Plate 1: Mound of rice with a single meat and vegetable dish.
Plate 2: Pile of rice with two meat and vegetable dishes.
Plate 3: Some rice with one meat dish, two meat and vegetable dishes, and one fish dish.
There are of course variations on what can go on the plate with its accompanying variable amount of rice. But one glance at the plate of each diner walking away from the rice stall in Thailand tells a story. A story of relative affluence mixed with absolute hunger.
Rich or poor, hunger treats everyone equally. But sadly, the poorer often have to go hungrier.
Showing posts with label introspection. Show all posts
Showing posts with label introspection. Show all posts
Tuesday, December 14, 2010
Monday, November 15, 2010
Gang Fights
Why ban gang fights?
Why not turn *Scape (or whatever its name) into a gang fighting ground from between 2 am and 5 am every morning?
Make it simple and accessible, like the Speakers' Corner. Register and fight, as long as religion and race are not involved.
Why not turn *Scape (or whatever its name) into a gang fighting ground from between 2 am and 5 am every morning?
Make it simple and accessible, like the Speakers' Corner. Register and fight, as long as religion and race are not involved.
Monday, May 03, 2010
Writing Proofs
I will be teaching a course in graph theory to some secondary school kids in about three weeks and as I prepared the course materials, one key point stuck out: Students need to write proofs.
Writing proofs is inevitable in dealing with most mathematics. Many theorems come with their most commonly used proof or proofs. The Pythagoras' Theorem, for instance, can be proven over a hundred ways.
In comparison, some problem solving questions require a proof as a solution but there are unfortunately no standard proofs that the instructor can rely on or turn to.
Particularly in graph theory, many questions require solutions that are highly demanding. It is not enough to say that the answer is "n". Often, you have to show why all other answers other than "n" are not acceptable, even though they satisfy the general conditions of the question.
In this regard, constructing a logically water-tight proof is difficult because many of us do not use contradictions and exhaustion as strategies, unless we are involved in certain types of work. It would not be suitable for me to exclaim the beauty and prowess of such proof techniques as I don't want to be guilty of playing up my areas of interest and "semi-expertise" but having a good grasp of the techniques can help solve a lot of problems quite elegantly.
The proof by contradiction is often elusive and hard to figure out. One needs to know which condition is likely to undergo "reductio ad absurdum". One common claim that relies on the proof by contradiction is "square root 2 cannot be expressed as a fraction with whole number numerators and denominators." Intuitively, this looks simple and the claim seems more like an axiom than something to be proven. However, it is not axiomatic and how do we construct a proof to validate our intuition? Interested readers can click on the word proof to see a proof by contradiction of that claim.
Proof by exhaustion is something elementary learners of mathematics used to resort to when they first come across claims such as "there is no largest integer." Frequently, a child who has learnt concepts such as a million, a billion, a trillion, and so on will attempt things like "a trillion trillion trillion" and when you tell them, "how about you add one?" they will quickly come to terms that exhaustion is plain exhausting. And frequently, exhaustion does not prove anything. Before long, proof by exhaustion becomes an antiquated technique to these learners of mathematics, until they are forced to face their inner demons again.
In graph theory, in particular, the need to establish uniqueness in the solution often means that the other competing answers must be rendered inadmissible. While it is probably not sensible to show a full graph theory question to elicit thoughts on how to construct answers that rely on the proof by exhaustion, folks who have a propensity for factorization might delight in seeing how the proof by exhaustion is daintly applied in this example: If n is an integer, then (n^7 - n) is a multiple of 7.
The study of mathematics can often lead its learners to develop logical thought processes. Writing proofs is one of the tools that play an important role in developing a person's logical acuity. As with all pursuits, there is no gain until one gets their hands dirty and begin practicing.
I hope my students will appreciate the package that I'm putting together for them. After all, whoever said learning was always easy?
Writing proofs is inevitable in dealing with most mathematics. Many theorems come with their most commonly used proof or proofs. The Pythagoras' Theorem, for instance, can be proven over a hundred ways.
In comparison, some problem solving questions require a proof as a solution but there are unfortunately no standard proofs that the instructor can rely on or turn to.
Particularly in graph theory, many questions require solutions that are highly demanding. It is not enough to say that the answer is "n". Often, you have to show why all other answers other than "n" are not acceptable, even though they satisfy the general conditions of the question.
In this regard, constructing a logically water-tight proof is difficult because many of us do not use contradictions and exhaustion as strategies, unless we are involved in certain types of work. It would not be suitable for me to exclaim the beauty and prowess of such proof techniques as I don't want to be guilty of playing up my areas of interest and "semi-expertise" but having a good grasp of the techniques can help solve a lot of problems quite elegantly.
