Tuesday, December 1, 2009
Life as Decision(-making)
Saturday, October 17, 2009
Steward or Sorcerer's Apprentice?
Saturday, October 10, 2009
The Purpose of Mathematics Education?
But after reading this: http://www.channelnewsasia.com/stories/singaporelocalnews/view/1010464/1/.html , it made me--out of the spirit of (mathematical) objectivity motivated even by a greater curiosity--to imagine what is mathematics education.
After reading this story in an objective spirit, I state what mathematics education is NOT:
(1) Mathematics education is not coming home from an exam, albeit an important one, and gesturing to your mom that your throat has recently been slit.
(2) Mathematics education is not coming home from an exam, albeit an important one, and getting very emotional before crying your heart out while trying to tell your mom amid tears and mucus that your hopes of an A* (i.e., read A-Star: the equivalent of a North American A+. For the simple at heart, it means either a perfect grade or somewhere a iota south of that--one can go no further academically or intellectually, which are of course, untrue) are dashed.
(3) Mathematics education is not about using a calculator, so that 'computational errors can be reduced'. If that were the case, the rocket that NASA just crashed on the Moon would have created a bigger plume of ash. As a matter of fact, use of calculators under examination pressures tends to entail 'errors of dexterity'. This means for a simple calculator, instead of keying in '8', you either key in '7', '5' or '9'--or all four at once.
(4) Mathematics education is not about big numbers so that inadvertently, you need the assistance of a calculator; which truly for the initiated, an abacus would have been much more efficient for elementary mathematics.
(5) Thus clearly, mathematics education at least for this level is not about calculations requiring calculators at all, unless of course, calculators are nice bling for examinations but we know that bling has nothing to do with math. QED on calculators.
(6) Mathematics education is not about 'breaking down in tears right after the exam'. As far as I know there are two kinds of tears associated with math. One, when you discover something like the incomplete theorem before you lose your mind; and two, when you win the Fields Medal for it. Or by an act of mathematical randomness, you win a Nobel Peace Prize for applying the incomplete theorem, which has happened by induction at least once in human history.
(7) And mathematics education is not about this kind of question:
"Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?"
Why? (we should truly ask more 'why' questions for mathematics education).
It took my unpracticed hand and mind nervously scrawling on two pieces of paper before I finally worked out the answer. Honestly, I would have done no better than the average kid on this type of questions. In fact, I would have flung if you locked me in the room with them and gave me the same time as everyone else.
But in solving this problem, I revisited how to do mathematical sums long-hand (without a calculator); remembered how to call concrete things X and Y again; relearned how to perform elementary functions with ratios and fractions; once again toyed with simultaneous equations; discovering where I made errors (yes, I was working backwards from the answer after a few 'computational' errors: the advantage of adulthood) and in it all, remembered that mathematics should be less frustrating and more fun, which concisely just summed up about all Polya said on this subject.
But this question--if this was in fact a representative of all questions for Paper 2 in the PSLE this year--sums up just about everything that is frustrating and obnoxious in mathematics education.
First, a mathematics word-question and its heuristics should aid in clarification and not in exacerbating confusion. About two minutes into re-reading and expressing the algebraic relationships to this question, I forgot who was Jim and what Ken bought. Perhaps a 12 year old brain has greater clarity. Nonetheless, in about another two minutes down this same track, I had forgotten who bought chocolates and who bought sweets. The 50-50 heuristic created by the question designer--doubtlessly trying to make things easy for that poor student--ended up mirroring and hence, worsening the identity problem in this math problem.
Second, a mathematical problem should never constrain possible solutions through the phrasing (or design) of the word problem itself. The problem asked, "How many sweets did Ken buy?". Why, I am also interested in finding out how many pieces of chocolates Jim bought! Because if I do so (which I did but more later), I can by that route find out how many sweets Ken bought using the same mathematical concepts and methods. As a matter of mathematical principle, there is no priority attached to either Ken's or Jim's purchase. So why prejudiced the math question from the angle of Ken? Clearly, the question-designer has not consulted some of the important literatures pertaining to psychological bias in the way we asked questions.
Third, if I did go by Jim's route, guess how many pieces of chocolates Jim bought? 308!!! (*correct me if I am wrong; the urge to write might have compromised my ability to do simultaneous equation).
