Summary of Alan J. Bishop's "Western Mathematics: The Secret Weapon of Cultural Imperialism"

Western mathematics, as part of western European culture that perpetuate imperialist goals, is seen as a secret weapon which maintains the imposition and domination of western cultural values on indigenous cultures around the world. Bishop used the term “secret weapon” to reveal how, even today, the belief that mathematics is a culturally neutral knowledge persists in contemporary schools.

This perception stems from the fact that universal validity of mathematical truths, which are abstractions from the real world, seemingly makes the knowledge as though it is neutral and context-free. To say, for instance, that a kilo of wild bananas harvested in Guinea Bissau equates to 2.20462 pounds is valid everywhere. However, it should be noted why kilo and pounds are used for standard measurement of mass and why the conversion from kilo to pound always equates to 2.20462.

The answer to these questions, according to Bishop, essentially points to an authority that determines the standardization of measurement and other mathematical ideas which, like any other ideas, are a product of cultural history and human construction. Mathematics, as Bishop argues, is a cultural product present not only in contemporary schools that uses standard Western mathematics but also in indigenous communities all over the world.

As shown in anthropological literature, alternative mathematical systems exist through the study of ethno-mathematics, defined as “a localized and specific set of mathematical ideas which may not aim to be as general or as systematized as ‘mainstream’ mathematics”. Through ethno-mathematics, we find out that different counting systems in the world exist; for instance, in Papua New Guinea, 600 various cycles of numbers and body-part counting system are documented (Lean, 1991). Also, even the conception of space differs from one culture to another; for instance, Menninger (1969) observed that in contrast to Euclidean geometry which relies on the object-oriented ideas of points, lines, planes, and solids, the Navajos perceive space as something that cannot be divided or objectified. Moreover, in contrast with western hierarchical classification matrix, people of Papua New Guinea adopt a linear form of classification resulting to a different logic and ways of relating to phenomena.

In the Philippines, a study on ethno-mathematics conducted by UP College of Baguio (1991) reveals the existence of algebra in the weaving patterns, gong music, and kinship system of the Kankana-ey in Mountain Province. These studies on ethno-mathematics provide us with better understanding of mathematics as a pan-cultural phenomenon. However, western mathematics, as part of western European culture, has succeeded in internationalizing and standardizing math for indigenous communities around the world for more than three hundred years.

With this, Bishop points to three major mediating agents in the cultural invasion of western mathematics in colonized countries: 1.) trade and commerce, 2.) administration and government, and 3.) education. The commercial field serves as the area where western currencies, measures, and units are employed and imposed on trade and business transactions. In the government, western numerical procedures are used for computation on tracking numbers of people and commodities. Most importantly, it is through education that western mathematical ideas and western culture are propagated. As Bishop views it, western mathematics is “abstract, irrelevant, and elitist” for indigenous students who are educated “away from their culture and away from their society”.

The adaptation of western mathematics by indigenous cultures has had and continues to have powerful implications in the indigenous culture when it comes to education, national development and continuation of cultural imperialism. The clusters of values associated by this system of knowledge have had tremendous impact their logic and ways of thinking. First, western mathematics embrace rationalism as its spirit which invigorates and drive human minds. Second, the value of objectism found in western mathematics forces indigenous cultures to decontextualize the way discrete objects are perceived and abstracted. Lastly, western mathematics emphasizes man’s power and control over his physical and social environment in contrast to other indigenous thinking.

Indeed, western mathematics has remained a powerful and useful tool for almost every country in the world. The mathematico-technological culture has rapidly grown and its implications are now being understood. As Bishop suggests, our responses to the domination of western mathematics should be that: 1.) we create interest in ethno-mathematics, 2.) produce greater awareness of one’s culture, and 3.) re-examine the history of western mathematics. In this way, even as the world has generally accepted western mathematics in its system, recognizing and understanding its implications on indigenous cultures is important for critical debate in education and resistance to cultural hegemony and imperialism.

Sources: 

Bishop, Alan J. 'Western Mathematics: The Secret Weapon of Cultural Imperialism'. Race and Class 32(2), 1990

UP College of Baguio. The Algebra of the Weaving Patterns, Music, and Kinship System of the Kankana-ey of Mountain Province, 1996.

