Three volumes were on the shelf. Combinatorics formulas. Problems with an Order Constraint
Annotation: Techniques for solving problems with restrictions on the order of succession or the order of choice are given. Particular solutions are given and general formulas are given. Problems on displacement of elements and pairs of elements are considered.
Problems with an Order Constraint
Until now, we have considered problems in which no restrictions or additional conditions were imposed on the order of elements in combinations. Or (as in combinations) the order was not taken into account at all. Consider problems with the constraint .
Task 1. The tamer of predatory animals wants to bring 5 lions and 4 tigers into the arena, while it is impossible for two tigers to follow each other. In how many ways can he arrange the animals?
Let's denote the lions with the letter L. There are 6 places for tigers.
L 1 _____L 2 _____L 3 ____L 4 _____L 5 ______
Lions can be arranged! In ways, that is, 120. On the six places for tigers, they can be arranged in ways.
The total number of ways.
For the problem in general terms, if available: tigers and lions.
But since 
then
This is possible only on the condition that
Task 2. A ladder is being built from point to point. Distance . The height of the step is 0.3 m, the width is 0.5 m or a multiple of 0.5 (Fig. 8.1). In how many ways can a staircase be built?
Rice. 8.1.
It can be seen from the condition that the staircase must have, while there are 10 places where you can arrange a step: and one extreme.
Therefore, it is necessary to choose 5 places for a step from 10: in ways.
Construction options are shown in fig. 8.2.
Rice. 8.2.
In the general case: if there are steps, then the stairs can be built in ways.
This task is similar to the previous one; the tamer cannot place two tigers, and the builder cannot make steps of double height. But there is a significant difference: all animals are different, but the steps are the same, so the builder has less choice.
A generalization of the ladder problem (to encrypt the ladder with 1 and 0.....) can be the following: in how many ways can zeros and ones be arranged so that two ones do not stand side by side.
This can be done in ways.
Selection Order Restrictions
Task 1. There are 12 books on the bookshelf. In how many ways can 5 of them be chosen so that no two of them are adjacent?
We encrypt the choice of 0 and 1: we assign 0 to each left book, 1 to each selected book. Thus, we have 5 ones and 7 zeros and the problem is reduced to the previous one.
In general: If there are books, and books that are not standing next to each other are selected, then this can be done
Task 2. There are 12 knights at King Arthur's round table. Each of them is at enmity with his neighbor. It is necessary to choose 5 knights (for example, on an expedition to free the bewitched princess), and so that there are no warring ones among them. (Fig. 8.3) In how many ways can this be done?
Rice. 8.3.
The difference from the previous problem is that the knights do not sit in a row, but in a circle. But it is easy to reduce it to the case when the knights sit in a row. To do this, take a knight, such as Sir Lancelot, and break the circle. All selected combinations fall into two classes: Sir Lancelot participates in one, and not in the other. Let's count how many combinations are included in each
The topic that the author explores is books and bookshelves. He asks himself: is the modern state of affairs, when books stand vertically on horizontal shelves, so obvious and inevitable? Readers will follow how a scroll from Antiquity turns into a codex, and that, in turn, into a book that we are used to, and learn how the task of storing book collections was solved at different times. This is a lavishly illustrated and captivatingly written book about a book—how it came into being and how we learned to keep it.
I. Books on bookshelves
The armchair in which I am accustomed to reading is facing the bookshelves; I see them every time I take my eyes off the page. Of course, “seeing them” is only a figure of speech: how often do we really see what we look at day after day? In fact, I see books rather than the shelves themselves. If I deliberately start thinking about them, focusing my eyes differently (as if I were looking at optical illusions in which the stairs go up and down or the cube turns right and left), then I will see the shelves, but rather just their edge or the lower part of the upper shelves; entire shelves can be seen much less often. Even when they are empty, I pay attention not to them, but to the absence of books, because the meaning of the shelves is in their purpose.
To tell you the truth, I can't even see books without shelves. The bottom edges of the books rest against the shelf, their rows stand straight, despite the force of gravity. The upper edges form an uneven line, but it also arises due to the shelf on which the books stand, and the straight line of the shelf only emphasizes this unevenness. Books and bookshelves are a technological system, and each element of it influences how we see other elements. Since we are dealing with both books and shelves, we ourselves become part of this system. Because of this, we look at it and its components differently and interact with them differently. Such is the nature of technology and the artifacts it creates.
Looking at bookshelves is no easy task. In my office, the shelves go from floor to ceiling, occupying almost an entire wall, but my office is not large, so I cannot move far enough away to immediately take in the entire wall. I didn’t succeed even when I just started using this office and the shelves were empty. It does not matter at what point I stand in front of the shelves: I see the undersides of some shelves, the tops of others, the left sides of some vertical supports and the right of others. I can't see at least one shelf in its entirety. Of course, it would be easier to assume that all shelves are the same and, having seen the bottom of one shelf, you see the bottom of all the others, but in such, albeit widespread, philosophizing, something still does not suit us.