Now, this is troubling. Because if I were 12 once more (I rather not be 17 again), and looking around even in prosperous Singapore, to have a kid, or a chocolate loving adult like myself, buying 308 pieces of chocolates at one go would have seriously revoked common sense. I might then look around the examination hall, and asked myself if anyone in the world would go out to a gourmet chocolate stand (that's where they sell pieces of chocolates and not 'some chocolates') and buy 308 pieces of chocolates. Because if I, the 12 year old boy with a precocious appetite for upmarket chocolates, can count, 308 pieces of chocolates would have cost me $924 at $3 a piece without 7% Goods and Service Tax. That's serious cash. If I am just as precocious in rudimentary economics, I would think $924 is cash one commits to a mortgage or rent, not to chocolates. In fact, it is downright irrational (i.e., unbelievable). That said, personally I find it comforting that the question designer has glimpsed a world where a boy might part with 154 pieces of chocolates for his friend, or $494.34 for the candy utility of his friend.
And because of this, I, as the 12 year old again (this is getting fun), would be inclined to tell myself that this is an utterly unbelievable answer. Although I am standing on firm ground, my psychology would be telling me otherwise. Should I believe in my psychological intuitions (believe me this counts)? Or should I believe unwaveringly in my mathematical capabilities (believe me this counts relatively little in the crisis scenario of an examination)? Assuming that a 12 year old may not know how to differentiate between his psychological intuitions and his mathematical certainties, then we have a recipe for disaster. Guess we know now why even A-Star students could not complete this examination--if this was in fact the careless way questions were designed and phrased.
Lastly, I am no fan of large numbers whether as a 34 year old adult-still-in-school, or a 12 year old schoolkid. In solving this problem, I had to work out calculations that went beyond my ability to calculate mentally. Maybe I am a notch below average on mental computation--I have been told that quite a few times. Nonetheless, does this impress fans of big numbers? Maybe. But mathematically, big numbers do nothing as far as mastery of the relevant mathematical concepts is concerned. By the highest common denominator of '4', Jim might have bought 77 pieces of chocolates and Ken 17 sweets and this problem could have been still the same. But wait, this would mean half a piece of chocolate and half a piece of sweet by the 50-50 heuristics right? Indeed. So in fact on our hands we have a compound problem--the 50-50 heuristics has complicated even the good intention to reduce these numbers. Thus if designers want to keep the heuristics, change the numbers; but if designers want to keep to a small number in the same ratio, change the heuristics. Mathematical thinking tells me this much, no? To force a choice on these preferences shows some guts in concept prioritization in mathematics; to waver shows incomplete understanding or worse, the absence of responsibility.
* * * * * * * * *
In sum, no child should be put through this sort of un-mathematical mental anguish, because this is not a test of proficiency for mathematics but something like a test of luck.
I behoove designers of such questions to take more responsibility so that students do not feel that their throats have been slit, or doomsday has arrived, or suffering from any of these un-mathematical fates. Most important of all, think like a child and feel the common sense of that child once more. After all, is this not the essence of all great mathematics?
Monday, October 5, 2009
Ought one buy a book for its cover too?
Some books are good but their covers plain. Some others are bad but their covers beautiful. Some books have good content and beautiful covers but you cannot take it on the bus with you--they are too big or too heavy; and some have beautiful covers but no content, so you can't really take another journey with it on the bus.
I chanced upon this little one at the bookstore yesterday--yes, indeed it was the cover--and quickly devour it, though in contrary to the behavior and mindset advocated in this book: Writings from the Zen Masters.
Here's an excerpt:
The Most Valuable Thing in the World
"Sozan, a Chinese Zen master, was asked by a student: 'What is the most valuable thing in the world?'
The master replied: 'The head of a dead cat.'
'Why is the head of the dead cat the most valuable thing in the world?' inquired the student.
Sozan replied: 'Because no one can name its price.'"
(p.95)
Sunday, September 6, 2009
On collecting, the collectible and being collected
On collecting, the collectible and being collected
a short essay by Jeffrey Chan
Are you a ‘collector’? I would be surprised if you are not one. It is human to collect. We collect what is owed to us--we try--but we also collect what fancy us. Therefore all of us perform the act of collecting to some degree. Yet only a handful can justly call ourselves as collectors.
