Monday, 26 July 2010
New GANTT chart
Today, I have adapted the GANTT chart to what I found to be more realistic. Also, this should help me with the problems I mentioned in my earlier post. I have made my GANTT chart end at the end of September so that if I stick by it, I will finish everything way before the deadline and will have a lot of time to begin working on my presentation and add any finishing touches to the dissertation.
Solution to my problems
I have mainly spent this weekend rethinking my project management and changing my GANTT chart. On Saturday 24th July, I updated my GANTT chart to where I am now. The red shows where I am in my GANTT chart and what I am doing and have done.
I am aware that the GANTT chart is very small on this blog. I don't know how to increase the size but I will be printing out all my updated GANTT charts of A4 size for my submission of the project.
I am aware that the GANTT chart is very small on this blog. I don't know how to increase the size but I will be printing out all my updated GANTT charts of A4 size for my submission of the project.
Saturday, 24 July 2010
Obstacles that I have come across
Firstly, I am not even halfway through Chance which is my first book to help me with my project. The next book that I am going to read (Chaos) is much longer than Chance, and so I will definitely not finish reading that in a week, which is what I had put in the GANTT chart. Chaos and Chance are the only books that I've actually managed to buy at the moment, and I was meant to buy all of my books last week. Luckily, I can get them for cheap prices on amazon.co.uk, and will hopefully do that soon.
Secondly, I feel as though I don't really know what I am doing. Obviously, I know that I'm looking for relevant sources to help me with my dissertation, but I have no idea of the stucture of my dissertation and what I actually want to include in it. At the moment, I feel as though I am working hard on this project, but I can't tell if the work is going to be useful to my dissertation.
Furthermore, as time goes on, I am beginning to realise how little time I have to complete this project. Most of the activities on my GANTT chart are to help me learn more about this project and get a large variety of helpful sources. I hope that by the end of this summer, I have enough information to know what my dissertation will consist of.
In conclusion, I guess the solutions to these problems and concerns could be to just keep going with hope that at some point, I will understand exactly what I want my dissertation to be like. Also, I think that my GANTT chart needs to be adapted as it does not seem very realistic at the moment.
Apart from these obstacles, I guess everything is going okay!
Secondly, I feel as though I don't really know what I am doing. Obviously, I know that I'm looking for relevant sources to help me with my dissertation, but I have no idea of the stucture of my dissertation and what I actually want to include in it. At the moment, I feel as though I am working hard on this project, but I can't tell if the work is going to be useful to my dissertation.
Furthermore, as time goes on, I am beginning to realise how little time I have to complete this project. Most of the activities on my GANTT chart are to help me learn more about this project and get a large variety of helpful sources. I hope that by the end of this summer, I have enough information to know what my dissertation will consist of.
In conclusion, I guess the solutions to these problems and concerns could be to just keep going with hope that at some point, I will understand exactly what I want my dissertation to be like. Also, I think that my GANTT chart needs to be adapted as it does not seem very realistic at the moment.
Apart from these obstacles, I guess everything is going okay!
Monkeys typing Hamlet
Quoted from Chance:
"There is a very, very small (very close to zero, but not quite quite zero) probability that a sequence of randomly typed letters will happen to form Shakespeare's Hamlet. Actually, we can compute the probability. Let's assume there are thirty kinds of typed characters in English: twenty-six letters, comma, period, semicolon, and colon-we will ignore spaces and capital letters; let's give this monkey a break! The chance that the monkey will type correctly the first letter in Hamlet, which is "a" (from "Act I"), is 1/30. We need to multiply this number by 1/30 for the second character typed to agree with Hamlet (meaning, to be the letter "c"). [...] Continuing the multiplication this way, for each of the one hundred forty-two thousand, nine hundred and forty-three characters in the entire tradegy Hamlet, we see that the answer is 1/30 raised to the power 142,943. This number is extremely close to zero-but not exactly zero. It is around 0.0... followed by over two hundred thousand zeros, then a one.[...] Given infinite time (whatever that means), a monkey will type the entire Shakespearean tradegy."
