Mathematics

From math and computer science writer Kevin Hartnett at Quanta: Over the last decade physicists and mathematicians have been exploring a surprising correspondence that has the potential to breathe new life into the venerable Feynman diagram and generate far-reaching insights in both fields. It has to do with the strange fact that the values calculated from Feynman diagrams seem to exactly match some of the most important numbers that crop up in a branch of mathematics known as algebraic geometry. These values are called “periods of motives,” and there’s no obvious reason why the same numbers should appear in both settings. Indeed, it’s as strange as it would be if every time you measured a cup of rice, you observed Read More ›

From at ScienceDaily: Scientific discoveries often arise from noticing the unexpected. Such was the case when researchers, studying a tiny device that has become increasingly important in disease diagnostics and drug discovery, observed the surprising way it funneled thousands of water droplets into an orderly single file, squeezing them drop by drop, out the tip of the device. Instead of occurring randomly, the droplets followed a predictable pattern. These observations led the researchers to deduce mathematical rules and understand why such rules exist. … “Beyond the immediate relevance to microfluidics, we believe our findings could one day be applied to forming nanocrystals into precise shapes,” Tang said. Researchers do not yet have a way to exert the sort of steady Read More ›

From professor of pharmacology David Colquhoun at Aeon: The aim of science is to establish facts, as accurately as possible. It is therefore crucially important to determine whether an observed phenomenon is real, or whether it’s the result of pure chance. If you declare that you’ve discovered something when in fact it’s just random, that’s called a false discovery or a false positive. And false positives are alarmingly common in some areas of medical science. … In 2005, the epidemiologist John Ioannidis at Stanford caused a storm when he wrote the paper ‘Why Most Published Research Findings Are False’, focusing on results in certain areas of biomedicine. He’s been vindicated by subsequent investigations. For example, a recent article found that Read More ›

MathematicianRoger Penrose recently published Fashion, Faith, and Fantasy in the New Physics of the Universe, reviewed by Richard Dawid in Nature. Dawid is peeved: There are similar issues with Penrose’s claim that fashion is the main reason for string theory’s influential position. His analysis of its problems is not up to the task of debunking proponents’ physics-based reasons for confidence. Penrose’s main complaint about string theory is that it lacks a clear specification of its number of degrees of freedom. He tries to show this in several contexts. However, he tends to omit information that could make the situation less confusing than he takes it to be. For example, he expresses unease about ‘gauge–gravity duality’, the claim that string theory Read More ›

Here: Science has made great strides in modeling space, time, mass and energy. Yet little attention has been paid to the precise representation of the information ubiquitous in nature. Introduction to Evolutionary Informatics fuses results from complexity modeling and information theory that allow both meaning and design difficulty in nature to be measured in bits. Built on the foundation of a series of peer-reviewed papers published by the authors, the book is written at a level easily understandable to readers with knowledge of rudimentary high school math. Those seeking a quick first read or those not interested in mathematical detail can skip marked sections in the monograph and still experience the impact of this new and exciting model of nature’s Read More ›

From Columbia mathematician Peter Woit at Not Even Wrong: To me, Facebook is perhaps the most worrisome of all the Big Data concerns of the book [Cathy O’Neil’s Weapons of Math Destruction ]. It now exercises an incredible amount of influence over what information people see, with this influence sometimes being sold to the highest bidder. Together with Amazon, Google and Apple, our economy and society have become controlled by monopolies to an unparalleled degree, monopolies that monitor our every move. In the context of government surveillance, Edward Snowden remarked that we are now “tagged animals, the primary difference being that we paid for the tags and they’re in our pockets.” A very small number of huge extremely wealthy corporations Read More ›

From Nanette Byrnes at Technology Review: We seem to be idolizing algorithms, imagining they are more objective than their creators. The dustup over Facebook’s “trending topics” list and its possible liberal bias hit such a nerve that the U.S. Senate called on the company to come up with an official explanation, and this week COO Sheryl Sandberg said the company will begin training employees to identify and control their political leanings. This is just one result, however, of a broader trend that Fred Benenson, Kickstarter’s former data chief, calls “mathwashing”: our tendency to idolize programs like Facebook’s as entirely objective because they have mathematics at their core.More. Grasshopper, who is the “we” who thought they weren’t biased? See also: Darwin’s Read More ›

From Pradeep Mutalik here: Three puzzles test whether the concept of infinity has purchase in the physical world. Editor’s note: The reader who submits the most interesting, creative or insightful solution (as judged by the columnist) in the comments section will receive a Quanta Magazine T-shirt. More. Readers can always submit here if they wish. T-shirt only by arrangement. See also: New Scientist vs. William Lane Craig on infinity explanations Follow UD News at Twitter!

