We had previously talked about problem with contexts given in mathematics problems. This is not new, Thorndike in 1926 made similar observations.
Unreal and Useless Problems
In a previous chapter it was shown that about half of the verbal problems given in standard courses were not genuine, since in real life the answer would not be needed. Obviously we should not, except for reasons of weight, thus connect algebraic work with futility. Similarly we should not teach the pupil to solve by algebra problems which in reality are better solved otherwise, for example, by actual counting or measuring. Similarly we should not set him to solve problems which are silly or trivial, connecting algebra in his mind with pettiness and folly, unless there is some clear, counterbalancing gain.
This may seem beside the point to some teachers, ”A problem is just a problem to the children,” they will say,
“The children don’t know or care whether it is about men or fairies, ball games or consecutive numbers.” This may be largely true in some classes, but it strengthens our criticism. For, if pupils^do not know what the problem is about, they are forming the extremely bad habit of solving problems by considering only the numbers, conjunctions, etc., regardless of the situation described. If they do not care what it is about, it is probably because the problems encountered have not on the average been worth caring about save as corpora vilia for practice in thinking.
Another objection to our criticism may be that great mathematicians have been interested in problems which are admittedly silly or trivial. So Bhaskara addresses a young woman as follows: ”The square root of half the number of a swarm of bees is gone to a shrub of jasmine; and so are eight-ninths of the swarm: a female is buzzing to one remaining male that is humming within a lotus, in which he is confined, having been allured to it by its fragrance at night. Say, lovely woman, the number of bees.” Euclid is the reputed author of: ”A mule and a donkey were going to market laden with wheat. The mule said,’If you gave me one measure I should carry twice as much as you, but if I gave you one we should bear equal burdens.’ Tell me, learned geometrician, what were their burdens.” Diophantus is said to have included in his preparations for death the composition of this for his epitaph : ” Diophantus passed one-sixth of his life in childhood one-twelfth in youth, and one-seventh more as a bachelor. Five years after his marriage was born a son, who died four years before his father at half his father’s age.”
My answer to this is that pupils of great mathematical interest and ability to whom the mathematical aspects of these problems outweigh all else about them will also be interested in such problems, but the rank and file of pupils will react primarily to the silliness and triviality. If all they experience of algebra is that it solves such problems they will think it a folly; if all they know of Euclid or Diophantus is that he put such problems, they will think him a fool. Such enjoyment of these problems as they do have is indeed compounded in part of a feeling of superiority.
– From Thorndike et al. The Psychology of Algebra 1926
Month: January 2019
Dialectic vs Algorithmic Mathematics
Dialectic mathematics is a rigorously logical science, where statements are either true or false, and where objects with specified properties either do or do not exist. Algorithmic mathematics is a tool for solving problems. Here we are concerned not only with the existence of a mathematical object, but also with the credentials of its existence. Dialectic mathematics is an intellectual game played according to titles about which there is a high degree of consensus. The rules ol the game of algorithmic mathematics vary according to the urgency of the problem on hand. We never could have put a man on the moon if we had insisted that the trajectories should be computed with dialectic rigor. The rules may also vary according to the computing equipment available. Dialectic mathematics invites contemplation. Algorithmic mathematics invites action. Dialectic mathematics generates insight. Algorithmic mathematics generates results.
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School as a manufacturing process
Over most of this century, school has been conceived as a manufacturing process in which raw materials (youngsters) are operated upon by the educational process (machinery), some for a longer period than others, and turned into finished products. Youngsters learn in lockstep or not at all (frequently not at all) in an assembly line of workers (teachers) who run the instructional machinery. A curriculum of mostly factual knowledge is poured into the products to the degree they can absorb it, using mostly expository teaching methods. The bosses (school administrators) tell the workers how to make the products under rigid work rules that give them little or no stake in the process.