"There is a very, very small (very close to zero, but not quite quite zero) probability that a sequence of randomly typed letters will happen to form Shakespeare's Hamlet. Actually, we can compute the probability. Let's assume there are thirty kinds of typed characters in English: twenty-six letters, comma, period, semicolon, and colon-we will ignore spaces and capital letters; let's give this monkey a break! The chance that the monkey will type correctly the first letter in Hamlet, which is "a" (from "Act I"), is 1/30. We need to multiply this number by 1/30 for the second character typed to agree with Hamlet (meaning, to be the letter "c"). [...] Continuing the multiplication this way, for each of the one hundred forty-two thousand, nine hundred and forty-three characters in the entire tradegy Hamlet, we see that the answer is 1/30 raised to the power 142,943. This number is extremely close to zero-but not exactly zero. It is around 0.0... followed by over two hundred thousand zeros, then a one.[...] Given infinite time (whatever that means), a monkey will type the entire Shakespearean tradegy."
Friday, 23 July 2010
Reading through Chance...
The book begins with probability. "Probability is humanity's attempt to understand the uncertainty of the universe,to define the undefinable. A probability is a quantitative measure of the likelihood of a given event." Amir D. Aczel goes on to talk about probability in a similar way to the Statistics 1 module of the Maths A level.
He then moves on to talk about objective and subjective probability and the de Finetti Game. "Bruno de finetti(1906-1985) was an Italian statistician [...] Incredibly, he found a way to objectively measure subjective probability"
The de Finetti game assess someone's true subjective probabiliy. Amir D. Aczel uses the example of a friend saying that they are 100 percent sure that they will get a perfect score in a test that they have just done.
"Tell your friend the following. 'Let's play a game. You have a choice. You can either draw a ball from a bag that has ninety-eight red balls and two black balls. If you happen to draw a red ball, I will give you one million dollars. Or you can decide to wait to see how you did on the test, and if you receive a perfect score on that test I will give you one million dollars. What's your choice: draw or wait?' Presumably your friend will say, 'Draw from the bag.' If he doesn't, it means he really has a subjective probability of one hundred percent of acing the test. If your friend's decisionis 'draw,' you ask the next question: 'Now there are eighty red balls in the bag and twenty black ones. Do you want to draw,and if you obtain a red ball get a million dollars,or wait to see how you did on the test and get a million if you aced it?'" The game carries on like this until the person cannot choose between drawing or waiting. This is their actual subjective probability.
I think that this game would be a good thing to use in my presentation, as it will allow me to interact with the audience and make the presentation more intersting for them. I could begin by talking about how something may never be totally random because of probability, as probability can help us predict random events. This would lead me onto picking balls out of a bag. I could get the audience to pick a ball out of a bag of different coloured balls, and ask them if this is random, or perhaps it is a pattern that is too complicated for us to understand. I could then do the de Finetti game, to talk about why it is important to have objective probability when handling an event.
He then moves on to talk about objective and subjective probability and the de Finetti Game. "Bruno de finetti(1906-1985) was an Italian statistician [...] Incredibly, he found a way to objectively measure subjective probability"
The de Finetti game assess someone's true subjective probabiliy. Amir D. Aczel uses the example of a friend saying that they are 100 percent sure that they will get a perfect score in a test that they have just done.
"Tell your friend the following. 'Let's play a game. You have a choice. You can either draw a ball from a bag that has ninety-eight red balls and two black balls. If you happen to draw a red ball, I will give you one million dollars. Or you can decide to wait to see how you did on the test, and if you receive a perfect score on that test I will give you one million dollars. What's your choice: draw or wait?' Presumably your friend will say, 'Draw from the bag.' If he doesn't, it means he really has a subjective probability of one hundred percent of acing the test. If your friend's decisionis 'draw,' you ask the next question: 'Now there are eighty red balls in the bag and twenty black ones. Do you want to draw,and if you obtain a red ball get a million dollars,or wait to see how you did on the test and get a million if you aced it?'" The game carries on like this until the person cannot choose between drawing or waiting. This is their actual subjective probability.
I think that this game would be a good thing to use in my presentation, as it will allow me to interact with the audience and make the presentation more intersting for them. I could begin by talking about how something may never be totally random because of probability, as probability can help us predict random events. This would lead me onto picking balls out of a bag. I could get the audience to pick a ball out of a bag of different coloured balls, and ask them if this is random, or perhaps it is a pattern that is too complicated for us to understand. I could then do the de Finetti game, to talk about why it is important to have objective probability when handling an event.
