Thursday, March 31, 2005

Another Day, Another Writing Exercise
The "Ants go Marching" song no longer haunts me - I took the chance. :-) Dunno how I did, though. I was 'me', so I hope I caught it.

New writing exercise: action. In this writing exercise, to keep the "Watcher at the Gates" at bay this time, I give myself permission to use cliché and stupid plots.

A 'prologue' cutscene from the mindset of a James-Bond/Indiana Jones-type.

"My story? You ... want to know how it's going? You'd think people would appreciate good deeds these days. I've masked my face and body in earthtones ... yeah, like playin' make-up. I've taken numerous vaccines and now look like a fuckin' druggie with so many red dots on my arms ... I've continually trained for hours on end, and studied a language and society I'd never heard of just two months ago! I've been given the 'Gentleman's handbooks' on Survival, Emergency, and 'Suicide made Easy'. I've been given just enough resources to enter this god-forsaken country unnoticed, reach my contacts, make my way among sixty-fuckin'-thousand people, through seven god-forsaken rocks of green and black separated by waters infested with creatures that can swim up your dick and lay eggs, so I can can reach the main island and capitol city, to baby-sit a crazed madman - a dictator and sicko of the highest order, and then wait ... not one week, not two weeks, but a month! JUST so that in his greatest moment of triumph over the world ( and no sooner) I get to ... open his mind ... not by much, mind you, but I have it on good authority that 22 millimeters will do wonders for a nasty disposition! Generous as I am, with my "free your mind" attitude, I then expanded the minds of his generals, commanders, and puppeteers, too! Their minds were expanded all over that bastard's palace.

Really.

So, do I get a parade? Do I get flowers?   No.

I want me a drink, and 60,000 people want me dead. Go figure.

How's that for justice? It might've had something to do with their belief of his relation to some god, but that's a story for another day ...

So, you know - I just killed the religious figurehead of sixty-thousand men, women, and children. Sixty-thousand. I could tell you "how it's going," but more interesting would be how I got out of this god-forsaken mess. And you know, Davids, that's a story you'll never hear UNLESS YOU GET OFF YOUR ASS AND GET OVER HERE! WHERE'S MY FUCKING TRANSPORT OFF THIS ROCK?! YOU THINK I CAN ENJOY THE ATMOSPHERE WHEN I LEFT BREADCRUMBS FOR THOUSANDS OF MURDEROUS HANZELS AND GRETTELS ?!     I SAID A.M. ! A.M. ! I HAD YOU REPEAT THE DAMN LETTERS! I'M OFF RISKING MY LIFE AND I'VE GOT A FUCKING ADHD POSTERCHILD AS MY LIFELINE?! WHERE'S THE JUSTICE?!"



Hmm, well that turned out well. How about the rest of the story? Let's do that from a different perspective! Whose? Take a wild guess!


... At that point, I turned off my radio. I could see that Agent '0055 was having his little prissy-fit, and I'd be damned if I was about to let him get the upper-hand and boss me around! No, sir. It was all his fault, of course - he knows those 12-hour clocks confuse me. And besides, his use of the Lord's name in vain was simply out of line. After that, I calmly ate my lunch, sauntered to my spiffy noise-cancelling hydrojet, left the naval base at 14:00h, saved him from certain doom at 18:00h, and we got back just in time to watch his favorite episode of "The Family Guy." I'd like to think he mellowed out somewhat after that. It's all about showing these bullies at work who's boss.

Wednesday, March 30, 2005

Unnecessary Trepidation

Life, happiness, pain, and suffering have ever been relative. As you may imagine, this translates quite naturally to the world of writing as well, with often humorous results. Topics relative to one person often end up meaningless to another, and points of elaboration cannot be trivially chosen. If you intend to take care in your writing, you may wish to analyze the positioning of your imagery, your drama, and your humor. For my narrative today, I give two perspectives of a classroom incident: one of simplicity, and another of high-quality verbose elaboration, which in my opinion can be considered a waste in time, energy, and semi-decent writing that could've been focused elsewhere. In other words, I think it's bs. And dangerous bs. A lot of masters created beautiful works on meaningless drivel this way, but many were also able to salvage it for more appropriate use.