Collectors are not necessarily connoisseurs. As a matter of contrary opinion, I think that collectorship is quite opposed to connoisseurship. You can collect shells for yourself on a lonely island (perhaps to amuse yourself amid this unbearably imaginary loneliness), but there, it is meaningless to call yourself a connoisseur of shells. After all, connoisseurs necessarily demand others who can recognize their connoisseurship, but collectors merely depend on themselves. Besides, one can collect just about anything that can be collected--even for things that do not fit into any collection; but the connoisseur is inclined to stick only to the good taste. Because of this, a connoisseur is likely to have been brainwashed. But as a collector, you just have to be yourself.
However it is said that the collector collects only what is collectible, generally deemed as what is rare. But rarity does nothing to make something collectible, unless rarity also makes the collectible valuable. By value I do not mean monetary value. After all if one collects because high rarity sometimes confers high monetary value, then one is hardly a collector than a merchant, quite ready to liquidate his collection when the price is right. In contrast, a collector is never quite capable of liquidating his collection; he can only dismantle it. No, by value, I am strictly implying the intrinsically valuable. One can only collect what is intrinsically valuable, because the extrinsically valuable is what one sells. Even so, I am not selling the beauty of pebbles or soda caps to you--I cannot--rather, I am suggesting that it is very hard to talk about the intrinsically valuable today even when this is the sole motivation for us to become collectors.
Does this mean that all that is intrinsically valuable is also automatically collectible? I reckon this is a foolish question; but collecting is a fool’s grasp: what is more foolish than collecting that which we can never truly own? I shall nonetheless answer this foolish question as a foolish collector: “no, even though we try”. A genuine smile, a worthy handshake, a good friend or an apt idea are all intrinsically valuable but none of them is collectible. Yet we try to collect them through photos and memories, via websites and books such that we heroically attempt to transcend what is uncollectible by collecting.
By suggesting that we collect all these things, I might have given you the impression that collecting equates accumulating. Nothing is further between these two actions. To collect is intentional; but to accumulate is unintentional. To collect requires an organizing theme or a plan beforehand; but to accumulate one only needs a working credit card and perhaps an all consuming life. A garage sale is the consequence from an accumulation of things--I know, because I had organized one before: I did not quite know I have so much things that had turned into stuff--but a collection is an organized thematization of things. Psychologists tell us that we collect because the collectibles grant us our identities. Yet I tend to think that we have to invent new identities for things before we can begin collecting them.
However vast this range of organizing themes (does one collect based on a certain color, a historical period or a certain appeal?) or plans (how does one begin to collect?) are, all organizing themes or plans for the collectible must include the criterion of either a set or a range. Indeed, a collection is either based on the completion of a finite set or the following of an infinitely expanding range. A collector who aims for the completion of a finite set is historic--he is always on the lookout for that one keystone to complete his collectible set. But a collector who aims for an expanding range is a futurist--he is set on following an infinite set that never ends. Collecting based on a finite set terminates when a set has been completed. However collecting based on an infinite range only terminates when a collector meets his Collector. The ethics of enoughness is therefore quite distinct--while the former rests on completion the latter relies on persistence.
This question of what qualifies as enough or self-limiting unfortunately puts collecting squarely in the vicinity of the moral. After all, E.F. Schumacher has remarked that any activity which fails to recognize a self-limiting principle is of the devil. Since I have not seen the devil working (so far) as a collector of things, going by Schumacher’s remark I must therefore assume that some self-limiting principles are working in the collecting of things. I have observed that many collectors rest on their well-deserved laurels after completing some self-congratulatory sets. Others who are more likely to persist in expanding their infinite collections take the occasional and apologetic hiatus (i.e., ‘my wife has capped my credit limit because she has uncapped hers’). But since I am neither near to the completion of a set, nor am I wedded to a credit-capping wife, I have therefore yet to formulate my own self-limiting principle.
As a matter of fact, collecting is one of the few remaining activities today where one can still find conviction despite the absence of a unifying creed or an organized religion. Go to one of these collectors’ shows--be it stamps, coins, antiques or fountain pens (yes I collect fountain pens)--and I would be surprised if you did not depart without that same glow of having seen God. To collect demands a remarkable level of faith--who knows where or when one would find that particular pen Luftwaffe officers used or that special Etruscan coin? Yet the true collector finds the signs leading to his potential collectible everywhere. Just like the first (and real) Templar who looked up to the sky: in hoc signo vinces (in this sign you will conquer), the collector marches with a truly unstoppable faith in order to find his collectible.
