Plan for my dissertation.

Because all my quotes and sources are scattered around this blog, I think it would be helpful to have one blog with all my sources so far, each libked to a section of my dissertation. This will make it easier for me when it comes to writing each section because I won't miss anything out.

The history of randomness - why is it important?:

Randomness by Deborah J. Bennett: "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 Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. 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."


Probability:

Laura Wherity: "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. Another good example of this are the weather models used for predicting the weather in forecasts. The better we can get at determining the initial conditions, the better our models will become. Of course in certain situations there may be a limit to the accuracies involved, and thus exact predictions or modelling may not be possible."

Jonathan Wright: "As an applied mathematician, all physical situations can be modelled mathematically, and as such we can predict all possible outcomes. 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."

Randomness - Deborah J Bennett
Also Chance and Reckoning with Risk

Short Introduction to Chaos and Quantum Mechanics:

Jim French: "However, in quantum theory (at least in the Copenhagen interpretation), it is meaningless to speak of a property of a particle (such as its position) before we go in and measure it. The particle is not sitting there, waiting for us to shine a light on it, revealing its location. All we can talk of is the probability of observing it in one place and not another. The Heisenberg Uncertainty Principle is related to this concept and it states that our certainty in predicting a particle's velocity is limited by our certainty in measuring its position (and vice versa). The more precisely we know where a particle is, the less precision we can have in knowing how fast it is moving. To be clear, this is not an engineering limitation, something that will be overcome in a hundred years’ time with improved technology; it is a fundamental property of nature. Before we have made a particular measurement, it is meaningless to talk of a particle’s position etc, since such properties simply do not exist. This has implications for predictability and randomness, since if a particle’s position (or velocity etc) does not objectively exist, it is impossible to predict precisely what that position will be measured to be and what the subsequent evolution of a system of particles will be."
Another quote: "...quantum mechanics gave predictions which couldn’t be explained by any locally real theory (that is, any theory which pictured particles as having objectively real, well-defined properties). Various experiments have demonstrated that nature does indeed obey the rules of quantum physics and we must therefore adopt this peculiar view of nature based probability and abstraction, rather than concrete realism."

Jonathan Wright: "Quantum theory on the other hand, may also appear to be random, but similarly I think it is just not fully understood. We may not know the exact position of electrons in an atom, so instead we give electrons a 'probability' of being in certain positions or states. This doesn't mean that the electrons are in a random place, just that we are unable to observe their exact position. (In fact, and here is where you should ask a physicist, I think the very process of looking into an atom changes the states of the electrons..So we dont know.) But does this make it random?"

Randomness: "Chaos theory, the science which predicts that the future state of most systems is unpredictable due to even small initial uncertainties, holds new meaning for the notion of randomness, and simulating these systems requires huge numbers of random digits. It has been shown that with even small deterministic systems, initial observational error and tiny disturbances grown exponentially and create enormous problems with predictability in the long run"

Wikipedia: "According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. That is, in an experiment where all causally relevant parameters are controlled, there will still be some aspects of the outcome which vary randomly. An example of such an experiment is placing a single unstable atom in a controlled environment; it cannot be predicted how long it will take for the atom to decay; only the probability of decay within a given time can be calculated. Thus, quantum mechanics does not specify the outcome of individual experiments but only the probabilities. Hidden variable theories are inconsistent with the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, properties with a certain statistical distribution are somehow at work "behind the scenes" determining the outcome in each case."

Chaos by James Gleick:
"The rotation of the waterwheel shares some of the properties of the rotating cylinders of the fluid in the process of convection. [...] Water pours in from the top at a steady rate. If the flow of the water in the waterwheel is slow, the top bucket never fills up enough to overcome friction, and the wheel never starts turning. [...]
If the flow is faster, the weight of the top bucket sets the wheel in motion (left). The waterwheel can settle into a rotation that continues at a steady rate (center).
But if the flow is faster still (right), the spin can become chaotic, because of the nonlinear effects built into the system. As buckets pass under the flowing water, how much they fill depends on the speed of the spin. If the wheel is spinning rapidly, the buckets have little time to fill up. [...] Also, if the wheel is spinning rapidly, buckets can start up the other side before they have time to empty. As a result, heavy buckets on the side moving upward can cause the spin to slow down and then reverse."

John Polkinghorne - Quantum Theory: A very Short Introduction
Introduction to random time and quantum randomness - Kai Lai Chung
Quantum: A guide for the perplexed - Jim Al-Khalili.
Quantum - Manjit Kumar


Random number generators:

Robert R. Coveyou (american mathematician) - "The generation of random numbers is too important to be left to chance."

Randomness - "Within any sequence generated by the computer through a programmed algorithm or formula, the next digit is a completely deterministic choice, not random in the sense that a dice throw, a spinning disc, an electronic pulse or even the infinite digits of the mysterious pi are random. The very notion that a deterministic formula could generate a random sequence seemed like a contradiction".

http://www.scholarpedia.org/article/Algorithmic_randomness: "Algorithmic randomness is the study of random individual elements in sample spaces, mostly the set of all infinite binary sequences. An algorithmically random element passes all effectively devised tests for randomness."


Uncertainty and Unpredictability.

A quote from Jim French: "Essentially, yes, in principle, if we knew enough about all the degrees of freedom (at its finest point, the positions and momenta of all particles in the system, though I suspect this could be done on a classical level, without recourse to quantum considerations), we could predict the result. Practically speaking, though, no. We would either need to set up such a precisely controlled system or know so much about the system under consideration, that it would be impractical and/or would require the power of a supercomputer that has better things to do with its time. At the very least, predicting the behaviour of a die with well-measured properties would actually be pretty trivial and it tells you little about whether or not truly random things do actually exist."

Jonathan Wright: "However, with both the roll of the dice or in predicting the weather, it is this 'knowing' of the starting conditions which creates the randomness that we experience I every day life. In the weather models, if your temperature measurement is off by 0.01 degrees, eventually, perhaps in hours, days or weeks time, the predictions made by the model will become drastically different from those you experience. In fact, this was how chaos was discovered; a seemingly well understood piece of theory, when run on a computer on two occasions, gave two drastically different answers with seemingly the same starting values. The difference was attributed to a difference in the 6th decimal place of the starting values.."

Randomness: "Chance is a fair way to determine moves in some games and in certain real-life situations; the random element allows each participant to believe, 'I have an oppurtunity equal to that of my opponent.'"

Reckoning with Risk

Conclusion

Okay, I didn't manage to include every single relevant quote in this, but I have written the titles of books that I may need to refer to.
Making this plan has made me feel a lot more confident about writing my dissertation.

Things to do this week:
Update GANTT Chart
Write Random number generator section of dissertation!!!