Tonight is the night before all deadlines; the end of Richards Discovering Mathematics module is in less than 24 hours. If you read my first blog post, you will know how much I did not want to do this module, ‘Maths Eugh’. But now, I am honestly gutted that it is finishing. I have enjoyed this module, much more than I thought I ever would. I have learned a lot over the course of the course of the module, and I thank every lecturer who has taken part and taught us all.

For my last blog of the module I have decided to dedicate it to the one and only, the amazing Alan Turing. Ever since I watched ‘The Imitation Game’ I have been fascinated by him. His contribution to breaking the Nazi Enigma code, eventually helped the Allied forces defeat Germany. However, the work that he did for the world was never known until one day a book was uncovered which was written by a former employee, as everything was covered up post war when Churchill ordered that all records of the place be destroyed in a huge bonfire.

The work that was completed during the Second World War at Bletchley Park, Station X, was so secret that none of the 10,000 people working there were able to tell anybody outside of the park what was happening in their day to day jobs. No wives, no husbands, friends or relatives. People were recruited based on their linguistic skills, knowledge of hieroglyphics, or brilliance at chess, in order to gain entry, all were expected to be able to solve the Telegraph crossword in less than six minutes. This is seen in the video below, (P.S I know for a fact that I could never have completed it in less than six minutes – Maybe try six hours more like)

The machine created was called an Enigma machine, and it was configured to work in million upon millions of different ways. It was kind of like a massive typewriter that would turn gibberish messages into meaningful sentences, due to this the machines were reset every day to make sure that they worked at decoding the new message’s being sent. Amazingly, they could uncover codes from the battlefields before they even reached Hitler in Berlin!!!

Alan Turing was not the only person to work on the Enigma machine; he was given a team to help him. The team turned out to be extraordinary, and a bit of a weird match but they worked together to crack the codes successfully.

• Hugh Alexander – British chess champion
• Joan Clarke – Codebreaker (seen in the video above)
• Stewart Menzies – Overall charge at Bletchley
• John Cairncross – Spy
• Peter Hilton – Mathematician
• Jack Good – Mathematician

Everyone in the team brought something new to the group, everyone a genius in their own right.

I cannot begin to imagine how differently the world would be, if it not been for Alan and his team working tirelessly at cracking the codes. Many say that because of them the war was lessened by 2 – 4 years. We all owe our thanks to this team of mathematical geniuses, and I for one will never forget what they did for the world.

Following the war, it could be stated that Alan did not have a very happy life following his time at Bletchley Park. He was arrested for ‘gross indecency’ in 1952, and I bet most of you will not be able to work out what is meant by that term? Well he was arrested for his homosexuality. After being taken to court he was placed on a hormone treatment course in the hope that this would solve his ‘issue’. For this failure of mankind, I am sorry. This man helped save all of our lives, shorten the war and bring home all of our men in a spectacular way, a mathematical genius way, and in return we ruined his. He committed suicide in 1954.

If this has shocked you, then be prepared to be shocked some more. In 2009 an Internet campaign started asking that then Prime Minister Gordon Brown, make an official public apology on behalf of the British government for the way in which Alan Turing was treated by the government that he aided, and was then failed by personally. This continued until 2013 when Queen Elizabeth II granted him a posthumous pardon.

I cannot speak on behalf of every person who will ever read this blog, but I know that I will always look up to Alan for what he and his team managed to accomplish, . I do not think that I will ever do anything that could even begin to compare to what they did for the world, but what I have managed to accomplish over the course of this module is special to me. Personally, I have been able to develop an understanding of fundamental maths, how and why we need maths and how it works within wider society. I may have started this module uninterested by mathematics and its role in society, but now Tara and Richard, I feel that you can both count me in as a lover of mathematics. Thank you.

If you have not seen the movie yet and I have managed to convince you to go and watch, then great!! If I have not then here is a little push,

Video 1 found at: https://www.youtube.com/watch?v=xBYkoH2WjTU

Video 2 found at: https://www.youtube.com/watch?v=j2jRs4EAvWM

Image found at: http://www.theguardian.com/film/2014/sep/08/the-imitation-game-review-script-fails-to-sizzle

Further information on Alan Turing: http://www.bbc.co.uk/timelines/z8bgr82

We had a very interesting lecture from Simon Reynolds, who is the Science Learning Manager at the Dundee Science Centre. I cannot pretend to know much about space. Yes I knew it was vast, but just how vast, I had no clue. Having engaged with Dr Simon Reynold’s input on space, I now have a better idea of just how big space is. Also, I have begun to realise just how crucial maths is to Science, and in particular Astronomy.

