Notes on Vertical Urban Farming

I was at the City Hall area yesterday when the haughty edifice by architect Moshe Safdie caught my eye. This edifice comprises of three imposing towers standing adjacent to the other towering maybe 60 stories into the air. On their common top straddles a vast, cantilevering plateau of steel and concrete. The next thing that I noticed was its still unadorned, unpainted and likely unfinished skin. Then an idea struck me: what if some of the skin of this vast building complex is used for vertical, urban farming?

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Imagine that we have 3,000 buildings in Singapore. Further imagine that each of these buildings is 10 stories high and the height between each storey is 2m. Lets also assume that each building has a linear footprint of 100m. And for simplicity’s sake lets also assume that this footprint is rectangular in shape and with the longer sides measuring 40m each. Hence without including the shorter sides, each building has 40m x 20m x 2 vertical surfaces, which is 1,600 square meters. If we add this number up for all 3,000 buildings in Singapore, then the aggregate number is 1,600 x 3,000, which is 4.8 million square meters.

4.8 million square meters is also 4.8 square kilometers of surface. This is still a tiny number in tiny Singapore with about 710 square kilometers of total land area.

But my calculations are erring on the conservative side. It is likely that we have much more vertical surface aggregating beyond 3,000 buildings of 10 storey each. I take into consideration all the public housing estates, the private estates and most of the commercial, public and private, non-classified buildings in this city-state.

It is in fact worthwhile to discover the exact number. But for argument’s sake lets imagine that my margin of error is 100% lower than the actual number.

If so, then in land-scarce Singapore, we have nearly 10 untapped square kilometers of surface now. This number is sure to increase with a continuous increase in population density. And you know what, as far as air space is concerned, there is no upper limit on this number…

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Sometimes ideas are weak and discounted as fictional or unrealistic because they stand in isolation to other ideas. But when these ideas are put together like hands and feet, things can work.

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Assuming that we dedicate these 10 square kilometers to intensive, high-yield urban, vertical farming. Lets further assume that about 51% of the citizens buy into this idea and would willingly—and profitably—contribute some of their time in the week (instead of shopping) to organize and work in this effort. Even so, we are talking of 1.6 million people working on this farming venture at any one time—would this not be the largest industry, spurring domestic demand then in Singapore? With a rising grey population and a longer but uncertain retirement livelihood in the world today, urban farming can become a sustainable source of income and psychological fulfillment for the golden years.

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I am not an agricultural expert. But I am an architectural designer who realizes that there is a problem of cladding buildings in plastic, granite and glass when the world is increasingly growing hungrier and (will become) bloodier from food conflicts. While my Hobbesian inclinations are clear, it is also clear to me that only architects and urban designers are trained—with support from public administrators and urban agricultural experts—to provide the aesthetical and technical spatial answers for this growing social and global problem.

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I have grown some tomatoes, potatoes and lady’s fingers successfully (in my garden). From this experience in primary school, I realized that Singapore has a full year of growing season.

Critics of urban farming may suggest that the use of water will surely increase exponentially for water-scarce Singapore. They are right. But equally true is that all vertical urban farms can capture rainwater that is lost right now through run-offs from these vertical surfaces. Imagine that half a centimeter of rain falls daily in Singapore for the whole year. That’s an incredible amount of water that can then be channeled for sustaining these farms.

Besides, depending on how these vertical farms are designed together with the façade, they are likely to reduce heat gain and at the same time, also reduce ambient temperatures. Indeed, these vertical farms present before us is a choice between the positive reinforcing cycle of air-conditioning use, or a negative feedback cycle of reducing air-conditioning use.

* * * * * * * *

I mentioned earlier that ideas ought to work together. Here we can begin to count the perks of this proposal:

 

(1)  Reduced emissions from food transportation. With a reduced demand for imported food—especially tonnage heavy agricultural products—we also reduce emissions attributed to trucks and planes carrying these products.