Because faith is inseparable from purpose, it is therefore prudent to ask just what purpose is served by the activity of collecting itself. Beyond the egocentric purpose of congratulating oneself (one has to do this from time to time just to remain sane in this world, I think), one possible and productive purpose is that collecting is also preserving. For this we have the many unstoppable saints of the collectibles to thank; for without their unstoppable efforts, large tracts of human histories would have either remained buried or more likely, bulldozed and razed, and bulldozed again by the quickening bulldozers of commercialism. Of note, I reserve my special thanks to the collectors of old and rare books, those decrepit volumes detailing unfashionable knowledge or oddities despised by both the philistine pedestrian and the peddlers of fashionable science. Largely because of the saintly efforts of such book collectors, some modicum of humanity--our historic ignorance--has been preserved than destroyed by the latest NYT-BS (I mean the New York Times Best Seller list).
Like all worthy questions that ultimately turn upon themselves, if we collect things then what (or whom) collect us? Unlike the foolish question I raised earlier, I like to think that this is a rather relevant question in an age of facebooks and linkedins. In my short life I have witnessed teachers collecting students (yes, but I also read Harry Potter), universities collecting professors and states collecting talents. I don’t really know if teachers actually form sets of their collectible students or if states pander after an infinite range of talents. However what I know is that to collect undeniably also means to exclude.
Frankly, I have no idea if I am being collected by something or someone. I don’t even have a clear opinion if being collected counts as being privileged or unfree. Oddly despite the fact that I have thought a little about collecting things, I am at a total loss on living human beings being collected. Assuming if I am being collected, what or who is collecting me? What is the theme of this collection? Is this collection organized by color, history or some appeal? And assuming if I am not being collected, why am I not being collected? Is it because I do not fit into pre-existing collections based on color, history or some appeal? Or am I actually a collector who cannot be collected?
I don’t presume to have answers to these questions: they are for you to work it out. All I have to chip in here is that to collect is human; and if you have yet to start, it is nice to begin a little collection of something.
Sunday, July 19, 2009
Insights and Instigations of Hope
What is hope? From my own reading, I found three passages that I enjoy very much; and on which I peruse repeatedly.
"...an ever-present reminder that men, though they must die, are not born in order to die, but in order to begin."
--Hannah Arendt, from 'The Human Condition'
"Thus even one of the Seven Sages says: 'Most people are bad', which is not far from Hobbes' opinion, which until recently
was almost overwhelmingly correct, that man is a wolf to man. But it is all a question of not agreeing with such opinions;
of recognizing the causes from which they will not spring nor need to spring for ever; knowing how bad so many things still
are, but knowing more deeply how good they could be."
--Ernst Bloch, from 'The Principle of Hope, Volume 2'
"I do not know of a better argument for an optimistic view of mankind, no better proof of their indestructible love
for truth and decency, of their originality and stubbornness and health, than the fact that this devastating system of education
has not utterly ruined them."
--Karl Popper, from 'The Open Society, Volume 1'
Wednesday, July 15, 2009
Facility X: A Short Story
a short story by Jeffrey Chan
Plausibly, nothing is worst than waiting on death row. Especially at Facility X.
Now, Facility X is not your usual run-of-the mill maximum security prison for psychopathic murderers or criminals against humanity. Quite the opposite, Facility X accommodates just about everyone. Why, I saw a man quite like myself the other day; and I am just an ordinary man.
Indeed, Facility X differs from those run-of-the mill maximum security prison in a few ways. First, everyone waits on death row here; there is no one stuck with a life sentence, nor is anyone privileged with an opportunity for either appeals or paroles. Second, it is said under more ordinary circumstances, one is trialed before imprisonment. But at Facility X, one is hauled here without any reason or knowledge of guilt; and quite instantly, before one could even utter a grunt of a protest, one has been sentenced to the death row.
Now, before you think that Facility X is this bleak and barbaric place just a few extreme rungs below your usual run-of-the mill maximum security prison, I ought to say the following: it is not. Instead of smelly cells, bad food, common bathrooms and cruel wardens--typical features we tend to associate with typical prisons--Facility X provides her inmates with unusually nice private rooms often overlooking an equally nice garden (and yes, personal decoration is encouraged in one’s room but never the garden, which is managed by professional gardeners); savory food and entertainment that have been certified by the Facility’s dietician and the Council for Entertainment (after all, neither the food nor the entertainment is supposed to kill you before your sentence is carried out); private bathroom where modesty is the best policy and perhaps the most unusual of all, polite but firm wardens who are always neatly dressed in grey suits and shiny black shoes. And I have never seen them carrying a baton in all my time at Facility X. Why, just the other day, one of them was politely inviting me to a discussion session.