True, it was an amazingly fun writing exercise in melodrama, and I heartily recommend it to you all,
so long as you clearly declare its purpose.


But overall, it is a warning: choose the emotional focal points of your scenes wisely.


#1: I got an 'A' on my Math 445 midterm!!!.

#2:
The summary below details a topic whose workload assisted me in nearly destroying my grades in other classes last year and this year.


      Today, in Cryptography, Professor Klaus Lux handed out our midterm results.

      Last year, in the same class (different teacher), this evil midterm mocked me with topics I could not comprehend, and cunningly convinced me to switch to audit while it taunted me, and told me to retreat while I had the chance.
      Now, one year later, I thank my lucky stars that I did retreat. But in that agonizingly long year, I was not idle; I eagerly plotted my triumphant revenge upon that midterm, and awaited the chance to carry out this deed of daring!

      This year, I stuck with the class, knowing I would be unable to change status by the time the midterm (the first test!) came around. It would be all or nothing! I knew my other classes would be in danger, but I felt ready for the challenge. I suffered through the classwork. I worked hard. My other classes faded to insignificance under the growing mountain of torcherous, mazelike terrain defined by the course material (Except the physics 182 lab course. GOD I LOVE that class! All jokes aside, I really do.) After armoring myself with abstract algebra and the foundation axioms of mathematics, I called Fermat, Euler, and Gauss to my right side, and countless mathmematicians from Ancient China who passed on the secret of the Chinese Remainder Theorem to my left! That fateful day, one week ago to the day, we waged war upon that midterm! Pencil versus paper, tooth and nail, graphite and erasor, I gave my all. In the end, there was no clear victor: the battle was over, but the waiting had just begun.

      For an agonizing week I did my best to bide time and relax. I gathered my energies, prayed, and caught up with all my other homework for the first time. (Thanks to an appreciated absence of math homework due this week. As a result, I'm about to finish all my extra physics textbook work for the rest of the semester!) I was approaching full circle and waited to cross the threshold past the landmark of my humiliating retreat last year.

      Before ending class today, Professor Lux took out the box of graded tests, searching through them as if checking each little monster was safely-restrained. - I easily identified mine on top due to the colored paper (This is why I use yellow legal pads to write my homework: it's easy to identify in a stack). To my horror, he then mentioned something about geography and briefly muttered my name under his breath. With a flourish, he tucked my midterm neatly away, imprisoned underneath his arm. He began calling out for students to pick up their tests.

      Name, after agonizing name, each student was called to claim an exam. And they did. They returned to their desks, packed their bags, and left.
One student remained uncalled.

      My test, I silently screamed. What about my test?!


      I knew I left out the final step in the fourth problem: across the battlefield, Fermat shouted ample warning to me, but I didn't understand until it was too late.

      I knew I was in over my head at the fifth problem: Euler had abandoned me far earlier, believing his services were required elsewhere.

      I began to worry if I had missed something even more dangerous; some final trick that the midterm had deviously crafted just for this occaision.

      Instantly, I recalled the incident at the testing center - it flooded my thoughts with volumetric depth and taunting clarity: I exceeded my time limit, and was compelled by policy (and the helpful staff members at the testing center) to sign suspiciously 'legalese'-styled paperwork explaining my predicament. Sure, they attempted to sooth my fears. Sure, they told me that this tradegy occurs often - so often they couldn't even count... they sympathized, they explained that only the hardest of hardass teachers would attack the grade resultant of a student's extended testing time.

      As it turned out, I was ... inconsolable. (Blatant "Kill Bill Volume #2" reference. Watch Kill Bill ! Great pair of movies right there!)

      I wondered if the score was zero. I wondered whether my score was simply so bad he didn't want anyone to see it, and would talk to me about it after class. Maybe it was just an accident, he forgot to hand it to me... And maybe not.