(2)  Eating healthier. This is subjective. But with an available local supply of agricultural products we may come to depend less on processed foods and more on natural foods, thereby also cutting down on paper, plastic and synthetic material wastes. This also means major cuts in emissions.

(3)  Hunger is on the rise in the world today. In a soon to be food-scarce world, increasing a domestic supply of food means food security if and when the barn-houses of the world reduce their exports for a near 100% imported-food dependent Singapore.

(4)  It may even be possible to have surpluses from this effort and to export some of these surpluses. With the market for organic agricultural products expanding in the world, vertical farming, because of its proximity to human activity, must be as organic as it can be. Is this not another place to explore the combination of these two ideas: between organic farming and vertical farming?

(5)  Communities in the city-state can be organized into self-sufficient communities specializing in different produce and strengthening local identities and trusts between people. All said, I do not hold onto a romantic ideal of socially edifying agricultural work. What I am suggesting is a much more modest and pragmatic vision where this can become another avenue for community involvement with tangible perks.

(6)  The probability of a universal carbon credit system is high in the near future. When this finally becomes reality, contributors to this system can exchange rebate-credits based on their individual production yields. This serves as an incentive for working in this socially ameliorative ‘industry’.

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What are some of the problems with this vision? Here, I count a few of them:

 

(1)  Not all buildings can be used for vertical farming. For example, buildings with a security nature; or buildings used for communication purposes and so on.

(2)  Architectural conformity. This is not so much a problem as it is still an open question. Architects have always been able to provide answers that have yet to be imagined. Imagine entire housing estates covered with trellis of tomatoes, lady’s fingers and other vegetables…It may strike some as delicious while some may find it a perverted version of the witch’s house in a new Hansen and Gretel story. But because no effort has been expended in envisioning a cityscape like this, there is still ample room for improvement and compromise.

(3)  Free-riding. Like all public goods, there will be some who would literally want to do nothing yet receive the same pay-offs as those who work on these vertical farms.

(4)  Initial high costs from public investment and private cooperation. But if we build it well and if it can last a long time, how is this different from building a subway or an effective airport?

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Many years ago, an American psychologist by the name of Abraham Maslow came up with a hierarchy of needs. For Maslow, food, water and sleep are foundational needs. Luxury, circus and entertainment(-gambling) for him are surely aspiration wants.

All around the world today we see more trade-offs along this trend: competitive advantages in agriculture traded for tourist-inducing golf-courses and thus, foreign exchange; resources that can be invested in sustainable production being consumed rapidly for higher immediate dividends but poorer longer term returns; and finally, a vast material investment in our visual and spatial productions that have nearly no relevance or gravity to the human condition today.

 

If there is preponderant attention paid on aspiration wants today, surely some attention—and vision—ought to be allocated to foundational needs as well?

            

Notes on My Educational Philosophy

Recently I was asked to render my educational philosophy. 

To write this 'educational philosophy', I reflected on my own teaching experience; and through this reflection, tried to sieve out a few enduring principles and convictions that I believe are at the core of what I practice in teaching and learning. However upon doing so, I realized that these principles, though workable in the classroom, have yet to address many of the concrete perplexities in the world today that education can no longer dismiss. 

For this reason, I started all over again. And here's the version I would like to share with everyone who reads this blog: 

       “We are not what we know, but what we are willing to learn.” -- Mary Catherine Bateson

Philosophy for me is still the love of wisdom. To this I shall just add that we tend to pursue what we love. Thus, my statement of educational philosophy is about the pursuit of wisdom through learning. I do not make this statement solely as a deductive exercise; instead, I shall explain why wisdom ought to be the paramount goal of education today. 

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For the longest time, the Classics was the linchpin of higher learning in both the Occidental and the Oriental scholastic traditions. This changed however with the rise of the sciences and the technical vocations. Today, I believe another change--no less tumultuous and perhaps more urgent--is underway. 

