Parrondos Paradox

Introduction

In this post we will have a look at Parrondos paradox. In a paper* entitled “Information Entropy and Parrondo’s Discrete-Time Ratchet”** the authors demonstrate a situation where, by switching between 2 losing strategies, we can create a winning strategy.

Setup

The setup to this paradox is as follows:

We have 2 games that we can play – if we win we get 1 unit of wealth, if we lose, it costs 1 unit of wealth. Game A gives us a payout of 1 with a probability of slightly less than 0.5. Clearly if we play this game for long enough we will end up losing.

Game B is a little more complicated in that it is defined with reference to our existing winnings. If our current level of wealth is a multiple of M we play a game where the probability of winning is slightly less than 0.1. If it is not a multiple of M, the probability of winning is slightly less than 0.75.…

By | November 11th, 2020|Uncategorized|0 Comments
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Basic Reverse Image Search Using an Autoencoder

Introduction

In this post we are going to create a simple reverse image search on the MNIST handwritten image dataset. That is to say, given any image, we want to return images that look most similar to it. To do this, we will use an autoencoder, trained using Tensorflow 2.

The dataset

The MNIST dataset is a commonly-used dataset in machine learning comprised of 28-by-28 images of handwritten digits between 0 and 9. For our purposes we would be interested in our image searcher returning images of the same number as the query images, i.e. if we input a 3 we want the images returned to all be 3s. However, if we had, say, four 3s and one 2 that mightn’t be too bad, considering how 2 and 3 look a bit similar. However, if we had three 3s, one 1 and a 7 we might say that the performance is not up to standard.…

By | October 21st, 2020|Uncategorized|0 Comments
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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
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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.…

By | January 21st, 2016|Fun, Uncategorized|3 Comments
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Mathematics in Africa – news from the EMS Newsletter

News from the EMS Newsletter, November 29, 2014:

1. CANP4, the fourth event in the Capacity and Network Project organized by the International Commission of Mathematical Instruction (ICMI) and supported by the International Council of Science (ICSU) held its first meeting in East Africa in Dar es Salaam, Tanzania, on September 1-12 204, with more than 80 participants from Tanzania, Kenya, Uganda and Rwanda, This event led to the creation of a new ‘East Africa Mathematics Education and Research Network’. The founding President is Dr Alphonse Uworwabayeho (Rwanda) and the founding Secretary is Dr. Angelina Bijura (Tanzania).

2. Call for Candidates for Ibni Prize 2014.
The Prize “Ibni Oumar Mahamat Saleh” has been created in memory of our colleague and to continue its commitment to Mathematics in Africa. The prize is awarded annually to a young mathematician from Central Africa or West Africa. Applications are evaluated by a scientific committee set up by CIMPA.…

By | November 30th, 2014|English, Level: Simple, News|0 Comments
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The fractals at the heart of African design

I am a mathematician, and I would like to stand on your roof.’ That is how Ron Eglash greeted many African families he met while researching the fractal patterns he’d noticed in villages across the continent.

Watch this TED Video by Ron Eglash, an ethno-mathematician, who studies the way math and cultures intersect. He has shown that many aspects of African design — in architecture, art, even hair braiding — are based on perfect fractal patterns.

Reference: TED web page.

How clear is this post?
…
By | November 24th, 2014|Background, English|1 Comment
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A foray into a new number system – an introduction to imaginary numbers

This is the introduction which I give to my first year mathematics class when they see imaginary numbers for the first time. I thought I’d type it up here as it’s received good reactions the two times that I’ve introduced it in this format. Note that this probably isn’t the canonical way to introduce complex numbers, but then most of my lectures don’t necessarily take the normal route…

Complex Numbers, a philosophical detour

Before we get on to talking about imaginary numbers and complex numbers, let’s try and break down our preconceptions about numbers in general.

We look at the world around us and see many things which we categorise. We see a computer, a piece of paper, we see other people, we see our hands. These are labels that we use to categorise the world, but these objects seem very physical and very real. We rarely question their existence, though if one wants to take the Cartesian view, we should also question the reality we are in.…

By | November 11th, 2014|Background, English, Level: Simple|0 Comments
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A project initiated at the AIMS-IMAGINARY workshop, November 2014, Cape Town | All Rights Reserved
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