I want to make a modest proposal. I want to propose the foundation of a National Paper Museum. It's a back-of-the-envelope notion, a paper-fed pipe-dream. But it's not impossible. Museums are made of paper anyway, founded on blueprints and letters to the Times, and fuelled by ancient documents and handwritten catalogue entries. In the mid-19th century, Richard Owen, superintendent of natural history at the British Museum, decided that his area of specialisation needed its own space, and so he set about making his argument – on paper, in letters and in campaigns.

In 1858, more than 100 naturalists signed a letter to the chancellor of the exchequer, complaining about the display of natural history in the British Museum. Thomas Huxley and Charles Darwin put together a petition. Owen published a booklet, On the Extent and Aims of a National Museum of Natural History. Money was raised. A competition was announced for the building of a new museum. Plans were submitted. Francis Fowke won the contest, on the strength of his perspective drawing. Interiors were sketched and designed. Plans became reality, and the new British Museum (Natural History) – what we know now simply as the Natural History Museum, one of the jewels in the crown of Albertopolis – finally opened to the public on Easter Monday 1881. We have a Science Museum, and a museum of the decorative arts. We have galleries aplenty and exhibitions everywhere. But we lack a national monument to the stuff that's made it all possible.

Civilisation is built on paper. Paper money has made our economies. Paper maps divided our land. Paper laws propped up our governments, and paper books helped shape our minds. Despite the obvious encroachments of the digital, we all still use so much paper to note, to register, to measure, to account for, to classify, authorise, endorse and generally to tot up, gee up and make good our lives that it would be a Joycean undertaking to provide a full history of all the paper in just one life on one day, never mind in one city on one day, or in the life of one nation. Fortunate for us, then, that Joyce has already undertaken it: Ulysses, one of the great constructions of the human imagination, is nothing if not a vast paper palace, made up of bits of posters, pamphlets, sandwich boards and boot blacking ads. Leopold Bloom himself is an advertising canvasser, soliciting ads for the Dublin paper the Freeman, and the novel is literally composed from scraps. "I make notes on the backs of advertisements," Joyce told a friend in 1917. He also made much use of waistcoast-pocket-sized pieces of paper, large enough to make multiple memos-to-self about Epps Cocoa, Bushmill's whiskey, Guinness, Ginger Ale, Pear's soap and Plumtree's potted meat, all of which feature largely and exuberantly throughout the novel. In one startling passage Bloom imagines an innovative travelling stationery advertisement, "a transparent show cart with two smart girls sitting inside writing letters, copybooks, envelopes, blotting paper. I bet that would have caught on."

I bet it would. But we need no further encouragement. We're already wedded to the stuff; paper is our second skin. This morning alone I came home with two reams of copier paper, two Silvine reporter's notebooks, some gummed envelopes, five HB pencils, a Belfast Telegraph, a Daily Telegraph, a Guardian, the Times, Daily Mail, World of Interiors and Boxing Monthly. And I'd only gone into the shop for some stamps. We consume more paper, pound for pound, than any other product, food included. We are paper omnivores. We devour it: any kind, from anywhere. During the course of this week I have fingered and handled not only books, newspapers and magazines, but also files, agendas, programmes, dry-cleaning tickets, cinema tickets, parking tickets, boarding cards, feedback forms, school reports, bills, invoices and packaging of all kinds, and my pockets, as always, are stuffed full with train tickets, money and receipts – so much so that sometimes at night I simply shake the contents out on to the floor, creating a paper shower that soon becomes a drift that eventually, if allowed, would overcome first my bedroom, then my house and then finally my life, like the American Collyer brothers, Homer and Langley, whose brownstone on Fifth Avenue in New York was filled from floor to ceiling with a lifetime's junk, and who eventually died in squalor and infamy in 1947, with the police removing over 100 tonnes of garbage from their home. Langley was crushed to death in one of the booby-trapped newspaper tunnels of his own construction. Homer starved to death.

