The Doric Column

January 18, 1999

The Library of Infinity Is Opening Near You
El Aleph and El Network
Titan of the Telecosm
Internet Timescapes Under Surveillance

[See Kevin Kelly's "Scan This Book!" in the New York Times Magazine, May 14, 2006.]

The Library of Infinity Is Opening Near You

The January 11th edition of the Wall Street Journal  ran a special section on "The Millennium: One Thousand Years of...People, Ideas, Work, Leisure, Finance & Companies, Trade & Commerce."

The collage on the cover featured pictures of a clipper ship, an hour glass, a stock certificate, a mandolin, William Shakespeare on a TV screen, the Mercury space capsule, a globe of the earth, and a Gutenberg Bible facsimile.

In the lower right-hand corner, juxtaposed to the gothic script of the Gutenberg Bible above, the universal linguistic currency that will take us into the new world of the next millennium appeared in subtle relief.



One of the more interesting articles in a paper loaded with interesting articles was "Think Big: What is the greatest technological innovation of the past 1,000 years? A hint: It's not just the thought that counts" by Bob Davis. That is, what one technology, had it never been invented, would have halted the millennium's progress?

A number were highly competitive.

  • eyeglasses
  • mass transportation
  • the factory system
  • medical advances
  • television
But the hands-down winner was printing. The invention of movable type "expanded by a factor of one million the amount of information available to literate individuals" according to one authority. It made the scientific revolution possible. Indeed, it made modern civilization possible.

But what about the next millennium? What one technology will rank with printing?

Colorado geophysicist Douglas Robertson, author of "The New Renaissance: Computers and the Next Level of Civilization," demurs a bit on predicting that far ahead, but not looking ahead 100 years. The ubiquity of computers and computer networks will produce a 100 millionfold increase in the information available world-wide compared with the precomputer era, in his view. That's orders of magnitude greater than that of the printing press.

"It's a new level of civilization," Robertson said.

A civilization that had its true beginning early in the present millennium, in13th century Spain. It began with a wooden mechanism of concentric circles covered with divine symbols, a mechanism that, "set in motion by the systematic investigator, would yield an indefinite and almost infinite number of concepts of a theological order." That's the perspective of the late Jorge Luis Borges, the great Argentine man of letters.

The "machine for thinking" was made by Raymundo Lulio (Llull), a Mallorcan mystic and poet who tried to encompass all knowledge in convergent points of unity using his apparatus.

Borges wrote that the "experimental science prophesied by Francis Bacon has now given us cybernetics, which has allowed man to set foot on the moon and whose computers are--if the phrase is acceptable--belated sisters of Llull's ambitious circles."

El Aleph and El Network

Jorge Luis Borges may seem an unlikely guide to the netherworld of machine language, global networks and emerging cybernetic civilizations. After all, he was a mythmaker who gradually went blind and who wrote in the basement of a library, the National Library in Buenos Aires.

Borges' worlds of fantasy captured me in the early 1980s. I was taking a Spanish class from Ruth Jones, a faculty member in University's Spanish and Portuguese department. On my own I bought a dual-language paperback to help me along. The Borges entry, "La forma de la espada," "The Shape of the Sword," sent me looking for more. His collections Labyrinths  (1962) and The Aleph and Other Stories, 1933-1969  (1970) and his regular appearance in the New Yorker  magazine kept me occupied for a long time.

Sometime back then Borges came to campus. I remember him sitting aslant on a chair in front of a modest turnout at Coffman Union. Leaning on his cane, he patiently answered the questions of faculty and students, his head bobbing as he spoke. I remember that his unseeing eyes were deeply set and appeared asymmetrical. A pronounced arch over his left eye suggested that eye had once taken the lead, at least in empirical matters.

The Academy owes a debt of gratitude to Señor Borges. The metaphysics of the one-time librarian have kept a regiment of scholars busy for four decades. Perhaps no other writer of our time has embodied the mysteries and paradoxes of 20th century physics and age-old philosophical disputes, such as the nominalist-realist controversy that has been simmering since the scholastic philosophers made it their cause célèbre during the Middle Ages.

When President Clinton testified that it depends on what the meaning of is  is, or some such, he was tipping his hat to that controversy, whether he knew it or not. Let's assume he didn't know.

In brief, the nominalist position holds that universals are mere names, corresponding to nothing in objective reality; the realist position is that universals have a real, objective existence outside the mind. By universals  is meant universal classes of entities or forms.

