However, I've never memorized anything this long before; the closest I've come was memorizing the third movement of Saint-Saen's third piano concerto for my high school orchestra's senior concert, and this piece is at least three times longer.  I've never had any memory problems during recitals, but there was one time where I blanked out on the beginning of Beethoven's first sonata while playing at piano juries and had to ask for the score.  That wasn't too embarassing since I was playing just for the piano faculty but it certainly wasn't pleasant.
<BR><BR>
Oh, well.  Three months.  I should at least know the piece well enough by then to fake the parts that I forget.]]>
    </content>
  </entry>
  <entry>
    <title>Liquid nitrogen burns...</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/27 - 000032.php" />
    <modified>2003-12-27T16:20:20Z</modified>
    <issued>2003-12-27T08:20:20-08:00</issued>
    <id>tag:,2003:/1.32</id>
    <created>2003-12-27T16:20:20Z</created>
    <summary type="text/plain">as I found out today when I went to the dermatologist. But at least I&apos;ll get rid of this persistent wart on my finger, which has been bothering me for months. It looks awful in its current state, though. The...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Personal News</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[as I found out today when I went to the dermatologist.  But at least I'll get rid of this persistent wart on my finger, which has been bothering me for months.<BR><BR>
It looks awful in its current state, though.  The doctor said it'll take at least ten days for the blister to fall off.  I would happily take a picture and show the world, but my camera has a focal length of roughly two miles and no optical zoom.  The <A HREF="http://exilim.casio.com" TITLE="The Exilim">Exilim</A> looks cool and is handy to carry around, but once the novelty wears off, its limitations quickly become annoying.]]>
      
    </content>
  </entry>
  <entry>
    <title>Current known issues and planned improvements</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/26 - 000031.php" />
    <modified>2003-12-26T15:22:43Z</modified>
    <issued>2003-12-26T07:22:43-08:00</issued>
    <id>tag:,2003:/1.31</id>
    <created>2003-12-26T15:22:43Z</created>
    <summary type="text/plain"><![CDATA[Current known issues: Japanese characters in any entry field get converted to &amp#xxxxx; form when put into a textbox or viewed in the entry list. This is more of an annoyance than an issue since I don't plan to write...]]></summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Site News</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[Current known issues:</P>

<UL>
<LI>Japanese characters in any entry field get converted to
&amp#xxxxx; form when put into a textbox or viewed in the entry list.  This is more of an annoyance than an issue since I don't plan to write a lot in Japanese, and they show up fine on the webpage itself.  Hopefully this will get fixed in the next version of <A HREF="http://www.movabletype.com" TITLE="MovableType">MovableType</A>.
</LI>
<LI>The blog administration console is still over an unencrypted connection.  It's protected by Stanford's WebAuth system but that only guarantees that non-Stanford people cannot access it.  It is possible that this vulnerability is exploitable.  I have to bother the IT people about this; hopefully I can get them to enable HTTPS, and then I could hack the code to check against WebAuth.
</LI>
<LI>Blog text inside HTML tags are not checked for characters that should be escaped.</LI>
<LI><STRIKE>That stupid extra slash that gets added when redirecting to cgi scripts.  It annoys the hell out of me.</STRIKE> <FONT COLOR="#ff0000">Fixed!</FONT>
</LI>
</UL>

<P>Planned improvements:</P>

<UL>
<LI><STRIKE>The MovableType icon will be displayed at the bottom of the page.</STRIKE> <FONT COLOR="#ff0000">Done!</FONT></LI>
<LI><STRIKE>The strange black-on-blue header style will be changed to something less ugly.</STRIKE> <FONT COLOR="#ff0000">Done!</FONT></LI>
<LI><STRIKE>More icons will be added, on the navbars as well as for topics.</STRIKE> <FONT COLOR="#ff0000">Done!</FONT></LI>
<LI>Icons for individual navbar entries will be added.</LI>
<LI>Syndication will be implemented.</LI>
<LI>More information will be added on the blog toolbar.</LI>
<LI><STRIKE>Tooltips for the links on the calendar.</STRIKE> <FONT COLOR="#ff0000">Done!</FONT></LI>
<LI>The web page title will consistently show up in the title bar.</LI>
<LI>An arrow will be added to show/hide the extended entry field of an entry, a la <A HREF="http://kuro5hin.org" TITLE="kuro5hin">kuro5hin</A>'s dynamic threaded view mode.</LI>
<LI>Comments and other nifty blog features will be enabled.</LI>
<LI>The archive templates will get cleaned up.</LI>
<LI>The image pages will be automated.  Then I can finally get around to putting my Japan pics up.</LI>
<LI>Make the calendar more useful.</LI>
<LI>Make the "Recent entries" navbar more useful.</LI>
<LI>Make the "Archives" navbar expandable.</LI>
</UL>]]>
      