Today, it has dawned upon us that more technology and improved ways of problem-solving are not always ameliorative for the human condition. But to this realization, we have no substantive answer yet. In the absence of a substantive answer, societies have elected to plow ahead faster with more development and better technology--as if by going faster, we can make up a worthy teleology through greater speed. 

This specious teleology centered on unbridled possibility over worthiness, accelerated progress rather than human purpose and technique at the expense of wisdom is the root cause of many pressing problems and risks facing the world today. These pressing problems do not ask for more technique or technical solutions--there are plenty available in every shade and size today. Instead, what these pressing problems behoove is wisdom to question the present course of actions and upon this reflection, to begin making worthy choices based on what we already have. 

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No matter where we stand on the political spectrum today, and no matter what our position on climate change is, it is unequivocally clear that the general human condition will deteriorate in the next 50 years, if not earlier. Even if we discount the predicted ramifications of climate change, an absolute rise in global population over the next two decades will simply imply a greater contestation of common resources (e.g., clean air, water and food). And with contestation frequently comes conflicts. From another perspective, many cities around the world today are wrestling with the repercussions of unplanned diversity and pluralism from globalization. Unplanned diversity and pluralism may inject new energy into the cultural lives of cities. But at the same time they can bring about socially counterproductive conflicts. 

In such a world, there will be competing goods. Even with governance specifically designed to oversee the distribution of resources, hard choices will have to be made. Should resources be consumed preponderantly by the native or the newcomer when both are equal but incommensurable good? And in the event of a climatic catastrophe, to what extent and for whom do we open the borders of our havens to? Is not every human life an equal, intrinsic good? 

Where there are such competing goods, there is likely also tragedy. As a scientific civilization, we have forgotten the vital moderating role of the tragic for the human condition. The tragic, I argue, will become more prevalent in the world of tomorrow. To navigate the tragic does not call for more refined techniques of Operations Research or rational decision-making. To navigate great complexity and resource constraints all amid the tragic inevitability that some goods would have to be sacrificed, wisdom is again required. 

* * * * * * * * * * 

On the other hand, modern education has a tendency to categorize knowledge without truly appraising it. Today we produce new knowledge of every category and discipline, but we have no good way of justifying for any of them. It is also said that the world today moves too fast; we have to learn how to learn because no formal education is ever sufficient for the complexity of practice and life. Learning to learn is still necessary but no longer sufficient for the future. To be sufficient, we need to periodically appraise our acquired knowledge. We also need to know what to do with the knowledge we have acquired and to steer this knowledge towards a sustainable human good, all which are wisdom in action. 

* * * * * * * * * * 

I do not pretend that wisdom is the magic pill. All I have tried to suggest here is that sustained human flourishing increasingly requires the exercise of wise decision-making--wisdom in action that modern education has scarcely made room to provide or teach. This is why I suggest that there is a tumultuous change in the air. The Financial Tsunami of 2008 has demonstrated the foolery of knowledgeable, intelligent men and women without wisdom. But in its wake it has left the palpable burden on educators to nurture wisdom: how can educators nurture or teach wisdom? 

* * * * * * * * * * 

No statement is complete without a few concretely stated propositions. In concluding my statement, I make the following propositions concerning the nurturing and the teaching of wisdom: 

(1) It is unwise to repeat great mistakes or to reinvent the wheel

On this I refer to the classics in every tradition, where thoughtful choices and conversations on nearly every category of human perplexities have already been explored in one way or another by great minds. It is wise to learn from these conversations; it is even wiser to master the foundational ideas underlying them. In the same way, it is wise not to repeat their mistakes. Only one thing the classics cannot provide: that is, how to navigate the novel and treacherous problems technology has burdened upon the human condition today.  

(2) It is unwise to learn alone or to hold a monologue with oneself

On this I deviate from the image of a wise old hermit in his cave. Sustained, independent inquiry is an admirable trait of any learned man or woman; but more impressive and certainly wiser is the willingness to test the outcomes of this inquiry in a community of other learners and thinkers. For this reason, it is wise to learn in a communicative and argumentative environment filled with dissonant ideas. 

