photographed in New Orleans, Louisiana on October 4, 2006

To fix the signs in terms in the expansion of a determinant of any order, the notion of an inversion is introduced. If, in an arrangement of positive integers, a greater precedes a less, there is said to be an inversion. Thus in the order 12543, there are three inversions: 5 before 4, 5 before 3, 4 before 3. In 2341576, there are four inversions. When applied to any term in the expansion of a determinant such as (7), we say there is an inversion of the order of the subscripts presents an inversion when the letters (apart from the subscripts) have the order abcd…1 of the principal diagonal. With respect to determinants of orders 2 and 3, it may be observed that the number of inversions is even when the term is positive, and that the number of inversions is odd when the term is negative.

Consistently with these conditions, we lay down the following

Definition. A square array of n² elements, such as has been considered in the cases n=2 and n=3, is called a determinant of the nth order. It is an abbreviation for the algebraic form of all the different products that can be formed by taking as factors one and only one element from each column and each row of the array, and giving to each term a positive or negative sign according as the number of inversions of the subscripts of the term is even or odd, when the letters have the same order as the principal diagonal.

Excerpted from Introductory College Alegbra by H.L. Rietz and A.R. Crathorne. Published by Henry Holt and Company, New York, 1923.

photographed in Pittsburgh, Pennsylvania on October 19, 2009

Ammon (or Hammon; Egyptian Amun, the hidden or veiled one). A god native to Libya and Upper Egypt. He was represented sometimes in the shape of a ram with enormous curving horns, sometimes in that of a ram-headed man, sometimes as a perfect man standing up or sitting on a throne. On his head was the royal emblems, with two high feathers standing up, the symbols of sovereignty over the upper and under worlds; in his hands were the sceptre and the sign of life. In works of art his figure is colored blue … His chief temple, with a far-famed oracle, stood in an oasis of the Libyan desert, twelve days’ journey from Memphis. Between this oracle and that of Zeus at Dodona a connexion is said to have existed from very ancient times, so that the Greeks early identified the Egyptian god with their own Zeus, as the Romans did afterward with their Jupiter; and his worship found an entrance as several places in Greece, at Sparta, Thebes, and also Athens … When the oracle was consulted by visitors, the god’s symbol, made of emerald and other stones, was carried round by women and girls, to the sound of hymns, on a golden ship hung round with votive cups of silver. His replies were given in tremulous shocks communicated to the bearers, which were interpreted by a priest.

Excerpted from A Dictionary of Classical Antiquities: Mythology, Religion, Literature & Art. Translated from German by Oskar Seyffert, revised and edited by Henry Nettleship and J.E. Sandys. Published by Macmillan and Company, New York, 1895.

Heidelberg, Germany. September 25, 2009.

The American psychologist James, and the Danish psychologist Lange, independently of each other, put forward this theory in the early eighties of the last century, and it has since remained a great topic for discussion. According to the theory, the emotion is the way the body feels while executing the various internal and expressive moments that occur on such occasions. The “stirred-up state of mind” is the complex sensation of the stirred-up state of the body. Just as fatigue or hunger is a complex of bodily sensations, so is anger, fear or grief, according to the theory.

James says, we do not tremble because we are afraid, but are afraid because we tremble. By that he means that the conscious state of being afraid is composed of the sensations of trembling (along with the sensations of other muscular and glandular responses). He means that the mental state of recognizing the presence of danger is not the stirred-up state of fear, until it has produced the trembling and other similar responses and got back the sensations of them. “Without the bodily states following on the perception” – i.e., perception of the external fact that arouses the whole emotional reaction – “the latter would be purely cognitive in form, pale, colorless, destitute of emotional warmth. We might then see the bear, and judge it best to run, receive the insult, and deem it right to strike, but we should not actually feel afraid or angry.”

Excerpted from Psychology: A Study of Mental Life by Robert S. Woodworth. Published by Henry Holt and Company, New York, 1921.

Western Pennsylvania. October 20, 2007.

As a summer resident the Red-winged Blackbird is a familiar sight in low meadows and along roadsides. At a little distance he appears only to be a plain, black bird, but as he extends his wings his brilliant epaulets come into prominence. The plumage of the female, though inconspicuous, is singularly beautiful when seen at close range. It looks like a fabric of which the warp is black and the woof a twisted thread of brown and yellow. The Red-wings are essentially early birds, often returning in spring when their marshy haunts are still frozen over. Their vocalization is suggestive of cool, moist ground and hidden springs; it continues until late July, and is briefly renewed in October. The deep nest is half hung, half twined between the stems of marsh-growing plants, and often holds two broods of a season; the boggy location chosen serves to protect it quite thoroughly from human invaders.