Even so, getting to know your fellow inmates at Facility X is intensely discouraged. All doors in Facility X--except those leading to the discussion and energy chambers (I shall tell you what those are in a minute)--are never locked but they are almost always closed. If no wardens are wandering about, it is actually quite safe to knock on another inmate’s door. But it is likely, well I shall say very likely, that no one would answer the door. In retrospect, I have only met a handful of inmates in all my time here; and I never had the opportunity to know them better between a taut smile and that subtle nod. Since meals could be served in one’s room at Facility X, inmates always end up eating in their own rooms, which further reinforced that tacit discouragement for general socializing here at Facility X.
No one seems to know where the wardens stay in Facility X. I have never quite figured this out myself. They are always around in full force, night and day, and even on weekends and on public holidays. And when they appear, they are always smiling in their neatly pressed grey suits, even though their smiles are always too taut to be real. They speak politely; though occasionally through my closed door I would overhear harsh words spoken to some poor inmate. Even so, words that follow from that reproach are usually glossed over with more oily politeness. I try hard to limit my conversations with these wardens; and when conversations are unavoidable, I try hard to appease them. So far, I have been successful. We greet each other cordially and I always follow what they tell me to do with the greatest effort on my part trying to seem all too willing.
Even so, these wardens never seemed to remember you personally. In my early days at Facility X, there was this warden with the blackest hair--it could not have been blacker if he dyed it with indian ink--who stopped by one day to invite me to my alloted discussion sessions. Of course I complied. A few days later he stopped by again and invited me to check out a new energy machine that Facility X had just imported from an unknown location. Yet he found me as if he had never met me in his life before. As he talked, his eyes were empty and parched, staring more or less straight through me onto the plastered wall of my room. It was as if I did not need to be there at all. Yet before he bade me goodbye in very much the same way, he gently reminded if I would remember to show up outside discussion chamber 703 at 8:59am the next morning.
Now, you must be wondering what kind of schedule inmates keep at Facility X. There is actually no schedule, except for the usual obligation of participating in one’s alloted discussion session, and reporting at one’s assigned energy chamber. Beyond these obligations and the usual habits one keeps to stay alive--solid eight hours of sleep and three warm meals plus three intervals for tea, mid-morning, afternoon and supper respectively, inmates are rather free to pursue their own forms of entertainment around here. There are few rules, and even fewer incidents of animosity; but there are a great number of books and movies and classes for sewing and cooking. Why, perhaps because of these reasons, most inmates do not seem concerned that they are in fact serving on death row at Facility X. This forgetfulness is further reinforced by the lengthy time towards one’s inevitable end, which can be quite a luxurious drag. But occasionally--and I repeat occasionally--when I catch a glimpse of an empty room all cleared out for a future inmate through a door ajar; or when an incidental ray of sunlight finds ‘Facility X’ printed in tiny, gold-speckled letters at the top of every wardens’ documents, do I realize that I am an inmate waiting on death row in Facility X.
* * * * * * * * * * * * * * * *
I must be boring you with the trite details of my daily life at Facility X. Perhaps you may find the business of energy chambers and discussion sessions in Facility X more interesting. Perhaps. During my orientation at Facility X quite a while ago, a warden remarked in one surprising moment of unabashed pride that energy chambers are the definitive hallmark of Facility X. I reckon that there are approximately about a thousand chambers located across Facility X (and I am only guessing since I have only been to chamber 989 and chamber 008, and walking past nearly every number in between). In the energy chamber I have visited, there are two columns of twenty four machines; each column neatly aligned and positioned in parallel to the other. Now, no one seems to know the scientific name of these machines, so at Facility X I have plainly and by convention, adopted the name, ‘energy machines’, since after all, they harvest energy from the inmates.
These energy machines, or at least the ones I have seen and used, resemble a mongrel breed between a treadmill and a cockpit. An energy machine is roughly nine feet in length and about three feet wide, hollowed out in the middle where a black rubber film runs the entire length of the machine. The machines I have seen are all made of a dull metal, unnumbered and unpainted, and the only thing that is ever colorful in them is the human body itself.
