Articles from the Institute Letter
Additional articles from new and past issues of the Institute Letter will continue to be posted over time and as they become available.
By Richard Taylor
Modular arithmetic has been a major concern of mathematicians for at least 250 years, and is still a very active topic of current research. In this article, I will explain what modular arithmetic is, illustrate why it is of importance for mathematicians, and discuss some recent breakthroughs.
For almost all its history, the study of modular arithmetic has been driven purely by its inherent beauty and by human curiosity. But in one of those strange pieces of serendipity which often characterize the advance of human knowledge, in the last half century modular arithmetic has found important applications in the “real world.” Today, the theory of modular arithmetic (e.g., Reed-Solomon error correcting codes) is the basis for the way DVDs store or satellites transmit large amounts of data without corrupting it. Moreover, the cryptographic codes which keep, for example, our banking transactions secure are also closely connected with the theory of modular arithmetic. You can visualize the usual arithmetic as operating on points strung out along the “number line.”
By George Dyson
I am thinking about something much more important than bombs. I am thinking about computers.––John von Neumann, 1946
By Aristotle Socrates
The desire to discover distant, rare, and strange objects dominated twentieth-century astronomy, for which increasingly larger and more sensitive telescopes were constructed.
By Mary L. Dudziak
Does war have a time? The idea of “wartime” is regularly invoked by scholars and policymakers, but the temporal element in warfare is rarely directly examined. I came to the Institute in 2007–08 intent on exploring the history of war’s impact on American law and politics, but assumptions about wartime were so prevalent in the literature that first I found myself puzzling over ideas about time. Ultimately, this resulted in a book, War ·Time: An Idea, Its History, Its Consequences (Oxford University Press, 2012).
The idea that time matters to warfare appears in Thomas Hobbes’s Leviathan: “War consisteth not in battle only, or the act of fighting, but in a tract of time, wherein the will to contend by battle is sufficiently known; and therefore the notion of time is to be considered in the nature of war.” Time’s importance calls for critical inquiry, but time is often treated as if it were a natural phenomenon with an essential nature, shaping human action and thought. Yet our ideas about time are a product of social life, Émile Durkheim and others have argued. Time is of course not produced by clocks, which simply represent an understanding of time. Instead, ideas about time are generated by human beings working in specific historical and cultural contexts. Just as clock time is based on a set of ideas produced not by clocks but by the people who use them, wartime is also a set of ideas derived from social life, not from anything inevitable about war itself.
Yet war seems to structure time, as does the clock. Stephen Kern argues that World War I displaced a multiplicity of “private times,” and imposed “homogenous time,” through an “imposing coordination of all activity according to a single public time.” During World War I, soldiers synchronized their watches before heading into combat. In Eric J. Leed’s description of trench warfare, war instead disrupted time’s usual order. Battle became an extended present, as considerations of past and future were suspended by the violence of the moment. “The roaring chaos of the barrage effected a kind of hypnotic condition that shattered any rational pattern of cause and effect,” so that time had no sequence. And so one meaning of “wartime” is the idea that battle suspends time itself.
By Jessica Ellen Sewell
The mid-1950s saw the invention of a new, highly mythologized housing type, the bachelor pad, articulated most fully in the pages of Playboy and in films. The bachelor pad is an apartment for a single professional man, organized for entertaining and pleasure, and displaying tasteful consumption. The bachelor pad was culturally salient at this particular historical moment because it linked a culture increasingly focused on consumption and what sociologists and cultural commentators in the late 1950s argued was a “crisis in masculinity.” The bachelor pad provided a compelling fantasy of individual consumption and economic and sexual power to counter that crisis, but at the same time, helped to produce the masculinity crisis by problematizing straight male domesticity.
As described in Playboy, the pad “is, or should be, the outward reflection of his [the bachelor’s] inner self—a comfortable, livable, and yet exciting expression of the person he is and the life he leads.”1 It is precisely this inner self that was seen to be in crisis in the late 1950s: men’s sense of themselves as individuals had been stripped away, a state that was blamed partly on the conformity of corporate America and partly on women.