The Blackbird’s clear notes are associated with those of the Meadowlark, as they are both early singers and are found in similar places. They are useful birds to the agriculturalist, as they are great destroyers of cutworms. They are sometimes polygamous, though as frequently found in pairs; being very gregarious birds, many nests are found in the same locality.

Excerpted from Birdcraft: A Field Book of Two Hundred Song, Game, and Water Birds, by Mabel Osgood Wright. Published by the Macmillan Company, New York, 1900.

New Orleans, Louisiana. July 31, 2009.

In short, the knowledge of “citizens” is symptomatic and therefore different from that of the police, at least when this knowledge functions strategically and doesn’t complete more superficial operations for appearances sake or to reassure people (such as patrolling or checking IDs in area considered high-risk). Thus, the typical citizens’ protest against police indifference is born, as well as a certain attitude of distance or irritation on the part of some police agents towards citizens:

In my opinion, an Italian who hires an extracommunitari is two-faced. On the one had, he could say, “I feel sorry for these poor people. Rather than seeing them out selling roses on street corners, I’ll give the something for taking care of my yard.” On the other hand, if you give someone a job illegally, then you, as an “employer” don’t pay any taxes, you don’t help pay for their health care, you don’t help pay for any assistance this worker would need if some work accident or anything like that happened.”

Excerpted from Non-Persons: The Exclusions of Migrants in a Global Society by Alessandro Dal Lago. Tranlsated by Marie Orton. Published by IPOC di Pietro Condemi, Italy, 2009.

Paris, France. September 19, 2009.

The allegories of the map discussed so far – positionality, movement and practices – set out the modalities through which subjects come to place themselves in the power-ridden, discursively-constituted, practically-limited, materially-bounded identities. The subject assumes, in both senses of the word, an identity on the basis of commonality with others and yet that subject, in both senses of the word, assumes that they are an individual: unique, sovereign. The formation of the subject also takes place, and fails, within the fields of encounters with others – but this field is striated with simultaneous, different power relations. Some anecdotes will help illuminate these rather dense introductory remarks: each will be set within a context which sheds light on the question of mapping subjectivity in the spaces and between the conflictual and incoherent self and the incommensurable and indissoluble other. There are five case stories.

[The first case story.] A man is sitting on a park bench, he is alone. Nothing stands in the way of the man’s presumption that the park is there for him to look at. His eye can roam over the landscape without challenge, nothing disturbs his power to look at whatever pleases him. The man is at the centre of his world – he owns what he sees and, in this scene, his is also self-possessed because nothing disturbs his thoughts. This ‘megalomania’ is shattered, however, by the intrusion of another into the park. The lord and master of all he surveys has suddenly become off-centered, the lines of power have become reoriented: the man no longer controls the scene, lines of power converge on the intersubjectivity between the two people and between them and the scene of the encounter.

Excerpted from Mapping the Subject: Geographies of Cultural Transformation, written and edited by Steve Pile and N. J. Thrift. Published by Routledge, London, 1995.

Afloat in the Caribbean Sea. July 25, 2009.

Team A listed their goal in communication as the simultaneous fulfillment of three objectives: (1) to provide a gestalt message (the whole message is greater than the sum of the parts/components), (2) to use a systems approach, and (3) to incorporate redundancy in the markers.

For the gestalt message, the purpose is to convey a message not just with words and pictures, but through the very vehicles of conveying the messages, and the messages themselves. That is, the marker materials, their construction, and their arrangement are such that future generations coming m upon the markers will understand the message that this place is not one where people would want to spend a lot of time. With the gestalt message, the emphasis is on communicating through the entire marker system.

The systems approach to designing and constructing markers is that the m various marker components are linked to each other and supplement the information (or fill in any gaps) from other marker components. Messages are provided in different levels of complexity, in different formats, and convey different aspects of the entire message.

The redundancy within the marker components provides enough individual markers of any one type (material or message or arrangement) so that if some are vandalized or degraded over time, there are sufficient numbers remaining to communicate the required message. The size and construction of the markers can also provide redundancy in that the form of the communication is overdone so that it can still communicate after degradation or defacement. With earthen berms (discussed later in this section), the size called for would allow the marker to withstand considerable erosion and still remain recognizable as a human construction marking an area.

Excerpted from ‘Expert Judgement on Markers to Deter Inadvertent Human Intrusion into the Waste Isolation Pilot Plant’ by Kathleen M. Trauth, Stephen C. Hora and Robert V. Guzowski. Published by Sandia National Laboratories, Albuquerque, New Mexico, for the United States Department of Energy, under contract DE-AC04-94AL8500.

Santa Catalina Island, California. June 13, 2009.