For better and for worse, paper remains our absolute all-time favourite self-extending prosthetic technology and device. It enables and represents the best of us, and the worst. Take art, for example. Of course, not all art takes place on paper. And not all art on paper is paper art. And some paper art may not be everyone's idea of art at all. Anyone for Lucio Fontana's paper-piercings? Or Gordon Matta Clark's paper slits and cuts? Joe Good's pellet-peppered paper? Martin Creed's Work No 88, A Sheet of A4 Paper, Crumpled Up Into a Ball (1994)? Or – my favourite, a masterpiece of its kind – Tom Friedman's 1000 Hours of Staring (1992-1997), stare on paper, 32½ins x 32½ ins, which is simply a plain white piece of paper that has been stared at. For a long time. But these are only the more obvious examples of the role of paper in art. It's possible to argue that the development of all modern art derives from what the critic Clement Greenberg called the "pasted-paper revolution". The use of paper collage in the early 20th century, according to Greenberg, liberated art from being merely decorative, an illustration of reality.

Take Joan Miró, who decided in the 1920s that his aim was to "assassinate painting". Miró's first, rather half-hearted act of rebellion was to stick postcards on canvas, but then in 1933 he began cutting images of machines and tools from catalogues and sticking them to large sheets of Ingres paper. He then began to use the outline shapes formed by these cutouts as models for his paintings: this was his revelation, his big breakthrough. Released from the constraints of self-expression and spontaneity, Miró had found an unexpected route to the vague symbolic language that characterises his later work, with its unique constellations of shapes, signs and lines. In order to find the true language and expression of his art, Miró, had to start with scissors and paper.

Then there's Matisse, who devoted the final few years of his life almost entirely to cutting paper. "The cutout paper," he explained in a letter in 1948, "allows me to draw in colour. It is a simplification." Paper allowed Matisse to get back to basics, to return to what mattered: this was "une seconde vie", his second life. "I have needed all that time to reach the stage where I can say what I want to say," he wrote, and he could only say it through paper. (The role of cardboard in the development of modern art is a subject, alas, that we cannot pursue, though it's perhaps worth noting in passing that at his nightclub, the Cabaret Voltaire, Hugo Ball used to recite his poems in a cardboard suit made for him by fellow dadaist Tristan Tzara; that Robert Rauschenberg in the 1970s, in his Cardboard series, confined himself entirely to working with used cardboard boxes; and that for the now legendary Freeze exhibition in 1988, the exhibition that inaugurated Brit Art, Damien Hirst simply mounted a few cardboard boxes on the wall.)

But, surely, that was then. Well, this is now: Harley Jessup, a production designer at Pixar Studios, who worked on Monsters, Inc and Ratatouille, has described a culture of paper drawing and picture-making at the company's headquarters in California that wouldn't seem out of place in an impressionist's studio in 19th-century Paris. At Pixar there are daily life drawing and painting classes, open to everyone, and the story department employs between five and 15 full-time artists solely to work on storyboards. (And a storyboard, as Jessup explains, just to be clear, "is literally a 4ft x 8ft bulletin board covered with rows of 3½in x 8in hand-drawn story panels": no gimmicks, no gizmos, no graphic design.) These story panels are scanned and cut together to produce story reels – basic black and white cartoon versions of the film – and are only then replaced by computer-graphic sequences, developed using yet further hand-drawn sketches, paintings and sculptures. Jessup adds up the number of storyboard drawings produced for various Pixar films thus:

A Bug's Life 27,555
Toy Story 2 28,244
Monsters, Inc 46,024
Finding Nemo 43,536
The Incredibles 21,081
Cars 47,000
Ratatouille 72,000

So, no signs of a paperless office at Pixar.

Nor, as far as I can see, anywhere else. All our modern businesses and institutions are built on paper, from plans to contracts to share certificates, to memos, to Post-Its and HP desktop printouts. Blizzards of paper. Tonnes of the stuff. Torrents. Avalanches. Foundations.

