Jeff Moser's "A Stick Figure Guide to the Advanced Encryption Standard (AES)" beautifully presents the history, context, and workings of one of the most important pieces of math in the modern world. AES is at the core of virtually every privacy technology you use, and it holds the promise of building an NSA-proof, unsnoopable Internet.
Boy is written by Deborah Heiligman, with illustrations by LeUyen Pham, and the pair really worked to weave numbers and mathematics through the text, with lively, fun illustrations of a young Erdős learning about negative numbers, becoming obsessed with prime numbers and leading his high-school chums on a mathematical tour of Budapest. They also go to great lengths to capture the upside and downside of Erdős's legendary eccentricity -- his inability to fend for himself and his helplessness when it came to everyday tasks like cooking and doing laundry; his amazing generosity and brilliance and empathy in his working and personal life.
Ultimately, this is a book that celebrates the idea of following your weird, wooing the muse of the odd, and playing to your strengths rather than agonizing over your weaknesses. It's an inspiring and sweet tale of one of humanity's greatest mathematicians, and a parable about the magic of passion and obsession.
My daughter, who is five, demanded that I read it to her three times in a row, over three bedtimes, which is always a vote of confidence.
Business Insider's Walter Hickey did the math on Monopoly, calculating the most frequently landed-up squares (taking into account dice probability, Go To Jail events, and Community Chest/Chance cards) and conceived of a supposedly optimal strategy for buying and building upon property. I still hate Monopoly, but I suspect that this would make it less boring (for a while, at least).
Samuel sez, "ACMEScience.com is the home of many math and science podcasts, including the mathematical story series Relatively Prime. It has been run for the past four years in the spare time between jobs, and with cheap or second-hand equipment. Now ACMEScience wants to change its lot and turn itself into a full-time operation for the next year, and it plans to do this through its new Kickstarter project. If the project is funded it would mean new episodes of Relatively Prime, as well as at least one episode a week of the interview shows ACMEScience News Now and Strongly Connected Components."
I'm a great fan of Relatively Prime -- they're the ones who did the great piece on Chinook, the champion checkers-playing computer.
Stanford's Dan Boneh is offering a free Cryptography course through Coursera. It has a 5-7 hour/week workload, and runs for six weeks. It's just started.
Cryptography is an indispensable tool for protecting information in computer systems. This course explains the inner workings of cryptographic primitives and how to correctly use them. Students will learn how to reason about the security of cryptographic constructions and how to apply this knowledge to real-world applications. The course begins with a detailed discussion of how two parties who have a shared secret key can communicate securely when a powerful adversary eavesdrops and tampers with traffic. We will examine many deployed protocols and analyze mistakes in existing systems. The second half of the course discusses public-key techniques that let two or more parties generate a shared secret key. We will cover the relevant number theory and discuss public-key encryption and basic key-exchange. Throughout the course students will be exposed to many exciting open problems in the field.
Cathy "Mathbabe" O'Neil is a former finance-industry quantitative analyst who escaped her former career and has advice for other quants looking to do something better with their lives. She works in a startup now, and offers a fascinating study of the contrasts between finance culture and startup culture:
First, I want to say it’s frustrating how risk-averse the culture in finance is. I know, it’s strange to hear that, but compared to working in a start-up, I found the culture and people in finance to be way more risk-averse in the sense of personal risk, not in the sense of “putting other people’s money at risk”.
People in start-ups are optimistic about the future, ready for the big pay-out that may never come, whereas the people in finance are ready for the world to melt down and are trying to collect enough food before it happens. I don’t know which is more accurate but it’s definitely more fun to be around optimists. Young people get old quickly in finance.
Second the money is just crazy. People seriously get caught up in a world where they can’t see themselves accepting less than $400K per year. I don’t think they could wean themselves off the finance teat unless the milk dried up.
Randall "XKCD" Munroe's new "What If?" feature answers one wild hypothetical per week. The first two are corkers: Relativistic Baseball baseball asks what would happen if a baseball pitcher could throw a ball at 0.9C; the second, SAT Guessing, looks at the (very long) odds against getting a perfect SAT by bubbling in random guesses. Here's a taste of Relativistic Baseball:
The ball is going so fast that everything else is practically stationary. Even the molecules in the air are stationary. Air molecules vibrate back and forth at a few hundred miles per hour, but the ball is moving through them at 600 million miles per hour. This means that as far as the ball is concerned, they’re just hanging there, frozen.