The physical domain contains a wide range of limitations, but generally relates to respiratory, metabolic, and musculoskeletal body functions associated with movement. The [2008 American Community Survey] focuses on ambulatory difficulties in question 17b of the 2008 questionnaire, which asked respondents aged 5 years and older, “Does this person have serious difficulty walking or climbing stairs?” In 2008, about 19.2 million people or 6.9 percent of the civilian noninstitutionalized population 5 years and older had an ambulatory difficulty …

For estimates of ambulatory difficulty, the [2008 Survey of Income and Program Participation] provides degrees of severity against which the ACS measure can be portrayed. Whereas the ACS measure asked about serious difficulty walking or climbing stairs, the SIPP measure asks about difficulty with each activity and follows up with questions about whether the respondent can perform the activity at all. The resulting measures show two levels of difficulty walking or climbing stairs. As shown in Figure 8, the ACS ambulatory difficulty measure falls in between the two SIPP measures, implying that it may capture difficulty that is more severe than the basic SIPP measure of difficulty walking or climbing stairs, but less severe than the measure of being unable to perform at least one of the activities.

Excerpted from Review of Changes to the Measurement of Disability in the 2008 American Community Survey by Matthew W. Brault. Published by the U.S. Census Bureau, September 22, 2009.

Schloß Heidelberg, Germany. September 25, 2009.

“Do you feel strong enough to tell us your story?” asked Captain Simon.

“I am strong enough,” said Professor Sherman, “and I want to first of all thank you three gentlemen for your kind attention. But, gentlemen,” he exclaimed, “as an honorary member of the Western American Explorers’ Club in San Francisco, I feel sincerely that I owe the first accounting of my extraordinary adventure to that illustrious fraternity!”

At this, of course, Captain John Simon was somewhat hurt. After all, he had ordered the rescue of Professor Sherman when he found him floating around almost dead in a maze of broken planks and empty balloons, he had saved his life. And the ship’s doctor had healed and tenderly nursed the Professor back on the road of recovery. The ship’s cook had gone out of his way to prepare special, delicate food for him. They were all three most disappointed. That also made them much more curious. They tried all sorts of ways to get him to tell his story. They tried arguing with, persuading, tricking, and agitating him. They tried to entice him with spirits. They gave him medicine which made him dopey. But he only seemed to become more and more firm as he exclaimed as loudly as his strength would permit, “This tale of mine shall first be heard in the auditorium of the Western American Explorers’ Club in San Francisco, of which I am an honorary member!”

“Will you at least give me your name?” asked Captain Simon. “So that I might make a proper entry and report of the rescue in the ship’s log.”

“That information I shall not withhold,” said the Professor. “My name is William Waterman Sherman.”

Excerpted from The Twenty-One Balloons by William Pène Du Bois. Published by Penguin Books, multiple years.

Outside Golden, Colorado. October 12, 2007.

The Western American Explorer’s Club, in the city of San Francisco, was honored as it had never been honored before in the first week of October 1883 by being promised to be first to hear the details of an unexplained, extraordinary adventure; the biggest news story of the year, the story the whole world was waiting impatiently to hear—the tale of Professor William Waterman Sherman’s singular voyage. Professor Sherman had left San Francisco August 15. He flew off in a giant balloon, telling reporters that he hoped to be the first man to fly across the Pacific Ocean. Three weeks later he was picked up in the Atlantic Ocean, half starved and exhausted, clinging to the debris of twenty deflated balloons. How he found himself in the Atlantic with so many balloons after starting out in the Pacific with one, caught and baffled the imagination of the world. When he was sighted and rescued in the middle of the wreckage of twenty balloons in the Atlantic by the Captain of the freighter S.S.Cunningham, en route to New York City, he was immediately put to bed, for he was sick and weary, suffering from cold and shock. He was treated with great care by the ship’s doctor, strengthened with food and brandy by the ship’s cook, honored by the personal attention of Captain John Simon of the S.S.Cunningham. When he was well enough to talk, the Doctor, Cook and Captain leaned over him at his bedside and said in excited tones, “How do you feel?”

“I could be worse,” said Professor Sherman, rather feebly.

Excerpted from The Twenty-One Balloons by William Pène Du Bois. Published by Penguin Books, multiple years.

St. Paul, Minnesota. October 10, 2009.

