# Monthly Archives: December 2011

## Are you 100% sure? Betting for the same team.

Christmas is often a time for getting together and getting in arguments. But some of the most heated arguments are between people who completely agree with each other.

Betting is often a good way of settling arguments: I bet you so much that my sports team will win against yours, can quickly lead to a resolution.

But what happens when you want to gamble with someone else, but both of you want to bet on the same outcome occurring? You could bet on a particular score being achieved, or the timing of an event. But what happens if the options are limited: is the correct direction to turn left or right ? Or if you have identical views: the game will end in a nil-nil draw, or a mutual friend will give up their resolution on a certain day because of some specific event?

The bet can go ahead if one of you is more sure than the other that they’re correct.  Continue reading

Filed under Accessible, Maths in Life

## Getting into Norms: a technical postscript

For mathematicians’ eyes only. The post doesn’t require much theoretical knowledge to understand, but I haven’t given many definitions.

In the last two posts I’ve been talking about an example I made with four-dimensional vectors $a, b, c$ such that $\|a\|_1 > \|b\|_1 > \|c\|_1$, $\|b\|_{2} > \|c\|_{2} > \|a\|_{2}$ and $\|c\|_{\infty}>\|a\|_{\infty}>\|b\|_{\infty}$. Finding it was more difficult than I at first expected, so I thought I would write the investigation up, which happily gives me an excuse to introduce a useful inequality.

My first thoughts were to choose something like $c=(10,0,0,0)$ and $a=(6,6,0,0)$ or $a=(4,4,4,0)$, and then I’d got stuck choosing $b$. So I decided to try to prove the opposite.

First of all, it’s not possible to create such an example in two dimensions. Continue reading

Filed under Technical

In the previous post I gave an example of students deciding who best guessed some lecturers’ ages.

I chose the numbers carefully so that under three reasonable methods of measuring:

Method  First place  Second place  Third place