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Le Corbusier, architecture and Chandigarh

Some years back I had heard that Chandigarh, though completely planned, was not a livable city, it somehow was not a comfortable place to be in. Now, while reading The Blank Slate by Steven Pinker I came across some background perspective on this.
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It’s not just behaviorists and Stalinists who forgot that a denial of human nature may have costs in freedom and happiness. Twentieth-century Marxism was part of a larger intellectual current that has been called Authoritarian High Modernism: the conceit that planners could redesign society from the top down using “scientific” principles.” The architect Le Corbusier, for example, argued that urban planners should not be fettered by traditions and tastes, since they only perpetuated the overcrowded chaos of the cities of his day.”We must build places where mankind will be reborn;’ he wrote. “Each man will live in an ordered relation to the whole,”? In Le Corbusier’s utopia, planners would begin with a “clean tablecloth” (sound familiar?) and mastermind all buildings and public spaces to service “human needs,” They had a minimalist conception of those needs: each person was thought to require a fixed amount of air, heat, light, and space for eating, sleeping, working, commuting, and a few other activities. It did not occur to Le Corbusier that intimate gatherings with family and friends might be a human need, so he proposed large communal dining halls to replace kitchens, Also missing from his list of needs was the desire to socialize in small groups in public places, so he planned his cities around freeways, large buildings, and vast open plazas, with no squares or crossroads in which people would feel comfortable hanging out to schmooze. Homes were “machines for living;” free of archaic inefficiencies like gardens and ornamentation, and thus were efficiently packed together in large, rectangular housing projects.
Le Corbusier was frustrated in his aspiration to flatten Paris, Buenos Aires, and Rio de Janeiro and rebuild them according to his scientific principles. But in the 1950s he was given carte blanche to design Chandigarh, the capital of the Punjab, and one of his disciples was given a clean tablecloth for Brasilia, the capital of Brazil. Today, both cities are notorious as uninviting wastelands detested by the civil servants who live in them.
– Steven Pinker (The Blank Slate, p. 170)

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The logician, the mathematician, the physicist, and the engineer

The logician, the mathematician, the physicist, and the engineer. “Look at this mathematician,” said the logician. “He observes that the first ninety-nine numbers are less than hundred and infers hence, by what he calls induction, that all numbers are less than a hundred.”
“A physicist believes,” said the mathematician, “that 60 is divisible by all numbers. He observes that 60 is divisible by 1, 2, 3, 4, 5, and 6. He examines a few more cases, as 10, 20, and 30, taken at random as he says. Since 60 is divisible also by these, he considers the experimental evidence sufficient.”
“Yes, but look at the engineers,” said the physicist. “An engineer suspected that all odd numbers are prime numbers. At any rate, 1 can be considered as a prime number, he argued. Then there come 3, 5, and 7, all indubitably primes. Then there comes 9; an awkward case, it does not seem to be a prime number. Yet 11 and 13 are certainly primes. ‘Coming back to 9’ he said, ‘I conclude that 9 must be an experimental error.'”
– George Polya (Induction and Analogy – Mathematics of Plausible Reasoning – Vol. 1, 1954)

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On mathematics

Mathematics is regarded as a demonstrative science. Yet this is only one of its aspects. Finished mathematics presented in a finished form appears as purely demonstrative, consisting of proofs only. Yet mathematics in the making resembles any other human knowledge in the making. You have to guess a mathematical theorem before you prove it; you have to guess the idea of the proof before you carry through the details. You have to combine observations and follow analogies; you have to try and try again. The result of the mathematician’s creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.
– George Polya (Induction and Analogy – Mathematics of Plausible Reasoning – Vol. 1, 1954)

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Unreal and Useless Problems

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

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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)

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Indiana Jones and The Art of Looting

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?
 
 

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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.
 
 

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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?
 

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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