When imagining a house, architects have traditionally done so on paper: when imagining a town or a city they have simply done so on slightly larger sheets of paper. Robert Fludd's 17th-century fortified city; Joseph Smith's plan for an ideal Mormon city; the pioneering socialist Robert Owen's "A view and plan of the agricultural and manufacturing village of Unity and Mutual Co-operation"; eccentric self-taught stenographer Ebenezer Howard's vision of the "garden city", which he promoted throughout the late 19th and early 20th centuries with pamphlets, maps and diagrams, and by touring the country giving lectures illustrated with lantern slides; and of course Le Corbusier's grand plans for a ville contemporaine, a contemporary city, presented in a 100sq m diorama at the Paris Salon d'Automne in 1922, and which was eventually made real, at least in part, in his work on the Indian city of Chandigarh – all these places exist first and foremost on paper. As do the plans to erase and destroy whatever people or buildings existed there before.

In Romania, in the early 1990s, I met an architect who told me a story about Ceausescu's plans and designs for his palace, the House of the Republic, in the centre of Bucharest. The self-styled "Genius of the Carpathians" apparently commissioned a vast cardboard architectural model of the city to be built in a gymnasium, with the strict requirement that none of it should be glued down. He then peremptorily swept away approximately a fifth of what had been made in model form, and set his people to work on designing a vast building to fill the gap. A new start. A nice fresh sheet of paper. Every morning Alvar Aalto's secretary would lay out on his desk sheets of thin, Finnish sketch paper – tervakoski luonnospaperi – cut to lengths of exactly 30cm, and he would line up his pencils in order of length and begin work. Between them, Aalto and his staff would make up to 5,000 sketches for any particular project: they were growing buildings from paper.

We paste it all over our walls. The earliest known wallpaper in England, discovered at Christ's College, Cambridge in 1911, dates back to 1509. Disappointingly, it consists merely of a wood-block print on the back of an old proclamation; more like a tatty poster than actual wallpaper. Paper wallhangings first became fashionable in England during the 17th century: the repeal of the wallpaper tax in 1836 and the development of a surface roller printing machine in 1839-40 meant that by the end of the 19th century the stuff was inescapable. When Gustave Flaubert climbed the Great Pyramid in 1849 he was appalled to find an ad for wallpaper at the top – "Imbeciles have written their names everywhere: 'Buffard, 79 Rue Saint-Martin, wallpaper manufacturer,' in black letters." Oscar Wilde, in his lonely first-floor room in the Hotel d'Alsace in Paris, famously complained that "My wallpaper is killing me, one of us must go." Wilde has gone. The hotel has been redecorated. But paper remains.

Ephemeral, it reminds us eternally of the eternal. It is unsurpassed as a spiritual technology – the perfect multi-faith, multi-purpose platform for almost any religious event and occasion. Whether protecting ourselves with paper amulets, making offerings of votive slips, or nailing it to Wittenberg church doors, paper has the advantage over other popular spiritual technologies – such as, say, blood, animal carcasses, crystals, hairshirts, metal cilices, or Scientology E-meters – of being light, flexible, inflammable, capable of being decorated and inscribed, and not requiring batteries. Perhaps the purest expression of paper's otherworldly aspects are Tibetan lungta papers (lung meaning "wind" and ta meaning "horse"), those beautiful, small, square pieces of thin paper that are thrown up into the air to carry prayers, to bless a journey, or just for good luck. Shide, white paper strips, are hung on ropes at Shinto shrines to mark the division between the sacred and profane. Hongbao – little red envelopes containing "lucky money" – are presented as a gift at weddings and at Chinese new year. Joss paper, or ghost money, is burned as an offering at funerals and at anniversaries, so that one's ancestors might live prosperously and in peace.