(3) It is unwise to remain as an armchair theorist trying to learn wisdom

On this I depend on the phrase, ‘to rise to the challenges’. What are the pressing problems today? What can I do about them? What is the value of my actions and how does this value resonate with a sound vision for the future? What are the anticipated consequences of my actions? What are their ethical repercussions? Are there limitations to what I can do independently and how do I address these limitations? And how and to whom should I pass my mantle in the natural course of things? To test one’s judgments on concrete issues and to act upon them; to anticipate the consequences of one’s actions and to reflect on their ethical repercussions; and finally to prepare in advance for one’s mortality--these have always been the hallmarks of wisdom. 

(4) It is unwise to be cynical

The line between wisdom and cynicism--the attitude of having seen it all and that nothing good can come out of anything--can be very thin. This is especially true today. Therefore, it is possible to say that the road to wisdom today is filled with many pitfalls of cynicism. How to rescue oneself from cynicism is critical for nurturing wisdom. On this I see the teacher playing an important role. This role consists of encouraging the student; of making constructive remarks and rebukes; and of building and envisioning rather than tearing and constricting. Most important of all, the teacher is to demonstrate how and why wisdom leads to life whereas cynicism leads to stagnation and decay. 

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This then is the concise statement of my educational philosophy. 

Protecting our Ecology and the Awareness for Life* (translated)

Protecting our Ecology and the Awareness for Life*

English Translation of 生态的保护与生命的觉醒 by Jeffrey Chan

(original Chinese article by 霍韬晦 appeared on Jan 11, 2010, Lianhe Zaobao, Singapore)

Humanity’s ecological problems are only getting worse. Everyone only sees his or her immediate benefit in a great narrowing of horizons. Except for the brink of disaster, no one is fully aware of today’s predicament. But when disaster strikes, it will be all too late! 

Humanity has entered a new era through the power of technology. But also because of the use of technology, new complex problems have emerged. The most obvious of these problems are: climate change, pollution, melting ice, dwindling resources, sinking land, vast reductions in forest lands, massive desertfication ...All these have caused countless worries: can there still be a tomorrow for the world? One wonders. Can man exist without his environment? 

It is precisely because of these worries that we have the 2009 Copenhagen Summit. The goal of the summit is to reduce global carbon emissions, and to ensure that warming in the century will not rise above the safe limit for survival. 190 countries were presented at the summit; and almost 120 leaders attended in an unprecedented summit that lasted nearly two weeks. But the entourage and convoys surrounding these leaders--bodyguards, bureaucrats, journalists and activists--had already ‘polluted’ Copenhagen. Pollution of planes and cars had antagonized thousands of environmental activists into a destructive display of social conflict with security at the summit. 

The Copenhagen Summit as Political Performance

Even after deploying so many leaders, minds and resources, the regrettable thing is that there is so little to show for it all. Each party in attendance seemed happy to merely say his or her piece without trying to close the mutual distance between parties. Whether it is the developed countries or the developing countries, nobody seemed willing to commit to new mutually binding agreements, nor to accept mutually binding regulations. This has made the plan emerging from the summit hollow and fictitious. 

The failure of Copenhagen has reflected the value of self-preservation and self-protectionism of these individual nation-states. Most of these political leaders are merely ‘performing’ in order to secure the confidence and votes of their respective constituency. For example the United States is the country with the largest emissions; but during the summit, the US has suggested an absolute standard of reduction for individual countries, rather than a relative one according to the needs of (developing) countries. This absolute standard is clearly unfair to China with 1.3 billion people or India with 1 billion in population. Because no one is willing to commit to greater emission cuts, the graver consequences following from this unwillingness will be a rise above the 2 degree Celsius average global temperature mark in this century--the very mark that demarcates a safer world from a more hazardous world. Despite the fact that everyone is claiming to accept responsibilities, reality is nearer to the adage of ‘each for himself and responsibility for the other’. Therefore after the summit, developed countries pointed the spearhead at China and by this act, complicated the Sino-American relationship. 

