I've just realised that I have forgotten to put "Read Choas" in my new GANTT chart. I am already fully aware of the fact that I may not have enough time to read all of the books. I have decided that, because I have so many quantum books to read, I will not read the second Quantum book (by Manjit Kumar) and that slot on my GANTT chart will be dedicated to reading Chaos.
Next week is half term and so hopefully I will have a lot of time to do extended project work. However, my Oxford maths admissions test is on November the 3rd (2 weeks time) so I will be doing a lot of preparation for that next week. Luckily I dont't have too much school work to do so I will make extended project a main priority.
Thursday, 21 October 2010
Tuesday, 19 October 2010
Probability section
I have begun collecting all sources and quotes in preparation for writing the Probability section of my dissertation.
Evaluation of Randomness
Deborah J. Bennett is assistant professor of mathematics at Jersey City State College, New Jersey. This shows that she is definitely a reliable source. Reading this book has helped me with my project in many ways.
Firstly, before reading the book I did not know much about the history of randomness, but now I do. This encouraged me to do more research on the history of the deabte of randomness, which I did not think of doing before.
Bennett made all the mathematical concepts (probabilities) very easy to understand and quite enjoyable. I liked how Bennett investigated a wide range of ideas about randomness. There were quotes about probability, random number generators and other topics that will be extremely useful to me when writing my dissertation.
"In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed." - J.A.Rial, American Scientist
"Deborah J. Bennett's book is a useful survey of an often misunderstood topic. Randomness is deceptively complex -- in particular, as Bennett points out, because aspects of it are counterintuitive. " www.complete-review.com
I will definitely be using quotes for this book in my dissertation.
Firstly, before reading the book I did not know much about the history of randomness, but now I do. This encouraged me to do more research on the history of the deabte of randomness, which I did not think of doing before.
Bennett made all the mathematical concepts (probabilities) very easy to understand and quite enjoyable. I liked how Bennett investigated a wide range of ideas about randomness. There were quotes about probability, random number generators and other topics that will be extremely useful to me when writing my dissertation.
"In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed." - J.A.Rial, American Scientist
"Deborah J. Bennett's book is a useful survey of an often misunderstood topic. Randomness is deceptively complex -- in particular, as Bennett points out, because aspects of it are counterintuitive. " www.complete-review.com
I will definitely be using quotes for this book in my dissertation.
Sunday, 17 October 2010
More from Quantum
"Consider a million identical radioactive nuclei that are unstable and will, sooner or later, spontaneously 'decay' by emitting a particle and changing into a more stable form. While quantum mechanics enables us to calculate something called the half-life (the time after which half of the nucleus will have decayed)it cannot tell us when any particular nucleus will decay. [...] We can calculate the probability that a nucleus will have decayed after any given time, but the fact that we cannot do any better that this is not due to our ignorance.[...] What we are lacking is a deeper understanding of Nature whereby we are able to predict exactly when any given nucleus might decay, just a fuller knowledge of all the forces involved in a toss of a coin would allow us to predict its outcome."
This is an example of quantum mechanics. This implies that although theoretically, if we knew everything about the conditions of the atom, we could predict when it would decay, it is impossible for us to actually know the conditions. It could then be argued that randomness does exist.
This is an example of quantum mechanics. This implies that although theoretically, if we knew everything about the conditions of the atom, we could predict when it would decay, it is impossible for us to actually know the conditions. It could then be argued that randomness does exist.
What am I doing right now?
At the moment, I am reading Quantum by Jim Al-Khalili. I am also writing the Random Number Generators section of my dissertation. I don't seem to have much to really say about number generators, despite the research I have done on them. I have typed up roughly 300 words, and don't really know where to go with it. I think I will leave this section for a while and begin another part, because it is stopping me from progressing.
I was just about to update my GANTT chart when I realised that I have nothing to add to it. I want to redo my GANTT chart again, but I feel as though I shouldn't keep doing this. The wholepoint of a GANTT chart is that it is there for you to stick by it, but if I keep changing it whenever I fall behind, I'm not really progressing, am I?
Having said that, I really think that a new GANTT chart is what I need right now. But I promise that this will be the last GANTT chart that I make!!
I am fully aware that I have a lot of books to read in a short amount of time. I will aim to always be ahead of this GANTT chart.
Things I need to do this week:
Evaluate Randomness
Finish reading Quantum - Jim Al-Khalili
I was just about to update my GANTT chart when I realised that I have nothing to add to it. I want to redo my GANTT chart again, but I feel as though I shouldn't keep doing this. The wholepoint of a GANTT chart is that it is there for you to stick by it, but if I keep changing it whenever I fall behind, I'm not really progressing, am I?
Having said that, I really think that a new GANTT chart is what I need right now. But I promise that this will be the last GANTT chart that I make!!
I am fully aware that I have a lot of books to read in a short amount of time. I will aim to always be ahead of this GANTT chart.
Things I need to do this week:
Evaluate Randomness
Finish reading Quantum - Jim Al-Khalili
Saturday, 16 October 2010
"Isaac Newton believes that every particle in the Universe should obey simple laws of motion subject to well-defined forces. This mechanistic view - one that was still shared universally by scientists and philosophers more than two centuries later - states that no matter how complex the workings of nature are, everything should be ultimately reducible to interactions between the fundamental building blocks of matter. [...] if we could know the precise position and state of motion of every particle in a given system, no matter how many are involved, then we should be able to predict, through Newton's laws, how these particles will interact and move, and hence how a system will look at any given time in the future. [...]
