The present bloggers, together with Francisco Aragon Artacho (University of Newcastle, Australia) and Peter Borwein (Simon Fraser University, Canada, and Jonathan Borwein’s brother), have just completed the paper Tools for visualizing real numbers: Planar number walks.
This manuscript describes analysis of the digits of pi and many other real numbers and quantifies various techniques of modern computer visualization. In most of these analyses, the authors address a real number (represented in base-4 digits, i.e., 0, 1, 2, 3) as a “random walk,” typically by moving one unit east, north, west or south, depending on whether the digit at a given
Continue reading New paper on visualizing digits of pi
Introduction
Since the middle of the last decade, well before the worldwide run-up in fuel prices during 2008, it has been widely believed that we are entering a new era of scarcity in carbon-based fuels such as oil and natural gas. Such concerns are not new, having first become prevalent in the 1970s. However, a rather quiet revolution is taking place on both fronts, leading to a new era of abundance that may prove as problematic as scarcity.
U.S. production
The United States, long an international symbol of profligate energy consumption, with a thirsty appetite for imported oil and gas,
Continue reading Feast or famine? Promoting green energy in an era of abundant gas and oil
Introduction
In the field most commonly known as “postmodern science studies” or, more specifically, “postmodern philosophy of science,” scholars attempt to critique science and mathematics from a high-level perspective. Two of these writers, Karl Popper and Thomas Kuhn, in the view of the present bloggers and many other working scientists, have significant and lasting merit and are worth taking seriously; for a mathematical perspective see, for example, our 2011 article [Exploratory Experimentation and Computation] and [Borwein2012]. Both Popper and Kuhn brought out their most influential books roughly fifty years ago.
Karl Popper
Karl Popper (1902-1994), the Austrian born British philosopher,
Continue reading Is modern science “forever tentative” and “socially constructed”? No Way!
In 1742, German mathematician Christian Goldbach wrote, in a letter to famed mathematician Leonhard Euler, that he believed “Every integer greater than two can be written as the sum of three primes.” In subsequent correspondence, the stronger version “Every even integer can be expressed as the sum of two primes” was suggested, as well as some other variants. The “odd” variant of the Goldbach conjecture is that every odd number greater than 7 can be expressed as the sum of three odd primes.
To this date, although extensive computer tests have found no counter-examples to these conjectures, no proofs are
Continue reading Terence Tao releases partial solution to the Goldbach conjecture
The 1969 movie “2001: A Space Odyssey” was a landmark science-fiction film, in many ways far ahead of its time. With the recent release of a 1080p Blu-Ray video version, home viewers can enjoy nearly the same stunning level of graphics and visual effects of the original big-screen theater release. Forty-three years later, in the wake of films like Star Wars, Star Trek, Alien and Avatar, and with full-time SciFi channels on cable/satellite TV, it is easy to underestimate the impact that “2001” made when it was first released. Steven Spielberg called it his film generation’s “big bang,” while in
Continue reading “2001: A Space Odyssey”: Art versus 2012 reality
Introduction
In the past few years, modern genome sequencing and computer technology have placed enormous volumes of DNA data at the fingertips of researchers worldwide. The first complete human genome sequence was completed in 2000, after a ten-year effort that cost over USD$500 million. But genome sequencing technology is advancing very rapidly — human genomes can now be sequenced for roughly $100,000, and some groups are targeting a price as low as $1,000 [Pollack2008]. This same sequencing technology has enabled biologists to study the genomes of thousands of other biological species, including many common (and not-so-common) plants and animals. This
Continue reading What does the latest DNA data say about evolution?
This year marks the 100th anniversary of the birth of famed British mathematician Alan Turing (23 June 1912 – 7 June 1954). The outline of his remarkable life and sad ending has by now become fairly well known. Turing laid numerous foundation stones of modern computing, ranging from the deepest mathematical nature of computing (using what are now called Turing machines he provided the modern approach to incompleteness and undecidability) to specific issues of practical design; he also contributed to mathematical biology (morphology) and much else. At the same time, he played a key role in the British government’s breaking
Continue reading Is your mate actually a computer? Would you pass the “Turing test”?
In his book Why Beliefs Matter: Reflections on the Nature of science, noted British mathematician E. Brian Davies surveys the sweeping landscape of modern philosophy of science and mathematics, with considerable skill and numerous thoughtful insights. Its closest analogue would be John Barrow’s 1992 book Pi in the Sky: Counting, Thinking and Being.
Davies is certainly qualified to write this book. He has published works in spectral theory, operator theory, quantum mechanics, and the philosophy of science. He served as the President of the London Mathematical Society from 2008-2009.
Some of Davies’ most intriguing comments relate to the nature of
Continue reading Book Review: “Why Beliefs Matter: Reflections on the Nature of Science”
The present bloggers have instituted a new category of brief postings under the rubric of “Numbers to note.” These are items that we see posted in news media or other sources with particularly interesting data of one type or another relating to either current events or to developments in science and/or technology. In many cases the notable numbers belie previous or current political bombast.
Our first posting comes from a very interesting set of charts just released by the U.S. Treasury entitled “The Financial Crisis Response in Charts”. This is chock-full of intriguing data on the recent financial crash of
Continue reading Numbers to note (#1): Treasury report on TARP program
Games are as old as human society as the image below illustrates. But as with all other parts of society, games and gaming are being profoundly changed by the computing and communication revolution.
Some of the changes are obvious, some are less so.
© Maler der Grabkammer der Nefertari. This work portrays the ancient Egyptian game of Senet
Computer games humans play
It is both useful and sobering to consider the enormous progress that has been made in computer technology over the past 50 years. Back in 1965 Intel co-founder Gordon Moore observed in a little-noticed article
Continue reading Are computers playing games with us?
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