Pickover was elected as a Fellow for the Committee for Skeptical Inquiry for his "significant contributions to the general public's understanding of science, reason, and critical inquiry through their scholarship, writing, and work in the media."[3] Other Fellows have included Carl Sagan and Isaac Asimov. He has been awarded almost 700 United States patents,[1] and his The Math Book was winner of the 2011 Neumann Prize.[4]
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.[2]
Work
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.[8] 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."[9] Pickover is an inventor with over 700 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.[2]
Pickover is author of hundreds of technical papers in diverse fields, ranging from the creative visualizations of fossil seashells,[10] genetic sequences,[11][12] cardiac[13] and speech sounds, and virtual caverns[14] and lava lamps,[15] to fractal and mathematically based studies.[16][17][18][19] 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").[20] Additional visualization work includes topics that involve breathing motions of proteins,[21] snow-flake like patterns for speech sounds,[22] cartoon-face representations of data,[23] and biomorphs.[24]
Pickover has also written extensively on the reported experiences of people on the psychotropic compound DMT.[25][26] Such apparent entities as Machine Elves are described as well as "Insects From A Parallel Universe".[26]
On November 4, 2006, he began Wikidumper.org, a popular blog featuring articles being considered for deletion by English Wikipedia.
Pickover stalks
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 set 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.[27][28]
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.[29]
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".[30]
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.[31]
In addition to "Vampire numbers",[32] a term Pickover actually coined, he has coined the following terms in the area of mathematics: Leviathan number,[33]factorion,[34]Carotid–Kundalini function and fractal,[35] batrachion,[36]Juggler sequence,[37] and Legion's number,[38] among others. For characterizing noisy data, he has used Truchet tiles and Noise spheres,[39] the later of which is a term he coined for a particular mapping, and visualization, of noisy data to spherical coordinates.
In 1990, he asked "Is There a Double Smoothly Undulating Integer?",[40] and he computed "All Known Replicating Fibonacci Digits Less than One Billion".[41] With his colleague John R. Hendricks, he was the first to compute the smallest perfect (nasik) magic tesseract.[42] The "Pickover sequence" dealing with e and pi was named after him,[43] as was the "Cliff random number generator"[44] and the Pickover attractor, sometimes also referred to as the Clifford Attractor.[45][46]
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.".[47] 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.
History of science and mathematics
Starting in 2008, Pickover's books began to focus on the history of science and mathematics, with such titles as Archimedes to Hawking, as well as The Math Book, The Physics Book, and The Medical Book—a trilogy of more than 1,500 pages that presents various historical milestones, breakthroughs, and curiosities.
WikiDumper.org
Wikidumper.org is a website created by Pickover that promises to permanently record a snapshot of the "best of the English Wikipedia 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.[48]
Benoit B. Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory.
The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not diverge to infinity when iterated starting at , i.e., for which the sequence , , etc., remains bounded in absolute value.
In mathematics, Lyapunov fractals are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values A and B.
Ahmes was an ancient Egyptian scribe who lived towards the end of the Fifteenth Dynasty and the beginning of the Eighteenth Dynasty. He transcribed the Rhind Mathematical Papyrus, a work of ancient Egyptian mathematics that dates to approximately 1550 BC; he is the earliest contributor to mathematics whose name is known. Ahmes claimed not to be the writer of the work but rather just the scribe. He claimed the material came from an even older document from around 2000 B.C.
Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus.
Scientific visualization is an interdisciplinary branch of science concerned with the visualization of scientific phenomena. It is also considered a subset of computer graphics, a branch of computer science. The purpose of scientific visualization is to graphically illustrate scientific data to enable scientists to understand, illustrate, and glean insight from their data. Research into how people read and misread various types of visualizations is helping to determine what types and features of visualizations are most understandable and effective in conveying information.
A cellular automaton (CA) is Life-like if it meets the following criteria:
In recreational mathematics, a vampire number is a composite natural number with an even number of digits, that can be factored into two natural numbers each with half as many digits as the original number, where the two factors contain precisely all the digits of the original number, in any order, counting multiplicity. The two factors cannot both have trailing zeroes. The first vampire number is 1260 = 21 × 60.
Mordechai Meirovitz is an Israeli telecommunications expert and games maker.
Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They are so named after the researcher Clifford Pickover, whose "epsilon cross" method was instrumental in their discovery. An "epsilon cross" is a cross-shaped orbit trap.
In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point on the chord a distance p from one end and a distance q from the other is a closed curve whose enclosed area is less than that of the original curve by . The theorem was published in 1858 by Rev. Hamnet Holditch. While not mentioned by Holditch, the proof of the theorem requires an assumption that the chord be short enough that the traced locus is a simple closed curve.
In number theory, a juggler sequence is an integer sequence that starts with a positive integer a0, with each subsequent term in the sequence defined by the recurrence relation:
The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success.
Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both free and commercial. Mobile apps are available to play or tinker with fractals. Some programmers create fractal software for themselves because of the novelty and because of the challenge in understanding the related mathematics. The generation of fractals has led to some very large problems for pure mathematics.
The following is a timeline of scientific computing, also known as computational science.
The Math Book is a book by American author Clifford A. Pickover.
The Sumario Compendioso was the first mathematics book published in the New World. The book was published in Mexico City in 1556 by a clergyman Juan Diez.
Hamid Naderi Yeganeh is an Iranian mathematical artist and digital artist. He is known for using mathematical formulas to create drawings of real-life objects, intricate and symmetrical illustrations, animations, fractals and tessellations. Naderi Yeganeh uses mathematics as the main tool to create artworks. Therefore, his artworks can be totally described by mathematical concepts. Mathematical concepts he uses in his work include trigonometric functions, exponential function, Fibonacci sequence, sawtooth wave, etc.
↑ Weisstein, Eric, W. "Leviathan Number". From MathWorld--A Wolfram Web Resource. Retrieved August 14, 2008.{{cite web}}: CS1 maint: multiple names: authors list (link)
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