The proof by contradiction is often elusive and hard to figure out. One needs to know which condition is likely to undergo "reductio ad absurdum". One common claim that relies on the proof by contradiction is "square root 2 cannot be expressed as a fraction with whole number numerators and denominators." Intuitively, this looks simple and the claim seems more like an axiom than something to be proven. However, it is not axiomatic and how do we construct a proof to validate our intuition? Interested readers can click on the word proof to see a proof by contradiction of that claim.
Proof by exhaustion is something elementary learners of mathematics used to resort to when they first come across claims such as "there is no largest integer." Frequently, a child who has learnt concepts such as a million, a billion, a trillion, and so on will attempt things like "a trillion trillion trillion" and when you tell them, "how about you add one?" they will quickly come to terms that exhaustion is plain exhausting. And frequently, exhaustion does not prove anything. Before long, proof by exhaustion becomes an antiquated technique to these learners of mathematics, until they are forced to face their inner demons again.
In graph theory, in particular, the need to establish uniqueness in the solution often means that the other competing answers must be rendered inadmissible. While it is probably not sensible to show a full graph theory question to elicit thoughts on how to construct answers that rely on the proof by exhaustion, folks who have a propensity for factorization might delight in seeing how the proof by exhaustion is daintly applied in this example: If n is an integer, then (n^7 - n) is a multiple of 7.
The study of mathematics can often lead its learners to develop logical thought processes. Writing proofs is one of the tools that play an important role in developing a person's logical acuity. As with all pursuits, there is no gain until one gets their hands dirty and begin practicing.
I hope my students will appreciate the package that I'm putting together for them. After all, whoever said learning was always easy?
Tuesday, December 15, 2009
Fundamental Mistakes 2
Longevity is not a desirable result of medical advancements. Instead, extending the human lifespan is the probably worst mistake that medical science have made for several reasons. First, humans should not tamper with nature. We have a life expectancy of around 60 years for a reason. Second, longevity comes at the end of a person's lifespan and not in the middle. Society has not managed to adapt to the new needs of the modern human-turtles. Third, medical measures have not moved with the times. Many of the health indicators are still based on data gleaned from my great-grandfathers' generation.
Human life expectancy is determined by the surroundings that a person is in. Where there is poor sanitation and malnutrition, people live shorter lives but while they are alive, they give birth to more babies. Where there is good sanitation and abundance of food, people live relatively longeer lives but they may decide to have fewer babies but instead invest more heavily on developing them. Such is the nature of natural selection.
What we have done now is to extend life years beyond accepted norms through medical intervention. Human lives are extended beyond their actual use by dates. Transplants, surgeries, vaccines and other interventionist measures have helped humans live longer. However, such a move runs counter to what nature intends for humans.
A certain amount of attrition along the human life cycle is necessary so that the larger Earth environment can be in equilibrium with the human population. What is happening now seems to be that the environment is strained because not enough deaths are happening. This is disastrous to Earth, especially when the increase in the life expectancy actually cause the older folks to strain on the younger folks, rather than make them contribute towards alleviating themselves as the burden on others.
This development is marked in the way society fails to move in tandem with increases in life spans. Even until now, with the average Singaporean gaining 15 years of life over the past generation, the Singaporean society has just increased retirement ages in baby steps from 55 to 57 to 60 to 62. Even then, raising the retirement ages have met with stiff resistance from both companies and workers alike.
One cannot really fault the companies for not willing to hire the overpaid, underperforming old fogies. The labour movement recently coined the term, "Cheap, fast and good," to spur the Singapore workforce to bounce back and become leaner, more productive and deliver higher quality products after emerging from the financial crisis. Think about it, how could we keep the old folks cheaply? We make them retire and then rehire them on contracts at reduced salaries. How can we make them fast? We move them down the job ladder because they should take on less responsibilities to justify their lower pay. Hopefully, they can keep up with the quick march that the companies demand of their younger colleagues in the lesser jobs. How can they be good? This is up to the management to decide and one litmus test is the renewal of their employment contracts.
Age increases have not been kind to the people, since the economically productive years have not risen in tandem with longevity. It is not a surprise, however, since the human body is designed to deteriorate and eventually self-destruct once it peaks at between 18 and 21 years of age. We have not managed to unlock the mystery to keep the body well-oiled and highly functional. We have only managed to stop the body from finding the self-destruct button fast enough. And perhaps we have also managed to find certain restart buttons to help the human body run a while longer on extra or borrowed time. And such times are often at the end of the human lifespan, where the body is no more than a mere vessel to keep the soul in.