In an energy machine, an inmate has the choice of either walking briskly in it, like a treadmill within the hollowed section, or lying down completely on the black rubber film, strapped to the machine like a corpse in a coffin. In either position, an inmate is connected to multiple grey cables with a face mask strapped across his face. I was told that these multiple grey cables, which all end in tiny sticky discs that are stuck to different parts of the body--quite a few in sensitive places--draw energy from the body, while the face mask provides air and absorbs nutrient rich carbon dioxide from the inmate during a typical energy withdrawal session. When an inmate is fully attached to these cables in his chosen position--either walking briskly on the treadmill or passively lying down in the machine--two large but thin monitors are lowered, one before the inmate so that he could observe his own vital signals and energy contributions, while the other displaying the same information faced a common corridor between the two columns of machines for that supervising warden in charged of the chamber.
According to my orientation warden, there are multiple versions of energy machines. But they all do the same thing although the newer ones perform much more efficiently--all these machines harvest energy from the inmates at Facility X. A typical session lasts about six hours, with two staggered tea breaks for rest. There is even a proper meal time of an hour alloted between the third and the fourth hour. But at the same time, these staggered breaks ensure that inmates do not get to talk to each other. It is quite possible for any inmate to stop at any one time, although the warden may demand a valid reason for doing so.
Initially, there was some physical discomfort, even pain, when those tiny discs at the end of the grey cables stuck too close to the skin for comfort’s sake. But surely as that warden said, all discomforts gradually ebbed, soon to be displaced by a general sense of monotony and that uneasy burden of meaninglessness. And sometimes, a pervading sense of gloom. Usually however, the pace of this energy harvesting is leisurely and as far as I could observe so far, inmates do not seem to mind at all. And usually for me, I ended up becoming more exhausted from the monotony of the hours spent in that confined space trying to keep myself sentient (yes, I very much prefer not to walk briskly in that thing) than for any real energy harvested from my body. After all, staring at that monitor with jumping numbers is the least interesting thing to do in the world, and falling asleep is strictly forbidden in an energy machine. This is perhaps why some inmates greatly prefer the option of walking briskly in the machine. And as far as I know, spending time in an energy machine occupies most of what every inmate does at Facility X.
Anyhow one day, the curious question of where all my ‘energy contributions’ were going to struck me. I remember that I was filled with a great reservation on whether I ought to ask this question, which occurred to me even then that it bordered on the unbecoming. But by the time I had detached the final sticky disc from my body, any remaining reservation had been utterly vanquished by my curiosity.
Cautiously, I approached the portly supervising warden of chamber 008 that day. Perpetually plastered with a tiny gray smile, she did not seem surprised as I approached her. I recall she tried to smile all the more, although the vast expanse of her grayish face did much to conceal any real extension of that smile. But just as I opened my mouth, her smile vanished instantly. I stuttered; but nonetheless, succeeded in masquerading my question as a general concern on where my energy contributions went. To this day, I could still remember her smattering of an answer. It was as if she was caught off guard; or perhaps the real answer never existed. “Oh well...the Great Society...the Government, and for the...many homes of the Earth and their appliances, which in any case must be for the society...” and so went on for a minute or two like a snake trying to catch its tail before suddenly, she became aware that she had in fact ran out of all sensible answers. There and then, she fixed a stare on me that I shall never forget as long as I lived in Facility X. It was a cold and empty stare, devoid of humanity and pronouncingly demonic.
I have never dared to raise a follow-up question on that matter again; nor have I witnessed another inmate approaching that level of foolhardiness as I had unwittingly suffered that day. But like every encounter with a warden in Facility X, she did not seem to remember our unfortunate encounter when I reported to chamber 008 again a few days later, greeting me with her usual tiny smile while I stepped into the chamber in great trepidation. Up till today, I still do not know if this warden was intentionally forgetful or in fact, she was acting rather mercifully whenever I see her in chamber 008.
* * * * * * * * * * * * * * * *
Now, the business of discussion sessions in Facility X is something else. For the uninitiated, it may even sound a tad too morbid. Incontrovertibly, Facility X differs again from the usual run-of-the mill prisons by never fully specifying the method for one’s death sentence ahead of time. Instead, different possibilities for one’s death sentence are debated and discussed endlessly in one of these discussion sessions (if one is lucky--I shall explain why). Sometimes, this sessions take a good four to five hours of one’s precious time. Although I have yet to decide if these sessions are a waste of time, they are however, rarely edifying.