Late one evening, when I was sitting in an armchair and reading, for some unknown reason, I suddenly looked differently at a bookshelf filled with books. It seemed to me a functional object that is taken for granted or not noticed at all; the shelf reminded me of a bridge under traffic, and I wanted to know more about the nature and origin of this ubiquitous object. But where to start? Maybe it's worth wondering why the shelf is horizontal and the books on it are vertical? Or is it so obvious that it needs no explanation? Perhaps we should go the other way and ask why we put books with their spines out? Or is this the only logical way to put them? Maybe books and shelves, like nuts and bolts, can only fit together one way?
It turns out that the history of the bookshelf is inextricably linked with the history of the book, and vice versa. Of course, books could exist without shelves. You can imagine how in the Library of Congress, or even in the district library, books are stored in boxes, piled on the floor - like firewood or coal. But there would be no bookshelves if there were no books. This does not mean that there would be no shelves at all, but they certainly would not be bookshelves. The bookshelf, like the book, has become an integral part of civilization. If there is a bookshelf in the house, this is an indicator that the owner is a civilized, educated, cultured person. The presence of bookshelves has a major impact on our behavior.
Why are book authors often photographed in front of bookshelves? After all, they did not write the books that stand in the background! Perhaps they want to show us how many books they have read in order to write their own, and that we will not have to read them if we delve into a detailed study or historical novel written by them, which has detailed notes and an extensive bibliography. It is unlikely that the book on the cover of which such a photo is printed is itself on this shelf - perhaps in this way we are hinted that we need to go to the bookstore and buy this book so that there is a complete set on the shelves.
But is it really possible to fully stock the shelves? In America alone, more than fifty thousand books are published each year. Can a person read so much in a lifetime? It's easy to calculate. Suppose we read about one book a day. This means that every three years we read about a thousand books. Suppose we read the first book at the age of four and lived a long life - up to ninety-four years. It turns out that in a lifetime we have read about thirty thousand books. How much space is needed for so many volumes? Let's assume that each book occupies 2.5 centimeters on the shelf. This means that the total length of the shelves should be about 762 meters. This number of books will fit in a house with six or seven large rooms, where every wall is occupied by shelves. This is no longer a house, but a bookstore, or a public library in a small town.
But if we go into such a house, what will we see there: books or bookshelves? What do we see when we enter the library? Almost always our attention is attracted only by books. Shelves, like steps of a ladder, on which people taking pictures stand, remain unnoticed: they are there, but they seem to be gone. They play a supporting role. But at the same time, the lack of shelves is striking. If we see that there is not a single book, not a single bookshelf in the house, then we will think about the owners like this: do they really only do what they watch TV?
It's funny how the bookshelf is a running TV prop: it keeps popping up in the background in various TV interviews, on shows ranging from Today to Nightline(1) . On C-SPAN(2), congressmen and senators hold press conferences in front of a rack that just fits into the frame (I wonder if the books are real?). When Newt Gingrich(3) performed in a tie with a picture of a bookshelf, you can say that he had books in front and behind. Journalists often interview lawyers and professors against the backdrop of bookshelves - probably the idea of the producers is that the authority of invited experts is supported by the authority of books.
The bookshelf serves as a support for books, but it also needs support. She is not only a decoration, but also a stage on which books line up to receive applause. But although the role of the bookshelf in the history of civilization is undoubtedly important, it is rarely mentioned in the program of this performance: the shelf is an extra in it, it is taken for granted, and simply ignored. There are many anecdotal examples of this.
One day when we were visiting, my colleague's wife went into my office to feed her newborn baby. Returning some time later with a sleeping baby in her arms, she said to me, “I hope you don’t mind that I ran through your bookshelves – I found some books there that I was pleased to remember.” Of course, there is nothing strange in the fact that she did not say a word about the shelves themselves. But when another guest came to my office on another occasion, he examined the books with such attention and did not notice the shelves at all, that it is worth telling about this in more detail.
One fine spring day, this guest was in my office: I was looking for a book to give him to read on the plane. Soon he began not just to look at books, but to leaf through them carefully; he studied books with a determination that was familiar to me. Going through other people's books is a game of chance, if not an act of voyeurism or an exercise in homegrown psychology. My guest didn't seem to miss a single volume, and told me that he always seemed interested in what kind of books people buy and read. This interest is understandable: my guest was a cognitive psychologist who worked as a consultant on computer interfaces. At the time, he was advising a large office equipment company on what products to develop and what to refine in them. He is the author of thoughtful works on the design of everyday objects, where special attention is paid to the use of these objects. I've read his books and I don't think he's capable of missing anything at all, no matter what he looks at.
