ACM: First off, let's talk about some things you have accomplished in the past.
What did you receive first prize for, in the Beauty of Physics Photo Competition? What was the photo of?
Pickover: I received first prize for a computer graphics rendition of a seashell based on a logarithmic spiral. The rendering was particularly realistic, and I've since taken the research further by representing more complicated fossil seashells that contained animals that lived during the time of the dinosaurs.
ACM: Tell me about your 3-D computer mouse.
Pickover: U.S. Patent 5,095,302 describes a mouse with a cavity into which a user places a finger, and the up-and-down motion of the finger in the hole can specify information that would be useful for 3-D motions. The patent also discusses the use of a ring, on a mouse, into which a user places a finger. The ring can then be moved up and down to specify additional information.
ACM: Tell me about your computer icons, what's so strange about them?
Pickover: U.S. patent 5,564,004 discusses several kinds of strange icons. In my favorite embodiments, the computer system uses artificial intelligence to predict icons that a user is next likely to use and, as a result, the icons swim to the mouse-driven cursor to facilitate their selection. In another embodiment, fuzzy icon selection permits users to be sloppy about placing their cursors directly on an icon. Simply being near the icon, based on Voronoi-polyhedra computations, is sufficient for icon selection.
ACM: At IBM, what have your awards been for?
Pickover: I've received many awards at IBM, most notably patent awards, research division awards, and external honor awards. One research division award was for my design of a 3-D virtual space- kaleidoscope, shown at SIGGRAPH, and which runs on IBM's new line of high-end personal computers called IntelliStations. Another research division award was for a 3-D graphics program used by circuit designers. The external honor awards were for my various editorial positions with journals such as Computers and Graphics, Computers and Physics, Theta, Leonardo, and others. The patent awards were for a range of ideas, many of which dealt with novel icons and windows, and their appearance and interactions.
ACM: Now let's talk about some of your current activities.
What's the "brain-boggler" column in Discover?
Pickover: Discover magazine is a popular science magazine that reaches several million readers each month. I write most of the brain-boggler columns. A column appears on the last page of each issue. My puzzles are meant to stimulate the imagination of readers of all ages and are therefore playful and diverse. For a typical puzzle, see a reprint of "Welcome to Worm World" which appears on my homepage.
ACM: What's "Leonardo?"
Pickover: Leonardo is a fascinating reviewed journal dealing with subjects at the intersection of art and technology. I'm on their editorial board and occasionally write book reviews for them. I also have published numerous papers in Leonardo.
ACM: What do you work on at IBM?
Pickover: My primary interests at IBM include scientific visualization and 3-D graphics. I often find that the line between science and art becomes blurred. Recently I have joined a group interested in promoting IBM's new IntelliStation, and for this project I create various eye-catching demonstrations using the blazingly fast graphics provided by this inexpensive, dual-processor professional workstation.
ACM: Now for some general questions:
Explain how your books meld art, science and mathematics.
Pickover: Imagery is the heart of much of the work in my books. To help understand what is around us, we need eyes to see it. Computers with graphics can be used to produce visual representations with a myriad of perspectives, many of which are beautiful to the eye. In many cases, the computer graphics function like a stain applied to a wood grain to bring out and highlight hidden structures. In my books, the applications are varied and include fields as diverse as speech synthesis, molecular biology, mathematics, and art. Yet I hope that they all combine to illustrate the wonder in "lateral thinking".
Lateral thinking is reasoning in a direction not naturally pointed to by a scientific discipline. It is reasoning in a direction unexpected from the actual goal one is working toward. In my books, the term "lateral thinking" is used in an extended way to indicate not only action motivated by unexpected results, but also the deliberate drift of thinking in new directions to discover what can be learned. It is also used to indicate the application of a single computer software tool to several unrelated fields.
ACM: Do you believe computers can expand the soul? If so, how?
Pickover: Computers, mathematics, and freedom -- three words which may never before have appeared together in a single sentence. However, computers and computation are now providing humankind with an unlimited landscape for exploration, and unparalleled aid for the imagination. Since their rapid growth following the Second World War, computers have changed the way we perform scientific research, conduct business, create art, and spend our leisure time. The Loom of God, like my other books, was written to illustrate the eclectic nature of computer territory. It contains a collage of topics, many which can be effectively explored using a computer, and many which deal with mind-numbing concepts of infinity, creation, mysticism and art. My strange book designs are meant to shape readers' views of of reality. This approach is probably apparent in poetry or fiction, but is too seldom used in science books.
I like to speculate on how computers can and will expand our souls. Who knows what intelligent machines and computers we will create that will be our ultimate heirs? These creatures might survive virtually forever, and our ideas, hopes, and dreams carried with them. There is a strangeness to the loom of our universe which may encompass time travel, higher dimensions, quantum superspace, and parallel universes -- worlds that resemble our own and perhaps even occupy the same space as our own in some ghostly manner. Our heirs, whatever or whoever they may be, will explore these new regions of the loom. They will explore space and time. They will seek their salvation in the stars.
ACM: The publicity material accompanying your book describes you as "one of the world's most prominent and controversial science writers." Can you give me one or two examples of controversies that you've caused, and can you explain why some people would find your work controversial?
Pickover: I suppose my work might sometimes be considered controversial because, in my prolificness, I often blend the seemingly-disparate fields of art, science, mathematics, computers, science fiction, astronomy, puzzles, and mysticism. My sometimes-serious, sometimes- playful conglomeration is not usually considered the typical domain of a scientist. One of my goals is to stimulate creativity, to expand the minds of both children and adults. I continually ask questions in my books. For example, I've published surveys in which I ask scientists and computer professionals to predict the impact of placing an IBM PS/2 in the year 1900. I ask about the impact of giving everyone on the planet a soda-canned-sized supercomputer with unlimited memory and computational power (published in Computers in Physics). I created ranking of the 10 most influential scientists in history for The History and Social Science Teacher. I've published "What if every computer failed tomorrow?" in IEEE Computer. Although I've won many awards for my computer art, there is still a controversy regarding whether mathematically-driven art is art at all.
ACM: On your Web site, you say that you want to shatter our minds. What does that mean? Won't that hurt?
Pickover: If the properties we assign to the natural world are partly expressions of the way we think and our capacity for understanding, then the introduction of new tools such as the computer will change those properties. The computer, like a microscope, expands the range of our senses. The world made visible by the computer seems limitless.
If Pablo Picasso were alive today, would he give up his canvas, oil paints, and brush for a computer terminal? What about Lenoardo da Vinci? Even if they could not obtain funding from the National Science Foundation or the National Endowment for the Arts, they could -- with just a personal computer -- create, manipulate, and store fairly sophisticated art works. Perhaps Leonardo would spend a large amount of his time inventing entirely new computer input devices to substitute for today's standard mouse. These devices would allow him to precisely emulate his own masterful brush strokes, the viscosity and drip of wet paint, or a chisel chipping away at an imaginary chunk of shiny marble. Voice recognition programs would allow Leonardo to make voice requests, and special goggles would allow him to peer into colorful new worlds limited only by computers, and the imagination.
THE LOOM OF GOD is meant to expand your mind To this end, chapters such as "Fractals and God," "The Eye of God," and "Perfection," and many others, attempt to tear the fabric of your ordinary thinking and to push your imagination to the breaking point. The seemingly incongruous juxtaposition of mind-stretching exercises with sections on Stonehenge, art, and mathematical proofs of God, should stimulate creative thinking. Art and science will eventually be seen to be as closely connected as two wings on a bird. Both are vital elements of order and its discovery. When science studies how and why things fit together it becomes art. And when art portrays the world in a way that withstands the test of time, its connection with science becomes clear.
ACM: The Net has moved more toward being an image-based medium than information-based, according to some people. Do you think this is true and, if so, is it a bad thing? Critics say the emphasis on graphics lessens the value of the Net as an educational tool. Do you disagree? If so, why are graphics important to the Net, other than for their value as advertising tools?
Pickover: The web is a marvelous medium for sharing images with colleagues, even though this method of exchange is slower than some would like. On my web page, I can conveniently share scientific visualizations, computer art, virtual caverns, educational JAVA applets.... The net has been indispensable for my own research -- for finding information and for permitting fruitful collaborations. Even for my artwork, the net has proven to be invaluable, with data coming from computers at one part of the world and rendered in my office. I have published many scientific papers with individuals I never met, and never would have met, except for the Net. I interact with high school students from around the world, with scientists, with some of the deepest thinkers of our time. Without the net, such convenient cross-fertilization of ideas would be impossible.
ACM: On your book "The Loom of God":
Tell me about your new book, "The Loom of God," published by Plenum.
Pickover: Mathematics and mysticism have fascinated humanity since the dawn of civilization. Has humanity's long-term fascination with mathematics arisen because the universe is constructed from a mathematical fabric? Is God a mathematician? Certainly, the world, the universe, and nature can be reliably understood using mathematics. Nature is mathematics. In THE LOOM OF GOD, I take the position that nature is almost always describable by simple formulas not because we have invented mathematics to do so but because of some hidden mathematical aspect of nature itself. I do not know if God is a mathematician, but mathematics is the loom upon which God weaves the fabric of the universe.
The book will be of particular interest to computer hobbyists because it contains simple computer recipes for exploring a range of numerical mysteries, doomsday scenarios, religion and art, and even asteroid impacts.
ACM: Would you give an example from your book of how mathematicians are probing some of mankind's deepest mysteries?
Pickover: We can hardly imagine a chimpanzee understanding the significance of prime numbers, yet the chimpanzee's genetic makeup differs from ours by only a few percentage points. These minuscule genetic differences in turn produce differences in our brains. Additional alterations of our brains would admit a variety of profound concepts to which we are now totally closed. What mathematics is lurking out there which we can never understand? How do our brains affect our ability to contemplate God? What new aspects of reality could we absorb with extra cerebrum tissue? And what exotic formulas could swim within the additional folds? Philosophers of the past have admitted that the human mind is unable to find answers to some of the most important questions, but these same philosophers rarely thought that our lack of knowledge was due to an organic deficiency shielding our psyches from higher knowledge.
If the Yucca moth, with only a few ganglia for its brain, can recognize the geometry of the yucca flower from birth, how much of our mathematical capacity is hardwired into our convolutions of cortex? Obviously specific higher mathematics is not inborn, because acquired knowledge is not inherited, but our mathematical capacity is a function of our brain. There is an organic limit to our mathematical depth.
How much mathematics can we know? The body of mathematics has generally increased from ancient times, although this has not always been true. Mathematicians in Europe during the 1500's knew less than Grecian mathematicians at the time of Archimedes. However, since the 1500's humans have made tremendous excursions along the vast tapestry of mathematics. Today there are probably around 300,000 mathematical theorems proved each year.
On a similar line of thought, a dog cannot understand Fourier transforms or gravitational wave theory. Human forebrains are a few ounces bigger than a dog's, and we can ask many more questions than a dog. Linguist Noam Chomsky once noted that a rat can learn to turn left at every second fork in a maze, but not at every fork corresponding to a prime number. The human mind, limited by the same kinds of biological constraints as the rat, may reach the edge of its ability to comprehend. We are flesh and blood, not Gods. Are there facets of the universe we can never know? Are there questions we can't ask? Our brains, which evolved to help us find food on the African plains, are not constructed to penetrate all the enigmas in the infinite mathematical cloak of our universe.
Note, however, we do have a chance of understanding a great deal about the universe. The fact that reality can be described or approximated by simple mathematical expressions suggests to me that nature has mathematics at its core. Formulas like E = m c sup 2 , F = m a , 1 + e (superscipt) (i pi ) = 0 , and lambda = h / m v all boggle the mind with their compactness and profundity.
ACM: How could God possibly be explained in numerical terms?
Pickover: In the Loom of God, to start you on your journey, I first trace the logic of mathematics far back in time and examine humanity's search for ultimate answers to the mystery of existence, God, and the universe. The initial focus is around 550 B.C. because numbers had an auspicious reign in ancient Greece, especially for the Pythagoreans, the secret society devoted to exploring the mysteries of numbers. To the Pythagoreans, mathematics was an ecstatic revelation. The Pythagoreans, like modern day fractalists, were akin to musicians. They created pattern and beauty as they discovered mathematical truths. Mathematical and theological blending began with Pythagoras, and eventually affected all religious philosophy in Greece, played a role in religion of the Middle Ages, and extended to Kant in modern times. Bertrand Russell felt that if it were not for Pythagoras, theologians would not have sought logical proofs of God and immortality.
ACM: Tell me about mathematical proofs for the end of the world.
Pickover: In the Loom of God I discuss many end-of-the-world scenarios -- from ancient theological prophesies to modern astrophysical predictions. Numbers have played a central role in both religious and scientific apocalypses. Population biologists have used formulas for predicting population explosions and the demise of the Earth. Astronomers have used numbers to predict the likelihood of obliteration by asteroids and comets. Religions and religions people have used numbers for determining precisely how and when the world will end.
ACM: Tell me about "theomatics."
Pickover: The emphasis of this book is on theomatics -- a word I use to denote the blending of mathematics and religion. In our modern era, God and mathematics are usually placed in totally separate arenas of human thought. But as this book will show, this has not always been the case, and even today many mathematicians find the exploration of mathematics akin to a spiritual journey. The line between religion and mathematics becomes indistinct. In the past, the intertwining of religion and mathematics has produced useful results and spurred new areas of scientific thought. Consider as just one small example numerical calendar systems first developed to keep track of religious rituals. Mathematics in turn has fed back and affected religion because mathematical reasoning and "proofs" have contributed to the development of theology.
In many ways, the mathematical quest to understand infinity parallels mystical attempts to understand God. Both religion and mathematics attempt to express relationships between humans, the universe, and infinity. Both have arcane symbols and rituals, and impenetrable language. Both exercise the deep recesses of our minds and stimulate our imagination. Mathematicians like priests seek "ideal", immutable, nonmaterial truths and then often try to apply these truths in the real world. Some atheists claim another similarity: mathematics and religion are the most powerful evidence of the inventive genius of the human race.
ACM: A couple of final questions:
Do you ever sleep?
Pickover: When people ask if I ever sleep, I reply that I sleep well, although most of my creative ideas come from the twilight realm between sleep and wakefulness. When I wake up I quickly write down my ideas, many of which are finally published in books. I owe much of my productivity to: efficiency, the desire to create, and having a supportive family life that permits time for creating.
ACM: If you had to choose one achievement of yours that ACM members should know about, what would it be?
Pickover: My books have been translated into Japanese, Polish, German, and Chinese, and judging from the 1000s of letter's I've received, my work is very much appreciated around the world.
Many readers may be curious about the diversity of my interests. My Ph.D. is from Yale University's the Department of Molecular Biophysics. I write on subjects ranging from art, to aliens, to mathematics. My hobbies include the practice of Ch'ang-Shih Tai-Chi Ch'uan (a form of martial arts) and Shaolin Kung Fu, raising golden and green severums (large tropic fish found in the central Amazon basin), and piano playing. I think of a patentable idea nearly every day, although most are never disclosed due to time constraints. I am fascinated by scientific visualization -- the use of the computer for exploring our universe, expanding our minds, producing beauty, and finding patterns in ways not possible before computers cohabited our planet.
My web site has attracted over 45,000 visitors, and my work has appeared on several TV shows and in all major, popular science magazines.
ACM: Last question: what are some nice things people have said about your work?
Pickover: I suppose among the nicest are:
ACM: Thank you so much for this interview, some of which appears in the May 1997 ACM Membernet. Good luck in all your extrordinary voyages and adventures of the mind.
Pickover: Thank you. I've enjoyed talking with you.