The truth is that even with a mutually binding accord, this accord will be inconsequential. Observing history, global summits tend to be merely filled with empty talks; it has never been easy to implement a mutually binding accord. Furthermore, implementation demands regulation: but who will perform this regulatory role? Even though the United Nations has the executive power to deploy troops, this executive act still demands the unanimous support of all constituent members at the UN. Moreover, what we are discussing here is the environment, which calls not for military action but political solidarity. And because our pressing problems call for political solidarity, they are therefore political problems that can only be solved by a political act. 

What does this tell us? It tells us that humanity’s ecological problems are only getting worse. Everyone only sees their immediate benefit. Except for the brink of disaster, nobody is aware of the danger. But when disaster strikes, awareness would be too late! 

This situation is likened to the Financial Tsunami. Before it occurred, many had already perceived the dangers. They have even tried sounding the alarm but no one believed them during those prosperous days. It was not until the Tsunami struck that people tried to think of an escape. But then, it had became all too late. 

The Consequences of Greed and Inertia is Foolishness

How is it that humanity is so foolish? This is because of greed and inertia. And this is because everyday reality is always nearer than faraway dangers. And although the individual may be alarmed to these dangerous prospects, this individual nonetheless believes that he or she will be spared. This pathology is the seed of self-conceit and is the root cause of self-destruction. 

The self-destructive tendency of humanity is evident in history. Self-destruction comes not because humanity is unintelligent, nor because humanity is incapable. Instead, it is the over-ambitiousness of mankind that is at the root of self-destruction. The father of Emperor Ching was a very successful entrepreneur and investor. But he gambled by investing in his unborn son. He was of course successful in this gambit because his son turned out to be the emperor that united China. Yet he was forced to death by this same son. Or take the example of the politician Sang in the Ching dynasty, who in order to change the political laws of his country coerced civilians into tools of war and in the same act, legislated draconian laws. However when he lost his political support, he fled to the borders. At the border, he tried to check in to an inn but fearful of what he had done, he did not dare to reveal his identity. Responding to his inability to provide identity the innkeeper said: without your identity you cannot check in, for this is the law mandated by the political Sang (himself)’. It was then that Sang realized that he had just caused his own demise. Or take another example during the Three Kingdoms. Yang Siu, a high official of Lord Cao, liked to flaunt his intelligence and wit. His habit of flaunting caused him to make many reckless remarks. In the end, one of these remarks exposed the hidden schemes of Lord Cao and Lord Cao put him to death. The stories of such self-destruction are too many. As the proverb goes, ‘making the law that causes one’s demise’ (作法自毙), many tyrants, usurpers, manipulators and flatterers all walked this path of self-destruction. 

This is one of the greatest mystery of life. In Buddhism, it is said that along with greed, passion and infatuation, humanity has 84,000 other anxieties and worries--all but one can cause one’s destruction. In Christianity, it is said that the original sin caused mankind to be expelled from the paradise of Eden to wander the ends of the earth. In Confucianism, it is said that to the one who causes his self-demise, he must accept the fruits of his own destruction. Even so, it is plain to see that for some reason, mankind has been unable to transcend the boundary of his limitation. Are not all the inventors of complex financial instruments very intelligent individuals? But the cause of the Financial Tsunami is also because of these intelligent individuals. In the same way, the ecological crisis and climate change are also the fruits of intelligent men and women. For unlimited profiteering and creature comforts in life, individuals of the past do not mind polluting the Earth or exploiting its resources. Today, it will become necessary to sacrifice many times more than these paltry profits and comforts in order to redeem the Earth. 

The Chinese has a saying: if one is to know beforehand his predicament today, why would he (want) take the same action yesterday? But mankind never has a ‘beforehand’. All criminals are those that try the law. Beside, innovation (in technology) is always well-justified: after all, civilization must progress, life demands improvements and prosperity must increase...These are all great justifications. But in the end, all these are merely seductive packaging--packaging that causes one’s own seduction and inevitable demise. 