– (Rubba, et al. Science Education in the United States: Editors Reflections. 1991)
Indiana Jones and The Art of Looting
The swashbuckling hero in form of Indiana Jones fascinated me as I was growing up. I always thought why do people stop him from doing what he is doing? All that he is doing is taking the various archaeological treasures to their rightful places, namely, the museums in the West? I always thought he must be right when overcoming all the obstacles that those villainous natives and those forbidden locations place in front of him. What better places that the relics have than in museums where people can admire them and they can be cared for. But now I ask this question
Was Dr. Jones right in the first place to remove the relics from the places where the people who made them placed?
I would like to reflect on a few themes which are implicit in the movies. They reek of a worldview which is colonial assumes a moral, ethical and cultural high-ground for the actions shown in the movie. The zeitgeist of the era is very well reflected in the movies. We reflect on the idea of culture and its implications on ideas about other people.
First of all the movies reek of the idea of cultural superiority. The Western culture is imposed on the rest of the world, as it is due to the colonial past. The very idea or removing an artefact which might be of deep significance (religious, spiritual or otherwise) for purposes of displaying it in a museum reeks of cultural insensitivity on one hand and absolute dominance that the West has over other cultures on the other. It plainly states “We don’t care what you think.” White man’s burden is imperative in the series, in which it is upto Jones to liberate savages from their artefacts. This I think is no different than the maxim of the US: Our oil is under your land.
The movie franchise presents and justifies a completely Western view of the world where rest of the world is full of (ig/noble?) savages. This is no different from the zeitgeist of the era in which Dr Jones operates. The very idea of anthropology as a scientific discipline was taking shape during that era. European colonialism was at its peak at the beginning to mid of the twentieth century. Set in this context the film franchise does just reflect the zeitgeist of the era. But to celebrate it in a post-colonial era is a different game. Should we look at Dr Jones as a hero or a thief who specialises in vandalising places of worship and steals cultural symbols of deep spiritual significance?
Thomas Kuhn on the role of textbooks in science education
The single most striking feature of this [science] education is that, to an extent wholly unknown in other fields, it is conducted entirely through textbooks. Typically, undergraduate and graduate students of chemistry, physics, astronomy, geology, or biology acquire the substance of their fields from books written especially for students.
Thomas Kuhn The Essential Tension
Here Kuhn is trying to show us the nature of science education which is usually divergent from the historical processes and events which led to the currently accepted theories. Most of the textbooks rather show the content matter which makes sense conceptually in a rationally organised manner. Of course, the ideal goal, at least in the physical sciences, is to create a hypothetico-deductive model in which a given theory, its predictions, explanations and implications can be derived from some basic definitions and axioms. For example, an introductory text on motion in physics usually starts with definitions and assumptions usually of a mass point, and/or operations that are defined on it. The text does not describe the historical conditions in which this conceptual approach arose, rather it adapts a very pragmatic pedagogical approach. It defines the term and ends it there, but in this process, it redefines the conceptual history. This approach assumes that there is no pedagogical merit or role in introducing a concept in its historical context. This perhaps is also linked to Poppers distinction of the context of discovery and the context of justification. What we see is a rational reconstruction of historical processes to make sense of them in a straightforward manner.
Science Education and Textbooks
What are the worst possible ways of approaching the textbooks for teaching science? In his book Science Teaching: The Role of History and Philosophy of Science pedagogue Michael Matthews quotes (p. 51) Kenealy in this matter. Many of the textbooks of science would fall in this categorisation. The emphasis lays squarely on the content part, and that too memorized testing of it.
Kenealy characterizes the worst science texts as ones which “attempt to spraypaint their readers with an enormous amount of ‘scientific facts,’ and then test the readers’ memory recall.” He goes on to observe that:
Reading such a book is much like confronting a psychology experiment which is testing recall of a random list of nonsense words. In fact, the experience is often worse than that, because the book is a presentation that purports to make sense, but is missing so many key elements needed to understand how human beings could ever reason to such bizarre things, that the reader often blames herself or himself and feels “stupid,” and that science is only for special people who can think “that way” … such books and courses have lost a sense of coherence, a sense of plot, a sense of building to a climax, a sense of resolution. (Kenealy 1989, p. 215)
What kind of pedagogical imagination and theories will lead to the textbooks which have a complete emphasis on the “facts of science”? This pedagogical imagination also intimately linked to the kind of assessments that we will be using to test the “learning”. Now if we are satisfied by assessing our children by their ability to recall definitions and facts and derivations and being able to reproduce them in writing (handwriting) in a limited time then this is the kind of syllabus that we will end up with. Is it a wonder if students are found to be full of misconceptions or don’t even have basic ideas about science, its nature and methods being correct? What is surprising, at least for me, that even in such a situation learning still happens! Students still get some ideas right if not all.