Such a sorry state of development brings about certain questions that bear rethinking. For instance, have biologists barked up the wrong tree? Who insisted that longevity was the only acceptable measure of medical advances? What about higher weights, taller heights, higher blood pressure, higher cholesterol levels, higher liver enzyme levels, higher blood lipid levels, lower bone densities, higher IQ, fewer neonatal illnesses, lower infant death rates, among other measures?
I have just thought about how I am considered way off the charts for certain measures when my indices are compared against charts applicable to my great-great-great-great-grandfather. I could be thin like my ancestor too. I can have my blood pressure, cholesterol and what not, all lowered till I meet the indices left behind by my ancestor. However, that would mean that I might have to spend 6 to 8 hours of my waking time exercising in a gym to simulate the living style of my agricultural ancestor. My great-great-great-great-grandfather probably spent his waking hours foraging or growing crops, moving around on his feet at all times. He may or may not get enough to eat - he probably did get enough to eat, so much so that he passed on a copy of the fat gene, which I inherited.
Take a step back and think about it. If I had to spend most of my waking hours exercising, then I would never have been able to push papers as a bureaucrat or lecture in an airconditioned classroom and sit down and exercise ONLY my brain to grade papers.
My lifestyle is entirely different from my ancestors'. How then can I be measured against those indices? And if I could, then how can I contribute anything at all to economic growth?
It probably does not take a rocket scientist to realise that there is a huge contradiction here but why do we still indulge ourselves that what we are looking at is the truth? It is not, because the earth is telling us that we have got it all messed up. And it is a big time mess up.
Honestly, I am not at all happy to have to pay for the collective human stupidity. I will eat all the meat I want, all the eggs I want and all the food I want. And since I get to have it, I will use all the medical services I need. Until one day the powers that be come to their senses, an ordinary man like me should just live out each day like it's his last day on earth.
Who knows? It just might be.
Human life expectancy is determined by the surroundings that a person is in. Where there is poor sanitation and malnutrition, people live shorter lives but while they are alive, they give birth to more babies. Where there is good sanitation and abundance of food, people live relatively longeer lives but they may decide to have fewer babies but instead invest more heavily on developing them. Such is the nature of natural selection.
What we have done now is to extend life years beyond accepted norms through medical intervention. Human lives are extended beyond their actual use by dates. Transplants, surgeries, vaccines and other interventionist measures have helped humans live longer. However, such a move runs counter to what nature intends for humans.
A certain amount of attrition along the human life cycle is necessary so that the larger Earth environment can be in equilibrium with the human population. What is happening now seems to be that the environment is strained because not enough deaths are happening. This is disastrous to Earth, especially when the increase in the life expectancy actually cause the older folks to strain on the younger folks, rather than make them contribute towards alleviating themselves as the burden on others.
This development is marked in the way society fails to move in tandem with increases in life spans. Even until now, with the average Singaporean gaining 15 years of life over the past generation, the Singaporean society has just increased retirement ages in baby steps from 55 to 57 to 60 to 62. Even then, raising the retirement ages have met with stiff resistance from both companies and workers alike.
One cannot really fault the companies for not willing to hire the overpaid, underperforming old fogies. The labour movement recently coined the term, "Cheap, fast and good," to spur the Singapore workforce to bounce back and become leaner, more productive and deliver higher quality products after emerging from the financial crisis. Think about it, how could we keep the old folks cheaply? We make them retire and then rehire them on contracts at reduced salaries. How can we make them fast? We move them down the job ladder because they should take on less responsibilities to justify their lower pay. Hopefully, they can keep up with the quick march that the companies demand of their younger colleagues in the lesser jobs. How can they be good? This is up to the management to decide and one litmus test is the renewal of their employment contracts.
Age increases have not been kind to the people, since the economically productive years have not risen in tandem with longevity. It is not a surprise, however, since the human body is designed to deteriorate and eventually self-destruct once it peaks at between 18 and 21 years of age. We have not managed to unlock the mystery to keep the body well-oiled and highly functional. We have only managed to stop the body from finding the self-destruct button fast enough. And perhaps we have also managed to find certain restart buttons to help the human body run a while longer on extra or borrowed time. And such times are often at the end of the human lifespan, where the body is no more than a mere vessel to keep the soul in.
Such a sorry state of development brings about certain questions that bear rethinking. For instance, have biologists barked up the wrong tree? Who insisted that longevity was the only acceptable measure of medical advances? What about higher weights, taller heights, higher blood pressure, higher cholesterol levels, higher liver enzyme levels, higher blood lipid levels, lower bone densities, higher IQ, fewer neonatal illnesses, lower infant death rates, among other measures?