In the morning of the same day I showed him the city. We stopped at the new building for the Faculty of Political Studies, which has received much praise for the attention the architect has given to its future use. As soon as we went inside, it immediately became clear that this was an unusual building. Numerous offices and conference rooms open onto galleries that line two sides of the common room, while the other two sides continue into tiers of open spaces that also open onto and frame the atrium. Going from one part of the building to another, you will definitely pass along the gallery or stairs from which this common hall is visible; in such a building, visitors must occasionally meet by chance with each other - no doubt, this was how it was intended. This layout reminded me of the building of the National Humanities Center (4) where visitors pass through the common room, which also serves as a dining room, where visiting scientists gather for communication, working on books on everything from pencils (5) to phenomenology. The care with which the design of the new building was thought out made a great impression on my guest: he paid attention to details that most of us would not notice, such as lamps above notice boards and door fittings, which he wrote about with special understanding and love. I was already thinking about this book at the time, so I was hoping to see how the bookshelves were arranged in the offices of the new building. Alas, we came on a Saturday and all the offices were closed.
Back in my office, we weren't talking about objects, not even about books as objects, but about the ideas they contained and how different categories of books were grouped on my shelves. My guest found familiar books in my possession, which of course he expected to see, such as Tracy Kidder's Soul of a New Machine and many books on bridge building, but some of the books surprised him. I explained that, for example, books on computer program design were sent to me and donated by readers of my own books on the design of bridges and other useful objects. Since I hold the view that design is design, regardless of its application, my collection of books reflects this unity, if not my over-enthusiasm for certain ideas. But I confessed to my guest that I find it difficult to decide where to put a book that deals with several aspects of the same topic. My guest must have formed an opinion about how I read and work in my office, but then we started talking about computers and what characteristics of a laptop I should pay attention to (I had just informed the guest that I was going to buy one).
If my guest formed an opinion about me by looking at the books on my shelves, this confirms one of my hypotheses: even the most attentive people who look at useful items do not notice the infrastructure that serves these items. My guest did not say anything about the shelves themselves, although I tried to lead the conversation in that direction. He could not have reached the very top shelves, but even this did not cause any reaction from the inveterate critic of everything in the world - from the design of telephone systems to the location of switches - no reaction. The "dust and silence of the upper shelf" about which Lord Macaulay wrote was also not discussed. Once set up and loaded with books, the shelf has no moving parts and no other task than to stay in place and support a row of books. It is like an ordinary bridge in the countryside: for those who walk on it every day, it is there, but it is not there. However, if the bridge is suddenly swept away by a flood, there will only be talk in the district about it. This is generally characteristic of technology: its presence is in its absence.
When I started working on this book, I began to see shelves where I had only seen books before, but not everyone shared my vision. At dinner with a historian who made his own wall-to-wall shelving—just the right size for storing paperback books, which are especially common among historians—I started talking about the bookshelves that I used to use when I was he was visiting, did not pay attention. First, we talked about the pride of the master (in fact, it is not easy to build such a rack), and then, of course, we switched to more general topics - books and their placement on the shelves. At the time, I was thinking a lot about how books were stored in the Middle Ages and about the evolution of bookshelves, so after dinner I tried to talk about shelves again. I was interested to know that the origin of these objects is not well known even to historians, especially those who do not specialize in the Middle Ages. A few months later, in a conversation with a professor of English, who was already retired, I again became convinced that book scholars who study later periods do not always understand what the physical nature of medieval books was, and they do not always know that they were chained to the shelves.
Not only from scientists, but also from librarians, I heard that few people know the history of the book and its care, as well as the evolution of furniture for storing and displaying books. I have repeatedly referred to one rather old work - The Chained Library by Burnett Hillman Streeter. The very title aroused the curiosity of the librarians whom I approached for this book. It came out in 1931(7), and it appears that in the first ten years thereafter, readers asked for it regularly, if not often. But the last return date stamped on the library card is October 28, 1941. Judging by the signatures on the form, which still lies in the pocket on the back flyleaf, no more than ten people have read this book in one of the best research libraries in the country. At least, I could not find traces of the fact that in the next ten years it was ordered at least once. What was her fate after that, I can not trace, because in the early fifties of the twentieth century, accounting procedures in libraries changed. Since then, the form with the return marks has remained on the back flyleaf; this is a sign of the time when the librarian probably knew everyone who signed the form by sight. One way or another, I realized that what the author of The Chained Library writes about (for example, the accounting of book circulation that existed before), as a rule, is unfamiliar to young librarians. They did not share my interest in the history of libraries, at least not in library furniture and book storage.
