Presentation

I did my presentation yesterday evening. It went okay. Members of the audience filled out an evaluation sheet so I could use this in my own evaluation. I could possibly represent the results on pie charts...?
I haven't blogged much because I was focusing on the presentation. Really need to prioritise writing the essay, as the deadline for the project is the 8th december.

Enough of reading for now...

I have 4 days to make my presentation, seeing as it is on Monday. I don't really know what I've been doing that has stopped me from already planning it, but that's life, I guess.

I want my presentation to be as interactive as possible. Clarity is extremely important too, as my topic can get a bit complicated and difficult to explain. I am debating whether to make my presentation a summary of my dissertation, or if it should be more about what I have done to get to my presentation. I may try to ask Mr Wright for advice, seeing as I missed the meeting about extended project presentations when I had a uni interview.

VERY rough structure of my presentation and helpful sources to go with it:

Introduction to myself and my project.
Should talk about why this topic interests me, what I wanted to get out of it. Structure of my project?

What is randomness?
"randomness implies a lack of predictability. More formally, in statistics, a random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution."
Breif history about randomness?

How I structured the project
My aims, Blog, GANTT chart etc.

What I've researched? (this will be a big part of my presentation)

Probability, Quantum Theory, Chaos, Random number generators... basically all the different parts of my dissertation. Examples of each of these concepts. Reference to books etc.

What I've learnt?
Conclusion. My personal opinion on randomness after doing this project.


OKAY. I definitely need to get cracking on the presentation now.

Does God Play Dice?

"When you roll a die, any one of the six possible faces may end up on top. The result of throwing a die is like an eigenstate - it is a special state that is selected by the measurement process. [...] A Copenhagenist would say that the presence of a table mysteriously causes a die to 'collapse' to one of the states 1, 2, 3, 4, 5, 6, an that the rest of the time it is in a superposition of those eigenstates - which is, of course, a mathematical fiction with no intrinsic physical meaning. Bohm would say that it does have a physical meaning but you can't observe it - at least with any conventional apparatus, and perhaps not at all. Diosi-to-Percival would say that as the die rolls along the table its state randomly jiggles, and eventually settles down to one of 1, 2, 3, 4, 5, or 6. [...]
The imgae of dice suggest that they might all be right -
- and all wrong.

Chaos teaches us that anybody, God or cat, can play dice deterministically, while to naive onlooker imagines that something random is going on. The Copenhagenists and Bohm do not notice the dynamical twists and turns of the rolling die as it bounces erratically but deterministically across the table-top. [...] Diosi-to-Percival notice the erratic jiggles of the die [...], not realising that underneath they are actually deterministic.
Nobody tries to write down the equations for a rolling die. [...] One good reason is that they think it can't be done."

This extract helps me to understand the different ideas around chaos and quantum theory. It is also the first extract that has made me see a connection between the two concepts. It isn't possible to determine the state of a die before it lands on a number - this is the same idea of a decaying nucleus. Only when it actually happens, can we determine its state.

The last part of this extract supports the point that I made about randomness just being events that we cannot mathematically model because of its complexity.

Reading through Does God Play Dice?

After yesterday's meeting, I have begun to crack down on reading the remaining books and specifically picking out the parts that I believe will be most relevant to me. Chapter 16 of "Does God Play Dice?" by Ian Stewart is called "Chaos and Quantum" and may be exactly what I need to help me with understanding these 2 concepts for my project.

Ian Stewart discusses the 'cat in a box' experiment. I came across this experiment in the book Quantum by Jim Al-Khalili but I don't think I blogged about it:
"Imagine a box that contains a source of radioactivity, a Geiger counter to detect the presence of radioactive particles, a bottle of (gaseous) poison, and a (live) cat. These are arranged so that if a radioactive atom decays and releases a particle, the then Geiger counter will detect it, set off some kind of machinery that crushes the bottle and kill the unfortunate cat. From outside the box, an observer cannot determinw the quantum state of the radioactive atom; it may either have decayed or not. So [...] the quantum state of the atom is a superposition of 'not decayed' and 'decayed' - and so is that of the cat, which is part alive and part dead at the same time. Until, that is, we open the box. At this instant the wave function of the atom instantly collapses, say to 'decayed', and that of the cat also correspondingly collapses instantly to 'dead'.

This extract has helped me understand quantum theory a bit more. It shows that it is impossible to know what state something is in, and therefore it can be said that they are in both states.

Today's supervision

My concerns before the meeting:
Whether I will have enough time to finish reading all my books and finish the essay before the deadline.
I missed the meeting about the presentation because I had an interview with Manchester university, so I wanted to ask if I missed anything important.

What we talked about during the meeting:
If I really feel like I am running out of time, I should choose to read chapters of books that I believe will help me, and the conclusion.
I may have been getting confused between the presentation date and the final deadline for my project. I do not need to have finished my project by the 29th (my presentation).