Back to Poetry (#1 - UP Diliman Series)

Strange, Stranger Gazes

In the library 
where books become walls

to people

whose looks resemble

their thoughts:

of finishing homework

and killing time,

of learning ahead

and spacing out.

In this place,

where silence and noise

become idle sounds,

my eyes are lost

among pages and spaces

you move around:

between the shelves,

behind the counter,

beside me.

But these walls keep

its rule of silence

my eyes have to defy.

I learn to speak

your language of gazes:

those tug of wars,

those hits and misses,

those stolen glances

that mock the silence

of this place.

In the library

where walls avenge

the foes of silence,

our gazes are muted

like words of pages 

housed in this place.

We do not belong here –

and words are blind

to the language of our eyes.

 09/10/2012, Sovesal

On Thinking about Thoughts

Language is dangerous. I say this because I am at awe with the realization about how language is used as a misleading tool for us to make sense of the world. There is no truth to the idea that language is what makes humans breathe with "understanding".

Pardon, what I am writing now is a product of raw thoughts converted into language so you can never expect consistency in what I say. See, this is what I want to demonstrate: right now, what I am doing is to make sense of an idea on how the use of language in reading, speaking, and writing is actually a dangerous task. I am doing this by ironically using language as a tool to clarify my idea. Even that, I still argue that this is a dangerous task.

For sure, philosophers might have thought about this idea that I am going to explore now. Well, of course they have, I recognize that. But I have to clarify that what I am about to write here stems from raw thinking; meaning I am thinking while I am typing and see if it makes sense. This thought-to-language-idea stems from me studying my own thoughts and how I make sense of them. It takes me back from what happened last week -- how my doctor cautioned me not to think too much otherwise my brain will send wrong signals to my body. Then I began to think more, thinking: how can I stop thinking? or more importantly, why I am always thinking excessively?

Instances of Thinking

The answer is that I find the truth in thinking -- in the raw forms of thought. I am in love with raw thoughts -- that's why I think a lot. I am in love with thought -- the truth, in its purest form. For instance, I love walking for hours in the morning because in that activity, I am able to foster my love for thoughts. I'll give a more concrete examples, when I walk, I look at nature.. I stop by and think whatever catches my eye. Two months ago, while jogging, I stopped by a small plant because the sun reflected the a shiny thread on it. It turned out that an orange spider was making its home. Until now, I am in love with that moment but until now, I cannot express it in words. This is a lame description of what I saw, of what I realized that day.

Another instance, I was passing by so many trees on the way to our dorm and I realized how nobody really touches these trees when they are living. We fail to realize that they, like us, are breathing too! They also have life but they can't talk, they are solitary, but they have life! I felt that it is so lonely to be a tree and just have a stationary life! But then again, the burden is on us, the people who can move because we have to wander, go somewhere, and find our home! I have already voiced this thought in poetry already when I wrote "Palm Trees" in 2011, but then I felt that the idea about trees and their existence with us is poorly articulated! Having so much time walking around UP and being able to pass by these solitary and stationary trees made me realize that, as a form of apology for grossly articulating my homage to them, I began patting them as I walk. Trees need warmth, I thought, so I slightly jump tap their leaves or lightly touch their branch.

Yes, I thought about those things -- those seemingly mundane occurrences in nature.  But I do not only think about trees and nature, I also think about dirt and trashes I see on the road while I walk. One time, I saw a trail of trash -- broken alcohol bottle, dog shit, biscuit wrapper, dead leaves -- and I wonder if there is a story behind them being there. I thought there must be a story behind these things why they are being dropped there. I thought -- the broken alcohol, the one who held it, surely something happened to him why he dropped it at that place. The dog, when it shat, it was mindless about the act but I wondered about what this lonely street dog ate! (Gross but it's lonely to think about: at night, where does it sleep? does the stray dog wake up and hopeful about the day ahead? About the biscuit wrapper, did a kid throw it and still felt hungry after?

Lastly, the dead leaves, even if lifeless, I thought of its fate -- its fate is to rot, even though the very act of its falling from the twig is, what is known us, freedom. As usual, I have written about dead leaves in an unfinished poem which remained unfinished because I could not fully articulate my thoughts -- the entire idea of what I am going to say -- in words. I talked about dead leaves "creeping for the color of the soil" -- leaves being in the state of decomposition and trying to blend with the soil's color and dying with it and becoming part of it.