After reading The Chained Library, and before it John Willis Clark's seminal work on the subject, Caring for Books, I went to Yale University's Beinecke Library, which has one of the finest collections of rare books in the world. This library was shown to me by a knowledgeable and sympathetic person, but when I asked if there were books in the library on which traces of the chains that once chained them to the shelves were preserved, he could not answer. However, the librarian searched the computer catalog for the word "chain". Many of the findings were about the chain stitch used to sew old bindings together, but there were also a few books with holes in their leather-lined and ornate covers, through which an iron chain once passed. According to the catalog, the library also had at least one book with a partially preserved chain. I asked to be shown it to me. The book is stored in a special box; several heavy black chain links are in a separate compartment, not where the book itself lies: so the skin of the binding does not rub against the iron. The library staff was just as curious to look at this artifact as I was. This only confirmed my belief that the story of the chained book, which is key to the history of the bookshelf, needs to be told once again. The point is not only that it is interesting in itself, but also that it is a concrete example of the evolution of an artifact, which can be used to explain how technology penetrates our culture and changes it.
It's understandable that most of us think more about books than shelves. But there were also those who paid tribute to the infrastructure. Thus, Henry Banner, who worked for many years as an editor in the humor magazine Pak, wrote:
Becoming rich and successful
I got myself a bookcase.
But I won’t get books in it -
I will not spoil the beauty.
Of course, books can ruin another bookcase, but sometimes it is the bookcase that does not fit the books at all and almost discourages taking them off the shelves. When I moved into my current office at Duke University, it already had bookcases—quite nice, with adjustable shelves. Because the shelves, made of heavy chipboard and finished in walnut, were deep enough, but not too long, they are so strong that they do not sag even under very heavy books. But they are not very high, so I adjusted the shelves so that at the right height I had the maximum number of shelves with books of different sizes. As a result, it turned out that the books are grouped by height and there is little space above them on the shelves. Sometimes it's hard to grab hold of a book and pull it off a shelf full of stuff. One book care guide has a question to help determine if they are sitting too tightly on a shelf: “Can you grasp a book with your index finger, middle finger, and thumb, and then carefully remove it without moving the adjacent books with either one, not on the other side? So I can't; I have to follow the good advice from Martha Steward's Living magazine: "To remove a book from a shelf, move the books to the right and left of it and gently pull."
Often, when there is enough space above the book, they do this: they put their finger on top and gently pull on the spine, pushing and turning the book until it becomes possible to take it by the sides. Living magazine disapproves of this: "Never put your finger on the spine." If the books are too tight, you can break a nail or tear the binding, which is possibly worse. One 19th-century “book of advice” says: “Never take a book off the shelf by the spine; do not dry them over the fire and do not sit on them, for "books are our good friends, their advice is useful to us, and they do not betray our secrets."
But the inventor Charles Coley from Culver City, California, looked at books and bookshelves from the point of view of a mechanic. He studied the problem of taking a book off the shelf and found that before him "a satisfactory solution to this problem did not exist." In 1977, he received a patent for a "book ejector". It is something like a wooden board on springs, located behind a row of books, across the back wall of a bookcase. It works on the principle of action - reaction. To push a book out of a row of books, you need, contrary to the obvious, to press it into the back wall of the cabinet. This will compress the spring behind the board and the spring force will push the book out. (This apparatus works in the same way as hidden latches in cabinet doors: to open the door, you need to push it.) Like many inventions, Kolya's apparatus requires habit; however, if the books are too tight on the shelf, it may simply not work.
Putting a book back on the shelf under these conditions is no easier than returning a sardine to a tin can. The bookshelf does not seem to tolerate empty space, so the empty space that is created when a book is removed from a shelf is rarely enough to put the book back in its place unhindered. The book in this respect is like an air mattress after use, or a map of the area that seems impossible to put together as intended. Opening the book and closing it, we seem to change its size. She no longer fits where she stood. We have to wield it like a wedge, pushing the once obedient neighbors so that the book can finally establish itself in its rightful place. The book I'm trying to fit onto the shelf naturally rubs against other books and pushes them back. If there is enough space above the books, it is quite easy to align them by hand. But in my office, it's not easy to get your hand between the books and the next shelf to align all the spines. There is only one way out: you have to move the entire row inward. But I also cannot bring all the books to the back edge of the shelf in this way: after all, they differ in width, which means that no even row of spines will work. Over time, so many books are pushed into the very depths that you have to take out the entire row and put it back closer to the front edge of the shelf.
It didn't bother me that the books were deep on the shelves, because I liked that there was five or six centimeters of free space from the front edge to the spines. I can't say exactly when I started arranging books this way or why. But at least I don't remember putting them straight at the front, unless the widest book was the same width as the shelf itself. In this case, if I needed an even row of spines, I had to push all the books forward. I started experimenting with leading edge alignment while working on this book. Before that, it seemed to me that a few centimeters of empty space in front of books was quite natural and desirable; after all, a few centimeters of empty space remain behind the books. Thus, the books stood in the center of the center line of the shelf, and the supports had almost the same load. From a purely constructive point of view, it looked neat and correct. In public libraries, the aisles between the rows of shelves are often narrow, and it is often not clear which books are on the edges of the shelf if they are pushed too deep, but in my home and office there is an empty wall opposite the shelves, and the distance to this wall is greater, than the width of the aisle in a public library. I can step back and look at them. If the books are at the very front edge of the shelf, then it seems that the cabinet for them is cramped (like a suit that has become small), and its upper part outweighs the lower one. In addition, if the books are placed at the very front edge, the cabinets look two-dimensional: they have no depth, they resemble wallpaper. Where there is a bit of free space above the books, there is certainly depth, but the top line is uneven, and the shadows falling on the books give their rows an even less neat look.