I have just thought about how I am considered way off the charts for certain measures when my indices are compared against charts applicable to my great-great-great-great-grandfather. I could be thin like my ancestor too. I can have my blood pressure, cholesterol and what not, all lowered till I meet the indices left behind by my ancestor. However, that would mean that I might have to spend 6 to 8 hours of my waking time exercising in a gym to simulate the living style of my agricultural ancestor. My great-great-great-great-grandfather probably spent his waking hours foraging or growing crops, moving around on his feet at all times. He may or may not get enough to eat - he probably did get enough to eat, so much so that he passed on a copy of the fat gene, which I inherited.
Take a step back and think about it. If I had to spend most of my waking hours exercising, then I would never have been able to push papers as a bureaucrat or lecture in an airconditioned classroom and sit down and exercise ONLY my brain to grade papers.
My lifestyle is entirely different from my ancestors'. How then can I be measured against those indices? And if I could, then how can I contribute anything at all to economic growth?
It probably does not take a rocket scientist to realise that there is a huge contradiction here but why do we still indulge ourselves that what we are looking at is the truth? It is not, because the earth is telling us that we have got it all messed up. And it is a big time mess up.
Honestly, I am not at all happy to have to pay for the collective human stupidity. I will eat all the meat I want, all the eggs I want and all the food I want. And since I get to have it, I will use all the medical services I need. Until one day the powers that be come to their senses, an ordinary man like me should just live out each day like it's his last day on earth.
Who knows? It just might be.
Thursday, July 09, 2009
Super Mario Galaxy
The Wii machine met a new friend last weekend. The new friend needs to be inserted into the machine's hole. And after inserting the friend, new pleasure results. In fact, it was so pleasurable that hours are spent trying to top each previosu climax as the positions got progressively more challenging and each round more tedious.
Welcome to my Super Mario Galaxy semi-addiction.
The game started slowly enough. The moves were initially clumsy and the movement slow. But trust me, at the grand old age of... heck, you'll figure out my age anyway. The point is, even if you can teach an old dog new tricks, you can't overcome the fact that aged joints and ancient habits are hard to overcome. I therefore concede: my moves are still clumsy and the movement slow. Trust me, you won't want to read how many times I steered Mario into the black hole. Ok, I didn't steer him into the black holes but the imprecision of my moves inevitably meant Mario became BH fodder one time too many. How many, you ask? Well, try from 15 lives to nothing and then from 10 to nothing and then another 1 more before I cleared some particularly difficult stages.
And you know what's even better about SMG? The programming folks allow you to return to the game from the last point you left off instead of requiring you to begin from scratch. So you get new frustrations when the positions and techniques don't work and new highs when they do. The mind keeps telling itself that it can top the stage and one reaches for the start button after each game over. The ass is rooted to the seat and the mind loses all track of time. (Maybe, Wii and a slower version of SMG can be introduced to old folks' home to keep the residents engaged. Maybe not; they might fight over who's turn it is.)
Yet, the amazing graphics aside, the trick is to know... the tricks. The programmers are not very smart. I've got them figured out mostly. In certain worlds or galaxies, I pick up so many lives that I was incredibly elated. At the same time, I knew the extras would never be enough; how does one pick up extra lives quickly enough a whole game when one needs 26 of them to clear some particularly tricky stage? I don't know how I managed to clear some of those inhuman stages, but I did.
One can usually progress after mentally working through the algorithm required to clear that stage; keeping Mario alive long enough to clear the stage is the larger problem for me. Unfortunately, though, mental dexterity did not make up for the lack of finesse in the finer movements. The fingers were not stiff - digital (pun intended) gravity works differently, I'd say. Of course there are many excuses. This is where I spend all my time moaning about my exciting life, regardless how exciting it really is. Did you expect otherwise?
For all the fun and pleasure it brings, SMG is a silent time killer. I take anywhere between 45 minutes and 3 hours to clear a stage and I've sat in front of the Wii for almost 6 hours yesterday. That is bad. Extremely bad, if you ask me. And at 1.30 am this morning, when I tried to sleep after my shower, all I saw when I shut my eyes were the stars and the coins I was supposed to pick up in the games. My mind was all hyperactive; I can't get to sleep. The brain was devising ways to pick up stars and coins in the various configuration set by and for itself.