When Astronomers describe how many stars there are the universe, it is usually written as 10²² stars (Reynolds, 2015). It is because space is so large, that numbers used in space are large also. For example, If you were to write this number out it would look like, 10,000,000,000,000,000,000,000. It’s a massive number isn’t it? These equations are an aspect of maths which astronomers have to solve daily, with extremely large numbers.

We also looked into the different planets in regards to spacing and size. The moon itself is approximately 384, 400 km from Earth, and the sun is 146 million km from the Earth. There is not only the planets to consider, but also the fact that space is huge, and is filled with big empty gaps between each planet. However, if you look at the image below, we seem to be relatively close to our neighbouring planets.  But as the numbers prove, this is in fact not the case.

We then discussed how big we think particular planets are by comparing them to objects such as beach balls, footballs etc. Of course the scale that this provided was not correct, but it gave an impression of the different sizes of the planets.

The image provided provides a more realistic interpretation of the size of our solar system, as it compares each individual planet to each other. This diagram is much more realistic than the objects, as the size of the sun is represented in a way that illustrates the vastness of our solar system. I have found that it is difficult to explain just how vast the universe is without some visual aid. Oh and did I forget to mention, my friend’s Godfather is the astronaut Tim Peake. Is that cool or what?

References

Reynolds, S. (2015) ‘Maths in Astronomy’ [PowerPoint presentation]ED21006:Discovering Mathematics. Available at: https://my.dundee.ac.uk/bbcswebdav/pid-4535880-dt-content-rid-2953578_2/courses/ED21006_SEM0000_1516/Simon%20Reynolds%20Maths%20and%20astronomy%20presentaion.pdf (Accessed: 19 November 2015).

We had an interesting lecture with Richard on the use of time a few days ago, I suppose that I had never really though too much about time before. I have always just assumed that time was a simple thing; non-confusing and quite easy to grasp. Then I remember that this view is from an adult’s stance, of course time is hard to grasp.

Firstly we discussed what exactly is time? What is linear time? I had a rough idea of what this term meant from my sci-fi love of tv, including shows such as Star Trek, Battlestar Galactica, Firefly and of course doctor who. Richard touched upon one of my favourite episodes from Doctor Who, ‘Blink’, if you have never seen this episode then go watch it now! It is a fantastic episode! And one of my all-time favourite doctor who lines is in it,

I love this line as it kind of resonates within me, in how I would describe time. Have you ever fallen asleep and woken up after a few hours? Of course you have. But have you ever felt like you just closed your eyes? How could time have passed that fast? You were so sure that it had only been 5/10 minutes since they closed. Someone must be playing a trick on you!

On a serious note though, time is one of the most important aspects of everyday life. If you think about it, what else is a constant every day? Passes at the same speed? (Even if we believe it has not). How would the world cope without time? Bus and train timetables, lecture timetables and school timetables are all examples of timetables which I use within my life, and that I need to know how to understand. Maths is clearly involved with timetables.

I had to wonder, before we had digital and analogue, how did we manage to tell time?  The answer is Sundials. This creation provided a means of being able telling the time based on the movement of the sun. The sun changes its position on the sundial throughout the day as it orbits, casting a shadow on the sundial. The fundamental maths behind this could be through movement and angles. But in today’s society we no longer deal with sundials, we deal with digital more and more, and analogue less and less.

This made me think back to my MA1 placement when I taught my p6’s and 7’s about time. I remember being shocked that children as old as 10 or 11 years old, were still unsure about time and how to tell it. Surely our child population can tell the time? After speaking with my pupils, I discovered that they would like to be able to tell the time but they just did not see the point in it. They all have laptops, mobiles and televisions which can tell them the time in a much simpler format in their opinion; digital. They did not understand why they had to learn analogue, as it was not a part of their life anymore and they felt like it was something of the past generations. I was shocked. Can I really be classified as that old?

Richard suggested that time has maybe become a life lesson, something that you should learn from your parents or carers. There are several life lessons which we learn at home, such as using cutlery or putting clothes on oneself, should time be the same? I remember growing up with analogue clocks around all of my home but then my mum is a big fan of analogue clocks. We had one in every room nearly, and I can’t help but wonder if this was a tactic used so my siblings and I would be comfortable with the time? Maybe.

In case I got you wanting to watch the doctor who episode, here is the trailer!