Because my bookshelves are pushed back, there's a bit of room in front of them where I can store all sorts of little knick-knacks like pencils and envelope cutters. All this seemed to me quite reasonable, until one day a writer looked into my office. He was surprised at how my books were displayed, saying that he himself always put them to the very front edge and thought that this was how it should be done. I couldn't give him a definite answer then, and I still can't. But I have since learned that the literary critic Alfred Kazin always pushed books back on the shelf so that there was room to put pictures of his grandchildren and put the books he was currently reading. As with many issues of design and human interaction with technology, arguments can be made in favor of both solutions. But in any case, I was pleased that my guest was interested in how I arranged the books: it meant that I was not the only one thinking about bookcases and their use. But how and in what direction do such thoughts develop?
A book on a bookshelf is the kind of thing that needs to be taken off the shelf and read. A bookshelf under a book is a thing that is hung up and forgotten about. One object serves another or dominates another - such is the generally accepted logic, and the subordinate object rarely gives us reason for reflection. But all people and objects - both ordinary hard workers and high-ranking persons - can tell some stories. And much more often than you might think, these stories are exciting, with unexpected twists, containing valuable information.
Is there a thing that has a more obvious form and function than a bookshelf? It seems that the idea that you can put books on a wooden board is as old as the books themselves. It seems that common sense and the laws of gravity dictate that the shelf be flat and horizontal. And the fact that books on a shelf should stand upright, their spines proudly erect, like a platoon of cadets, is not a matter of course for any library, large or small? We are confused by the portraits of Renaissance scientists: their offices are quite neat, but the books are everywhere but on the shelves. And if, nevertheless, they are located on the shelves, then whatever, but not vertically and not with the spine out. Isn't the vertical arrangement of a book on a horizontal shelf a law of nature? If not, why not? How and when did our present way of storing books become almost universal practice?
The story of the bookshelf cannot be told without telling the story of the book, its evolution from scroll to manuscript and from manuscript to printed volume. One should not think that all this is the dark deeds of the past, in no way connected with life in the new millennium. On the contrary, this information is incredibly important for understanding the history of civilization. It allows you to understand how technology is developing today and make predictions for the future (which will be much more like the present and past than we are usually led to believe).
Looking at a bookshelf (as well as any other object) with a fresh eye, without prejudice, is useful in itself: in particular, this is how we learn about the world in a new way and interact with it. Since the books and the shelf below them are inextricably linked, if we focus on a hitherto forgotten bookshelf, then we will be able to take a different look at the book - so to speak, turn it upside down. When we look at something as familiar as a book with new eyes, we see a completely different object, the qualities of which distinguish it from all other things in the world and at the same time make it similar to many things that we know.
If there are only two books on the shelf, then they stand in an awkward position, like wrestlers in the ring. The three books on the shelf are reminiscent of basketball when two defenders pin down an attacking player. If there are even more books, then they look like schoolchildren playing leapfrog in the schoolyard. But more often than not, the half-filled shelf is a commuter train, where passengers lean on each other and balance in wobbly poses, though they are hindered by the speed of the movement.
A book on a bookshelf is an interesting thing. If she's not fat enough, she won't be able to stand on her own. A thin book, which nothing supports, now and then falls in one direction or another - just like some frail on the beach, who himself is embarrassed by his own frailty, and a thick book that has no neighbors swells up: maybe , it is bursting with pride or the cellulose covered with typographic marks is to blame, because the heavy pages bend the spine and push the covers apart, like a powerful sumo wrestler crouching in front of an opponent on spread legs: come on, push.
Anne Fadiman, author of the excellent collection of essays on books, Bookplate, tells how she lost a 29-page brochure “so thin that its bright red spine couldn’t fit the title.” This pamphlet "gets lost between two chubby neighbors, like a thin blouse in a stuffed wardrobe that you can't find for months." In another essay, she explains why she prefers a bookcase to a wardrobe: “When my brother and I climbed our parents' bookcases, it gave us much more food for wild fantasies about their tastes and desires than studying wardrobes. If you want a sense, look at the shelf.