Solitary, Dangerous Thoughts

Because of excessive thinking, people (like me) are already physically affected by mere thoughts. By that, I mean that thoughts breed loneliness because of the very reason of its existence. Thoughts are nebulous abstraction of how make sense of the world around us, of our existence, of our being here. The very nature of its existence cannot be "concretized" because they are raw and pure. They are solitary and not "graspable" by anyone or anything. I think about the sad lonely state of our ideas being "in the head" perhaps because I am an Atheist searching for the meaning of existence. I believe that people stick to the idea of having a "creator" lurking around the corner because the thought of someone being there for us is very comforting.

For many people, the thought that humans breathe upon their very thoughts that are solitary, unexplainable, and "unshareable" with other people is almost unimaginable. Being alone with thoughts can potentially kill, can destroy our very existence. It is more comforting for the religious to think that someone is there listening and knowing our thoughts. Comfort then becomes a refuge for many people -- it feeds their spirit. But I am not like many people. I am queer in my love for thoughts which others despise -- that's why they look for other people and share their views on things so the thought or idea won't be alone.

I am an atheist who has somehow resigned to the existentialist view on things: there is no meaning in our existence and it is us who create that meaning in our lifetime. Life is here and now. This is heaven and hell. When we die, we die like the leaves "creeping for the color of the soil". But why are human beings burdened by having thoughts? Why we? I still could not grasp that purpose. If I look at it in a rational manner, it is because through time, the human brain has acquired the mental capacity to fully grasp the things around us. That is why we have reached this level of civilization because humans fought with the loneliness of thoughts and, through time, created our preoccupation (and distraction) -- the technology. I could go and on with that discussion, but what if I will answer that purely from a philosophical perspective? Why are we given these lonely thoughts? If we look at it, these are the ones that somehow humanizes us because in it, we feel genuine sadness as well as love for mundane things that exist around us.

Dangers of Language

But is it useful to contemplate deeply, excessively, and fall in love with our raw thoughts? From my experience, no.. thinking does not do anything good for my physical health. But, in a way, I still marvel at the idea how pure our thoughts are and how language can subject it to danger. I am talking about the conversion of our thoughts. Thought brings about loneliness that we all avoid, either because we despise loneliness and our culture dictates that we aim for the "pursuit of happiness" OR being alone with mere thoughts naturally poses danger to our existence, to our physical health.

Because of the tendency for people to avoid being alone with thoughts, the natural mechanism is to convert it into language -- so that the thought will be free and it can interact with other ideas that will be useful to the existence of humanity. Language is an indispensable tool that made our existence, the human civilization, possible. I recognize that. I also recognize that using language is the only activity we can do to concretize our thoughts.. to give meaning to it.. to voice it out.. to let it free.

But then language itself is an obstacle and the word I will use to describe it is "dangerous" because of its very nature to be dynamic, to be fluid, to change. Earlier, I have established how thoughts in itself already present danger and uncomfortable feeling to those who possess them and love them (i.e. thinkers and writers suffer from mental illness precisely because they are alone with their thinking). I will argue that also the act of "freeing" thoughts through language is equally dangerous because it misleads our thinking, our decisions, then our actions, and our lives in general.

 1.) The act of converting thought to language

The first process that people naturally do to free their thoughts is to convert it into language. However, language is a limited tool because it cannot fully articulate an experience. We use language to voice out our thoughts through speaking. We also write to objectify thoughts through letters and words. Speaking poses more danger than writing because it is spontaneous. The conversion of thoughts to language is thought to be simultaneously existing with our thoughts. Conversion in speaking happens in a flash. Writing, on the other hand, takes time to complete.

I see the danger in speaking because contemplation is lacking. Remember, thoughts are already dangerous and when your thoughts become unexamined, they lose their true meaning. It is sad how society has somehow privileged the act of speaking than writing. In our daily lives, those people who interact well and who are "in control" of their thoughts and language appears to be the confident one, whereas the people who have a hard time gathering their thoughts are considered less. I am one of the people who is having a hard time with her thoughts while speaking. I feel like I am always in danger when I speak because I feel the need to ascertain my conversion of thoughts into language. I never noticed that, until in college, my good friends pointed how there are times that I am blabbering the things that I want to say. My mind is disoriented and I am too cautious with my conversion of thoughts into language.