Mankind is weak. To satiate this weakness is natural; but unlimited satisfaction leads to decadence and destruction. 

I am not suggesting for the regression of civilization. The philosopher Lao Zhi once said that man must return to his original state of nature, or to the idea of the noble savage where he would be just as innocent and pure as a baby. Clearly this is merely an empty thought experiment because who would want to go against his nature of growth? But this is not unthinkable if mankind attains change through education and enlightenment (教化). 

Where would we find this education and enlightenment? We would find them in religious thinking and philosophy, and in Confucianism. But in the modern society where extrinsic success is so valued, the voices of religious thinking, philosophy and Confucianism are remotely small: who can hear them? Confronting now the dual challenges of mankind--both the threat to ecology (environment) and life--are you willing to become ‘aware’? 

How do we find optimism in pessimism? And how do we stand firm before temptations and seductions? These are the perennial questions that have yet to be satisfactorily answered. In the same way, these questions also stand as veritable tests for mankind’s culture and civilization. But if culture and civilization cannot aid mankind in these tests, do we still have a use for them? 

2010 has already arrived. To the one who has rightful ambition this is food for thought. 

霍韬晦 (Huo TaoHui) is the Research Director of Singapore East Asia Research Institute (新加坡东亚人文研究所)

Translated by Jeffrey Chan

*Translator notes: 

(1) I translated this chinese article for non-commercial reason and because this article parallels my own interest. It is also because I cannot afford the english translation by some online software from the newspaper company. 

(2) I have taken a direct translation rhetoric, and hence a few lines here and there may seem rather awkward in english. 

(3) I have translated 生态 as ‘ecology’ in some places and in other places, interpreted as ‘the environment’. 

(4) For bi-lingual readers, please comment and correct my translation where possible and needed. 

Life as Decision(-making)

Decision-making has been studied at least in psychology, organizational science, behavioral economics, design theory and of course, in ethics. All these different disciplines try to formulate general decision-making mechanism into something explicit and tangible. Yet certain decision-making remains as elusive as ever, especially for decisions that cannot be symbolically represented or circumscribed by clear decision parameters.

Consider this classic case. Describing his encounter with a young man who was split asunder between staying with his remaining family or departing for a noble (albeit risky) mission during WWII, Sartre had only this to say to the young man: "You are free, so choose; in other words, invent. No general code of ethics can tell you what you ought to do; there are no signs in this world." (existentialism is a humanism, pp. 33)

Or consider another case. This one is by Joseph Fletcher whose example is really quite beautiful not to quote in full. Here goes:

"It is night, black dark. A man (you or I) is in a small boat, drifting down toward a roaring waterfall. He can hear, but he cannot see or be seen. He is wide-awake. Any choice he makes may be meaningless. If he rows, madly and no matter how hard, he may be swept over the edge. If he does nothing at all, he may be wedged safely against a rock until daylight and rescue come. He cannot know what to do. The current carries him along whatever he decides. It is impossible to ask for time out until he can pretest alternatives. And after all, not to choose either way is to choose one way. Not to make a decision is itself a decision. He cannot escape his freedom. He is bound to be free." (situational ethics, pp. 154)

Neither case is a comfortable one for the conscientious decision-maker. Sartre asks us to invent. But this suggestion merely further begs the question: 'on what premise ought my invention be based upon?'. Is there an invention without reference or premise? Can there be one without reference or premise? Can we just simply invent out of the blue? To invent with neither reference nor premise is not inventing; it is like...burping (defined: as an uncontrollable and non-cognitive bodily phenomenon). Hence does the Sartrean freedom ultimately commit us to decision-making as burping? I don't think so. While Sartre's point is well-taken, he has merely demurred on the real decision to be made. 