They spend a lot of time on the shelves of books. They seem to be waiting on the side of the road when they come up to them and offer something to do. Books are ladies without gentlemen at the ball, who stand against the wall and support each other; only neighbors help each to maintain its position. The books are like the character in the movie Marty, who ends up in the same place every Saturday. Books in dust jackets are a queue at a bus stop, passengers buried in newspapers. Books are bandits on identification at the station: they all fit the signs, but the witness will point out only one. Books are what we are looking for.
Some books are private houses filled with essays and articles on the same topic; some are anthology apartment buildings. The books on the shelf are Baltimore's row houses, Philadelphia's clinging houses, Chicago's townhouses, New York's mansions; in front of them - a narrow sidewalk, behind - courtyards that are visible only to the owners. Stepped roofs form a common silhouette - a chart of fates, an urban landscape. As in all cities, passers-by walk along the sidewalk about their daily business and hardly see either individual buildings or their inhabitants. We may not notice a number of books at all until we start looking for some name, code, specific address.
Not every book is doomed to get lost among others, to merge with the crowd. Bestsellers are shining stars. But no matter how many famous or outstanding books there are on the bookshelf and how many paparazzi are trampling around it, the shelf itself is a doormat. The shelves are the infrastructure of the library, a bridge on a country road and a local highway from point A to point B; and new high-speed roads have already been laid nearby, which pave the way for the information highway (8) .
Bookcases are the main furniture in offices, bookstores, libraries. A bookshelf is a floor on which books stand; the bed they sleep in until a prince reader wakes them up or a talent scout promises them a star career. Books open hearts to readers, and shelves wither with annoyance.
What are the bookshelves waiting for? Of course, books. It rarely happens that someone fills the entire shelf in one fell swoop - unless, of course, the library belongs to a juggler who can, by tossing a box of cigars, pinch it in the air between two others, and then keep the whole structure in balance, and the audience in admiration. This trick can be done with books, but not with a whole shelf! Usually we put on the shelves a few books or one or two that we received as a birthday present or just bought. The bookshelf is not always full. For librarians, this may be a joy, but for bibliophiles it is a burden: they like it better when the shelf cannot be seen under the books.
A bookcase not completely filled with books is like a notebook of an absent-minded student: half of the lines in it remain free. If the closet is half full, then of course it is also half empty. The books in it lean left and right, forming the letters M, N, V and W between clusters of vertical (and not very vertical) I.
Although shelves are always ready to support books from below, they cannot always support an unstable book from the side. For tall or short books, bookends may (or may not) work—curious contraptions that are supposed to hold books back like a dam to water. But sometimes, as happens with dams, the bookends are dislodged and collapse; gaps form in the once almost monolithic facade of the spines, and entire groups of books fall on their side - unsightly heaps are obtained. Before us, as in a video game, is the eternal conflict between the movement "up-down" and the movement "right-left", between the obelisk and the sleigh (9) - both objects are subject to gravity, but each in its own way. Gravity, the very force by which bookends perform their function, determines the vertical of books. But the same force also acts in the horizontal plane. It affects the frictional force caused by the weight of the bookend, a force opposite to that which causes sliding.
Contrary to popular belief, the simplest mechanism is not a wedge, but a block. A Victorian guide to building a home library states that "the best device for keeping books "upright is made from a six-inch cube of wood, sawn in half diagonally." The bookends (many of which are just carved bars) create a horizontal pressure that keeps the books from falling. It's all about the force of friction, of course, but like any mechanism, the pressure that the bookend can withstand is limited because the friction that occurs between the bookend and the shelf is also limited. The heavier and taller the holder, the better, and the rougher the mating surfaces, the better. There are probably no other ways to improve the functionality of the bookend.
Some bookends have a thin metal base that is placed under the first few books in a row: the weight of the books will provide pressure, which will then affect the friction between the holder and the shelf. Some holders are made from sheet steel, stamped and bent to the desired angle - a simple and clever solution. Such holders were patented in the 70s of the XIX century and have since become widespread, but they are not always suitable for a home library: they may not be hard enough to withstand the pressure of heavy books and maintain an upright position. Much more elegantly, this principle is implemented in such holders, where the vertical part is made of pleasant-looking wood, and the horizontal base is made of durable metal. My wife and I once found such bookends in a shop in Indiana. Beautiful wooden planks were inlaid with almost invisible small ceramic mosaics, and the base was a heavy plate of galvanized metal; a thin foam rubber sole was glued to its underside to increase friction between the plate and the bookshelf. These bookends do their job well: they always stand upright and hold books in the same position. Alas, nothing is perfect: a too thick base gives the holder stability, but also raises the books standing on it by three millimeters above the shelf level. It's hard not to notice. A gap is formed under the books, which attracts attention. In addition, it rarely happens that the last book, under which the base of the holder lies, fits completely on it. Thus, it seems to stand on two steps, and the spine is noticeably deformed, since one cover of the binding is higher than the other. (The best holders are obtained from unnecessary books: they leave only bindings and fill these bindings with something heavy. But many book lovers will not even want to hear about such barbarism. Bookends are also made of hardwood or stone: on the one hand they cut out "roots". Such holders most often do not cause irritation.)