We may think that we are realists--that a rose is a rose is a rose, that you can see it, feel it, smell it, and hold it in your hand, that it has an existence independent of your perception of it. But Borges would describe us as "inveterate nominalists" in the view of Floyd Merrell, author of Unthinking Thinking: Jorge Luis Borges, Mathematics, and the New Physics  (Purdue Research Foundation, 1991).

"In medieval times the debate concerning the relationship between words and their referents became the realist-nominalist controversy--found at the core of Borges 'metaphysical narrative,'" Merrell wrote. The magic of the spoken word, dominant in Greek, Roman, and Medieval civilizations, reigned supreme "until the age of the printed word, when the visual linguistic image gradually became the image for assimilating knowledge."

The language of visual linguistic image-symbols that the printed word represented was followed by the mathematical language of symbolic logic fashioned by Charles Peirce, Alfred North Whitehead and Bertrand Russell, and its offspring, computer language, computerized images and computer thought.

Language is the "quintessential symbol-manipulating system" writes MIT's Steven Pinker in "Out of the Minds of Babes" (Science , January 1, 1999). Commenting on a recent study in which infants as young as seven months were found to be capable of thinking in terms of simple algebra-like rules and abstractions, Pinker observes that "one of the mechanisms that makes computers intelligent--manipulating symbols according to rules--may be a basic mechanism of the human brain as well."

When we look at a rose on a computer screen, when we move it about on the screen with a mouse, the rose takes on a reality quite different from the one, say, a peasant in the pre-print era was familiar with, which was a reality not associated so much with mental constructs or symbols derived from printed words or graphic images or "virtual" objects.

Today the computer is rapidly becoming the principal agent for the nominalists. Indeed, computer-mediated environments are the expanding province of the "symbolic analysts," the manipulators of symbols, the class of technically skilled, well-paid and highly sought professionals and jobbers in the emerging economy described by former labor secretary Robert Reich in his book The Work of Nations  (1992). That was before the rise of the Internet.

Even libraries, the fonts of knowledge, are now beginning to occupy the technological space trafficked by the symbolic analysts, the knowledge workers.

Consider M.C. Escher's Circle Limit I above. If you imagine the circle as a sphere, it represents graphically what Borges constructed verbally in his story The Library of Babel. In that fable the former cataloger of the octagonal National Library describes an imaginary library consisting of a universe of infinite hexagonal galleries of bookshelves containing all books--unbounded space at the service of knowledge.

"If an eternal traveler should journey in any direction," Borges wrote about a library of universal knowledge, a library of the past, present and future and all the words and symbols therein, "he would find after untold centuries that the same volumes are repeated in the same disorder--which, repeated, becomes order: the Order. My solitude is cheered by that elegant hope."

Borges' mystical time-space travels took place the basement of the National Library, a distant descendant of the Library of Alexandria in Egypt where knowledge was first collected and systematically organized in what Carl Sagan called "the first true research institute in the history of world," the first community of scholars, the global brain of its time. Today, what remains is a "dank and forgotten cellar."

With a 100 millionfold growth in the information available on computer networks over the next century, and the corresponding minuscule advance in human brain evolution, for our purposes that amounts to the "Library of Infinity Opening Near You."

On your PC, the Aleph of the 21st century.

And unlike the narrator of El Aleph , or its creator, or visitors to the remains of the Library of Alexandria, most of you will not have to descend to basements and cellars to begin the journey.

Titan of the Telecosm

The expanding universe of nominalists and symbolic analysts, already traveling at warp speed thanks to the PC and now the Internet, is about to enter what George Gilder calls the "Ethersphere" in his Telecosm Series.

The Ethersphere concept is a take-off on that of the visionary and science-fiction writer Arthur C. Clarke articulated in Wireless  magazine in 1945. A belt of satellites situated 22,000 miles above the equator could theoretically accomplish for global telecommunications what the Jesuit mystic Pierre Teilhard de Chardin's "Noösphere," a sort of global membrane acting as a super-brain, would accomplish for organic evolution.

Gilder is a leading technoguru and presumed nominalist who is always well situated, a sort of intelligence-gathering satellite stationed over Silicon Valley who makes occasional forays to the foyers where venture capitalists gather to prospect for the next blockbuster technology.

That was the case last March when he ventured to Zurich, Switzerland, to the "iridescent slopes of Davos" where "capitalist carousers" celebrated the début of what could be the "Intel of the Telecosm."

