University Of Cambridge Alumni

"Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations of value of the symbols or expressions employed... all the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form, though particular in value, are results likewise of symbolical algebra, where they are general in value as well as in form: thus the product of a^{m} and a^{n}, which is a^{m+n} when m and n are whole numbers, and therefore general in form though particular in value, will be their product likewise when m and n are general in value as well as in form: the series for (a+b)^{n}, determined by the principles of arithmetical algebra, when n is any whole number, if it be exhibited in a general form, without reference to a final term, may be shewn, upon the same principle, to the equivalent series for (a+b)^n, when n is general both in form and value."

"In arithmetical algebra we consider symbols as representing numbers, and the operations to which they are submitted as included in the same definitions as in common arithmetic; the signs + and - denote the operations of addition and subtraction in their ordinary meaning only, and those operations are considered as impossible in all cases where the symbols subjected to them possess values which would render them so in case they were replaced by digital numbers; thus in expressions such as a + b we must suppose a and b to be quantities of the same kind; in others, like a - b, we must suppose a greater than b and therefore homogeneous with it; in products and quotients, like ab and \frac{a}{b} we must suppose the multiplier and divisor to be abstract numbers; all results whatsoever, including negative quantities, which are not strictly deducible as legitimate conclusions from the definitions of the several operations must be rejected as impossible, or as foreign to the science."

"I have separated arithmetical from symbolical algebra, and I have devoted the present volume entirely to the exposition of the principles of the former science and their application to the theory of numbers and of arithmetical processes: the second volume, which is now in the press, will embrace the principles of symbolical algebra: it will be followed, if other and higher duties should allow me the leisure to complete them, by other works, embracing all the more important departments of analysis, with the view of presenting their principles in such a form, as may make them component parts of one uniform and connected system."

"This work... was designed in the first instance to be a second edition of a Treatise on Algebra, published in 1830, and which has been long out of print; but I have found it necessary, in carrying out the principles developed in that work, to present the subject in so novel a form, that I could not with propriety consider it in any other light than as an entirely new treatise."

"It is now more than twenty years since I somewhat rashly undertook to write the Life of Dr. Young. For many years, however, after making this engagement, I found myself so much occupied by the duties of a very laborious college office, that I had no leisure to commence the work; and when the possession of leisure would have enabled me to have done so, my health became so seriously deranged that I felt myself unequal to any continued and severe literary labour. The undertaking was consequently abandoned, and it was proposed to transfer it to other hands; but it was not found easy to secure the services of a person who possessed sufficient scientific knowledge to enable him to write the life of an author whose works were so various in their character and not unfrequently so difficult to understand and analyse, as those of Dr. Young."

"I assure you that I shall never cease to exert myself to the utmost in the cause of reform, and that I will never decline any office which may increase my power to effect it. I am nearly certain of being nominated to the office of Moderator in the year 1818-1819, and as I am an examiner in virtue of my office, for the next year I shall pursue a course even more decided than hitherto, since I shall feel that men have been prepared for the change, and will then be enabled to have acquired a better system by the publication of improved elementary books. I have considerable influence as a lecturer, and I will not neglect it. It is by silent perseverance only, that we can hope to reduce the many-headed monster of prejudice and make the University answer her character as the loving mother of good learning and science."

"Time, as we experience it, is continuous; it contains no discrete “events.” The events are put there by reflection on the past. As the past becomes more remote the remembered events become fewer in num­ ber and more limited in kind. It is for psychologists to say just why we remember this and forget that, but at the end of the day, the remembered past reflects our interests. It makes us what we are now."