A curriculum which does not see a point in assessing concepts has no right to lament at students not being able to understand them or lacking conceptual understanding. As Position Paper on Teaching of Science in NCF 2005 remarks
‘What is not assessed at the Board examination is never taught’
So, if the assessment is not at a conceptual level why should the students ever spend their time on understanding concepts? What good will it bring them in a system where a single mark can decide your future?
Just for fun or how to invite readers to immerse in your book
These problems are for fun. I never meant them to be taken too seriously. Some you will find easy enough to answer. Others are enormously difficult, and grown men and women make their livings trying to answer them. But even these tough ones are for fun. I am not so interested in how many you can answer as I am in getting you to worry over them.
What I mainly want to show here is that physics is not something that has to be done in a physics building. Physics and physics problems are in the real, everyday world that we live, work, love, and die in. And I hope that this book will capture you enough that you begin to find your own flying circus of physics in your own world. If you start thinking about physics when you are cooking, flying, or just lazing next to a stream, then I will feel the book was worthwhile. Please let me know what physics you do find, along with any corrections or comments on the book. However, please take all this as being just for fun.
From Preface of Jearl Walkers The Flying Circus of Physics
Two Cultures
When C. P. Snow talked about Two Cultures, he had in mind the two supposedly different ways of life. The sciences and the humanities. Snow tries to see the differences between the two cultures and makes it a point to show that the two are indeed different. Recently I read Stephen J Gould’s The Fox, The Hedgehog, and the Magister’s Pox. Gould tries to establish that the so-called divide between the sciences and the humanities never existed but was created unnecessarily.
In this article, I am also going to talk about two cultures, but not the ones that Snow choose. I am going to talk about academic and administrative cultures. Any research institute along with its academic staff has a `supporting’ administrative staff. Theoretically, if you ask, the tasks of the two are defined clearly. The academicians are supposed to do academics, that is, to do research, or at least what they consider research or worth doing. The outcome of academicians is to be measured by fellow academicians, in terms of the quality and the quantity of research or visible work done by them.
The academic life is usually one which is not-so-high paying. At least in India, this seems to be the case. A person who retires as the Director of an Institute hardly draws a salary as compared to the ones in the industry with their kind of experience. But that will take us into another discussion about Academics and Corporates, which I don’t want to enter into now. The perks of academic life are in many cases, if not in all, are the curiosity and the associated satisfaction that one derives from the problems that one tackles. When a person starts an academic career, the paths diverge sharply from their colleagues’ paths who have to choose a corporate way. When one enters academics, one of the things that are retained is a sense of freedom. Again this might not be true in all cases, I have seen juniors, especially the Graduate Students being ruled upon like a dictator by senior Professors. But this misses the point that I want to make. The point is that if you can, at least theoretically speaking, pursue your own research agendas, your research questions. For some people, it is the question that drives their academic lives.
Every now and then you hear examples of so-called `nerds’, who do weird things. They are the people who have `devoted’ themselves to their field. I am not trying to defend anyone here for doing all the weird things that they do, but just trying to illustrate the fact that the field that the researcher chooses, is what drives them on in life. It is just due to the handful of these people that makes the difference. Many times it is just sheer genius, many times it is hard work of years. They are the leaders of their field. Well not always, you may find a mediocre person leading the field, with all the proper political connections…
But this is not always the case; there are always misfits. I do know of people who do not have any commitment to the field that they are working in, per se. But they choose the research field as any other job, the enthusiasm is lacking. And they lament upon those who show some enthusiasm. And such people may be quite numerous. They are the followers. In many cases, it is not that they lack the enthusiasm, but it is entirely missing. What I mean by that is they just like workers in a stone quarry, just doing what the supervisor tells you to do, without much understanding. They are like academic coolies. Maybe the term sounds harsh, but that is what it is supposed to be. Whether you are like this or not will strongly depend on who is your reporting authority in the field. These people, if asked, will have no opinion themselves, and even if they do, it will be a carbon copy of somebody else’s.