The ideas of aerodynamics don’t apply here. Normally, air would flow around anything moving through it. But the air molecules in front of this ball don’t have time to be jostled out of the way. The ball smacks into them hard that the atoms in the air molecules actually fuse with the atoms in the ball’s surface. Each collision releases a burst of gamma rays and scattered particles.
fusion illustration fusion zone of baseball
These gamma rays and debris expand outward in a bubble centered on the pitcher’s mound. They start to tear apart the molecules in the air, ripping the electrons from the nuclei and turning the air in the stadium into an expanding bubble of incandescent plasma. The wall of this bubble approaches the batter at about the speed of light—only slightly ahead of the ball itself.
A couple of years ago, Cory posted a really interesting story about the mathematics behind seemingly cause-less traffic jams. It's pretty interesting. Shorter version: The researchers think jams like this are caused by one person braking, and the response to that slow down moves through dense traffic in a way that is mathematically very similar to the shock wave from an explosion. Once you have enough density of cars on a road, jams are inevitable.
Cory's post included a simulation, showing what the mathematics might look like in the real world. Basically, a computer algorithm figured out how drivers would behave if the mathematical theory were correct and turned that behavior into a little cartoon of cars moving around a track.
But here's the really cool thing. This effect has actually been demonstrated in meatspace. Yesterday, a friend sent me a video from 2008, showing real life drivers behaving in almost the exact same way as the simulation video from Cory's post. That's what you see posted above. Now, these are not exactly real-world conditions. A flat circular track may, or may not, be a good representative for what happens on the highway—I, for one, would be interested in seeing how on/off ramps, hills, and curves change the patterns. Also, the drivers in this case were other students and faculty from the Nakanihon Automotive College, and the study doesn't say whether they knew why they were driving in circles. Again, these details could affect the outcome.
I've not been able to find any studies that test this mathematical model by documenting real-world traffic flows. But if you've got links, I'd love to see them! The idea behind this theory certainly makes sense and it would be interesting to know whether it matches up with the reality you and I experience.
A collection of Max Newman's hand-annotated offprints from sixteen of Alan Turing's eighteen books have been purchased by the Bletchley Park Trust with help from the National Heritage Memorial Fund and a USD100,000 donation from Google. The papers were up for auction, and had they not been bought by the Trust, they likely would have gone to a private collection. They will now be available to the public at the wonderful Bletchley Park museum.
The collection of articles belonged to Professor Max Newman, Turing's friend and fellow Bletchley Park codebreaking genius. It includes offprints of sixteen of Turing's eighteen published works including his momentous paper 'On Computable Numbers' A limited number of the offprints would have been produced at the time and Turing's gifting them to Newman bears testimony to their unique relationship. The set includes articles which have been annotated by Newman, along with Max Newman's name inscribed in pencil in Turing's hand. Accompanying the set of offprints is the Newman household visitors' book with several signatures of Turing, that of Turing's mother and, of special significance to Bletchley Park, signatures of other wartime codebreaking giants.
The Turing-Newman Collaboration Collection is particularly rare, important and valuable as very few physical traces of Turing's work or personal belongings still exist. Most of the wartime records at Bletchley Park were destroyed after the war, while Turing himself kept little of his work and very few personal belongings...
Turing's close relationship with Newman was crucial to the historic contribution Turing made, starting with Newman's encouragement to investigate 'mechanical processes' and his help in securing Turing a fellowship at Princeton to continue his research. In 1952 at a time when homosexuality was illegal in the UK, Turing was convicted of having a sexual relationship with another man. Turing was sentenced to a hormone treatment that amounted to chemical castration. The conviction robbed him of his security clearance for GCHQ, for which he still worked, and made him the target for surveillance at the start of the cold war. Having made one of the most outstanding contributions of the twentieth century, he died after eating an apple laced with cyanide.