Most intriguingly, an inmate is always given some discretion on deciding the method of his or her own death sentence, although the exact degree of this discretion has never been completely divulged. Why, this discretion is mysteriously confined to the willing press of a yellow button.
Just the other day, after the discussion machine had simmered down, I was warmly invited to approach the long mahogany desk where twelve vials of what seemed to be barbiturate sat awaiting my inspection. I was told that a few vials were rather sweet and sticky, like autumn Muscato, and one particular vial with a clear liquid nearly tasteless. Before I could quite decide by taste which vial would be more ideal, one senior warden--who looked more like a doctor than a warden--gently chimed in that I could also elect to consume from another vial (which he also hinted should taste rather salty) by having small doses from that vial added to my food over a period of time. Before this senior warden could actually finish this suggestion, three other senior wardens sitting next to him started a rousing debate on whether his recommendation would work. Apparently, I was still quite a young and healthy lad, perhaps not susceptible to the cumulative effects of slow poisoning yet.
Debates like these are common sights in all discussion sessions. Each discussion session--or at least all the ones I have attended--are chaired by seven senior wardens before a large but slender glassy inverted cone structure filled with countless tiny colored balls (mostly white) within a hollow ovoid discussion chamber. This large inverted cone structure is the ‘discussion machine’, which dispenses color-coded balls prescribing the method for one’s death sentence.
A discussion machine comprises of a great many interlocking spirals--like a nautilus shell but only more convoluted--within its glassy structure. Rising about thirty-five feet in height and spanning nearly twenty-five feet in diameter at the top of the machine before tipping to a mere six inches at the bottom, one marvels at how this inverted conical machine can even stand up on its own. Nine glassy pipes feed different colored balls into the machine from the ceiling of the chamber. In this machine, these tiny, countless colored balls circulate ceaselessly like blood in living but spirally interlocking capillaries. Within each interlocking spiral, colored balls clash and collide; bouncing and jumping onto another trajectory while others rush on in their place. Ultimately, ten colored balls are ejected from the tip of the inverted cone onto a stainless steel trough the size of a long ashtray in front of everyone in the chamber. These ten colored balls then prescribe the fate of the inmate.
Now, if this is all there is to the discussion machine it would seem unwholesomely deterministic. Before each of these senior wardens there is also a green button, which can be pushed multiple times in any discussion session depending on their mood for that occasion. Each push of the green button introduces eighty or so green balls into the machine from one of the nine glassy pipes suspended over the machine. Similarly, there is a yellow button before the inmate. Pushing this yellow button introduces about seven hundred yellow balls into the machine from the same pipes above. The yellow button perhaps represents the ultimate discretion on the part of the inmate to affect the outcome of his verdict; or perhaps, just to introduce an element of uncertainty into this whole business of death specification. Nevertheless, the inmate is only permitted to push this yellow button once.
Civilly, everyone takes their turn in pushing the buttons, with the inmate last in doing so. The discussion machine then speeds up into a transparent twirl of countless twirling colored balls--white, green, yellow, and occasionally, uncommon streaks of reds and some blurred blues--spiraling along the entire section of the machine at dizzying speeds. Despite the machine’s ungainly invertedness, it seems to brace up all the more elegantly like a spinning top awakened by its own momentum. Indeed, it is quite a sight to behold this machine as its internal twirling speeds up; it hums with a certain focused energy that always end with some prescriptions for death.
The discussion machine is permitted to twirl and churn its countless colored balls like that for a while. I have never tried counting the time, because like everyone in the chamber--the seven senior wardens, plus the warden accompanying me, all nine of us--we are usually transfixed on that beautiful machine of unspeakable raw power. But when the machine finally stops, ten tiny colored balls are dispensed onto a stainless steel trough before us all. It is possible for these ten balls to be composed of an assortment of different colors, or for all ten to be all of the same color: either white, green, yellow, or even red or blue. I was told that no one really knows the number of colored balls in the machine at any one time (at least because each of these senior warden could effectively introduce more green balls by pressing their button more than once, which sometimes cannot be differentiated from tapping one’s fingers in great impatience from the vantage point of the inmate). But it is reasonable to say that there are always more white balls than any colored balls; and far fewer reds and blues than greens or yellows as far as I could observe. While there are many tiny colored balls at any one time, their numbers are by no means infinite.