At that moment, I think I'm getting out of control. I need to do something quick. I got out of bed, removed the Super Mario Galaxy CD, returned it into its cover and asked for it to be returned. I can't be addicted to it. I can play other things like Wii Sports. That's fine, because there is a limiting factor called physical exhaustion. Wii Sports require you to mimick the actual sports action and with such physical activity, you get worn out and at the opportune moment, you'll decide you've got enough of a workout, turn off the Wii and resume life. SMG does not wear you out. It makes you addicted. And I worry about addiction.
So, there'll be come cold turkey today. And I'll be back to Wii Sporting.
Oh, did I tell you I chose Princess Peach as my avatar? I wanted to choose Queen Bitch if it (Note at edit: Oh man, that's a Freudian slip!) existed. But then what would I do with Q**nsy? Sigh. So, Princess Peach... that's right. Sounds like Princess Bitch anyway.
This semi-addiction seems worse than I imagine...
Welcome to my Super Mario Galaxy semi-addiction.
The game started slowly enough. The moves were initially clumsy and the movement slow. But trust me, at the grand old age of... heck, you'll figure out my age anyway. The point is, even if you can teach an old dog new tricks, you can't overcome the fact that aged joints and ancient habits are hard to overcome. I therefore concede: my moves are still clumsy and the movement slow. Trust me, you won't want to read how many times I steered Mario into the black hole. Ok, I didn't steer him into the black holes but the imprecision of my moves inevitably meant Mario became BH fodder one time too many. How many, you ask? Well, try from 15 lives to nothing and then from 10 to nothing and then another 1 more before I cleared some particularly difficult stages.
And you know what's even better about SMG? The programming folks allow you to return to the game from the last point you left off instead of requiring you to begin from scratch. So you get new frustrations when the positions and techniques don't work and new highs when they do. The mind keeps telling itself that it can top the stage and one reaches for the start button after each game over. The ass is rooted to the seat and the mind loses all track of time. (Maybe, Wii and a slower version of SMG can be introduced to old folks' home to keep the residents engaged. Maybe not; they might fight over who's turn it is.)
Yet, the amazing graphics aside, the trick is to know... the tricks. The programmers are not very smart. I've got them figured out mostly. In certain worlds or galaxies, I pick up so many lives that I was incredibly elated. At the same time, I knew the extras would never be enough; how does one pick up extra lives quickly enough a whole game when one needs 26 of them to clear some particularly tricky stage? I don't know how I managed to clear some of those inhuman stages, but I did.
One can usually progress after mentally working through the algorithm required to clear that stage; keeping Mario alive long enough to clear the stage is the larger problem for me. Unfortunately, though, mental dexterity did not make up for the lack of finesse in the finer movements. The fingers were not stiff - digital (pun intended) gravity works differently, I'd say. Of course there are many excuses. This is where I spend all my time moaning about my exciting life, regardless how exciting it really is. Did you expect otherwise?
For all the fun and pleasure it brings, SMG is a silent time killer. I take anywhere between 45 minutes and 3 hours to clear a stage and I've sat in front of the Wii for almost 6 hours yesterday. That is bad. Extremely bad, if you ask me. And at 1.30 am this morning, when I tried to sleep after my shower, all I saw when I shut my eyes were the stars and the coins I was supposed to pick up in the games. My mind was all hyperactive; I can't get to sleep. The brain was devising ways to pick up stars and coins in the various configuration set by and for itself.
At that moment, I think I'm getting out of control. I need to do something quick. I got out of bed, removed the Super Mario Galaxy CD, returned it into its cover and asked for it to be returned. I can't be addicted to it. I can play other things like Wii Sports. That's fine, because there is a limiting factor called physical exhaustion. Wii Sports require you to mimick the actual sports action and with such physical activity, you get worn out and at the opportune moment, you'll decide you've got enough of a workout, turn off the Wii and resume life. SMG does not wear you out. It makes you addicted. And I worry about addiction.
So, there'll be come cold turkey today. And I'll be back to Wii Sporting.
Oh, did I tell you I chose Princess Peach as my avatar? I wanted to choose Queen Bitch if it (Note at edit: Oh man, that's a Freudian slip!) existed. But then what would I do with Q**nsy? Sigh. So, Princess Peach... that's right. Sounds like Princess Bitch anyway.
This semi-addiction seems worse than I imagine...
Wednesday, November 19, 2008
Am I really crazy?
Find out more about yourself at The IPIP-NEO.
My results are published in the link "Understanding Teflonman" in the left margin.
Special thanks to Probligo for this, cos I found my way there from his blog.
My results are published in the link "Understanding Teflonman" in the left margin.
Special thanks to Probligo for this, cos I found my way there from his blog.
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