Among the most imposing bookends in my collection is a 635mm piece of real steel rail (it's funny how rails often serve as a metaphor for infinity). Of all my holders, this is the most massive; I glued a piece of felt to its lower end so that the steel would not scratch the shelf. Even the heaviest books are not able to budge him. But tall books sometimes overturn it: it is in the very shape of the rail that its upper part is heavier than the lower one. I haven't come across the perfect bookend yet, and I don't think I ever will. For every advantage there is a disadvantage, sometimes just as significant. Such is the nature of man-made objects: to increase their advantages and reduce their disadvantages - this is the goal of engineering and design in general.
Often a board attached to the wall with brackets acts as a shelf. In hardware stores, it is she who is usually sold under the name "bookshelf". When such shelves are placed one above the other, they are most often not closed at the ends - therefore, they need some kind of bookends. Sometimes the brackets of the shelf located above serve as limiters. For maximum effect, you can put a book on the bracket exactly at the height of the shelf. There is another option, in which the books themselves become the limiters: either some particularly thick volume holds back the neatly displayed books, or a part of the books is placed horizontally on the shelf and provides the necessary mass, which the silent mechanism converts into friction when required. But everyone knows that if a long row of books begins to tilt, then there is hardly a holder in the whole world that will provide sufficient friction: a turbulent stream of books will rush from the shelf.
Bookstores of the late Victorian era sold such bookshelves. They were made from light boards and steel rods. These shelves had to be hung on the wall
If the shelves are not attached to the wall with brackets but built into the bookcase, bookends may or may not be needed. If the books fill the entire shelf, the holders are no longer needed: vertical boards take on their role, and the books themselves become holders for their neighbors: one historical study props up another, the novel kisses the novel. Thus, a shelf in a bookcase is not just a horizontal board, but a board with vertical limiters. Vertical boards, unlike bookends, allow you to easily squeeze some books between others: not only the force of friction is involved here. If the shelves themselves are strong enough to support the weight of the books, then the cabinet will always be able to accommodate everything that can be crammed into it.
Bookends should not slide on the shelf, but this is not the case for books. In my office, the wooden bookcase is painted with cream-coloured semi-gloss paint. The shelves are dotted with marks from the bindings of the previous owner's books (mostly red and blue). I suspect that he wanted to get his books out of their boxes as soon as possible, or take them off the floor and put them on brand new shelves, which he probably made and painted himself. He did not wait for the shelves to dry properly. As a result, some paint from the bindings remained on the sticky surface of the shelves.
When a friend of mine arranged his library on freshly varnished shelves, he noticed that some books were more difficult to remove from the shelves than others. Worst of all slid massive volumes on engineering. He reasoned that the friction that occurs between the shelf and the binding prevents slipping. He decided to wax the shelves like skis and polish them to a shine: after that, it became easy to remove books.
One professional bookcase designer solved the problem of friction between a book and a shelf in a different way: he painted the shelves with automotive paint: it has "great impact resistance and makes books slide easily." And for some book designers, the physical characteristics of a book are more important than ease of use: In 1853, inventor Charles Goodyear published a book printed on rubber pages and bound in rubber. This volume most likely stuck to any shelf and neighboring books like a tire to asphalt.
What is a book or bookshelf? As is often the case, the answer depends on the definition, and definitions change over time. Perhaps there is a bibliological analogue of the biological law, according to which ontogeny in general terms repeats phylogeny; at least the resemblance is enough to enable us to utter this familiar sonorous phrase here. Sometimes, especially if we are young, we make bookshelves for ourselves, which do not always turn out to be strictly horizontal and vertical, but this is unintentional. As children, we build bookcases out of anything - for example, turn a wooden orange box on its side, and you can put another box on top. Everyone knows that thin children's books never stand upright on their own; children put them on the shelves at random. But if you just put a book on a horizontal surface, that surface won't become a shelf. If the books are on the desk - even if it is even, neat, between the holders - the table does not turn into a shelf. Books on a windowsill are just books on a windowsill.
But it is books that make a board a bookshelf and a drawer a bookcase. Before the advent of books, boards and boxes remain boards and boxes. As we grow up, our tastes change. Many students went through the "bricks and boards" stage. Such shelves have an important advantage: they are easy to transport if the owner often moves from place to place. But at some point, most of us have a desire to have real shelves created specifically for storing books. We are moving up in the service, earning more and more, and now we already want the best built-in bookshelves in the house, preferably in a real office or even better - in the room that belongs to our books, that is, in the home library.