The way one is moulded in academic life strongly depends upon one’s own capacity for independent thinking and the kind of support that one gets from the colleagues, including and most importantly from the supervisor. The graduate student years decide what kind of academic person you will become. If all your thoughts are nipped in the bud, at all the times, will you be able to think independently? This is also the question that the supervisor has to ask himself/herself: What my student should be like? I guess many of them would differ in the answer that they give and the thing that they actually practice.
Research Institutes are constituted so as to make an academic atmosphere. By this it is meant that the place should provide support for the activities that the researchers do, that is those activities apart from doing research per se. This support if necessary so that the researchers can concentrate on their work completely. Well isn’t that the idea of having a research institute. The researchers are paid for doing that, and many of them if not all do precisely this. They are not doing research as some part-time job, they are professionals, and at least some of them are committed to the field.
A Paradigm as variously defined by Thomas Kuhn would be a more proper term here for the field. As a philosopher, Kuhn redefined many of our existing understanding in the field of science, especially our understanding _about_ science as a field of human endeavour.
Researchers come and join a paradigm, most of them stay within the paradigm and solve puzzles. Only a few lucky of them come up with problems that are unsolvable within the paradigm, and then the revolutions follow. But let us not go further in this interlude. We
will talk about Kuhn some other time.
So coming back to research institutes, we can settle on one thing that a research institute is a place where research is done, and it is meant for that purpose. In a research institute, the agenda is to provide facilities for research. Various people form the infrastructure that is is thus required. Generally, any research institute has a few categories of people. The faculty, the graduate students and the scientific staff other than the previously mentioned ones. The other staff in the institute includes the technical, administrative
and the auxiliary staff, peons, cleaners etc.
The administrative staff is supposed to help the academic staff to lessen their burden from the non-academic work that they have to do. This `non-academic’ work includes managing the finance of the institute, maintaining the premises, handling at recruitments, and looking at various other facilities and services. But in some institute, the administrative staff becomes increasingly powerful, so much so that they dictate the terms to the academics. Promotions are stalled, so are new recruitments and procurements. All this by citing some obscure rules or just sitting on the files for months. This particularly happens when the incumbent person perceived to be “weak”. On the other hand when the incumbent person is perceived to be “strong”, the administration falls in line. The “strong” person at the helm, can ask the administration to bend the rules, or keep them on hold, or even circumvent at times. This makes the institutes grow. On the other hand, following the rules too strictly and with convenience denial makes it difficult for any growth.
Personal vendettas and fragile egos mark office politics. This is a power struggle, which decides the fate of the institute.
The Forbidden Library
What do you do when you find something offensive? Whether it be a book, a film or any other art form? You ask for a ban. You not only ban the book, perhaps want to ban the creator of the said object, including all their other work. We will explore Let us look at the dictionary meaning of ban:
Over the centuries, the powers to be, have banned books and other materials or ideas which they found offensive. But the idea for bans is not always from the state. Grieved individuals often take upon themselves to argue for a ban on a given book or other material. But why would anyone want to ban anything? There seem to be two major reasons, both ideological for this. Both of them involve cultural and societal values.
Every society has some agreed upon norms about behaviour in public, interactions between individuals and things which are considered “normal”. Now, if you look at different cultures, it does take a genius to see those different cultures have different norms. If you look at the same culture historically, you will see that norms change with time. What was blasphemous in the last generation is acceptable now. For example, in the Indian context consider inter-caste marriages. It would be almost impossible to think of it (especially if the female is from the higher caste) in our grandfather’s generation. Manusmriti has
In an earlier post, I had discussed the absurdity of television censorship. The main reason seems to be that in the case of television the continuous flow of images with sound creates a sense of participation for the viewers, whereas they are just consuming. The attention span of the viewers on the television is the most treasured commodity. To keep the viewers glued to the screen, the content creators use a variety of means. The spectacle is out there. Feeding the viewers, satiating their bored lives showing them things that they will never ever get. Playboy and National Geographic are essentially same, they show you things that you are never going to see by yourselves. They create a reality away from reality in which the viewer is lured in and then stuck in a quagmire. In this state, the opinions can be changed, altered as per the desires of the creators.