      After most of the other students left, save my fellow kinsmen of the classroom, I walked up to the teacher and asked about my test.
      He looked up at me, startled. "Oh, right! Sorry, you were at the far side of the room, and I had thought to hand it to you after calling someone closer ..." He began shuffling through the much smaller stack of papers.
      With a smile and a quick exhalation that bordered upon hyperventilating, I huffed, "No worries."
      He pulled my test out of the small pile of bloodthirsty, papercutting beasts, and handed it to me, folded so the score wouldn't be visible to others, and resumed packing his lecture materials.

      I accepted the paper thankfully, and found it inanimate in my hand - no papercut, no surface marks save the scars of grey and black where my pencil had struck. I unfolded it to reveal a mysterious set of symbols: the capital greek letter Sigma (summation symbol) followed by '103P' in fine red ink.

      Spontaneously, Professor Lux pointed to the extra-credit problem on the bottom of the first page, where he had encased some of my text in red parentheses and chuckled, "Well I had to give you some credit for this one, eh?"

      I hesitated. "Um, this ... what ... this can't ... does this mean," I rambled, as I usually do if I lose focus on my thoughts. Intuitively, I felt I knew what the symbols meant, but the still-skeptical symbol-reader in me needed full clarification before any emotions could safely dance across my face.
      He turned to me in contemplation, maybe with a raised eyebrow or maybe just a grimace, as though I were a grossly-incorrect math statement. Then he smiled at me. Grinning, he read the digits back to me, "Well, this is a one, this is a zero, and this is a three!"

      My score: one hundred and three. Out of one hundred.


Houston, we are "go" for launch.


[/end hilarious writing exercise]

Monday, March 28, 2005

On Meaningless Matters...
You'd think there were some things so easy to understand that anyone could apply them. If you're actually right, then optimism is not one of those things.
There's finding a bright side to anything, and then there's categorizing people and things into good or bad, regardless of intentions or results, simply so that these "optimists" can ignore the 'bad' stuff.

The latter also show up often as loudmouths, people who cut you off because they 'already knew what you were going to say', those afraid of trying out new things because somehow they've managed to connect it with tempting the devil with their soul... yes, even people like that still exist.

Everything from Modern Medicine to Multimedia comes with a balance: you can choose to ignore them, to try and get the most from them, or to simply investigate for yourself - and if you do research, I commend you, but be careful: there are always multiple angles to any story, no matter what your research tells you.

Do come to me with your opinions. I love opinions. Don't come to me with idiocy. I hate idiocy, and I hate loudmouths. I will respect your views. I won't bite, but if you're going give me your opinion, then tell me it's your opinion.

Whoever you are, wherever you are, strike up a chat with me if you wish.
I will be brutally, but faithfully honest, from now on.

Sunday, March 27, 2005

It'd be nice to socialize with those of different ideas, opinions, cultures, and gender. How and why am I chained to geekdom ?

My graduation plan. No jokes, please.
----------------
Fall '05: CS 440 & 453 (AI & Compilers)
Spri '06: CS 433 & 452 (Graphics & Operating Systems)
Fall '06: CS 460 (Databases)


Dave Matthews' Band song "Ants Marching" is stuck in my head, and the lyrics attack me with relevance that the composer never intended. So many interesting people and personalities, so many chances, and such little notice; so many destinations with the wrong directions; so many free-rides, often going the wrong way.

I just think things should work properly.
Like Mr Dyson.

Saturday, March 26, 2005

On Preventing the Re-Invention of the Wheel:
Thoughts on Object-Oriented Programming.

Abstract: Alan Turing described us humans as Universal Turing Machines since we can simulate all other Turing Machines using just pen, paper, and some time ... Thus we are at the top of the top of computational models, and we can show that the UTM can extend its own boundaries beyond that of standard Turing Machines. Intellectually, we don't fully understand what our limits are because the possibilities are extended by advancements in science. I think there's a way to turn that boundary into a variable by treating concepts as hypothetical machines (For instance, a conjecture that relies on an unsolved problem), where we can flesh them out and see what we would need to do to make these machines real.

