## Captain Raymond Holt vs Claude Shannon

Overview

In this post I am going to introduce a pretty famous riddle, made popular recently by the police sitcom Brooklyn Nine-Nine as well as the idea of the entropy of a probability distribution, made popular by Claude Shannon. Then I am going to go through a solution that is presented in Information Theory, Inference, and Learning Algorithms (2), a brilliant book on the topic by the late David MacKay, as well as some intuitions from his lecture series on the topic. Hopefully, by the end of it, you will be familiar with another property of a probability distribution and be able to impress your friends with your riddle-solving abilities.

The Riddle

The riddle is presented by Captain Holt (pictured above) to his team of detectives as follows (1):

‘There are 12 men on an island, 11 weigh exactly the same amount, but 1 of them is slightly lighter or heavier: you must figure which.* The island has no scales, but there is a see-saw.

By | October 23rd, 2019|English, Fun|0 Comments

## Do You Find Mathematics Scary?

A few weeks ago I attended a lecture by Johnathan Lewin, regarding the use of technology when teaching and it was brilliant, and I’m not even talking about his use of technology. The passion that Johnathan speaks with and the passion he has for Mathematics is explosive and practically contagious.

He uses a number of different programmes and applications to assist him in the classroom. He even records his lectures (he captures the audio and a visual of the learning materials and then makes them available to his students). He is in favour of designing the materials in front of the learners in order for them to see how the Mathematics is created rather than to arrive with some neatly prepared sides and show them what Mathematics looks like. He wants them to engage in it at all levels and not just see the perfect final product, if you wish.…

## How Many Languages Do You Speak?

I’m not sure how, but it’s been a month since my last post. It feels like it was just the other day that I was working on its first draft… Since my first blog dealt with the language of Mathematics, I thought I might continue the language theme for now as it is something that really interests me.

Let me start by asking you this: How often do you take being a First Language English speaker for granted? (Has this thought ever even crossed your mind?) Have you ever traveled to a foreign country and needed to communicate and found it difficult? Were you frustrated by this? What happens when you don’t have a very good grasp of a particular Language, would you want to speak it? Or read it? Or perhaps worse still, write it?

Well, I think this is the challenge that a number of learners face and they are often left feeling frustrated and misunderstood in their classrooms, particularly in South Africa, where we have 11 official languages.…

By | February 22nd, 2016|English, Fun|4 Comments

## You’re (probably) a Bayesian – whether you like it or not!

Statisticians have long been separated into two camps as to how they philosophically interpret their trade. These schools of thought are usually called Frequentists and Bayesians.

Frequentists believe that a probability, $p\in[0~ 1]$, associated with a specific possible outcome of an observable occurrence or process, is simply telling you that, could you observe this occurrence (or process) infinitely many times, the fraction of such observations that would yield that specific outcome is $p$ . Using the age-old coin toss example: tossing the coin is the occurrence or process and recording a Heads or Tails are the two observation. The number 0.5 $\left(P(\text{Tails})=0.5=P(\text{Heads})\right)$ tells a Frequentist that, in the pursuit of infinitely many coin tosses, the ratio of Heads recorded to the number of tosses performed asymptotically approaches 0.5. And that’s all! The value should not be interpreted as the most likely outcome for the next observation or sample taken from the process (though I’ve always wondered how a Frequentist would gamble…).…

## Hello World

So this is my first post and any real “nerd” will know why I named my post “Hello World”. Many years ago, I dabbled in a little bit of computer programming and the first program you ever write, as kind of a rite of passage, is to make the screen say “Hello World”. Needless to say, it wasn’t always easy, but nothing worthwhile in life ever is. At times, I really did want to pull my hair out though, with things like syntax errors. Firstly, I had to work out what a syntax error was… Basically, in layman’s terms, it’s like making a grammar or punctuation error in an essay. Secondly, I needed to find this syntax error (or errors), most of the time it was a missing semi-colon, in my thirty or forty lines of code. Did I mention that the technology didn’t even give you a hint as to where you might begin to look for it.…

## How much does a Dougie weigh on Jupiter?

I spent an evening with old friends just after Christmas. One of their sons is fascinated by Space, and always has great questions for me about it. This year he asked how much he would weigh on Jupiter. I admitted that I didn’t know the answer, but that a) It wasn’t a single number, as the surface of Jupiter (if one exists) is not very well understood and different heights in the atmosphere would give different weights and b) I would find out. It took a little Googling to find some information about the density profile of Jupiter, which includes information about Saturn too. The paper is the following, with abstract:

Taken from http://www.nature.com/nature/journal/v520/n7546/full/nature14278.html

In this paper is the following pair of graphs:

Taken from http://www.nature.com/nature/journal/v520/n7546/images/nature14278-sf4.jpg

Which is all we need to calculate how much Dougie weighs on Jupiter. In the lower plot we see two different models of the density of Jupiter at different heights.…