In the May 1998 edition of the Gilder Technology Report , Gilder laid the groundwork for the next microcosmic or terrestrial phase. The semiconductor industry is now producing around 25 square miles of chips a year, with about 46 thousand trillion transistors, those tiny switches that have changed everything.

Bandwith or communications power has been the bottleneck, Gilder writes. But that is about to change. Two principles will govern the era we are now entering:

  • Bandwith will replace both switching and power.

  • Optical and wireless bandwith will rule. They are growing at least twice as fast as [Intel's Gordon] Moore's Law, which doubles silicon efficiency every 18 months.

"In the new era, rather than using transistor switches and power to compensate for inadequate bandwith, successful companies will use bandwith to make up for inadequate power and silicon area," in Gilder's view. "The new Intels will race down the learning curve with ever more cost effective broadband components."

One of the leaders in the race, the focus of the soirée in Zurich, is a company named Uniphase based in San Jose. Uniphase makes an erbium-doped fiber amplifier. Amplifiers like these, from Gilder's elevated perspective, are "the key devices for linking the network computers of the future to the crystal cathedrals of an all optical web."

And in a true Borgesian paradox, these optical amplifiers create, in effect, more space in less room  for signals to flow because the path of light, characterized by chromatic dispersion in current fiber networks, adopts a "straight and narrow" wavelength under their influence.

"Just as the original IC [integrated circuit] of [Robert] Noyce and Moore ultimately put an entire computing system on a single sliver of silicon," Gilder writes, "so the new integrated circuit promises to put an entire communications system on a seamless seine of silica."

It is as if today's technologists are adopting the mindset of the Medieval scholastic philosopher and archnominalist William of Ockham, he of "Occam's Razor" fame. His principle of logic counsels to "shave off" those concepts, variables or constructs not really necessary to explain something. Choose the straight line. Chromatic dispersion has gotta go.

Internet Timescapes Under Surveillance

Gilder's reports are replete with charts and graphs showing the growth of worldwide fiber and fiber networks, Internet traffic, web development tools, E-commerce, PCs vs. TVs, and optoelectronic components.

For the past three years, since the National Science Foundation gave up its stewardship role, the Internet has developed willy-nilly. The new connections made every hour among its backbones have not been systematically tracked. Thus, we haven't been able to evaluate its job performance, nor can we diagnose incipient disease.

What we need, say some, is a connectivity "catscanner" that will give network operators, designers, and researchers a window through which to visualize its evolution, especially as its use expands for 'streaming' audio and video, distance education, entertainment, and telephony.

Researchers at the University of California's San Diego Supercomputer Center report in the British journal Nature  that they have devised just such a tool. Called "skitter," the tool tracks Internet tomography by sending data-packet scouts to tens of thousands pre-determined destinations and plotting what paths they take.

Routing behavior among provider networks can be tracked by skitter. From the patterns that show up--the labyrinthine patterns of global connectivity--optimal gateway protocols can be designed and packet-traffic congestion avoided.

The predicament of a packet poised at a gateway is shared by some of Borges' characters. Which path to follow? Which tortuous path should be pursued and stamped in time? Or in the "infinite series of times, a growing, dizzying web of divergent, convergent, and parallel times" that results in "a fabric of times" that "forks, perpetually, into countless futures." That's the haunting vision of the Borges' character Stephen Albert.

Albert contemplates the lost labyrinth of Ts'ui Pen in The Garden of Forking Paths. He reflects Borges' own personal dilemma of projecting mathematical worlds while being bound nostagically to his own, the one that ceaslessly nurtured his imagination with its mysteries, its allegories, and its humanity.

    It was under English trees that I meditated on that lost labyrinth: I pictured it perfect and inviolate on the secret summit of a mountain; I pictured its outlines blurred by rice paddies, or underwater; I pictured it as infinite--a labyrinth not of octagonal pavilions and paths that turn back upon themselves, but of rivers and provinces and kingdoms....I imagined a labyrinth of labyrinths, a maze of mazes, a twisting, turning, ever-widening labyrinth that contained both past and future and somehow implied the stars.... The evening was near, yet infinite.

      --The Garden of Forking Paths
       Jorge Luis Borges
       Buenos Aires, 1942

    --William Hoffman

Disclaimer: The opinions expressed herein are the writer's own.

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Circle Limit I. 1958. M.C. Escher works (c) Cordon Art-Baarn-the Netherlands. All rights reserved. Used by permission.