Of course in practice such determinism is impossible for all but the simplest systems."
This is similar to what I have researched previously; randomness may just be a lack of knowledge. It could be a pattern that is just too complex for us to be able to understand right now.
Of course in practice such determinism is impossible for all but the simplest systems."
This is similar to what I have researched previously; randomness may just be a lack of knowledge. It could be a pattern that is just too complex for us to be able to understand right now.
Really interesting example of quantum mechanics from the book
This is quite a long extract so I'll try to cut it down to the most relevant parts. There are some really useful diagrams that I may take pictures of and blog them because they explain this very well. I cannot upload photos onto this blog via my mobile though, so will have to do it another time.
"First, a beam if light is shone on a screen with two narrow slits in it that allow some light to pass through to a second screen where an interference pattern is seen. This is a sequence of light and dark bands that are due to the way the separate light waves emerging from the two slits spread out, overlap and merge before hitting the back screen."
I remember being shown this experiment in a gcse science lesson.
"Next, a similar experiment is carried out using sand. This time the second screen is placed below the one with the slits and gravity does the work. As the sand falls onto the first screen, separate piles gradually build up on the lower one beneath the two slits. This is not surprising since each grain of sand must pass through one or the other of the two slits; we are not dealing with waxes now and there is no interference. The two piles if sand will be if the same height provided the two slits are of the same size and the sand is poured from a position above their mid-point."
"Now for the interesting part: repeating the trick with atoms. A special apparatus - let us call it an atomic gun for want of a better name - fires a beam if atoms at a screen with two appropriately narrow slits. On the other side, the second screen is treated with coating that shows up a tiny bright spot wherever a single atom hits it. [...] First, we run the experiment with just one slit open. Not surprisingly, we get a spread of light spots on the back screen behind the open slit. [...] Next, we open the second slit and wait for the spots to appear on the screen. If I asked you now to predict the distribution if the bright spots that build up you would naturally guess that it would look like the two piles on sand. [...]
Instead, we see an interference pattern of light and dark fringes just as we did with light. [...]
With a detector in place that records which slit each atom passes through, the interference pattern disappears. It is as though the atoms do not wish to be caught in the act of going both ways at once, and only travel through one slit of the other. Two bands form on the screen adjacent to the slits as a result of particle-like behaviour, similar to what happens with the sand.
With the detector turned off we now have no knowledge of the route taken by each atom. Now that their secret is safe, the atoms revert to their mysterious wave-like behaviour and the interference pattern comes back!"
I find this so fascinating! I dont even know what to say in order to evaluate this extract.
"How can we assess the legitimacy or truth of an account of a phenomenon that we can never, even in principle, check? As soon as we try, we alter the outcome. [...] Physicists have been forces to admit that, in the case of the double slit trick, there is no rational way out. We can explain what we see but not why. However strange you may find the predictions of quantum mechanics, it must be emphasized that it is not the theory - mankind's invention - that is strange, but rather Nature herself that insists on such a strange kind of reality on the microscopic scale".
"First, a beam if light is shone on a screen with two narrow slits in it that allow some light to pass through to a second screen where an interference pattern is seen. This is a sequence of light and dark bands that are due to the way the separate light waves emerging from the two slits spread out, overlap and merge before hitting the back screen."
I remember being shown this experiment in a gcse science lesson.
"Next, a similar experiment is carried out using sand. This time the second screen is placed below the one with the slits and gravity does the work. As the sand falls onto the first screen, separate piles gradually build up on the lower one beneath the two slits. This is not surprising since each grain of sand must pass through one or the other of the two slits; we are not dealing with waxes now and there is no interference. The two piles if sand will be if the same height provided the two slits are of the same size and the sand is poured from a position above their mid-point."
"Now for the interesting part: repeating the trick with atoms. A special apparatus - let us call it an atomic gun for want of a better name - fires a beam if atoms at a screen with two appropriately narrow slits. On the other side, the second screen is treated with coating that shows up a tiny bright spot wherever a single atom hits it. [...] First, we run the experiment with just one slit open. Not surprisingly, we get a spread of light spots on the back screen behind the open slit. [...] Next, we open the second slit and wait for the spots to appear on the screen. If I asked you now to predict the distribution if the bright spots that build up you would naturally guess that it would look like the two piles on sand. [...]
Instead, we see an interference pattern of light and dark fringes just as we did with light. [...]
With a detector in place that records which slit each atom passes through, the interference pattern disappears. It is as though the atoms do not wish to be caught in the act of going both ways at once, and only travel through one slit of the other. Two bands form on the screen adjacent to the slits as a result of particle-like behaviour, similar to what happens with the sand.
With the detector turned off we now have no knowledge of the route taken by each atom. Now that their secret is safe, the atoms revert to their mysterious wave-like behaviour and the interference pattern comes back!"
I find this so fascinating! I dont even know what to say in order to evaluate this extract.
"How can we assess the legitimacy or truth of an account of a phenomenon that we can never, even in principle, check? As soon as we try, we alter the outcome. [...] Physicists have been forces to admit that, in the case of the double slit trick, there is no rational way out. We can explain what we see but not why. However strange you may find the predictions of quantum mechanics, it must be emphasized that it is not the theory - mankind's invention - that is strange, but rather Nature herself that insists on such a strange kind of reality on the microscopic scale".
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