    </content>
  </entry>
  <entry>
    <title>Surprisingly good music...</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/26 - 000030.php" />
    <modified>2003-12-26T15:14:10Z</modified>
    <issued>2003-12-26T07:14:10-08:00</issued>
    <id>tag:,2003:/1.30</id>
    <created>2003-12-26T15:14:10Z</created>
    <summary type="text/plain">Evanescence is. Over half of their album I gave three starts or more in iTunes, and it even managed to draw me away from my J-pop for a while. Granted, the lyrics are a bit angsty to take seriously. (Highlights...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Music</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[<A HREF="http://www.evanescence.com" TITLE="Evanescence">Evanescence</A> is.  Over half of their album I gave three starts or more in <A HREF="http://www.apple.com/itunes" TITLE="iTunes">iTunes</A>, and it even managed to draw me away from my J-pop for a while.
<BR><BR>
Granted, the lyrics are a bit angsty to take seriously.  (Highlights include someone screaming "I want to die!")  But the vocalist's voice harmonizes very well and the heavy guitars are a change from the oft sugary accompaniments of J-pop songs.]]>
      
    </content>
  </entry>
  <entry>
    <title>Adventures in OS land</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/25 - 000029.php" />
    <modified>2003-12-26T02:52:57Z</modified>
    <issued>2003-12-25T18:52:57-08:00</issued>
    <id>tag:,2003:/1.29</id>
    <created>2003-12-26T02:52:57Z</created>
    <summary type="text/plain">So I finally got a basic kernel to work in my highly irregular Cygwin environment....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>CS</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[So I finally got a basic kernel to work in my highly irregular <A HREF="http://www.cygwin.org" TITLE="Cygwin">Cygwin</A> environment.]]>
      <![CDATA[However, there are still some problems.  Here is how the process goes:
</P>
<OL>
<LI>Make a <A HREF="http://www.gnu.org/software/grub/" TITLE="Grand Unified Boot Loader">GRUB</A> boot image from the stage1 and stage2 files.  Currently, I just cat them together and boot from that.  It was a pain in the ass as I spent a lot of time trying to figure out how to get GRUB to compile under Cygwin and finally just downloaded the images from one of Stanford's Linux boxes.  It is still a bit annoying, since I have to manually point to where my kernel is when I boot up; I'll have to figure out how to get a grub.cfg into the image.</LI>
<LI>Compile the kernel loader code (which is in assembler) with NASM.  You have to compile it in Windows' PE format.</LI>
<LI>Compile the kernel code (which is in C++) with the appropriate switches to turn off runtime type information and the standard library.</LI>
<LI>Link all the files together in Windows' PE format.  Currently I get a warning that the entry point could not be found and that a default should be used, even though I do define the entry point.  I'll have to look at that one, too.  Also, g++ mangles function names differently from gcc, so instead of calling _main from the kernel loader code I have to call __Z6k_mainv.  Needless to say, it is probably not a good idea to hardcode this.  I suppose I could use objdump to modify the kernel loader on the fly...</LI>
<LI>Convert the PE file into ELF using objcopy.</LI>
<LI>Write the kernel ELF image to a floppy image using <A HREF="http://www.winimage.com" TITLE="WinImage">WinImage</A>.  This is problematic because WinImage has very little command line control, and so I have to manually type in the image filename every time.  I'm still looking for a more command line-friendly program, which would probably help with the grub boot image, too.</LI>
<LI>Finally, load <A HREF="http://bochs.sf.net" TITLE="Bochs">Bochs</A> with the boot and the kernel image as the first and second floppy drive image, respectively.  Marvel as the words "Hello World" are displayed on the screen.</LI>
</OL>
<P>
Also, there's the added caveat that debugging the kernel will be quite difficult.  I wonder if Bochs has debugging capabilities.  Hmm.
<BR><BR>
In any case, once I get these snags worked out, this is going to be sweet.  This is what <A HREF="http://cs140.stanford.edu" TITLE="CS 140 -- Operating Systems">CS 140</A> should have been; not that lame <A HREF="http://www.cs.washington.edu/homes/tom/nachos/" TITLE="NachOS">NachOS</A> stuff.]]>
    </content>
  </entry>
  <entry>
    <title>Stanford Concerto Competition</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/23 - 000028.php" />
    <modified>2003-12-23T15:22:27Z</modified>
    <issued>2003-12-23T07:22:27-08:00</issued>
    <id>tag:,2003:/1.28</id>
    <created>2003-12-23T15:22:27Z</created>
    <summary type="text/plain">Yep, I&apos;m planning to enter that, which will take place around the beginning of April. I will be playing Rachmaninoff&apos;s Rhapsody on a Theme of Paganini, of which the XVIIIth variation, incidentally, has been popularized by the movie Somewhere in...</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Piano</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[Yep, I'm planning to enter that, which will take place around the beginning of April.  I will be playing Rachmaninoff's Rhapsody on a Theme of Paganini, of which the XVIIIth variation, incidentally, has been popularized by the movie <A HREF="http://www.imdb.com/title/tt0081534/" TITLE="Somewhere in Time">Somewhere in Time</A>, and thus you probably know it, even if the name doesn't ring a bell.<BR><BR>
I actually thought it was the easiest of Rachmaninoff's piano concerti, but I've searched for information online and it turns out some people consider it to be the hardest.  Having dabbled in both the second and third Rachmaninoff piano concerti, I'll have to stick with my opinion, though.  If it is indeed the hardest, at least it gradually builds up to the technically challenging parts, instead of beating you over the head with it two pages in (the third) or scaring you off with big scary chords in the beginning (the second).<BR><BR>
Of course, claiming it's the easiest concerto isn't saying much, since this is Rachmaninoff we're talking about here.  Some of the variations, especially toward the end of the piece, make me doubt if I can get it ready in four months.  Some of the highlights include:
</P>
<UL>
<LI>At least three cadenzas or cadenza-like passages that I can remember.</LI>
<LI>The XVIIIth variation which I <B>have</B> to know like the back of my hand, since it's the climax of the piece, and the most well-known part, to boot.</LI>
<LI>The last (XXIVth) variation, which is almost Scriabin-like in its chromaticism.</LI>
<LI>The orchestra tacet near the middle of the piece (the XVth variation) which might as well be a cadenza because of its sheer virtuosic demands.</LI>
</UL>
<P>
But it's a fun piece.  I'm entering the competition more to spur myself to learn it rather than any real desire to win it (although that would be sweet).  Also, I've jotted down some <A HREF="misc/rach-rhapsody.html" TITLE="Notes on Learning Rachmaninoff's Rhapsody on a Theme of Paganini">notes</A>.]]>
      