In the biography of Edward Bernays (an advertising genius who undertook to promote everything from Dixie cardboard cups to Mack Trucks - and who was called the father of PR), it is written that built-in bookshelves became popular with architects, contractors and interior designers in 1930s, when Bernays was commissioned by publishers to boost book sales. According to one version of the story, he asked "respected and famous people to talk about the importance of books to civilization" and then convinced those in charge of furnishing houses to install bookcases in them. The owner of the house had no choice but to start buying books: Bernays agreed with the aphorism he is said to have carved on a wooden board: "Where there are bookshelves, there will be books." But not all shelves were so necessary. Ann Fadiman, whose parents had about seven thousand books, writes: “As soon as we moved into a new house, a carpenter would come and make shelves for us, a total length of about a quarter of a mile. When we left, the new tenants immediately removed these shelves.” When Thomas Jefferson's books were brought to the devastated Library of Congress after the Washington fire, the shelves, which were actually pine boxes that could be stacked one on top of the other, had special lids nailed to the front to keep the books from falling out.
A small homemade bookcase: a wooden box with a shelf in the middle, bookends with slots nailed to the sides. Such a cabinet can be moved from place to place without even taking out most of the books.
During the Renaissance, all sorts of shelves displayed works of art and various collections. In the early 19th century, James Nesmith, the Scottish engineer who invented the steam hammer, wrote of his artist father who moved from his studio to another location: it is the work of his own hands.” This tradition is still alive today among collectors: quite often you can see a room in the house with shelves on which there are all sorts of things - from model trains to dolls; however, we will not find a single book here. (In the house of an enthusiastic collector, there are probably various books with addresses of art dealers and antique dealers, catalogs of advertisements for buying and selling, directories with model numbers and prices, but all this is most likely located in the bedroom: corner tables and even the corners themselves turn into a kind of office where business literature is stored, which the collector looks through before going to bed.)
In one gift album with magnificent photographs of the desks of famous people, mostly writers, you can see the office of Admiral William Crowe, Jr. At the time of filming, he was Chairman of the US Joint Chiefs of Staff. Behind his desk is a luxurious wall-length bookcase, and on the shelves is a collection of hats, mostly military. These are hats, caps, helmets from all over the world, but there are no books in the closet. (If you look closely, you can see several books in the photo: it seems to be a desktop dictionary and "Famous Quotations" (10) , but they are as invisible as the unblinking eyes of a palace guard, over which a ceremonial bear hat is pulled down. However, they will immediately attract the attention of a child, and the same thing happens to Admiral Crowe's books as soon as we see them.) On the shelves behind the desk of the illustrator David Macaulay are rows of toys, models, a variety of objects - everything in the world except books.
Most of us still put books on the bookshelves, and this is what we are talking about in our story, in which we will definitely have to touch on the history of the book - a subject that is deceptively simple, but in fact incredibly complex. Let us immediately agree on the terms denoting different parts of the book here. The back cover is the part that comes into contact with the table when we put the book on it, title side up, so that it can be opened and read. When a book stands upright on a shelf, the part that touches the shelf is called the bottom edge and the opposite part is called the top edge. The edge that is pushed inward is called the front edge - today it sounds paradoxical, but once it was he who looked out. Finally, that part of the book that we see when looking at a shelf filled with books is called the spine. For centuries, books were placed spine-in on the shelf. In the history of the humble bookshelf, this is one of the most curious facts. These facts, and there are many of them, are what make this story interesting.
The history of the bookshelf and the ways in which books are stored on it is the history of an object that acquires meaning only in context, only through use. Will a horizontal board be a bookshelf if there are no books on it? This question points to a defining difference between technology and art: technology must always be judged in terms of utility, while art can only be judged in terms of aesthetics. The most beautiful bridge that cannot be crossed is not a technological achievement, and hardly a work of art either. Even a very beautiful bookcase that collapses under the load of books is not a bookcase, but an engineering failure. Is it possible to say that a tree is noisy if no one hears it? Is it safe to say that “an empty shelf” is an oxymoron?
The evolution of the book and the evolution of the bookshelf are indeed inseparable, and both are examples of the evolution of technology. Technological factors related to materials, functions, economy, use, have influenced the appearance of the book and book furniture more than literary factors. So, the evolution of the bookshelf is a model of technological development. But technology does not exist without the social and cultural context in which it operates and which, in turn, significantly influences. Therefore, the history of such a product of technology as a book or a bookshelf cannot be fully understood without understanding those aspects of it that at first glance are not related to technology.
If we describe how the way of making a book, caring for it, and storing it has changed over the past two thousand years, we will have an interesting and simple way to understand the development of technology in principle. It will also help us to better understand modern technologies, the development of which is so closely connected with our own development that we hardly notice anything beyond the superficial changes that occur in everyday life. If we can better understand the mechanisms of technological evolution, then we can better understand what is happening with technology now, and thus predict what to expect from it in the future. This understanding is always valuable, whether we are investing in securities, creating and selling new products, or just want to learn more about how the world works.