We are not born knowing how to communicate; it is something we learn just as we learn to tie our shoes (or wear them). Clearly, if we do not come with the knowledge “built in,” is knowledge we must “pick up” elsewhere. We can speak of children being “inducted” into the use of appropriate symbols for our culture, much as we speak of adults being inducted into an army (Frank, 1966, p. 7). Since children learn communication, this implies that it would be possible to observe children as they learn what is involved in communication, as in fact social scientists can and do. Only through learning how to communicate appropriate [sic] do we join other humans and become a society. “Communicative competence is not just another useful skill, like shoemaking; it is one’s ticket of admission to human and social life” (Thayer, 1982, p. x). Our primary job as children is to learn to understand and display the appropriate communicative system for the group of people into which we are born. Thus:

a child must learn to transform the world of actual things and events, of signals and signs, into a symbolic world of meanings and purposive striving in accordance with the symbolic patterns which have been devised to make human living more orderly and goal-seeking. (Frank, 1966, p. 7).

Excerpted from Communication in Everyday Life: A Social Interpretation, by Wendy Leeds-Hurwitz. Published 1989 by Ablex Publishing Corporation, Westport, Connecticut.

I-29 south of Sioux Falls, South Dakota. October 9, 2009.

The sense of the singular loneliness of the Plains at such a time is overpowering; and one is forced to admire the courage of the pioneers of this highway – plunging as they did into an unknown and uncharted wilderness, fixing their daily position by the sun, or “catching” one of the stars at night in the blazing galaxy overhead, which seems now to magnify to the eye the vastness and emptiness of the great plain below. The view is clear for miles ahead and behind you, while the low sand-bluffs off to the left seem to have gained in distance so that they now appear to be no more than a dark smudge on the southern horizon. Suddenly from out of their shadows comes the wailing, almost human cry of some wandering coyote, the lean and hungry scavenger of the desert. He has seen our fire, and being with all his cunning but a cowardly brute, fear keeps him at his distance; but his scent is keen, and instinct or experience no doubt tells him that in a few hours the flame will have smoldered, and we shall be miles away, leaving him a free range among the bones and scraps and usual debris of a deserted camp, so he bides his time.

Excerpted from Across the Plains in ’65. A Youngster’s Journal, from “Gotham” to “Pike’s Peak”. Self-published by Frank C. Young, 1905, Denver.

Brooklyn, New York, New York. November 1, 2009.

Of all the American contenders to try and break the 27-year men’s drought in the New York City Marathon, Meb Keflezighi may have represented the American dream more than any of them. Born in war-torn Eritrea, one of 11 siblings in a village with no electricity, Keflezighi now wears his American citizenship on his chest. He was the one American contender who wore the letters U.S.A. on his running top Sunday.

Keflezighi pointed to those letters as the Central Park crowd roared as they crossed the finishe line first, capturing the first American victory since Alberto Salazar last won it in 1982. When his victory was assured, Keflezighi dropped to the ground, tears streaming down his face. It was the first marathon victory of his career and washed away years of American futility here.

“U.S.A. gave me all the opportunity in the world, education, sports, lifestyle,” Keflezighi said. “This is so special to me.”

Excerpted from ‘Keflezighi’s ‘U.S.A.’ Breaks the Tape First‘ in The New York Times, by Lynn Zinser. Published November 1, 2009.

July 31, 2009. New Orleans, Louisiana.

Like any other tourist, he made his way east on Marlbourough Street and down Frederic Street and then walked along Shirley Street until he reached the Public Library. He had already heard about this curious place, but it was nothing like what he imagined. Like everything else in Nassau, it was tinier…and touched with the taint of…seediness. It was a circular building, no more than twenty feet in diameter, best Peepgass could judge, with seven or eight open cubicles along the circumference. In the cubicles were shelves of books along two sides and a window on the third. In the center of the circle was a small wooden enclosure where a rather bored brown-skinned librarian sat. From her post she could see into every cubicle, although she seemed to have no particular interest in doing so. The building, which was now close to 200 years old, had originally been built as the town jail. What were now library cubicles had originally been cells with barred windows and doors; and where now sat a librarian who could see into every cubicle had been a warden who could see into every cell. All at once it occurred to Peepgass—and probably no one else in Nassau that day—that 200 years ago, at the turn of the century, the particular prison had been the very latest in modern penology. All at once he froze, staring fixedly at this odd little room, and his spirits plummeted. Modern penology…he’d learn about modern penology, all right at the turn of this century, if he took a misstep in this little…overseas venture…But damn it, Peepgass, are you going to remain a wimp, a dork, a staff nerd until it’s too late to do anything about it? Are you going to keep your red dog chained up until PlannersBanc gives you a Steuben glass phoenix—which was already known, intramurally, as “getting the bird”—the bank was far too cheap to give retiring drudges something made of precious metal, such as a gold watch, anymore—are you going to wait until Lomprey or some other hunchback gives you the bird and waves bye-bye? That—your own willing self-imprisonment—would be a fate far worse than actual incarceration, is it not so?

Excerpted from A Man in Full by Tom Wolfe. Published by Random House, 1998, New York.