"In a 1967 article, “Virgin Birth,” Leach astutely foreshadowed the reflexivity of the late 1970’s and 1980’s, calling attention to the fact that anthropologists call their own practice religion but assert that other peoples practice magic. In the present volume he presents the dramatic case of the fabrication of the Aryan invasion, which shows how profoundly the seemingly objective academic endeavors are af­ fected by the mentalité of the culture to which they belong. Leach de­ scribes how cherished but erroneous assumptions in linguistics and anthropology were accepted without question. If the mentalité of the academic culture was in part responsible for the fabrication, geo­ politics was even more responsible for upholding the Aryan invasion as history. The theory fit the Western or British vision of their place in the world at the time. The conquest of Asian civilization needed a mythical charter to serve as the moral justification for colonial ex­ pansion. Convenient, if not consciously acknowledged, was the Aryan invasion by a fair-skinned people, speaking the so-called Proto-Indo-European language, militarily conquering the dark- skinned, peasant Dasa (Dasyu), who spoke a non-European language and with whom the conquerors lived, as Leach puts it, in a “system of sexual apartheid.” The first civilization in India, thus, was built by the Aryan invaders. A remarkable case of Orientalism indeed."

"The Aryan invasions never happened at all. Of course no one is going to believe that."

"Yet here is precisely where anthropologists might make a useful contribution, if only their scholarly associates would stop thinking of the Rig Veda as a garbled history book."

"The origin myth of British colonial imperialism helped the elite administrators in the Indian Civil Service to see themselves as bringing `pure' civilization to a country in which civilization of the most sophisticated (but `morally corrupt') kind was already nearly 6,000 years old. Here I will only remark that the hold of this myth on the British middle-class imagination is so strong that even today, 44 years after the death of Hitler and 43 years after the creation of an independent India and independent Pakistan, the Aryan invasions of the second millennium BC are still treated as if they were an established fact of history."

"Because of their commitment to a unilineal segmentary history of language development that needed to be mapped onto the ground, the philologists took it for granted that proto-Indo-Iranian was a language that had originated outside either India or Iran. Hence it followed that the text of the Rig Veda was in a language that was actually spoken by those who introduced this earliest form of Sanskrit into India. From this we derived the myth of the Aryan invasions. QED."

"The details of the theory fit in with this racist framework. Just as each member of the total family of Indo-European languages is lineally descended from one or another of a number of extinct “protolanguages,” so also are the speakers of these languages; hence the people who speak any particular language constitute an independent racial stock."

"Where the Indo-European philologists are concerned, the invasion argument is tied in with their assumption that if a particular language is identified as having been used in a particular locality at a particular time, no attention need be paid to what was there before; the slate is wiped clean. Obviously, the easiest way to imagine this happening in real life is to have a military conquest that obliterates the previously existing population!"

"Why is this sort of thing attractive? Who finds it attractive? Why has the development of early Sanskrit come to be so dogmatically associated with an Aryan invasion? In some cases the association seems to be a matter of intellectual inertia."

"The Allchins, in their archeological capacity, have consistently emphasized the continuity that links the residues of the Indus civilization with those of the later classical India in the Ganges basin and further south. Furthermore, they repeatedly emphasized that archeology provides no clear evidence of any mass movement of peoples from Central Asia into northern India. So why do they continue to pay deference to the “racist” notions of nineteenth-century philologists in this way? (Incidentally, there is no “general agreement that the Indo- Iranian languages . . . were originally spoken in the steppes of Eurasia”)"

"At one time social anthropologists used to complain that their archeologist colleagues had no sense of the overall coherence of human societies. Now, under the influence of Dumézil, who was himself in­ fluenced by Durkheim and Granet, most of the prehistorians who have specialized in India and Pakistan and most of their Indo- Europeanist philological colleagues have become committed to a functionalism of a wholly naive sort. They seem to assume that cultural systems and language systems are bonded together and intrinsically stable over long periods of time. If societies are left alone, they stay put; otherwise, they roll across the landscape like impermeable billiard balls. If the archeological record shows that in fact changes have occurred, their occurrence is always explained as the consequence of a movement of population that carries with it the products (both material and immaterial) of a preexisting, alien, self-contained culture. As a rule, the alleged movement of people takes the form of a military conquest. The mythology of the Dorian invaders of ancient Greece who reduced their Ionian predecessors to serfdom matches point for point the mythology of the Aryan invasion of northern India."

"Why do serious scholars persist in believing in the Aryan invasions?"

"In other words, the prominent place given to horses and chariots in the Rig Veda can tell us virtually nothing that might distinguish any real society for which the Rig Veda might provide a partial cosmology. If anything, it suggests that in the real society (as opposed to its mythological counterpart), horses and chariots were a rarity, ownership of which was a mark of aristocratic or kingly distinction."