There is an entire science for decoding the possible permutations of these ten colored balls. I shall not bother explaining to you what each possible permutation means, either by sequence or by an aggregation of colors, because it is like reading tea leaves. Yet, I was told that all ten balls of either red or blue have never turned up before in the entire history of Facility X. Similarly, all greens and all yellows are unheard of as well. Perhaps there are always fewer than ten of reds and blues in the machine--I am simply guessing here. Really, I did not want to know what a straight ace of reds, blues, greens or yellows entail for the inmate, especially at Facility X. On the other hand, a straight ace of ten white balls has happened quite a few times before. In this unfortunate event when an inmate receives ten white balls as the outcome of the machine, the death sentence is promptly served at an undisclosed location in Facility X--according to the prescription for death etched on the first or last white ball.
Most of the time however, inmates tend to receive a mixture of colored balls. Often in my experience, it is mostly white inter-dispersed with one or two greens or yellows; and perhaps in exceeding rare occasions, maybe a red or a blue. As far as my discussion sessions went, the implications of receiving these rare colored balls were never clear. So far, I noticed that a red ball in the pack of ten would earn me a few frowns, while a blue ball always made quite a few senior wardens smile openly. By the way, I have never received more than either one red or one blue in all my allotments of ten colored balls.
However clearly, on all the white balls are etched some prescription for the method of one’s death sentence. In all my experience at these sessions, I have only observed very humane methods such as dignified poison ingestion, or carbon monoxide poisoning, or some other measures akin to these two; but certainly nothing violent like bludgeoning, hanging, or the firing squad, although I have overheard a senior warden once said that a small number of white balls etched with these options are always among the countless humane ones twirling in the machine at any one time.
As I said before, in most instances (fortunately, I might add), inmates would receive ten colored balls comprising of some whites, greens and yellows. One single green ball represents a defensive position to be taken up by one senior warden who would then argue on the behalf of the inmate--mostly on why he thinks the methods prescribed by the white balls are unsuitable for the inmate. A single yellow ball permits the inmate to argue on his or her own behalf, although an intelligent inmate always relinquishes this right to the senior warden, who in any case, always make a more compelling case on the inmate’s behalf. And so two green balls make for two defensive positions, and two yellow balls for two defensive rights on the part of the inmate, and so on. The amusing thing is of course when the inmate receives only a mixture of green and yellow balls. In that event or so I heard, the discussion session is promptly canceled with great consternation on the spot, and another session scheduled in the near future. Till this day, I am still unable to make up my mind if the inmate who received a mixture of only green and yellow balls has lucked out, or if he has merely procrastinated the inevitability of his death sentence.
In any case, I should return to that incident on examining the twelve vials of barbiturate the other day. During that discussion session, I received the verdict of six white balls, three green balls and one yellow ball; and of that yellow ball I cleverly ceded my rights back to the senior wardens involved in my session. Incidentally, all the six white balls I received simultaneously prescribed dignified lethal poisoning, which according to a soft murmur echoing in that chamber, had not happened for quite a while. And there and then, just as a vivid demonstration that all prescriptions for death on those white balls have their corresponding material artifacts, twelve vials of what seemed to be different concoctions of barbiturate were immediately presented before me. I was then warmly invited to come forward to inspect these vials of liquid death.
Honestly, I did not know what to think of my good fortune of getting six instead of ten white balls, even though I was quite aware of that absurd tussle between the uncertainty of the method but the certain inevitability of death for myself. As I began my lackluster inspection of these vials, four of the senior wardens began arguing among themselves on why ingesting poison was unsuited for me. That was when the doctor-like senior warden suggested that the poisonous liquid in one particular vial could be added in small doses in my food over time, which was tantamount to a different take on poison ingestion but at the same time, likely to amount to the same outcome of death. Without remorse, his dignified suggestion was quite consistent to the judicial values that had invented the discussion machine.
Like most discussions, that one ended without clear insights or further specification for the method of my death sentence. Truly, these discussion sessions so far only burdened me with ever greater uncertainties on the manner of my death, even though as far as the death sentence is concerned, it is all quite certain. For a period of time after that particular session, I looked at the food I eat differently. But now I have stopped doing so. For after a while, surely and nonetheless, I will be a dead man at Facility X.
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