Name: Jason Bucata
Member since: 2002-11-03 05:44:54
Last Login: N/A


I'm the same person as JB318, but I lost the password for that account. I frequently hang out on #debian on as JB318.


Articles Posted by jbucata

Recent blog entries by jbucata

16 Aug 2003 (updated 16 Aug 2003 at 06:36 UTC) »

OK, who's running the betting pool? What odds will you give me that the Great Northeast Blackout was in fact caused by a set of computers controlling key grid points that were running unpatched versions of Microsoft Windows?

If I'm proven right, just remember, you heard it here first :).

... there are good reasons to believe that nonstandard analysis, in some version or other, will be the analysis of the future. Kurt Gödel [1973]

Had a late night last night reading some more on nonstandard analysis, aka deriving calculus from infinitesimals (like Leibniz always intended), instead of from epsilon-delta limits.

My first taste was from the aforementioned Where Mathematics Comes From some months back, so I already knew pretty much what was going on at an intuitive level--now I was wanting some more rigorous meat to flesh it out. (BTW, it was so thought-provoking that, between that and inertia/laziness, I'm probably going to keep it after all.)

I dug these pages up via Google a number of weeks ago but didn't give them more than a passing glance. First I looked at this page and its subpages. The subpage How to make infinitesimals taxed my math minor to its limit (no pun intended).

Actually, it taxed it beyond its limit: I then figured out that I was missing some crucial bit of information by not knowing what it meant when it casually said that the function m() was a measure. So I dug around on Mathworld a while, learning about sigma algebras (and wondering how the completion of a measure by adding subsets of measure zero can be claimed to be another sigma algebra, since there's no evident guarantee that the complements of these newly-added sets are also being added [by virtue of also having measure zero], which is required by its definition) and superstructures, and browsing various related entries in the process. Somewhere in there I also looked at their own nonstandard analysis page.

Armed with that new knowledge and my still-thoroughly-taxed math minor, I went back to the original page and slogged my way through each step, understanding pretty much everything as I went.

Not satiated, I then sailed over to Another View of Nonstandard Analysis for more. It promised to take an easier, more relaxed approach that wouldn't tax my math minor so hard. It was easier to follow, but that may have been because of my (now extensive) prior exposure to the concepts--which was good, so that I didn't have to feel like several hours' worth of reading went down the drain... I managed to prove all the theorems stated as "consequences" of the axioms, except for the ultrafilter one. Though the one about sequences of zeroes and ones mapping to zero or to one took me until my shower this morning to finally see through (hint for those of you trying this at home: In classic Inventor's Paradox fashion, it's easier to prove a stronger result pertaining to such a bit vector and its complement).

One thing it omitted from the axioms in section 2 is the definition of less-than, which I had to borrow from the first section (I managed to prove that that definition is equivalent to the definition used in the first writeup).

Sleep drove me away from the screen before I could fully digest the last section, on transfer principles. I might yet take a crack at it before I log off for the night...

Yikes, been a while. I drifted from the scene for a while there... Got too many other interesting things going on that distract me (is this what's known colloquially as "a life"? ;) ).

As far as Free Software, most of my time is spent either hanging out in IRC (to the extent that counts as a contribution to the cause) or, typically more productively, checking packages for the Debian IPv6 Project. I always go for the packages that either obviously have no network component, or that are likely to not be IPv6-compliant and are likely easy to prove such. I'm not qualified to proclaim something compliant, but it's a lot easier to pick through things like the CPAN module that lets you write Perl programs in Latin, and proclaim them entirely networking-free.

amars, obi: Joe Celko's tree query article is definitely a worthwhile read, but after you've read that go read Trees in SQL: Nested Sets and Materialized Path.

Inundated with interesting diary entries and other pieces to read. Must try to respond briefly to them...

Came across these two pieces from tonight. Wow. The essential, slightly-exaggerated thesis is that most of the modern-day antivirus software industry is a sham. A must-read.

bgeiger: Funny, I saw a Go set at Barnes and Noble (brick & mortar edition) a few weeks ago, in the Games section. I'm quite sure it was less than $30, too.

palsky: Hey, if people don't like 'em, they'll just rate your diary down so they don't have to read 'em. From where I stand, at the moment your diary's rated 7.7, which is pretty good, so I wouldn't be concerned. What you have to say looks pretty topical to me.

Maybe smaller chunks more frequently would help, though. Maybe you could have split the version control commentary off to another diary entry a few days later, for example.

Educational Systems

zhaoway: Wow. Very good article there, and I definitely agree with your assessment. My WACGYR rating for you just went up by one :).

Digging into my bookmarks: An excellent follow-on to that is The Six-Lesson Schoolteacher.

After you've read that second nice, short piece, go peruse through this E-book for an answer on what to do about it: Engines for Education. This one's worth allocating a few hours to read.

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