This is an expansion of a post of mine from another thread. Hat tip to HeKS for bringing the debate around to Ontology vs Epistemology. In another thread, Seversky rejects the objective nature of morality based on the fact you cannot prove its existence or specific values like you can, say, the speed of light or the gravitational constant. Seversky is making a claim that since there is no satisfying epistemological methodology for establishing – precisely – the good or evil value of a moral proposition, then it must be the case that good and evil, ontologically speaking, are completely subjective commodities. This is not, of course, a logically valid inference. Just because a commodity has no satisfying or precise, Read More ›

It Takes Ganas: Jaime Escalante’s secret to inspired learning Great teachers are typically unknown beyond the immediate circle of their students, colleagues, and families. That was not the case with Jaime Escalante. Escalante taught calculus with outstanding success at Garfield High, in a tough Hispanic neighborhood of East Lost Angeles. Escalante’s success was portrayed in the 1988 film Stand and Deliver, for which Edward James Olmos, who played Escalante, received an Oscar nomination. At its height, Escalante’s program at Garfield saw 85 students pass the Advanced Placement calculus test, more than at any but a handful of high schools across the nation. Most people these days, if they remember Escalante, immediately think of Stand and Deliver. That film ended on Read More ›

Why do people who think math is just something humans evolved to relate to our world (and has only an accidental relationship with correctness) think it is important if statistics are just made up? Clearly they do care (language warning), as is evident from an interview with stats critic Tim Harford More or Less at Vice: All of this is more relevant now than ever before, because most news operations are 24-hour rolling cycles, where press releases, particularly those from official-sounding bodies, may be posted unchecked. The shared parental-leave story ended up being analyzed by politicians and comment writers, and everything they were saying was based on utter, utter bullshit. And that’s just traditional news sources. Increasingly, we are getting Read More ›

The response to Barry’s recent post, How Did Mathematics Come to be Woven Into the Fabric of Reality? pretty much lays bare the issues: “Why is the universe we live in connected by an unreasonably beautiful, elegant and effective mathematical structure?” The naturalist says we just evolved to see the world as making sense, but don’t really know. Defending Darwin means that much to him … At 73, I noted, Aleta at 81: Sorry, that won’t work. Either man is observing something that underlies the universe and working within those given results or mathematics is an adaptation for survival (it could be completely irrational and is only tangentially related to how the universe works). The second position saves naturalism (and Read More ›

We all learned pi in school in the context of circles.  Pi is the ratio of a circle’s circumference to its diameter.  It is an irrational number approximated by 3.14. It turns out that pi shows up all over the place, not just in circles.  Here is just one instance.  Take a piece of paper and a stick.  Draw several lines along the paper so that the lines are the length of the stick from each other.  Then randomly drop the stick on the paper.  The probability that the stick will land so that it cuts a line is exactly 2/pi, or about 64%.  If one were to perform millions of trials, one could use the results to perform a Read More ›

Recently, we noted a claim that nature prefers hexagons, but a reader has written in to say that nature prefers squares. He adduces in evidence: Science published an interesting paper last year about the fact that the square shape of the seahorse tail creates a robust, rigid, yet flexible tail, more so than the typical circular/cylindrical shape you see in animal tails. Explanation: Most animals and plants approximate a cylinder in shape, and where junctions occur (as with branches of trees or limbs on animals), those corners are “faired,” meaning smoothly curved so that one surface grades into the next (1). When living organisms deviate from the norm, there’s usually a good biomechanical reason: a clue to some specific problem Read More ›

Says Philip Ball at Nautilus: The ancient Greek philosopher Pappus of Alexandria thought that the bees must be endowed with “a certain geometrical forethought.” And who could have given them this wisdom, but God? According to William Kirby in 1852, bees are “Heaven-instructed mathematicians.” Charles Darwin wasn’t so sure, and he conducted experiments to establish whether bees are able to build perfect honeycombs using nothing but evolved and inherited instincts, as his theory of evolution would imply. More. Note how in pop science culture, a simple question like Why hexagons? turns into a hymn of praise to Darwin vs. others. You know, the author of the single greatest idea anyone ever had. Incidentally, this kind of thing is what makes Read More ›