I have a new toy. ‘Ox Blocks’ box promises “Noughts and Crosses with a novel twist”.
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As you may well know, Star Trek was a science fiction TV show in the late 1960s. It featured futuristic technology and science fiction ideas such as warp drives, transporters, strange new worlds, time travel, and green alien space babes. And the possibility of all these things has, in the past, been discussed by experts, and nerds, in great detail. Especially that last one about green space babes.
But dammit, I’m a mathematician, not a physicist. So, instead of talking about the science of Star Trek yet again, what about the maths of Star Trek? After all, Star Trek is science fiction, but there is no such thing as maths fiction – so any mathematics featured on the show is sure to be on firmer ground. Right? Or as Spock himself says in ‘The Conscience of the King’;
SPOCK: Even in this corner of the galaxy, Captain, two plus two equals four.
Should we even expect much maths to feature on a simple space adventure show? In fact, many interesting mathematical ideas were raised during the show’s short run of 79 episodes, including; the probability we are alone in universe; a paradox that upset 20th century mathematicians as well as 23rd century androids; the mathematics of alien and Earth biology; and the most important question of all – when on a dangerous away mission, does the colour of your shirt really affect your chances of survival?
The Institute of Mathematics and its Applications has launched a new journal, Information and Inference: a Journal of the IMA. This aims to
publish high quality mathematically-oriented articles, furthering the understanding of the theory, methods of analysis, and algorithms for information and data.
Articles should be written in a way accessible to researchers in the associated topics in pure and applied mathematics, statistics, computer sciences, and electrical engineering. Articles are published in, but not limited to: information theory, statistical inference, network analysis, numerical analysis, learning theory, applied and computational harmonic analysis, probability, combinatorics, signal processing, and high-dimensional geometry.
According to the website, “all content will be free to access for the first two years of publication of the journal”. You can sign up for free email table of contents alerts.
The first paper, ‘The masked sample covariance estimator: an analysis using matrix concentration inequalities‘, has been made available for advanced online access.
More information: Oxford Journals: Information and Inference: a Journal of the IMA.
The table never lies, or so they say. So when Manchester City were crowned Premier League Champions last week everyone seemed to agree that they were the best team in the league. As Roberto Mancini said, they had scored more than United and conceded less and beaten them twice in the league. Although United finished on the same number of points it would be difficult to find a measure by which they deserved the title over City. Or would it?
Let’s suppose that:
- $60\%$ of students who study Chinese are artistic and love poetry.
- $20\%$ of students who study Business are artistic and love poetry, and
- Only about $1\%$ of students study Chinese, whereas about $15\%$ of students study Business.
Thus, out of every $1000$ students, there are $10$ studying Chinese, of whom $6$ are artistic and love poetry, and also there are $150$ studying Business, of whom $30$ are artistic and love poetry.
So if a student is artistic and loves poetry, it’s $5$ times more likely she’s studying Business than Chinese.
So much for preconceptions (and “correlation”).
The classic birthday problem asks how many people are required to ensure a greater than 50% chance of having at least one birthday match, meaning that two or more people share a birthday. The surprisingly small answer, assuming that all birthdays are equally likely and ignoring leap years like 2012, is 23 people.
• Puzzle 1. Suppose I have a box of jewels. The average value of a jewel in the box is \$10. I randomly pull one out of the box. What’s the probability that its value is at least \$100?
• Puzzle 2. Suppose I have a box full of numbers—they can be arbitrary real numbers. Their average is zero, and their standard deviation is 10. I randomly pull one out. What’s the probability that it’s at least 100?
John Baez and Brendan Fong claim to have answered questions like these, but in a general way that is useful for quantum mechanics: