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He is currently an associate editor for the scientific journal Computers and Graphics and is an editorial board member for Odyssey and Leonardo. He is also the Brain-Strain columnist for Odyssey magazine, and, for many years, he was the Brain-Boggler columnist for Discover magazine.
Pickover has received more than 100 IBM invention achievement awards, three research division awards, and four external honor awards.
In the 1990s, Pickover created virtual caverns from extremely simple numerical simulations that reminded him of the Lechuguilla Cave, pictured here.
Example of Pickover stalks in a detail of the Mandelbrot set
Pickover's primary interest is in finding new ways to expand creativity by melding art, science, mathematics, and other seemingly disparate areas of human endeavor.
In The Math Book and his companion book The Physics Book, Pickover explains that both mathematics and physics "cultivate a perpetual state of wonder about the limits of thoughts, the workings of the universe, and our place in the vast space-time landscape that we call home."
Pickover is an inventor with over 600 patents, the author of puzzle calendars, and puzzle contributor to magazines geared to children and adults. His Neoreality and Heaven Virus science-fiction series explores the fabric of reality and religion.
Pickover is author of hundreds of technical papers in diverse fields, ranging from the creative visualizations of fossil seashells, genetic sequences, cardiac and speech sounds, and virtual caverns and lava lamps, to fractal and mathematically based studies. He also has published articles in the areas of skepticism (e.g. ESP and Nostradamus), psychology (e.g. temporal lobe epilepsy and genius), and technical speculation (e.g. "What if scientists had found a computer in 1900?" and "An informal survey on the scientific and social impact of a soda can-sized super-super computer"). Additional visualization work includes topics that involve breathing motions of proteins, snow-flake like patterns for speech sounds, cartoon-face representations of data, and biomorphs.
Pickover has also written extensively on the reported experiences of people on the psychotropic compound DMT. Such apparent entities as Machine Elves are described as well as "Insects From A Parallel Universe".
Pickover stalks are certain kinds of details that are empirically found in the Mandelbrot set in the study of fractal geometry. In the 1980s, Pickover proposed that experimental mathematicians and computer artists examine the behavior of orbit trajectories for the Mandelbrot in order to study how closely the orbits of interior points come to the x and y axes in the complex plane. In some renditions of this behavior, the closer that the point approaches, the higher up the color scale, with red denoting the closest approach. The logarithm of the distance is taken to accentuate the details. This work grew from his earlier work with Julia sets and "Pickover biomorphs," the latter of which often resembled microbes.
Frontiers of Scientific Visualization
In "Frontiers of Scientific Visualization" (1994) Pickover explored "the art and science of making the unseen workings of nature visible". The books contains contributions on "Fluid flow, fractals, plant growth, genetic sequencing, the configuration of distant galaxies, virtual reality to artistic inspiration", and focuses on use of computers as tools for simulation, art and discovery.
Visualizing Biological Information
In "Visualizing Biological Information" (1995) Pickover considered "biological data of all kinds, which is proliferating at an incredible rate". According to Pickover, "if humans attempt to read such data in the form of numbers and letters, they will take in the information at a snail's pace. If the information is rendered graphically, however, human analysts can assimilate it and gain insight much faster. The emphasis of this work is on the novel graphical and musical representation of information containing sequences, such as DNA and amino acid sequences, to help us find hidden pattern and meaning".
Vampire numbers and other mathematical highlights
In mathematics, a vampire number or true vampire number is a compositenatural numberv, with an even number of digitsn, that can be factored into two integersx and y each with n/2 digits and not both with trailing zeroes, where v contains all the digits from x and from y, in any order. x and y are called the fangs.
As an example, 1260 is a vampire number because it can be expressed as 21 × 60 = 1260.
Note that the digits of the factors 21 and 60 can be found, in some scrambled order, in 1260.
Similarly, 136,948 is a vampire because 136,948 = 146 × 938.
Vampire numbers first appeared in a 1994 post by Clifford A. Pickover to the Usenet group sci.math, and the article he later wrote was published in chapter 30 of his book Keys to Infinity.
In 1990, he asked "Is There a Double Smoothly Undulating Integer?", and he computed "All Known Replicating Fibonacci Digits Less than One Billion". With his colleague John R. Hendricks, he was the first to compute the smallest perfect (nasik) magic tesseract. The "Pickover sequence" dealing with e and pi was named after him, as was the "Cliff random number generator" and the Pickover attractor, sometimes also referred to as the Clifford Attractor.
Culture, religion, belief
Starting in about 2001, Pickover's books sometimes began to include topics beyond his traditional focus on science and mathematics. For example, Dreaming the Future discusses various methods of divination that humans have used since stone-age times. The Paradox of God deals with topics in religion. Perhaps the most obvious departure from his earlier works includes Sex, Drugs, Einstein, and Elves: Sushi, Psychedelics, Parallel Universes, and the Quest for Transcendence, which explores the "borderlands of science" and is "part memoir and part surrealist perspective on culture.". Pickover follows-up his "quest for transcendence" and examination of popular culture with A Beginner's Guide to Immortality: Extraordinary People, Alien Brains, and Quantum Resurrection.
Wikidumper.org is a website created by Pickover that promises to permanently record a snapshot of the "best of the English popflock.com resource rejects", articles that are slated for deletion at the English Wikipedia. WikiDumper was launched on November 4, 2006, and accepts user submissions. Although the site doesn't specify its criteria for inclusion, many of its articles don't cite their sources. The site has been criticized as likely to be less accurate than English Wikipedia.