Mathematics

I understand why someone living in the city might get a slice of pizza - they don't want to carry a box of pizza back to the office, and there is something nice about sitting down and having a quick bite. But I have never understood why anyone buys a medium pizza, much less a small. If you understand what a circle is, and you understand what a dollar is, it makes no sense. First, the dollar. The economics should be obvious; like buying any food in bulk, you can see there are fixed costs. A small pizza or a large has someone making it, it has an oven in a shop. Those costs are fixed regardless…

Two computer scientists at at the University of Liverpool think they have successfully cracked the Erdős discrepancy problem (for a particular discrepancy bound C=2), an 80 year old maths puzzle proposed by the Hungarian mathematician Paul Erdős, who offered $500 for its solution. They just can't be sure, because it is too big for a human to replicate.The resulting proof generated is an enormous 13 gigabytes, 30 percent larger than downloading all of the content on Wikipedia. Erdős was fascinated by the extent to which an infinite sequence of numbers containing nothing but +1s and -1s…

There is a reason some schools on the coast of California only have a 25 percent vaccination rate. Not 25 percent exemption, 25 percent vaccination. In California overall, exemptions rates rose by 25 percent just between 2008 and 2010 and that trend has been mirrored in states like Washington and Oregon. The recent rash in anti-vaccination hysteria can be mathematically modeled, say scholars from the University of Guelph and the University of Waterloo. Writing in Proceedings of the Royal Society B, the authors say their model can foresee the observed patterns of population behavior and…

When it comes to discussion about public schools, the administation's education experts call the educators and students they claim to support 'dismal' on a regular basis. But that isn't really so, unless the goal for students is to teach them how to take standardized tests, which educators don't like and was the chief criticism of the bipartisan No Child Left Behind program signed into law by former President George W. Bush. No Child Left Behind was actually quite successful, boys and girls achieved math parity for the first time in history, but it was still solving the wrong problem. The…

Stock price movements are predictable during short windows, according to a paper written by academics in the Tippie College of Business at the University of Iowa. They write that price movements can be predicted with a better than 50-50 accuracy for anywhere up to one minute after the stock leaves the confines of its bid-ask spread. Probabilities continue to be significant until about five minutes after it leaves the spread. By 30 minutes, the predictability window has closed. So if you have a billion dollars to arbitrage, you can make some money. Otherwise, caveat emptor. Nick…

An infinite number of mathematicians walk into a bar. The first mathematician orders a beer. The second orders two beers. The next orders four. Followed by the next who orders eight. The bartender interrupts them: "ok guys, cut the crap: you owe me one beer". --------------------------------------------- A recently posted Numberphile video is heading towards 2 million hits on YouTube. That is an impressive score for a video focusing on a math subject. The two physicists in the video try to convince the viewer that all positive integers add up to -1/12. Yes, you read that correctly: these…

The difference between 1 and 2 and 101 and 102 is the same, yet children perceive 1 and 2 as being much farther apart, because two is twice as much as one. It takes years of education to recognize that the numbers in both sets are only one integer apart on a number line. But a new paper shows that different is not necessarily weaker and  educated adults retain traces of their childhood number sense — and that innate ability is more powerful than recognized.  Children understand numbers differently than adults. For kids, one and two seem much further apart then 101 and 102…

Dependence between variables, even within their contemporaneous and extreme movements, are not limited to linear relationships defined through the Pearson correlation, ρ.  The ρ is the most common correlation calculation and looks at the parameterized covariance between two random variables, and confines the result to within -1 and 1.   We discuss in our blog note here the method to consider ρ for more than two variables. On the other hand, the Spearman correlation, r, removes the marginal distribution of the parameterized data,…

As you know, when heat in soup is increased, it will eventually boil. When time and space are heated, an expanding universe can emerge, without requiring anything like a "Big Bang", according to a new math paper. The math behind this phase transition between a boring empty space and an expanding universe containing mass is a connection between quantum field theory and Einstein's theory of relativity. Everybody knows of the transitions between liquid, solid and gaseous phases. But also time and space can undergo a phase transition, as the physicists Steven Hawking and Don Page pointed out in…

Quantum entanglement, the phenomenon of quantum mechanics that Albert Einstein once referred to as "spooky action at a distance," could be even spookier - hypothetically. Quantum entanglement occurs when a pair or a group of particles interact in ways that dictate that each particle's behavior is relative to the behavior of the others. In a pair of entangled particles, if one particle is observed to have a specific spin, for example, the other particle observed at the same time will have the opposite spin. The "spooky" part is that, as research has confirmed, the relationship holds true no…