Thursday, 22 July 2010
Proposal
This is 400 word (418 to be exact) proposal on my extended project.
The working title of my extended project is going to be "An Investigation into whether pure randomness exists". I will explore many different arguments and opinions, and then draw my own conclusion from them. My project will meet all of the assessment objectives.
To meet AO1, I have made a GANTT chart to manage my project and help with time management too. I am prepared to change the chart if or when needed. Also, I am keeping a blog (zkswanzy.blogspot.com) which will provide evidence of all my project management.
I will meet AO2 by purchasing many books related to my chosen topic. I will also look on the internet for sources and have allocated some time on the GANTT chart for analysing and evaluating said sources. Not all sources will be used, and I will therefore explain why I have chosen to include some sources rather than others in my dissertation. This may be because of reliability, for example.
I have never used a blog before, and so creating one to document my progress in the project will help me meet AO3. I will talk about all my thoughts, problems and decisions on the blog. At the moment, I do not know enough about randomness to have an opinion on it, and so hopefully by the end of the project I will have developed enough to be able to make my own strong argument about it. I will be having regular meetings with my supervisor which will also help me with AO3 as Ms Caroussis will be able to help me decide on my next step in the project. I have already met with a mathematician at Manchester University and hope to talk to many more. This will help me improve my project and evaluate my position in it.
I will meet AO4 by drawing to a conclusion in the dissertation about whether pure randomness exists. My conclusion will evaluate everything that I have learnt throughout the project. I will also be reviewing things during the whole project, for example, the books that I will read. After I have done a task on the GANTT chart, for example, collecting internet sources, I will review them as see how it will fit into my assessment objectives.
My presentation will most likely be interactive with a lot of different arguments about whether random exists. This is so I will be able to get the audience thinking and making their own conclusions about randomness, like my project will help me do.
Shortly after writing this, I realised that I did not include a list of sources. I forgot to do this as I already have a list of sources on this blog already, but for the sake of having everything in one place, here is a list of sources so far that I have found or been recommended:
Chance - Amir Aczel
Chaos - James Gleick
Reckoning with Risk - Gerd Gigerenzer
John Polkinghorne - Quantum Theory: A very Short Introduction
Feynman's Theory
Introduction to random time and quantum randomness- Kai Lai Chung
Wikipedia
The working title of my extended project is going to be "An Investigation into whether pure randomness exists". I will explore many different arguments and opinions, and then draw my own conclusion from them. My project will meet all of the assessment objectives.
To meet AO1, I have made a GANTT chart to manage my project and help with time management too. I am prepared to change the chart if or when needed. Also, I am keeping a blog (zkswanzy.blogspot.com) which will provide evidence of all my project management.
I will meet AO2 by purchasing many books related to my chosen topic. I will also look on the internet for sources and have allocated some time on the GANTT chart for analysing and evaluating said sources. Not all sources will be used, and I will therefore explain why I have chosen to include some sources rather than others in my dissertation. This may be because of reliability, for example.
I have never used a blog before, and so creating one to document my progress in the project will help me meet AO3. I will talk about all my thoughts, problems and decisions on the blog. At the moment, I do not know enough about randomness to have an opinion on it, and so hopefully by the end of the project I will have developed enough to be able to make my own strong argument about it. I will be having regular meetings with my supervisor which will also help me with AO3 as Ms Caroussis will be able to help me decide on my next step in the project. I have already met with a mathematician at Manchester University and hope to talk to many more. This will help me improve my project and evaluate my position in it.
I will meet AO4 by drawing to a conclusion in the dissertation about whether pure randomness exists. My conclusion will evaluate everything that I have learnt throughout the project. I will also be reviewing things during the whole project, for example, the books that I will read. After I have done a task on the GANTT chart, for example, collecting internet sources, I will review them as see how it will fit into my assessment objectives.
My presentation will most likely be interactive with a lot of different arguments about whether random exists. This is so I will be able to get the audience thinking and making their own conclusions about randomness, like my project will help me do.