This thematic idea is captured very well in this couplet by Piyush Mishra in a song from Gulaal.
जैसे हर एक बात पे डिमॉक्रेसी में लगने लग गयो बैन
Just like in democracy there is a ban for everything in democracy.
The banning of books or that of materials which the state or a group of people seem inappropriate is perhaps the easiest way to
https://web.archive.org/web/20090413002834/http://title.forbiddenlibrary.com/
On the same theme, some of the stand-up comedians in India have expressed their opinions in this video I am Offended. It is a good watch, particularly the intolerant times in which we are. This video, I think points to many of the issues that we have considered here particularly in the current social Indian context.
Two works resonate the idea of censorship and banning of books very well. They are Nineteen Eighty-Four and Fahrenheit 451. In both these works, the core idea is the control of ideas, information and knowledge. So much so that the language to be used by the people is restricted. Certain words are removed from public memory by force. Any use of these words is akin to treason. Nineteen Eighty-Four has Thought Police, who control and report what is said. Even saying thinking about something taboo is a crime. We can see a certain trend in the contemporary Indian context. This MO has been effectively used to discredit dissent. Using in the age of connected computers this becomes even easier. It is easy to target people sitting in the comfort of your bed, in a sustained and meticulously planned manner. The so-called Keyboard Warriors are now being employed for making life hell for dissenting people. Anything goes.
Seemingly normal works of literature can be banned by using various contexts at different times and places. Just have a look at the list of books banned by governments across the globe. You will see many familiar titles there, and some of the reasons for their ban are even more bizzare. In the Indian context, history is highly coloured. The general public seems to consider historical fiction works as the history. I am a bit acquainted with Maratha history and seeing it being portrayed in a highly problematic manner in many of the popular titles makes me cringe. Yet, these titles remain on the best seller list. People reading these take them to be the de facto history without any need for evidence to the events depicted in these. When challenged about historical facts they cite these works of fiction as if they are some well researched historical documents supported by evidence. One can imagine what kind of conceptual edifice one will create with such misconceived notions about the past.
Alan Moore has interesting views on being a writer: Words are magic, they can change and transform things. If we think about this, this indeed is the case. Ideas in the form of words do dictate our lives, whether we are aware of it or not. Ideologies in the form of literature does control our life. So, a writer can write against what is popularly accepted. There are writers who are conformists, and there are writers who will swim against the flow. And it is the later ones who will find their work on the banned list more often than nought. Ideas and words are far more dangerous than mere physical humans. Writing in this era of perpetual ephemeral nature of electronic media makes this case even stronger. Entire works of a particular theme can be removed in a blink of an eye. Electronic media though makes it easy for the authors to publish and disseminate their work, it can also be controlled and removed as easily as with a simple click. Force and intimidation are used when direct banning is not possible. Don’t feed the trolls. When such a thing becomes the norm, we start to self-censor, the worst form of censoring. Because the moment you start to nip the thoughts in the bud, your entity changes.
It is forbidden to dream again;
We maim our joys or hide them:
George Orwell categorises the intentions for writing into these four
- Sheer egoism:
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Aesthetic enthusiasm:
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Historical impulse:
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Political purpose:
The last of these he expands
Using the word ‘political’ in the widest possible sense. Desire to push the world in a certain direction, to alter other peoples’ idea of the kind of society that they should strive after. Once again, no book is genuinely free from political bias. The opinion that art should have nothing to do with politics is itself a political attitude.
This is where authors who usually end up on the list of banned work find themselves. Perhaps the world-view that the author subscribes to is something against the incumbent and the inherent traditions of a given milieu. Whatever the reasons, mere words can make those in power feel threatened or humiliated. So it indeed the case that words do have magic, if it was not so we would not have works being banned at mere thought.