----
A whole lot of people have studied and created machines more powerful than standard Turing machines. Even Alan Turing himself gave examples, and there's already a large body of field-work on the subject. My goal isn't exactly the same idea although it does coincide often:

Purpose: provide and refine a simple, elegant structure that extends the application of Computability Theory ( and 'Hypercomputation' ) to Abstraction Theory, using 'concepts', conjectures, and proofs in a useful fashion (which often gives highly mnemonic and re-usable results). This structure can thus be restated as: a practical system to measure, refine, approximate, derive, and classify hypothetical/ abstract/ imaginary concepts and algorithms into facts and objects.

Current background reading:
Theory of Mathematical Evidence, Computability Theory, 'Hypercomputation', Abstraction Theory, (soon)Artificial Intelligence, and most importantly, yet surprisingly, Object-Oriented Programming - this is the basic idea, I suppose.

Eventually, although it may need 'refinement' and many exceptions, I want to be able to apply abstract algebra (groups, fields, polynomials) to any given concept. (Side note: it really hurt my brain just to type that last sentence in.)

You can even use this towards refining completely paradoxical and silly ideas into something that actually gives astonishing truth-statements and properties about such trivial ideas.

I will formalize two versions: a version that allows full application of Computability Theory, and a version that's quick and easy to use in a less mathematically-sound fashion.


At last, the Punchline! The joke is that the quick and easy version of this system is object-oriented programming! It's a paradigm many programmers have been working with for the past thirty-six years! Ha ! To use these tools, we simply need to program in our favorite object-oriented programming language or pseudocode - but from then on, it gets tricky: The second half is actually the study of Compilers (& Turing-Completeness), Abstraction, Discrete Mathematics, Mathematical Evidence ... the list goes on, and we must also ensure that we use standard operators and define them using the axioms of mathematics as a guide. In short, we must utilize Computer Science.

This is why I'm a programmer.
And it's also why I love C++ and SML ;-)

Friday, March 25, 2005

I'll lead a "real" life when my school gives me a bit more of the "real" time it steals from me ;-)

In the meantime, while I commute to and fro opposite corners of town, I'll continue to study and make weird, unprovable conjectures on the side.

In fact, after some time, I've reformulated my thoughts on the possibility of machines beyond Turing ...
let's call them Transcendental Machines with the following properties:

1.) A Transcendental Machine (TDM) (if it exists) recognizes/decides all languages recognizeable/decidable by Turing Machines, (regular languages, context-free languages, Turing-recognizable languages) and at least one or more non-Turing-decidable/recognizable..

2.) While TDMs can recognize and simulate Turing Machines (TM), The opposite is not necessarily true. As far as modern Theory of Computation is concerned (and as far as it should be concerned, realistically), the Turing Machine is the most versatile model of computation. But ironically, if TDMs do exist, then Turing Machines (and thus humans) may not be able to direcly detect them ... or even prove their existence as a certainty within Turing-recognizable rules).

3.)Due to the fact that I'm exploring these possibilities, I'm forced to accept the possibility that a Turing Machine can still indirectly describe higher-level machines, and that given the proper resources, perhaps a Turing Machine could even simulate a TDM.

4.) There may be even more higher-level supersets of machines than TDMs: These would be considered TDMs of Order 2, Order 3, etc - but there is a catch: while such a conjecture is easily plausible, the main problem with TDMs is that the set would hold rather large subclasses of various machines that recognize/decide wildly varying sets of Turing-unrecognizable/undecidable languages, each unioned with all Turing-recognizable/decidable languages. In such a case, ordering of sets would by necessity, also make sense on a per-subset basis, although some TDM classes might even be uncountably infinite.

In general, let us temporarily assume there exists a being/machine (who can do what we can't, essentially) who can determine the existence of integer roots from a multi-variable polynomial in the set of real numbers, given a finite time limit (preferably a short one) - then we have an example of a transcendental machine.

Regarding giving such an unwieldly name to these machines, I feel justified due to the definition(until someone gives a better name :-D after all, these machines may already have a name), since the term "transcendental" has also been given to a specific set of irrational numbers such as pi. The preliminary name was "Chaos Machine" but such a name conveys the scientific notion of a Chaotic system as described by Chaos Theory, which can be recognized by Turing Machines.

