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Physicists working at the Large Hadron Collider (LHC) at the CERN facility on the French-Swiss border today confirmed what many have suspected over the past few months — they have discovered a new subatomic particle that appears to be the long-sought Higgs boson, which is widely regarded as the key to why some elementary particles have mass, and thus why a universe with matter (and us) exists at all.
With the words “I think we have it,” director Rolf-Dieter Heuer signaled the longest (and most expensive!) search in the history of science. While more work needs to be done, the
Continue reading Higgs discovery underscores effectiveness of mathematical theory
In a previous Math Drudge blog, we mentioned the increasing number of instances of scientific fraud. We also noted how in many cases, mathematical and statistical methods have been utilized to uncover this fraud.
In November 2011, Netherlands psychologist Diederik Stapel was accused of publishing “several dozen” articles with falsified data. For example, one article claimed that disordered environments such as littered streets make people more prone to stereotyping and discrimination. After being accused of massive fraud in Science, Stapel confessed that the allegations were largely correct.
Now another Netherlands social scientist is in hot water. Some clever statistical analysis
Continue reading New case of scientific fraud
We woke up last Friday (in Oz) and Thursday (in the US). As usual, we scanned a selection of online newspapers, magazines and blogs: “Eurozone crisis will cost world’s poorest countries $238bn” blared the UK Guardian (once known as the Manchester Grauniad because of its typographic lapses). Really, not $237 billion or $239 billion? Perhaps this was just a dodgy headline. Sadly it was not — the article soberly reports that the cost will be exactly this figure, an impossible level of certainty for an economic forecast!
Many other such examples come to mind. On 18 Oct 2006, the venerable
Continue reading Bad numbers are bad news
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”?
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