    </content>
  </entry>
  <entry>
    <title>The job search co...d&apos;oh!</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/18 - 000027.php" />
    <modified>2003-12-18T22:48:08Z</modified>
    <issued>2003-12-18T14:48:08-08:00</issued>
    <id>tag:,2003:/1.27</id>
    <created>2003-12-18T22:48:08Z</created>
    <summary type="text/plain">Looks like I spoke too soon! I didn&apos;t move on to second round interviews for Cerner. I guess they just wanted to tell me that personally. Oh, well. The prospect of working in Kansas City was a little strange, anyway....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Personal News</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      <![CDATA[Looks like I spoke too soon!  I didn't move on to second round interviews for Cerner.  I guess they just wanted to tell me that personally.  Oh, well.  The prospect of working in Kansas City was a little strange, anyway.
<BR><BR>
Also, I finally officially switched my music major to a music minor.  Sad.
<BR><BR>
Oh, and my resum&#233; got updated.  It gets harder and harder every quarter to keep it under one page.  Urgh.]]>
      
    </content>
  </entry>
  <entry>
    <title>Current mathematical interests</title>
    <link rel="alternate" type="text/html" href="http://archives.akalin.cx/archives/2003/12/16 - 000026.php" />
    <modified>2003-12-16T15:17:47Z</modified>
    <issued>2003-12-16T07:17:47-08:00</issued>
    <id>tag:,2003:/1.26</id>
    <created>2003-12-16T15:17:47Z</created>
    <summary type="text/plain">Infinitesimal analysis. Non-standard analysis. Category theory....</summary>
    <author>
      <name>akalin</name>
      
      
    </author>
    <dc:subject>Mathematics</dc:subject>
    <content type="text/html" mode="escaped" xml:lang="en" xml:base="http://archives.akalin.cx/">
      Infinitesimal analysis.  Non-standard analysis.  Category theory.
      <![CDATA[Infinitesimal analysis and non-standard analysis both deal with reintroducing the concepts of infinitesimals to calculus.  However, the former does so with non-zero nil-square numbers, whereas the latter does so with reciprocals of infinitely large numbers.  It's cool and all, but it doesn't seem as flexible as the limit concept, especially since in my infinitesimal analysis primer only smooth functions (infinitely differentiable functions) were considered.
<BR><BR>
Category theory is a relatively new mathematical development; it has been fondly referred to as "abstract mumbo-jumbo."  Basically, it abstracts almost everything out of mathematics--even more so than set theory.  All you have to work with are objects and composable maps.  It's been put forth as a possible replacement for set theory as a basis for all of mathematics, although not without opposition, which is why I'm interested in it.  It also has connections to computer science via lambda calculus and type theory; I'm still a bit hazy about it since I've just ordered a primer from <A HREF="http://www.amazon.com" TITLE="Amazon.com">Amazon.com</A>.  Hopefully I'll understand more of it when I start reading up on it.]]>
    </content>
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