The Labyrinth Key

by Howard V. Hendrix

  As early as 1984, David Deutsch realized that computers, too, ought to obey the laws of quantum physics, as those laws are more fundamental than the laws of classical physics. A classical computer can address only one question at a time—a sequential approach that is much slower than if the computer can address many questions at the same time, as a quantum computer can. For cryptology, think of keys and locks: A classical computer faced with many billions of possible keys for a lock must try each key in the lock, one after the other. A quantum computer, however, can try all the keys in the lock simultaneously.

  Q. How is this done?

  A. One group of physicists (the superpositionists) view the quantum computer as performing all those billions of keyings simultaneously in a single machine. Another group of physicists (the manyworlders or multiversalists) view the quantum computer as billions of quantum computers, each machine in a separate universe, each trying just one key. For the former group, the answer arises from summing over the billions of superposed states of a single machine in a single universe. For the latter group, the answer arises from summing over billions of universes, each with its own machine. Curiously enough, the latter explanation is now becoming increasingly accepted.

  Q. How are governments and corporations using computers for cryptology, cryptography, and cryptanalysis?

  A. First we need to define those terms. Cryptology, the study of the hidden, is usually broken down into cryptography (the creation of hidden writing, or code making) and cryptanalysis (the analytical revealing of the hidden, or code breaking). Computers are the paramount tool in all these areas today, because most codes are broken mathematically. That's why the U.S. National Security Agency is the world's single largest employer of mathematicians.

  Quantum computing is a logical extension in all these areas. However, it also generates interesting results for the whole secrecy business. Looked at one way, quantum computing is the death of cryptography, for with such systems it should be possible to break any code. Looked at another way, quantum computing is the death of cryptanalysis, since with such systems it should be possible to create codes that cannot be broken. The entire situation is like the old theological conundrum about whether or not God could create a rock so heavy that God could not lift it.

  Many theorists believe that, in the long informational arms race between the cryptographers and the cryptanalysts, quantum computing means that the cryptographers have at last won out. That's why a quantum crypto hardline runs from the Pentagon to the White House—for supposedly invulnerable encrypted communication.

  I don't think such invulnerability can really be achieved, however. Even when messages are successfully transferred over channels that cannot be eavesdropped upon or otherwise compromised, those messages must eventually become plaintext in machines that are not quantum-secure, or in the minds of human beings, who are also notoriously prone to side-band attacks (which can include just about anything, from bribes to sexual favors).

  As for the cryptanalysts, especially those working in more complex contexts, it is appropriately humbling to recall Hamlet's words to his college friend: "There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy."

  Q. Might these "more things in heaven and earth" include multiple universes?

  A. They might.

  Q. What are the schools of thought relating to single vs. multiple universes? What studies are being done in relation to multiple universes, and by whom?

  A. As mentioned earlier, the primary split is between the superpositionists, who propose a single real universe, and the multiversalists, who hold with multiple, real, but "apparently virtual" universes. The labyrinthists and the mazists, as I like to think of them.

  I would like to think that a Principle of Complementarity applies here too, where mazes precipitate into labyrinths and labyrinths sublime into mazes. One of the most important developments out of this contest between superpositionists and multiversalists concerns the finitude or infinitude of the cosmos, and the plurality or singularity of its components.

  Among those who tend to talk about universes in the singular are the supporters of the holographic principle, who believe that, just as all the information describing a 3-D scene can be encoded into patterns of light and dark on a 2-D piece of film, so too can our seemingly 3-D universe be understood as completely equivalent to quantum fields and physical laws "painted" on a distant, vast, but usually spherical and finite, surface.

  Among those who tend to talk about universes in the plural, the multiversalists most prominently speak about an infinitude of universes in essentially infinite space.

  These positions may appear irreconcilable, but I don't think they are. The holographic position stems from Albert Einstein's work on gravity and Claude E. Shannon's work in information theory, pushed by John A. Wheeler in his suggestion that the physical world should be regarded as made of information, with matter and energy as secondary in importance. This position is particularly popular around Princeton—both the university and the Institute for Advanced Study—and includes among its proponents people like Edward Witten, Steven Gubser, Igor Klebanov, and Alexander Polyakov.

  Appropriately, those who are fans of the multiversalist position tend to be more thinly spread over more institutions, and they have proposed at least four different types of multiverses: limit-of-observation, bubble nucleation, quantum, and physical law-differentiated. Oddly enough, the work of John A. Wheeler is very important to this group too.

  What I try to get at with my vast memory palace in this novel is a reconciliation of the two, through the reconciling of infinite number with finite extent. The finite space from 0 to 1 on the number line, for instance, can be infinitely divided so as to represent all possible numbers in that space. Likewise, perhaps the system of all possible universes exists in a space—spherical, finite, unbounded, and consistent—in whose surface is holographically encoded an infinite number of possible universes, all mutually inconsistent with each other, all literally bounded by infinity. An infinity of discrete universes bounded by the finite continuum of the plenum.

  Q. What are the ramifications of these studies in relation to our lives?

  A. The more the idea of parallel universes, multiverses, and what I have called the "plenum" become scientifically accepted, the more likely it is that the idea of "historic inevitability" will be discredited. And, if and when full scientific acceptance of the alternativity of universes does come, that acceptance will in many ways be due to quantum computing and quantum cryptology.

  Even here on the classical (as opposed to quantum) scale, when we are told to "Remember!" the singular event—rather than think about its possible causes—we are led to obliterate the possibility of considering what might otherwise have been. We are not allowed to think about how American economic and foreign policy might have influenced the events of December 7, 1941, at Pearl Harbor, or September 11, 2001, in New York City and Washington, D.C. We are told that, given the enormity of such events, there's no reason to make use of reason—and that the only response to an unalterable inevitability is unthinking reaction.

  However, a quantum understanding of reality significantly undermines this idea of blind, historical inevitability. We are free to think again, no matter what the enormity of the event, because we are able to realize that even the most tragic event was not an act of God or nature, but something done by human beings, for human reasons, and therefore may properly be analyzed by human reason.

  In discussing "apocalyptic" events, it is all too appropriate to speak of religion here—and science, too. The Greek root word of apocalypse (apokaluptein) means to "reveal," to "lift the veil" of this world and see through to truth—a fundamentally cryptanalytic operation. Science, too, has long been obsessed with revealing secrets, or as the sixteenth-century French diplomat and cryptologist Vigenère, who is quoted in The Labyrinth Key, actually said:

  All the things in the world constitute a cipher. All nature is merely
a cipher and a secret writing. The great name and essence of God and his wonders, the very deeds, projects, words, actions, and demeanor of mankind—what are they for the most part but a cipher?

  So perhaps it's not so very strange that my research eventually led me from the mathematical and cryptological into the numerological and mystical.

  The final limiting cases—and ultimate side-band attacks—on all of this are to be found in the "wet-war" dimension, the realm of hearts and minds where ethics and morals are the deciding factors. What we do with our classical "hard-war" or quantum "soft-war" machinery is up to the subtler "wetwar" machineries found in our cultures and in our heads. Machineries that may, one day, overcome the desire for war itself.

  In the end, it's up to us to decide whether the "apocalypse" we choose is the cryptanalytic "lifting" of the veil in our search for truth—or the cryptographic "rending" of that veil in destruction, extinction, and oblivion. As we move more deeply into the Age of Code—that epoch begun with the decoding of organic life and DNA begun by Watson, Crick, and Wilkins, and the encoding of an artificial life of bits and bytes begun by Turing, von Neuman, and Gödel—our choice becomes more important than we can remember, more important than we can know, more important than we can even imagine.

  I suggest we choose carefully—and, let us hope, wisely.

  SELECTED BIBLIOGRAPHY

  On the history of memory systems and mnemonics, I recommend in particular The Art of Memory by Frances Yates, The Book of Memory by Mary Carruthers, and Logic and the Art of Memory by Paolo Rossi.

  Many of Giordano Bruno's ideas and connections are documented in Paul-Henri Michel's The Cosmology of Giordano Bruno, Antoinette Paterson's The Infinite Worlds of Giordano Bruno, Frances Yates's Giordano Bruno and the Hermetic Tradition, Frances Boldereff's Hermes to His Son Thoth, Hilary Gatti's Giordano Bruno and Renaissance Science, and Karen Silvia DeLeon-Jones's Giordano Bruno and the Kabbalah.

  For my understanding of Ricci generally and his interest in memory palaces particularly, I am indebted to The Memory Palace of Matteo Ricci by Jonathan D. Spence, and Matteo Ricci's Scientific Contributions by Henri Bernard, S.J. I also found Spence's The Search for Modern China and God's Chinese Son very helpful as well.

  Books like David Deutsch's The Fabric of Reality, Dirk Bouwmeester's The Physics of Quantum Information Systems, and Colin P. Williams's Ultimate Zero and One—as well as a burgeoning number of Web sites—all discuss the link between quantum computing and multiple universes. Those interested in DNA computing and its possible links to quantum computing would do well to peruse Georghe Paun's DNA Computing.

  For those interested in further investigating the policy dimensions of memory and secrecy, I recommend James Bamford's The Puzzle Palace and Body of Secrets and a host of Web sites (including those put up by the National Security Agency itself), all of which provided invaluable detail on the workings of the NSA.

  Manuel De Landa's War in the Age of Intelligent Machines, Clifford Stoll's The Cuckoo's Egg, Robert L. Bateman's Digital War, Bert-Jaap Koop's The Crypto Controversy, Craig R. Eisendrath's National Insecurity, D. Curtis Schleher's Electronic Warfare in the Information Age, Bruce D. Berkowitz's Best Truth, Winn Schwartau's CyberShock and Information Warfare, Jeffrey Richelson's The Wizards of Langley, Simon Singh's The Code Book, and David Kahn's The Codebreakers all provided insight into the history and politics, as well as the mathematics, science, and linguistics, of what Michael Wilson calls "soft-war."

  For those interested in the connections between and among mathematics, numerology, cryptology, and mysticism, I recommend Amir D. Aczel's The Mystery of the Aleph, Isaac Myer's Qabbalah, and Daniel C. Matt's The Essential Kabbalah.

  The Labyrinth Key is a work of fiction. Names, places, and incidents either are products of the author’s imagination or are used fictitiously.

  2006 Del Rey Mass Market Edition

  Copyright © 2004 by Howard V. Hendrix

  All rights reserved.

  Published in the United States by Del Rey Books, an imprint of The Random House Publishing Group, a division of Random House, Inc., New York.

  DEL REY is a registered trademark and the Del Rey colophon is a trademark of Random House, Inc.

  Originally published in trade paperback in the United States by Del Rey Books, an imprint of The Random House Publishing Group, a division of Random House, Inc., in 2004.

  www.delreybooks.com

  eISBN: 978-0-345-49102-2

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