Picture available at: http://www.yourfriendelle.com/david-tennants-best-doctor-who-lines/

Video available at: https://www.youtube.com/watch?v=KFBZmw4nSww

Everyone has heard of the children’s song ’10 green bottles’, but do we all actually realise how mathematical the song is? Especially from the perspective of a child?

Nursery rhymes are used as a technique to teach children maths but in a fun and engaging way. It was not until I looked into maths within music that I remembered the amount of childhood nursery rhymes which I sang as a child, that involve mathematics. Such as ‘Ten in a Bed’, ‘Five Little Speckled Frogs’, ‘Five Little Ducks’, ‘One, Two Buckle My Shoe’ and ‘Round and Round the Garden’. The nursery rhyme which sticks in my head most is ’10 Green Bottles’,

10 Green Bottles video – https://www.youtube.com/watch?v=T0ooQv7oHvw

The song follows the format of;

Ten green bottles hanging on the wall,

Ten green bottles hanging on the wall,

And if one green bottle should accidently fall,

There’ll be nine green bottles hanging on the wall.

Nine green bottles hanging on the wall,

Nine green bottles hanging on the wall,

And if one green bottle should accidently fall,

There’ll be eight green bottles hanging on the wall.

(Continue singing until only one green bottle is left)

One green bottle hanging on the wall,

One green bottle hanging on the wall,

And if that one green bottle should accidently fall,

There’ll be no green bottles hanging on the wall.

No green bottles hanging on the wall.

It is obvious that the song involves subtracting and the ability to be able to count backwards. However, children may find this very difficult. As adults we take for granted our ability to perform basic maths and can sing these nursery rhymes easily and without hesitation. But for most children they will have to continuously work on remembering what number comes next in the countdown, whilst also placing it into its literate context within the song. This is difficult for children and should be remembered next time you hear a young child singing a nursery rhyme as they pass you.

The repetitive nature of the song is catchy and young children feel comfort in the fact that the verses are the same bar the decreasing number. It is only one variable in each verse compared to popular pop songs which may contain several different verses.  Early years children will also appreciate the actions which accompany the songs, as they help them to remember the words in the songs.

I studied music at high school and it has been one of my main passions ever since. Even now I am sitting listening to music as I write this blog post – Adele if you are wondering – and listen to different artists/genres for every piece of writing I complete. I just can’t focus in silence; I need the beat, tempo, words and rhythm in order to concentrate. This is something that I have never been able to understand, shouldn’t I be able to concentrate without Bowie or John Newman singing into my mind?

Following our input with Anna (in which we discovered some mathematics that is involved in music), I decided to discover just how much maths actually influences music. In my mind it does not influence music very much, as they are such different areas. How could maths influence something so creative and beautiful? In my mind, mathematics is rigid and stable, non-changing and uncreative. Basically the opposite to music.

After researching these two topics, I can now say that my perception of maths and music was wrong. They actually identify and connect with each other more than I thought, and in more ways than one.

Anna provided us with various examples of how basic mathematics is used within music, such as rhythmic patterns, which we attempted to recreate through various clapping exercises. In this activity we discovered that counting and speed are crucial to clapping in time to the beat which we were shown. This exercise became harder when we were split into groups and each group was given a different clapping sequence to complete at various times to other groups. Finally adding them all together so that the different rhythms overlapped each other, an example of this is shown below. This is a simple way of mathematics – counting, speed and rhythm – being involved within music which is transferable into the primary school.

(Robb, 2015)

Throughout primary school and high I learned how to play different brass instruments, and now contain the knowledge to play them all. I remember being taught the number value of each note, and when playing from sheet music told to imagine the numbers instead of the shapes of the notes. This is something which I still do today and find it easier to comprehend than working from the notes themselves. This is an example of how I use mathematics myself when I play instruments. Also, when I tune my instruments I use frequency in order to determine if the pitch is correct. Another mathematical term which I forgot was involved within music.

However it is not only when I play my instruments that I use mathematics, but also when I dance. I use rhythm and beat in order to keep in pace with the music and also other dancers. Within Irish dancing we count in sets of 8 and will work steps into routines based on the 8 count rule. This is an example of how repetition influences my dancing, a further mathematical concept found within music.

References 

Robb, A. (2015) ‘Discovering Maths: Music’. [PowerPoint presentation] ED21006: Discovery mathematics (University Elective). Available at: https://my.dundee.ac.uk/webapps/portal/frameset.jsp?tab_tab_group_id=_2_1&url=%2Fwebapps%2Fblackboard%2Fexecute%2Flauncher%3Ftype%3DCourse%26id%3D_54593_1%26url%3D (Accessed on: 10 November 2015).