The most interesting plagiarism-catching technique (mathematically speaking) is stylom-etry, which uses statistical methods to compare the style of one document to another – meaning that if a student's writing style in exam conditions is significantly different to their style in other submissions, there may again be cause to investigate further.
For example, the writer invariant technique considers the fifty most common words used by a writer.
In each chunk of the document, those words are counted, giving an identifier of 50 numbers for each bit of text.
The method then uses principal component analysis to find the plane of best fit for all of the identifiers; if the planes match up between two documents, it is very likely they share an author.
Stylometry is a very neat trick, as it can also catch people who use essay-writing services, and hopefully prevent them from prospering.#6041•
Several stylometric analyses have suggested that some of Shakespeare's plays were at least co-authored with Christopher Marlowe.#6029•
Chapter 7
Is astrology plausible? Astrology suggests that the movement of distant planets across the heavens somehow affects our everyday lives. The exact mechanism by which they do this is never explained, of course, but there is only one force known to act at a distance: gravity.
So, how much effect does a planet – for instance, Venus, the closest planet to Earth – have on our everyday lives?
This can be calculated using Newton's laws of motion: the acceleration on Earth due to the gravity of any body is 2GMr/R, where G is the gravitational constant (6.67 × 10-11 Nm kg-2), M is the mass of the body (for Venus, 4.87 ×1024 kg), r is the distance from the centre of Earth (6.37 × 106 m) and R is the distance to the body (at its very closest, about 3.8 × 1010m).
Plugging those numbers into the equation gives 7.54 × 10-11 N.
The weight of a feather is about 7.5 × 10-1 N. The force due to Venus (our closest planet) at its very closest, is one ten-billionth of that.#6030•
Prejudice
Why do minorities encounter more bias? One model of prejudice in the workplace (or elsewhere) gives an explanation of why any group that is in a minority experiences a disproportional amount of abuse – even if the majority is not any more prejudiced than the minority group.
Imagine that out of 100 people working at a firm, 90 are right-handed and 10 left-handed. Let us suppose that 10% of each group are hostile and abusive once a week to someone who writes with the other hand. What happens?
Nine of the right-handers abuse a random lefty; one of the southpaws is nasty to a random right-hander. But in terms of experiencing abuse, the ten left-handers experience nine incidents of abuse each week (so you would expect every one of them to experience an abusive incident within a little over a week).
By contrast, only one of the 90 right-handers is on the wrong end of abuse in any given week; on average, a right-hander would go nearly two years without being abused by a lefty.#6037•
This idea is known as the Petrie multiplier (it is mathematically similar to Lanchester's Laws for battles). The imbalance can be reduced by employing a higher proportion of left-handers. Although the expected number of incidents would remain the same, fewer anti-left-hander incidents would be spread between more people, while the increase in anti-right-hander incidents would barely register for the average employee.
A better solution is to reduce the prejudice rate and for everyone to see the merits in the other hand.#6026•
What you can do is improve your chances of winning big, given that you do hit the jackpot.
The first thing that you can do is wait until times when the prizes are bigger. The bigger the jackpot, the bigger your payout if you win (although you may have to share it with more people, on average.)
The second thing is to pick unpopular numbers. Because the jackpot is shared between however many people pick those numbers, you want to minimize the chances of anyone else having your numbers. Most people, when playing the lottery, make their choices based on lucky numbers, family birthdays, or numbers that look nicely spread out – so you want to exploit those patterns by doing the opposite#6045•