"...nothing in the archeological record suggests that the Ganges plain society was radically discontinuous from its Indus predecessor. Nor is there any independent archeological evidence for a massive intrusion of foreigners from the northwest. The suggestion in parts of the recent archeological literature that such evidence does exist is quite misleading. The “Painted Grey Ware Culture” of these writers would never have been interpreted as such if they had not started out by treating the Rig Veda as a history book."

"Common sense might suggest that here was a striking example of a refutable hypothesis that had in fact been refuted. Indo-European scholars should have scrapped all their historical reconstructions and started again from scratch. But that is not what happened. Vested interests and academic posts were involved. Almost without exception the scholars in question managed to persuade themselves that despite appearances the theories of the philologists and the hard evidence of archeology could be made to fit together. The trick was to think of the horse-riding Aryans as conquerors of the cities of the Indus civilization in the same way that the Spanish conquistadores were conquerors of the cities of Mexico and Peru or the Israelites of the Exodus were conquerors of Jericho. The lowly Dasa of the Rig Veda , who had previously been thought of as primitive savages, were now reconstructed as members of a high civilization who were destined to subordination because of their dark skins. The Aryan invaders could still be considered the originators of Indian civilization because they wiped out by fire and slaughter whatever was there before."

"If we accept all this, then the Aryan invaders appear as a race of chariot-riding heroes who conquer a population of servile peasant barbarians, the Dasa (Dasyu). This is a familiar story. Crossland, writing as a skeptic about traditions concerning the origin of Greco-Roman civilization, remarks: ‘The role of the Indo-European peoples in the ancient world has been portrayed too often as the incarnation of northern virility sweeping down in massed chariots to bring new vigour to the decadant south’ (1971:826). Where India is concerned, the construction of this mytho-history was complete by 1920 and it was being written about as if it were fully authenticated history…."

"It had the following form: Away back, long before the dawn of true history, Aryan invaders (who spoke a proto-European language and were therefore close kin to the Greeks, Romans, and Persians, who were the acknowledged founders of European civilization) had brought the first civilization to India, establishing themselves as an elitist military aristocracy among a population of barbarian serfs. They followed the precepts of a morally pure religious system, “The Vedic Religion,” which was very different from “the modem Brahmanic religion, as founded in the Puranas and Tantras, [which] consists in a belief in Vishnu, Siva and Brahma, and manifests itself in the worship of the most hideous idols”. After many centuries, during which the high culture of these original Aryans gradually decayed into gross immorality and superstition, a new wave of Indo-Europeans was now repeating the process. Once again the conquerors were establishing themselves as an elitist military aristocracy under the banner of a morally pure religion (Christianity)."

"The history of European colonialism covers many centuries and takes diverse forms, but whereas the European explorers and conquerors of the Americas, Africa, and Oceania usually took it for granted that the local inhabitants could be enslaved or butchered or driven into the hinterland at the whim of the invaders, the literate nations of Asia were initially treated as peoples toward whom the courtesies of European diplomacy should be applied. At the end of the day these Asian civilizations were likewise mostly subdued by force of arms, but such conquest needed some kind of moral justification, a mythical charter. The Rig Veda as interpreted by Max Müller and his contemporaries provided just such a myth."

"History is only true for the time being; each new generation of scholars rewrites the work of its predecessors. But such revisers rarely go back to the beginning and start from scratch. Instead they build uncritically on “generally accepted” foundations laid down by their predecessors. These traditional, established truths of history have a large symbolic component of which their exponents are usually unaware."

"I am well aware that for an outsider to attempt to bring about a shift in this entrenched paradigm is like trying to cut down a 300-year-old oak tree with a penknife. But the job will have to be done one day."

"In this essay I am mainly concerned with one particular case in which an oral tradition has been treated as if it were a datable written record and myth has been confused with history as it actually happened."

"Records are preserved because they provide a charter for what historians believe about the present. Different historians may believe different things, and the records are interpreted (and modified) accordingly."

"In the quantitative models that appear in leading economics journals and textbooks, nature is taken to be a fixed, indestructible factor of production. The problem with the assumption is that it is wrong: nature consists of degradable resources."

"What does an income tax schedule look like, which takes account of the trade-off between equity and efficiency? This question was first asked by Mirrlees (1971) who developed the standard model of the optimal nonlinear income tax. Since then innumerable papers have generalized, refined, or corrected his analysis. It has also been realized that the second-best approach to income taxation pertains to a wide variety of economic problems such as monopoly pricing or contract theory in general. In this respect Mirrlees’ article has opened an important and fascinating strand of economic thought."

"An approximately linear income tax schedule is desirable; and in particular negative income tax proposals are strongly supported,"

"The income tax is a much less effective tool for reducing inequalities than has often been thought."

"I must confess that I had expected the rigorous analysis of income taxation in the utilitarian manner to provide arguments for high tax rates. It has not done so."

"Economics takes a while to learn, even if much of it is in a way quite simple. It is simple to be wrong as well as to be right, and it is none too easy to distinguish between them."

"As proposals for estimating the social scarcity prices of natural resources remain contentious, economic accountants ignore them and governments remain wary of doing anything about them."

"You could not have evolved a complex system like a city or an organism - with an enormous number of components - without the emergence of laws that constrain their behavior in order for them to be resilient."

"A book unwritten is a delightful universe of infinite possibilities. Set down one word, however, and immediately it becomes earthbound. Set down one sentence and its halfway to being just like every other bloody book that's ever been written. But the best must never be allowed to drive out the good. In the absence of genius there is always craftsmanship. One can at least try to write something that will arrest the readers' attention, that will encourage them, after reading the first paragraph, to take a look at the second, and then the third."

"Of all human activities, writing is the one for which it is easiest to find excuses not to begin – the desk's too big, the desk's too small, there's too much noise, there's too much quiet, it's too hot, it's too cold, too early, too late. I had learned over the years to ignore them all and simply to start."

"Heathrow the next morning looked like one of those bad science fiction movies "set in the near future" after the security forces have taken over the state. Two armored personnel carriers were parked outside the terminal. A dozen men with Rambo machine guns and bad haircuts patrolled outside. Vast lines of passengers queued to be frisked and X-rayed, carrying their shoes in one hand and their pathetic tolietries in a clear plastic bag in the other. Travel is sold as freedom, but we were free as lab rats. This is how they'll manage the next holocaust, I thought, as I shuffled forward in my stockinged feet: they'll simply issue us with air tickets and we'll do whatever we're told."

"Economics hasn't had an Einstein because it hasn't had a Galileo yet."

"Every fundamental law has exceptions. But you still need the law or else all you have is observations that don’t make sense. And that’s not science. That’s just taking notes."

"It’s hard to kill a city, but easy to kill a company."

"Cities are the crucible of civilization."

"The good news is cities are extraordinarily resilient. The bad news is that they are also very hard to change."

"The paradigm of physics - with its interplay of data, theory and prediction - is the most powerful in science."

"A human being at rest runs on 90 watts. That’s how much power you need just to lie down. And if you’re a hunter-gatherer and you live in the Amazon, you’ll need about 250 watts. That’s how much energy it takes to run about and find food. So how much energy does our lifestyle [in America] require? Well, when you add up all our calories and then you add up the energy needed to run the computer and the air-conditioner, you get an incredibly large number, somewhere around 11,000 watts. Now you can ask yourself: What kind of animal requires 11,000 watts to live? And what you find is that we have created a lifestyle where we need more watts than a blue whale. We require more energy than the biggest animal that has ever existed. That is why our lifestyle is unsustainable. We can’t have seven billion blue whales on this planet. It’s not even clear that we can afford to have 300 million blue whales."

"Once we started to urbanize, we put ourselves on this treadmill. We traded away stability for growth. And growth requires change."

"I’ve always wanted to find the rules that govern everything. It’s amazing that such rules exist. It’s even more amazing that we can find them."

"Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society's predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development"

"Everything around us is scale dependent. It's woven into the fabric of the universe."