On the other hand, we can look at writing as one of the activities that is closest to thought. But still danger lurks in writing because language, through letters, tries to make the thought "visible" or "graspable". The danger for the conversion of thought to writing lies in the fact that once thought is converted into language, it is now being objectified and becomes the subject of articulation. This is dangerous because the conversion itself is not what is really meant -- it is not the raw thought and we do not have the capacity for the conversion (earlier, I have established that how the thought is solitary and "unshareable" -- that is my basis for saying this sentence).

I have to say though that the closest way that language can articulate experience is through poetry. Poetry aims to create an experience out of words. That experience is capable of replicating raw thoughts that will imitate the original experience of the writer. But then the original thought lies on the writer, what we feel after reading a great poem is a poor replica of an experience. Some might argue that at least an experience is still created BUT it is very rare among us to be moved by an experience. The impact of a poem varies from person to person, depending on the level of concentration, level of understanding, the context, and the experiences that one has. The effect of a moving results to raw thoughts, that when we try to articulate more, we will doubly fail in misery.

2.) The act of concretizing language  

Because conversion is insufficient and unreliable, it can be said that speaking or writing the thoughts through language is misleading and unreal. For instance, most of us do not know what we do in life simply because language is incapable of making sense about what our thoughts wanted say. If what we try to say and write are unreal, the danger lies when these unreal "thoughts" are concretized into language. Concretization means that the thought is "released" through language by hearing the "thoughts", recording the "thoughts" and writing the "thoughts".

Once the illusion is created that the "thought" is free, people around us will now have the basis, on written or verbal record, about our supposed "idea". The assumption that what is written or heard is real can be dangerous because thoughts are subjected to influence. People around a person will take note of the "freed thought" on the assumption that it is the clear and right idea of a person. With this concretization lies the danger of influence because people will play with the idea through discourse and communication. Hence, the "fallacious" thought is being reinforced, played, and upheld!

3.) The role of influence and manipulation

Since thoughts are, by nature, unarticulated and unshareable, there is danger for it to be inconsistent through the process of converting it into language. Now, people around you who are misled that what you are speaking or writing are real can be the same people who can make you feel at loss. This is because they are misled by the conversion of language and we too are misled by other people's conversion of language. That is why misunderstanding is very prevalent in the society because our thoughts can never be fully realized or converted into language.

The danger of being miserably misled to take the wrong path lies in our articulation of thoughts. Once you articulate what you want, it does not always the thing that you really wanted... but then you concretize it and people assume that that is such. Then, they will try to feed your "thoughts" (the inconsistent once) with their own (which is also inconsistent!)

Love is in Thought

In my previous blog, I have articulated my thoughts on love and nature -- that love is imitative of nature in the sense that its existence is effortless. But now I realize that love resides in pure thought -- the raw ones, the real feeling -- that is free from language!

I guess I have to end my speculation about thoughts by quoting my previous essay about love -- simply because further discussion about thoughts and love require more intense love for thoughts, which I consider to be dangerous.

"I long to witness that moment when one actually reaches for the same wavelength -- without saying anything because words, in itself, do not have pure intentions, in the same way that raw thoughts and inner feelings have. The moment you convert feelings into words, it loses its natural form -- that is why we have poets who, with all their might, try to capture emotions in its purest form through poetry, but still couldn't quite make sense of an experience. 

This process makes writing more powerful than speaking because of internal communication and because of the time spent thinking about words closest to the thought. Composing words, as they are, is an attempt to physically manifest thoughts, but it is not the actual and pure thought you held deeply. Meanings are concealed in words and it is only through sensitivity that we can unlock its true intention and significance."

Sharing a Poem Written for me by a Dear Friend

Will forever be thankful to a good friend of mine who was able to articulate my emotions and capture them into words.