Tuesday, March 22, 2005

I just thought of something rather interesting regarding Turing machines and God :
well, actually, I've been thinking about it for a long time, and have some interesting facts for you all regarding the Universe from a computational standpoint.

But first:

1. The question of whether or not God exists is not Turing-solvable ... i.e. we cannot truly prove or disprove God's existence from a scientific perspective. Ever.

2. Regardless, We can still conjecture certain properties of God and/or the Universe based on either of the two assumptions of God's existence.

3. In fact, I have many such conjectures; the majority of which I shall release at togehter (at a later date), and continue to add on incrementally, but not now. For now, I leave this interesting tidbit:

Read the note if you're either unsure of what a Turing Machine is, or if you believe the human brain is not a Turing Machine. Otherwise, skip down to the good stuff.

Quick note before I begin: I must aid setting the record straight: Turing Machines are NOT machines per se - they are computational models. They are just descriptions of one particular class of computational measurement, and in fact, they are at the very top of the heirarchy in regards to computational power -- the most beautiful and spectacular model of which is the human being.
In other words, to suggest a human is not a Turing Machine is actually ludicrous and self-insulting, since a Turing Machine (TM) is considered a TM if and only if it can simulate the operation of any other full TM or TM code (where the "code" is an algorithm ... what's an algorithm? A cooking recipe is a perfect example, as are directions to get from one place to another, any set of instructions, or list of daily chores, etc.)
In short, the classification of the Turing Machine in the mathematical sense is obviously broad: we sometimes lose sight of the usefulness unless we confine our related discussions to specific sub-classes. This lays the foundation for the ideas organized below. You should now at least have a basic understanding of Turing Machines. (If not, just google-search for Turing Machines)


Now we may begin:

We have two possibilites: God(and/or similar being(s)) exists, or God does not. We shall explore the ramifications of both possibilites. Let us start by assuming that the first possibility is true:

If God exists, then regardless of the fact that God's existence cannot be verified or refuted, our standard definition of God easily fits the computational model of a Turing Machine. At the same time, God would then contain an extension to the standard model that allows recognition of all possible Turing Machines. (Most likely something even more exotic than the Quantum Turing Machine) What's more, it's easily possible that God's processing scope extends far beyond that of a Turing Machine, for it's obvious that if God were a standard model, then God could not conceivably create a contradictory event such as an attempt to lift a rock that was created specifically to be unliftable by God.

But then, if God is not Turing-recognizeable as we assume from our standard description of God (since the mind of man might not be fit to understand the wisdom of God), then not only would there exist other computational models of "higher order" that encompass and extend the model of a Turing Machine, but simply by the nature of a Turing Machine, none of these models of computation could be directly/ completely understood, detected, or simulated by any normal Turing Machine, and thus they are all infathomable (!but not completely!) by mankind ! (And actually, to some extent, the topic of how much (if any) must a person know about an object before they can consider themselves able to simulate its output is arguable (yet unsolvable, once again, as-predicted)

This description of our Deity-in-question does allow such a process as parodoxical actions to occur: the reasoning here is that God and/or similar beings who also may or may not believe in/ know for sure / question the belief of God made the underlying framework of our reality. Our notions of computation and Turing Machines is based on our perceptions of the environment in which we interact. Thus, if logical structures exist beyond these perceptions, we may not be able to directly perceive them. If you feel so inclined, this can be considered a nonscientific generalization of Heisenberg's Uncertainty Principle.

More will come later.

I've already taken away too much time from my studies.

Good night.
At last ! I have found the mathematician's Amazon.com !
MAA online ! Go there !

Whew ... long time, no post. I have two midterms in two days (yes, they're a few weeks late - why don't you go and tell that to my professors? I'm sure they'll listen with open ears ;-P )

After sharing horror stories about evil past-professors (Fall registration is near), some fellow students and I derived the following academic life lesson:
"Some people should not be teachers, and some teachers should not be people" :-)