In contrast, Fletcher's case is only descriptive. I suppose most human beings caught in Fletcher's case err not so much in 'he cannot know what to do' rather than 'he does not know what to do'. Furthermore, no human being has the freedom not to choose, so to speak. Because of this, I conclude to the opposite of Fletcher: the human being is not free, because he cannot not choose. In other words, he or she can never do nothing (because even doing nothing is doing something). 

Although it is tempting, I do not intend to explain the bad things happening in the world today by scaling up from these two cases demonstrating the perplexities of decision-making (even if we tried). Neither am I trying to insinuate that freedom is a metaphysical form of non-action. All said, these two cases do show that for the most perplexing decisions we can ever make, they are often only good guesses even when made under the most calculative conscientiousness.

Hence should we stop making decisions? I believe I have showed that it is impossible not to make one. How can we make good decisions? I believe I have showed that nobody--at least not yet--has a good answer for this question. 

Finally, what is the take-away point on this issue? On this question I think I have a pragmatic answer: be gracious--to all if possible--for no one yet knows how to make a good decision. 

Steward or Sorcerer's Apprentice?

Recently, my teacher pointed me to a book titled, Steward or Sorcerer's Apprentice? The Evaluation of Technical Progress: A Systematic Overview of Theories and Opinions by Dr. Johan Hendrik Jacob van der Pot (1994). This is truly as magnum opus as it comes: two volumes of nearly 1,500 pages and 247 chapters in all. For those who may question why would anyone be interested (or touched) to write such a work, consider this fact: JHJ van der Pot himself was inmate at 6 concentration camps during World War II and survived. For what he has seen or heard in these 6 camps, the very idea of questioning technological progress should now be doubtlessly clear. 

Here, I attach an excerpt from Chapter 193, a rather timely piece from the 1970 on today's health care debate. 

"Where once the refinement of tools was intimately related to our housing, agriculture, hunting, and sheer survival, today our tools have become separated from basic human needs. As middle-class tool makers and users have risen to affluence, burgeoning technical means have displaced human ends to become ends in themselves, symbols of 'development', 'progress', and 'science'. Even those techniques ostensibly dedicated to the preservation of human life and healing are clearly considered of more intrinsic interest and merit than the human beings they are supposed to save... The conclusion is unavoidable. There is more joy (and money) in elaborating a technique than in giving thousands of desperate people more life, health, and strength through the application of that technique. Technological 'progress' has been running further and further ahead of the people it is supposed to serve, who have died of neglect and malnutrition while a heedless profession ogled at the latest gadget. Medical costs climb out of sight in geometric progression partly because hospitals must be tooled up with the latest devices and people must be trained to use them. 'The best way' must be employed even if the patients who receive the benefits are relatively few, and relatively rich or lucky. One gets the unpleasant feeling that the real function of the patient is to test the technique and be occasionally televised as a symbolic tribute to medical research. It is no coincidence, then, that modern America produces techniques of staggering sophistication, side by side with unmet needs of equally staggering yet tragic proportions, for which there are no available techniques or resources. This inexorable divergence between what is feasible technically and what is needed humanly is the result of groveling before the God of Technique, of resolving what to do next by following meekly the direction in which the tool itself pointed, even though it pointed away from human needs towards the 'opportunity' of a circus in space and other distractions."  

- Charles Hampden-Turner cited in Chapter 193: The Mismatch Between Modern Technology and Real Human Needs in Steward or Sorcerer's Apprentice? The Evaluation of Technical Progress: A Systematic Overview of Theories and Opinions (1994) by J.H.J. van der Pot

The Purpose of Mathematics Education?

I am not a teacher of mathematics. I am also neither a philosopher of mathematics nor a designer of math questions. I am not even good at math.

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?

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. 

But the Penguin Great Ideas series seems to have it all: classic content in a nifty format always packaged in beautifully illustrated covers. Now even the few I have find their home inside my favorite chocolate box, which is a bonus for any organized bookshelf. 

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)