Things I learnt from the supervision:
Forget about the essay right now-focus on reading the books.
Begin preparing the presentation.

Supervision has been rescheduled to Thursday.

RIGHT...

I spoke to Mr Wright yesterday and the date of my presentation is the 29th November. My supervision was supposed to be last Tuesday but it got rescheduled to today, in about 2 hours time.

Here's my updated GANTT Chart:


It is obvious that I need to read the rest of the books, as they are what is stopping me from being able to write my dissertation.

So, reading through Quantum Theory:

John Polkinghorne talks about Paul Dirac, an English theoretical physicist who was one of the founders of quantum mechanics, and one of his lectures on quantum theory.

"He took a piece of chalk and broke it in two. Placing one fragment on one side of his lectern and the other on the other side, Dirac said that classically there is a state where the piece of chalk is 'here' and one where the piece of chalk is 'there', and there are the only two possibilities. Replace the chalk, however, by an electron and in the quantum world there are not only states of 'here' and 'there' but also a whole host of other states that are mixturs of each possibilities - a bit of 'here' and a bit of 'there' added together.

Quantum theory permits the mixing together of states that classically would be mutually exclusive of each other."

He then goes on to describe the double slit experiment, which I have already come across in Quantum by Jim Al-Khalili.

So far this book is really helping me to understand the basic concepts of quantum theory. It is a world of the unknown - which is evidence to why randomness exists.

Reading through Quantum Theory

The book begins with the history of the discovery of quantum theory. John polkinghorne talks about the roles of different professionals in this discovery. This includes people such as Planck, Einstein, Young, maxwell and Bohr. Although this is interesting, I don't think that the history of quantum mechanics is terribly important in my dissertation. What is relevant is why quantum mechanics is evidence that randomness does exist.

I realised that my GANTT chart says that I should be reading An Introduction to Quantum theory, not Does God Play Dice?. So I have begun reading that instead. My next supervision is on Tuesday.

Writing "The history of randomness"

I have begun to write this section. I have collected most of the relevant quotes and sources - now I just need to sort them out.

Here is what I have so far (At the moment, it's pretty much just a bunch of sources)
The debate of whether randomness exists has been around for a very long time. The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. Chance mechanisms have been used since antiquity and people took advantage of its unpredictability to make quick decisions events such as settling disputes among neighbours and choosing which strategy to follow in the course of battle. In her book, Randomness, by Deborah J. Bennett states that "The purpose of randomizers such as lots or dice was to eliminate the possibility of human manipulation and thereby to give the gods a clear channel through which to express their divine will. Even today, some people see a chance outcome as fate or destiny, that which was 'meant to be'". This extract coincides with Albert Einstein’s famous quote – “God does not play dice”. To humans, it may seem as though there is no explanation for a random event, but in reality, it is just too complicated for our minds to understand.

The first atomist, Leucippus (circa 450 B.C.), said, 'Nothing happens at random; everything happens out of reason and by necessity'. The atomic school contended that chance could not mean uncaused, since everything is caused. Chance must instead mean hidden cause.
Another quote from Randomness:"[...] Newtonian physics - a system of thought which represented the full bloom of the Scientific Revolution in the late seventeenth century. [...] a belief developed among scientists that everything about the natural world was knowable through mathematics. And if everything conformed to mathematics, then a Grand Designer must exist. Pure chance or randomness had no place in this philosophy."
Another quote: "Though not always recognized or acknowledged as such, chance mechanisms have been used since antiquity: to divide property, delegate civic responsibilities or privileges, settle disputes among neighbors, choose which strategy to follow in the course of battle, and drive the play in games of chance."

Wikipedia - "Some theologians have attempted to resolve the apparent contradiction between an omniscient deity, or a first cause, and free will using randomness. Discordians have a strong belief in randomness and unpredictability. Buddhist philosophy states that any event is the result of previous events (karma), and as such, there is no such thing as a random event or a first event.

A quote by Jim French (physics PhD) : "The concept of being able to predict and describe the future behaviour of anything we wanted dates back to the 18th century and is typically associated with the French mathematician Pierre-Simon Laplace and something called Laplace's Demon, which is some hypothetical creature that he thought of as (in principle and possibly way into the future) possessing sufficient knowledge of all the positions and speeds of all particles in the universe as to be able to perfectly predict the entire future evolution of the universe. This concept of causal or Newtonian determinism seemed unavoidable at the time, though it had some uncomfortable questions for the nature of free will, until the beginning of the twentieth century, when it ran into the twin problems of quantum theory and chaos theory. The latter presents no conflict with the principle of determinism, but it does in a practical sense. The physics of chaotic systems are still governed by underlying deterministic processes, but what was realised in the middle of the last century was that putting any knowledge of initial conditions into an actual prediction was far harder than previously realised. A small lack of precision in our knowledge of an initial state can quickly lead into huge uncertainty in the state of the system at some later time."