So much for lungta and lucky money. What of hard science? In his book on the discovery of the structure of DNA, The Double Helix (1968), James Watson describes how the team at the Cavendish Laboratory in Cambridge would build models out of metal in their attempt to understand the structure and working mechanism of human life. One afternoon, while waiting for some of the models to be constructed, Watson became impatient, "so I spent the rest of the afternoon cutting accurate representations of the bases out of stiff cardboard". The next morning, he writes, "I quickly cleared away the papers from my desk" and set to work with the cardboard, trying to come up with a new shape and pattern to form representational pairs of cardboard bases connected by notional hydrogen bonds. By lunchtime, Watson's lab partner, Francis Crick was telling everyone in the pub that "we had found the secret of life."

Paper also played an important role in the development of computing. Charles Babbage's design for his so-called Analytical Engine, the first general purpose programmable computer, relied on cardboard as an essential part of its apparatus. Indeed, Babbage mocked up his earlier Difference Engine using cardboard cutouts, all worked out in his voluminous "scribbling books". His perforated cardboard cards were inspired by and adapted from the cards used by Joseph Marie Jacquard in his programmable weaving loom. This was an important machine in the history not just of technology but of human evolution, according to Manuel de Landa in War in the Age of Intelligent Machines, because it "transferred control (and structure) from the human body to the machine in the form of a primitive program stored as punched holes in paper cards, the earliest form of software". Paper helped to inaugurate not just the modern age of computers, therefore, but also the postmodern age of cybernetics. In the mid 20th century, the computer giant IBM's entire business relied on paper, with its famous punch cards ("Do not fold, spindle or mutilate") being used to record units of information in the form of code. The rustling sound of paper can still be heard distantly today in the paper prototyping methods used by Microsoft and others to develop user interfaces.

Writers tend to have huge – and often unusual – appetites for paper. Kipling, for example, used writing-blocks made especially for him, "to an unchanged pattern of large, off-white, blue sheets". Walter Benjamin was a stationery fetishist. "Avoid haphazard writing materials", he advises in the 1928 essay "One Way Street", though this is not an admonition he seems to have heeded, having used a bewildering range of notebooks and index cards in tandem and in parallel. Byron was even more slapdash: parts of Don Juan were written on the back of playbills. Tolkien scribbled bits of The Lord of the Rings on the back of undergraduates' exam papers. Dickens tended to use rough blue paper, not unlike the blue paper used on Warren's Blacking pots, which he'd tear in half, writing quickly and firmly on one side only, sometimes using the reverse for corrections and additions. He speaks in a letter of "writing and planning and making notes over an immense number of little bits of paper". These bits and sheets he called his "slips", almost as though they were merely receipts or dockets, loading bays for his vast cargo of characters.

It was in Dickens's London that paper became omnipresent. The great paper historian Dard Hunter explains how the introduction of the Fourdrinier paper machine in the early decades of the 19th century led to a steady increase in paper production – and how with the advent of wood-pulping processes in the 1840s, production simply exploded. Paper manufacturers no longer had to rely on supplies of rags to make their pulp: the mills began spewing paper into the atmosphere, and out on to the streets, as the factories were bellowing out smoke. The effect was both suffocating and intoxicating. In a popular engraving from 1862, The Bill Poster's Dream, the bill poster himself sits slumped like a drunk against a lamppost, exhausted, glue-pot by his side, examples of his handiwork illuminating the night sky. In an article on "Bill-Sticking" in Household Words from March 1851, Dickens described the sides of an old warehouse peeling away with layers of decomposing posters, "as if they were interminable".

Interminable, but not everlasting. The history of paper is the history of our lives, but unless saved for posterity in a real or an imaginary museum it is destined, ultimately, for oblivion. In Posters: A Critical Study of the Development of Poster Design in Continental Europe, England and America (1913), Charles Matlack Price warned: "When a poster fails, its failure is utter and irretrievable, and its inevitable destiny is its consignment to the limbo of waste paper." At the dawning of the Age of the Digital, isn't it time we acknowledged and celebrated the Age of Paper?