[Untitled]

That fountain behind you knows
better than the two of us, gushing
on the edge of your shoulder
where I have always imagined
my head
leaning,
asleep.
Water gives in
to the pull
and it’s beautiful
with surrender, yielding
to greater law such as leaves,
rain, footsteps, teardrop. Lump
falling and rising in our throats, sigh
rising and falling in our chests,
making us familiar
strangers: how dare
we allow ourselves
to float and refuse
to land?


 - Roger Garcia

Introduction to Postcolonial Theory: Departing from ‘Points of Departure’

The task of writing a reaction and summary to An Introduction to Postcolonial Theory has allowed me to go back and reflect on my initial impressions prior to enlisting CL 123 as a determinant subject for pursuing a graduate degree in comparative literature. It dawned on me that my understanding of postcolonial theory has always been leaning towards what is obvious and simplistic. Postcolonial to me then meant after the end of colonization in areas which are formerly under the colonial control of the West.

One cannot be faulted though for having such a simplistic view about what postcolonial theory is. After all, this literal understanding of what is postcolonial stems from derivation of words to acquire meaning; such that ‘post’ is understood as a prefix of ‘after’ and ‘colonial’ is characterized as ‘a territory under the complete control of a state’. In my view, the entire debate about the scope and definition began the moment ‘post’ was attached after the word ‘colonial’ to describe the study of colonial discourse.

 For one, the prefix ‘post’ directly entails a complete end of colonization which then implies that the period of European colonial control and domination is entirely over. However, as what the authors of the introductory reading emphasize, the “persistence of colonialism” is, up to now, still apparent through indirect economic, political, and cultural control of Western powers over its former colonies. In this sense, colonialism has not actually left us, but has merely evolved in a more deceptive form known as neocolonialism, a phase of imperialism that aims to globalize capitalism. As Gayatri Spivak puts it, “we live in a postcolonial neo colonial world”, which means that colonialism is still with us – fully present, ever-changing, and deceptively pervasive.

Although it is determined that the attachment of ‘post’ to ‘colonialism’ makes the definition of ‘postcolonial’ problematic, there is absence of an alternative term to describe the complexity of history and diversity of experiences in different areas which are subject to colonial control. It is a clear misfortune that there is a limit to what our language can actually define or describe. As such, it is quite understandable, in my view, that the term postcolonial is used to describe the entire study of colonial discourse, provided that if asked ‘when is the postcolonial?’ the answer should altogether include the “then” (colonial), “now” (postcolonial), and “not quite yet” (neo colonization). 

From what I understand in the introductory reading, the “in-betweenness” of the postcolonial period is exactly what characterizes it as an “anticipatory discourse” that incessantly searches to describe a condition that does not yet exist or has not yet come into being. With this, it is important to emphasize that the role of postcolonial discourse is for the “reflection and illumination” of colonial, postcolonial, and neocolonial subjects as well as their resistance against the dominant colonial forces in these historical periods. 

Moreover, it should be remembered that even with such broad periodization of postcolonial history, our understanding of postcolonial terminology can still remain problematic because some literary critics attempt to generalize the answers to when, where, who, and what is postcolonial. To generalize the complex and ambiguous experiences of colonial subjects is to miserably fail in seeing the different histories and conditions of colonization in various parts of the globe. The attempt to generally define and describe the colonial situation is impossible given the subjective experiences of colonial subjects and the complexity of their histories.

In attempting to know when is postcolonial, we are faced with the fact about the incompleteness and unevenness of postcolonial period. In attempting to locate the where is postcolonial, we are presented with the complexity in the shift from the idea of nation state to transnationalism. In attempting to answer who is the postcolonial, we are faced with “unsettling identities” of colonial subjects who are faced with the task of recovering and creating their own identities.

Lastly, in attempting to answer what is postcolonial, we are presented with the impossibility of defining an ever-changing term which, according to Spivak, is “never consistent with itself”. As long as colonialism continues to remain elusive, our understanding of what is postcolonial will remain to be uneven and incomplete. However, it is reassuring to know that the role of postcolonial discourse in the academe is to contribute in our understanding to reflect, recognize, and resist colonialism in all its mutated form.

Source: 

Childs, Peter; Williams, Patrick. Introduction To Post-Colonial Theory. London : Prentice Hall/Harvester Wheatsheaf, 1997.