A quote from wikipedia: "In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.

. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of the calculus had a positive impact on the formal study of randomness. In the 1888 edition of his book The Logic of Chance John Venn wrote a chapter on "The conception of randomness" which included his view of the randomness of the digits of the number Pi by using them to construct a random walk in two dimensions.

The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, as various approaches for a mathematical foundations of probability were introduced. In the mid to late twentieth century ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.

Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases such randomized algorithms outperform the best deterministic methods."

I have just emailed my suppervisor to arrange another meeting somtime next week.

Probability

Here are the 954 words that make upthe section of my dissertation titled "Probability".

I'm not 100% satisfied with it, but it'll have to do for now. There are too many tasks that need to be done.


“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

In this section, I will talk about how probability helps us to understand the concept of randomness.

Sometimes, when I think of a random event, I imagine something that is totally impossible to predict or understand. Probability shows that some random events are not as unpredictable as people assume. In July, I attended a maths taster day at Queen Mary University of London, called “Inevitable patterns in mathematics”. There were about 50 of us at the taster day. The lecturers, Ben Green and Imre Leader,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 they made all the students who had birthdays in September stand up. This included me. They 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 they 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 in a group of 50 people is 1-(365/365)(364/365)(363/365)(362/365)...(316/365) which is around 0.97.
Amir Aczel also talk about a similar situation in the book, Chance- the probability that 2 balls land in the same box, if a number of balls are dropped into a number of boxes at random. There are 2 equations that are stated which I found quite interesting:

"1.2 times the square root of the number of categories gives the number of 'balls' required for even odds that at least two share some characteristic.
And:
1.6 times the square root of the number of categories gives the number of 'balls' required for ninety-five percent probability that at least two share some characteristic."

So, if we go back to the Birthday Problem that I came across at the maths taster day, I can now work estimate:
1) 1.2 times the square root of 365 = 22.926, so 23 people have a 50 percent probability of at least one shared birthday.

2) 1.6 times the square root of 365 = 30.57, so 31 people have a 95 percent probabily of at least one shared birthday.

Now it is easy to see why, in my group of 50 people, there was an extremely high probability (97 percent) that we would find a shared birthday.

Now, let us take the classic example of a rolling of a die. Although one can not predict the next number to show up on the die, we know that after 60 rolls, each number should show up roughly ten times. This is because each number on the die has a 1 in 6 probability of being shown. Obviously, this doesn’t mean that every number will actually appear 1 in 6 times. There is a chance that if a die was rolled 60 times, the number 1 would appear every single time, but the probability of that happening is very small, so we know that this event is extremely unlikely. To conclude, it is possible to roughly predict the amount of times a number should appear on a die if the die has been rolled many times. However, it is impossible to predict what the next outcome on the die will be. Or is it?

I asked some physics and maths graduates: “Do you believe with enough research, one will be able to predict a random event (e.g. the outcome of a dice roll) in the future?” Laura Wherity, a maths graduate, answered: “Rolling a die may appear to be random, but in fact it depends on your starting conditions. For example, if you could control the experiment such that the die is always rolled from the same height, at the same angle with the same forces etc. then it should be possible to achieve the same outcome each time. What would appear to be random actually depends on the starting state. Extending this idea, it may be possible to control the starting conditions of other events aswell, so in this sense events that appear 'random' at present may become more predictable in the future as we understand the conditions in more detail.”

Jonathan Wright, another mathematics graduate, said “If we roll a dice in exactly the same way 100 times, 100 times it would give us the same result. If we model the roll of the die, given the starting conditions we could predict the outcome every time.”

So technically, rolling a die isn’t a random event. It is our lack of knowledge of the mechanics of the die which forces us to call it random, although it actually isn’t. Theoretically, it may be possible to one day understand all the conditions of a random event such as a dice roll, and therefore predict the outcome. This may be able to be applied to other such events, and therefore it will be proven that randomness does not exist.


"Probability is humanity's attempt to use pure mathematics to understand the un-understandable. It is our way of trying to learn something about the workings of chance. Chance remains forever untamable, for fate does what it wants to us and to the world around us."

I feel as though I had something else to say, but I can't remember it...

Anyway, TASKS FOR THE WEEKEND/UPCOMING WEEK:
Read Does God Play Dice
Finish writing Random Number Generators and/or The History of Randomness
Email supervisor tomorrow about next meeting.

Back from half term

I didn't manage to blog during the half term because I found myself with a lot of other work to do. My maths admissions text for Oxford univeristy was this morning, so, with that out the way, I can now try to focus on this project. During the half term I managed to begin writing the probability AND history of randomness section of my dissertation. I don't think I am going to read Chaos - I have already got many quotes from it and I am quickly running out of time.

I need to arrange a supervision with my supervisior soon, probably next week.