Shortly after writing this, I realised that I did not include a list of sources. I forgot to do this as I already have a list of sources on this blog already, but for the sake of having everything in one place, here is a list of sources so far that I have found or been recommended:
Chance - Amir Aczel
Chaos - James Gleick
Reckoning with Risk - Gerd Gigerenzer
John Polkinghorne - Quantum Theory: A very Short Introduction
Feynman's Theory
Introduction to random time and quantum randomness- Kai Lai Chung
Wikipedia
Thursday 22nd July
I have submitted my 400 word proposal to Ms Caroussis. I bought Chance by Amir Aczel and Chaos by James Gleick today. I have realised that I may need to allocate more time to read these books as they are quite long. For now, I will just see how the upcoming week goes, in relation to buying/ordering and reading all the books. I have begun reading Chance.
Saturday, 17 July 2010
Supervision
Yesterday(Friday 16th July)I had a meeting with my supervisor, Ms Caroussis. My concern before the meeting was about whether my progress so far was enough. We discussed the GANTT chart I made and how I will go about completing the tasks on it. We realised that I will need to find professionals i.e. mathematicians that I can talk to so that my sources are not just books and the internet. I think that an obstacle that I may come across later on in the project will be having to find a wide range of sources. My main focus now is to write the 400 word descriptionof my project and begin reading the books.
Tuesday, 13 July 2010
Another book and the maths taster day
I was looking through different internet forums to gain an idea of the sort of arguments around randomness. One person suggested this book:
Chaos by James Gleick
Yesterday (Monday 12th July), I attended a maths taster day at Queen Mary University of London. The topic was Inevitable patterns in mathematics. The lecturers were Ben Green and Imre Leader.
1) Misleading patterns
- Birthday coincidences: There were about 50 of us at the taster day. The lecturer called out all the months of the year and asked us to raise our hand when he said the month that our birthday was in. The most popular month was September, so he made all the students who had birthdays in September stand up. This included me. The then asked us what date in September we were born in, and if no one else shared that birthday, the person would sit down. When he came to me, I stated that my birthday was on the 17th of September and funnily enough, another girl who was standing up said that she was also born on that day.
I was very surprised that out of a group of 50 people, it was possible that two people shared the same birthday. As Imre Leader later explained, it was almost certain that two people would share the same birthday: The probability that there is a repeated birthday ina group of 50 people is 1-(365/365)(364/365)(363/365)(362/365)...(316/365) which is around 0.97.
Chaos by James GleickYesterday (Monday 12th July), I attended a maths taster day at Queen Mary University of London. The topic was Inevitable patterns in mathematics. The lecturers were Ben Green and Imre Leader.
1) Misleading patterns
- Birthday coincidences: There were about 50 of us at the taster day. The lecturer called out all the months of the year and asked us to raise our hand when he said the month that our birthday was in. The most popular month was September, so he made all the students who had birthdays in September stand up. This included me. The then asked us what date in September we were born in, and if no one else shared that birthday, the person would sit down. When he came to me, I stated that my birthday was on the 17th of September and funnily enough, another girl who was standing up said that she was also born on that day.
I was very surprised that out of a group of 50 people, it was possible that two people shared the same birthday. As Imre Leader later explained, it was almost certain that two people would share the same birthday: The probability that there is a repeated birthday ina group of 50 people is 1-(365/365)(364/365)(363/365)(362/365)...(316/365) which is around 0.97.
Project Management
I have decided produce a GANTT chart to help me with time management throughout the project. Every few weeks I will produce a new GANTT chart to show my progress. I may also add more tasks as time goes on because at the moment, I may not know exactly everything that I will need to do for my extended project.
My GANTT chart only includes tasks related to my dissertation. I may produce another one for my presentation later on in the project but for now, I believe that the research and production of my dissertation is most important.
My GANTT chart only includes tasks related to my dissertation. I may produce another one for my presentation later on in the project but for now, I believe that the research and production of my dissertation is most important.
Title of my project
I have decided that the most suitable title for my project will be "An Investigation on whether pure randomness exists". The word investigation shows that I will be using many different sources to produce my own conclusive opinion on randomness. I think this is important as I need to make it clear that there isn't a proven conclusion to this subject.
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