Every year Discover magazine lists its 100 Top Science Stories, and a number of these stories, particularly those involving physics and engineering, require a lot of math in their execution. Beyond that, however, four of the stories feature mathematics centrally. In numerical order:
- In #51 A Computer Rosetta Stone we find a computer program that deciphers ancient heiroglyphics statistically. MIT computer scientist Regina Barzilay has developed the program, which compares unknown letters and words to letters and words of known languages in order to find parallels. When she tested it by seeing how much of ancient Ugaritic the program could decipher using the related language Hebrew as the ‘parallel’, the program correctly matched 29 of the 30 Ugaritic letters to their Hebrew equivalent, and 60% of the Ugaratic words that had Hebrew cognates. More importantly, it did the work in a matter of hours, whereas human translators needed decades (and the chance find of an ancient Ugaritic axe that had the word “axe” carved on it) to accomplish similar feats. While the program certainly cannot replace the intuition and feel for language that human scientists possess, “it is a powerful tool that can aid the human decipherment process,” and could already be of use in expanding the number of languages that machine translators can handle.
- #60 Fighting Crime with Mathematics details the work of UCLA mathematicians Martin Short and Andrea Bertozzi who, along with UCLA anthropologist Jeff Brantingham, developed a mathematical model of the formation and behavior of crime ‘hotspots.’ After calibrating the model with real-world data, it appears that hotspots come in two varieties: “One type forms when an area experiences a large-scale crime increase, such as when a park is overrun by drug dealers. Another develops when a small number of criminals—say, a pair of burglars—go on a localized crime spree.” According to the work, the typical police reaction of targeting the hotspots appears to work much better on the first type of hotspot, but hotspots of the second type usually just relocate to a less-patrolled area. As the story notes, “By analyzing police reports as they come in, Short hopes to determine which type of hot spot is forming so police can handle it more effectively.”
- There seems to be a steady stream of stories recently that remark on how some animals instinctively know the best way to do things. One example from this blog is Iain Couzin’s work on animal migration. And here’s another: #92 Sharks Use Math to Hunt. Levy flight is the name given a search pattern which has been long suspected by mathematicians of being one of the most effective hunting strategies when food is scarce. David Sims of the Marine Biological Association of
the United Kingdom logged the movements of 55 marine animals from 14 different species over 5,700 days, and confirmed that the fish movements closely matched Levy flight. (The marine animals included tuna and marlin, by the way, but sharks always get the headlines.)
- #95 Rubik’s Cube Decoded covers a story already mentioned on this blog about “God’s Number”, the maximum number of moves that an omniscient being would need in order to solve any starting position of Rubik’s cube. The answer, as you can read in this story or by reading my earlier blog post, is 20.
The whole Top 100 is worth going through as well. It’s remarkable to realize how much and how quickly science is learning in this day and age.
This is an older story but I couldn’t resist mentioning it here once I’d heard about it: Burkard Polster has determined the best ways to lace a shoe. Now if you’re like me you may have gone through much of your life blind to the endless shoelace arrangements out there. The diagram above provides you (and me) some clue about the 43,200 possibilities there are. (The 43,200 number is for six eyelets on each side; as the number of eyelets goes up the possibilities increase exponentially.) Which arrangements are cooler or more attractive than the others is a matter of taste, but in terms of things quantifiable it’s apparent that some lacings require more shoelace than others, and that some lacings are stronger than others. Thinking in those terms, which shoelace arrangements give you the strongest fit for your buck? Dr. Polster, a mathematician from the University of Monash in Australia, has done the work to figure it out. His findings help confirm why I and so many others have been so ignorant all these years.
The shoe-tying world is dominated by two lacings. The most popular is a simple crisscross, each end of the shoelace pulled through the next eyelet on the opposite flap. The second common way is to pass one end of the lace from the last eyelet across to the top eyelet on the opposite flap and then zigzag the other end in an N pattern through the eyelets….When the eyelets are narrowly spaced and the flaps relatively far apart, the crisscross lacing is strongest. If the eyelets are farther apart, then the zigzagging N pattern provides the tightest tie.
In short, Dr. Polster has demonstrated that sometime in the past the human brain had already “evolutionarily” figured out the optimal ways to lace shoes, and we’ve been largely doing so ever since. The original scientific article detailing the findings appeared in Nature, and the story was then picked up by National Geographic and the NY Times (where the quote above is taken). If you Google Polster and shoelaces, you’ll see that his foot work has garnered Polster mentions on literally hundreds of websites devoted to shoes, and even a mention of sorts in the May 2007 Women’s Health magazine….where they unfortunately decided he was “nutso” for bothering with the calculations. On a more positive note, Polster was inspired to write a short book about his explorations entitled The Shoelace Book: A Mathematical Guide to the Best (And Worst) Ways to Lace Your Shoes, which appears from the online reviews to be a little more appreciated.
People have been solving Rubik’s Cube since it was invented in 1974, and some have gotten quite fast at it. But just how fast is possible? In other words, if you were an omniscient solver, what’s the most number of moves it would take you to solve any starting position of Rubik’s cube? Since there are 43,252,003,274,489,856,000 possible starting positions, many of which require different strategies to solve, answering that question seemed outside the realm of possibility: a computer dealing with each starting position in less than 20 seconds would still require 35 years of analysis. But by using some high-powered mathematics to chop the problem down to size, a team consisting of a mathematician, a Google engineer, a math teacher, and a programmer (and yes, a powerful computer) have indeed answered the question, determining that all starting positions are solvable in 20 moves or less. The story was picked up by a number of news outlets, including NPR, Discover, BBC News, and others.
The NY Times Magazine annually publishes its The Year in Ideas issue, devoted entirely to “the most clever, important, silly and just plain weird innovations … from all corners of the thinking world.” A surprising number of these ideas are based on a study or research article or something similar that employs some bit of mathematical and/or statistical analysis. The ones I’ve listed below are chosen as being the ones that most prominently feature mathematics ideas, or feature mathematics and/or mathematicians centrally. Listed alphabetically:
- Black Quarterbacks Are Underpaid by Jason Zengerle describes the statistical analysis of two economists, David J. Berri and Rob Simmons, who discovered that in the NFL black quarterbacks are typically paid much less than white quarterbacks. Their analysis goes farther, however, and notes that the apparent cause is not necessarily racism. Instead, the NFL quarterback rating statistic is the culprit. NFL contracts are often based on hitting certain statistical levels, and for quarterbacks the statistic used is often the QB rating. Since QB rating fails to count rushing yards at all–something that black quarterbacks typically excel at–black quarterbacks are typically ‘discounted’, QB rating-wise.
- Forensic Polling Analysis visits a topic seen already here in this blog: the suspicious polling numbers of the polling firm Strategic Vision LLC. You can visit that entry or the Times article for more info.
- In a blow to meritocracy-lovers everywhere, another entry notes that Random Promotions, rather than merit-based ones, can actually produce better businesses (and typically do, at least in simulations). The article by Clive Thompson describes a study done by a trio of Italian scientists in which the researchers created a virtual 160-person company and then tried out various different promotion schemes within the company, with the aim of seeing which scheme improved the company’s productivity the most. Promoting on merit turned out to be a lousy idea (at least for the company as a whole) while promoting at random turned out to be the top strategy. In the middle was the curious idea of alternately promoting the best and then the worst employees. The fact that the mixed best/worst strategy outperformed the merit strategy is yet another example of Parrando’s Paradox, a phenomenon first identified by game theory.
- Massively Collaborative Mathematics features the first mathematical theorem proved by a ‘collective mind’, if you will. In January 2009, Timothy Gowers, one of the top mathematicians in the field, proposed on his blog that the mathematical community, as a whole–or at least that portion that knew and read his blog–attack a long-standing unsolved problem in mathematics known as the Density Hales-Jewett Theorem. Contributors ranged from eminent mathematicians to high school teachers, and hundreds of thousands of words worth of ideas were eventually proposed, developed, discarded, combined, and so forth. Gowers had initially set the bar low, hoping this ‘Polymath’ project would result in “anything that could count as genuine progress toward an understanding of the problem.” Instead, six weeks later the problem was completely solved. A paper detailing the result, authored by D.H.J. Polymath, has been submitted to a leading journal.
- Finally, the (alphabetically) last idea listed, “Zombie-Attack Science,” features a story that appeared on this blog previously. See that entry, or the Times article, of course, for details.